Discussion on climate oscillations CMIP5 general circulation models versus asemi-empirical harmonic model based on astronomical cycles

Nicola Scafetta 12

1 Active Cavity Radiometer Irradiance Monitor (ACRIM) Lab Coronado CA 92118 USA

2 Duke University Durham NC 27708 USA

Abstract

Power spectra of global surface temperature (GST) records (available since 1850) reveal major periodicities at about 91 10-11 19-22 and 59-62 years Equivalent oscillations are found in numerous multisecular paleoclimatic records The CoupledModel Intercomparison Project 5 (CMIP5) general circulation models (GCMs) to be used in the IPCC Fifth AssessmentReport (AR5 2013) are analyzed and found not able to reconstruct this variability In particular from 2000 to 20135 aGST plateau is observed while the GCMs predicted a warming rate of about 2 oCcentury In contrast the hypothesisthat the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scalesFor example a quasi 60-year natural oscillation simultaneously explains the 1850-1880 1910-1940 and 1970-2000 warmingperiods the 1880-1910 and 1940-1970 cooling periods and the post 2000 GST plateau This hypothesis implies that about50 of the sim 05 oC global surface warming observed from 1970 to 2000 was due to natural oscillations of the climatesystem not to anthropogenic forcing as modeled by the CMIP3 and CMIP5 GCMs Consequently the climate sensitivityto CO2 doubling should be reduced by half for example from the 20-45 oC range (as claimed by the IPCC 2007) to10-23 oC with a likely median of sim 15 oC instead of sim 30 oC Also modern paleoclimatic temperature reconstructionsshowing a larger preindustrial variability than the hockey-stick shaped temperature reconstructions developed in early2000 imply a weaker anthropogenic effect and a stronger solar contribution to climatic changes The observed naturaloscillations could be driven by astronomical forcings The sim 91 year oscillation appears to be a combination of longsoli-lunar tidal oscillations while quasi 10-11 20 and 60 year oscillations are typically found among major solar andheliospheric oscillations driven mostly by Jupiter and Saturn movements Solar models based on heliospheric oscillationsalso predict quasi secular (eg sim 115 years) and millennial (eg sim 983 years) solar oscillations which hindcast observedclimate oscillations during the Holocene Herein I propose a semi-empirical climate model made of six specific astronomicaloscillations as constructors of the natural climate variability spanning from the decadal to the millennial scales plus a 50attenuated radiative warming component deduced from the GCM mean simulation as a measure of the anthropogenic plusvolcano contribution to climatic changes The semi-empirical model reconstructs the 1850-2013 GST patterns significantlybetter than any CMIP5 GCM simulation Under the same CMIP5 anthropogenic emission scenarios the model projectsa possible 2000-2100 average warming ranging from about 03 oC to 18 oC This range is significantly below the originalCMIP5 GCM ensemble mean projections spanning from about 1 oC to 4 oC Future research should investigate space-climate coupling mechanisms in order to develop more advanced analytical and semi-empirical climate models TheHadCRUT3 and HadCRUT4 UAH MSU RSS MSU GISS and NCDC GST reconstructions and 162 CMIP5 GCM GSTsimulations are analyzedPlease cite this article as Scafetta N (2013) Discussion on climate oscillations CMIP5 general circulation modelsversus a semi-empirical harmonic model based on astronomical cycles Earth-Science Reviews 126 321-357httpdxdoiorg101016jearscirev201308008

Keywords Natural climate variability global surface temperature climate models astronomical harmonic forcings 21stcentury climate projections statistical analysis

Preprint submitted to Earth-Science Reviews October 29 2013

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1 Introduction

Natural cyclical variability has been observed in geo-physical systems at many time scales from a few hours toseveral hundred thousand and million years The physicalorigin of many climatic oscillations has often been foundin astronomical mechanisms (eg House 1995) Persistentquasi decadal bidecadal 60-years 80-90 years 115-years1000-years and other oscillations have been found in globaland regional temperature records in the Atlantic Multi-decadal Oscillation (AMO) in North Atlantic Oscillation(NAO) in the Pacific Decadal Oscillation (PDO) in globalsea level rise indexes monsoon records Greenland tempera-tures and in many other climate proxy records covering cen-turies and millennia Similar oscillations have been foundalso in luni-solar tidal cycles solar and historical auroralong records and in planetary oscillations (eg Agnihotriand Dutta 2003 Bond et al 2001 Chylek and Lesins 2008Chylek et al 2011 2012 Cook 1997 Currie 1984 Davisand Bohling 2001 Gray et al 2004 Hoyt and Schatten1997 Humlum et al 2011 Keeling and Whorf 1997aaKlyashtorin et al 2009 Knudsen et al 2011 Kobashi etal 2010 Jevrejeva et al 2008 Mazzarella and Scafetta2012 Ogurtsov et al 2002 Qian and Lu 2010 Steinhilberet al 2012 Schulz and Paul 2002 Sinha et al 2005 Stock-ton et al 1983 Yadava and Ramesh 2007 Scafetta 20102012ac 2013abc Scafetta et al 2013 Scafetta and Will-son 2013ab) These results suggest an astronomical originof the observed decadal to millennial climatic oscillations

Figure 1 shows power spectral analyses (Press et al1997) of all available global surface temperature (GST) records(HadCRUT4 HadCRUT3 GISS and NCDC) These graphsshow prominent power spectral peaks at about 91 10-1119-22 and 59-62 year periods since 1850 Similar frequen-cies are found in major astronomical records which arehighlighted in Figure 1A with red boxes (Scafetta 20102012abcd 2013a Scafetta et al 2013 Scafetta and Will-son 2013a)

Theoretical climate models should ideally be able to pre-dict the observed GST oscillations In case of significantmismatches solutions requiring minor adjustments of themodels (for example tweaking the forcings) may be pro-posed However some of the basic physical assumptionsof the models may also be flawed In the latter case newmechanisms need to be identified in order to upgrade themodels Because of non-reducible uncertainties (Curry andWebster 2011) alternative semi-empirical modeling strate-gies should also be developed and considered parallel to theanalytic GCM methodology

Scafetta (2012b) tested all Coupled Model Intercompari-son Project 3 (CMIP3) GCMs used by the IPCC (2007) andfound that those models poorly reconstruct the observeddecadal and multidecadal GST oscillations at about 91 10-11 20 and 60 year periods since 1850 Herein the ability ofthe GCMs of the Coupled Model Intercomparison Project 5(CMIP5) to reproduce the historical global surface temper-ature patterns since 1850 is tested as well As an alternateI conjecture that a significant component of the observedGST variations can be more efficiently modeled using a set

of astronomically induced harmonics of solar and lunar ori-gin whose mechanisms are not included in the GCMs yet

A GCM failure to reproduce large natural multidecadaloscillations (periods amplitudes and phases) has relevanttheoretical implications For example Figure 95a and bpublished by the U N Intergovernmental Panel on ClimateChange (IPCC 2007) (httpwwwipccchpublications_and_dataar4wg1enfigure-9-5html) show GCM sim-ulations obtained with all adopted natural and anthropogenicforcings (figure 95a) and with natural (solar and volcano)forcings alone (figure 95b) respectively The results de-picted by this figure were used to claim that more than 90of the warming observed since 1900 (about 08 oC) and prac-tically 100 of the warming observed since 1970 (about 05oC) could only be explained by anthropogenic forcing (seefigure in 95a) The reasoning was that when only solarand volcano forcings alone were used the GCMs predicted aslight cooling since 1970 (see figure 95b) The theory emerg-ing from these computer simulations is commonly knownas the anthropogenic global warming theory (AGWT) How-ever if the warming observed since 1970 could be producedby a non-modeled multidecadal natural oscillation linked tomajor ocean andor astronomical-solar oscillations then theAGWT should be questioned andor significantly revised

The AGWT may be erroneous because of large uncer-tainties in the forcings (in particular in the aerosol forcinghttpwwwipccchpublications_and_dataar4wg1en

figure-spm-2html) and in the equilibrium climate sensi-tivity to radiative forcing The GCMs used by the IPCC(2007) claim that a doubling of CO2 atmospheric concen-tration induces a warming between 2 and 45 oC with atotal range spanning between 1 and 9 oC (see Forest etal (2006) and httpwwwipccchpublications_and_

dataar4wg1enbox-10-2-figure-1html) The equi-librium climate sensitivity derives from the direct CO2 green-house warming effect plus the warming contribution its cli-matic feedbacks For example the direct CO2 warmingwould be significantly enhanced by a water vapor feedbacksince water vapor is a greenhouse gas (GHG) as well How-ever the strength and the nature of the various feedbacksis still quite uncertain while the CO2 greenhouse propertiesare experimentally determined and are undisputed with-out feedbacks a doubling of CO2 amounts to a forcing ofabout 37 Wm2 that should cause a warming of about 1 oC(Rahmstorf 2008) The strength of the feedbacks is esti-mated in various ways and also calculated using the GCMsthemselves In the latter case the calculated climate sen-sitivity value is a simple byproduct of the physical mecha-nisms and of the parameters currently implemented in theGCMs such as those related to the parametrization of thecloud formation and water vapor feedbacks (Hansen et al1988) If the modeled feedback mechanisms are erroneousthen the modeled climate sensitivity would be inaccurate

Indeed some authors have pointed out that observa-tional data indicate that positive and negative climate feed-backs to CO2 variations compensate each other leaving anet equilibrium climate sensitivity to CO2 doubling rangingbetween 05 oC and 13 oC (Lindzen and Choi 2009 2011Spencer and Braswell 2010 2011) Chylek and Lohmann

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Figure 1 [A] Power spectra of the HadCRUT4 GST (1850-2012) (black) and of the Northern Hemisphere and Southern Hemisphere using theMaximum entropy Method (MEM) red boxes represents major astronomical oscillations associated to a decadal soli-lunar tidal cycle (about 91years) and to the major heliospheric harmonics associated to Jupiter and Saturn gravitational and electromagnetic effects and to solar cycles(about 10-12 15 19-22 59-63 years) [B] MEM and periodogram for HadCRUT3 (1850-2011) [C] MEM and periodogram for HadCRUT3GISS and NCDC GSTs from 1880 to 2011 See Scafetta (2010 2012abcd 2013a) for details

(2008) found a climate sensitivity between 13 oC and 23oC due to doubling of atmospheric concentration of CO2Ring et al (2012) found a climate sensitivity between 15oC to 20 oC and Lewis (2013) found a range from 12 oCto 22 oC (median 16 oC) The model proposed by Scafetta(2010 2012b 2013a) which herein will be reviewed and up-dated implies a climate sensitivity from about 09 oC to 20oC (median 135 oC) Moreover despite some controversyabout the tropospheric records (Thorne et al 2007) NOAA

balloon measurements do not show the GCM-predicted CO2

induced hot-spot maximum trend in the tropical region at analtitude of about 10 km (Douglass et al 2007 Singer 2011)Vonder Haar et al (2012) showed data that could severelyquestion the existence of a strong GCM global water vaporfeedback to anthropogenic GHGs These findings suggestthat current GCMs severely overestimate the climatic effectof the anthropogenic GHG forcing

As an alternative I propose a semi-empirical model com-

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Figure 2 HadCRUT4 global surface temperature record (Jan1850 - Jun2013) (black) Four CMIP5 GCM ensemble means based on thehistorical forcings and four alternative 21st century projections

posed of six major specific astronomically-deduced oscilla-tions spanning from the decadal to the millennial scales(Scafetta 2010 2012c) Climatic oscillations can be to afirst approximation empirically modeled in particular if theyhave an astronomical physical origin even if their specific mi-croscopic physical mechanisms remain unknown Astronom-ically based harmonic constituent models have been used topredict ocean tides since ancient times (Ptolemy 2nd cen-tury Kepler 1601 Ehret 2008) The oscillations that willbe used are found among solar lunar and planetary har-monics Climatic effects due to volcano activity and anthro-pogenic emissions and the chaotic internal variability of theclimate are modeled to a first approximation by properly at-tenuating the GCM outputs

It will be shown that the proposed semi-empirical modelreconstructs and hindcasts the 1850-2013 climatic patternssignificantly better than any CMIP5 GCM simulation andtheir ensemble mean and may provide more reliable projec-tions for the 21st century under the same emission scenar-ios The finding would suggest that important astronomicalforcings of the climate system and the climatic feedbacks tothem are still missing and possibly not yet known The re-sult reinforces Scafetta (2010) where it was found that powerspectra of global temperature records are more coherent tosolarastronomical gravitational and electromagnetic oscil-lations and to soli-lunar tidal long-scale oscillations thanto power spectra deduced from current GCM simulations

Therefore the author proposes that future research shouldincorporate additional astronomical mechanism of climatechange

2 Simple analysis of GST and the CMIP5 ensemblemean simulations

All CMIP5 GCM simulations studied were downloadedfrom Climate Explorer (httpclimexpknminl for de-tails see also httpcmip-pcmdillnlgovcmip5) Theserecords are 162 monthly resolved temperature-at-surface (tas)historical simulations from 48 models plus numerous simula-tions for the 21st century These are classified under four al-ternative representative concentration pathway (RCP) emis-sion scenarios labeled as RCP 85 (rcp85) business-as-usual emission scenario RCP 60 (rcp60) lower emissionscenario RCP 45 (rcp45) stabilization emission scenarioRCP 26 (rcp26) strong mitigation emission scenario TheRCP number indicates the rising radiative forcing pathwaylevel (in Wm2) from 2000 to 2100

Figure 2 compares the HadCRUT4 GST (httpwwwcruueaacuk) (Morice et al 2012) from Jan1850 toJun2013 against the CMIP5 model ensemble mean simula-tions under the four alternative 21st century emission sce-narios The curves are plotted using a common 1900-2000baseline with the GCM curves downshifted by 1 oC for vi-sual clarity

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Figure 2 HadCRUT4 global surface temperature record (Jan1850 - Jun2013) (black) Four CMIP5 GCM ensemble means based on thehistorical forcings and four alternative 21st century projections

posed of six major specific astronomically-deduced oscilla-tions spanning from the decadal to the millennial scales(Scafetta 2010 2012c) Climatic oscillations can be to afirst approximation empirically modeled in particular if theyhave an astronomical physical origin even if their specific mi-croscopic physical mechanisms remain unknown Astronom-ically based harmonic constituent models have been used topredict ocean tides since ancient times (Ptolemy 2nd cen-tury Kepler 1601 Ehret 2008) The oscillations that willbe used are found among solar lunar and planetary har-monics Climatic effects due to volcano activity and anthro-pogenic emissions and the chaotic internal variability of theclimate are modeled to a first approximation by properly at-tenuating the GCM outputs

It will be shown that the proposed semi-empirical modelreconstructs and hindcasts the 1850-2013 climatic patternssignificantly better than any CMIP5 GCM simulation andtheir ensemble mean and may provide more reliable projec-tions for the 21st century under the same emission scenar-ios The finding would suggest that important astronomicalforcings of the climate system and the climatic feedbacks tothem are still missing and possibly not yet known The re-sult reinforces Scafetta (2010) where it was found that powerspectra of global temperature records are more coherent tosolarastronomical gravitational and electromagnetic oscil-lations and to soli-lunar tidal long-scale oscillations thanto power spectra deduced from current GCM simulations

Therefore the author proposes that future research shouldincorporate additional astronomical mechanism of climatechange

2 Simple analysis of GST and the CMIP5 ensemblemean simulations

All CMIP5 GCM simulations studied were downloadedfrom Climate Explorer (httpclimexpknminl for de-tails see also httpcmip-pcmdillnlgovcmip5) Theserecords are 162 monthly resolved temperature-at-surface (tas)historical simulations from 48 models plus numerous simula-tions for the 21st century These are classified under four al-ternative representative concentration pathway (RCP) emis-sion scenarios labeled as RCP 85 (rcp85) business-as-usual emission scenario RCP 60 (rcp60) lower emissionscenario RCP 45 (rcp45) stabilization emission scenarioRCP 26 (rcp26) strong mitigation emission scenario TheRCP number indicates the rising radiative forcing pathwaylevel (in Wm2) from 2000 to 2100

Figure 2 compares the HadCRUT4 GST (httpwwwcruueaacuk) (Morice et al 2012) from Jan1850 toJun2013 against the CMIP5 model ensemble mean simula-tions under the four alternative 21st century emission sce-narios The curves are plotted using a common 1900-2000baseline with the GCM curves downshifted by 1 oC for vi-sual clarity

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Figure 3 [A] 8-year moving average of the detrended HadCRUT4 GST plotted against itself with a 615-year lag shift (red) The quadraticfitting trend applied is f(t) = 00000298 lowast (tminus 1850)2 minus 0384 [B] Four GST records (HadCRUT3 HadCRUT4 GISS and NCDC) after beingdetrended of their upward trend and smoothed with a 49-month moving average algorithm against the 4-frequency harmonic model (yellowarea) proposed in Scafetta (2010 2012ac) [C] and [D] show the HadCRUT records detrended of their warming trend and band-pass filteredto highlight their quasi bi-decadal oscillation The two black oscillating curves with periods of about 20 years and 60 years are two majorastronomical oscillations of the solar system induced by Jupiter and Saturn (Scafetta 2010)

period GST-trend GCM-trend

1860-1880 +101plusmn024 +050plusmn0061880-1910 -056plusmn009 +028plusmn0071910-1940 +133plusmn008 +072plusmn0031940-1960 -047plusmn016 +018plusmn0041940-1970 -026plusmn009 -033plusmn0041970-2000 +168plusmn008 +150plusmn005

2000-20135 +035plusmn022 +188plusmn004

Table 1 Comparison of 30-year period trends in oCcentury betweenthe HadCRUT4 GST and the CMIP5 GCM ensemble mean simulationdepicted in Figure 1

The GST warmed about 080-085 oC since 1850 TheGST also presents complex dynamical patterns dominatedby a quasi 60-year oscillation revolving around an upwardtrend 1850-1880 1910-1940 and 1970-2000 were warmingperiods and 1880-1910 and 1940-1970 were cooling periodsSince 2000 the GST has been fairly steady

Figure 3 highlights the GST decadal and multidecadalpatterns Figure 3A shows the HadCRUT4 GST smoothed

and detrended of its quadratic polynomial fit and plottedagainst itself with a lag-shift of 615 years The figure demon-strates that the GST modulation from 1880 to 1940 is verysimilar to the modulation from 1940 to 2000 This auto-correlation pattern highlights the existence of a possiblequasi 60-year oscillation Additional modulations inducedby other patterns may exist For example the climate sys-tem may also be modulated by a 80-90 year oscillation thathas been detected in long solar and climatic proxy records(Knudsen et al 2011 Ogurtsov et al 2002 Scafetta andWillson 2013a) However a 80-90 year oscillation cannot beseparated from a 60-year oscillation using the current GSTrecords since a 163-year long record is too short

Figure 3B highlights both the decadal and the multi-decadal GST oscillations by showing four global surface tem-perature records (HadCRUT3 HadCRUT4 GISS and NCDC)after detrending the upward quadratic trend and smooth-ing the data with a 49-month moving average algorithmThe harmonic model (yellow) proposed in Scafetta (20102012ab) approximately reproduces the decadal and multi-decadal patterns observed in the detrended GST curves

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Figure 4 HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black) The number of individual available simulationssimultaneously plotted is in parenthesis

Figure 3C shows the HadCRUT3 and HadCRUT4 recordsdetrended of their warming trend as above Figure 3D showstwo band-pass filtered curves of HadCRUT3 (similar patternis observed for the HadCRUT4 record) to highlight its quasibi-decadal oscillations The two black oscillating curves withperiods of about 20 years and 60 years are two major astro-nomical oscillations of the solar system These can be easilyobserved for example in the speed of the Sun relative to

the barycenter of the solar system and in the beats of thegravitational tides induced by Jupiter and Saturn (Scafetta2010 2012ac 2013a Scafetta and Willson 2013a) Theobserved climatic oscillations appear synchronized with thetwo depicted astronomical oscillations Similar results areobtained with the alternative GST records

Table 1 compares the warming or cooling trends of theHadCRUT4 GST and of the GCM ensemble mean simula-

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Figure 5 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

tions depicted in Figure 2 for the periods 1860-1880 1880-1910 1910-1940 1940-1960 1940-1970 1970-2000 and 2000-20135 (1) from 1880 to 1910 the GST cooled while theGCMs predict a warming (2) the 1910-1940 GST warmingtrend is almost twice than that predicted by the GCMs (3)the GST cooled since the 1940s while the GCMs predict awarming from 1940 to 1960 which is interrupted by volcanoeruptions in the early 1960s (4) from 1970 to 2000 there isan approximate agreement between the GST and the GCMs

(5) since 2000 a strong divergence between the modeled andobserved temperatures is observed Thus only during theperiod 1970-2000 do the GCM simulations present a meanwarming trend somewhat compatible with that found in theGST During the other intervals the GST trends differ sig-nificantly from those predicted by the GCM ensemble meansimulations In particular the 1910-1940 strong warmingand the steady temperature since 2000 cannot be explainedby anthropogenic emissions plus a small solar forcing effect

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Figure 6 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

as assumed by the current CMIP3 and CMIP5 GCMsAlso the GST volcano cooling spikes are not as deep as

those predicted by the synthetic record For example thereis no observational evidence of the strong modeled volcanocooling associated with the eruption of the Krakatau in 1883Also other volcano signatures appear to be overestimatedby the GCMs and produce a spurious recurrence pattern atabout 70-80 years (Scafetta 2012b)

These results suggest missing mechanisms and a signifi-

cant overestimation of the climate sensitivity to the adoptedradiative forcings which is particularly evident in the over-estimation of the volcano signatures On a 163-year pe-riod since 1850 only the 19702000 warming trend (about20 of the total period) has been approximately recoveredby using known forcings Thus the ability of the CMIP5GCM ensemble mean simulations to project or predict cli-mate change 30 years ahead with any reasonable accuracyis questionable Indeed it is possible that the 1970-2000

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1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GFDL-CM3 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GFDL-ESM2G (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GFDL-ESM2M (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-H p1 (6 sim)HadCRUT42

Figure 7 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

GCM-data matching could be coincidental and simply dueto a fine-tuning calibration of the model parameters to re-produce this period

3 Scale-by-scale comparison between GST and theCMIP5 simulations

In 48 panels (one for each GCM) Figures 4-11 depict all162 CMIP5 GCM individual available simulations that are

herein analyzed against the HadCRUT4 GST record TheCMIP5 GCM simulations are shifted downward for visualconvenience

The GCM simulations vaguely reproduce a warming from1860 to 2010 However significant discrepancies versus theGST record are observed at all time scales Often the vol-cano signatures appear significantly overestimated Somemodel simulations present a monotonic warming during theentire period while others show an almost flat temperature

9

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-H p2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

GISS-E2-H p3 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GISS-E2-H-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GISS-E2-R p1 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GISS-E2-R p2 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

10

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-R-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

HadGEM2-AO (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

HadGEM2-CC (1 sim)HadCRUT42

-2

-15

-1

-05

0

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1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

HadGEM2-ES (4 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

inmcm4 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

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mp

A

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m

(oC

)

[A] year

IPSL-CM5A-MR (3 sim)HadCRUT42

-2

-15

-1

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05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

IPSL-CM5B-LR (1 sim)HadCRUT42

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1

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mp

A

no

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(oC

)

[C] year

MIROC5 (5 sim)HadCRUT42

-2

-15

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05

1

1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[D] year

MIROC-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

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05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

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1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

-15

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(oC

)

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MRI-ESM1 (1 sim)HadCRUT42

-2

-15

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1860 1880 1900 1920 1940 1960 1980 2000

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no

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(oC

)

[E] year

NorESM1-M (3 sim)HadCRUT42

-2

-15

-1

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0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

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ma

ly (

oC

)

15

10

05

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-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-2

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-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

ACCESS1-0 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

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m

(oC

)

[B] year

ACCESS1-3 (3 sim)HadCRUT42

-2

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mp

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m

(oC

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bcc-csm1-1 (3 sim)HadCRUT42

-2

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1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

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m

(oC

)

[D] year

bcc-csm1-1-m (3 sim)HadCRUT42

-2

-15

-1

-05

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05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

BNU-ESM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

CanESM2 (5 sim)HadCRUT42

Figure 4 HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black) The number of individual available simulationssimultaneously plotted is in parenthesis

Figure 3C shows the HadCRUT3 and HadCRUT4 recordsdetrended of their warming trend as above Figure 3D showstwo band-pass filtered curves of HadCRUT3 (similar patternis observed for the HadCRUT4 record) to highlight its quasibi-decadal oscillations The two black oscillating curves withperiods of about 20 years and 60 years are two major astro-nomical oscillations of the solar system These can be easilyobserved for example in the speed of the Sun relative to

the barycenter of the solar system and in the beats of thegravitational tides induced by Jupiter and Saturn (Scafetta2010 2012ac 2013a Scafetta and Willson 2013a) Theobserved climatic oscillations appear synchronized with thetwo depicted astronomical oscillations Similar results areobtained with the alternative GST records

Table 1 compares the warming or cooling trends of theHadCRUT4 GST and of the GCM ensemble mean simula-

6

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

CCSM4 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

CESM1-BGC (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

CESM1-CAM5 (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

CESM1-CAM5-1-FV2 (4 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

CESM1-FASTCHEM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

CESM1-WACCM (1 sim)HadCRUT42

Figure 5 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

tions depicted in Figure 2 for the periods 1860-1880 1880-1910 1910-1940 1940-1960 1940-1970 1970-2000 and 2000-20135 (1) from 1880 to 1910 the GST cooled while theGCMs predict a warming (2) the 1910-1940 GST warmingtrend is almost twice than that predicted by the GCMs (3)the GST cooled since the 1940s while the GCMs predict awarming from 1940 to 1960 which is interrupted by volcanoeruptions in the early 1960s (4) from 1970 to 2000 there isan approximate agreement between the GST and the GCMs

(5) since 2000 a strong divergence between the modeled andobserved temperatures is observed Thus only during theperiod 1970-2000 do the GCM simulations present a meanwarming trend somewhat compatible with that found in theGST During the other intervals the GST trends differ sig-nificantly from those predicted by the GCM ensemble meansimulations In particular the 1910-1940 strong warmingand the steady temperature since 2000 cannot be explainedby anthropogenic emissions plus a small solar forcing effect

7

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

CMCC-CESM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

CMCC-CM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

CMCC-CMS (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

CNRM-CM5 (10 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

CSIRO-Mk3-6-0 (10 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

EC-EARTH (9 sim)HadCRUT42

Figure 6 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

as assumed by the current CMIP3 and CMIP5 GCMsAlso the GST volcano cooling spikes are not as deep as

those predicted by the synthetic record For example thereis no observational evidence of the strong modeled volcanocooling associated with the eruption of the Krakatau in 1883Also other volcano signatures appear to be overestimatedby the GCMs and produce a spurious recurrence pattern atabout 70-80 years (Scafetta 2012b)

These results suggest missing mechanisms and a signifi-

cant overestimation of the climate sensitivity to the adoptedradiative forcings which is particularly evident in the over-estimation of the volcano signatures On a 163-year pe-riod since 1850 only the 19702000 warming trend (about20 of the total period) has been approximately recoveredby using known forcings Thus the ability of the CMIP5GCM ensemble mean simulations to project or predict cli-mate change 30 years ahead with any reasonable accuracyis questionable Indeed it is possible that the 1970-2000

8

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

FGOALS-g2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

FIO-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GFDL-CM3 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GFDL-ESM2G (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GFDL-ESM2M (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-H p1 (6 sim)HadCRUT42

Figure 7 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

GCM-data matching could be coincidental and simply dueto a fine-tuning calibration of the model parameters to re-produce this period

3 Scale-by-scale comparison between GST and theCMIP5 simulations

In 48 panels (one for each GCM) Figures 4-11 depict all162 CMIP5 GCM individual available simulations that are

herein analyzed against the HadCRUT4 GST record TheCMIP5 GCM simulations are shifted downward for visualconvenience

The GCM simulations vaguely reproduce a warming from1860 to 2010 However significant discrepancies versus theGST record are observed at all time scales Often the vol-cano signatures appear significantly overestimated Somemodel simulations present a monotonic warming during theentire period while others show an almost flat temperature

9

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-H p2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

GISS-E2-H p3 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GISS-E2-H-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GISS-E2-R p1 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GISS-E2-R p2 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

10

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-R-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

HadGEM2-AO (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

HadGEM2-CC (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[D] year

HadGEM2-ES (4 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

inmcm4 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

IPSL-CM5A-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

IPSL-CM5B-LR (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MIROC5 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MIROC-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MRI-ESM1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

NorESM1-M (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

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1985 1990 1995 2000 2005 2010

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ture

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73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

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CESM1-WACCM (1 sim)HadCRUT42

Figure 5 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

tions depicted in Figure 2 for the periods 1860-1880 1880-1910 1910-1940 1940-1960 1940-1970 1970-2000 and 2000-20135 (1) from 1880 to 1910 the GST cooled while theGCMs predict a warming (2) the 1910-1940 GST warmingtrend is almost twice than that predicted by the GCMs (3)the GST cooled since the 1940s while the GCMs predict awarming from 1940 to 1960 which is interrupted by volcanoeruptions in the early 1960s (4) from 1970 to 2000 there isan approximate agreement between the GST and the GCMs

(5) since 2000 a strong divergence between the modeled andobserved temperatures is observed Thus only during theperiod 1970-2000 do the GCM simulations present a meanwarming trend somewhat compatible with that found in theGST During the other intervals the GST trends differ sig-nificantly from those predicted by the GCM ensemble meansimulations In particular the 1910-1940 strong warmingand the steady temperature since 2000 cannot be explainedby anthropogenic emissions plus a small solar forcing effect

7

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CSIRO-Mk3-6-0 (10 sim)HadCRUT42

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EC-EARTH (9 sim)HadCRUT42

Figure 6 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

as assumed by the current CMIP3 and CMIP5 GCMsAlso the GST volcano cooling spikes are not as deep as

those predicted by the synthetic record For example thereis no observational evidence of the strong modeled volcanocooling associated with the eruption of the Krakatau in 1883Also other volcano signatures appear to be overestimatedby the GCMs and produce a spurious recurrence pattern atabout 70-80 years (Scafetta 2012b)

These results suggest missing mechanisms and a signifi-

cant overestimation of the climate sensitivity to the adoptedradiative forcings which is particularly evident in the over-estimation of the volcano signatures On a 163-year pe-riod since 1850 only the 19702000 warming trend (about20 of the total period) has been approximately recoveredby using known forcings Thus the ability of the CMIP5GCM ensemble mean simulations to project or predict cli-mate change 30 years ahead with any reasonable accuracyis questionable Indeed it is possible that the 1970-2000

8

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GISS-E2-H p1 (6 sim)HadCRUT42

Figure 7 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

GCM-data matching could be coincidental and simply dueto a fine-tuning calibration of the model parameters to re-produce this period

3 Scale-by-scale comparison between GST and theCMIP5 simulations

In 48 panels (one for each GCM) Figures 4-11 depict all162 CMIP5 GCM individual available simulations that are

herein analyzed against the HadCRUT4 GST record TheCMIP5 GCM simulations are shifted downward for visualconvenience

The GCM simulations vaguely reproduce a warming from1860 to 2010 However significant discrepancies versus theGST record are observed at all time scales Often the vol-cano signatures appear significantly overestimated Somemodel simulations present a monotonic warming during theentire period while others show an almost flat temperature

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GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

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(oC

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IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

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MIROC5 (5 sim)HadCRUT42

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MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

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NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

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harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

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mp

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(oC

)

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CMCC-CESM (1 sim)HadCRUT42

-2

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)

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-2

-15

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)

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-2

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(oC

)

[E] year

CSIRO-Mk3-6-0 (10 sim)HadCRUT42

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1

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mp

A

no

m

(oC

)

[F] year

EC-EARTH (9 sim)HadCRUT42

Figure 6 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

as assumed by the current CMIP3 and CMIP5 GCMsAlso the GST volcano cooling spikes are not as deep as

those predicted by the synthetic record For example thereis no observational evidence of the strong modeled volcanocooling associated with the eruption of the Krakatau in 1883Also other volcano signatures appear to be overestimatedby the GCMs and produce a spurious recurrence pattern atabout 70-80 years (Scafetta 2012b)

These results suggest missing mechanisms and a signifi-

cant overestimation of the climate sensitivity to the adoptedradiative forcings which is particularly evident in the over-estimation of the volcano signatures On a 163-year pe-riod since 1850 only the 19702000 warming trend (about20 of the total period) has been approximately recoveredby using known forcings Thus the ability of the CMIP5GCM ensemble mean simulations to project or predict cli-mate change 30 years ahead with any reasonable accuracyis questionable Indeed it is possible that the 1970-2000

8

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)

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FGOALS-g2 (5 sim)HadCRUT42

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FIO-ESM (3 sim)HadCRUT42

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mp

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(oC

)

[F] year

GISS-E2-H p1 (6 sim)HadCRUT42

Figure 7 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

GCM-data matching could be coincidental and simply dueto a fine-tuning calibration of the model parameters to re-produce this period

3 Scale-by-scale comparison between GST and theCMIP5 simulations

In 48 panels (one for each GCM) Figures 4-11 depict all162 CMIP5 GCM individual available simulations that are

herein analyzed against the HadCRUT4 GST record TheCMIP5 GCM simulations are shifted downward for visualconvenience

The GCM simulations vaguely reproduce a warming from1860 to 2010 However significant discrepancies versus theGST record are observed at all time scales Often the vol-cano signatures appear significantly overestimated Somemodel simulations present a monotonic warming during theentire period while others show an almost flat temperature

9

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GISS-E2-H p2 (5 sim)HadCRUT42

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Te

mp

A

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(oC

)

[F] year

GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

10

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GISS-E2-R-CC p1 (1 sim)HadCRUT42

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HadGEM2-AO (1 sim)HadCRUT42

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HadGEM2-CC (1 sim)HadCRUT42

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HadGEM2-ES (4 sim)HadCRUT42

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inmcm4 (1 sim)HadCRUT42

-2

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mp

A

no

m

(oC

)

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IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

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IPSL-CM5A-MR (3 sim)HadCRUT42

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MIROC5 (5 sim)HadCRUT42

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MIROC-ESM (3 sim)HadCRUT42

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A

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(oC

)

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MIROC-ESM-CHEM (1 sim)HadCRUT42

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05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

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mp

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(oC

)

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MPI-ESM-MR (3 sim)HadCRUT42

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)

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MPI-ESM-P (2 sim)HadCRUT42

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MRI-CGCM3 (3 sim)HadCRUT42

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MRI-ESM1 (1 sim)HadCRUT42

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NorESM1-M (3 sim)HadCRUT42

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1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

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0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

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05

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15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

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0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

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05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-2

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-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

FGOALS-g2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

FIO-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GFDL-CM3 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GFDL-ESM2G (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GFDL-ESM2M (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-H p1 (6 sim)HadCRUT42

Figure 7 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

GCM-data matching could be coincidental and simply dueto a fine-tuning calibration of the model parameters to re-produce this period

3 Scale-by-scale comparison between GST and theCMIP5 simulations

In 48 panels (one for each GCM) Figures 4-11 depict all162 CMIP5 GCM individual available simulations that are

herein analyzed against the HadCRUT4 GST record TheCMIP5 GCM simulations are shifted downward for visualconvenience

The GCM simulations vaguely reproduce a warming from1860 to 2010 However significant discrepancies versus theGST record are observed at all time scales Often the vol-cano signatures appear significantly overestimated Somemodel simulations present a monotonic warming during theentire period while others show an almost flat temperature

9

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-H p2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

GISS-E2-H p3 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

GISS-E2-H-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

GISS-E2-R p1 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

GISS-E2-R p2 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

10

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-R-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

HadGEM2-AO (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

HadGEM2-CC (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

HadGEM2-ES (4 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

inmcm4 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

IPSL-CM5A-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

IPSL-CM5B-LR (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MIROC5 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MIROC-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MRI-ESM1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

NorESM1-M (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

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1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[A] year

GISS-E2-H p2 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

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mp

A

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(oC

)

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GISS-E2-H p3 (6 sim)HadCRUT42

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mp

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(oC

)

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GISS-E2-H-CC p1 (1 sim)HadCRUT42

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mp

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)

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GISS-E2-R p1 (6 sim)HadCRUT42

-2

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05

1

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mp

A

no

m

(oC

)

[E] year

GISS-E2-R p2 (6 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

GISS-E2-R p3 (6 sim)HadCRUT42

Figure 8 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

trend until 1970 and a rapid rise since then In a numberof cases the 1970-2000 GCM warming rate is visibly higherthan the observed 1970-2000 GST warming rate By look-ing only at the decadal to the multidecadal scales numerousmismatches are observed as well It is easy to notice peri-ods as long as 10-30 years showing divergent trends betweenthe GST record and the GCM simulations The fast fluc-tuations at a multi-annual scale are also not reproduced bythe models Indeed the GCMs reproduce a variability at all

time scales but it appears to be uncorrelated with the GSTobservations In general all GCM simulations significantlydiffer from each other

In the following subsections three alternative strategiesare adopted to study how well the CMIP5 GCM individualsimulations reproduce the GST patterns at multiple scalesThe following tests are discussed (1) the records are de-composed using a limited set of major harmonics detectedby power spectrum analyses as shown in Figure 1 and the

10

-2

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1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

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GISS-E2-R-CC p1 (1 sim)HadCRUT42

-2

-15

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0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[B] year

HadGEM2-AO (1 sim)HadCRUT42

-2

-15

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05

1

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mp

A

no

m

(oC

)

[C] year

HadGEM2-CC (1 sim)HadCRUT42

-2

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mp

A

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m

(oC

)

[D] year

HadGEM2-ES (4 sim)HadCRUT42

-2

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-1

-05

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05

1

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mp

A

no

m

(oC

)

[E] year

inmcm4 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

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mp

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(oC

)

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IPSL-CM5A-MR (3 sim)HadCRUT42

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05

1

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mp

A

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(oC

)

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IPSL-CM5B-LR (1 sim)HadCRUT42

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1

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mp

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(oC

)

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MIROC5 (5 sim)HadCRUT42

-2

-15

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0

05

1

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mp

A

no

m

(oC

)

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MIROC-ESM (3 sim)HadCRUT42

-2

-15

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-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

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mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

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-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

-2

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0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

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-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

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-05

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05

1

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mp

A

no

m

(oC

)

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MRI-ESM1 (1 sim)HadCRUT42

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05

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mp

A

no

m

(oC

)

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NorESM1-M (3 sim)HadCRUT42

-2

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0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

GISS-E2-R-CC p1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

HadGEM2-AO (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

HadGEM2-CC (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

HadGEM2-ES (4 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

inmcm4 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

IPSL-CM5A-LR (6 sim)HadCRUT42

Figure 9 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

ability of each GCM simulation to reproduce each GST com-ponent is tested (2) a Fourier band-pass filter decomposi-tion methodology is adopted to decompose each sequencein four band-pass frequency components and the ability ofeach GCM simulation to reproduce each GST band-pass fre-quency component is tested (3) power spectra in the periodrange from 7 years to 100 years are evaluated for all recordsand the ability of each GCM simulations to reproduce theGST power spectrum is tested The scale-by-scale compar-

ison uses a technique similar to the multiresolution correla-tion analysis (Scafetta et al 2004) The HadCRUT4 recordand all model simulations are analyzed from Jan1861 toDec2005 which is the common period

31 Scale-by-scale harmonic decomposition comparison

Scafetta (2010 2012ab) showed that to a first order ap-proximation the HadCRUT3 GST record can be geometri-cally decomposed into four major harmonics found in astro-

11

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

IPSL-CM5A-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

IPSL-CM5B-LR (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MIROC5 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MIROC-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MRI-ESM1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

NorESM1-M (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

IPSL-CM5A-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

IPSL-CM5B-LR (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MIROC5 (5 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MIROC-ESM (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

MIROC-ESM-CHEM (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

MPI-ESM-LR (3 sim)HadCRUT42

Figure 10 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

nomical records with periods of about 91 104 20 and 60years plus a second order polynomial trending componentHere the calibration is repeated using the same harmonicsand the HadCRUT4 GST record from Jan1861 to Dec2005to obtain

h60(t) = 0111 cos(2π(tminus 200129)60) (1)

h20(t) = 0043 cos(2π(tminus 200143)20) (2)

h104(t) = 0030 cos(2π(tminus 200293)104) (3)

h91(t) = 0044 cos(2π(tminus 199782)91) (4)

p(t) =339

105(tminus 1850)2 minus 946

104(tminus 1850)minus 036 (5)

The above amplitudes present a statistical error of about15 and together with the phases they were estimatedby linear regression on the GST This yields the following

12

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[D] year

MRI-ESM1 (1 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[E] year

NorESM1-M (3 sim)HadCRUT42

-2

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

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-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000

Te

mp

A

no

m

(oC

)

[A] year

MPI-ESM-MR (3 sim)HadCRUT42

-2

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mp

A

no

m

(oC

)

[B] year

MPI-ESM-P (2 sim)HadCRUT42

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mp

A

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m

(oC

)

[C] year

MRI-CGCM3 (3 sim)HadCRUT42

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m

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MRI-ESM1 (1 sim)HadCRUT42

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mp

A

no

m

(oC

)

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NorESM1-M (3 sim)HadCRUT42

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05

1

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Te

mp

A

no

m

(oC

)

[F] year

NorESM1-ME (1 sim)HadCRUT42

Figure 11 Continues HadCRUT4 GST (blue) vs CMIP5 GCM simulations (red) Eq 6 (black)

function

f(t) = h60(t) + h20(t) + h104(t) + h91(t) + p(t) (6)

Eq 6 is plotted in black in Figures 4-11 and reproducesthe decadal and multidecadal GST patterns relatively wellFigures 4-11 also plot Eq 6 against the GCM simulations onthe common baseline The latter comparison assists a visualcheck of the ability of the GCM simulations to reproduce the

decadal and multidecadal GST patterns which is generallypoor

Note that p(t) is only a convenient second order polyno-mial geometrical description of the upward warming trendfrom Jan1861 to Dec2005 This function does not haveany hindcasting or forecasting ability outside the interval18612005 because its derivation is geometrical not physicalThe justification of p(t) is purely mathematical and derivesdirectly from Taylorrsquos theorem Essentially a second order

13

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

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06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

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1980 1985 1990 1995 2000 2005 2010 2015

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p A

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mod42 rcp45HadCRUT42

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12

1980 1985 1990 1995 2000 2005 2010 2015

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p A

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(o

C)

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mod39 rcp85HadCRUT42

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mod32 rcp26HadCRUT42

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12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-02

0

02

04

06

08

1

12

14

16

18

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff[A] model number

harmonic predictionalpha-60average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[B] model number

harmonic predictionalpha-20average

-1

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[C] model number

harmonic predictionalpha-104

average

-1

-05

0

05

1

15

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[D] model number

harmonic predictionalpha-91average

02

04

06

08

1

12

14

16

18

2

0 20 40 60 80 100 120 140 160 180

regress

ion coe

ff

[E] model number

harmonic predictionbeta

average

Figure 12 Regression coefficients calculated using Eq 7 referring to all GCM runs as reported in Table 2 The GCM number -0- correspondsto the CMIP5 model mean simulation depicted in Figure 2 The yellow area around 1 corresponds to the harmonic model confidence regionThe blue bars are the average values with relative error bars

polynomial is used because this function is required to cap-ture the accelerating GST warming trend from 1861 to 2005Simultaneously it should be as orthogonal as possible to a60-year cycle on a 145-year period see also Scafetta (2013bfigure 4) In section 5 the geometrical function p(t) is substi-tuted with a more physically-based function by taking intoaccount secular and millennial cycles (Humlum et al 2011Scafetta 2012c 2013a) plus the contribution from volcanoand anthropogenic forcings

In contrast the four chosen harmonics are supposed torepresent real dynamical mechanisms related to astronom-ical cycles Thus they may have within certain limitshindcastforecast capabilities outside the interval 1850-2010

as it was explicitly tested in multiple ways (Scafetta 20102012abc) However numerous other harmonics may existas it happens for the tidal system where up to 40 harmonicsare used Additional harmonics are ignored in this analysis

The GCM simulations should simultaneously reproduceharmonics and an upward trend statistically compatible withthose found in the GST record Thus we use the samestrategy implemented in Scafetta (2012b) and adopt thefollowing regression model

g(t) = α60h60(t) + α20h20(t) + α104h104(t)

+α91h91(t) + βp(t) + γ(7)

14

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

where α β and γ are appropriate regression coefficientsthat are evaluated for each GCM simulation m(t) by us-ing the usual minimization of the residual square functionsum

x[m(t) minus g(t)]2 during the period Jan1861 - Dec2005The parameter γ has only a baseline meaning

If the evaluated regression coefficients α and β are closeto 1 then the GCM simulation could well reproduce thecorresponding temperature constituent pattern captured byEq 6 For example if α60 asymp 1 then the analyzed GCM sim-ulation function m(t) could reconstruct the 60-year mod-ulation found in the temperature record as captured by theconstituent function h60(t) However such a condition isnecessary but not sufficient to guarantee the matching be-tween the two records at the given frequency On the con-trary if the evaluated regression coefficients are statisticallydifferent from 1 then the GCM simulation can not recon-struct the correspondent GST pattern

Table 2 reports the six regression coefficients α β and γfor the ensemble mean and for each of the 162 GCM simu-lations These results are also depicted in Figure 12 Theresults are quite unsatisfactory All GCM simulations failto reproduce the four decadal and multidecadal GST oscil-lations sufficiently well

The averages of the 162 results give values between 04and 07 with a standard deviation between 03 and 05Thus most regression coefficients fall outside the yellow areaof the harmonic model confidence reported in the first lineof Table 2 Even if occasionally a regression coefficient fallsclose to 1 as shown in Figure 13 it is likely a coincidence asthe GCM simulations should simultaneously reproduce alldecadal and multidecadal patterns A comprehensive sta-tistical test is provided by using the following reduced χ2

values that are reported in Table 2 and are defined as

χ2 =1

5

[(α60m minus α60T )2

∆α260m + ∆α2

60T

+(α20m minus α20T )2

∆α220m + ∆α2

20T

+

(α104m minus α104T )2

∆α2104m + ∆α2

104T

+(α91m minus α91T )2

∆α291m + ∆α2

91T

+

(βm minus βT )2

∆β2m + ∆β2

T

]

(8)

The suffix lsquomrsquo indicates the correspondent regression coeffi-cient for the GCM model the suffix lsquoTrsquo indicates the cor-respondent regression coefficient for the harmonic model re-ported in the first line of Table 2 Values of χ2 1 wouldindicate that the model performs well in reproducing thedecadal and multidecadal patterns shown in the data How-ever as the table reports χ2 varies between 35 and 161(mean=51) among the 162 individual simulations χ2 is 14for the ensemble mean model Values χ2 1 indicate thatthese GCMs do not reconstruct the GST decadal and mul-tidecadal scales

Table 2 also reports the root mean square deviation(RMSD) from Eq 6 for both the GST record and for allGCM simulations shown in Figure 4-11 RMSD(ξ θ) =radicsumN

i=1(ξi minus θi)2N This function measures the ability of

a simulated sequence ξi to reconstruct the observed se-quence θi The RMSD is calculated after both the GST

record and the GCM simulations are smoothed with a 49-month moving average algorithm to highlight the decadalmodulation as done in Figure 3B For the GCMs RMSDranges between 008 oC and 022 oC with an average of 014oC On the contrary the harmonic model (Eq 6) presentsa RMSD of 005 oC indicating that the latter is statisticallymore accurate in representing the GST records by a factorbetween 2 and 44 compared with the CMIP5 GCMs as alsofound for the CMIP3 GCMs (Scafetta 2012b)

32 Scale-by-scale band-pass filter decomposition compari-son

A Fourier band-pass filter decomposition captures all dy-namical details of a time sequence at complementary time-scales Figures 13A and 13B show the decomposition of theHadCRUT4 GST and of the GCM ensemble mean simula-tion S1 corresponds to time-scales larger than 6 monthsand shorter than 7 years and captures most of the fast vari-ability of the signal such as ENSO oscillations and volcanoeruptions S2 corresponds to scales between 7 and 14 yearsand captures the decadal scale S3 corresponds to scales be-tween 14 and 28 years and captures the bi-decadal oscil-lation S4 corresponds to scales between 28 and 104 yearsand captures the multidecadal scale such as the quasi 60-year oscillation A second order polynomial given by Eq5 is detrended from all sequences to make them stationaryto a first order approximation

If Tc(t) is a measured band-pass temperature componentfunction and Mc(t) is the correspondent GCM temperatureband-pass component function the regression coefficient Φis given by the formula

Φ =

sumMc(t)Tc(t)sumTc(t)Tc(t)

(9)

If Φ is close to 1 then the functions Mc(t) and Tc(t) arestatistically compatible according to this measure Againsuch a condition is necessary but not sufficient to guaranteethe matching between the two records at the given frequencyband

Table 3 reports the four scale-by-scale regression coeffi-cients calculated for the GCM ensemble mean and the 162GCM simulations versus the correspondent GST frequencyband-pass components The same coefficients are depictedin Figure 14 All GCM simulations including the GCMensemble mean (number -0- in the figure) perform muchless well in reconstructing the temperature components al-though occasionally a single regression coefficient may fallclose to 1 The average values relative to the four band-passcomponents are statistically different from 〈Φ〉 = 1 plusmn 015(a reasonable 15 error from the ideal Φ = 1 is assumedfor all values as approximately found in Table 2 for the har-monic model components) for S1 〈Φ〉 = 003 plusmn 004 forS2 〈Φ〉 = 038 plusmn 022 for S3 〈Φ〉 = 080 plusmn 036 for S4〈Φ〉 = 061plusmn 030

Table 3 also reports a reduced χ2 test using an equationsimilar to Eq 13 However only the three components re-lated to the S2-scale S3-scale and S4-scale are used in the

15

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[A] year

HadCRUT4

S1

S2

S3

S4-1

-05

0

05

1860 1880 1900 1920 1940 1960 1980 2000

Tem

p A

mon (oC

)

[B] year

GCM ensemble average

Figure 13 Scale-by-scale Fourier band-pass frequency decomposition [A] HadCRUT4 GST [B] GCM ensemble mean Quadratic polynomialfit Eq 5 (red) S1 captures time-scales shorter than 7 years S2 captures scales between 7 and 14 years S3 captures scales between 14 and 28years S4 captures scales between 28 and 104 years Note in [A] the clear quasi 60-year oscillation in the HadCRUT4 GST S4 record and thebeat modulation in the HadCRUT4 GST S2 curve caused by the 91 and 104 year oscillations

test as

χ2 =1

3

[(ΦS4 minus 1)2

0152+

(ΦS3 minus 1)2

0152+

(ΦS2 minus 1)2

0152

] (10)

The S1-scale is excluded because the GCM models evidentlydo not reconstruct the fast fluctuations at scales shorter than7 years Again χ2 1 for all models Thus as in the pre-vious subsection also these results suggest that the CMIP5GCMs do not properly reconstruct the observed GST dy-namics at multiple time scales although a significant varia-tion among the individual simulations is observed

33 Direct power spectrum comparison

Figure 15 depicts a final statistical test that estimates theability of the GCMs in reconstructing the power spectrumof the GST within the period range from 7 to 100 years

Figure 15A shows in red the periodogram of the Had-CRUT4 GST and of the GCM ensemble mean Figure 15Bshows in red the maximum entropy method (MEM) powerspectrum of the HadCRUT4 GST and of the GCM ensemblemean The periodogram and MEM algorithms were takenfrom Press et al (1997) and calculated after detrending fromall records Eq 5 The figures highlight for example thatthe GCM ensemble mean macroscopically fails to reproducethe quasi 60-year oscillation by presenting a spectral peakat a period of sim 75 years instead of the observed sim 61 yearssee also Figure 3A

As alternatively demonstrated in Scafetta (2012b fig-ure 2) the autocorrelation peak at a time-lag of 70-80 yearsfound in the GCM simulations is mostly driven by the strongGCM volcano eruption signatures In fact there is a quasi80-year lag between the two GCM large volcano eruptionsignatures of Krakatoa (1883) and Agung (1963-1964) andbetween the volcano signatures of Santa Maria (1902) and

16

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180reg

ressio

n coef

f[A] model number

requirement range 15S1 05-70 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[B] model number

requirement range 15S2 70-140 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[C] model number

requirement range 15S3 14-28 year

average

-05

0

05

1

15

2

0 20 40 60 80 100 120 140 160 180

regres

sion c

oeff

[D] model number

requirement range 15S4 28-104 year

average

Figure 14 Regression coefficients φ calculated using Eq 9 referring to all GCM runs as reported in Table 3 [A] φS1 band-pass range 05-70year [B] φS2 band-pass range 70-140 year [C] φS3 band-pass range 14-28 year [D] φS4 band-pass range 28-104 year The GCM number -0-corresponds to the CMIP5 model mean simulation depicted in Figure 1 The yellow area around 1 corresponds to the chosen confidence regionof 15 The blue bars are the average values with relative error bars

El Chichon (1982) Note that the quasi 80-year recurrentpattern in the volcano signature could have been responsi-ble for the slight shift of the peak of the GST periodogramat a value slightly larger than 60 years as mostly observedin Figure 15A

A coherence test is made by simply calculating the cross-correlation coefficient r between the GST power spectrumdepicted in the figure and each of the GCM power spectraValues of r close to 1 indicate a good spectral coherencebetween the GST record and the GCM simulations Notehowever that this is a less stringent test than the casesdiscussed in subsections 31 and 32 because a mere power

spectrum correlation test ignores the phase positions of theharmonics which is a necessary component that the modelsshould reconstruct as well

The comparison between the GST record and the GCMensamble mean record gives r = 079 using the periodogramsand r = minus002 using the MEM power spectra which presentsharper peaks The test is repeated for all 162 GCM sim-ulations The results are depicted in Figues 15C and 15Dand reported in the last two columns of Table 3 The av-erage correlation coefficient is 〈r〉 = 063 plusmn 025 using theperiodograms and 〈r〉 = 008 plusmn 021 using the MEM powerspectra

17

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

0

0002

0004

0006

0008

001

0012

0014

0 20 40 60 80 100

po

we

r sp

ectr

um

- p

erio

do

gra

m (

oC

2)

[A] period (year)

HadCRUT4GCM ensemble mean

1e-005

00001

0001

001

01

1

0 20 40 60 80 100

po

we

r sp

ectr

um

- M

EM

(oC

2)

[B] period (year)

HadCRUT4GCM ensemble mean

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

- r -

[C] model number

periodogramaverage

-04

-02

0

02

04

06

08

1

0 20 40 60 80 100 120 140 160 180

spec

tral c

ohere

nce

r -

[D] model number

MEMaverage

Figure 15 [A] Periodograms of the GST record (red) and of the GCM ensemble mean simulation (blue) [B] Maximum entropy method (MEM)power spectrum of the GST record (red) and of the GCM ensemble mean simulation (blue) [C] Spectral correlation coefficients between theGST recorcd and all GCM simulations using the periodograms [D] Spectral correlation coefficients between the GST record and all GCMsimulations using the MEM power spectra See Table 3 last two columns

Thus the GCMs do not reproduce the natural harmon-ics of the climate system even in the less stringent senseof a mere power spectrum correlation test that ignores thephase positions of the harmonics These results indicate arelatively poor spectral coherence at the dacadal and multi-decadal scale between the GST and the GCM simulationsThe performance of the individual GCM simulations variesgreatly

4 Visual examples of CMIP5 GCM deficiencies

Typical major deficiencies found in the GCM simula-tions are briefly discussed in the following two subsectionsA simple visual analysis of the records suffices to highlightsevere mismatches between the GCM simulations and theGST record

41 Example 1 the GCM simulations significantly divergefrom the GST record since 2000

Most CMIP5 GCM simulations using the historical forc-ings end in Dec2005 Since 2006 the models are run usingprojected forcings for the 21st century Four scenarios have

18

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[B] year

mod42 rcp45HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[D] year

mod39 rcp85HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[A] year

mod32 rcp26HadCRUT42

-06

-04

-02

0

02

04

06

08

1

12

1980 1985 1990 1995 2000 2005 2010 2015

Tem

p A

nom

(o

C)

[C] year

mod25 rcp60HadCRUT42

Figure 16 HadCRUT4 record (blue) versus the CMIP5 GCM projections [A] the rcp26 simulations made of 32 models [B] the rcp45 simulationsmade of 42 models [C] the rcp60 simulations made of 25 models [D] the rcp85 simulations made of 39 models All records are annually resolvedand baselined in the 1980-2000 period Note that in 2013 the temperature which is approximately steady since 1997 runs cooler than allCMIP5 GCM simulations

been proposed and labeled as rcp26 rcp45 rcp60 rcp85as also shown in Figure 2

Figure 16 shows the annually resolved available simula-tions in the four cases versus the annually resolved Had-CRUT4 record (the 2013 value is based on data from Jan-uary to June) The records are baselined during the period1980-2000 The rcp26 simulations are made of 32 modelsrcp45 of 42 models rcp60 of 25 models and rcp85 of 39models

Figure 16 clearly shows that the models have signifi-cantly overestimated the global warming rate since 2000see also the detailed analysis proposed by For the year2013 all models have predicted a global mean surface tem-perature that is found to be 00-05 oC warmer than theGST record The linear rate of the HARCRUT4 recordsince 2000 is 03plusmn 04 oCcentury which indicates that nowarming has been observed in the GST record since 2000

In contrast the CMIP5 simulations have predicted a strongwarming rate of [A] rcp26 22plusmn02 oCcentury [B] rcp4521 plusmn 02 oCcentury [C] rcp60 19 plusmn 02 oCcentury [D]rcp85 21plusmn 02 oCcentury

42 Example 2 a detailed qualitative visual study of theCanESM2 GCM simulations

Figure 17 reinterprets figure 1 of Gillett et al (2012)that compares the GST record and a set of simulationsof CanESM2 GCM which produces some of the best re-sults among all GCMs For example its simulations pro-duce the best multidecadal result with a 3 lt χ2 lt 15 (seeTables 2-3 and the correspondent figures) However eventhe CanESM2 simulations macroscopically fail to reproducethe observed steady GST pattern since 2000 CanESM2 ap-pears to be finely tweaked with the aerosol uncertain forcingbut still fails to reconstruct important temperature patterns

19

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

The GCM simulations fail to reproduce the steady GST observed since 2000

The GCM simulations produce too deep and wide volcano cooling spikeswhich are not observed in the GST

GST shows a 1880-1910 cooling and 1910-1940 warming The GCM simulations shows a 1880-1940 steady warming

A strong aerosol cooling effectafter 1950 partially compensatesthe strong GHG warming effect up to 2000 After 2000 AER is not able to compensate GHG

A ALL B NAT

C GHG D AER1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

1850 1900 1950 2000

year year

year year

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

15

10

05

1000

-05

SA

T a

no

ma

ly (

oC

)

Figure 17 A reproduction of figure 1 in Gillett et al (2012) with additional comments that highlight major mismatches between the GSTrecord (black) and a set of simulations made with CanESM2 The figure highlights problems common to all CMIP5 GCMs

which are far better reconstructed by the harmonic modeldiscussed in Section 6 In fact for the CanESM2 simula-tions RMSD ranges from 013 to 015 oC while Eq 13 hasa RMSD of about 004 oC

In the simulations depicted in Figure 17 CanESM2 GCMis forced with (a) anthropogenic and natural forcings (ALL)(b) natural forcings only (NAT) (c) greenhouse gases only(GHG) and (d) aerosols only (AER) The comments addedto the figure highlight typical common problems found inall CMIP5 GCMs when compared with the GST record (1)The GCM does not reproduce the 2000-2012 steady GSTtrend (2) The volcano cooling spikes are too large com-pared to the signature that can be qualitatively deducedfrom the GST record (3) GST shows a clear 60-year modu-lation made of a 1880-1910 cooling plus a 1910-1940 warm-ing while the GCM shows a 1880-1940 steady warming (4)The GCM needs a strong aerosol cooling effect after 1950 topartially compensate the strong GHG warming effect up to2000 but after 2000 the aerosol cooling effect is not able tocompensate the strong GHG warming effect and the simu-

lations strongly diverge from the observations

5 Discussion

The general failure of the CMIP5 GCMs to accuratelyreconstruct the dacadal and multidecadal GST scales in-cluding that the GST has not warmed during the last 17years (essentially since about 1997) brings into question thereliability of these models In fact Knight et al (2009) ob-served that ldquoNear-zero and even negative trends are com-mon for intervals of a decade or less in the simulationsdue to the modelrsquos internal climate variability The simu-lations rule out (at the 95 level) zero trends for intervalsof 15 year or more suggesting that an observed absence ofwarming of this duration is needed to create a discrepancywith the expected present-day warming raterdquo The results ofthis analysis suggest that major physical flaws exist in theCMIP3 and CMIP5 GCMs which may cast doubts on their21st century projections as well

20

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

Figure 18 [A] Global sea level record (Jevrejeva et al 2008) (left) and its MSAA colored diagram (right) [B] North Atlantic Oscillation(NAO) (Luterbacher et al 1999 2002) (left) and its MSAA colored diagram (right) In [B] the colors are inverted Note the common quasi 60year oscillation since 1700 indicated by the alternating green and red regions within the 30-100 year scales From Scafetta (2013c)

The inability of the GCMs to model the observed oscilla-tions and in particular the post-2000 temperature plateauhas been justified in various ways In general it has beenspeculated that the models andor their forcings need to beslightly corrected Effects of missing volcano forcing aerosolforcing andor some internal unforced dynamics of the cli-mate system have typically been speculated but problemsarise with these interpretations

For example Booth et al (2012) speculated that thecooling from 1940 to 1970 was due to poorly modeled aerosolforcing However the temperature also presents an equiv-alent cooling period from 1880 to 1910 that was not recon-structed by their model Kaufmann et al (2011) specu-lated that the steady GST between 1998-2008 was causedby an increase of atmospheric sulfate production (primarilyfrom China) that countered the greenhouse gas warmingHowever Remer et al (2008) (see their figure 5) showedno change in global aerosol optical depth during the period2000-2007 Meehl et al (2011) speculated that GST hiatus

periods could be caused by occasional deep-ocean heat up-take and showed that GCM simulations may occasionallypresent at random times an up-to-a-decade of steady tem-perature despite an increasing anthropogenic forcing How-ever the CCSM4 GCM used in Meehl et al (2011) (whichis one of the models analyzed above) does not reproducethe steady temperature observed from 2000 to 2013 TheCCSM4 GCMs only produce hiatus periods occurring in2040-2050 and 2070-2080 which appear as random red-noisefluctuations of the model (see their figure 1a) The lattervariability is commonly referred to as internal unforced dy-namics of the climate system and it is claimed to be unpre-dictable

However because the lack of warming since 19971998 isjust an aspect of the problem the above speculations appearphysically unsatisfactory A comprehensive and consistenttheory of climate change must simultaneously interpret theentire GST dynamics observed since 1850 at least from thedecadal scale up Although aerosols and internal dynamics

21

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

certainly may have some effects the GST also appears topresent quasi regular oscillations The findings of the previ-ous sections indicate that the CMIP5 GCMs fail to simulta-neously capture the decadal and multidecadal GST dynam-ical patterns observed since 1850 such as the four identifiedmajor oscillations with approximate periods of 91 10-1120 and 60 years (Scafetta 2010) These oscillations gener-ate a network of dynamical synchronization within the cli-mate system also not reproduced by the models (Wyatt etal 2011) The tables 2 and 3 show that the GCM perfor-mance varies greatly both among the models and among theindividual model runs produced by the same model

Quasi-decadal bidecadal and 60-year oscillations andother longer oscillations have been detected in numerousrecords covering centuries and millennia For example Jevre-jeva et al (2008) and Chambers et al (2012) showed a quasi60-year cycle in the sea level rise rate since 1700 Klyashtorinet al (2009) showed that numerous climate indexes present along-term 50-70 year oscillations during the last 1500 yearsKnudsen et al (2011) showed a persistent quasi 60-year cy-cle in the Atlantic Multidecadal Oscillation throughout thelast 8000 years a quasi 20-year and 60-year oscillations alsoappear for centuries and millennia in some Greenland tem-perature records (Davis and Bohling 2001 Chylek et al2012) The Introduction section contains additional sug-gested references showing these oscillations

For example Figure 18 reproduces figure 10 in Scafetta(2013c) that shows two relatively global climatic indexessince 1700 the global sea level record (Jevrejeva et al2008) and the North Atlantic Oscillation (NAO) reconstruc-tion (Luterbacher et al 1999 2002) The right panels showthe multi-scale acceleration analysis (MSAA) of these tworecords and highlight the presence of a common major quasi60-year oscillation since 1700 This oscillation is revealed bythe alternating green and red colors indicating that the localacceleration of the records varies from negative to positivevalues that is there is an oscillation

The existence of large quasi-60 year oscillations lastingcenturies (for example Scafetta et al (2013) found a quasi-60 year oscillation in the ice core GISP2 temperature recordsince 1350) questions interpretations such as that proposedby Imbers et al (2013) that the quasi 60-year modulationobserved in the GST record since 1850 could be due to somekind of red noise produced by short memory processes ex-emplified by AR(1) models or by long memory processeswhich were claimed to modulate the internal variability ofthe global mean surface temperature In fact a genericstochastic model would not be able to reproduce a quasiharmonic signal lasting centuries in an energetically dissipa-tive system such as the climate without the help of a specificharmonic forcing

Indeed the climate system appears to be chaotically os-cillating around a dominant complex harmonic componentmade of multiple specific frequencies plus some additionalcontribution from volcano and anthropogenic forcings Theinternal variability more likely chaotically perturbs the os-cillations but does not produce them This harmonic com-ponent looks complex but also predictable It appears moresimilar in principle to the tidal oscillations of the ocean

which are forced by numerous astronomical harmonics thanto a hypothetical random internal unforced dynamics of theclimate system

Evidence has been presented that the observed decadaland multidecadal oscillations might have an astronomicalorigin (Scafetta 2010 2012abcd 2013a)

For example the quasi 91-year oscillation appears to berelated to long solarlunar tidal oscillations see also Keelingand Whorf (1997a) and Wang et al (2012) The rationaleis the following The lunar nodes complete a revolution in186 years and the Saros soli-lunar eclipse cycle completesa revolution in 18 years and 11 days These two cycles in-duce 93 year and 9015 year tidal oscillations correspondingrespectively to Sun-Earth-Moon and Sun-Moon-Earth tidalconfigurations Moreover the lunar apsidal precession com-pletes one rotation in 885 years causing a correspondinglunar tidal cycle Thus three interfering major soli-lunartidal cycles clustered between 885 year and 93 year peri-ods are expected which should generate a major varyingoscillation with an average period around 906 years Thissoli-lunar tidal induced cycle could peak for example in1997-1998 when the solar and lunar eclipses occurred closeto the equinoxes (this happens every sim 9 years) when thesolilunar tidal torque is reasonably at the equator In gen-eral it is evident that the GST can be influenced by oceanicoscillations induced by soli-lunar gravitational tides whichproduce a very complex set of harmonics at multiple timescales (Keeling and Whorf 1997ab Wang et al 2012)

The other decadal and multidecadal oscillations shown inFigure 1 appear to be mostly related to solarplanetary os-cillations induced by Jupiter and Saturn and are seen in thesolar wobbling and in the solar activity These astronomi-cal oscillations are indicated by the black curves depicted inFigure 2C and 2D which refer to the speed of the sun relativeto the barycenter of the solar system Scafetta analysed sev-eral other multisecular proxy temperature models and alsoshowed that it is possible to hindcast the 1950-2010 GST os-cillations using a harmonic model calibrated on the period1850-1950 and vice versa

There is considerable empirical evidence showing a strongcorrelation between climate and solar records at multiplescales (Hoyt and Schatten 1997 Bond et al 2001 Kerr2001 Kirkby 2007 Svensmark 2007 Svensmark and Friis-Christensen 2007 Steinhilber et al 2012 Kokfelt and Muscheler2013) Numerous authors (eg Scafetta and West 2007Scafetta 2009a Kirkby 2007 etc) have argued that to in-terpret recent paleoclimate temperature reconstructions andtheir patterns since the Maunder solar minimum (1640-1715)it is necessary to postulate a climatic response to solar vari-ations significantly larger than that predicted by the cur-rent GCMs GCMs assume the existence of a total solarirradiance (TSI) forcing although this is a very small con-tribution to climate change (IPCC 2007) However a 1-3astronomically-induced modulation of the Earthrsquos albedocan easily provide the strong needed climatic amplificationeffect to solar variation up to a factor of 10 For exampleScafetta (2012a) calculated that differentiating directly theStefanBoltzmanns black-body equation a climate sensitivityof kS = 0053 KWmminus2 is found (this value uses the metric

22

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

-04

-02

0

02

04

06

08

1985 1990 1995 2000 2005 2010

Tem

pera

ture

Ano

mal

y (o C

)

year

ISCCP Global Cloud CoverHadCRUT3 Global Surface Temperture

73

71

69

67

65

63

61

Clo

ud C

over

(

)

Figure 19 Global surface temperature (black) against monthly variations in total global cloud cover since July 1983 (red) Correlationcoefficient ro = minus052 for 318 points P (|r| ge |ro|) lt 00005 The cloud data are from the International Satellite Cloud Climatology Project(ISCCP) Cloud data from httpisccpgissnasagovpubdataD2BASICSB8glbpdat

adopted in Scafetta (2012a) which differs from the commonmetric) However if a solar activity variation of 1 Wm2 in-duces also a 1 variation of the albedo a climate sensitivityof kS = 036 KWmminus2 would be found which is about anorder of magnitude larger than the previous value

Scafetta and Willson (2013a) found evidence for a quasi60-year oscillation (and others) in aurora records since 1530linked to astronomical oscillations If electromagnetic spaceweather mechanisms induce small oscillations in the upperstrata of the atmosphere that drive coherent oscillations (ap-proximately 1-3) in the albedo by regulating the cloudcover system this may suffice to produce GST oscillationssynchronized with astronomical oscillations by means of analbedo-related modulation of the amount of solar radiationreaching and warming the surface (Svensmark 2007 Tins-ley 2008 Scafetta 2012a) This may happen because so-lar activity can modulate the incoming flux of galactic cos-mic ray or other electromagnetic mechanisms related to thephysical properties of the Parker spiral of the Sunrsquos magneticfield as it extends through the solar system Despite the factthat preliminary attempts to include some physical connec-tions such as those between cosmic rays ions nucleationand cloud drops have showed up to now a relatively weakmodel response (Pierce and Adams 2009) there still existsmuch debate (Svensmark et al 2012) and more advancedmodels and alternative space weather mechanisms may bebetter understood in the future For example Svensmarket al (2013) have recently discovered physical processes not

included yet in current theoretical models Moreover so-lar UV radiation can also influence the stratospheric ozonevariability (Lu 2009) Indeed UV varies in percentage sig-nificantly more than total solar irradiance (TSI) Reichler etal (2012) have also proposed a stratospheric direct drivingof the oceanic climate variability

In support of the above theory Figure 19 shows theglobal surface temperature plotted against the monthly vari-ations in the total global cloud cover (TGCC) available sinceJuly 1983 obtained from the International Satellite CloudClimatology Project (ISCCP) (httpisccpgissnasagovindexhtml) The TGCC record is flipped upside-down for visual convenience The temperature record is wellcorrelated (negatively) with TGCC (correlation coefficientro = minus052 for 318 points P (|r| ge |ro|) lt 00005) In factTGCC decreases from 69 to 645 during the 1983-2000warming period and increased slightly from 645 to 655during the 2000-2010 quasi-plateau temperature period Asimilar pattern is observed in the record of total precipitablewater (TPW) since 1988 (Vonder Haar et al 2012) A vari-ation of a few percent in global cloud cover can easily causea variation of a fraction of Celsius degree on the surfaceglobal temperature (Scafetta 2012b) Moreover Soon etal (2011) showed a good correlation between a solar activ-ity proxy model the surface temperature of China (whichalso shows a clear cooling from 1940 to 1970) and a recordof sunshine duration over Japan which is related to cloudcover variation since 1890 (Stanhill and Cohen 2008) These

23

4400

4200

4000

3800

3600

3400

3200

3000

2800

1950 1960 1970 1980 1990 2000 2010

Cos

mic

Ray

Inte

nsity

year

CLIMAX record

Figure 20 CLIMAX cosmic ray count The scale is inverted because cosmic ray flux is negatively correlated with solar activity The figuresuggests that solar activity might have increased on average from 1970 to 2000 (similarly to ACRIM TSI satellite composite (Willson andMordvinov 2003 Scafetta and Willson 2009)) causing a global warming by inducing a decrease in the cloud cover (observed in the data Figure19) via a reduction of cosmic ray flux The red curve is a simple regression model made of a linear trend plus a 60-year oscillation used tohighlight the multidecadal modulating pattern Data from httpulyssessrunheduNeutronMonitorMiscneutron2html

records also present a clear 60-year cyclical modulation syn-chronous to the temperature record The cooling from 1940to 1970 was a global phenomenon Le Mouel et al (2008) alsohighlighted in the newspapers of the time Gwynee (1975)Xia (2012) showed that cloud cover decreased slightly inChina during 1954-2005 although most decrease occurredfrom 1970 to 2000 when GST increased Indeed from 1970to 2000 the cosmic ray count decreased slightly on averageas shown in Figure 20 According Svensmarkrsquos theory thiswould imply a decreasing cloud cover (as the data in Figure19 show) and cause a global warming

On the contrary CO2 atmospheric concentration andin general the net anthropogenic forcing monotonically in-creased since the 1980s (eg Hansen et al 2011) and af-ter 2000 do not correlate with the observed temperatureplateau The above results indicate that the cloud coverand the temperature are responding to some other physi-cal mechanism possibly driven by solar and lunar forcings(Scafetta 2010 2012b) rather than to the forcings currentlyincluded in the GCMs Since 1980 the latter are domi-nated by anthropogenic forcing which was still increasingfrom 2000 to 2013 In general the net radiative forcings asused in the CMIP5 GCMs has increased since 2000 as im-plicitly demonstrated in the GCM simulations shown in Fig-

ures 16 and 17 Indeed despite the importance of the cloudcover system in shaping the GST records the CMIP5 GCMsare found to poorly reconstruct the cloud system (Nam etal 2012)

A serious source of uncertainty refers to the solar forc-ing functions that have to be used in the GCMs see alsoGray et al (2010) for a general discussion on the topic Forexample CMIP5 GCMs used only a TSI forcing functiondeduced from Wang et al (2005) but TSI functions are cur-rently extremely uncertain (eg Hoyt and Schatten 1993Lockwood 2011 Shapiro et al 2011) Using correct solarforcing functions in the GCMs is fundamental if the climatesystem is very sensitive to solar variations as the above stud-ies suggest Direct TSI satellite measurements started in1978 However an upward TSI trend from 1980 to 2000 fol-lowed by a decrease since 2000 is implied by the ACRIM TSIsatellite composite (Willson and Mordvinov 2003 Scafettaand Willson 2009) which uses the TSI experimental dataas published by the original science teams An alternativeTSI satellite composite the PMOD based on altered TSIdata (Frohlich 2006 2009) shows a gradual TSI decreasefrom 1980 to 2010 ACRIM and PMOD TSI satellite com-posites are compared in Figure 21 Before 1980 only highlycontroversial solar proxy reconstructions exist

24

Figure 21 ACRIM (Willson and Mordvinov 2003) and PMOD Frohlich (2009) total solar irradiance satellite composites

The CMIP5 GCMs use the recommended TSI proxy modelprepared by Lean and collaborators (Wang et al 2005Kopp and Lean 2011) which does not show a TSI increasefrom 1980 to 2000 presents a peak around 1960 as alsoshown by the sunspot number record and presents a rela-tively small secular variability since the Maunder solar min-imum of the 17th century On the contrary some alterna-tive TSI reconstructions present a larger secular variability(Hoyt and Schatten 1993 1997) peak in the 1940s and inthe 2000 and correlate with the GST records far better thanLeanrsquos TSI proxy models (Loehle and Scafetta 2011 Soon2005 2009 Soon et al 2011) Also solar cycle length mod-els (Thejll and Lassen 2000) peak in the 1940s instead ofsim1960 Schrijver et al (2011) Shapiro et al (2011) andVieira et al (2011) have recently proposed quite contrastingTSI reconstructions with a range of secular variability fromvery small to very large secular variability and significantlydiffer from Leanrsquos TSI models

Figure 22A compares the latest Lean model (Kopp andLean 2011) and the model proposed by Hoyt and Schatten(1993) Figure 22B shows that the solar model proposed by

Hoyt and Schatten (1993 1997) well correlates with the cen-tral England temperature (CET) reconstruction (Parker etal 1992) since 1700 suggesting a strong climate sensitivityto solar changes Figure 22B suggests that the sun couldhave contributed about half of the 20th century warmingin England see Scafetta (2013ab) for additional detailsIn any case even if the proposed TSI reconstructions differfrom each other in important details there exists a generalagreement that solar activity during the second half of the20th century was higher than the previous centuries sug-gesting that the observed global warming since 1900 couldhave been partially caused by the increased solar activity(Scafetta and West 2007 Scafetta 2009a)

Because the CMIP5 GCMs use Leanrsquos TSI model it isalso important to point out that despite serious controversyover the TSI dynamical behavior before 1992 the exper-imental TSI satellite groups (ACRIM and PMOD) agreethat the TSI minimum in 1996 was higher than the TSIminimum in 2008 by at least 02-03 Wm2 see ACRIMand PMOD TSI satellite composites at httpacrimcomTSI20Monitoringhtm) The open solar magnetic flux the

25

Figure 21 ACRIM (Willson and Mordvinov 2003) and PMOD Frohlich (2009) total solar irradiance satellite composites

The CMIP5 GCMs use the recommended TSI proxy modelprepared by Lean and collaborators (Wang et al 2005Kopp and Lean 2011) which does not show a TSI increasefrom 1980 to 2000 presents a peak around 1960 as alsoshown by the sunspot number record and presents a rela-tively small secular variability since the Maunder solar min-imum of the 17th century On the contrary some alterna-tive TSI reconstructions present a larger secular variability(Hoyt and Schatten 1993 1997) peak in the 1940s and inthe 2000 and correlate with the GST records far better thanLeanrsquos TSI proxy models (Loehle and Scafetta 2011 Soon2005 2009 Soon et al 2011) Also solar cycle length mod-els (Thejll and Lassen 2000) peak in the 1940s instead ofsim1960 Schrijver et al (2011) Shapiro et al (2011) andVieira et al (2011) have recently proposed quite contrastingTSI reconstructions with a range of secular variability fromvery small to very large secular variability and significantlydiffer from Leanrsquos TSI models

Figure 22A compares the latest Lean model (Kopp andLean 2011) and the model proposed by Hoyt and Schatten(1993) Figure 22B shows that the solar model proposed by

Hoyt and Schatten (1993 1997) well correlates with the cen-tral England temperature (CET) reconstruction (Parker etal 1992) since 1700 suggesting a strong climate sensitivityto solar changes Figure 22B suggests that the sun couldhave contributed about half of the 20th century warmingin England see Scafetta (2013ab) for additional detailsIn any case even if the proposed TSI reconstructions differfrom each other in important details there exists a generalagreement that solar activity during the second half of the20th century was higher than the previous centuries sug-gesting that the observed global warming since 1900 couldhave been partially caused by the increased solar activity(Scafetta and West 2007 Scafetta 2009a)

Because the CMIP5 GCMs use Leanrsquos TSI model it isalso important to point out that despite serious controversyover the TSI dynamical behavior before 1992 the exper-imental TSI satellite groups (ACRIM and PMOD) agreethat the TSI minimum in 1996 was higher than the TSIminimum in 2008 by at least 02-03 Wm2 see ACRIMand PMOD TSI satellite composites at httpacrimcomTSI20Monitoringhtm) The open solar magnetic flux the

25

1357

1358

1359

1360

1361

1362

1700 1750 1800 1850 1900 1950 2000

TS

I (W

m2 )

[A] year

Kopp and Lean (2011)Hoyt and Schatten (1993) (rescaled)ACRIM TSI composite (since 1981)

8

85

9

95

10

105

11

1700 1750 1800 1850 1900 1950 2000

Tem

pera

ture

(o C

)

[B] year

Central England Temperature (CET)rescaled TSI reconstruction - Hoyt and Schatten (1700-1980) + ACRIM (1980-2012)

Figure 22 [A] Total solar irradiance (TSI) reconstruction by Hoyt and Schatten (1993) (red) rescaled on the updated ACRIM3 record (Willsonand Mordvinov 2003) (since 1981) (blue) vs the updated Lean model (Wang et al 2012 Kopp and Lean 2011) (green) [B] Comparisonbetween the Central England Temperature (CET) record (black) Parker et al (1992) and the TSI model by Hoyt and Schatten merged withthe ACRIM TSI record since 1981 Good correlation is observed at least since 1772

galactic cosmic ray (GCR) flux and other solar indexes alsosuggest that solar activity was higher in 1996 than in 2008(Lockwood 2012 Schrijver et al 2011 Shapiro et al 2011Vieira et al 2011) However the updated Leanrsquos TSI proxymodel (Kopp and Lean 2011) fails to reproduce this patternby predicting a 1996 TSI minimum (13607370 Wm2) lowerthan the 2008 TSI minimum (13608217 Wm2)(httplaspcoloradoedudatasorcetsi_dataTSI_TIM_Reconstructiontxt)

Recently Liu et al (2013) used the ECHO-G model andshowed that to reproduce the sim 07 oC global cooling ob-served from the Medieval Warm Period (MWP 900-1300) to

the Little Ice Age (LIA 1400-1800) according to recent pa-leoclimatic temperature reconstructions (eg Christiansenand Ljungqvist 2012 Ljungqvist 2010 Mann et al 2008Moberg et al 2005) a TSI model with a secular variabilitysim 35 times larger than that shown by Leanrsquos TSI modelwould be required

Thus there is a realistic possibility that for their climaticsimulations the current GCMs are not using sufficient solar-climate physical mechanisms and by adopting Leanrsquos TSImodel are not even using a sufficiently accurate solar radia-tive forcing record In the next section an alternative solarmodel based on astronomical harmonic constituents will be

26

used This model is constructed adopting a very differentmethodology than those used to construct the above TSIproxy models A strength of the proposed harmonic solarmodel is that it has been shown to hindcast quite well ma-jor solar and climate patterns during the Holocene (Scafetta2012c)

The author notes that Benestad and Schmidt (2009)using theoretical results derived from the GISS GCM sim-ulations criticized some of Scafettarsquos preliminary studies(Scafetta and West 2005 2006) that demonstrated a sig-nificant solar contribution (up to 40-70) to the 1850-2000warming they claimed that the sun contributed about 7of the 20th century warming However GISS models do notreproduce the observed oscillations at multiple time scales(Scafetta 2010 2012b) and cannot be used to validate orcontradict studies based on data analysis Scafetta (2009a)confirmed his previous results with hindcast based mod-els Moreover Benestad and Schmidt (2009)rsquos work alsocontains flawed models in particular with regard to use oflinear regression algorithms and the wavelet decompositionalgorithm (Scafetta 2009b 2013b) Linear regression algo-rithms are inefficient when the constructors are collinearand during the 20th century the solar forcing is collinearwith the anthropogenic forcing both trend upward Us-ing linear regression algorithms in non-collinear situationsScafetta (2013b) showed (1) GISS ModelE significantly un-derestimate the solar signature by a factor from 3 to 8 and(2) modern paleoclimatic temperature reconstructions implythat the sun contributed significantly to the 20th centurywarming Moreover Benestad and Schmidt (2009) used theperiodic padding in the wavelet algorithm which is highlyinappropriate for decomposing trending sequences insteadof the reflection one which minimizes Gibbs boundary ar-tifacts Figures 7 and 8 in Benestad and Schmidt (2009)demonstrate the mathematical error the increased solar ac-tivity from the solar minimum in 1995 to the solar maximumin 2002 is claimed to have induced a significant cooling inthe climate system which would imply a nonphysical neg-ative climate sensitivity to radiative forcing from 1995 to2002 This is just a boundary artifact due to Benestad andSchmidt (2009)rsquos erroneous implementation of the waveletalgorithm see Scafetta (2013b) for details

In conclusion the GCM implemented analytical approachcannot take into account unknown physical mechanisms anduncertain forcings On the contrary empirical modelingmay reconstruct geometrical dynamical patterns such ascycles independently of their microscopic physical cause Itis important not to draw a logically flawed conclusion that astrong climatic response to solarastronomical inputs doesnot exist simply because current GCMs are not able to re-produce it (Lockwood 2012) Because of the existence ofnumerous physical uncertainties it may be useful to investi-gate the possibility of an empirical methodology alternativeto the analytical GCM one

6 The astronomically-based empirical harmonicmodel

In the following subsections I summarize a number ofpieces of empirical evidence suggesting a significant climatesensitivity to astronomicalsolar forcings A semi-empiricalharmonic constituent climate model is proposed It is madeof specific astronomical oscillations that can be used to sim-ulate natural climatic variability The proposed model out-performs all CMIP5 GCMs

61 Millennial solar cycle paleoclimatic temperature recon-structions and their interpretation

Understanding the natural variability of the climate ofthe past is necessary to properly interpret the climate changesoccurred since 1850 If pre-industrial climate changes weresimilar to those observed since the industrialization periodnatural variability might have been the major determinantof the present climatic changes On the contrary if theclimatic changes that occurred since 1850 were anomalousrelative to the preceding climate this would support an-thropogenic forcing as the major determinant of the 20thcentury global warming

From 1998 to 2004 some preliminary studies claimed thatthe preindustrial GST since Medieval times varied very lit-tle by about 02 oC while GST anomalously increased since1900 (Mann et al 1999 Mann and Jones 2003) the shapeof these proxy temperature reconstructions resembled thatof an hockey stick with a MWP as warm as the 1900-1920period A number of climate model studies concluded thatthe solar radiative forcing plus volcanic and anthropogenicforcings were sufficient to explain those paleoclimatic GSTrecords for the last millennium This type of analysis led tothe conclusion that the warming observed since 1900 couldbe due only to anthropogenic forcing (Crowley 2000 Shin-dell et al 2003 Hegerl et al 2006 Fyfe et al 2013)

Crowley (2000) explicitly stated ldquoThe very good agree-ment between models and data in the preanthropogenic inter-val also enhances confidence in the overall ability of climatemodels to simulate temperature variability on the largest scalesrdquowhich suggests that in 2000 some climate scientists thoughtthat the available climate models supporting the anthro-pogenic global warming theory for the 20th century werealready sufficiently accurate (that is the science was consid-ered sufficiently settled) because of their ability to hindcastthe hockey stick GST proxy reconstructions This interpre-tation was strongly advocated and promoted by the IPCCin 2001 and 2007 and greatly contributed to support theanthropogenic global warming theory and the GCMs thatpredicted it

However since 2005 a number of studies have demon-strated a larger global pre-industrial temperature variabil-ity For example it was found a cooling of about 04-10oC from the MWP to the LIA and a MWP as warm asthe 1950-2000 period (Moberg et al 2005 Mann et al2008 Loehle and Mc Culloch 2008 Kobashi et al 2010Ljungqvist 2010 McShane and Wyner 2011 Christiansenand Ljungqvist 2012) The new emerging millennial GSTpattern stresses the existence of a large millennial climatic

27

-06

-04

-02

0

02

04

06

08

1

12

14

16

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Tem

pera

ture

Ano

m (

K)

[A] year

LIA

MWP

Loehle and Mc Culloch (2008)

Mann et al (1999)

Original Crowleyrsquos model (2000)

Ljungqvist (2010)

-10

-05

0

05

-05

0

05

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Tem

pera

ture

Ano

m (

K)

[B] year

Moberg et al (2005) + instrumental data since 1850

Crowleyrsquos model rescaled on the data (blue)07volcano + 3Sun + 045(GHG+Aer) - 0175

original Crowleyrsquos model (red)Volcano + Sun + GHG + Aerosol

Figure 23 [A] Comparison between the original energy balance model prediction by Crowley (2000) versus the hockey stick temperature graphby Mann et al (1999) implying a MWP as warm as the 1900-1920 period and two non-hockey stick recent paleoclimate GST reconstructions(Loehle and Mc Culloch 2008 Ljungqvist 2010) showing a far larger preindustrial variability and a MWP as warm as the 1940-2000 period[B](Bottom) the volcano solar and GHG+Aerosol temperature signature components produced by Crowley (2000) model are scaled to fit(Moberg et al 2005) paleoclimate GST reconstruction corrected since 1850 by HadCRUT4 which also shows a MWP as warm as the 1940-1970 period See Scafetta (2013ab) for more details

oscillation A quasi millennial climatic oscillation is alsofound to correlate well with the millennial solar oscillationobserved throughout the Holocene (Bond et al 2001 Kerr2001 Ogurtsov et al 2002 Kirkby 2007 Steinhilber et al2012 Scafetta 2012c)

The climate models that predicted a very small natu-ral variability and that were used to fit the hockey sticktemperature records can not fit the recent proxy GST re-constructions casting doubts on their accuracy Still re-cent millennium simulation studies using modern solar mod-

28

els (that is Wang et al 2005) are able to predict onlyhockey-stick temperature graph showing an average cool-ing from the 900-1300 MWP to the 1300-1800 LIA up tosim03 oC and just half of the empirically measured 11-yearsolar signature on the climate (see Feulner and Rahmstorf(2010) and IPCC (2007) figure 614 httpwwwipccch

publications_and_dataar4wg1enfigure-6-14html)These results are unsatisfactory as also Liu et al (2013)noted by demonstrating the need of assuming a far strongersolar effect to properly interpret the modern paleoclimatictemperature reconstructions

For example Ljungqvist (2010) and Christiansen andLjungqvist (2012) estimations of the last 2000 years of extra-tropical Northern Hemisphere (30-90 oN) decadal mean tem-perature variations present two large millennial cycles TheseGST reconstructions claim that the Roman Maximum andthe MWP were as warm as todayrsquos temperatures Indeedthese reconstructions might be quite plausible because theyagree with inferences deduced from numerous historical doc-uments (Guidoboni et al 2011) For example the me-dieval Vikingsrsquo villages in Greenland clearly indicate a MWPwarmer than todayrsquos temperature at least in the North At-lantic (Esper et al 2012 Surge and Barret 2012) How-ever a medieval warm period does not appear to be limitedto the Northern Atlantic region Similar evidence exists alsofor China (Ge et al 2003) South America (Neukom et al2011) South Africa (Tyson et al 2000) the Indo-Pacificregion (Oppo et al 2009) and other locations (Soon andBaliunas 2003) Thus the MWP phenomenon was likelymore global than was believed in 2000

Figure 23 illustrates the paradigm-shift issue related tothe current understanding of the historical climate Figure23A depicts the original climate model by Crowley (2000)against the temperature reconstruction by Mann et al (1999)(note the good pre-1900 fit) and against two non hockey-sticktemperature reconstructions (Loehle and Mc Culloch 2008Ljungqvist 2010) (note the poor fit) Figure 23B depictsthe temperature model by Moberg et al (2005) (1000-1850)merged with the historical GST measurements since 1850against the original climate model by Crowley (2000) (notethe poor fit) and against an empirical model made by sim-ply rescaling via linear regression the same climatic (solarvolcano and GHG+Aerosol) components predicted by Crow-leyrsquos model in such a way as to best fit the depicted tem-perature record (note the recovered overall good fit) Themathematical formula used in the regression model is re-ported in the figure see Scafetta (2013ab) for an extendeddiscussion on this exercise

The rescaled climate model indicates that for reproduc-ing recent paleoclimate temperature reconstructions withtheir larger millennial GST cycle the solar impact on theclimate needs to be increased by at least a factor of three rel-ative to the Crowleyrsquos original estimate which was alreadytwice that predicted by the current CMIP3 GCM modelssee Scafetta (2013b) for additional details This also meansthat a significant fraction of the warming observed since1900 (up to around 50 using different solar models) canbe ascribed to the sun as was calculated in Scafetta andWest (2007) and Scafetta (2009a) using alternative meth-

ods The volcano effect needs to be reduced by 30 andthe anthropogenic forcing effect (GHG plus Aerosol forcing)needs to be reduced by about 50 The latter result wellagrees with the correction implemented in Scafetta (2012b)that used an alternative reasoning based on the existenceof a 60-year natural oscillation from 1970 to 2000 not mod-eled by the GCMs The above finding also quantitativelyconfirms Eichler et al (2009) and Zhou and Tung (2012)and contradicts the IPCC (2007) Benestad and Schmidt(2009) and Lean and Rind (2008) which claimed that 90or more of the 20th century warming had to be caused byanthropogenic activity

In conclusion around 2000 hockey-stick shaped GST graphsimplied a very small natural climatic variability (and a smallsolar effect) and a strong anthropogenic effect on climateThat evidence was consistent with the outputs of prelimi-nary energy balance models and is still consistent with thepredictions of the CMIP3 and CMIP5 GCMs Howeverrecent paleoclimatic GST graphs have demonstrated a farlarger preindustrial natural climate variability The new ev-idence shifts the scientific paradigm The climate should behighly sensitive to solarastronomical related forcings be-cause the novel GST reconstructions show a large millennialcycle that well correlates with solarastronomical records(Bond et al 2001 Kerr 2001 Kirkby 2007 Ogurtsov etal 2002 Steinhilber et al 2012) Consequently the cur-rent GCMs should overestimate the anthropogenic effect onclimate

As also commented in Scafetta (2013a) Crowley (2000)and others would have had a significantly lower confidencein the overall ability of climate models to simulate tempera-ture variability if in 2000 the current paleoclimatic tempera-ture reconstructions had been available The scientific com-munity would have more likely concluded that importantastronomically-related climate change mechanisms were stillunknown and needed to be investigated before they couldbe implemented to make reliable analytical GCMs

62 Construction of the astronomicalsolar harmonics

Scafetta (2010 2012ab) proposed that the quasi 60-yearGST oscillation observed during 1850-2012 which has anamplitude of about 03 oC (see also Figure 2A) could indi-cate that about 50 of the 05 oC warming observed from1970 to 2000 could have been due to this natural oscillationduring its warming phase Zhou and Tung (2012) reacheda similar result using the Atlantic Multidecadal Oscillationwhich also presents a clear quasi 60-year oscillation (egMorner 1989 1990 Manzi et al 2012) as a constituentregression model component to reconstruct the GST record

The existence of a large natural oscillation causing about50 of the 1970-2000 warming would mean that the net an-thropogenic effect on the climate has been overestimated bythe GCMs by at least the same percentage and needs tobe reduced on average by about a 05 factor as alterna-tively demonstrated above (Section 61) using an approachbased on recent paleoclimate temperature records Conse-quently also a significant fraction of the 1850-2013 warming(about 040-045 oC) could not be reconstructed by the sameGCMs Note that part of the residual warming could also be

29

-06

-04

-02

0

02

04

06

08

1

12

14

16

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Tem

pera

ture

Ano

m (

K)

[A] year

LIA

MWP

Loehle and Mc Culloch (2008)

Mann et al (1999)

Original Crowleyrsquos model (2000)

Ljungqvist (2010)

-10

-05

0

05

-05

0

05

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Tem

pera

ture

Ano

m (

K)

[B] year

Moberg et al (2005) + instrumental data since 1850

Crowleyrsquos model rescaled on the data (blue)07volcano + 3Sun + 045(GHG+Aer) - 0175

original Crowleyrsquos model (red)Volcano + Sun + GHG + Aerosol

Figure 23 [A] Comparison between the original energy balance model prediction by Crowley (2000) versus the hockey stick temperature graphby Mann et al (1999) implying a MWP as warm as the 1900-1920 period and two non-hockey stick recent paleoclimate GST reconstructions(Loehle and Mc Culloch 2008 Ljungqvist 2010) showing a far larger preindustrial variability and a MWP as warm as the 1940-2000 period[B](Bottom) the volcano solar and GHG+Aerosol temperature signature components produced by Crowley (2000) model are scaled to fit(Moberg et al 2005) paleoclimate GST reconstruction corrected since 1850 by HadCRUT4 which also shows a MWP as warm as the 1940-1970 period See Scafetta (2013ab) for more details

oscillation A quasi millennial climatic oscillation is alsofound to correlate well with the millennial solar oscillationobserved throughout the Holocene (Bond et al 2001 Kerr2001 Ogurtsov et al 2002 Kirkby 2007 Steinhilber et al2012 Scafetta 2012c)

The climate models that predicted a very small natu-ral variability and that were used to fit the hockey sticktemperature records can not fit the recent proxy GST re-constructions casting doubts on their accuracy Still re-cent millennium simulation studies using modern solar mod-

28

els (that is Wang et al 2005) are able to predict onlyhockey-stick temperature graph showing an average cool-ing from the 900-1300 MWP to the 1300-1800 LIA up tosim03 oC and just half of the empirically measured 11-yearsolar signature on the climate (see Feulner and Rahmstorf(2010) and IPCC (2007) figure 614 httpwwwipccch

publications_and_dataar4wg1enfigure-6-14html)These results are unsatisfactory as also Liu et al (2013)noted by demonstrating the need of assuming a far strongersolar effect to properly interpret the modern paleoclimatictemperature reconstructions

For example Ljungqvist (2010) and Christiansen andLjungqvist (2012) estimations of the last 2000 years of extra-tropical Northern Hemisphere (30-90 oN) decadal mean tem-perature variations present two large millennial cycles TheseGST reconstructions claim that the Roman Maximum andthe MWP were as warm as todayrsquos temperatures Indeedthese reconstructions might be quite plausible because theyagree with inferences deduced from numerous historical doc-uments (Guidoboni et al 2011) For example the me-dieval Vikingsrsquo villages in Greenland clearly indicate a MWPwarmer than todayrsquos temperature at least in the North At-lantic (Esper et al 2012 Surge and Barret 2012) How-ever a medieval warm period does not appear to be limitedto the Northern Atlantic region Similar evidence exists alsofor China (Ge et al 2003) South America (Neukom et al2011) South Africa (Tyson et al 2000) the Indo-Pacificregion (Oppo et al 2009) and other locations (Soon andBaliunas 2003) Thus the MWP phenomenon was likelymore global than was believed in 2000

Figure 23 illustrates the paradigm-shift issue related tothe current understanding of the historical climate Figure23A depicts the original climate model by Crowley (2000)against the temperature reconstruction by Mann et al (1999)(note the good pre-1900 fit) and against two non hockey-sticktemperature reconstructions (Loehle and Mc Culloch 2008Ljungqvist 2010) (note the poor fit) Figure 23B depictsthe temperature model by Moberg et al (2005) (1000-1850)merged with the historical GST measurements since 1850against the original climate model by Crowley (2000) (notethe poor fit) and against an empirical model made by sim-ply rescaling via linear regression the same climatic (solarvolcano and GHG+Aerosol) components predicted by Crow-leyrsquos model in such a way as to best fit the depicted tem-perature record (note the recovered overall good fit) Themathematical formula used in the regression model is re-ported in the figure see Scafetta (2013ab) for an extendeddiscussion on this exercise

The rescaled climate model indicates that for reproduc-ing recent paleoclimate temperature reconstructions withtheir larger millennial GST cycle the solar impact on theclimate needs to be increased by at least a factor of three rel-ative to the Crowleyrsquos original estimate which was alreadytwice that predicted by the current CMIP3 GCM modelssee Scafetta (2013b) for additional details This also meansthat a significant fraction of the warming observed since1900 (up to around 50 using different solar models) canbe ascribed to the sun as was calculated in Scafetta andWest (2007) and Scafetta (2009a) using alternative meth-

ods The volcano effect needs to be reduced by 30 andthe anthropogenic forcing effect (GHG plus Aerosol forcing)needs to be reduced by about 50 The latter result wellagrees with the correction implemented in Scafetta (2012b)that used an alternative reasoning based on the existenceof a 60-year natural oscillation from 1970 to 2000 not mod-eled by the GCMs The above finding also quantitativelyconfirms Eichler et al (2009) and Zhou and Tung (2012)and contradicts the IPCC (2007) Benestad and Schmidt(2009) and Lean and Rind (2008) which claimed that 90or more of the 20th century warming had to be caused byanthropogenic activity

In conclusion around 2000 hockey-stick shaped GST graphsimplied a very small natural climatic variability (and a smallsolar effect) and a strong anthropogenic effect on climateThat evidence was consistent with the outputs of prelimi-nary energy balance models and is still consistent with thepredictions of the CMIP3 and CMIP5 GCMs Howeverrecent paleoclimatic GST graphs have demonstrated a farlarger preindustrial natural climate variability The new ev-idence shifts the scientific paradigm The climate should behighly sensitive to solarastronomical related forcings be-cause the novel GST reconstructions show a large millennialcycle that well correlates with solarastronomical records(Bond et al 2001 Kerr 2001 Kirkby 2007 Ogurtsov etal 2002 Steinhilber et al 2012) Consequently the cur-rent GCMs should overestimate the anthropogenic effect onclimate

As also commented in Scafetta (2013a) Crowley (2000)and others would have had a significantly lower confidencein the overall ability of climate models to simulate tempera-ture variability if in 2000 the current paleoclimatic tempera-ture reconstructions had been available The scientific com-munity would have more likely concluded that importantastronomically-related climate change mechanisms were stillunknown and needed to be investigated before they couldbe implemented to make reliable analytical GCMs

62 Construction of the astronomicalsolar harmonics

Scafetta (2010 2012ab) proposed that the quasi 60-yearGST oscillation observed during 1850-2012 which has anamplitude of about 03 oC (see also Figure 2A) could indi-cate that about 50 of the 05 oC warming observed from1970 to 2000 could have been due to this natural oscillationduring its warming phase Zhou and Tung (2012) reacheda similar result using the Atlantic Multidecadal Oscillationwhich also presents a clear quasi 60-year oscillation (egMorner 1989 1990 Manzi et al 2012) as a constituentregression model component to reconstruct the GST record

The existence of a large natural oscillation causing about50 of the 1970-2000 warming would mean that the net an-thropogenic effect on the climate has been overestimated bythe GCMs by at least the same percentage and needs tobe reduced on average by about a 05 factor as alterna-tively demonstrated above (Section 61) using an approachbased on recent paleoclimate temperature records Conse-quently also a significant fraction of the 1850-2013 warming(about 040-045 oC) could not be reconstructed by the sameGCMs Note that part of the residual warming could also be

29

els (that is Wang et al 2005) are able to predict onlyhockey-stick temperature graph showing an average cool-ing from the 900-1300 MWP to the 1300-1800 LIA up tosim03 oC and just half of the empirically measured 11-yearsolar signature on the climate (see Feulner and Rahmstorf(2010) and IPCC (2007) figure 614 httpwwwipccch

publications_and_dataar4wg1enfigure-6-14html)These results are unsatisfactory as also Liu et al (2013)noted by demonstrating the need of assuming a far strongersolar effect to properly interpret the modern paleoclimatictemperature reconstructions

For example Ljungqvist (2010) and Christiansen andLjungqvist (2012) estimations of the last 2000 years of extra-tropical Northern Hemisphere (30-90 oN) decadal mean tem-perature variations present two large millennial cycles TheseGST reconstructions claim that the Roman Maximum andthe MWP were as warm as todayrsquos temperatures Indeedthese reconstructions might be quite plausible because theyagree with inferences deduced from numerous historical doc-uments (Guidoboni et al 2011) For example the me-dieval Vikingsrsquo villages in Greenland clearly indicate a MWPwarmer than todayrsquos temperature at least in the North At-lantic (Esper et al 2012 Surge and Barret 2012) How-ever a medieval warm period does not appear to be limitedto the Northern Atlantic region Similar evidence exists alsofor China (Ge et al 2003) South America (Neukom et al2011) South Africa (Tyson et al 2000) the Indo-Pacificregion (Oppo et al 2009) and other locations (Soon andBaliunas 2003) Thus the MWP phenomenon was likelymore global than was believed in 2000

Figure 23 illustrates the paradigm-shift issue related tothe current understanding of the historical climate Figure23A depicts the original climate model by Crowley (2000)against the temperature reconstruction by Mann et al (1999)(note the good pre-1900 fit) and against two non hockey-sticktemperature reconstructions (Loehle and Mc Culloch 2008Ljungqvist 2010) (note the poor fit) Figure 23B depictsthe temperature model by Moberg et al (2005) (1000-1850)merged with the historical GST measurements since 1850against the original climate model by Crowley (2000) (notethe poor fit) and against an empirical model made by sim-ply rescaling via linear regression the same climatic (solarvolcano and GHG+Aerosol) components predicted by Crow-leyrsquos model in such a way as to best fit the depicted tem-perature record (note the recovered overall good fit) Themathematical formula used in the regression model is re-ported in the figure see Scafetta (2013ab) for an extendeddiscussion on this exercise

The rescaled climate model indicates that for reproduc-ing recent paleoclimate temperature reconstructions withtheir larger millennial GST cycle the solar impact on theclimate needs to be increased by at least a factor of three rel-ative to the Crowleyrsquos original estimate which was alreadytwice that predicted by the current CMIP3 GCM modelssee Scafetta (2013b) for additional details This also meansthat a significant fraction of the warming observed since1900 (up to around 50 using different solar models) canbe ascribed to the sun as was calculated in Scafetta andWest (2007) and Scafetta (2009a) using alternative meth-

ods The volcano effect needs to be reduced by 30 andthe anthropogenic forcing effect (GHG plus Aerosol forcing)needs to be reduced by about 50 The latter result wellagrees with the correction implemented in Scafetta (2012b)that used an alternative reasoning based on the existenceof a 60-year natural oscillation from 1970 to 2000 not mod-eled by the GCMs The above finding also quantitativelyconfirms Eichler et al (2009) and Zhou and Tung (2012)and contradicts the IPCC (2007) Benestad and Schmidt(2009) and Lean and Rind (2008) which claimed that 90or more of the 20th century warming had to be caused byanthropogenic activity

In conclusion around 2000 hockey-stick shaped GST graphsimplied a very small natural climatic variability (and a smallsolar effect) and a strong anthropogenic effect on climateThat evidence was consistent with the outputs of prelimi-nary energy balance models and is still consistent with thepredictions of the CMIP3 and CMIP5 GCMs Howeverrecent paleoclimatic GST graphs have demonstrated a farlarger preindustrial natural climate variability The new ev-idence shifts the scientific paradigm The climate should behighly sensitive to solarastronomical related forcings be-cause the novel GST reconstructions show a large millennialcycle that well correlates with solarastronomical records(Bond et al 2001 Kerr 2001 Kirkby 2007 Ogurtsov etal 2002 Steinhilber et al 2012) Consequently the cur-rent GCMs should overestimate the anthropogenic effect onclimate

As also commented in Scafetta (2013a) Crowley (2000)and others would have had a significantly lower confidencein the overall ability of climate models to simulate tempera-ture variability if in 2000 the current paleoclimatic tempera-ture reconstructions had been available The scientific com-munity would have more likely concluded that importantastronomically-related climate change mechanisms were stillunknown and needed to be investigated before they couldbe implemented to make reliable analytical GCMs

62 Construction of the astronomicalsolar harmonics

Scafetta (2010 2012ab) proposed that the quasi 60-yearGST oscillation observed during 1850-2012 which has anamplitude of about 03 oC (see also Figure 2A) could indi-cate that about 50 of the 05 oC warming observed from1970 to 2000 could have been due to this natural oscillationduring its warming phase Zhou and Tung (2012) reacheda similar result using the Atlantic Multidecadal Oscillationwhich also presents a clear quasi 60-year oscillation (egMorner 1989 1990 Manzi et al 2012) as a constituentregression model component to reconstruct the GST record

The existence of a large natural oscillation causing about50 of the 1970-2000 warming would mean that the net an-thropogenic effect on the climate has been overestimated bythe GCMs by at least the same percentage and needs tobe reduced on average by about a 05 factor as alterna-tively demonstrated above (Section 61) using an approachbased on recent paleoclimate temperature records Conse-quently also a significant fraction of the 1850-2013 warming(about 040-045 oC) could not be reconstructed by the sameGCMs Note that part of the residual warming could also be

29

0

05

1

15

2

0 500

RWP

DACP

MWP

LIA

CWP

1000 1500 2000

Gen

eric

Uni

ts

[A] year

Modulated Three Frequency Harmonic ModelNH Surface Temperature (Ljungqvist 2010)

Harmonic h115(t) P=115 yr and T=1980

0

05

1

15

2

1600 1700 1800 1900 2000 2100

Gen

eric

Uni

ts

[B] year

Modulated Three Frequency Harmonic Model

Harmonic P=983 yr and T=2060 59-63 year cycle maxima

Maunder

Dalton

Moberg et al (2005)HadCRUT4 GST

Figure 24 Scafetta (2012c) three-frequency solar model (red) [A] Against the Norther Hemisphere temperature reconstruction by Ljungqvist(2010) (black) The bottom depicts a filtering of the temperature reconstruction (black) that highlights the 115-year oscillation h115(t) (blue)[B] The same solar model (red) is plotted against the HadCRUT4 GST (black) merged in 1850-1900 with the proxy temperature model byMoberg et al (2005) (blue) The green curves highlight the quasi millennial oscillation h983(t) with its skewness that approximately reproducesthe millennial temperature oscillation Note the hindcast of the Maunder and Dalton solar mimima and relative cool periods and the projectedquasi 61-year oscillation from 1850 to 2150 Adapted from Scafetta (2013a)

due to poorly corrected urban heat island (UHI) and landuse change (LUC) effects (McKitrick and Michaels 2007McKitrick and Nierenberg 2010 Loehle and Scafetta 2011)Thus a reduction to a 05 factor of the output of the GCMsmay be considered an upper limit However herein such

a hypothesis is not taken into consideration and the GSTrecords are assumed to show true climatic changes

Figures 1 and 2 and Eq 1-4 proposed a possible astro-nomical origin of the decadal and multidecadal GST oscil-lations Interestingly natural climatic oscillations linked to

30

astronomical cycles with multidecadal periods of about 20and 60 years and longer secular and quasi-millennial cyclesappear to have been well-known in ancient times and in theMiddle Ages through the Renascence These astronomicaloscillations could be easily deduced from the conjunctionperiods of Jupiter and Saturn and from their dynamical ro-tation along the Zodiac These oscillations were includedfor example in Chinese and Indian calendars and consti-tuted the basis for a kind of astrological climatology In-deed these oscillations could be observed in climate recordseg in the monsoon oscillations and inferred from histori-cal chronologies describing the fall and rise of human civi-lizations (Ptolemy 2nd century Marsquosar 886 Kepler 1601Iyengar 2009) see more details about the ancient under-standing of climate changes in Scafetta (2013a)

A link between planetary oscillations and climatic cyclescould be indirect Planetary oscillations may modulate solarchanges that then induce climatic changes Indeed Scafetta(2012c) analyzed in details the sunspot number record andnoted that the 11-year Schwabe sunspot cycle is made ofat least three harmonics interfering together at about 993years 1087 years and 1186 years The harmonic at 993years corresponds to the JupiterSaturn spring tidal periodand the 1186 year corresponds to the Jupiter orbital pe-riod The central period at 1087 years could be generatedby the solar dynamo itself by means of a dynamical syn-chronization process with the other two cycles or by a com-bination of the recurrent tidal cycles produced by VenusEarth and Jupiter that present peaks at about 104 and111 years This finding suggests a planetary modulationof solar activity as first proposed by Wolf (1859) whosephysical mechanisms and additional empirical evidences areextensively discussed in a number of publications (Abreu etal 2012 Brown 1900 Fairbridge and Shirley 1987 Hung2007 Landscheidt 1999 Wolff and Patrone 2010 Scafetta2010 2012acd Scafetta and Willson 2013ab)

In particular Scafetta (2012d) argued that the Sun mightbe working as a huge amplifier of planetary gravitational os-cillations because the planetary tidal work released to thesun although quite small could nevertheless be greatly am-plified up to a 4 million factor by triggering a modulationof the core nuclear fusion rate Electromagnetic planet-suninteractions can also be hypothesized (Scafetta and Willson2013ab) Preliminary calculations suggests that Scafettarsquosmodel could produce luminosity oscillations up to one orderof magnitude compatible with the observed TSI oscillationSuch signal could be sufficiently powerful to modulate thesolar dynamo mechanisms and produce a final TSI outputapproximately synchronized to planetary harmonics

The three harmonics at 993 years 1087 years and 1186years beat together forming a complex dynamics as shownin Figure 24 (red curve) Four major additional multi-decadal secular and millennial solarastronomical oscilla-tions emerge a quasi 61-year oscillation (maximum around2002) a 115-year oscillation (maximum around 1980) anda minor 130-year oscillation (maximum around 2035) anda large quasi 983-year oscillation (maximum around 2060)The beats of Scafetta (2012c) three-frequency model wellcorrelate with the observed major solar and climatic varia-

tions for millennia throughout the Holocene see also Figure24 and the extended discussion in Scafetta (2012c)

A 115-year oscillation can be observed in proxy temper-ature models going back for 2000 years (eg Ogurtsov etal 2002 Qian and Lu 2010) and can be correlated withgrand-solar minima such as the Maunder Dalton and thesolar minimum around 1910 and other grand solar minimaduring the last 1000 years The 115-year oscillation is pro-jected to reach a minimum in 2030-2040 Figure 24A sug-gests that this oscillations may be characterized by a tem-perature variation between 005 and 015 oC This cycle canbe approximated as

h115(t) = 005 cos(2π(tminus 1980)115) (11)

A great millennial oscillation is observed throughout theHolocene (Bond et al 2001 Kerr 2001 Ogurtsov et al2002 Kirkby 2007 Steinhilber et al 2012 Scafetta 2012c)and was responsible for the Roman Warm Period the DarkAge Cold Period the Medieval Warm Period the Little IceAge and the Current Warm Period and would peak around2060 see Figure 24A As evident from poleoclimatic temper-ature proxy models the millennial oscillation is skewed byother multisecular harmonics with a likely minimum around1680 during the Maunder Solar Minimum see also Humlumet al (2011) and Figures 23 and 24 Assuming that the mil-lennial temperature oscillation presents a variation of about07 plusmn 03 oC as approximately shown in Ljungqvist (2010)and in Moberg et al (2005) (see Figures 23 and 24) it maybe approximately modeled from 1680 to 2060 as

h983(t) = 035 cos(2π(tminus 2060)760) (12)

where the adoption of the shorter period of 760 years takesinto account the skewness of the millennial cycle with a min-imum in the middle of the Maunder solar minimum around1680 and a predicted maximum in 2060 Note that if thecloud system is modulated by these solarastronomical cy-cles the GST could be modulated by these oscillations rela-tively quickly with a time lags spanning from a few monthsto just a few years as the frequency decreases (Scafetta 20082009a)

Figure 24A shows the proposed solar model versus theextra-tropical Norther Hemisphere temperature reconstruc-tion by Ljungqvist (2010) (black) Note the two synchronousquasi millennial cycles and the common 115-year oscilla-tion modulation which is also highlighted at the bottomof the figure with an appropriate filtering of the tempera-ture record The blue curve at the bottom is the functionh115(t) The figure highlights also the Roman Warm period(RWP) Dark Ages Cold Period (DACP) Medieval WarmPeriod (MWP) Little Ice Age (LIA) and Current Warm Pe-riod (CWP) Figure 24B depicts the solar model (red) versusHadCRUT4 (annual smooth black) merged in 1850-1900with the proxy temperature model by Moberg et al (2005)(blue) Note the synchronous occurrence of both the colderperiods during the Maunder and Dalton modeled solar min-ima and the quasi 61-year modulation from 1850 to 2010The solar model predicts a sim61-year oscillation from 1850to 2150 whose maxima are highlighted by the black circles

31

Before 1850 the 61-oscillation weakens The Sun may be en-tering into a (minor) grand minimum centered in the 2030sIndeed sunspot cycles 19-23 (1955-2008) resemble sunspotcycles 1-4 (1755-1798) that preceded the Dalton solar min-imum (1790-1830) and sunspot cycle 24 (2008-2021) isapproximately replicating the low sunspot cycle 5 (Scafetta2012c Fig 10) The millennial modulation h983(t) is alsohighlighted in the figure (green)

63 The six-harmonic astronomicalsolar model for climatechange

With the above information a first approximation six-harmonic astronomicalsolar model for climate change canbe constructed which phenomenologically simulates the cor-responding natural oscillations that the GCMs are currentlynot able to reproduced The additional radiative forcingcomponent (eg GHG aerosol volcano effects) can to afirst approximation be simulated by using the CMIP5 meanprojections reduced by a given factor β Thus the semi-empirical model is given by the equation

H(t) = h983(t) + h115(t) + h60(t) + h20(t) + h104(t)

+h91(t) + β lowastm(t) + const(13)

where the function m(t) is a CMIP5 ensemble mean simu-lation depicted in Figure 2

Figure 25 shows that to reproduce accurately the Had-CRUT4 GST warming trend since 1850 it is necessary to useβ = 05plusmn01 This result is reasonably compatible with thatfound in Scafetta (2012b) where a value of β = 045 plusmn 005was chosen using the CMIP3 models and the HadCRUT3GST with a slight lower secular global warming than theHadCRUT4 GST record Scafetta (2012b) determined thecoefficient β only using an argument based on the GSTresidual from the harmonic model during the period 1970-2000 Indeed because from 1970 to 2000 the HadCRUT4GST warms a little bit more than the HadCRUT3 recordthe same argument used in Scafetta (2012b) but applied tothe HadCRUT4 record yields β asymp 05 The fact that withβ = 05 Eq 13 simultaneously reconstructs both the 1970-2000 calibrating period and the entire 1850-2013 period val-idates the model with a hindcast test

The result implies that the climate sensitivity to radia-tive forcing has been overestimated by the CMIP5 GCMsby about a factor of 2 Thus the climate sensitivity to CO2

doubling should be reduced from the IPCC (2007) claimed20-45 oC range to a 10-23 oC range with a likely medianof sim 15 oC instead of sim 30 oC

A reduction by about half of the climate sensitivity toradiative forcing is compatible with the results discussedin the subsection 61 and shown in Figure 23B concerningthe interpretation of modern paleoclimatic temperature re-constructions with a larger pre-industrial variability with aMWP as warm as the 1950-2000 period The result is alsoconsistent with those by Chylek and Lohmann (2008) whofound a climate sensitivity between 13 oC and 23 oC due todoubling of atmospheric concentration of CO2 by Ring etal (2012) who found a climate sensitivity in the range from

about 15 oC to 20 oC and by Lewis (2013) who founda climate sensitivity range from 12 oC to 22 oC (median16 oC) The result is also consistent with Zhou and Tung(2012) and Chylek et al (2013) who found that the anthro-pogenic warming has been overestimated by about a factorof 2

The quasi 60-year harmonic component of the modelmay be sufficiently valid for the period 1880-2150 becauseScafetta (2012c) three-frequency solar model predicts thatduring this period the major natural patterns in the solardynamics may be described by a quasi 60-year oscillationslightly modulated by the 115-year oscillation while the mil-lennial oscillation is at its maximum

The author notes that the CMIP5 models contain alsoa solar signature but it is very small because the CMIP5adopted TSI (Wang et al 2005) has a smaller secular trendthan the TSI records adopted for the CMIP3 GCMs in theIPCC (2007) Herein this correction is ignored becausewithin the 20 error associated to the β = 05 factor al-though the presence of a solar signature in m(t) may slightlyamplify the decadal cycle in H(t) Note that Eq 13 is notoptimized for periods before 1850 because no GST are avail-able before 1850 and the climate response to the deep grandsolar minima (Dalton Maunder etc) could necessitate ad-ditional frequencies such as a 80-90 year oscillation (Scafettaand Willson 2013a) and probably the inclusion of nonlineardynamical effect The 80-90 year cycle modulates the 60year cycle by producing a beat with a period of 210 yearsknown as the Suess (aka de Vries) solar cycle

Figure 26 compares the four CMIP5 ensemble averageprojections (panel A) and the solar-astronomical semi-empiricalmodel using β = 05 in Eq 13 (panel B) against the Had-CRUT4 GST record a common 1900-2000 baseline is usedThe figure highlights the superior performance of the solar-astronomical semi-empirical model versus the CMIP5 en-semble mean models Eq 13 reconstructs all major decadaland multidecadal temperature patterns observed since 1860The temperature plateau observed since 2000 is better re-constructed by the semi-empirical model than by the GCMmean projections Thus the 2000-2013 GST plateau ap-pears to be due to the cooling phase of a natural quasi60-year oscillation that has balanced a strongly reduced pro-jected anthropogenic warming trend The four adopted CMIP5GCM mean projections display a 2000-2100 warming be-tween a minimum of about 1 oC to a maximum of about 4 oC(see figure 26A) However as Figure 26B shows the four cor-rected projections predict a 2000-2100 warming between aminimum of about 03 oC to a maximum of about 18 oC us-ing the same anthropogenic scenarios The inserts magnifythe period 1990-2030 to highlight the strong mismatch be-tween the GST and the GCM simulations since 2000 that isresolved with the solar-astronomical semi-empirical model

Figure 27 is similar to Figure 26 but with all CMIP5model individual simulations used in Eq 13 with β = 05Again the figure highlights the superior performance of thesolar-astronomical semi-empirical model versus the CMIP5model simulations The solar-astronomical semi-empiricalmodel also causes a reduction of the range among the sim-ulation by a factor of two The root-mean-square deviation

32

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-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000 2020

Tem

pera

ture

Ano

mal

y (o C

)

year

HadCRUT42 GSTEq 13 with β=06Eq 13 with β=04

corrected GCM component by β=056-frequency harmonic component alone

Figure 25 The semi-empirical model Eq 13 using β = 04 (blue) and β = 06 (red) attenuation of the CMIP5 ensemble mean simulationvs HadCRUT4 GST record since 1860 The upward warming trending and all decadal and multidecadal patterns are well reconstructed Thebottom depicts the 6-frequency harmonic component that models the harmonic natural variability (green) and the GCM radiative componentcorrected by β = 05 (grey) respectively

(RMSD) value between the 49-month average smooth GSTand the full empirical model is about 004 oC while for theRMSD for the GCM model mean is twice 009 oC and forthe single GCM runs is normally larger (see Table 2)

Figure 28 magnifies the period 1980-2020 and uses sixglobal temperature estimates (HadCRUT3 HadCRUT4 UAHMSU RSS MSU GISS and NCDC) that appear to agreesufficiently well with each other and all of them disagreewith the CMIP5 simulations after 2000 The temperaturemay slightly increase from 2013 to 2016 and decrease from2016 to 2020 because of the two decadal cycles Howeverfast ENSO temperature fluctuations at scales shorter than7 years may mask the result

In conclusion because the temperature patterns appearswell correlated with solarastronomical oscillations at mul-tiple scales and that semi-empirical models based on theseoscillations reconstruct and hindcast GST variations signif-icantly better than the current GCMs it is very likely thatthe observed GST oscillations have an astronomical originwhose mechanisms are not implemented in the GCMs yetTo better appreciate the finding it is important to stressthat the harmonic constituents of the proposed model suchas the frequencies and the phases are coherent with majorastronomical oscillations Although in the future the em-

pirical model may be improved with a better understandingof these oscillations the proposed semi-empirical model al-ready appears to outperform all CMIP5 GCMs

7 Conclusion

As for the CMIP3 GCMs used by the IPCC 2007 (Scafetta2012b) the upgraded CMIP5 GCMs to be used in the IPCCFifth Assessment Report (AR5 2013) do not reproduce thedetectable decadal and multidecadal climate oscillations ob-served in the GST records since 1850 Multiple analysessuggest that these GCMs overestimate the anthropogenicwarming effect by about 50 This would also imply thatthe climate sensitivity to the radiative forcing should be sig-nificantly lowered by half It may be sim 15 oC (or less if partof the warming is spurious for example due to uncorrectedUHI effects) and it may possibly range between 1 oC and23 oC instead of the IPCC (2007) proposed range from 2oC to 45 oC Very important physical mechanisms neces-sary for reproducing multiple climatic oscillations which areresponsible for about half of the 1850-2010 warming appearto be still missing in the GCMs

The physical origin of the detected climatic oscillationsis currently uncertain but in this paper it has been ar-

33

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[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT42 GSTCMIP5 rcp26CMIP5 rcp45CMIP5 rcp60CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT42 GSTwith CMIP5 rcp26with CMIP5 rcp45with CMIP5 rcp60with CMIP5 rcp85

Harmonic natural vaiability

Figure 26 [A] The four CMIP5 ensemble average projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empiricalmodel Eq 13 with β = 05 against the HadCRUT4 GST record a common 1900-2000 baseline is used The figure highlights the betterperformance of the solar-astronomical semi-empirical model versus the CMIP5 models which is particularly evident since 2000 as shown in theinserts

gued that they may be astronomically induced This conclu-sion derives from the coherence found among astronomicaland climate oscillations from the decadal to the millennialtime scales This harmonic component cannot be ignoredin properly interpreting and forecasting climate change Ihave shown that an empirical model based on specific ma-jor astronomical harmonics plus a correction of the outputsof the current CMIP5 GCM simulations simultaneously re-constructs the decadal multidecadal and secular patternsobserved in the GST records since 1850

The most reasonable conclusion is that the climate sys-tem is synchronized to the natural oscillations found in thesolar system and that this harmonic dynamics constitutes animportant component of the Earthrsquos climate The proposedsemi-empirical model may produce more reliable projectionsfor the 21st century which are far less alarmist than thecurrent CMIP5 projections Under the same anthropogenicemission scenarios the model projects a possible 2000-2100warming ranging from 03 oC to 18 oC This range is sig-nificantly below the original CMIP5 GCM ensemble mean

projections spanning from about 1 oC to 4 oCIn conclusion multiple statistical tests suggest that the

proposed semi-empirical GST model based on astronomi-cally induced harmonics plus an anthropogenic plus volcanocontribution reduced by about 50 from the CMIP5 GCMprediction outperforms all CMIP5 GCMs in reconstructingand interpreting the GST patterns observed since 1850 Themodel would be compatible also with modern paleoclimaticreconstructions showing a larger pre-industrial variabilitywith a medieval period as warm as the 1950-2000 globalsurface temperatures

Future research should investigate space-climate couplingmechanisms in order to develop more advanced analyticaland semi-empirical climate models Figure 29 schematicallyrepresents a possible network of physical interactions caus-ing climatic changes

Appendix

The proposed harmonic model Eq 13 uses a specific setof harmonics first determined in Scafetta (2010) Scafetta

34

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[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

astronomical cycles with multidecadal periods of about 20and 60 years and longer secular and quasi-millennial cyclesappear to have been well-known in ancient times and in theMiddle Ages through the Renascence These astronomicaloscillations could be easily deduced from the conjunctionperiods of Jupiter and Saturn and from their dynamical ro-tation along the Zodiac These oscillations were includedfor example in Chinese and Indian calendars and consti-tuted the basis for a kind of astrological climatology In-deed these oscillations could be observed in climate recordseg in the monsoon oscillations and inferred from histori-cal chronologies describing the fall and rise of human civi-lizations (Ptolemy 2nd century Marsquosar 886 Kepler 1601Iyengar 2009) see more details about the ancient under-standing of climate changes in Scafetta (2013a)

A link between planetary oscillations and climatic cyclescould be indirect Planetary oscillations may modulate solarchanges that then induce climatic changes Indeed Scafetta(2012c) analyzed in details the sunspot number record andnoted that the 11-year Schwabe sunspot cycle is made ofat least three harmonics interfering together at about 993years 1087 years and 1186 years The harmonic at 993years corresponds to the JupiterSaturn spring tidal periodand the 1186 year corresponds to the Jupiter orbital pe-riod The central period at 1087 years could be generatedby the solar dynamo itself by means of a dynamical syn-chronization process with the other two cycles or by a com-bination of the recurrent tidal cycles produced by VenusEarth and Jupiter that present peaks at about 104 and111 years This finding suggests a planetary modulationof solar activity as first proposed by Wolf (1859) whosephysical mechanisms and additional empirical evidences areextensively discussed in a number of publications (Abreu etal 2012 Brown 1900 Fairbridge and Shirley 1987 Hung2007 Landscheidt 1999 Wolff and Patrone 2010 Scafetta2010 2012acd Scafetta and Willson 2013ab)

In particular Scafetta (2012d) argued that the Sun mightbe working as a huge amplifier of planetary gravitational os-cillations because the planetary tidal work released to thesun although quite small could nevertheless be greatly am-plified up to a 4 million factor by triggering a modulationof the core nuclear fusion rate Electromagnetic planet-suninteractions can also be hypothesized (Scafetta and Willson2013ab) Preliminary calculations suggests that Scafettarsquosmodel could produce luminosity oscillations up to one orderof magnitude compatible with the observed TSI oscillationSuch signal could be sufficiently powerful to modulate thesolar dynamo mechanisms and produce a final TSI outputapproximately synchronized to planetary harmonics

The three harmonics at 993 years 1087 years and 1186years beat together forming a complex dynamics as shownin Figure 24 (red curve) Four major additional multi-decadal secular and millennial solarastronomical oscilla-tions emerge a quasi 61-year oscillation (maximum around2002) a 115-year oscillation (maximum around 1980) anda minor 130-year oscillation (maximum around 2035) anda large quasi 983-year oscillation (maximum around 2060)The beats of Scafetta (2012c) three-frequency model wellcorrelate with the observed major solar and climatic varia-

tions for millennia throughout the Holocene see also Figure24 and the extended discussion in Scafetta (2012c)

A 115-year oscillation can be observed in proxy temper-ature models going back for 2000 years (eg Ogurtsov etal 2002 Qian and Lu 2010) and can be correlated withgrand-solar minima such as the Maunder Dalton and thesolar minimum around 1910 and other grand solar minimaduring the last 1000 years The 115-year oscillation is pro-jected to reach a minimum in 2030-2040 Figure 24A sug-gests that this oscillations may be characterized by a tem-perature variation between 005 and 015 oC This cycle canbe approximated as

h115(t) = 005 cos(2π(tminus 1980)115) (11)

A great millennial oscillation is observed throughout theHolocene (Bond et al 2001 Kerr 2001 Ogurtsov et al2002 Kirkby 2007 Steinhilber et al 2012 Scafetta 2012c)and was responsible for the Roman Warm Period the DarkAge Cold Period the Medieval Warm Period the Little IceAge and the Current Warm Period and would peak around2060 see Figure 24A As evident from poleoclimatic temper-ature proxy models the millennial oscillation is skewed byother multisecular harmonics with a likely minimum around1680 during the Maunder Solar Minimum see also Humlumet al (2011) and Figures 23 and 24 Assuming that the mil-lennial temperature oscillation presents a variation of about07 plusmn 03 oC as approximately shown in Ljungqvist (2010)and in Moberg et al (2005) (see Figures 23 and 24) it maybe approximately modeled from 1680 to 2060 as

h983(t) = 035 cos(2π(tminus 2060)760) (12)

where the adoption of the shorter period of 760 years takesinto account the skewness of the millennial cycle with a min-imum in the middle of the Maunder solar minimum around1680 and a predicted maximum in 2060 Note that if thecloud system is modulated by these solarastronomical cy-cles the GST could be modulated by these oscillations rela-tively quickly with a time lags spanning from a few monthsto just a few years as the frequency decreases (Scafetta 20082009a)

Figure 24A shows the proposed solar model versus theextra-tropical Norther Hemisphere temperature reconstruc-tion by Ljungqvist (2010) (black) Note the two synchronousquasi millennial cycles and the common 115-year oscilla-tion modulation which is also highlighted at the bottomof the figure with an appropriate filtering of the tempera-ture record The blue curve at the bottom is the functionh115(t) The figure highlights also the Roman Warm period(RWP) Dark Ages Cold Period (DACP) Medieval WarmPeriod (MWP) Little Ice Age (LIA) and Current Warm Pe-riod (CWP) Figure 24B depicts the solar model (red) versusHadCRUT4 (annual smooth black) merged in 1850-1900with the proxy temperature model by Moberg et al (2005)(blue) Note the synchronous occurrence of both the colderperiods during the Maunder and Dalton modeled solar min-ima and the quasi 61-year modulation from 1850 to 2010The solar model predicts a sim61-year oscillation from 1850to 2150 whose maxima are highlighted by the black circles

31

Before 1850 the 61-oscillation weakens The Sun may be en-tering into a (minor) grand minimum centered in the 2030sIndeed sunspot cycles 19-23 (1955-2008) resemble sunspotcycles 1-4 (1755-1798) that preceded the Dalton solar min-imum (1790-1830) and sunspot cycle 24 (2008-2021) isapproximately replicating the low sunspot cycle 5 (Scafetta2012c Fig 10) The millennial modulation h983(t) is alsohighlighted in the figure (green)

63 The six-harmonic astronomicalsolar model for climatechange

With the above information a first approximation six-harmonic astronomicalsolar model for climate change canbe constructed which phenomenologically simulates the cor-responding natural oscillations that the GCMs are currentlynot able to reproduced The additional radiative forcingcomponent (eg GHG aerosol volcano effects) can to afirst approximation be simulated by using the CMIP5 meanprojections reduced by a given factor β Thus the semi-empirical model is given by the equation

H(t) = h983(t) + h115(t) + h60(t) + h20(t) + h104(t)

+h91(t) + β lowastm(t) + const(13)

where the function m(t) is a CMIP5 ensemble mean simu-lation depicted in Figure 2

Figure 25 shows that to reproduce accurately the Had-CRUT4 GST warming trend since 1850 it is necessary to useβ = 05plusmn01 This result is reasonably compatible with thatfound in Scafetta (2012b) where a value of β = 045 plusmn 005was chosen using the CMIP3 models and the HadCRUT3GST with a slight lower secular global warming than theHadCRUT4 GST record Scafetta (2012b) determined thecoefficient β only using an argument based on the GSTresidual from the harmonic model during the period 1970-2000 Indeed because from 1970 to 2000 the HadCRUT4GST warms a little bit more than the HadCRUT3 recordthe same argument used in Scafetta (2012b) but applied tothe HadCRUT4 record yields β asymp 05 The fact that withβ = 05 Eq 13 simultaneously reconstructs both the 1970-2000 calibrating period and the entire 1850-2013 period val-idates the model with a hindcast test

The result implies that the climate sensitivity to radia-tive forcing has been overestimated by the CMIP5 GCMsby about a factor of 2 Thus the climate sensitivity to CO2

doubling should be reduced from the IPCC (2007) claimed20-45 oC range to a 10-23 oC range with a likely medianof sim 15 oC instead of sim 30 oC

A reduction by about half of the climate sensitivity toradiative forcing is compatible with the results discussedin the subsection 61 and shown in Figure 23B concerningthe interpretation of modern paleoclimatic temperature re-constructions with a larger pre-industrial variability with aMWP as warm as the 1950-2000 period The result is alsoconsistent with those by Chylek and Lohmann (2008) whofound a climate sensitivity between 13 oC and 23 oC due todoubling of atmospheric concentration of CO2 by Ring etal (2012) who found a climate sensitivity in the range from

about 15 oC to 20 oC and by Lewis (2013) who founda climate sensitivity range from 12 oC to 22 oC (median16 oC) The result is also consistent with Zhou and Tung(2012) and Chylek et al (2013) who found that the anthro-pogenic warming has been overestimated by about a factorof 2

The quasi 60-year harmonic component of the modelmay be sufficiently valid for the period 1880-2150 becauseScafetta (2012c) three-frequency solar model predicts thatduring this period the major natural patterns in the solardynamics may be described by a quasi 60-year oscillationslightly modulated by the 115-year oscillation while the mil-lennial oscillation is at its maximum

The author notes that the CMIP5 models contain alsoa solar signature but it is very small because the CMIP5adopted TSI (Wang et al 2005) has a smaller secular trendthan the TSI records adopted for the CMIP3 GCMs in theIPCC (2007) Herein this correction is ignored becausewithin the 20 error associated to the β = 05 factor al-though the presence of a solar signature in m(t) may slightlyamplify the decadal cycle in H(t) Note that Eq 13 is notoptimized for periods before 1850 because no GST are avail-able before 1850 and the climate response to the deep grandsolar minima (Dalton Maunder etc) could necessitate ad-ditional frequencies such as a 80-90 year oscillation (Scafettaand Willson 2013a) and probably the inclusion of nonlineardynamical effect The 80-90 year cycle modulates the 60year cycle by producing a beat with a period of 210 yearsknown as the Suess (aka de Vries) solar cycle

Figure 26 compares the four CMIP5 ensemble averageprojections (panel A) and the solar-astronomical semi-empiricalmodel using β = 05 in Eq 13 (panel B) against the Had-CRUT4 GST record a common 1900-2000 baseline is usedThe figure highlights the superior performance of the solar-astronomical semi-empirical model versus the CMIP5 en-semble mean models Eq 13 reconstructs all major decadaland multidecadal temperature patterns observed since 1860The temperature plateau observed since 2000 is better re-constructed by the semi-empirical model than by the GCMmean projections Thus the 2000-2013 GST plateau ap-pears to be due to the cooling phase of a natural quasi60-year oscillation that has balanced a strongly reduced pro-jected anthropogenic warming trend The four adopted CMIP5GCM mean projections display a 2000-2100 warming be-tween a minimum of about 1 oC to a maximum of about 4 oC(see figure 26A) However as Figure 26B shows the four cor-rected projections predict a 2000-2100 warming between aminimum of about 03 oC to a maximum of about 18 oC us-ing the same anthropogenic scenarios The inserts magnifythe period 1990-2030 to highlight the strong mismatch be-tween the GST and the GCM simulations since 2000 that isresolved with the solar-astronomical semi-empirical model

Figure 27 is similar to Figure 26 but with all CMIP5model individual simulations used in Eq 13 with β = 05Again the figure highlights the superior performance of thesolar-astronomical semi-empirical model versus the CMIP5model simulations The solar-astronomical semi-empiricalmodel also causes a reduction of the range among the sim-ulation by a factor of two The root-mean-square deviation

32

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Tem

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ture

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)

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HadCRUT42 GSTEq 13 with β=06Eq 13 with β=04

corrected GCM component by β=056-frequency harmonic component alone

Figure 25 The semi-empirical model Eq 13 using β = 04 (blue) and β = 06 (red) attenuation of the CMIP5 ensemble mean simulationvs HadCRUT4 GST record since 1860 The upward warming trending and all decadal and multidecadal patterns are well reconstructed Thebottom depicts the 6-frequency harmonic component that models the harmonic natural variability (green) and the GCM radiative componentcorrected by β = 05 (grey) respectively

(RMSD) value between the 49-month average smooth GSTand the full empirical model is about 004 oC while for theRMSD for the GCM model mean is twice 009 oC and forthe single GCM runs is normally larger (see Table 2)

Figure 28 magnifies the period 1980-2020 and uses sixglobal temperature estimates (HadCRUT3 HadCRUT4 UAHMSU RSS MSU GISS and NCDC) that appear to agreesufficiently well with each other and all of them disagreewith the CMIP5 simulations after 2000 The temperaturemay slightly increase from 2013 to 2016 and decrease from2016 to 2020 because of the two decadal cycles Howeverfast ENSO temperature fluctuations at scales shorter than7 years may mask the result

In conclusion because the temperature patterns appearswell correlated with solarastronomical oscillations at mul-tiple scales and that semi-empirical models based on theseoscillations reconstruct and hindcast GST variations signif-icantly better than the current GCMs it is very likely thatthe observed GST oscillations have an astronomical originwhose mechanisms are not implemented in the GCMs yetTo better appreciate the finding it is important to stressthat the harmonic constituents of the proposed model suchas the frequencies and the phases are coherent with majorastronomical oscillations Although in the future the em-

pirical model may be improved with a better understandingof these oscillations the proposed semi-empirical model al-ready appears to outperform all CMIP5 GCMs

7 Conclusion

As for the CMIP3 GCMs used by the IPCC 2007 (Scafetta2012b) the upgraded CMIP5 GCMs to be used in the IPCCFifth Assessment Report (AR5 2013) do not reproduce thedetectable decadal and multidecadal climate oscillations ob-served in the GST records since 1850 Multiple analysessuggest that these GCMs overestimate the anthropogenicwarming effect by about 50 This would also imply thatthe climate sensitivity to the radiative forcing should be sig-nificantly lowered by half It may be sim 15 oC (or less if partof the warming is spurious for example due to uncorrectedUHI effects) and it may possibly range between 1 oC and23 oC instead of the IPCC (2007) proposed range from 2oC to 45 oC Very important physical mechanisms neces-sary for reproducing multiple climatic oscillations which areresponsible for about half of the 1850-2010 warming appearto be still missing in the GCMs

The physical origin of the detected climatic oscillationsis currently uncertain but in this paper it has been ar-

33

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT42 GSTCMIP5 rcp26CMIP5 rcp45CMIP5 rcp60CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT42 GSTwith CMIP5 rcp26with CMIP5 rcp45with CMIP5 rcp60with CMIP5 rcp85

Harmonic natural vaiability

Figure 26 [A] The four CMIP5 ensemble average projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empiricalmodel Eq 13 with β = 05 against the HadCRUT4 GST record a common 1900-2000 baseline is used The figure highlights the betterperformance of the solar-astronomical semi-empirical model versus the CMIP5 models which is particularly evident since 2000 as shown in theinserts

gued that they may be astronomically induced This conclu-sion derives from the coherence found among astronomicaland climate oscillations from the decadal to the millennialtime scales This harmonic component cannot be ignoredin properly interpreting and forecasting climate change Ihave shown that an empirical model based on specific ma-jor astronomical harmonics plus a correction of the outputsof the current CMIP5 GCM simulations simultaneously re-constructs the decadal multidecadal and secular patternsobserved in the GST records since 1850

The most reasonable conclusion is that the climate sys-tem is synchronized to the natural oscillations found in thesolar system and that this harmonic dynamics constitutes animportant component of the Earthrsquos climate The proposedsemi-empirical model may produce more reliable projectionsfor the 21st century which are far less alarmist than thecurrent CMIP5 projections Under the same anthropogenicemission scenarios the model projects a possible 2000-2100warming ranging from 03 oC to 18 oC This range is sig-nificantly below the original CMIP5 GCM ensemble mean

projections spanning from about 1 oC to 4 oCIn conclusion multiple statistical tests suggest that the

proposed semi-empirical GST model based on astronomi-cally induced harmonics plus an anthropogenic plus volcanocontribution reduced by about 50 from the CMIP5 GCMprediction outperforms all CMIP5 GCMs in reconstructingand interpreting the GST patterns observed since 1850 Themodel would be compatible also with modern paleoclimaticreconstructions showing a larger pre-industrial variabilitywith a medieval period as warm as the 1950-2000 globalsurface temperatures

Future research should investigate space-climate couplingmechanisms in order to develop more advanced analyticaland semi-empirical climate models Figure 29 schematicallyrepresents a possible network of physical interactions caus-ing climatic changes

Appendix

The proposed harmonic model Eq 13 uses a specific setof harmonics first determined in Scafetta (2010) Scafetta

34

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

5

6

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

Before 1850 the 61-oscillation weakens The Sun may be en-tering into a (minor) grand minimum centered in the 2030sIndeed sunspot cycles 19-23 (1955-2008) resemble sunspotcycles 1-4 (1755-1798) that preceded the Dalton solar min-imum (1790-1830) and sunspot cycle 24 (2008-2021) isapproximately replicating the low sunspot cycle 5 (Scafetta2012c Fig 10) The millennial modulation h983(t) is alsohighlighted in the figure (green)

63 The six-harmonic astronomicalsolar model for climatechange

With the above information a first approximation six-harmonic astronomicalsolar model for climate change canbe constructed which phenomenologically simulates the cor-responding natural oscillations that the GCMs are currentlynot able to reproduced The additional radiative forcingcomponent (eg GHG aerosol volcano effects) can to afirst approximation be simulated by using the CMIP5 meanprojections reduced by a given factor β Thus the semi-empirical model is given by the equation

H(t) = h983(t) + h115(t) + h60(t) + h20(t) + h104(t)

+h91(t) + β lowastm(t) + const(13)

where the function m(t) is a CMIP5 ensemble mean simu-lation depicted in Figure 2

Figure 25 shows that to reproduce accurately the Had-CRUT4 GST warming trend since 1850 it is necessary to useβ = 05plusmn01 This result is reasonably compatible with thatfound in Scafetta (2012b) where a value of β = 045 plusmn 005was chosen using the CMIP3 models and the HadCRUT3GST with a slight lower secular global warming than theHadCRUT4 GST record Scafetta (2012b) determined thecoefficient β only using an argument based on the GSTresidual from the harmonic model during the period 1970-2000 Indeed because from 1970 to 2000 the HadCRUT4GST warms a little bit more than the HadCRUT3 recordthe same argument used in Scafetta (2012b) but applied tothe HadCRUT4 record yields β asymp 05 The fact that withβ = 05 Eq 13 simultaneously reconstructs both the 1970-2000 calibrating period and the entire 1850-2013 period val-idates the model with a hindcast test

The result implies that the climate sensitivity to radia-tive forcing has been overestimated by the CMIP5 GCMsby about a factor of 2 Thus the climate sensitivity to CO2

doubling should be reduced from the IPCC (2007) claimed20-45 oC range to a 10-23 oC range with a likely medianof sim 15 oC instead of sim 30 oC

A reduction by about half of the climate sensitivity toradiative forcing is compatible with the results discussedin the subsection 61 and shown in Figure 23B concerningthe interpretation of modern paleoclimatic temperature re-constructions with a larger pre-industrial variability with aMWP as warm as the 1950-2000 period The result is alsoconsistent with those by Chylek and Lohmann (2008) whofound a climate sensitivity between 13 oC and 23 oC due todoubling of atmospheric concentration of CO2 by Ring etal (2012) who found a climate sensitivity in the range from

about 15 oC to 20 oC and by Lewis (2013) who founda climate sensitivity range from 12 oC to 22 oC (median16 oC) The result is also consistent with Zhou and Tung(2012) and Chylek et al (2013) who found that the anthro-pogenic warming has been overestimated by about a factorof 2

The quasi 60-year harmonic component of the modelmay be sufficiently valid for the period 1880-2150 becauseScafetta (2012c) three-frequency solar model predicts thatduring this period the major natural patterns in the solardynamics may be described by a quasi 60-year oscillationslightly modulated by the 115-year oscillation while the mil-lennial oscillation is at its maximum

The author notes that the CMIP5 models contain alsoa solar signature but it is very small because the CMIP5adopted TSI (Wang et al 2005) has a smaller secular trendthan the TSI records adopted for the CMIP3 GCMs in theIPCC (2007) Herein this correction is ignored becausewithin the 20 error associated to the β = 05 factor al-though the presence of a solar signature in m(t) may slightlyamplify the decadal cycle in H(t) Note that Eq 13 is notoptimized for periods before 1850 because no GST are avail-able before 1850 and the climate response to the deep grandsolar minima (Dalton Maunder etc) could necessitate ad-ditional frequencies such as a 80-90 year oscillation (Scafettaand Willson 2013a) and probably the inclusion of nonlineardynamical effect The 80-90 year cycle modulates the 60year cycle by producing a beat with a period of 210 yearsknown as the Suess (aka de Vries) solar cycle

Figure 26 compares the four CMIP5 ensemble averageprojections (panel A) and the solar-astronomical semi-empiricalmodel using β = 05 in Eq 13 (panel B) against the Had-CRUT4 GST record a common 1900-2000 baseline is usedThe figure highlights the superior performance of the solar-astronomical semi-empirical model versus the CMIP5 en-semble mean models Eq 13 reconstructs all major decadaland multidecadal temperature patterns observed since 1860The temperature plateau observed since 2000 is better re-constructed by the semi-empirical model than by the GCMmean projections Thus the 2000-2013 GST plateau ap-pears to be due to the cooling phase of a natural quasi60-year oscillation that has balanced a strongly reduced pro-jected anthropogenic warming trend The four adopted CMIP5GCM mean projections display a 2000-2100 warming be-tween a minimum of about 1 oC to a maximum of about 4 oC(see figure 26A) However as Figure 26B shows the four cor-rected projections predict a 2000-2100 warming between aminimum of about 03 oC to a maximum of about 18 oC us-ing the same anthropogenic scenarios The inserts magnifythe period 1990-2030 to highlight the strong mismatch be-tween the GST and the GCM simulations since 2000 that isresolved with the solar-astronomical semi-empirical model

Figure 27 is similar to Figure 26 but with all CMIP5model individual simulations used in Eq 13 with β = 05Again the figure highlights the superior performance of thesolar-astronomical semi-empirical model versus the CMIP5model simulations The solar-astronomical semi-empiricalmodel also causes a reduction of the range among the sim-ulation by a factor of two The root-mean-square deviation

32

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000 2020

Tem

pera

ture

Ano

mal

y (o C

)

year

HadCRUT42 GSTEq 13 with β=06Eq 13 with β=04

corrected GCM component by β=056-frequency harmonic component alone

Figure 25 The semi-empirical model Eq 13 using β = 04 (blue) and β = 06 (red) attenuation of the CMIP5 ensemble mean simulationvs HadCRUT4 GST record since 1860 The upward warming trending and all decadal and multidecadal patterns are well reconstructed Thebottom depicts the 6-frequency harmonic component that models the harmonic natural variability (green) and the GCM radiative componentcorrected by β = 05 (grey) respectively

(RMSD) value between the 49-month average smooth GSTand the full empirical model is about 004 oC while for theRMSD for the GCM model mean is twice 009 oC and forthe single GCM runs is normally larger (see Table 2)

Figure 28 magnifies the period 1980-2020 and uses sixglobal temperature estimates (HadCRUT3 HadCRUT4 UAHMSU RSS MSU GISS and NCDC) that appear to agreesufficiently well with each other and all of them disagreewith the CMIP5 simulations after 2000 The temperaturemay slightly increase from 2013 to 2016 and decrease from2016 to 2020 because of the two decadal cycles Howeverfast ENSO temperature fluctuations at scales shorter than7 years may mask the result

In conclusion because the temperature patterns appearswell correlated with solarastronomical oscillations at mul-tiple scales and that semi-empirical models based on theseoscillations reconstruct and hindcast GST variations signif-icantly better than the current GCMs it is very likely thatthe observed GST oscillations have an astronomical originwhose mechanisms are not implemented in the GCMs yetTo better appreciate the finding it is important to stressthat the harmonic constituents of the proposed model suchas the frequencies and the phases are coherent with majorastronomical oscillations Although in the future the em-

pirical model may be improved with a better understandingof these oscillations the proposed semi-empirical model al-ready appears to outperform all CMIP5 GCMs

7 Conclusion

As for the CMIP3 GCMs used by the IPCC 2007 (Scafetta2012b) the upgraded CMIP5 GCMs to be used in the IPCCFifth Assessment Report (AR5 2013) do not reproduce thedetectable decadal and multidecadal climate oscillations ob-served in the GST records since 1850 Multiple analysessuggest that these GCMs overestimate the anthropogenicwarming effect by about 50 This would also imply thatthe climate sensitivity to the radiative forcing should be sig-nificantly lowered by half It may be sim 15 oC (or less if partof the warming is spurious for example due to uncorrectedUHI effects) and it may possibly range between 1 oC and23 oC instead of the IPCC (2007) proposed range from 2oC to 45 oC Very important physical mechanisms neces-sary for reproducing multiple climatic oscillations which areresponsible for about half of the 1850-2010 warming appearto be still missing in the GCMs

The physical origin of the detected climatic oscillationsis currently uncertain but in this paper it has been ar-

33

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT42 GSTCMIP5 rcp26CMIP5 rcp45CMIP5 rcp60CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT42 GSTwith CMIP5 rcp26with CMIP5 rcp45with CMIP5 rcp60with CMIP5 rcp85

Harmonic natural vaiability

Figure 26 [A] The four CMIP5 ensemble average projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empiricalmodel Eq 13 with β = 05 against the HadCRUT4 GST record a common 1900-2000 baseline is used The figure highlights the betterperformance of the solar-astronomical semi-empirical model versus the CMIP5 models which is particularly evident since 2000 as shown in theinserts

gued that they may be astronomically induced This conclu-sion derives from the coherence found among astronomicaland climate oscillations from the decadal to the millennialtime scales This harmonic component cannot be ignoredin properly interpreting and forecasting climate change Ihave shown that an empirical model based on specific ma-jor astronomical harmonics plus a correction of the outputsof the current CMIP5 GCM simulations simultaneously re-constructs the decadal multidecadal and secular patternsobserved in the GST records since 1850

The most reasonable conclusion is that the climate sys-tem is synchronized to the natural oscillations found in thesolar system and that this harmonic dynamics constitutes animportant component of the Earthrsquos climate The proposedsemi-empirical model may produce more reliable projectionsfor the 21st century which are far less alarmist than thecurrent CMIP5 projections Under the same anthropogenicemission scenarios the model projects a possible 2000-2100warming ranging from 03 oC to 18 oC This range is sig-nificantly below the original CMIP5 GCM ensemble mean

projections spanning from about 1 oC to 4 oCIn conclusion multiple statistical tests suggest that the

proposed semi-empirical GST model based on astronomi-cally induced harmonics plus an anthropogenic plus volcanocontribution reduced by about 50 from the CMIP5 GCMprediction outperforms all CMIP5 GCMs in reconstructingand interpreting the GST patterns observed since 1850 Themodel would be compatible also with modern paleoclimaticreconstructions showing a larger pre-industrial variabilitywith a medieval period as warm as the 1950-2000 globalsurface temperatures

Future research should investigate space-climate couplingmechanisms in order to develop more advanced analyticaland semi-empirical climate models Figure 29 schematicallyrepresents a possible network of physical interactions caus-ing climatic changes

Appendix

The proposed harmonic model Eq 13 uses a specific setof harmonics first determined in Scafetta (2010) Scafetta

34

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

5

6

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

-15

-1

-05

0

05

1

1860 1880 1900 1920 1940 1960 1980 2000 2020

Tem

pera

ture

Ano

mal

y (o C

)

year

HadCRUT42 GSTEq 13 with β=06Eq 13 with β=04

corrected GCM component by β=056-frequency harmonic component alone

Figure 25 The semi-empirical model Eq 13 using β = 04 (blue) and β = 06 (red) attenuation of the CMIP5 ensemble mean simulationvs HadCRUT4 GST record since 1860 The upward warming trending and all decadal and multidecadal patterns are well reconstructed Thebottom depicts the 6-frequency harmonic component that models the harmonic natural variability (green) and the GCM radiative componentcorrected by β = 05 (grey) respectively

(RMSD) value between the 49-month average smooth GSTand the full empirical model is about 004 oC while for theRMSD for the GCM model mean is twice 009 oC and forthe single GCM runs is normally larger (see Table 2)

Figure 28 magnifies the period 1980-2020 and uses sixglobal temperature estimates (HadCRUT3 HadCRUT4 UAHMSU RSS MSU GISS and NCDC) that appear to agreesufficiently well with each other and all of them disagreewith the CMIP5 simulations after 2000 The temperaturemay slightly increase from 2013 to 2016 and decrease from2016 to 2020 because of the two decadal cycles Howeverfast ENSO temperature fluctuations at scales shorter than7 years may mask the result

In conclusion because the temperature patterns appearswell correlated with solarastronomical oscillations at mul-tiple scales and that semi-empirical models based on theseoscillations reconstruct and hindcast GST variations signif-icantly better than the current GCMs it is very likely thatthe observed GST oscillations have an astronomical originwhose mechanisms are not implemented in the GCMs yetTo better appreciate the finding it is important to stressthat the harmonic constituents of the proposed model suchas the frequencies and the phases are coherent with majorastronomical oscillations Although in the future the em-

pirical model may be improved with a better understandingof these oscillations the proposed semi-empirical model al-ready appears to outperform all CMIP5 GCMs

7 Conclusion

As for the CMIP3 GCMs used by the IPCC 2007 (Scafetta2012b) the upgraded CMIP5 GCMs to be used in the IPCCFifth Assessment Report (AR5 2013) do not reproduce thedetectable decadal and multidecadal climate oscillations ob-served in the GST records since 1850 Multiple analysessuggest that these GCMs overestimate the anthropogenicwarming effect by about 50 This would also imply thatthe climate sensitivity to the radiative forcing should be sig-nificantly lowered by half It may be sim 15 oC (or less if partof the warming is spurious for example due to uncorrectedUHI effects) and it may possibly range between 1 oC and23 oC instead of the IPCC (2007) proposed range from 2oC to 45 oC Very important physical mechanisms neces-sary for reproducing multiple climatic oscillations which areresponsible for about half of the 1850-2010 warming appearto be still missing in the GCMs

The physical origin of the detected climatic oscillationsis currently uncertain but in this paper it has been ar-

33

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT42 GSTCMIP5 rcp26CMIP5 rcp45CMIP5 rcp60CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT42 GSTwith CMIP5 rcp26with CMIP5 rcp45with CMIP5 rcp60with CMIP5 rcp85

Harmonic natural vaiability

Figure 26 [A] The four CMIP5 ensemble average projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empiricalmodel Eq 13 with β = 05 against the HadCRUT4 GST record a common 1900-2000 baseline is used The figure highlights the betterperformance of the solar-astronomical semi-empirical model versus the CMIP5 models which is particularly evident since 2000 as shown in theinserts

gued that they may be astronomically induced This conclu-sion derives from the coherence found among astronomicaland climate oscillations from the decadal to the millennialtime scales This harmonic component cannot be ignoredin properly interpreting and forecasting climate change Ihave shown that an empirical model based on specific ma-jor astronomical harmonics plus a correction of the outputsof the current CMIP5 GCM simulations simultaneously re-constructs the decadal multidecadal and secular patternsobserved in the GST records since 1850

The most reasonable conclusion is that the climate sys-tem is synchronized to the natural oscillations found in thesolar system and that this harmonic dynamics constitutes animportant component of the Earthrsquos climate The proposedsemi-empirical model may produce more reliable projectionsfor the 21st century which are far less alarmist than thecurrent CMIP5 projections Under the same anthropogenicemission scenarios the model projects a possible 2000-2100warming ranging from 03 oC to 18 oC This range is sig-nificantly below the original CMIP5 GCM ensemble mean

projections spanning from about 1 oC to 4 oCIn conclusion multiple statistical tests suggest that the

proposed semi-empirical GST model based on astronomi-cally induced harmonics plus an anthropogenic plus volcanocontribution reduced by about 50 from the CMIP5 GCMprediction outperforms all CMIP5 GCMs in reconstructingand interpreting the GST patterns observed since 1850 Themodel would be compatible also with modern paleoclimaticreconstructions showing a larger pre-industrial variabilitywith a medieval period as warm as the 1950-2000 globalsurface temperatures

Future research should investigate space-climate couplingmechanisms in order to develop more advanced analyticaland semi-empirical climate models Figure 29 schematicallyrepresents a possible network of physical interactions caus-ing climatic changes

Appendix

The proposed harmonic model Eq 13 uses a specific setof harmonics first determined in Scafetta (2010) Scafetta

34

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

5

6

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT42 GSTCMIP5 rcp26CMIP5 rcp45CMIP5 rcp60CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT42 GSTwith CMIP5 rcp26with CMIP5 rcp45with CMIP5 rcp60with CMIP5 rcp85

Harmonic natural vaiability

Figure 26 [A] The four CMIP5 ensemble average projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empiricalmodel Eq 13 with β = 05 against the HadCRUT4 GST record a common 1900-2000 baseline is used The figure highlights the betterperformance of the solar-astronomical semi-empirical model versus the CMIP5 models which is particularly evident since 2000 as shown in theinserts

gued that they may be astronomically induced This conclu-sion derives from the coherence found among astronomicaland climate oscillations from the decadal to the millennialtime scales This harmonic component cannot be ignoredin properly interpreting and forecasting climate change Ihave shown that an empirical model based on specific ma-jor astronomical harmonics plus a correction of the outputsof the current CMIP5 GCM simulations simultaneously re-constructs the decadal multidecadal and secular patternsobserved in the GST records since 1850

The most reasonable conclusion is that the climate sys-tem is synchronized to the natural oscillations found in thesolar system and that this harmonic dynamics constitutes animportant component of the Earthrsquos climate The proposedsemi-empirical model may produce more reliable projectionsfor the 21st century which are far less alarmist than thecurrent CMIP5 projections Under the same anthropogenicemission scenarios the model projects a possible 2000-2100warming ranging from 03 oC to 18 oC This range is sig-nificantly below the original CMIP5 GCM ensemble mean

projections spanning from about 1 oC to 4 oCIn conclusion multiple statistical tests suggest that the

proposed semi-empirical GST model based on astronomi-cally induced harmonics plus an anthropogenic plus volcanocontribution reduced by about 50 from the CMIP5 GCMprediction outperforms all CMIP5 GCMs in reconstructingand interpreting the GST patterns observed since 1850 Themodel would be compatible also with modern paleoclimaticreconstructions showing a larger pre-industrial variabilitywith a medieval period as warm as the 1950-2000 globalsurface temperatures

Future research should investigate space-climate couplingmechanisms in order to develop more advanced analyticaland semi-empirical climate models Figure 29 schematicallyrepresents a possible network of physical interactions caus-ing climatic changes

Appendix

The proposed harmonic model Eq 13 uses a specific setof harmonics first determined in Scafetta (2010) Scafetta

34

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

5

6

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

5

6

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

ALL CMIP5 MODELS

mod32 rcp26mod42 rcp45mod25 rcp60mod39 rcp85

HadCRUT42

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

with mod32 rcp26with mod42 rcp45with mod25 rcp60with mod39 rcp85

HadCRUT42

Figure 27 [A] All CMIP5 model projections versus the HadCRUT4 GST record [B] The solar-astronomical semi-empirical model Eq 13 withβ = 05 against the HadCRUT4 GST record a common 1980-2000 baseline and annually resolved records are used in the large figures whilethe monthly GST record is used in the inserts The figure highlights the better performance of the solar-astronomical semi-empirical modelversus the CMIP5 models

(2013a) also proposed a model with slightly different decadaland multidecadal frequencies harmonics with period of 102years 21 years and 61 years were used instead of harmonicswith period of 104 years 20 years and 60 years Scafetta(2013a) choice was justified by spectral analysis results andby the possibility that the observed harmonics could be in-duced by multiple closed astronomical frequencies with adifferent physical origin

For example the quasi 20-year GST oscillation could beinduced by a combination of the 186-year lunar nutationcycle of the 1985-year oscillation of the speed of the wob-bling sun related to the conjunction of Jupiter and Saturnand of the quasi 22-year Hale solar magnetic cycle IndeedChylek et al (2011) found evidence in multisecular ice-coredata for a prominent near 20-year time-scale oscillation thatbeats and appears to be composed of three close frequenciesSimilarly the quasi 60-year GST oscillation could be causedby the 596 years cycle in the speed of the wobbling sun andby the 61-year tidal beat between Jupiter orbit (1186 years)and Jupiter and Saturnrsquos spring tide (993 years) It is ev-

ident that if the planets are modulating solar activity anddirectly or indirectly the climate of the Earth numerousharmonics may be involved in the process as also found inScafetta and Willson (2013ab)

By analogy the harmonic constituent model currentlyused to predict the ocean tides (Kelvin 1881 Ehret 2008)uses 30-40 harmonics whose frequencies are deduced fromthe orbits of the sun and of the moon Many of the tidalharmonics are closely clustered (see httpenwikipediaorgwikiTheory_of_tidesTidal_constituents) For ex-ample the semi-diurnal tidal oscillation is modeled using 8frequencies spanning from 116 h (the shallow water semidi-urnal cycle) to 129 h (the lunar elliptical semidiurnal second-order cycle)

Thus the proposed harmonic model Eq 13 which isbased on a choice of just six harmonics spanning from thedecadal to the millennial scales should be interpreted as aminimal first approximation model Future research shouldbetter define the true physical harmonics involved in theprocess which may be numerous In any case from a practi-

35

-02

0

02

04

06

08

1

1980 1985 1990 1995 2000 2005 2010 2015 2020

Tem

pera

ture

Ano

mal

y (o C

)

year

GISSTEMRSS MSUUAH MSU

HadCRUT3HadCRUT42

CMIP5 ensemble mean modelEq 13 with β=05

Figure 28 Eq 13 with β = 05 (blue) and the original CMIP5 ensemble mean model (red) against six global tempera-ture estimates (HadCRUT3 HadCRUT4 UAH MSU RSS MSU GISS and NCDC) which were base-lined with HadCRUT4 fromJan1980 to Dec1999 Temperature data from httpwwwncdcnoaagov httpwwwmetofficegovuk httpdatagissnasagovhttpwwwremsscom httpvortexnsstcuahedu

cal point of view the alternative model proposed in Scafetta(2013a) produces similar results to Eq 13 as shown in Fig-ure 30 that reproduces Figure 26 with the alternative modeland data

References

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Agnihotri R Dutta K 2003 Centennial scale variationsin monsoonal rainfall (Indian east equatorial and Chinesemonsoons) Manifestations of solar variability CurrentScience 85 459-463

Benestad RE Schmidt GA 2009 Solar trends andglobal warming Journal of Geophysical Research 114D14101

Brown EW 1900 A Possible Explanation of the Sun-spotPeriod Monthly Notices of the Royal Astronomical Soci-ety 60 599-606

Bond G Kromer B Beer J Muscheler R Evans MNShowers W Hoffmann S Lotti-Bond R Hajdas IBonani G 2001 Persistent solar influence on North At-lantic climate during the Holocene Science 294 21302136

Booth BB Dunstone NJ Halloran PR Andrews TBellouin N 2012 Aerosols implicated as a prime driver oftwentieth-century North Atlantic climate variability Na-ture 484228-232

Chambers DP Merrifield MA Nerem RS 2012 Isthere a 60-year oscillation in global mean sea level Geo-phys Res Lett 39 L18607

Chylek P Lohmann U 2008 Aerosol radiative forcingand climate sensitivity deduced from the Last GlacialMaximum to Holocene transition Geophysical ResearchLetters 35(4) L04804

Chylek P Lesins G 2008 Multidecadal variability of At-lantic hurricane activity 1851-2007 J Geophys Res 113D22106

Chylek P Folland CK Dijkstra HA Lesins G DubeyMK 2011 Ice-core data evidence for a prominent near 20year time-scale of the Atlantic Multidecadal OscillationGeophys Res Lett 38 L13704

36

Figure 29 Network of the possible physical interaction between planetary harmonics solar variability and climate and environments changeson planet Earth (adapted with permission after Morner (2012) see also Scafetta (2013b))

Chylek P Folland C Frankcombe L Dijkstra HLesins G Dubey M 2012 Greenland ice core evidencefor spatial and temporal variability of the Atlantic Multi-decadal Oscillation Geophys Res Lett 39 L09705

Chylek P Dubey MK Lesins G Li J HengartnerN 2013 Imprint of the Atlantic multi-decadal oscillationand Pacific decadal oscillation on southwestern US cli-mate past present and future Climate Dynamics DOI101007s00382-013-1933-3 In press

Cook ER Meko DM Stockton CW 1997 A NewAssessment of Possible Solar and Lunar Forcing of theBidecadal Drought Rhythm in the Western United StatesJ Climate 10 1343-1356

Christiansen B Ljungqvist FC 2012 The extra-tropicalNorthern Hemisphere temperature in the last two mil-lennia reconstructions of low-frequency variability ClimPast 8 765-786

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Currie RG 1984 Evidence for 186 year lunar nodaldrought in western North America during the past mil-lennium J Geophys Res 89 1295-1308

Curry JA Webster PJ 2011 Climate Science and theUncertainty Monster Bull Amer Meteor Soc 92 1667-1682

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Fairbridge RW Shirley JH 1987 Prolonged minima

37

0

02

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08

1

12

1995 2005 2015 2025

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0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

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Ano

mal

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)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT4 GST

CMIP5 rcp60CMIP5 rcp45CMIP5 rcp26

CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT4 GST

with CMIP5 rcp60with CMIP5 rcp45with CMIP5 rcp26

with CMIP5 rcp85

Harmonic natural variability

Figure 30 Reproduction of Figure 26 with the alternative model and data proposed in Scafetta (2013a) that uses slight different decadal andmultidecadal harmonics

and the 179-year cycle of the solar inertial motion So-lar Physics 10 191-210

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Foukal P Frohlich C Spruit H Wigley TML 2006Variations in solar luminosity and their effect on theEarthrsquos climate Nature 443 161-166

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Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

Scafetta N 2012a A shared frequency set between thehistorical mid-latitude aurora records and the global sur-face temperature J of Atmospheric and Solar-TerrestrialPhysics 74 145-163

Scafetta N 2012b Testing an astronomically baseddecadal-scale empirical harmonic climate model versus theIPCC (2007) general circulation climate models Journalof Atmospheric and Solar-Terrestrial Physics 80 124-137

Scafetta N 2012c Multi-scale harmonic model for solarand climate cyclical variation throughout the Holocenebased on Jupiter-Saturn tidal frequencies plus the 11-yearsolar dynamo cycle Journal of Atmospheric and Solar-Terrestrial Physics 80 296-311

Scafetta N 2012d Does the Sun work as a nuclear fu-sion amplifier of planetary tidal forcing A proposal fora physical mechanism based on the mass-luminosity rela-tion Journal of Atmospheric and Solar-Terrestrial Physics81-82 27-40

Scafetta N 2013a Solar and planetary oscillation controlon climate change hind-cast forecast and a comparisonwith the CMIP5 GCMs Energy amp Environment 24(3-4)455496

41

Figure 29 Network of the possible physical interaction between planetary harmonics solar variability and climate and environments changeson planet Earth (adapted with permission after Morner (2012) see also Scafetta (2013b))

Chylek P Folland C Frankcombe L Dijkstra HLesins G Dubey M 2012 Greenland ice core evidencefor spatial and temporal variability of the Atlantic Multi-decadal Oscillation Geophys Res Lett 39 L09705

Chylek P Dubey MK Lesins G Li J HengartnerN 2013 Imprint of the Atlantic multi-decadal oscillationand Pacific decadal oscillation on southwestern US cli-mate past present and future Climate Dynamics DOI101007s00382-013-1933-3 In press

Cook ER Meko DM Stockton CW 1997 A NewAssessment of Possible Solar and Lunar Forcing of theBidecadal Drought Rhythm in the Western United StatesJ Climate 10 1343-1356

Christiansen B Ljungqvist FC 2012 The extra-tropicalNorthern Hemisphere temperature in the last two mil-lennia reconstructions of low-frequency variability ClimPast 8 765-786

Crowley TJ 2000 Causes of Climate Change Over thePast 1000 Years Science 289 270-277

Currie RG 1984 Evidence for 186 year lunar nodaldrought in western North America during the past mil-lennium J Geophys Res 89 1295-1308

Curry JA Webster PJ 2011 Climate Science and theUncertainty Monster Bull Amer Meteor Soc 92 1667-1682

Davis JC Bohling G 2001 The Search for Patterns inIce-Core Temperature Curves in LC Gerhard WEHarrison BM Hanson eds Geological Perspectives ofGlobal Climate Change 213-229

Douglass DH Christy JR Pearson BD Singer SF2007 A comparison of tropical temperature trends withmodel predictions Int J Climatol 28 1693-1701

Ehret T 2008 Old brass brainsmechanical prediction oftides ACSM Bulletin 6 4144

Eichler A Olivier S Henderson K Laube A Beer JPapina T Gaggeler HW Schwikowski M 2009 Tem-perature response in the Altai region lags solar forcingGeophys Res Lett 36 L01808

Esper J Frank DC Timonen M Zorita E WilsonRJS Luterbacher J Holzkamper S Fischer N Wag-ner S Nievergelt D Verstege A Buntgen U 2012Orbital forcing of tree-ring data Nature Climate Change2 862-866

Fairbridge RW Shirley JH 1987 Prolonged minima

37

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT4 GST

CMIP5 rcp60CMIP5 rcp45CMIP5 rcp26

CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT4 GST

with CMIP5 rcp60with CMIP5 rcp45with CMIP5 rcp26

with CMIP5 rcp85

Harmonic natural variability

Figure 30 Reproduction of Figure 26 with the alternative model and data proposed in Scafetta (2013a) that uses slight different decadal andmultidecadal harmonics

and the 179-year cycle of the solar inertial motion So-lar Physics 10 191-210

Feulner G Rahmstorf S 2010 On the effect of a newgrand minimum of solar activity on the future climate onEarth Geophys Res Lett 37 L05707

Forest CE Stone PH Sokolov AP 2006 EstimatedPDFs of climate system properties including natural andanthropogenic forcings Geophys Res Lett 33 L01705

Foukal P Frohlich C Spruit H Wigley TML 2006Variations in solar luminosity and their effect on theEarthrsquos climate Nature 443 161-166

Frohlich C 2006 Solar irradiance variability since 1978revision of the PMOD composite during solar cycle 21Space Science Reviews 125 53-65

Frohlich C 2009 Evidence of a long-term trend in totalsolar irradiance Astronomy amp Astrophysics 501(3)L27-L30

Fyfe JC Gillett NP Zwiers FW 2013 Overestimatedglobal warming over the past 20 years Nature ClimateChange 3 767-769

Ge Q Zheng J Fang X Zhang X Zhang P 2003Winter half-year temperature reconstruction for the mid-dle and lower reaches of the Yellow River and Yangtze

River China during the past 2000 years The Holocene13 933-940

Gillett NP Arora VK Flato GM Scinocca JF vonSalzen K 2012 Improved constraints on 21st-centurywarming derived using 160 years of temperature observa-tions Geophys Res Lett 39 L01704

Gray ST Graumlich LJ Betancourt JL PedersonGT 2004 A tree-ring based reconstruction of the At-lantic Multidecadal Oscillation since 1567 AD GeophysRes Lett 31 L12205

Gray LJ Beer J Geller M Haigh JD Lockwood MMatthes K Cubasch U Fleitmann D Harrison GHood L Luterbacher J Meehl GA Shindell D vanGeel B White W 2010 Solar influences on climateRev Geophys 48 RG4001

Guidoboni E Navarra A Boschi E 2011 The spiral ofclimate civilizations of the mediterranean and climatechange in history (Bononia University Press BolognaItaly)

Gwynee P 1975 The Cooling World Newsweek April 28p 64 See the discussion at the voice ldquoGlobal Coolingrdquo onwikipediaorg

38

Hansen J Fung I Lacis A Rind D Lebedeff SRuedy R Russell G Stone P 1988 Global climatechanges as forecast by Goddard Institute for Space Stud-ies three-dimensional model J Geophys Res 93 9341-9364

Hansen J Sato M Kharecha P von Schuckmann K2011 Earthrsquos energy imbalance and implications AtmosChem Phys 11 13421-13449

Hegerl CG Crowley TJ Hyde WT Frame DJ2006 Climate sensitivity constrained by temperature re-constructions over the past seven centuries Nature 4401029-1032

House MR 1995 Orbital forcing timescales an introduc-tion Geological Society London Special Publications 851-18

Hoyt DV Schatten KH 1993 A Discussion of PlausibleSolar Irradiance Variations 1700-1992 J of GeophysicalResearch 98 18895-18906

Hoyt DV Schatten KH 1997 The Role of the Sun inthe Climate Change Oxford Univ Press New York

Humlum O Solheim J-E Stordahl K 2011 Identify-ing natural contributions to late Holocene climate changeGlobal and Planetary Change 79 145-156

Hung C-C 2007 Apparent Relations Between Solar Ac-tivity and Solar Tides Caused by the Planets NASATM-2007-214817

Imbers J Lopez A Huntingford C Allen MR2013 Testing the robustness of the anthropogenic cli-mate change detection statements using different empiri-cal models J Geophys Res 118 3192-3199

Iyengar RN 2009 Monsoon rainfall cycles as depicted inancient Sanskrit texts Current Science 97 444-447

IPCC Solomon S et al (eds) 2007 in Climate Change2007 The Physical Science BasisContribution of Work-ing Group I to the Fourth Assessment Report of the Inter-governmental Panel on Climate Change Cambridge Uni-versity Press Cambridge

Jevrejeva S Moore JCGrinsted A P Woodworth2008 Recent global sea level acceleration started over 200years ago Geophys Res Lett 35 L08715

Kaufmann RK Kauppi H Mann ML Stock JH 2011Reconciling anthropogenic climate change with observedtemperature 19982008 PNAS 108 1179011793

Keeling CD Whorf TP 1997a Possible forcing of globaltemperature by the oceanic tides PNAS 94 8321-8328

Keeling CD Whorf TP 1997b The 1800-year oceanictidal cycle A possible cause of rapid climate changePNAS 97 3814-3819

Kepler J 1601 On the More Certain Fundamentals of As-trology In Brackenridge JB and Rossi MA (Eds)Proceedings of the American Philosophical Society 123(2)85-116 (1979)

Kerr RA 2001 A variable Sun paces millennial climateScience 294 1431-1433

Kirkby J 2007 Cosmic rays and climate Surveys in Geo-physics 28 333375

Klyashtorin LB Borisov V Lyubushin A 2009 Cyclicchanges of climate and major commercial stocks of theBarents Sea Mar Biol Res 5 4-17

Knight J Kenned JJ Folland C Harris G JonesGS Palmer M Parke D Scaife A Stott P 2009Do global temperature trends over the last decade falsifyclimate predictions in ldquoState of the Climate in 2008rdquoBull Amer Meteor Soc 90 (8) S1S196

Knudsen MF Seidenkrantz M-S Jacobsen BH andKuijpers A 2011 Tracking the Atlantic MultidecadalOscillation through the last 8000 years Nature Commu-nications 2 178

Kobashi T Severinghaus JP Barnola J-M KawamuraK Carter T Nakaegawa T 2010 Persistent multi-decadal Greenland temperature fluctuation through thelast millennium Climatic Change 100 733-756

Kokfelt U Muscheler R 2013 Solar forcing of climateduring the last millennium recorded in lake sedimentsfrom northern Sweden The Holocene 23(3) 447-452 Doi1011770959683612460781

Kopp G Lean JL 2011 A New Lower Value of To-tal Solar Irradiance Evidence and Climate SignificanceGeophys Res Letters 38 L01706

Landscheidt T 1999 Extrema in sunspot cycle linked toSuns motion Solar Physics 189 415-426

Lean JL Rind DH 2008 How natural and anthro-pogenic influences alter global and regional surface tem-peratures 1889 to 2006 Geophys Res Lett 35 L18701

Lewis N 2013 An objective Bayesian improved approachfor applying optimal fingerprint techniques to estimate cli-mate sensitivity Journal of Climate DOI101175JCLI-D-12-004731

Lindzen RS Choi Y-S 2009 On the determination ofclimate feedbacks from erbe data Geophys Res Lett 36L16705

Lindzen RS and Choi Y-S 2011 On the observationaldetermination of climate sensitivity and its implicationsAsia Pacific J Atmos Sci 47 377-390

Liu J Wang B Cane MA Yim S-Y Lee J-Y 2013Divergent global precipitation changes induced by naturalversus anthropogenic forcing Nature 493 656-659

39

Ljungqvist FC 2010 A new reconstruction of temperaturevariability in the extra-tropical Northern Hemisphere dur-ing the last two millennia Geogra-fiska Annaler Series A92 339-351

Lockwood M 2011 Shining a light on solar impacts Na-ture Climate Change 1 (2) 98-99

Lockwood M 2012 Solar influence on global and re-gional climates Surveys in Geophysics pages 1-32 DOI101007s10712-012-9181-3

Loehle C Mc Culloch JH 2008 Correction to A 2000-year global temperature reconstruction based on non-treering proxies Energy amp Environment 19 93-100

Loehle C Scafetta N 2011 Climate Change AttributionUsing Empirical Decomposition of Climatic Data TheOpen Atmospheric Science J 5 74-86

Lu Q-B 2009 Correlation between Cosmic Rays andOzone Depletion Phys Rev Lett 102 118501

Luterbacher J Schmutz C Gyalistras D Xoplaki E Wan-ner H 1999 Reconstruction of monthly NAO and EU in-dices back to AD 1675 Geophys Res Lett 26 2745-2748

Luterbacher J Xoplaki E Dietrich D Jones PD DaviesTD Portis D Gonzalez-Rouco JF von Storch HGyalistras D Casty C Wanner H 2002 ExtendingNorth Atlantic Oscillation reconstructions back to 1500Atmos Sci Lett doi101006asle20010044

Mann ME Bradley RS Hughes MK 1999 North-ern hemisphere temperatures during the past millenniumInferences uncertainties and limitations Geophys ResLett 26(6) 759-762

Mann ME Jones PD 2003 Global surface temperatureover the past two millennia Geophy Res Lett 30 1820-1824

Mann ME Zhang Z Hughes MK Bradley RSMiller SK Rutherford S Ni F 2008 Proxy-basedreconstructions of hemispheric and global surface temper-ature variations over the past two millennia PNAS 10513252-13257

Manzi V Gennari R Lugli S Roveri M ScafettaN Schreiber C 2012 High-frequency cyclicity in theMediterranean Messinian evaporites evidence for solar-lunar climate forcing J of Sedimentary Research 82 991-1005

Marsquosar A 886 On Historical Astrology - The Book of Re-ligions and Dynasties (On the Great Conjunctions) KYamamoto and C Burnett Eds Brill 2000

Mazzarella A Scafetta N 2012 Evidences for a quasi 60-year North Atlantic Oscillation since 1700 and its meaningfor global climate change Theor Appl Climatol 107(3-4) 599-609

McKitrick RR Michaels PJ 2007 Quantifying the in-fluence of anthropogenic surface processes and inhomo-geneities on gridded global climate data J Geophys Res112 D24S09

McKitrick RR Nierenberg N 2010 Socioeconomic Pat-terns in Climate Data Journal of Economic and SocialMeasurement 35 149-175

McShane B B Wyner A J 2011 A statistical analysis ofmultiple temperature proxies Are reconstructions of sur-face temperatures over the last 1000 years reliable AnnAppl Statist 5 5-44

Meehl GA Arblaster JM Fasullo JT Hu A Tren-berth KE 2011 Model-based evidence of deep-oceanheat uptake during surface-temperature hiatus periodsNature Climate Change 1 360-364

Moberg A Sonechkin DM Holmgren K DatsenkoNM Karlen W 2005 Highly variable Northern Hemi-sphere temperatures reconstructed from low- and high-resolution proxy data Nature 433 613-617

Morice CP Kennedy JJ Rayner NA Jones PD2012 Quantifying uncertainties in global and regionaltemperature change using an ensemble of observational es-timates The HadCRUT4 dataset J Geophys Res 117D08101

Morner N-A 1989 Changes in the Earths rate of rotationon an El Nino to century basis In Geomagnetism andPaleomagnetism (FJ Lowes et al eds) 45-53 KluwerAcad Publ

Morner N-A 1990 The Earths differential rotation hy-drospheric changes Geophysical Monographs 59 27-32AGU and IUGG 1990

Morner N-A 2012 Planetary beat solar wind and terres-trial climate In Solar wind emission technologies andimpacts p 47-66 Ed Escarope Borrega C D and AFBeiros Cruz eds (Nova Publ Co)

Le Mouel J-L Courtillot V Blanter E Shnirman M2008 Evidence for a solar signature in 20th-century tem-perature data from the USA and Europe Geoscience 340421-430

Nam C Bony S DufresneJ-L Chepfer H 2012 Thelsquotoo few too brightrsquo tropical low-cloud problem in CMIP5models Geophys Res Lett 39 L21801

Neukom R Luterbacher J Villalba R Kttel M FrankD Jones P Grosjean M Wanner H Aravena J-CBlack D Christie D DrsquoArrigo R Lara A MoralesM Soliz-Gamboa C Srur A Urrutia R Gunten L2011 Multiproxy summer and winter surface air tempera-ture field reconstructions for southern South America cov-ering the past centuries Climate Dynamics 37 35-51

40

Ogurtsov MG Nagovitsyn YA Kocharov GEJungner H 2002 Long-period cycles of the Sunrsquos activ-ity recorded in direct solar data and proxies Solar Phys211 371-394

Oppo DW Rosenthal Y Linsley BK 2009 2000-year-long temperature and hydrology reconstructions from theIndo-Pacific warm pool Nature 460 1113-1116

Parker DE Legg TP Folland CK 1992 A new dailyCentral England Temperature Series 1772-1991 Interna-tional Journal of Climate 12 317-342

Pierce JR Adams PJ 2009 Can cosmic rays affect cloudcondensation nuclei by altering new particle formationrates Geophys Res Lett 36 L09820

Press WH Teukolsky SA Vetterling WT FlanneryBP 1997 Numerical Recipes in C Cambridge UniversityPress Cambridge

Ptolemy C 2nd century Tetrabiblos FE Robbins Ed1940 Harvard University Press Loeb Classical LibraryCambridge MA

Qian W-H Lu B 2010 Periodic oscillations in millennialglobal-mean temperature and their causes Chinese SciBull 55 4052-4057

Rahmstorf S 2008 Anthropogenic Climate Change Re-visiting the Facts pp 34-53 In Zedillo E Ed GlobalWarming Looking Beyond Kyoto Brookings InstitutionPress

Reichler T Kim J Manzini E Kroger J 2012 A strato-spheric connection to Atlantic climate variability NatureGeoscience 5 783-787

Remer LA et al 2008 Global aerosol climatology fromthe MODIS satellite sensors J Geophys Res 113D14S07

Ring MJ Lindner D Cross EF Schlesinger ME2012 Causes of the Global Warming Observed since the19th Century Atmospheric and Climate Sciences 2(4)401-415

Santer B D Thorne P W Haimberger L Taylor KE Wigley T M L Lanzante J R Solomon S FreeM Gleckler P J Jones P D Karl T R Klein SA Mears C Nychka D Schmidt G A SherwoodS C Wentz F J 2008 Consistency of modelled andobserved temperature trends in the tropical troposphereInternational Journal of Climatology 28 1703-1722

Scafetta N Grigolini P 2002 Scaling detection in timeseries diffusion entropy analysis Physical Review E 66036130

Scafetta N Grigolini P Imholt T Roberts JA WestBJ 2004 Solar turbulence in earthrsquos global and regionaltemperature anomalies Phys Rev E 69 026303

Scafetta N West B J 2005 Estimated solar contributionto the global surface warming using the ACRIM TSI satel-lite composite Geophysical Research Letters 32 L18713

Scafetta N West BJ 2006 Phenomenological solar sig-nature in 400 years of reconstructed Northern Hemi-sphere temperature record Geophysical Research Letters33(17) L17718

Scafetta N and West BJ 2007 Phenomenological recon-structions of the solar signature in the Northern Hemi-sphere surface temperature records since 1600 J Geo-phys Res 112 D24S03

Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

Scafetta N 2012a A shared frequency set between thehistorical mid-latitude aurora records and the global sur-face temperature J of Atmospheric and Solar-TerrestrialPhysics 74 145-163

Scafetta N 2012b Testing an astronomically baseddecadal-scale empirical harmonic climate model versus theIPCC (2007) general circulation climate models Journalof Atmospheric and Solar-Terrestrial Physics 80 124-137

Scafetta N 2012c Multi-scale harmonic model for solarand climate cyclical variation throughout the Holocenebased on Jupiter-Saturn tidal frequencies plus the 11-yearsolar dynamo cycle Journal of Atmospheric and Solar-Terrestrial Physics 80 296-311

Scafetta N 2012d Does the Sun work as a nuclear fu-sion amplifier of planetary tidal forcing A proposal fora physical mechanism based on the mass-luminosity rela-tion Journal of Atmospheric and Solar-Terrestrial Physics81-82 27-40

Scafetta N 2013a Solar and planetary oscillation controlon climate change hind-cast forecast and a comparisonwith the CMIP5 GCMs Energy amp Environment 24(3-4)455496

41

0

02

04

06

08

1

12

1995 2005 2015 2025

year

0

02

04

06

08

1

12

1995 2005 2015 2025

year

-1

0

1

2

3

4

1880 1910 1940 1970 2000 2030 2060 2090

Tem

pera

ture

Ano

mal

y (o C

)

[A] year

CMIP5 ENSEMBLE MODELS

HadCRUT4 GST

CMIP5 rcp60CMIP5 rcp45CMIP5 rcp26

CMIP5 rcp85

1880 1910 1940 1970 2000 2030 2060 2090

[B] year

SOLAR-ASTRONOMICAL MODEL

HadCRUT4 GST

with CMIP5 rcp60with CMIP5 rcp45with CMIP5 rcp26

with CMIP5 rcp85

Harmonic natural variability

Figure 30 Reproduction of Figure 26 with the alternative model and data proposed in Scafetta (2013a) that uses slight different decadal andmultidecadal harmonics

and the 179-year cycle of the solar inertial motion So-lar Physics 10 191-210

Feulner G Rahmstorf S 2010 On the effect of a newgrand minimum of solar activity on the future climate onEarth Geophys Res Lett 37 L05707

Forest CE Stone PH Sokolov AP 2006 EstimatedPDFs of climate system properties including natural andanthropogenic forcings Geophys Res Lett 33 L01705

Foukal P Frohlich C Spruit H Wigley TML 2006Variations in solar luminosity and their effect on theEarthrsquos climate Nature 443 161-166

Frohlich C 2006 Solar irradiance variability since 1978revision of the PMOD composite during solar cycle 21Space Science Reviews 125 53-65

Frohlich C 2009 Evidence of a long-term trend in totalsolar irradiance Astronomy amp Astrophysics 501(3)L27-L30

Fyfe JC Gillett NP Zwiers FW 2013 Overestimatedglobal warming over the past 20 years Nature ClimateChange 3 767-769

Ge Q Zheng J Fang X Zhang X Zhang P 2003Winter half-year temperature reconstruction for the mid-dle and lower reaches of the Yellow River and Yangtze

River China during the past 2000 years The Holocene13 933-940

Gillett NP Arora VK Flato GM Scinocca JF vonSalzen K 2012 Improved constraints on 21st-centurywarming derived using 160 years of temperature observa-tions Geophys Res Lett 39 L01704

Gray ST Graumlich LJ Betancourt JL PedersonGT 2004 A tree-ring based reconstruction of the At-lantic Multidecadal Oscillation since 1567 AD GeophysRes Lett 31 L12205

Gray LJ Beer J Geller M Haigh JD Lockwood MMatthes K Cubasch U Fleitmann D Harrison GHood L Luterbacher J Meehl GA Shindell D vanGeel B White W 2010 Solar influences on climateRev Geophys 48 RG4001

Guidoboni E Navarra A Boschi E 2011 The spiral ofclimate civilizations of the mediterranean and climatechange in history (Bononia University Press BolognaItaly)

Gwynee P 1975 The Cooling World Newsweek April 28p 64 See the discussion at the voice ldquoGlobal Coolingrdquo onwikipediaorg

38

Hansen J Fung I Lacis A Rind D Lebedeff SRuedy R Russell G Stone P 1988 Global climatechanges as forecast by Goddard Institute for Space Stud-ies three-dimensional model J Geophys Res 93 9341-9364

Hansen J Sato M Kharecha P von Schuckmann K2011 Earthrsquos energy imbalance and implications AtmosChem Phys 11 13421-13449

Hegerl CG Crowley TJ Hyde WT Frame DJ2006 Climate sensitivity constrained by temperature re-constructions over the past seven centuries Nature 4401029-1032

House MR 1995 Orbital forcing timescales an introduc-tion Geological Society London Special Publications 851-18

Hoyt DV Schatten KH 1993 A Discussion of PlausibleSolar Irradiance Variations 1700-1992 J of GeophysicalResearch 98 18895-18906

Hoyt DV Schatten KH 1997 The Role of the Sun inthe Climate Change Oxford Univ Press New York

Humlum O Solheim J-E Stordahl K 2011 Identify-ing natural contributions to late Holocene climate changeGlobal and Planetary Change 79 145-156

Hung C-C 2007 Apparent Relations Between Solar Ac-tivity and Solar Tides Caused by the Planets NASATM-2007-214817

Imbers J Lopez A Huntingford C Allen MR2013 Testing the robustness of the anthropogenic cli-mate change detection statements using different empiri-cal models J Geophys Res 118 3192-3199

Iyengar RN 2009 Monsoon rainfall cycles as depicted inancient Sanskrit texts Current Science 97 444-447

IPCC Solomon S et al (eds) 2007 in Climate Change2007 The Physical Science BasisContribution of Work-ing Group I to the Fourth Assessment Report of the Inter-governmental Panel on Climate Change Cambridge Uni-versity Press Cambridge

Jevrejeva S Moore JCGrinsted A P Woodworth2008 Recent global sea level acceleration started over 200years ago Geophys Res Lett 35 L08715

Kaufmann RK Kauppi H Mann ML Stock JH 2011Reconciling anthropogenic climate change with observedtemperature 19982008 PNAS 108 1179011793

Keeling CD Whorf TP 1997a Possible forcing of globaltemperature by the oceanic tides PNAS 94 8321-8328

Keeling CD Whorf TP 1997b The 1800-year oceanictidal cycle A possible cause of rapid climate changePNAS 97 3814-3819

Kepler J 1601 On the More Certain Fundamentals of As-trology In Brackenridge JB and Rossi MA (Eds)Proceedings of the American Philosophical Society 123(2)85-116 (1979)

Kerr RA 2001 A variable Sun paces millennial climateScience 294 1431-1433

Kirkby J 2007 Cosmic rays and climate Surveys in Geo-physics 28 333375

Klyashtorin LB Borisov V Lyubushin A 2009 Cyclicchanges of climate and major commercial stocks of theBarents Sea Mar Biol Res 5 4-17

Knight J Kenned JJ Folland C Harris G JonesGS Palmer M Parke D Scaife A Stott P 2009Do global temperature trends over the last decade falsifyclimate predictions in ldquoState of the Climate in 2008rdquoBull Amer Meteor Soc 90 (8) S1S196

Knudsen MF Seidenkrantz M-S Jacobsen BH andKuijpers A 2011 Tracking the Atlantic MultidecadalOscillation through the last 8000 years Nature Commu-nications 2 178

Kobashi T Severinghaus JP Barnola J-M KawamuraK Carter T Nakaegawa T 2010 Persistent multi-decadal Greenland temperature fluctuation through thelast millennium Climatic Change 100 733-756

Kokfelt U Muscheler R 2013 Solar forcing of climateduring the last millennium recorded in lake sedimentsfrom northern Sweden The Holocene 23(3) 447-452 Doi1011770959683612460781

Kopp G Lean JL 2011 A New Lower Value of To-tal Solar Irradiance Evidence and Climate SignificanceGeophys Res Letters 38 L01706

Landscheidt T 1999 Extrema in sunspot cycle linked toSuns motion Solar Physics 189 415-426

Lean JL Rind DH 2008 How natural and anthro-pogenic influences alter global and regional surface tem-peratures 1889 to 2006 Geophys Res Lett 35 L18701

Lewis N 2013 An objective Bayesian improved approachfor applying optimal fingerprint techniques to estimate cli-mate sensitivity Journal of Climate DOI101175JCLI-D-12-004731

Lindzen RS Choi Y-S 2009 On the determination ofclimate feedbacks from erbe data Geophys Res Lett 36L16705

Lindzen RS and Choi Y-S 2011 On the observationaldetermination of climate sensitivity and its implicationsAsia Pacific J Atmos Sci 47 377-390

Liu J Wang B Cane MA Yim S-Y Lee J-Y 2013Divergent global precipitation changes induced by naturalversus anthropogenic forcing Nature 493 656-659

39

Ljungqvist FC 2010 A new reconstruction of temperaturevariability in the extra-tropical Northern Hemisphere dur-ing the last two millennia Geogra-fiska Annaler Series A92 339-351

Lockwood M 2011 Shining a light on solar impacts Na-ture Climate Change 1 (2) 98-99

Lockwood M 2012 Solar influence on global and re-gional climates Surveys in Geophysics pages 1-32 DOI101007s10712-012-9181-3

Loehle C Mc Culloch JH 2008 Correction to A 2000-year global temperature reconstruction based on non-treering proxies Energy amp Environment 19 93-100

Loehle C Scafetta N 2011 Climate Change AttributionUsing Empirical Decomposition of Climatic Data TheOpen Atmospheric Science J 5 74-86

Lu Q-B 2009 Correlation between Cosmic Rays andOzone Depletion Phys Rev Lett 102 118501

Luterbacher J Schmutz C Gyalistras D Xoplaki E Wan-ner H 1999 Reconstruction of monthly NAO and EU in-dices back to AD 1675 Geophys Res Lett 26 2745-2748

Luterbacher J Xoplaki E Dietrich D Jones PD DaviesTD Portis D Gonzalez-Rouco JF von Storch HGyalistras D Casty C Wanner H 2002 ExtendingNorth Atlantic Oscillation reconstructions back to 1500Atmos Sci Lett doi101006asle20010044

Mann ME Bradley RS Hughes MK 1999 North-ern hemisphere temperatures during the past millenniumInferences uncertainties and limitations Geophys ResLett 26(6) 759-762

Mann ME Jones PD 2003 Global surface temperatureover the past two millennia Geophy Res Lett 30 1820-1824

Mann ME Zhang Z Hughes MK Bradley RSMiller SK Rutherford S Ni F 2008 Proxy-basedreconstructions of hemispheric and global surface temper-ature variations over the past two millennia PNAS 10513252-13257

Manzi V Gennari R Lugli S Roveri M ScafettaN Schreiber C 2012 High-frequency cyclicity in theMediterranean Messinian evaporites evidence for solar-lunar climate forcing J of Sedimentary Research 82 991-1005

Marsquosar A 886 On Historical Astrology - The Book of Re-ligions and Dynasties (On the Great Conjunctions) KYamamoto and C Burnett Eds Brill 2000

Mazzarella A Scafetta N 2012 Evidences for a quasi 60-year North Atlantic Oscillation since 1700 and its meaningfor global climate change Theor Appl Climatol 107(3-4) 599-609

McKitrick RR Michaels PJ 2007 Quantifying the in-fluence of anthropogenic surface processes and inhomo-geneities on gridded global climate data J Geophys Res112 D24S09

McKitrick RR Nierenberg N 2010 Socioeconomic Pat-terns in Climate Data Journal of Economic and SocialMeasurement 35 149-175

McShane B B Wyner A J 2011 A statistical analysis ofmultiple temperature proxies Are reconstructions of sur-face temperatures over the last 1000 years reliable AnnAppl Statist 5 5-44

Meehl GA Arblaster JM Fasullo JT Hu A Tren-berth KE 2011 Model-based evidence of deep-oceanheat uptake during surface-temperature hiatus periodsNature Climate Change 1 360-364

Moberg A Sonechkin DM Holmgren K DatsenkoNM Karlen W 2005 Highly variable Northern Hemi-sphere temperatures reconstructed from low- and high-resolution proxy data Nature 433 613-617

Morice CP Kennedy JJ Rayner NA Jones PD2012 Quantifying uncertainties in global and regionaltemperature change using an ensemble of observational es-timates The HadCRUT4 dataset J Geophys Res 117D08101

Morner N-A 1989 Changes in the Earths rate of rotationon an El Nino to century basis In Geomagnetism andPaleomagnetism (FJ Lowes et al eds) 45-53 KluwerAcad Publ

Morner N-A 1990 The Earths differential rotation hy-drospheric changes Geophysical Monographs 59 27-32AGU and IUGG 1990

Morner N-A 2012 Planetary beat solar wind and terres-trial climate In Solar wind emission technologies andimpacts p 47-66 Ed Escarope Borrega C D and AFBeiros Cruz eds (Nova Publ Co)

Le Mouel J-L Courtillot V Blanter E Shnirman M2008 Evidence for a solar signature in 20th-century tem-perature data from the USA and Europe Geoscience 340421-430

Nam C Bony S DufresneJ-L Chepfer H 2012 Thelsquotoo few too brightrsquo tropical low-cloud problem in CMIP5models Geophys Res Lett 39 L21801

Neukom R Luterbacher J Villalba R Kttel M FrankD Jones P Grosjean M Wanner H Aravena J-CBlack D Christie D DrsquoArrigo R Lara A MoralesM Soliz-Gamboa C Srur A Urrutia R Gunten L2011 Multiproxy summer and winter surface air tempera-ture field reconstructions for southern South America cov-ering the past centuries Climate Dynamics 37 35-51

40

Ogurtsov MG Nagovitsyn YA Kocharov GEJungner H 2002 Long-period cycles of the Sunrsquos activ-ity recorded in direct solar data and proxies Solar Phys211 371-394

Oppo DW Rosenthal Y Linsley BK 2009 2000-year-long temperature and hydrology reconstructions from theIndo-Pacific warm pool Nature 460 1113-1116

Parker DE Legg TP Folland CK 1992 A new dailyCentral England Temperature Series 1772-1991 Interna-tional Journal of Climate 12 317-342

Pierce JR Adams PJ 2009 Can cosmic rays affect cloudcondensation nuclei by altering new particle formationrates Geophys Res Lett 36 L09820

Press WH Teukolsky SA Vetterling WT FlanneryBP 1997 Numerical Recipes in C Cambridge UniversityPress Cambridge

Ptolemy C 2nd century Tetrabiblos FE Robbins Ed1940 Harvard University Press Loeb Classical LibraryCambridge MA

Qian W-H Lu B 2010 Periodic oscillations in millennialglobal-mean temperature and their causes Chinese SciBull 55 4052-4057

Rahmstorf S 2008 Anthropogenic Climate Change Re-visiting the Facts pp 34-53 In Zedillo E Ed GlobalWarming Looking Beyond Kyoto Brookings InstitutionPress

Reichler T Kim J Manzini E Kroger J 2012 A strato-spheric connection to Atlantic climate variability NatureGeoscience 5 783-787

Remer LA et al 2008 Global aerosol climatology fromthe MODIS satellite sensors J Geophys Res 113D14S07

Ring MJ Lindner D Cross EF Schlesinger ME2012 Causes of the Global Warming Observed since the19th Century Atmospheric and Climate Sciences 2(4)401-415

Santer B D Thorne P W Haimberger L Taylor KE Wigley T M L Lanzante J R Solomon S FreeM Gleckler P J Jones P D Karl T R Klein SA Mears C Nychka D Schmidt G A SherwoodS C Wentz F J 2008 Consistency of modelled andobserved temperature trends in the tropical troposphereInternational Journal of Climatology 28 1703-1722

Scafetta N Grigolini P 2002 Scaling detection in timeseries diffusion entropy analysis Physical Review E 66036130

Scafetta N Grigolini P Imholt T Roberts JA WestBJ 2004 Solar turbulence in earthrsquos global and regionaltemperature anomalies Phys Rev E 69 026303

Scafetta N West B J 2005 Estimated solar contributionto the global surface warming using the ACRIM TSI satel-lite composite Geophysical Research Letters 32 L18713

Scafetta N West BJ 2006 Phenomenological solar sig-nature in 400 years of reconstructed Northern Hemi-sphere temperature record Geophysical Research Letters33(17) L17718

Scafetta N and West BJ 2007 Phenomenological recon-structions of the solar signature in the Northern Hemi-sphere surface temperature records since 1600 J Geo-phys Res 112 D24S03

Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

Scafetta N 2012a A shared frequency set between thehistorical mid-latitude aurora records and the global sur-face temperature J of Atmospheric and Solar-TerrestrialPhysics 74 145-163

Scafetta N 2012b Testing an astronomically baseddecadal-scale empirical harmonic climate model versus theIPCC (2007) general circulation climate models Journalof Atmospheric and Solar-Terrestrial Physics 80 124-137

Scafetta N 2012c Multi-scale harmonic model for solarand climate cyclical variation throughout the Holocenebased on Jupiter-Saturn tidal frequencies plus the 11-yearsolar dynamo cycle Journal of Atmospheric and Solar-Terrestrial Physics 80 296-311

Scafetta N 2012d Does the Sun work as a nuclear fu-sion amplifier of planetary tidal forcing A proposal fora physical mechanism based on the mass-luminosity rela-tion Journal of Atmospheric and Solar-Terrestrial Physics81-82 27-40

Scafetta N 2013a Solar and planetary oscillation controlon climate change hind-cast forecast and a comparisonwith the CMIP5 GCMs Energy amp Environment 24(3-4)455496

41

Hansen J Fung I Lacis A Rind D Lebedeff SRuedy R Russell G Stone P 1988 Global climatechanges as forecast by Goddard Institute for Space Stud-ies three-dimensional model J Geophys Res 93 9341-9364

Hansen J Sato M Kharecha P von Schuckmann K2011 Earthrsquos energy imbalance and implications AtmosChem Phys 11 13421-13449

Hegerl CG Crowley TJ Hyde WT Frame DJ2006 Climate sensitivity constrained by temperature re-constructions over the past seven centuries Nature 4401029-1032

House MR 1995 Orbital forcing timescales an introduc-tion Geological Society London Special Publications 851-18

Hoyt DV Schatten KH 1993 A Discussion of PlausibleSolar Irradiance Variations 1700-1992 J of GeophysicalResearch 98 18895-18906

Hoyt DV Schatten KH 1997 The Role of the Sun inthe Climate Change Oxford Univ Press New York

Humlum O Solheim J-E Stordahl K 2011 Identify-ing natural contributions to late Holocene climate changeGlobal and Planetary Change 79 145-156

Hung C-C 2007 Apparent Relations Between Solar Ac-tivity and Solar Tides Caused by the Planets NASATM-2007-214817

Imbers J Lopez A Huntingford C Allen MR2013 Testing the robustness of the anthropogenic cli-mate change detection statements using different empiri-cal models J Geophys Res 118 3192-3199

Iyengar RN 2009 Monsoon rainfall cycles as depicted inancient Sanskrit texts Current Science 97 444-447

IPCC Solomon S et al (eds) 2007 in Climate Change2007 The Physical Science BasisContribution of Work-ing Group I to the Fourth Assessment Report of the Inter-governmental Panel on Climate Change Cambridge Uni-versity Press Cambridge

Jevrejeva S Moore JCGrinsted A P Woodworth2008 Recent global sea level acceleration started over 200years ago Geophys Res Lett 35 L08715

Kaufmann RK Kauppi H Mann ML Stock JH 2011Reconciling anthropogenic climate change with observedtemperature 19982008 PNAS 108 1179011793

Keeling CD Whorf TP 1997a Possible forcing of globaltemperature by the oceanic tides PNAS 94 8321-8328

Keeling CD Whorf TP 1997b The 1800-year oceanictidal cycle A possible cause of rapid climate changePNAS 97 3814-3819

Kepler J 1601 On the More Certain Fundamentals of As-trology In Brackenridge JB and Rossi MA (Eds)Proceedings of the American Philosophical Society 123(2)85-116 (1979)

Kerr RA 2001 A variable Sun paces millennial climateScience 294 1431-1433

Kirkby J 2007 Cosmic rays and climate Surveys in Geo-physics 28 333375

Klyashtorin LB Borisov V Lyubushin A 2009 Cyclicchanges of climate and major commercial stocks of theBarents Sea Mar Biol Res 5 4-17

Knight J Kenned JJ Folland C Harris G JonesGS Palmer M Parke D Scaife A Stott P 2009Do global temperature trends over the last decade falsifyclimate predictions in ldquoState of the Climate in 2008rdquoBull Amer Meteor Soc 90 (8) S1S196

Knudsen MF Seidenkrantz M-S Jacobsen BH andKuijpers A 2011 Tracking the Atlantic MultidecadalOscillation through the last 8000 years Nature Commu-nications 2 178

Kobashi T Severinghaus JP Barnola J-M KawamuraK Carter T Nakaegawa T 2010 Persistent multi-decadal Greenland temperature fluctuation through thelast millennium Climatic Change 100 733-756

Kokfelt U Muscheler R 2013 Solar forcing of climateduring the last millennium recorded in lake sedimentsfrom northern Sweden The Holocene 23(3) 447-452 Doi1011770959683612460781

Kopp G Lean JL 2011 A New Lower Value of To-tal Solar Irradiance Evidence and Climate SignificanceGeophys Res Letters 38 L01706

Landscheidt T 1999 Extrema in sunspot cycle linked toSuns motion Solar Physics 189 415-426

Lean JL Rind DH 2008 How natural and anthro-pogenic influences alter global and regional surface tem-peratures 1889 to 2006 Geophys Res Lett 35 L18701

Lewis N 2013 An objective Bayesian improved approachfor applying optimal fingerprint techniques to estimate cli-mate sensitivity Journal of Climate DOI101175JCLI-D-12-004731

Lindzen RS Choi Y-S 2009 On the determination ofclimate feedbacks from erbe data Geophys Res Lett 36L16705

Lindzen RS and Choi Y-S 2011 On the observationaldetermination of climate sensitivity and its implicationsAsia Pacific J Atmos Sci 47 377-390

Liu J Wang B Cane MA Yim S-Y Lee J-Y 2013Divergent global precipitation changes induced by naturalversus anthropogenic forcing Nature 493 656-659

39

Ljungqvist FC 2010 A new reconstruction of temperaturevariability in the extra-tropical Northern Hemisphere dur-ing the last two millennia Geogra-fiska Annaler Series A92 339-351

Lockwood M 2011 Shining a light on solar impacts Na-ture Climate Change 1 (2) 98-99

Lockwood M 2012 Solar influence on global and re-gional climates Surveys in Geophysics pages 1-32 DOI101007s10712-012-9181-3

Loehle C Mc Culloch JH 2008 Correction to A 2000-year global temperature reconstruction based on non-treering proxies Energy amp Environment 19 93-100

Loehle C Scafetta N 2011 Climate Change AttributionUsing Empirical Decomposition of Climatic Data TheOpen Atmospheric Science J 5 74-86

Lu Q-B 2009 Correlation between Cosmic Rays andOzone Depletion Phys Rev Lett 102 118501

Luterbacher J Schmutz C Gyalistras D Xoplaki E Wan-ner H 1999 Reconstruction of monthly NAO and EU in-dices back to AD 1675 Geophys Res Lett 26 2745-2748

Luterbacher J Xoplaki E Dietrich D Jones PD DaviesTD Portis D Gonzalez-Rouco JF von Storch HGyalistras D Casty C Wanner H 2002 ExtendingNorth Atlantic Oscillation reconstructions back to 1500Atmos Sci Lett doi101006asle20010044

Mann ME Bradley RS Hughes MK 1999 North-ern hemisphere temperatures during the past millenniumInferences uncertainties and limitations Geophys ResLett 26(6) 759-762

Mann ME Jones PD 2003 Global surface temperatureover the past two millennia Geophy Res Lett 30 1820-1824

Mann ME Zhang Z Hughes MK Bradley RSMiller SK Rutherford S Ni F 2008 Proxy-basedreconstructions of hemispheric and global surface temper-ature variations over the past two millennia PNAS 10513252-13257

Manzi V Gennari R Lugli S Roveri M ScafettaN Schreiber C 2012 High-frequency cyclicity in theMediterranean Messinian evaporites evidence for solar-lunar climate forcing J of Sedimentary Research 82 991-1005

Marsquosar A 886 On Historical Astrology - The Book of Re-ligions and Dynasties (On the Great Conjunctions) KYamamoto and C Burnett Eds Brill 2000

Mazzarella A Scafetta N 2012 Evidences for a quasi 60-year North Atlantic Oscillation since 1700 and its meaningfor global climate change Theor Appl Climatol 107(3-4) 599-609

McKitrick RR Michaels PJ 2007 Quantifying the in-fluence of anthropogenic surface processes and inhomo-geneities on gridded global climate data J Geophys Res112 D24S09

McKitrick RR Nierenberg N 2010 Socioeconomic Pat-terns in Climate Data Journal of Economic and SocialMeasurement 35 149-175

McShane B B Wyner A J 2011 A statistical analysis ofmultiple temperature proxies Are reconstructions of sur-face temperatures over the last 1000 years reliable AnnAppl Statist 5 5-44

Meehl GA Arblaster JM Fasullo JT Hu A Tren-berth KE 2011 Model-based evidence of deep-oceanheat uptake during surface-temperature hiatus periodsNature Climate Change 1 360-364

Moberg A Sonechkin DM Holmgren K DatsenkoNM Karlen W 2005 Highly variable Northern Hemi-sphere temperatures reconstructed from low- and high-resolution proxy data Nature 433 613-617

Morice CP Kennedy JJ Rayner NA Jones PD2012 Quantifying uncertainties in global and regionaltemperature change using an ensemble of observational es-timates The HadCRUT4 dataset J Geophys Res 117D08101

Morner N-A 1989 Changes in the Earths rate of rotationon an El Nino to century basis In Geomagnetism andPaleomagnetism (FJ Lowes et al eds) 45-53 KluwerAcad Publ

Morner N-A 1990 The Earths differential rotation hy-drospheric changes Geophysical Monographs 59 27-32AGU and IUGG 1990

Morner N-A 2012 Planetary beat solar wind and terres-trial climate In Solar wind emission technologies andimpacts p 47-66 Ed Escarope Borrega C D and AFBeiros Cruz eds (Nova Publ Co)

Le Mouel J-L Courtillot V Blanter E Shnirman M2008 Evidence for a solar signature in 20th-century tem-perature data from the USA and Europe Geoscience 340421-430

Nam C Bony S DufresneJ-L Chepfer H 2012 Thelsquotoo few too brightrsquo tropical low-cloud problem in CMIP5models Geophys Res Lett 39 L21801

Neukom R Luterbacher J Villalba R Kttel M FrankD Jones P Grosjean M Wanner H Aravena J-CBlack D Christie D DrsquoArrigo R Lara A MoralesM Soliz-Gamboa C Srur A Urrutia R Gunten L2011 Multiproxy summer and winter surface air tempera-ture field reconstructions for southern South America cov-ering the past centuries Climate Dynamics 37 35-51

40

Ogurtsov MG Nagovitsyn YA Kocharov GEJungner H 2002 Long-period cycles of the Sunrsquos activ-ity recorded in direct solar data and proxies Solar Phys211 371-394

Oppo DW Rosenthal Y Linsley BK 2009 2000-year-long temperature and hydrology reconstructions from theIndo-Pacific warm pool Nature 460 1113-1116

Parker DE Legg TP Folland CK 1992 A new dailyCentral England Temperature Series 1772-1991 Interna-tional Journal of Climate 12 317-342

Pierce JR Adams PJ 2009 Can cosmic rays affect cloudcondensation nuclei by altering new particle formationrates Geophys Res Lett 36 L09820

Press WH Teukolsky SA Vetterling WT FlanneryBP 1997 Numerical Recipes in C Cambridge UniversityPress Cambridge

Ptolemy C 2nd century Tetrabiblos FE Robbins Ed1940 Harvard University Press Loeb Classical LibraryCambridge MA

Qian W-H Lu B 2010 Periodic oscillations in millennialglobal-mean temperature and their causes Chinese SciBull 55 4052-4057

Rahmstorf S 2008 Anthropogenic Climate Change Re-visiting the Facts pp 34-53 In Zedillo E Ed GlobalWarming Looking Beyond Kyoto Brookings InstitutionPress

Reichler T Kim J Manzini E Kroger J 2012 A strato-spheric connection to Atlantic climate variability NatureGeoscience 5 783-787

Remer LA et al 2008 Global aerosol climatology fromthe MODIS satellite sensors J Geophys Res 113D14S07

Ring MJ Lindner D Cross EF Schlesinger ME2012 Causes of the Global Warming Observed since the19th Century Atmospheric and Climate Sciences 2(4)401-415

Santer B D Thorne P W Haimberger L Taylor KE Wigley T M L Lanzante J R Solomon S FreeM Gleckler P J Jones P D Karl T R Klein SA Mears C Nychka D Schmidt G A SherwoodS C Wentz F J 2008 Consistency of modelled andobserved temperature trends in the tropical troposphereInternational Journal of Climatology 28 1703-1722

Scafetta N Grigolini P 2002 Scaling detection in timeseries diffusion entropy analysis Physical Review E 66036130

Scafetta N Grigolini P Imholt T Roberts JA WestBJ 2004 Solar turbulence in earthrsquos global and regionaltemperature anomalies Phys Rev E 69 026303

Scafetta N West B J 2005 Estimated solar contributionto the global surface warming using the ACRIM TSI satel-lite composite Geophysical Research Letters 32 L18713

Scafetta N West BJ 2006 Phenomenological solar sig-nature in 400 years of reconstructed Northern Hemi-sphere temperature record Geophysical Research Letters33(17) L17718

Scafetta N and West BJ 2007 Phenomenological recon-structions of the solar signature in the Northern Hemi-sphere surface temperature records since 1600 J Geo-phys Res 112 D24S03

Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

Scafetta N 2012a A shared frequency set between thehistorical mid-latitude aurora records and the global sur-face temperature J of Atmospheric and Solar-TerrestrialPhysics 74 145-163

Scafetta N 2012b Testing an astronomically baseddecadal-scale empirical harmonic climate model versus theIPCC (2007) general circulation climate models Journalof Atmospheric and Solar-Terrestrial Physics 80 124-137

Scafetta N 2012c Multi-scale harmonic model for solarand climate cyclical variation throughout the Holocenebased on Jupiter-Saturn tidal frequencies plus the 11-yearsolar dynamo cycle Journal of Atmospheric and Solar-Terrestrial Physics 80 296-311

Scafetta N 2012d Does the Sun work as a nuclear fu-sion amplifier of planetary tidal forcing A proposal fora physical mechanism based on the mass-luminosity rela-tion Journal of Atmospheric and Solar-Terrestrial Physics81-82 27-40

Scafetta N 2013a Solar and planetary oscillation controlon climate change hind-cast forecast and a comparisonwith the CMIP5 GCMs Energy amp Environment 24(3-4)455496

41

Ljungqvist FC 2010 A new reconstruction of temperaturevariability in the extra-tropical Northern Hemisphere dur-ing the last two millennia Geogra-fiska Annaler Series A92 339-351

Lockwood M 2011 Shining a light on solar impacts Na-ture Climate Change 1 (2) 98-99

Lockwood M 2012 Solar influence on global and re-gional climates Surveys in Geophysics pages 1-32 DOI101007s10712-012-9181-3

Loehle C Mc Culloch JH 2008 Correction to A 2000-year global temperature reconstruction based on non-treering proxies Energy amp Environment 19 93-100

Loehle C Scafetta N 2011 Climate Change AttributionUsing Empirical Decomposition of Climatic Data TheOpen Atmospheric Science J 5 74-86

Lu Q-B 2009 Correlation between Cosmic Rays andOzone Depletion Phys Rev Lett 102 118501

Luterbacher J Schmutz C Gyalistras D Xoplaki E Wan-ner H 1999 Reconstruction of monthly NAO and EU in-dices back to AD 1675 Geophys Res Lett 26 2745-2748

Luterbacher J Xoplaki E Dietrich D Jones PD DaviesTD Portis D Gonzalez-Rouco JF von Storch HGyalistras D Casty C Wanner H 2002 ExtendingNorth Atlantic Oscillation reconstructions back to 1500Atmos Sci Lett doi101006asle20010044

Mann ME Bradley RS Hughes MK 1999 North-ern hemisphere temperatures during the past millenniumInferences uncertainties and limitations Geophys ResLett 26(6) 759-762

Mann ME Jones PD 2003 Global surface temperatureover the past two millennia Geophy Res Lett 30 1820-1824

Mann ME Zhang Z Hughes MK Bradley RSMiller SK Rutherford S Ni F 2008 Proxy-basedreconstructions of hemispheric and global surface temper-ature variations over the past two millennia PNAS 10513252-13257

Manzi V Gennari R Lugli S Roveri M ScafettaN Schreiber C 2012 High-frequency cyclicity in theMediterranean Messinian evaporites evidence for solar-lunar climate forcing J of Sedimentary Research 82 991-1005

Marsquosar A 886 On Historical Astrology - The Book of Re-ligions and Dynasties (On the Great Conjunctions) KYamamoto and C Burnett Eds Brill 2000

Mazzarella A Scafetta N 2012 Evidences for a quasi 60-year North Atlantic Oscillation since 1700 and its meaningfor global climate change Theor Appl Climatol 107(3-4) 599-609

McKitrick RR Michaels PJ 2007 Quantifying the in-fluence of anthropogenic surface processes and inhomo-geneities on gridded global climate data J Geophys Res112 D24S09

McKitrick RR Nierenberg N 2010 Socioeconomic Pat-terns in Climate Data Journal of Economic and SocialMeasurement 35 149-175

McShane B B Wyner A J 2011 A statistical analysis ofmultiple temperature proxies Are reconstructions of sur-face temperatures over the last 1000 years reliable AnnAppl Statist 5 5-44

Meehl GA Arblaster JM Fasullo JT Hu A Tren-berth KE 2011 Model-based evidence of deep-oceanheat uptake during surface-temperature hiatus periodsNature Climate Change 1 360-364

Moberg A Sonechkin DM Holmgren K DatsenkoNM Karlen W 2005 Highly variable Northern Hemi-sphere temperatures reconstructed from low- and high-resolution proxy data Nature 433 613-617

Morice CP Kennedy JJ Rayner NA Jones PD2012 Quantifying uncertainties in global and regionaltemperature change using an ensemble of observational es-timates The HadCRUT4 dataset J Geophys Res 117D08101

Morner N-A 1989 Changes in the Earths rate of rotationon an El Nino to century basis In Geomagnetism andPaleomagnetism (FJ Lowes et al eds) 45-53 KluwerAcad Publ

Morner N-A 1990 The Earths differential rotation hy-drospheric changes Geophysical Monographs 59 27-32AGU and IUGG 1990

Morner N-A 2012 Planetary beat solar wind and terres-trial climate In Solar wind emission technologies andimpacts p 47-66 Ed Escarope Borrega C D and AFBeiros Cruz eds (Nova Publ Co)

Le Mouel J-L Courtillot V Blanter E Shnirman M2008 Evidence for a solar signature in 20th-century tem-perature data from the USA and Europe Geoscience 340421-430

Nam C Bony S DufresneJ-L Chepfer H 2012 Thelsquotoo few too brightrsquo tropical low-cloud problem in CMIP5models Geophys Res Lett 39 L21801

Neukom R Luterbacher J Villalba R Kttel M FrankD Jones P Grosjean M Wanner H Aravena J-CBlack D Christie D DrsquoArrigo R Lara A MoralesM Soliz-Gamboa C Srur A Urrutia R Gunten L2011 Multiproxy summer and winter surface air tempera-ture field reconstructions for southern South America cov-ering the past centuries Climate Dynamics 37 35-51

40

Ogurtsov MG Nagovitsyn YA Kocharov GEJungner H 2002 Long-period cycles of the Sunrsquos activ-ity recorded in direct solar data and proxies Solar Phys211 371-394

Oppo DW Rosenthal Y Linsley BK 2009 2000-year-long temperature and hydrology reconstructions from theIndo-Pacific warm pool Nature 460 1113-1116

Parker DE Legg TP Folland CK 1992 A new dailyCentral England Temperature Series 1772-1991 Interna-tional Journal of Climate 12 317-342

Pierce JR Adams PJ 2009 Can cosmic rays affect cloudcondensation nuclei by altering new particle formationrates Geophys Res Lett 36 L09820

Press WH Teukolsky SA Vetterling WT FlanneryBP 1997 Numerical Recipes in C Cambridge UniversityPress Cambridge

Ptolemy C 2nd century Tetrabiblos FE Robbins Ed1940 Harvard University Press Loeb Classical LibraryCambridge MA

Qian W-H Lu B 2010 Periodic oscillations in millennialglobal-mean temperature and their causes Chinese SciBull 55 4052-4057

Rahmstorf S 2008 Anthropogenic Climate Change Re-visiting the Facts pp 34-53 In Zedillo E Ed GlobalWarming Looking Beyond Kyoto Brookings InstitutionPress

Reichler T Kim J Manzini E Kroger J 2012 A strato-spheric connection to Atlantic climate variability NatureGeoscience 5 783-787

Remer LA et al 2008 Global aerosol climatology fromthe MODIS satellite sensors J Geophys Res 113D14S07

Ring MJ Lindner D Cross EF Schlesinger ME2012 Causes of the Global Warming Observed since the19th Century Atmospheric and Climate Sciences 2(4)401-415

Santer B D Thorne P W Haimberger L Taylor KE Wigley T M L Lanzante J R Solomon S FreeM Gleckler P J Jones P D Karl T R Klein SA Mears C Nychka D Schmidt G A SherwoodS C Wentz F J 2008 Consistency of modelled andobserved temperature trends in the tropical troposphereInternational Journal of Climatology 28 1703-1722

Scafetta N Grigolini P 2002 Scaling detection in timeseries diffusion entropy analysis Physical Review E 66036130

Scafetta N Grigolini P Imholt T Roberts JA WestBJ 2004 Solar turbulence in earthrsquos global and regionaltemperature anomalies Phys Rev E 69 026303

Scafetta N West B J 2005 Estimated solar contributionto the global surface warming using the ACRIM TSI satel-lite composite Geophysical Research Letters 32 L18713

Scafetta N West BJ 2006 Phenomenological solar sig-nature in 400 years of reconstructed Northern Hemi-sphere temperature record Geophysical Research Letters33(17) L17718

Scafetta N and West BJ 2007 Phenomenological recon-structions of the solar signature in the Northern Hemi-sphere surface temperature records since 1600 J Geo-phys Res 112 D24S03

Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

Scafetta N 2012a A shared frequency set between thehistorical mid-latitude aurora records and the global sur-face temperature J of Atmospheric and Solar-TerrestrialPhysics 74 145-163

Scafetta N 2012b Testing an astronomically baseddecadal-scale empirical harmonic climate model versus theIPCC (2007) general circulation climate models Journalof Atmospheric and Solar-Terrestrial Physics 80 124-137

Scafetta N 2012c Multi-scale harmonic model for solarand climate cyclical variation throughout the Holocenebased on Jupiter-Saturn tidal frequencies plus the 11-yearsolar dynamo cycle Journal of Atmospheric and Solar-Terrestrial Physics 80 296-311

Scafetta N 2012d Does the Sun work as a nuclear fu-sion amplifier of planetary tidal forcing A proposal fora physical mechanism based on the mass-luminosity rela-tion Journal of Atmospheric and Solar-Terrestrial Physics81-82 27-40

Scafetta N 2013a Solar and planetary oscillation controlon climate change hind-cast forecast and a comparisonwith the CMIP5 GCMs Energy amp Environment 24(3-4)455496

41

Ogurtsov MG Nagovitsyn YA Kocharov GEJungner H 2002 Long-period cycles of the Sunrsquos activ-ity recorded in direct solar data and proxies Solar Phys211 371-394

Oppo DW Rosenthal Y Linsley BK 2009 2000-year-long temperature and hydrology reconstructions from theIndo-Pacific warm pool Nature 460 1113-1116

Parker DE Legg TP Folland CK 1992 A new dailyCentral England Temperature Series 1772-1991 Interna-tional Journal of Climate 12 317-342

Pierce JR Adams PJ 2009 Can cosmic rays affect cloudcondensation nuclei by altering new particle formationrates Geophys Res Lett 36 L09820

Press WH Teukolsky SA Vetterling WT FlanneryBP 1997 Numerical Recipes in C Cambridge UniversityPress Cambridge

Ptolemy C 2nd century Tetrabiblos FE Robbins Ed1940 Harvard University Press Loeb Classical LibraryCambridge MA

Qian W-H Lu B 2010 Periodic oscillations in millennialglobal-mean temperature and their causes Chinese SciBull 55 4052-4057

Rahmstorf S 2008 Anthropogenic Climate Change Re-visiting the Facts pp 34-53 In Zedillo E Ed GlobalWarming Looking Beyond Kyoto Brookings InstitutionPress

Reichler T Kim J Manzini E Kroger J 2012 A strato-spheric connection to Atlantic climate variability NatureGeoscience 5 783-787

Remer LA et al 2008 Global aerosol climatology fromthe MODIS satellite sensors J Geophys Res 113D14S07

Ring MJ Lindner D Cross EF Schlesinger ME2012 Causes of the Global Warming Observed since the19th Century Atmospheric and Climate Sciences 2(4)401-415

Santer B D Thorne P W Haimberger L Taylor KE Wigley T M L Lanzante J R Solomon S FreeM Gleckler P J Jones P D Karl T R Klein SA Mears C Nychka D Schmidt G A SherwoodS C Wentz F J 2008 Consistency of modelled andobserved temperature trends in the tropical troposphereInternational Journal of Climatology 28 1703-1722

Scafetta N Grigolini P 2002 Scaling detection in timeseries diffusion entropy analysis Physical Review E 66036130

Scafetta N Grigolini P Imholt T Roberts JA WestBJ 2004 Solar turbulence in earthrsquos global and regionaltemperature anomalies Phys Rev E 69 026303

Scafetta N West B J 2005 Estimated solar contributionto the global surface warming using the ACRIM TSI satel-lite composite Geophysical Research Letters 32 L18713

Scafetta N West BJ 2006 Phenomenological solar sig-nature in 400 years of reconstructed Northern Hemi-sphere temperature record Geophysical Research Letters33(17) L17718

Scafetta N and West BJ 2007 Phenomenological recon-structions of the solar signature in the Northern Hemi-sphere surface temperature records since 1600 J Geo-phys Res 112 D24S03

Scafetta N 2008 Comment on lsquoHeat capacity time con-stant and sensitivity of Earthrsquos climate systemrsquo bySchwartz Journal of Geophysical Research 113 D15104

Scafetta N 2009a Empirical analysis of the solar contri-bution to global mean air surface temperature changeJournal of Atmospheric and Solar-Terrestrial Physics 711916-1923

Scafetta N 2009b Comments on ldquoSolar Trends And GlobalWarmingrdquo by Benestad and Schmidt Climate ScienceRoger Pielke Sr httppielkeclimatesciwordpresscom

Scafetta N Willson RC 2009 ACRIM-gap and TSItrend issue resolved using a surface magnetic flux TSIproxy model Geophys Res Lett 36 L05701

Scafetta N 2010 Empirical evidence for a celestial originof the climate oscillations and its implications J of At-mospheric and Solar-Terrestrial Physics 72 951-970

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43

Table 2 See Section 31 The regression coefficients are evaluatedusing Eq 7 for all available 162 GCM simulations and for theirensemble mean (which is numbered -0- in the list) The table re-ports the χ2 test values which were calculated using Eq 13 andthe root-mean-square deviation (RMSD) values for each simula-tions from the harmonic model Eq 6 which were calculated usinga 49-month running mean of the original time sequences See alsoFigure 12

Model Simulation α α α α β γ χ2 RMSD (60-years) (20-years) (104=years) (91-years) (upward trend) (bias)

GST 1 plusmn 005 1 plusmn 012 1 plusmn 017 1 plusmn 011 1 plusmn 002 00 plusmn 001 0 005

0 GCM mean 063 plusmn 003 073 plusmn 008 044 plusmn 012 040 plusmn 008 104 plusmn 001 -055 plusmn 000 143 009

1 ACCESS1-0 0 039 plusmn 005 092 plusmn 014 088 plusmn 020 070 plusmn 013 084 plusmn 002 012 plusmn 001 214 014

2 ACCESS1-3 0 046 plusmn 005 089 plusmn 012 105 plusmn 017 002 plusmn 012 058 plusmn 002 008 plusmn 000 694 0143 1 067 plusmn 005 081 plusmn 012 023 plusmn 017 -007 plusmn 012 051 plusmn 002 007 plusmn 000 817 0154 2 075 plusmn 004 133 plusmn 011 008 plusmn 016 -003 plusmn 011 039 plusmn 002 006 plusmn 000 1236 015

5 bcc-csm1-1 0 129 plusmn 005 062 plusmn 014 019 plusmn 019 055 plusmn 013 142 plusmn 002 017 plusmn 001 514 0146 1 064 plusmn 006 041 plusmn 014 059 plusmn 020 103 plusmn 014 172 plusmn 002 022 plusmn 001 1299 0197 2 077 plusmn 006 069 plusmn 015 060 plusmn 022 057 plusmn 015 150 plusmn 002 019 plusmn 001 583 017

8 bcc-csm1-1-m 0 040 plusmn 006 083 plusmn 015 081 plusmn 022 048 plusmn 015 144 plusmn 002 020 plusmn 001 557 0169 1 031 plusmn 007 073 plusmn 017 119 plusmn 025 109 plusmn 017 146 plusmn 003 018 plusmn 001 541 01810 2 025 plusmn 007 107 plusmn 019 068 plusmn 026 101 plusmn 018 165 plusmn 003 023 plusmn 001 866 022

11 BNU-ESM 0 082 plusmn 006 112 plusmn 016 019 plusmn 023 -018 plusmn 016 178 plusmn 002 027 plusmn 001 1315 020

12 CanESM2 0 088 plusmn 007 085 plusmn 017 014 plusmn 024 004 plusmn 017 117 plusmn 003 017 plusmn 001 123 01513 1 117 plusmn 006 139 plusmn 016 051 plusmn 023 066 plusmn 015 105 plusmn 002 015 plusmn 001 35 01314 2 089 plusmn 006 048 plusmn 016 060 plusmn 022 083 plusmn 015 110 plusmn 002 016 plusmn 001 45 01315 3 085 plusmn 006 100 plusmn 016 078 plusmn 022 -022 plusmn 015 116 plusmn 002 017 plusmn 001 146 01316 4 117 plusmn 006 120 plusmn 016 111 plusmn 023 011 plusmn 015 119 plusmn 002 017 plusmn 001 127 014

17 CCSM4 0 074 plusmn 006 075 plusmn 015 103 plusmn 022 013 plusmn 015 158 plusmn 002 024 plusmn 001 815 01718 1 074 plusmn 005 068 plusmn 014 -002 plusmn 020 047 plusmn 013 164 plusmn 002 025 plusmn 001 1077 01619 2 063 plusmn 006 027 plusmn 015 083 plusmn 021 082 plusmn 014 155 plusmn 002 024 plusmn 001 780 01520 3 059 plusmn 006 060 plusmn 015 -006 plusmn 022 098 plusmn 015 159 plusmn 002 024 plusmn 001 854 01721 4 058 plusmn 006 045 plusmn 015 073 plusmn 021 028 plusmn 014 160 plusmn 002 024 plusmn 001 928 01722 5 056 plusmn 005 116 plusmn 014 083 plusmn 020 075 plusmn 014 159 plusmn 002 025 plusmn 001 926 016

23 CESM1-BGC 0 067 plusmn 005 045 plusmn 014 109 plusmn 020 107 plusmn 014 150 plusmn 002 023 plusmn 001 646 015

24 CESM1-CAM5 0 029 plusmn 005 066 plusmn 012 030 plusmn 017 078 plusmn 012 088 plusmn 002 013 plusmn 000 279 01125 1 101 plusmn 005 101 plusmn 012 080 plusmn 017 058 plusmn 012 079 plusmn 002 011 plusmn 000 137 01026 2 099 plusmn 005 055 plusmn 013 141 plusmn 018 048 plusmn 012 092 plusmn 002 013 plusmn 000 57 010

27 CESM1-CAM5-1-FV2 0 087 plusmn 006 004 plusmn 016 132 plusmn 023 063 plusmn 016 071 plusmn 002 009 plusmn 001 222 01528 1 105 plusmn 006 034 plusmn 014 148 plusmn 020 008 plusmn 014 072 plusmn 002 010 plusmn 001 271 01129 2 077 plusmn 005 -008 plusmn 014 011 plusmn 020 -005 plusmn 014 085 plusmn 002 012 plusmn 001 238 01130 3 061 plusmn 006 064 plusmn 016 -006 plusmn 022 016 plusmn 015 081 plusmn 002 011 plusmn 001 203 013

31 CESM1-FASTCHEM 0 062 plusmn 006 079 plusmn 015 025 plusmn 021 092 plusmn 014 172 plusmn 002 026 plusmn 001 1228 01932 1 077 plusmn 006 097 plusmn 014 072 plusmn 020 052 plusmn 014 166 plusmn 002 025 plusmn 001 1068 01633 2 058 plusmn 006 086 plusmn 014 060 plusmn 021 115 plusmn 014 182 plusmn 002 028 plusmn 001 1618 020

34 CESM1-WACCM 0 065 plusmn 006 059 plusmn 015 -047 plusmn 022 089 plusmn 015 155 plusmn 002 023 plusmn 001 760 017

35 CMCC-CESM 0 050 plusmn 007 001 plusmn 018 -015 plusmn 025 -011 plusmn 017 049 plusmn 003 007 plusmn 001 674 016

36 CMCC-CM 0 056 plusmn 005 -055 plusmn 012 104 plusmn 017 009 plusmn 011 089 plusmn 002 014 plusmn 000 350 012

37 CMCC-CMS 0 066 plusmn 006 049 plusmn 015 098 plusmn 021 -017 plusmn 014 063 plusmn 002 009 plusmn 001 441 016

38 CNRM-CM5 0 042 plusmn 006 096 plusmn 015 113 plusmn 021 039 plusmn 014 092 plusmn 002 014 plusmn 001 156 01339 1 067 plusmn 005 124 plusmn 012 072 plusmn 017 081 plusmn 012 099 plusmn 002 014 plusmn 000 56 00840 2 070 plusmn 005 127 plusmn 013 054 plusmn 019 064 plusmn 013 091 plusmn 002 014 plusmn 000 75 01141 3 092 plusmn 005 057 plusmn 013 035 plusmn 018 094 plusmn 012 120 plusmn 002 018 plusmn 000 139 01142 4 056 plusmn 005 093 plusmn 014 101 plusmn 020 055 plusmn 013 085 plusmn 002 014 plusmn 001 137 01243 5 045 plusmn 005 098 plusmn 013 098 plusmn 019 059 plusmn 013 110 plusmn 002 018 plusmn 000 153 01144 6 120 plusmn 005 097 plusmn 013 056 plusmn 019 070 plusmn 013 095 plusmn 002 014 plusmn 000 35 01045 7 036 plusmn 005 059 plusmn 013 -001 plusmn 019 036 plusmn 013 118 plusmn 002 019 plusmn 000 310 01346 8 071 plusmn 005 021 plusmn 012 073 plusmn 018 086 plusmn 012 074 plusmn 002 012 plusmn 000 271 01147 9 107 plusmn 005 088 plusmn 013 -007 plusmn 018 062 plusmn 012 115 plusmn 002 017 plusmn 000 112 011

48 CSIRO-Mk3-6-0 0 053 plusmn 006 132 plusmn 015 -042 plusmn 022 064 plusmn 015 070 plusmn 002 011 plusmn 001 347 01649 1 098 plusmn 005 035 plusmn 014 107 plusmn 020 -047 plusmn 013 060 plusmn 002 010 plusmn 001 561 01650 2 112 plusmn 005 066 plusmn 013 121 plusmn 018 000 plusmn 012 078 plusmn 002 012 plusmn 000 209 01251 3 088 plusmn 006 139 plusmn 015 105 plusmn 021 030 plusmn 014 045 plusmn 002 006 plusmn 001 756 01752 4 080 plusmn 006 074 plusmn 017 -007 plusmn 024 034 plusmn 016 070 plusmn 002 010 plusmn 001 245 01753 5 060 plusmn 006 077 plusmn 014 054 plusmn 020 035 plusmn 014 069 plusmn 002 011 plusmn 001 318 01554 6 052 plusmn 005 022 plusmn 013 029 plusmn 018 009 plusmn 012 076 plusmn 002 012 plusmn 000 358 01355 7 107 plusmn 006 054 plusmn 014 021 plusmn 020 055 plusmn 014 063 plusmn 002 009 plusmn 001 371 01556 8 036 plusmn 005 -031 plusmn 013 043 plusmn 019 031 plusmn 013 077 plusmn 002 013 plusmn 000 444 01457 9 039 plusmn 005 063 plusmn 014 -022 plusmn 019 001 plusmn 013 080 plusmn 002 013 plusmn 001 360 014

58 EC-EARTH 0 048 plusmn 005 075 plusmn 012 051 plusmn 017 037 plusmn 011 141 plusmn 002 019 plusmn 000 638 01459 1 -013 plusmn 005 108 plusmn 012 094 plusmn 016 006 plusmn 011 154 plusmn 002 021 plusmn 000 1473 01660 2 053 plusmn 005 040 plusmn 012 083 plusmn 017 -004 plusmn 012 135 plusmn 002 019 plusmn 000 547 01361 3 014 plusmn 004 084 plusmn 012 077 plusmn 016 028 plusmn 011 140 plusmn 002 023 plusmn 000 832 01462 4 038 plusmn 005 041 plusmn 012 009 plusmn 017 069 plusmn 011 154 plusmn 002 020 plusmn 000 1059 01563 5 077 plusmn 004 104 plusmn 011 018 plusmn 016 018 plusmn 011 147 plusmn 002 018 plusmn 000 753 01464 6 031 plusmn 005 103 plusmn 012 051 plusmn 017 -001 plusmn 011 144 plusmn 002 019 plusmn 000 862 01465 7 071 plusmn 004 007 plusmn 011 051 plusmn 016 097 plusmn 011 138 plusmn 002 018 plusmn 000 546 01166 8 059 plusmn 005 103 plusmn 012 090 plusmn 017 086 plusmn 012 138 plusmn 002 018 plusmn 000 471 013

67 FGOALS-g2 0 037 plusmn 004 026 plusmn 010 009 plusmn 015 -001 plusmn 010 100 plusmn 002 015 plusmn 000 361 01068 1 072 plusmn 004 010 plusmn 010 001 plusmn 014 -003 plusmn 010 095 plusmn 001 010 plusmn 000 254 00869 2 071 plusmn 004 -007 plusmn 011 005 plusmn 016 -005 plusmn 011 095 plusmn 002 014 plusmn 000 256 01070 3 049 plusmn 004 047 plusmn 011 015 plusmn 015 008 plusmn 010 084 plusmn 002 010 plusmn 000 326 01171 4 051 plusmn 004 014 plusmn 010 -004 plusmn 015 -004 plusmn 010 095 plusmn 002 012 plusmn 000 323 010

72 FIO-ESM 0 031 plusmn 005 026 plusmn 014 057 plusmn 020 002 plusmn 014 133 plusmn 002 021 plusmn 001 538 01373 1 035 plusmn 005 069 plusmn 013 085 plusmn 018 012 plusmn 013 123 plusmn 002 019 plusmn 000 367 01074 2 036 plusmn 005 -011 plusmn 013 -040 plusmn 019 019 plusmn 013 146 plusmn 002 023 plusmn 000 890 013

75 GFDL-CM3 0 160 plusmn 006 149 plusmn 016 -007 plusmn 023 057 plusmn 016 049 plusmn 002 005 plusmn 001 692 01876 1 139 plusmn 006 101 plusmn 015 110 plusmn 021 047 plusmn 014 056 plusmn 002 007 plusmn 001 522 01577 2 077 plusmn 006 095 plusmn 016 124 plusmn 022 034 plusmn 015 052 plusmn 002 007 plusmn 001 524 01778 3 112 plusmn 007 113 plusmn 017 057 plusmn 025 026 plusmn 017 063 plusmn 003 008 plusmn 001 291 01879 4 127 plusmn 007 111 plusmn 017 012 plusmn 024 098 plusmn 017 027 plusmn 003 002 plusmn 001 1051 021

80 GFDL-ESM2G 0 085 plusmn 007 142 plusmn 017 014 plusmn 024 014 plusmn 016 085 plusmn 003 011 plusmn 001 114 01681 1 019 plusmn 005 127 plusmn 014 080 plusmn 019 010 plusmn 013 089 plusmn 002 013 plusmn 001 336 01282 2 033 plusmn 006 080 plusmn 015 -033 plusmn 021 055 plusmn 014 102 plusmn 002 014 plusmn 001 219 013

83 GFDL-ESM2M 0 022 plusmn 006 048 plusmn 016 018 plusmn 023 040 plusmn 015 095 plusmn 002 013 plusmn 001 246 014

84 GISS-E2-H p1 0 029 plusmn 004 050 plusmn 011 025 plusmn 015 043 plusmn 010 137 plusmn 002 023 plusmn 000 722 01385 1 033 plusmn 004 052 plusmn 010 029 plusmn 015 067 plusmn 010 134 plusmn 002 021 plusmn 000 625 01286 2 035 plusmn 004 022 plusmn 011 051 plusmn 016 067 plusmn 011 130 plusmn 002 021 plusmn 000 531 01287 3 041 plusmn 004 053 plusmn 011 034 plusmn 015 013 plusmn 010 132 plusmn 002 021 plusmn 000 579 01288 4 040 plusmn 004 076 plusmn 010 090 plusmn 014 046 plusmn 010 133 plusmn 001 021 plusmn 000 562 01189 5 040 plusmn 004 073 plusmn 010 041 plusmn 015 065 plusmn 010 124 plusmn 002 016 plusmn 000 387 011

90 GISS-E2-H p2 0 054 plusmn 005 052 plusmn 012 048 plusmn 017 035 plusmn 012 105 plusmn 002 017 plusmn 000 156 01291 1 025 plusmn 005 094 plusmn 012 030 plusmn 017 075 plusmn 011 106 plusmn 002 018 plusmn 000 280 01292 2 043 plusmn 004 091 plusmn 011 016 plusmn 015 054 plusmn 010 112 plusmn 002 018 plusmn 000 239 01193 3 040 plusmn 005 058 plusmn 012 047 plusmn 017 044 plusmn 011 103 plusmn 002 017 plusmn 000 210 01294 4 045 plusmn 004 057 plusmn 010 063 plusmn 015 057 plusmn 010 107 plusmn 002 018 plusmn 000 200 010

44

95 GISS-E2-H p3 0 036 plusmn 005 050 plusmn 012 096 plusmn 018 026 plusmn 012 136 plusmn 002 022 plusmn 000 570 01496 1 032 plusmn 004 055 plusmn 011 020 plusmn 015 070 plusmn 010 166 plusmn 002 026 plusmn 000 1614 01797 2 041 plusmn 005 031 plusmn 012 034 plusmn 017 037 plusmn 011 147 plusmn 002 024 plusmn 000 852 01598 3 065 plusmn 004 072 plusmn 011 045 plusmn 015 044 plusmn 010 142 plusmn 002 023 plusmn 000 636 01399 4 031 plusmn 005 101 plusmn 012 072 plusmn 017 028 plusmn 011 136 plusmn 002 022 plusmn 000 621 014100 5 045 plusmn 005 099 plusmn 012 028 plusmn 017 019 plusmn 011 129 plusmn 002 017 plusmn 000 449 013

101 GISS-E2-H-CC p1 0 037 plusmn 004 077 plusmn 011 043 plusmn 016 050 plusmn 011 160 plusmn 002 023 plusmn 000 1277 016

102 GISS-E2-R p1 0 019 plusmn 004 021 plusmn 011 030 plusmn 015 019 plusmn 010 097 plusmn 002 015 plusmn 000 439 011103 1 031 plusmn 004 103 plusmn 011 076 plusmn 015 032 plusmn 010 110 plusmn 002 017 plusmn 000 302 010104 2 051 plusmn 004 061 plusmn 010 020 plusmn 015 043 plusmn 010 102 plusmn 002 016 plusmn 000 184 009105 3 049 plusmn 004 071 plusmn 011 086 plusmn 016 054 plusmn 011 109 plusmn 002 017 plusmn 000 170 010106 4 027 plusmn 004 105 plusmn 011 078 plusmn 016 036 plusmn 011 115 plusmn 002 018 plusmn 000 339 011107 5 032 plusmn 005 083 plusmn 012 046 plusmn 017 058 plusmn 011 096 plusmn 002 015 plusmn 000 233 012

108 GISS-E2-R p2 0 042 plusmn 004 048 plusmn 011 026 plusmn 016 041 plusmn 011 088 plusmn 002 014 plusmn 000 265 011109 1 063 plusmn 004 -052 plusmn 011 023 plusmn 016 050 plusmn 011 072 plusmn 002 012 plusmn 000 497 013110 2 017 plusmn 004 034 plusmn 011 115 plusmn 016 061 plusmn 011 078 plusmn 002 013 plusmn 000 500 012111 3 058 plusmn 005 068 plusmn 012 080 plusmn 017 055 plusmn 012 065 plusmn 002 010 plusmn 000 432 014112 4 021 plusmn 004 086 plusmn 011 047 plusmn 016 033 plusmn 011 072 plusmn 002 012 plusmn 000 554 013113 5 039 plusmn 004 080 plusmn 011 050 plusmn 015 036 plusmn 010 071 plusmn 002 011 plusmn 000 497 012

114 GISS-E2-R p3 0 031 plusmn 005 078 plusmn 012 046 plusmn 017 028 plusmn 011 095 plusmn 002 015 plusmn 000 270 012115 1 024 plusmn 004 056 plusmn 011 051 plusmn 016 088 plusmn 011 119 plusmn 002 018 plusmn 000 398 011116 2 056 plusmn 005 073 plusmn 012 074 plusmn 018 070 plusmn 012 124 plusmn 002 019 plusmn 000 244 012117 3 045 plusmn 004 129 plusmn 012 063 plusmn 016 001 plusmn 011 117 plusmn 002 019 plusmn 000 312 011118 4 017 plusmn 005 102 plusmn 012 033 plusmn 017 001 plusmn 012 108 plusmn 002 017 plusmn 000 404 012119 5 037 plusmn 004 117 plusmn 012 061 plusmn 016 084 plusmn 011 114 plusmn 002 018 plusmn 000 240 011

120 GISS-E2-R-CC p1 0 027 plusmn 004 052 plusmn 011 045 plusmn 015 038 plusmn 010 109 plusmn 002 015 plusmn 000 338 011

121 HadGEM2-AO 0 122 plusmn 005 156 plusmn 014 156 plusmn 020 038 plusmn 013 080 plusmn 002 010 plusmn 001 169 013

122 HadGEM2-CC 0 098 plusmn 005 077 plusmn 014 021 plusmn 020 049 plusmn 013 030 plusmn 002 003 plusmn 001 1209 019

123 HadGEM2-ES 0 103 plusmn 005 065 plusmn 014 -016 plusmn 020 053 plusmn 013 048 plusmn 002 006 plusmn 001 733 016124 1 076 plusmn 006 109 plusmn 015 006 plusmn 022 065 plusmn 015 049 plusmn 002 006 plusmn 001 630 019125 2 104 plusmn 005 146 plusmn 013 070 plusmn 018 033 plusmn 012 065 plusmn 002 008 plusmn 000 375 013126 3 040 plusmn 006 094 plusmn 015 059 plusmn 021 -044 plusmn 014 068 plusmn 002 009 plusmn 001 497 017

127 inmcm4 0 036 plusmn 003 017 plusmn 009 021 plusmn 012 001 plusmn 008 102 plusmn 001 016 plusmn 000 419 008

128 IPSL-CM5A-LR 0 089 plusmn 006 025 plusmn 015 073 plusmn 021 021 plusmn 014 160 plusmn 002 025 plusmn 001 893 018129 1 106 plusmn 005 067 plusmn 013 -033 plusmn 019 -011 plusmn 013 165 plusmn 002 026 plusmn 000 1223 018130 2 112 plusmn 005 093 plusmn 013 068 plusmn 019 037 plusmn 013 152 plusmn 002 024 plusmn 000 714 015131 3 053 plusmn 006 094 plusmn 014 061 plusmn 020 024 plusmn 014 167 plusmn 002 026 plusmn 001 1169 018132 4 065 plusmn 006 019 plusmn 015 089 plusmn 021 057 plusmn 014 155 plusmn 002 025 plusmn 001 785 017133 5 092 plusmn 005 135 plusmn 014 -006 plusmn 019 008 plusmn 013 136 plusmn 002 021 plusmn 001 431 014

134 IPSL-CM5A-MR 0 055 plusmn 005 096 plusmn 013 065 plusmn 018 042 plusmn 012 130 plusmn 002 021 plusmn 000 357 012135 1 063 plusmn 005 091 plusmn 014 062 plusmn 019 -002 plusmn 013 154 plusmn 002 024 plusmn 001 852 016136 2 086 plusmn 005 047 plusmn 013 044 plusmn 018 016 plusmn 012 166 plusmn 002 026 plusmn 000 1271 017

137 IPSL-CM5B-LR 0 004 plusmn 005 010 plusmn 013 088 plusmn 019 017 plusmn 013 143 plusmn 002 024 plusmn 000 919 016

138 MIROC5 0 088 plusmn 006 001 plusmn 016 125 plusmn 022 015 plusmn 015 070 plusmn 002 007 plusmn 001 294 014139 1 062 plusmn 006 080 plusmn 014 036 plusmn 020 061 plusmn 014 081 plusmn 002 010 plusmn 001 159 013140 2 083 plusmn 005 095 plusmn 014 089 plusmn 020 025 plusmn 013 088 plusmn 002 010 plusmn 001 84 011141 3 052 plusmn 006 024 plusmn 015 106 plusmn 021 024 plusmn 014 068 plusmn 002 007 plusmn 001 374 014142 4 059 plusmn 006 020 plusmn 014 041 plusmn 020 072 plusmn 014 079 plusmn 002 010 plusmn 001 213 014

143 MIROC-ESM 0 084 plusmn 005 049 plusmn 013 035 plusmn 018 080 plusmn 012 115 plusmn 002 018 plusmn 000 108 011144 1 028 plusmn 005 -021 plusmn 014 -070 plusmn 019 016 plusmn 013 112 plusmn 002 018 plusmn 001 455 015145 2 062 plusmn 005 077 plusmn 014 -004 plusmn 019 037 plusmn 013 106 plusmn 002 016 plusmn 001 127 013

146 MIROC-ESM-CHEM 0 049 plusmn 004 136 plusmn 011 -052 plusmn 016 072 plusmn 011 105 plusmn 002 016 plusmn 000 221 010

147 MPI-ESM-LR 0 011 plusmn 006 011 plusmn 015 017 plusmn 022 070 plusmn 015 144 plusmn 002 022 plusmn 001 761 018148 1 009 plusmn 005 041 plusmn 014 057 plusmn 020 107 plusmn 013 154 plusmn 002 024 plusmn 001 1052 016149 2 041 plusmn 006 088 plusmn 014 092 plusmn 020 -081 plusmn 014 131 plusmn 002 020 plusmn 001 563 014

150 MPI-ESM-MR 0 058 plusmn 005 041 plusmn 013 -042 plusmn 019 -051 plusmn 013 140 plusmn 002 021 plusmn 000 722 015151 1 010 plusmn 005 113 plusmn 013 086 plusmn 019 077 plusmn 013 140 plusmn 002 021 plusmn 000 731 014152 2 054 plusmn 005 072 plusmn 012 -002 plusmn 018 060 plusmn 012 139 plusmn 002 020 plusmn 000 543 014

153 MPI-ESM-P 0 039 plusmn 005 071 plusmn 013 117 plusmn 019 005 plusmn 013 146 plusmn 002 023 plusmn 000 751 015154 1 033 plusmn 006 067 plusmn 014 -013 plusmn 020 034 plusmn 014 147 plusmn 002 022 plusmn 001 757 017

155 MRI-CGCM3 0 013 plusmn 005 029 plusmn 012 033 plusmn 017 017 plusmn 012 072 plusmn 002 011 plusmn 000 638 012156 1 042 plusmn 005 060 plusmn 013 039 plusmn 019 046 plusmn 013 052 plusmn 002 008 plusmn 000 763 015157 2 052 plusmn 005 036 plusmn 013 016 plusmn 018 045 plusmn 013 070 plusmn 002 011 plusmn 000 397 013

158 MRI-ESM1 0 054 plusmn 005 056 plusmn 014 -014 plusmn 019 052 plusmn 013 089 plusmn 002 013 plusmn 001 177 011

159 NorESM1-M 0 072 plusmn 005 043 plusmn 012 000 plusmn 018 039 plusmn 012 082 plusmn 002 013 plusmn 000 202 010160 1 042 plusmn 005 063 plusmn 012 -002 plusmn 017 080 plusmn 012 087 plusmn 002 013 plusmn 000 234 011161 2 032 plusmn 005 049 plusmn 013 076 plusmn 018 030 plusmn 012 086 plusmn 002 013 plusmn 000 293 011

162 NorESM1-ME 0 055 plusmn 005 103 plusmn 014 058 plusmn 020 064 plusmn 013 087 plusmn 002 012 plusmn 001 134 011

average 058 plusmn 030 068 plusmn 042 048 plusmn 048 039 plusmn 037 109 plusmn 036 016 plusmn 006 5130 014

45

Table 3 See Sections 32 and 33 The regression coefficients φ usingEq 10 for band-pass frequency scales S1 S2 S3 and S4 for allavailable 162 GCM simulations and for their ensemble mean (whichis numbered -0- in the list) The χ2 test values were calculatedusing Eq 9 Last two columns report the correlation coefficientsbetween the GST power spectrum (periodogram and MEM) andthe correspondent GCM power spectra See also Figures 13 14and 15

model simulation S1 S2 S3 S4 χ2 Corr Coeff Corr Coeff 05-7 years 7-14 years 14-28 years 28-104 years Periodogram MEM

0 ensemble mean 005 036 081 063 86 079 -002

1 ACCESS1-0 0 -005 053 091 051 69 034 008

2 ACCESS1-3 0 006 012 122 055 153 048 -0073 1 -003 -011 114 077 194 063 0124 2 003 -003 122 078 171 081 028

5 bcc-csm1-1 0 003 037 121 108 67 097 0366 1 005 063 092 079 27 079 0197 2 006 062 133 070 51 093 032

8 bcc-csm1-1-m 0 002 057 118 023 120 025 -0119 1 009 100 091 063 21 021 -00610 2 000 083 175 020 183 050 -008

11 BNU-ESM 0 002 029 156 078 128 084 -003

12 CanESM2 0 -006 024 122 075 102 079 00213 1 -002 057 112 111 31 087 00914 2 -003 060 057 087 53 079 00015 3 005 007 086 090 133 077 -00416 4 -001 055 082 111 37 089 025

17 CCSM4 0 008 038 126 068 81 093 00118 1 -001 048 113 061 65 094 04219 2 010 057 067 049 82 093 01120 3 013 069 074 052 58 088 -00821 4 009 030 097 048 113 094 01322 5 003 041 150 049 128 084 004

23 CESM1-BGC 0 002 072 088 051 49 096 -003

24 CESM1-CAM5 0 004 047 068 025 140 081 04025 1 013 057 091 097 29 097 00326 2 003 053 058 111 59 087 006

27 CESM1-CAM5-1-FV2 0 009 037 041 077 118 085 -01128 1 005 028 057 101 105 097 -00229 2 009 -006 026 072 260 098 04530 3 000 034 069 059 103 064 009

31 CESM1-FASTCHEM 0 005 053 130 056 75 087 00632 1 006 063 089 071 34 093 00133 2 003 076 124 044 63 091 001

34 CESM1-WACCM 0 -001 063 143 050 84 090 029

35 CMCC-CESM 0 -004 003 -016 041 389 071 013

36 CMCC-CM 0 004 038 -053 040 459 034 003

37 CMCC-CMS 0 -005 -019 011 036 388 001 -004

38 CNRM-CM5 0 002 062 102 045 67 015 00139 1 -004 062 098 070 34 088 -00140 2 004 041 107 078 59 069 -00141 3 008 060 096 099 24 087 04442 4 009 064 118 053 57 078 00643 5 011 052 097 064 54 046 01344 6 004 054 103 104 32 098 06345 7 000 029 097 054 106 025 -01046 8 007 055 030 063 122 094 01947 9 003 030 092 110 76 088 046

48 CSIRO-Mk3-6-0 0 004 070 107 080 20 022 -01249 1 005 026 066 115 102 057 -01050 2 008 035 066 110 81 090 04651 3 -002 032 148 110 104 057 -00652 4 -003 014 096 122 118 042 -01053 5 007 011 075 085 131 034 -00954 6 008 026 043 054 160 050 -00355 7 004 060 061 117 50 066 -00756 8 004 015 007 048 275 017 00157 9 -006 031 028 062 169 016 -008

58 EC-EARTH 0 003 034 091 045 111 076 -00559 1 007 047 098 002 185 068 02360 2 001 005 089 053 167 087 00861 3 004 034 090 013 178 077 -00862 4 010 059 061 034 113 081 01163 5 001 006 101 081 138 094 00164 6 005 021 084 048 136 083 -00465 7 005 057 060 063 72 081 01466 8 001 075 130 057 51 089 -004

67 FGOALS-g2 0 000 006 019 021 320 048 -00768 1 -003 -004 034 056 252 090 07469 2 -001 -005 -006 046 372 078 08670 3 -001 020 024 033 247 083 -00371 4 -002 003 026 035 284 065 044

72 FIO-ESM 0 003 004 026 019 314 068 -01273 1 001 031 035 017 236 044 -00774 2 005 012 -007 021 377 053 001

75 GFDL-CM3 0 -003 033 106 163 125 087 -00676 1 002 070 082 127 29 098 01177 2 -003 062 052 100 55 055 -01278 3 010 044 094 128 57 058 00279 4 007 032 083 141 98 076 014

80 GFDL-ESM2G 0 005 009 126 081 138 063 01881 1 -002 016 119 031 180 -002 -00282 2 007 025 086 039 142 011 -003

83 GFDL-ESM2M 0 015 035 079 029 143 029 -011

84 GISS-E2-H p1 0 001 037 070 041 123 033 00685 1 005 049 082 036 102 047 02886 2 004 052 062 041 107 037 -00887 3 010 017 066 042 169 072 01688 4 005 053 077 042 92 083 -00689 5 007 047 095 045 88 069 000

90 GISS-E2-H p2 0 003 045 088 057 75 045 -01191 1 006 057 074 037 96 006 -01492 2 004 039 104 057 83 050 00793 3 004 036 109 057 90 029 -01394 4 002 053 080 054 71 053 -003

95 GISS-E2-H p3 0 003 049 091 056 69 057 -007

46

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion

Thorne PW Parker DE Santer BD McCarthy MPSexton DMH Webb MJ Murphy JM Collins MTitchner HA Jones GS 2007 Tropical vertical tem-perature trends A real discrepancy Geophys Res Lett34 16702

Tinsley B A 2008 The global atmospheric electric circuitand its effects on cloud microphysics Reports on Progressin Physics 71 066801

Tyson PD Karlen W Holmgren K Heiss GA 2000The Little Ice Age and medieval warming in South AfricaSouth African Journal of Science 96 121-126

Vieira LEA Solanki SK Krivova NA UsoskinI 2011 Evolution of the solar irradiance during theHolocene Astronomy amp Astrophysics 531 A6

Vonder Haar TH Bytheway J Forsythe JM 2012Weather and climate analyses using improved global wa-ter vapor observations Geophys Res Lett 39 L15802

Wang Y-M Lean JL Sheeley Jr NR 2005 Modelingthe Suns magnetic field and irradiance since 1713 Astro-phys J 625 522-538

Wang Z Wu D Song X Chen X Nicholls S 2012Sun-Moon gravitation-induced wave characteristics andclimate variation J Geophys Res 117 D07102

Willson RC Mordvinov V 2003 Secular total solar ir-radiance trend during solar cycles 21-23 Geophys ResLett 30 1199

Wyatt MG Kravtsov S and Tsonis AA 2012 AtlanticMultidecadal Oscillation and Northern Hemispheres cli-mate variability Climate Dynamics 38 929-949

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Xia X 2012 Significant decreasing cloud cover during19542005 due to more clear-sky days and less overcastdays in China and its relation to aerosol Ann Geophys30 573-582

Yadava MG Ramesh R 2007 Significant longer-term pe-riodicities in the proxy record of the Indian monsoon rain-fall New Astronomy 12 544-555

Zhou J Tung K-K 2012 Deducing Multi-decadal An-thropogenic Global Warming Trends Using Multiple Re-gression Analysis J of the Atmospheric Sciences doi101175JAS-D-12-02081

43

Table 2 See Section 31 The regression coefficients are evaluatedusing Eq 7 for all available 162 GCM simulations and for theirensemble mean (which is numbered -0- in the list) The table re-ports the χ2 test values which were calculated using Eq 13 andthe root-mean-square deviation (RMSD) values for each simula-tions from the harmonic model Eq 6 which were calculated usinga 49-month running mean of the original time sequences See alsoFigure 12

Model Simulation α α α α β γ χ2 RMSD (60-years) (20-years) (104=years) (91-years) (upward trend) (bias)

GST 1 plusmn 005 1 plusmn 012 1 plusmn 017 1 plusmn 011 1 plusmn 002 00 plusmn 001 0 005

0 GCM mean 063 plusmn 003 073 plusmn 008 044 plusmn 012 040 plusmn 008 104 plusmn 001 -055 plusmn 000 143 009

1 ACCESS1-0 0 039 plusmn 005 092 plusmn 014 088 plusmn 020 070 plusmn 013 084 plusmn 002 012 plusmn 001 214 014

2 ACCESS1-3 0 046 plusmn 005 089 plusmn 012 105 plusmn 017 002 plusmn 012 058 plusmn 002 008 plusmn 000 694 0143 1 067 plusmn 005 081 plusmn 012 023 plusmn 017 -007 plusmn 012 051 plusmn 002 007 plusmn 000 817 0154 2 075 plusmn 004 133 plusmn 011 008 plusmn 016 -003 plusmn 011 039 plusmn 002 006 plusmn 000 1236 015

5 bcc-csm1-1 0 129 plusmn 005 062 plusmn 014 019 plusmn 019 055 plusmn 013 142 plusmn 002 017 plusmn 001 514 0146 1 064 plusmn 006 041 plusmn 014 059 plusmn 020 103 plusmn 014 172 plusmn 002 022 plusmn 001 1299 0197 2 077 plusmn 006 069 plusmn 015 060 plusmn 022 057 plusmn 015 150 plusmn 002 019 plusmn 001 583 017

8 bcc-csm1-1-m 0 040 plusmn 006 083 plusmn 015 081 plusmn 022 048 plusmn 015 144 plusmn 002 020 plusmn 001 557 0169 1 031 plusmn 007 073 plusmn 017 119 plusmn 025 109 plusmn 017 146 plusmn 003 018 plusmn 001 541 01810 2 025 plusmn 007 107 plusmn 019 068 plusmn 026 101 plusmn 018 165 plusmn 003 023 plusmn 001 866 022

11 BNU-ESM 0 082 plusmn 006 112 plusmn 016 019 plusmn 023 -018 plusmn 016 178 plusmn 002 027 plusmn 001 1315 020

12 CanESM2 0 088 plusmn 007 085 plusmn 017 014 plusmn 024 004 plusmn 017 117 plusmn 003 017 plusmn 001 123 01513 1 117 plusmn 006 139 plusmn 016 051 plusmn 023 066 plusmn 015 105 plusmn 002 015 plusmn 001 35 01314 2 089 plusmn 006 048 plusmn 016 060 plusmn 022 083 plusmn 015 110 plusmn 002 016 plusmn 001 45 01315 3 085 plusmn 006 100 plusmn 016 078 plusmn 022 -022 plusmn 015 116 plusmn 002 017 plusmn 001 146 01316 4 117 plusmn 006 120 plusmn 016 111 plusmn 023 011 plusmn 015 119 plusmn 002 017 plusmn 001 127 014

17 CCSM4 0 074 plusmn 006 075 plusmn 015 103 plusmn 022 013 plusmn 015 158 plusmn 002 024 plusmn 001 815 01718 1 074 plusmn 005 068 plusmn 014 -002 plusmn 020 047 plusmn 013 164 plusmn 002 025 plusmn 001 1077 01619 2 063 plusmn 006 027 plusmn 015 083 plusmn 021 082 plusmn 014 155 plusmn 002 024 plusmn 001 780 01520 3 059 plusmn 006 060 plusmn 015 -006 plusmn 022 098 plusmn 015 159 plusmn 002 024 plusmn 001 854 01721 4 058 plusmn 006 045 plusmn 015 073 plusmn 021 028 plusmn 014 160 plusmn 002 024 plusmn 001 928 01722 5 056 plusmn 005 116 plusmn 014 083 plusmn 020 075 plusmn 014 159 plusmn 002 025 plusmn 001 926 016

23 CESM1-BGC 0 067 plusmn 005 045 plusmn 014 109 plusmn 020 107 plusmn 014 150 plusmn 002 023 plusmn 001 646 015

24 CESM1-CAM5 0 029 plusmn 005 066 plusmn 012 030 plusmn 017 078 plusmn 012 088 plusmn 002 013 plusmn 000 279 01125 1 101 plusmn 005 101 plusmn 012 080 plusmn 017 058 plusmn 012 079 plusmn 002 011 plusmn 000 137 01026 2 099 plusmn 005 055 plusmn 013 141 plusmn 018 048 plusmn 012 092 plusmn 002 013 plusmn 000 57 010

27 CESM1-CAM5-1-FV2 0 087 plusmn 006 004 plusmn 016 132 plusmn 023 063 plusmn 016 071 plusmn 002 009 plusmn 001 222 01528 1 105 plusmn 006 034 plusmn 014 148 plusmn 020 008 plusmn 014 072 plusmn 002 010 plusmn 001 271 01129 2 077 plusmn 005 -008 plusmn 014 011 plusmn 020 -005 plusmn 014 085 plusmn 002 012 plusmn 001 238 01130 3 061 plusmn 006 064 plusmn 016 -006 plusmn 022 016 plusmn 015 081 plusmn 002 011 plusmn 001 203 013

31 CESM1-FASTCHEM 0 062 plusmn 006 079 plusmn 015 025 plusmn 021 092 plusmn 014 172 plusmn 002 026 plusmn 001 1228 01932 1 077 plusmn 006 097 plusmn 014 072 plusmn 020 052 plusmn 014 166 plusmn 002 025 plusmn 001 1068 01633 2 058 plusmn 006 086 plusmn 014 060 plusmn 021 115 plusmn 014 182 plusmn 002 028 plusmn 001 1618 020

34 CESM1-WACCM 0 065 plusmn 006 059 plusmn 015 -047 plusmn 022 089 plusmn 015 155 plusmn 002 023 plusmn 001 760 017

35 CMCC-CESM 0 050 plusmn 007 001 plusmn 018 -015 plusmn 025 -011 plusmn 017 049 plusmn 003 007 plusmn 001 674 016

36 CMCC-CM 0 056 plusmn 005 -055 plusmn 012 104 plusmn 017 009 plusmn 011 089 plusmn 002 014 plusmn 000 350 012

37 CMCC-CMS 0 066 plusmn 006 049 plusmn 015 098 plusmn 021 -017 plusmn 014 063 plusmn 002 009 plusmn 001 441 016

38 CNRM-CM5 0 042 plusmn 006 096 plusmn 015 113 plusmn 021 039 plusmn 014 092 plusmn 002 014 plusmn 001 156 01339 1 067 plusmn 005 124 plusmn 012 072 plusmn 017 081 plusmn 012 099 plusmn 002 014 plusmn 000 56 00840 2 070 plusmn 005 127 plusmn 013 054 plusmn 019 064 plusmn 013 091 plusmn 002 014 plusmn 000 75 01141 3 092 plusmn 005 057 plusmn 013 035 plusmn 018 094 plusmn 012 120 plusmn 002 018 plusmn 000 139 01142 4 056 plusmn 005 093 plusmn 014 101 plusmn 020 055 plusmn 013 085 plusmn 002 014 plusmn 001 137 01243 5 045 plusmn 005 098 plusmn 013 098 plusmn 019 059 plusmn 013 110 plusmn 002 018 plusmn 000 153 01144 6 120 plusmn 005 097 plusmn 013 056 plusmn 019 070 plusmn 013 095 plusmn 002 014 plusmn 000 35 01045 7 036 plusmn 005 059 plusmn 013 -001 plusmn 019 036 plusmn 013 118 plusmn 002 019 plusmn 000 310 01346 8 071 plusmn 005 021 plusmn 012 073 plusmn 018 086 plusmn 012 074 plusmn 002 012 plusmn 000 271 01147 9 107 plusmn 005 088 plusmn 013 -007 plusmn 018 062 plusmn 012 115 plusmn 002 017 plusmn 000 112 011

48 CSIRO-Mk3-6-0 0 053 plusmn 006 132 plusmn 015 -042 plusmn 022 064 plusmn 015 070 plusmn 002 011 plusmn 001 347 01649 1 098 plusmn 005 035 plusmn 014 107 plusmn 020 -047 plusmn 013 060 plusmn 002 010 plusmn 001 561 01650 2 112 plusmn 005 066 plusmn 013 121 plusmn 018 000 plusmn 012 078 plusmn 002 012 plusmn 000 209 01251 3 088 plusmn 006 139 plusmn 015 105 plusmn 021 030 plusmn 014 045 plusmn 002 006 plusmn 001 756 01752 4 080 plusmn 006 074 plusmn 017 -007 plusmn 024 034 plusmn 016 070 plusmn 002 010 plusmn 001 245 01753 5 060 plusmn 006 077 plusmn 014 054 plusmn 020 035 plusmn 014 069 plusmn 002 011 plusmn 001 318 01554 6 052 plusmn 005 022 plusmn 013 029 plusmn 018 009 plusmn 012 076 plusmn 002 012 plusmn 000 358 01355 7 107 plusmn 006 054 plusmn 014 021 plusmn 020 055 plusmn 014 063 plusmn 002 009 plusmn 001 371 01556 8 036 plusmn 005 -031 plusmn 013 043 plusmn 019 031 plusmn 013 077 plusmn 002 013 plusmn 000 444 01457 9 039 plusmn 005 063 plusmn 014 -022 plusmn 019 001 plusmn 013 080 plusmn 002 013 plusmn 001 360 014

58 EC-EARTH 0 048 plusmn 005 075 plusmn 012 051 plusmn 017 037 plusmn 011 141 plusmn 002 019 plusmn 000 638 01459 1 -013 plusmn 005 108 plusmn 012 094 plusmn 016 006 plusmn 011 154 plusmn 002 021 plusmn 000 1473 01660 2 053 plusmn 005 040 plusmn 012 083 plusmn 017 -004 plusmn 012 135 plusmn 002 019 plusmn 000 547 01361 3 014 plusmn 004 084 plusmn 012 077 plusmn 016 028 plusmn 011 140 plusmn 002 023 plusmn 000 832 01462 4 038 plusmn 005 041 plusmn 012 009 plusmn 017 069 plusmn 011 154 plusmn 002 020 plusmn 000 1059 01563 5 077 plusmn 004 104 plusmn 011 018 plusmn 016 018 plusmn 011 147 plusmn 002 018 plusmn 000 753 01464 6 031 plusmn 005 103 plusmn 012 051 plusmn 017 -001 plusmn 011 144 plusmn 002 019 plusmn 000 862 01465 7 071 plusmn 004 007 plusmn 011 051 plusmn 016 097 plusmn 011 138 plusmn 002 018 plusmn 000 546 01166 8 059 plusmn 005 103 plusmn 012 090 plusmn 017 086 plusmn 012 138 plusmn 002 018 plusmn 000 471 013

67 FGOALS-g2 0 037 plusmn 004 026 plusmn 010 009 plusmn 015 -001 plusmn 010 100 plusmn 002 015 plusmn 000 361 01068 1 072 plusmn 004 010 plusmn 010 001 plusmn 014 -003 plusmn 010 095 plusmn 001 010 plusmn 000 254 00869 2 071 plusmn 004 -007 plusmn 011 005 plusmn 016 -005 plusmn 011 095 plusmn 002 014 plusmn 000 256 01070 3 049 plusmn 004 047 plusmn 011 015 plusmn 015 008 plusmn 010 084 plusmn 002 010 plusmn 000 326 01171 4 051 plusmn 004 014 plusmn 010 -004 plusmn 015 -004 plusmn 010 095 plusmn 002 012 plusmn 000 323 010

72 FIO-ESM 0 031 plusmn 005 026 plusmn 014 057 plusmn 020 002 plusmn 014 133 plusmn 002 021 plusmn 001 538 01373 1 035 plusmn 005 069 plusmn 013 085 plusmn 018 012 plusmn 013 123 plusmn 002 019 plusmn 000 367 01074 2 036 plusmn 005 -011 plusmn 013 -040 plusmn 019 019 plusmn 013 146 plusmn 002 023 plusmn 000 890 013

75 GFDL-CM3 0 160 plusmn 006 149 plusmn 016 -007 plusmn 023 057 plusmn 016 049 plusmn 002 005 plusmn 001 692 01876 1 139 plusmn 006 101 plusmn 015 110 plusmn 021 047 plusmn 014 056 plusmn 002 007 plusmn 001 522 01577 2 077 plusmn 006 095 plusmn 016 124 plusmn 022 034 plusmn 015 052 plusmn 002 007 plusmn 001 524 01778 3 112 plusmn 007 113 plusmn 017 057 plusmn 025 026 plusmn 017 063 plusmn 003 008 plusmn 001 291 01879 4 127 plusmn 007 111 plusmn 017 012 plusmn 024 098 plusmn 017 027 plusmn 003 002 plusmn 001 1051 021

80 GFDL-ESM2G 0 085 plusmn 007 142 plusmn 017 014 plusmn 024 014 plusmn 016 085 plusmn 003 011 plusmn 001 114 01681 1 019 plusmn 005 127 plusmn 014 080 plusmn 019 010 plusmn 013 089 plusmn 002 013 plusmn 001 336 01282 2 033 plusmn 006 080 plusmn 015 -033 plusmn 021 055 plusmn 014 102 plusmn 002 014 plusmn 001 219 013

83 GFDL-ESM2M 0 022 plusmn 006 048 plusmn 016 018 plusmn 023 040 plusmn 015 095 plusmn 002 013 plusmn 001 246 014

84 GISS-E2-H p1 0 029 plusmn 004 050 plusmn 011 025 plusmn 015 043 plusmn 010 137 plusmn 002 023 plusmn 000 722 01385 1 033 plusmn 004 052 plusmn 010 029 plusmn 015 067 plusmn 010 134 plusmn 002 021 plusmn 000 625 01286 2 035 plusmn 004 022 plusmn 011 051 plusmn 016 067 plusmn 011 130 plusmn 002 021 plusmn 000 531 01287 3 041 plusmn 004 053 plusmn 011 034 plusmn 015 013 plusmn 010 132 plusmn 002 021 plusmn 000 579 01288 4 040 plusmn 004 076 plusmn 010 090 plusmn 014 046 plusmn 010 133 plusmn 001 021 plusmn 000 562 01189 5 040 plusmn 004 073 plusmn 010 041 plusmn 015 065 plusmn 010 124 plusmn 002 016 plusmn 000 387 011

90 GISS-E2-H p2 0 054 plusmn 005 052 plusmn 012 048 plusmn 017 035 plusmn 012 105 plusmn 002 017 plusmn 000 156 01291 1 025 plusmn 005 094 plusmn 012 030 plusmn 017 075 plusmn 011 106 plusmn 002 018 plusmn 000 280 01292 2 043 plusmn 004 091 plusmn 011 016 plusmn 015 054 plusmn 010 112 plusmn 002 018 plusmn 000 239 01193 3 040 plusmn 005 058 plusmn 012 047 plusmn 017 044 plusmn 011 103 plusmn 002 017 plusmn 000 210 01294 4 045 plusmn 004 057 plusmn 010 063 plusmn 015 057 plusmn 010 107 plusmn 002 018 plusmn 000 200 010

44

95 GISS-E2-H p3 0 036 plusmn 005 050 plusmn 012 096 plusmn 018 026 plusmn 012 136 plusmn 002 022 plusmn 000 570 01496 1 032 plusmn 004 055 plusmn 011 020 plusmn 015 070 plusmn 010 166 plusmn 002 026 plusmn 000 1614 01797 2 041 plusmn 005 031 plusmn 012 034 plusmn 017 037 plusmn 011 147 plusmn 002 024 plusmn 000 852 01598 3 065 plusmn 004 072 plusmn 011 045 plusmn 015 044 plusmn 010 142 plusmn 002 023 plusmn 000 636 01399 4 031 plusmn 005 101 plusmn 012 072 plusmn 017 028 plusmn 011 136 plusmn 002 022 plusmn 000 621 014100 5 045 plusmn 005 099 plusmn 012 028 plusmn 017 019 plusmn 011 129 plusmn 002 017 plusmn 000 449 013

101 GISS-E2-H-CC p1 0 037 plusmn 004 077 plusmn 011 043 plusmn 016 050 plusmn 011 160 plusmn 002 023 plusmn 000 1277 016

102 GISS-E2-R p1 0 019 plusmn 004 021 plusmn 011 030 plusmn 015 019 plusmn 010 097 plusmn 002 015 plusmn 000 439 011103 1 031 plusmn 004 103 plusmn 011 076 plusmn 015 032 plusmn 010 110 plusmn 002 017 plusmn 000 302 010104 2 051 plusmn 004 061 plusmn 010 020 plusmn 015 043 plusmn 010 102 plusmn 002 016 plusmn 000 184 009105 3 049 plusmn 004 071 plusmn 011 086 plusmn 016 054 plusmn 011 109 plusmn 002 017 plusmn 000 170 010106 4 027 plusmn 004 105 plusmn 011 078 plusmn 016 036 plusmn 011 115 plusmn 002 018 plusmn 000 339 011107 5 032 plusmn 005 083 plusmn 012 046 plusmn 017 058 plusmn 011 096 plusmn 002 015 plusmn 000 233 012

108 GISS-E2-R p2 0 042 plusmn 004 048 plusmn 011 026 plusmn 016 041 plusmn 011 088 plusmn 002 014 plusmn 000 265 011109 1 063 plusmn 004 -052 plusmn 011 023 plusmn 016 050 plusmn 011 072 plusmn 002 012 plusmn 000 497 013110 2 017 plusmn 004 034 plusmn 011 115 plusmn 016 061 plusmn 011 078 plusmn 002 013 plusmn 000 500 012111 3 058 plusmn 005 068 plusmn 012 080 plusmn 017 055 plusmn 012 065 plusmn 002 010 plusmn 000 432 014112 4 021 plusmn 004 086 plusmn 011 047 plusmn 016 033 plusmn 011 072 plusmn 002 012 plusmn 000 554 013113 5 039 plusmn 004 080 plusmn 011 050 plusmn 015 036 plusmn 010 071 plusmn 002 011 plusmn 000 497 012

114 GISS-E2-R p3 0 031 plusmn 005 078 plusmn 012 046 plusmn 017 028 plusmn 011 095 plusmn 002 015 plusmn 000 270 012115 1 024 plusmn 004 056 plusmn 011 051 plusmn 016 088 plusmn 011 119 plusmn 002 018 plusmn 000 398 011116 2 056 plusmn 005 073 plusmn 012 074 plusmn 018 070 plusmn 012 124 plusmn 002 019 plusmn 000 244 012117 3 045 plusmn 004 129 plusmn 012 063 plusmn 016 001 plusmn 011 117 plusmn 002 019 plusmn 000 312 011118 4 017 plusmn 005 102 plusmn 012 033 plusmn 017 001 plusmn 012 108 plusmn 002 017 plusmn 000 404 012119 5 037 plusmn 004 117 plusmn 012 061 plusmn 016 084 plusmn 011 114 plusmn 002 018 plusmn 000 240 011

120 GISS-E2-R-CC p1 0 027 plusmn 004 052 plusmn 011 045 plusmn 015 038 plusmn 010 109 plusmn 002 015 plusmn 000 338 011

121 HadGEM2-AO 0 122 plusmn 005 156 plusmn 014 156 plusmn 020 038 plusmn 013 080 plusmn 002 010 plusmn 001 169 013

122 HadGEM2-CC 0 098 plusmn 005 077 plusmn 014 021 plusmn 020 049 plusmn 013 030 plusmn 002 003 plusmn 001 1209 019

123 HadGEM2-ES 0 103 plusmn 005 065 plusmn 014 -016 plusmn 020 053 plusmn 013 048 plusmn 002 006 plusmn 001 733 016124 1 076 plusmn 006 109 plusmn 015 006 plusmn 022 065 plusmn 015 049 plusmn 002 006 plusmn 001 630 019125 2 104 plusmn 005 146 plusmn 013 070 plusmn 018 033 plusmn 012 065 plusmn 002 008 plusmn 000 375 013126 3 040 plusmn 006 094 plusmn 015 059 plusmn 021 -044 plusmn 014 068 plusmn 002 009 plusmn 001 497 017

127 inmcm4 0 036 plusmn 003 017 plusmn 009 021 plusmn 012 001 plusmn 008 102 plusmn 001 016 plusmn 000 419 008

128 IPSL-CM5A-LR 0 089 plusmn 006 025 plusmn 015 073 plusmn 021 021 plusmn 014 160 plusmn 002 025 plusmn 001 893 018129 1 106 plusmn 005 067 plusmn 013 -033 plusmn 019 -011 plusmn 013 165 plusmn 002 026 plusmn 000 1223 018130 2 112 plusmn 005 093 plusmn 013 068 plusmn 019 037 plusmn 013 152 plusmn 002 024 plusmn 000 714 015131 3 053 plusmn 006 094 plusmn 014 061 plusmn 020 024 plusmn 014 167 plusmn 002 026 plusmn 001 1169 018132 4 065 plusmn 006 019 plusmn 015 089 plusmn 021 057 plusmn 014 155 plusmn 002 025 plusmn 001 785 017133 5 092 plusmn 005 135 plusmn 014 -006 plusmn 019 008 plusmn 013 136 plusmn 002 021 plusmn 001 431 014

134 IPSL-CM5A-MR 0 055 plusmn 005 096 plusmn 013 065 plusmn 018 042 plusmn 012 130 plusmn 002 021 plusmn 000 357 012135 1 063 plusmn 005 091 plusmn 014 062 plusmn 019 -002 plusmn 013 154 plusmn 002 024 plusmn 001 852 016136 2 086 plusmn 005 047 plusmn 013 044 plusmn 018 016 plusmn 012 166 plusmn 002 026 plusmn 000 1271 017

137 IPSL-CM5B-LR 0 004 plusmn 005 010 plusmn 013 088 plusmn 019 017 plusmn 013 143 plusmn 002 024 plusmn 000 919 016

138 MIROC5 0 088 plusmn 006 001 plusmn 016 125 plusmn 022 015 plusmn 015 070 plusmn 002 007 plusmn 001 294 014139 1 062 plusmn 006 080 plusmn 014 036 plusmn 020 061 plusmn 014 081 plusmn 002 010 plusmn 001 159 013140 2 083 plusmn 005 095 plusmn 014 089 plusmn 020 025 plusmn 013 088 plusmn 002 010 plusmn 001 84 011141 3 052 plusmn 006 024 plusmn 015 106 plusmn 021 024 plusmn 014 068 plusmn 002 007 plusmn 001 374 014142 4 059 plusmn 006 020 plusmn 014 041 plusmn 020 072 plusmn 014 079 plusmn 002 010 plusmn 001 213 014

143 MIROC-ESM 0 084 plusmn 005 049 plusmn 013 035 plusmn 018 080 plusmn 012 115 plusmn 002 018 plusmn 000 108 011144 1 028 plusmn 005 -021 plusmn 014 -070 plusmn 019 016 plusmn 013 112 plusmn 002 018 plusmn 001 455 015145 2 062 plusmn 005 077 plusmn 014 -004 plusmn 019 037 plusmn 013 106 plusmn 002 016 plusmn 001 127 013

146 MIROC-ESM-CHEM 0 049 plusmn 004 136 plusmn 011 -052 plusmn 016 072 plusmn 011 105 plusmn 002 016 plusmn 000 221 010

147 MPI-ESM-LR 0 011 plusmn 006 011 plusmn 015 017 plusmn 022 070 plusmn 015 144 plusmn 002 022 plusmn 001 761 018148 1 009 plusmn 005 041 plusmn 014 057 plusmn 020 107 plusmn 013 154 plusmn 002 024 plusmn 001 1052 016149 2 041 plusmn 006 088 plusmn 014 092 plusmn 020 -081 plusmn 014 131 plusmn 002 020 plusmn 001 563 014

150 MPI-ESM-MR 0 058 plusmn 005 041 plusmn 013 -042 plusmn 019 -051 plusmn 013 140 plusmn 002 021 plusmn 000 722 015151 1 010 plusmn 005 113 plusmn 013 086 plusmn 019 077 plusmn 013 140 plusmn 002 021 plusmn 000 731 014152 2 054 plusmn 005 072 plusmn 012 -002 plusmn 018 060 plusmn 012 139 plusmn 002 020 plusmn 000 543 014

153 MPI-ESM-P 0 039 plusmn 005 071 plusmn 013 117 plusmn 019 005 plusmn 013 146 plusmn 002 023 plusmn 000 751 015154 1 033 plusmn 006 067 plusmn 014 -013 plusmn 020 034 plusmn 014 147 plusmn 002 022 plusmn 001 757 017

155 MRI-CGCM3 0 013 plusmn 005 029 plusmn 012 033 plusmn 017 017 plusmn 012 072 plusmn 002 011 plusmn 000 638 012156 1 042 plusmn 005 060 plusmn 013 039 plusmn 019 046 plusmn 013 052 plusmn 002 008 plusmn 000 763 015157 2 052 plusmn 005 036 plusmn 013 016 plusmn 018 045 plusmn 013 070 plusmn 002 011 plusmn 000 397 013

158 MRI-ESM1 0 054 plusmn 005 056 plusmn 014 -014 plusmn 019 052 plusmn 013 089 plusmn 002 013 plusmn 001 177 011

159 NorESM1-M 0 072 plusmn 005 043 plusmn 012 000 plusmn 018 039 plusmn 012 082 plusmn 002 013 plusmn 000 202 010160 1 042 plusmn 005 063 plusmn 012 -002 plusmn 017 080 plusmn 012 087 plusmn 002 013 plusmn 000 234 011161 2 032 plusmn 005 049 plusmn 013 076 plusmn 018 030 plusmn 012 086 plusmn 002 013 plusmn 000 293 011

162 NorESM1-ME 0 055 plusmn 005 103 plusmn 014 058 plusmn 020 064 plusmn 013 087 plusmn 002 012 plusmn 001 134 011

average 058 plusmn 030 068 plusmn 042 048 plusmn 048 039 plusmn 037 109 plusmn 036 016 plusmn 006 5130 014

45

Table 3 See Sections 32 and 33 The regression coefficients φ usingEq 10 for band-pass frequency scales S1 S2 S3 and S4 for allavailable 162 GCM simulations and for their ensemble mean (whichis numbered -0- in the list) The χ2 test values were calculatedusing Eq 9 Last two columns report the correlation coefficientsbetween the GST power spectrum (periodogram and MEM) andthe correspondent GCM power spectra See also Figures 13 14and 15

model simulation S1 S2 S3 S4 χ2 Corr Coeff Corr Coeff 05-7 years 7-14 years 14-28 years 28-104 years Periodogram MEM

0 ensemble mean 005 036 081 063 86 079 -002

1 ACCESS1-0 0 -005 053 091 051 69 034 008

2 ACCESS1-3 0 006 012 122 055 153 048 -0073 1 -003 -011 114 077 194 063 0124 2 003 -003 122 078 171 081 028

5 bcc-csm1-1 0 003 037 121 108 67 097 0366 1 005 063 092 079 27 079 0197 2 006 062 133 070 51 093 032

8 bcc-csm1-1-m 0 002 057 118 023 120 025 -0119 1 009 100 091 063 21 021 -00610 2 000 083 175 020 183 050 -008

11 BNU-ESM 0 002 029 156 078 128 084 -003

12 CanESM2 0 -006 024 122 075 102 079 00213 1 -002 057 112 111 31 087 00914 2 -003 060 057 087 53 079 00015 3 005 007 086 090 133 077 -00416 4 -001 055 082 111 37 089 025

17 CCSM4 0 008 038 126 068 81 093 00118 1 -001 048 113 061 65 094 04219 2 010 057 067 049 82 093 01120 3 013 069 074 052 58 088 -00821 4 009 030 097 048 113 094 01322 5 003 041 150 049 128 084 004

23 CESM1-BGC 0 002 072 088 051 49 096 -003

24 CESM1-CAM5 0 004 047 068 025 140 081 04025 1 013 057 091 097 29 097 00326 2 003 053 058 111 59 087 006

27 CESM1-CAM5-1-FV2 0 009 037 041 077 118 085 -01128 1 005 028 057 101 105 097 -00229 2 009 -006 026 072 260 098 04530 3 000 034 069 059 103 064 009

31 CESM1-FASTCHEM 0 005 053 130 056 75 087 00632 1 006 063 089 071 34 093 00133 2 003 076 124 044 63 091 001

34 CESM1-WACCM 0 -001 063 143 050 84 090 029

35 CMCC-CESM 0 -004 003 -016 041 389 071 013

36 CMCC-CM 0 004 038 -053 040 459 034 003

37 CMCC-CMS 0 -005 -019 011 036 388 001 -004

38 CNRM-CM5 0 002 062 102 045 67 015 00139 1 -004 062 098 070 34 088 -00140 2 004 041 107 078 59 069 -00141 3 008 060 096 099 24 087 04442 4 009 064 118 053 57 078 00643 5 011 052 097 064 54 046 01344 6 004 054 103 104 32 098 06345 7 000 029 097 054 106 025 -01046 8 007 055 030 063 122 094 01947 9 003 030 092 110 76 088 046

48 CSIRO-Mk3-6-0 0 004 070 107 080 20 022 -01249 1 005 026 066 115 102 057 -01050 2 008 035 066 110 81 090 04651 3 -002 032 148 110 104 057 -00652 4 -003 014 096 122 118 042 -01053 5 007 011 075 085 131 034 -00954 6 008 026 043 054 160 050 -00355 7 004 060 061 117 50 066 -00756 8 004 015 007 048 275 017 00157 9 -006 031 028 062 169 016 -008

58 EC-EARTH 0 003 034 091 045 111 076 -00559 1 007 047 098 002 185 068 02360 2 001 005 089 053 167 087 00861 3 004 034 090 013 178 077 -00862 4 010 059 061 034 113 081 01163 5 001 006 101 081 138 094 00164 6 005 021 084 048 136 083 -00465 7 005 057 060 063 72 081 01466 8 001 075 130 057 51 089 -004

67 FGOALS-g2 0 000 006 019 021 320 048 -00768 1 -003 -004 034 056 252 090 07469 2 -001 -005 -006 046 372 078 08670 3 -001 020 024 033 247 083 -00371 4 -002 003 026 035 284 065 044

72 FIO-ESM 0 003 004 026 019 314 068 -01273 1 001 031 035 017 236 044 -00774 2 005 012 -007 021 377 053 001

75 GFDL-CM3 0 -003 033 106 163 125 087 -00676 1 002 070 082 127 29 098 01177 2 -003 062 052 100 55 055 -01278 3 010 044 094 128 57 058 00279 4 007 032 083 141 98 076 014

80 GFDL-ESM2G 0 005 009 126 081 138 063 01881 1 -002 016 119 031 180 -002 -00282 2 007 025 086 039 142 011 -003

83 GFDL-ESM2M 0 015 035 079 029 143 029 -011

84 GISS-E2-H p1 0 001 037 070 041 123 033 00685 1 005 049 082 036 102 047 02886 2 004 052 062 041 107 037 -00887 3 010 017 066 042 169 072 01688 4 005 053 077 042 92 083 -00689 5 007 047 095 045 88 069 000

90 GISS-E2-H p2 0 003 045 088 057 75 045 -01191 1 006 057 074 037 96 006 -01492 2 004 039 104 057 83 050 00793 3 004 036 109 057 90 029 -01394 4 002 053 080 054 71 053 -003

95 GISS-E2-H p3 0 003 049 091 056 69 057 -007

46

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion

Table 2 See Section 31 The regression coefficients are evaluatedusing Eq 7 for all available 162 GCM simulations and for theirensemble mean (which is numbered -0- in the list) The table re-ports the χ2 test values which were calculated using Eq 13 andthe root-mean-square deviation (RMSD) values for each simula-tions from the harmonic model Eq 6 which were calculated usinga 49-month running mean of the original time sequences See alsoFigure 12

Model Simulation α α α α β γ χ2 RMSD (60-years) (20-years) (104=years) (91-years) (upward trend) (bias)

GST 1 plusmn 005 1 plusmn 012 1 plusmn 017 1 plusmn 011 1 plusmn 002 00 plusmn 001 0 005

0 GCM mean 063 plusmn 003 073 plusmn 008 044 plusmn 012 040 plusmn 008 104 plusmn 001 -055 plusmn 000 143 009

1 ACCESS1-0 0 039 plusmn 005 092 plusmn 014 088 plusmn 020 070 plusmn 013 084 plusmn 002 012 plusmn 001 214 014

2 ACCESS1-3 0 046 plusmn 005 089 plusmn 012 105 plusmn 017 002 plusmn 012 058 plusmn 002 008 plusmn 000 694 0143 1 067 plusmn 005 081 plusmn 012 023 plusmn 017 -007 plusmn 012 051 plusmn 002 007 plusmn 000 817 0154 2 075 plusmn 004 133 plusmn 011 008 plusmn 016 -003 plusmn 011 039 plusmn 002 006 plusmn 000 1236 015

5 bcc-csm1-1 0 129 plusmn 005 062 plusmn 014 019 plusmn 019 055 plusmn 013 142 plusmn 002 017 plusmn 001 514 0146 1 064 plusmn 006 041 plusmn 014 059 plusmn 020 103 plusmn 014 172 plusmn 002 022 plusmn 001 1299 0197 2 077 plusmn 006 069 plusmn 015 060 plusmn 022 057 plusmn 015 150 plusmn 002 019 plusmn 001 583 017

8 bcc-csm1-1-m 0 040 plusmn 006 083 plusmn 015 081 plusmn 022 048 plusmn 015 144 plusmn 002 020 plusmn 001 557 0169 1 031 plusmn 007 073 plusmn 017 119 plusmn 025 109 plusmn 017 146 plusmn 003 018 plusmn 001 541 01810 2 025 plusmn 007 107 plusmn 019 068 plusmn 026 101 plusmn 018 165 plusmn 003 023 plusmn 001 866 022

11 BNU-ESM 0 082 plusmn 006 112 plusmn 016 019 plusmn 023 -018 plusmn 016 178 plusmn 002 027 plusmn 001 1315 020

12 CanESM2 0 088 plusmn 007 085 plusmn 017 014 plusmn 024 004 plusmn 017 117 plusmn 003 017 plusmn 001 123 01513 1 117 plusmn 006 139 plusmn 016 051 plusmn 023 066 plusmn 015 105 plusmn 002 015 plusmn 001 35 01314 2 089 plusmn 006 048 plusmn 016 060 plusmn 022 083 plusmn 015 110 plusmn 002 016 plusmn 001 45 01315 3 085 plusmn 006 100 plusmn 016 078 plusmn 022 -022 plusmn 015 116 plusmn 002 017 plusmn 001 146 01316 4 117 plusmn 006 120 plusmn 016 111 plusmn 023 011 plusmn 015 119 plusmn 002 017 plusmn 001 127 014

17 CCSM4 0 074 plusmn 006 075 plusmn 015 103 plusmn 022 013 plusmn 015 158 plusmn 002 024 plusmn 001 815 01718 1 074 plusmn 005 068 plusmn 014 -002 plusmn 020 047 plusmn 013 164 plusmn 002 025 plusmn 001 1077 01619 2 063 plusmn 006 027 plusmn 015 083 plusmn 021 082 plusmn 014 155 plusmn 002 024 plusmn 001 780 01520 3 059 plusmn 006 060 plusmn 015 -006 plusmn 022 098 plusmn 015 159 plusmn 002 024 plusmn 001 854 01721 4 058 plusmn 006 045 plusmn 015 073 plusmn 021 028 plusmn 014 160 plusmn 002 024 plusmn 001 928 01722 5 056 plusmn 005 116 plusmn 014 083 plusmn 020 075 plusmn 014 159 plusmn 002 025 plusmn 001 926 016

23 CESM1-BGC 0 067 plusmn 005 045 plusmn 014 109 plusmn 020 107 plusmn 014 150 plusmn 002 023 plusmn 001 646 015

24 CESM1-CAM5 0 029 plusmn 005 066 plusmn 012 030 plusmn 017 078 plusmn 012 088 plusmn 002 013 plusmn 000 279 01125 1 101 plusmn 005 101 plusmn 012 080 plusmn 017 058 plusmn 012 079 plusmn 002 011 plusmn 000 137 01026 2 099 plusmn 005 055 plusmn 013 141 plusmn 018 048 plusmn 012 092 plusmn 002 013 plusmn 000 57 010

27 CESM1-CAM5-1-FV2 0 087 plusmn 006 004 plusmn 016 132 plusmn 023 063 plusmn 016 071 plusmn 002 009 plusmn 001 222 01528 1 105 plusmn 006 034 plusmn 014 148 plusmn 020 008 plusmn 014 072 plusmn 002 010 plusmn 001 271 01129 2 077 plusmn 005 -008 plusmn 014 011 plusmn 020 -005 plusmn 014 085 plusmn 002 012 plusmn 001 238 01130 3 061 plusmn 006 064 plusmn 016 -006 plusmn 022 016 plusmn 015 081 plusmn 002 011 plusmn 001 203 013

31 CESM1-FASTCHEM 0 062 plusmn 006 079 plusmn 015 025 plusmn 021 092 plusmn 014 172 plusmn 002 026 plusmn 001 1228 01932 1 077 plusmn 006 097 plusmn 014 072 plusmn 020 052 plusmn 014 166 plusmn 002 025 plusmn 001 1068 01633 2 058 plusmn 006 086 plusmn 014 060 plusmn 021 115 plusmn 014 182 plusmn 002 028 plusmn 001 1618 020

34 CESM1-WACCM 0 065 plusmn 006 059 plusmn 015 -047 plusmn 022 089 plusmn 015 155 plusmn 002 023 plusmn 001 760 017

35 CMCC-CESM 0 050 plusmn 007 001 plusmn 018 -015 plusmn 025 -011 plusmn 017 049 plusmn 003 007 plusmn 001 674 016

36 CMCC-CM 0 056 plusmn 005 -055 plusmn 012 104 plusmn 017 009 plusmn 011 089 plusmn 002 014 plusmn 000 350 012

37 CMCC-CMS 0 066 plusmn 006 049 plusmn 015 098 plusmn 021 -017 plusmn 014 063 plusmn 002 009 plusmn 001 441 016

38 CNRM-CM5 0 042 plusmn 006 096 plusmn 015 113 plusmn 021 039 plusmn 014 092 plusmn 002 014 plusmn 001 156 01339 1 067 plusmn 005 124 plusmn 012 072 plusmn 017 081 plusmn 012 099 plusmn 002 014 plusmn 000 56 00840 2 070 plusmn 005 127 plusmn 013 054 plusmn 019 064 plusmn 013 091 plusmn 002 014 plusmn 000 75 01141 3 092 plusmn 005 057 plusmn 013 035 plusmn 018 094 plusmn 012 120 plusmn 002 018 plusmn 000 139 01142 4 056 plusmn 005 093 plusmn 014 101 plusmn 020 055 plusmn 013 085 plusmn 002 014 plusmn 001 137 01243 5 045 plusmn 005 098 plusmn 013 098 plusmn 019 059 plusmn 013 110 plusmn 002 018 plusmn 000 153 01144 6 120 plusmn 005 097 plusmn 013 056 plusmn 019 070 plusmn 013 095 plusmn 002 014 plusmn 000 35 01045 7 036 plusmn 005 059 plusmn 013 -001 plusmn 019 036 plusmn 013 118 plusmn 002 019 plusmn 000 310 01346 8 071 plusmn 005 021 plusmn 012 073 plusmn 018 086 plusmn 012 074 plusmn 002 012 plusmn 000 271 01147 9 107 plusmn 005 088 plusmn 013 -007 plusmn 018 062 plusmn 012 115 plusmn 002 017 plusmn 000 112 011

48 CSIRO-Mk3-6-0 0 053 plusmn 006 132 plusmn 015 -042 plusmn 022 064 plusmn 015 070 plusmn 002 011 plusmn 001 347 01649 1 098 plusmn 005 035 plusmn 014 107 plusmn 020 -047 plusmn 013 060 plusmn 002 010 plusmn 001 561 01650 2 112 plusmn 005 066 plusmn 013 121 plusmn 018 000 plusmn 012 078 plusmn 002 012 plusmn 000 209 01251 3 088 plusmn 006 139 plusmn 015 105 plusmn 021 030 plusmn 014 045 plusmn 002 006 plusmn 001 756 01752 4 080 plusmn 006 074 plusmn 017 -007 plusmn 024 034 plusmn 016 070 plusmn 002 010 plusmn 001 245 01753 5 060 plusmn 006 077 plusmn 014 054 plusmn 020 035 plusmn 014 069 plusmn 002 011 plusmn 001 318 01554 6 052 plusmn 005 022 plusmn 013 029 plusmn 018 009 plusmn 012 076 plusmn 002 012 plusmn 000 358 01355 7 107 plusmn 006 054 plusmn 014 021 plusmn 020 055 plusmn 014 063 plusmn 002 009 plusmn 001 371 01556 8 036 plusmn 005 -031 plusmn 013 043 plusmn 019 031 plusmn 013 077 plusmn 002 013 plusmn 000 444 01457 9 039 plusmn 005 063 plusmn 014 -022 plusmn 019 001 plusmn 013 080 plusmn 002 013 plusmn 001 360 014

58 EC-EARTH 0 048 plusmn 005 075 plusmn 012 051 plusmn 017 037 plusmn 011 141 plusmn 002 019 plusmn 000 638 01459 1 -013 plusmn 005 108 plusmn 012 094 plusmn 016 006 plusmn 011 154 plusmn 002 021 plusmn 000 1473 01660 2 053 plusmn 005 040 plusmn 012 083 plusmn 017 -004 plusmn 012 135 plusmn 002 019 plusmn 000 547 01361 3 014 plusmn 004 084 plusmn 012 077 plusmn 016 028 plusmn 011 140 plusmn 002 023 plusmn 000 832 01462 4 038 plusmn 005 041 plusmn 012 009 plusmn 017 069 plusmn 011 154 plusmn 002 020 plusmn 000 1059 01563 5 077 plusmn 004 104 plusmn 011 018 plusmn 016 018 plusmn 011 147 plusmn 002 018 plusmn 000 753 01464 6 031 plusmn 005 103 plusmn 012 051 plusmn 017 -001 plusmn 011 144 plusmn 002 019 plusmn 000 862 01465 7 071 plusmn 004 007 plusmn 011 051 plusmn 016 097 plusmn 011 138 plusmn 002 018 plusmn 000 546 01166 8 059 plusmn 005 103 plusmn 012 090 plusmn 017 086 plusmn 012 138 plusmn 002 018 plusmn 000 471 013

67 FGOALS-g2 0 037 plusmn 004 026 plusmn 010 009 plusmn 015 -001 plusmn 010 100 plusmn 002 015 plusmn 000 361 01068 1 072 plusmn 004 010 plusmn 010 001 plusmn 014 -003 plusmn 010 095 plusmn 001 010 plusmn 000 254 00869 2 071 plusmn 004 -007 plusmn 011 005 plusmn 016 -005 plusmn 011 095 plusmn 002 014 plusmn 000 256 01070 3 049 plusmn 004 047 plusmn 011 015 plusmn 015 008 plusmn 010 084 plusmn 002 010 plusmn 000 326 01171 4 051 plusmn 004 014 plusmn 010 -004 plusmn 015 -004 plusmn 010 095 plusmn 002 012 plusmn 000 323 010

72 FIO-ESM 0 031 plusmn 005 026 plusmn 014 057 plusmn 020 002 plusmn 014 133 plusmn 002 021 plusmn 001 538 01373 1 035 plusmn 005 069 plusmn 013 085 plusmn 018 012 plusmn 013 123 plusmn 002 019 plusmn 000 367 01074 2 036 plusmn 005 -011 plusmn 013 -040 plusmn 019 019 plusmn 013 146 plusmn 002 023 plusmn 000 890 013

75 GFDL-CM3 0 160 plusmn 006 149 plusmn 016 -007 plusmn 023 057 plusmn 016 049 plusmn 002 005 plusmn 001 692 01876 1 139 plusmn 006 101 plusmn 015 110 plusmn 021 047 plusmn 014 056 plusmn 002 007 plusmn 001 522 01577 2 077 plusmn 006 095 plusmn 016 124 plusmn 022 034 plusmn 015 052 plusmn 002 007 plusmn 001 524 01778 3 112 plusmn 007 113 plusmn 017 057 plusmn 025 026 plusmn 017 063 plusmn 003 008 plusmn 001 291 01879 4 127 plusmn 007 111 plusmn 017 012 plusmn 024 098 plusmn 017 027 plusmn 003 002 plusmn 001 1051 021

80 GFDL-ESM2G 0 085 plusmn 007 142 plusmn 017 014 plusmn 024 014 plusmn 016 085 plusmn 003 011 plusmn 001 114 01681 1 019 plusmn 005 127 plusmn 014 080 plusmn 019 010 plusmn 013 089 plusmn 002 013 plusmn 001 336 01282 2 033 plusmn 006 080 plusmn 015 -033 plusmn 021 055 plusmn 014 102 plusmn 002 014 plusmn 001 219 013

83 GFDL-ESM2M 0 022 plusmn 006 048 plusmn 016 018 plusmn 023 040 plusmn 015 095 plusmn 002 013 plusmn 001 246 014

84 GISS-E2-H p1 0 029 plusmn 004 050 plusmn 011 025 plusmn 015 043 plusmn 010 137 plusmn 002 023 plusmn 000 722 01385 1 033 plusmn 004 052 plusmn 010 029 plusmn 015 067 plusmn 010 134 plusmn 002 021 plusmn 000 625 01286 2 035 plusmn 004 022 plusmn 011 051 plusmn 016 067 plusmn 011 130 plusmn 002 021 plusmn 000 531 01287 3 041 plusmn 004 053 plusmn 011 034 plusmn 015 013 plusmn 010 132 plusmn 002 021 plusmn 000 579 01288 4 040 plusmn 004 076 plusmn 010 090 plusmn 014 046 plusmn 010 133 plusmn 001 021 plusmn 000 562 01189 5 040 plusmn 004 073 plusmn 010 041 plusmn 015 065 plusmn 010 124 plusmn 002 016 plusmn 000 387 011

90 GISS-E2-H p2 0 054 plusmn 005 052 plusmn 012 048 plusmn 017 035 plusmn 012 105 plusmn 002 017 plusmn 000 156 01291 1 025 plusmn 005 094 plusmn 012 030 plusmn 017 075 plusmn 011 106 plusmn 002 018 plusmn 000 280 01292 2 043 plusmn 004 091 plusmn 011 016 plusmn 015 054 plusmn 010 112 plusmn 002 018 plusmn 000 239 01193 3 040 plusmn 005 058 plusmn 012 047 plusmn 017 044 plusmn 011 103 plusmn 002 017 plusmn 000 210 01294 4 045 plusmn 004 057 plusmn 010 063 plusmn 015 057 plusmn 010 107 plusmn 002 018 plusmn 000 200 010

44

95 GISS-E2-H p3 0 036 plusmn 005 050 plusmn 012 096 plusmn 018 026 plusmn 012 136 plusmn 002 022 plusmn 000 570 01496 1 032 plusmn 004 055 plusmn 011 020 plusmn 015 070 plusmn 010 166 plusmn 002 026 plusmn 000 1614 01797 2 041 plusmn 005 031 plusmn 012 034 plusmn 017 037 plusmn 011 147 plusmn 002 024 plusmn 000 852 01598 3 065 plusmn 004 072 plusmn 011 045 plusmn 015 044 plusmn 010 142 plusmn 002 023 plusmn 000 636 01399 4 031 plusmn 005 101 plusmn 012 072 plusmn 017 028 plusmn 011 136 plusmn 002 022 plusmn 000 621 014100 5 045 plusmn 005 099 plusmn 012 028 plusmn 017 019 plusmn 011 129 plusmn 002 017 plusmn 000 449 013

101 GISS-E2-H-CC p1 0 037 plusmn 004 077 plusmn 011 043 plusmn 016 050 plusmn 011 160 plusmn 002 023 plusmn 000 1277 016

102 GISS-E2-R p1 0 019 plusmn 004 021 plusmn 011 030 plusmn 015 019 plusmn 010 097 plusmn 002 015 plusmn 000 439 011103 1 031 plusmn 004 103 plusmn 011 076 plusmn 015 032 plusmn 010 110 plusmn 002 017 plusmn 000 302 010104 2 051 plusmn 004 061 plusmn 010 020 plusmn 015 043 plusmn 010 102 plusmn 002 016 plusmn 000 184 009105 3 049 plusmn 004 071 plusmn 011 086 plusmn 016 054 plusmn 011 109 plusmn 002 017 plusmn 000 170 010106 4 027 plusmn 004 105 plusmn 011 078 plusmn 016 036 plusmn 011 115 plusmn 002 018 plusmn 000 339 011107 5 032 plusmn 005 083 plusmn 012 046 plusmn 017 058 plusmn 011 096 plusmn 002 015 plusmn 000 233 012

108 GISS-E2-R p2 0 042 plusmn 004 048 plusmn 011 026 plusmn 016 041 plusmn 011 088 plusmn 002 014 plusmn 000 265 011109 1 063 plusmn 004 -052 plusmn 011 023 plusmn 016 050 plusmn 011 072 plusmn 002 012 plusmn 000 497 013110 2 017 plusmn 004 034 plusmn 011 115 plusmn 016 061 plusmn 011 078 plusmn 002 013 plusmn 000 500 012111 3 058 plusmn 005 068 plusmn 012 080 plusmn 017 055 plusmn 012 065 plusmn 002 010 plusmn 000 432 014112 4 021 plusmn 004 086 plusmn 011 047 plusmn 016 033 plusmn 011 072 plusmn 002 012 plusmn 000 554 013113 5 039 plusmn 004 080 plusmn 011 050 plusmn 015 036 plusmn 010 071 plusmn 002 011 plusmn 000 497 012

114 GISS-E2-R p3 0 031 plusmn 005 078 plusmn 012 046 plusmn 017 028 plusmn 011 095 plusmn 002 015 plusmn 000 270 012115 1 024 plusmn 004 056 plusmn 011 051 plusmn 016 088 plusmn 011 119 plusmn 002 018 plusmn 000 398 011116 2 056 plusmn 005 073 plusmn 012 074 plusmn 018 070 plusmn 012 124 plusmn 002 019 plusmn 000 244 012117 3 045 plusmn 004 129 plusmn 012 063 plusmn 016 001 plusmn 011 117 plusmn 002 019 plusmn 000 312 011118 4 017 plusmn 005 102 plusmn 012 033 plusmn 017 001 plusmn 012 108 plusmn 002 017 plusmn 000 404 012119 5 037 plusmn 004 117 plusmn 012 061 plusmn 016 084 plusmn 011 114 plusmn 002 018 plusmn 000 240 011

120 GISS-E2-R-CC p1 0 027 plusmn 004 052 plusmn 011 045 plusmn 015 038 plusmn 010 109 plusmn 002 015 plusmn 000 338 011

121 HadGEM2-AO 0 122 plusmn 005 156 plusmn 014 156 plusmn 020 038 plusmn 013 080 plusmn 002 010 plusmn 001 169 013

122 HadGEM2-CC 0 098 plusmn 005 077 plusmn 014 021 plusmn 020 049 plusmn 013 030 plusmn 002 003 plusmn 001 1209 019

123 HadGEM2-ES 0 103 plusmn 005 065 plusmn 014 -016 plusmn 020 053 plusmn 013 048 plusmn 002 006 plusmn 001 733 016124 1 076 plusmn 006 109 plusmn 015 006 plusmn 022 065 plusmn 015 049 plusmn 002 006 plusmn 001 630 019125 2 104 plusmn 005 146 plusmn 013 070 plusmn 018 033 plusmn 012 065 plusmn 002 008 plusmn 000 375 013126 3 040 plusmn 006 094 plusmn 015 059 plusmn 021 -044 plusmn 014 068 plusmn 002 009 plusmn 001 497 017

127 inmcm4 0 036 plusmn 003 017 plusmn 009 021 plusmn 012 001 plusmn 008 102 plusmn 001 016 plusmn 000 419 008

128 IPSL-CM5A-LR 0 089 plusmn 006 025 plusmn 015 073 plusmn 021 021 plusmn 014 160 plusmn 002 025 plusmn 001 893 018129 1 106 plusmn 005 067 plusmn 013 -033 plusmn 019 -011 plusmn 013 165 plusmn 002 026 plusmn 000 1223 018130 2 112 plusmn 005 093 plusmn 013 068 plusmn 019 037 plusmn 013 152 plusmn 002 024 plusmn 000 714 015131 3 053 plusmn 006 094 plusmn 014 061 plusmn 020 024 plusmn 014 167 plusmn 002 026 plusmn 001 1169 018132 4 065 plusmn 006 019 plusmn 015 089 plusmn 021 057 plusmn 014 155 plusmn 002 025 plusmn 001 785 017133 5 092 plusmn 005 135 plusmn 014 -006 plusmn 019 008 plusmn 013 136 plusmn 002 021 plusmn 001 431 014

134 IPSL-CM5A-MR 0 055 plusmn 005 096 plusmn 013 065 plusmn 018 042 plusmn 012 130 plusmn 002 021 plusmn 000 357 012135 1 063 plusmn 005 091 plusmn 014 062 plusmn 019 -002 plusmn 013 154 plusmn 002 024 plusmn 001 852 016136 2 086 plusmn 005 047 plusmn 013 044 plusmn 018 016 plusmn 012 166 plusmn 002 026 plusmn 000 1271 017

137 IPSL-CM5B-LR 0 004 plusmn 005 010 plusmn 013 088 plusmn 019 017 plusmn 013 143 plusmn 002 024 plusmn 000 919 016

138 MIROC5 0 088 plusmn 006 001 plusmn 016 125 plusmn 022 015 plusmn 015 070 plusmn 002 007 plusmn 001 294 014139 1 062 plusmn 006 080 plusmn 014 036 plusmn 020 061 plusmn 014 081 plusmn 002 010 plusmn 001 159 013140 2 083 plusmn 005 095 plusmn 014 089 plusmn 020 025 plusmn 013 088 plusmn 002 010 plusmn 001 84 011141 3 052 plusmn 006 024 plusmn 015 106 plusmn 021 024 plusmn 014 068 plusmn 002 007 plusmn 001 374 014142 4 059 plusmn 006 020 plusmn 014 041 plusmn 020 072 plusmn 014 079 plusmn 002 010 plusmn 001 213 014

143 MIROC-ESM 0 084 plusmn 005 049 plusmn 013 035 plusmn 018 080 plusmn 012 115 plusmn 002 018 plusmn 000 108 011144 1 028 plusmn 005 -021 plusmn 014 -070 plusmn 019 016 plusmn 013 112 plusmn 002 018 plusmn 001 455 015145 2 062 plusmn 005 077 plusmn 014 -004 plusmn 019 037 plusmn 013 106 plusmn 002 016 plusmn 001 127 013

146 MIROC-ESM-CHEM 0 049 plusmn 004 136 plusmn 011 -052 plusmn 016 072 plusmn 011 105 plusmn 002 016 plusmn 000 221 010

147 MPI-ESM-LR 0 011 plusmn 006 011 plusmn 015 017 plusmn 022 070 plusmn 015 144 plusmn 002 022 plusmn 001 761 018148 1 009 plusmn 005 041 plusmn 014 057 plusmn 020 107 plusmn 013 154 plusmn 002 024 plusmn 001 1052 016149 2 041 plusmn 006 088 plusmn 014 092 plusmn 020 -081 plusmn 014 131 plusmn 002 020 plusmn 001 563 014

150 MPI-ESM-MR 0 058 plusmn 005 041 plusmn 013 -042 plusmn 019 -051 plusmn 013 140 plusmn 002 021 plusmn 000 722 015151 1 010 plusmn 005 113 plusmn 013 086 plusmn 019 077 plusmn 013 140 plusmn 002 021 plusmn 000 731 014152 2 054 plusmn 005 072 plusmn 012 -002 plusmn 018 060 plusmn 012 139 plusmn 002 020 plusmn 000 543 014

153 MPI-ESM-P 0 039 plusmn 005 071 plusmn 013 117 plusmn 019 005 plusmn 013 146 plusmn 002 023 plusmn 000 751 015154 1 033 plusmn 006 067 plusmn 014 -013 plusmn 020 034 plusmn 014 147 plusmn 002 022 plusmn 001 757 017

155 MRI-CGCM3 0 013 plusmn 005 029 plusmn 012 033 plusmn 017 017 plusmn 012 072 plusmn 002 011 plusmn 000 638 012156 1 042 plusmn 005 060 plusmn 013 039 plusmn 019 046 plusmn 013 052 plusmn 002 008 plusmn 000 763 015157 2 052 plusmn 005 036 plusmn 013 016 plusmn 018 045 plusmn 013 070 plusmn 002 011 plusmn 000 397 013

158 MRI-ESM1 0 054 plusmn 005 056 plusmn 014 -014 plusmn 019 052 plusmn 013 089 plusmn 002 013 plusmn 001 177 011

159 NorESM1-M 0 072 plusmn 005 043 plusmn 012 000 plusmn 018 039 plusmn 012 082 plusmn 002 013 plusmn 000 202 010160 1 042 plusmn 005 063 plusmn 012 -002 plusmn 017 080 plusmn 012 087 plusmn 002 013 plusmn 000 234 011161 2 032 plusmn 005 049 plusmn 013 076 plusmn 018 030 plusmn 012 086 plusmn 002 013 plusmn 000 293 011

162 NorESM1-ME 0 055 plusmn 005 103 plusmn 014 058 plusmn 020 064 plusmn 013 087 plusmn 002 012 plusmn 001 134 011

average 058 plusmn 030 068 plusmn 042 048 plusmn 048 039 plusmn 037 109 plusmn 036 016 plusmn 006 5130 014

45

Table 3 See Sections 32 and 33 The regression coefficients φ usingEq 10 for band-pass frequency scales S1 S2 S3 and S4 for allavailable 162 GCM simulations and for their ensemble mean (whichis numbered -0- in the list) The χ2 test values were calculatedusing Eq 9 Last two columns report the correlation coefficientsbetween the GST power spectrum (periodogram and MEM) andthe correspondent GCM power spectra See also Figures 13 14and 15

model simulation S1 S2 S3 S4 χ2 Corr Coeff Corr Coeff 05-7 years 7-14 years 14-28 years 28-104 years Periodogram MEM

0 ensemble mean 005 036 081 063 86 079 -002

1 ACCESS1-0 0 -005 053 091 051 69 034 008

2 ACCESS1-3 0 006 012 122 055 153 048 -0073 1 -003 -011 114 077 194 063 0124 2 003 -003 122 078 171 081 028

5 bcc-csm1-1 0 003 037 121 108 67 097 0366 1 005 063 092 079 27 079 0197 2 006 062 133 070 51 093 032

8 bcc-csm1-1-m 0 002 057 118 023 120 025 -0119 1 009 100 091 063 21 021 -00610 2 000 083 175 020 183 050 -008

11 BNU-ESM 0 002 029 156 078 128 084 -003

12 CanESM2 0 -006 024 122 075 102 079 00213 1 -002 057 112 111 31 087 00914 2 -003 060 057 087 53 079 00015 3 005 007 086 090 133 077 -00416 4 -001 055 082 111 37 089 025

17 CCSM4 0 008 038 126 068 81 093 00118 1 -001 048 113 061 65 094 04219 2 010 057 067 049 82 093 01120 3 013 069 074 052 58 088 -00821 4 009 030 097 048 113 094 01322 5 003 041 150 049 128 084 004

23 CESM1-BGC 0 002 072 088 051 49 096 -003

24 CESM1-CAM5 0 004 047 068 025 140 081 04025 1 013 057 091 097 29 097 00326 2 003 053 058 111 59 087 006

27 CESM1-CAM5-1-FV2 0 009 037 041 077 118 085 -01128 1 005 028 057 101 105 097 -00229 2 009 -006 026 072 260 098 04530 3 000 034 069 059 103 064 009

31 CESM1-FASTCHEM 0 005 053 130 056 75 087 00632 1 006 063 089 071 34 093 00133 2 003 076 124 044 63 091 001

34 CESM1-WACCM 0 -001 063 143 050 84 090 029

35 CMCC-CESM 0 -004 003 -016 041 389 071 013

36 CMCC-CM 0 004 038 -053 040 459 034 003

37 CMCC-CMS 0 -005 -019 011 036 388 001 -004

38 CNRM-CM5 0 002 062 102 045 67 015 00139 1 -004 062 098 070 34 088 -00140 2 004 041 107 078 59 069 -00141 3 008 060 096 099 24 087 04442 4 009 064 118 053 57 078 00643 5 011 052 097 064 54 046 01344 6 004 054 103 104 32 098 06345 7 000 029 097 054 106 025 -01046 8 007 055 030 063 122 094 01947 9 003 030 092 110 76 088 046

48 CSIRO-Mk3-6-0 0 004 070 107 080 20 022 -01249 1 005 026 066 115 102 057 -01050 2 008 035 066 110 81 090 04651 3 -002 032 148 110 104 057 -00652 4 -003 014 096 122 118 042 -01053 5 007 011 075 085 131 034 -00954 6 008 026 043 054 160 050 -00355 7 004 060 061 117 50 066 -00756 8 004 015 007 048 275 017 00157 9 -006 031 028 062 169 016 -008

58 EC-EARTH 0 003 034 091 045 111 076 -00559 1 007 047 098 002 185 068 02360 2 001 005 089 053 167 087 00861 3 004 034 090 013 178 077 -00862 4 010 059 061 034 113 081 01163 5 001 006 101 081 138 094 00164 6 005 021 084 048 136 083 -00465 7 005 057 060 063 72 081 01466 8 001 075 130 057 51 089 -004

67 FGOALS-g2 0 000 006 019 021 320 048 -00768 1 -003 -004 034 056 252 090 07469 2 -001 -005 -006 046 372 078 08670 3 -001 020 024 033 247 083 -00371 4 -002 003 026 035 284 065 044

72 FIO-ESM 0 003 004 026 019 314 068 -01273 1 001 031 035 017 236 044 -00774 2 005 012 -007 021 377 053 001

75 GFDL-CM3 0 -003 033 106 163 125 087 -00676 1 002 070 082 127 29 098 01177 2 -003 062 052 100 55 055 -01278 3 010 044 094 128 57 058 00279 4 007 032 083 141 98 076 014

80 GFDL-ESM2G 0 005 009 126 081 138 063 01881 1 -002 016 119 031 180 -002 -00282 2 007 025 086 039 142 011 -003

83 GFDL-ESM2M 0 015 035 079 029 143 029 -011

84 GISS-E2-H p1 0 001 037 070 041 123 033 00685 1 005 049 082 036 102 047 02886 2 004 052 062 041 107 037 -00887 3 010 017 066 042 169 072 01688 4 005 053 077 042 92 083 -00689 5 007 047 095 045 88 069 000

90 GISS-E2-H p2 0 003 045 088 057 75 045 -01191 1 006 057 074 037 96 006 -01492 2 004 039 104 057 83 050 00793 3 004 036 109 057 90 029 -01394 4 002 053 080 054 71 053 -003

95 GISS-E2-H p3 0 003 049 091 056 69 057 -007

46

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion

95 GISS-E2-H p3 0 036 plusmn 005 050 plusmn 012 096 plusmn 018 026 plusmn 012 136 plusmn 002 022 plusmn 000 570 01496 1 032 plusmn 004 055 plusmn 011 020 plusmn 015 070 plusmn 010 166 plusmn 002 026 plusmn 000 1614 01797 2 041 plusmn 005 031 plusmn 012 034 plusmn 017 037 plusmn 011 147 plusmn 002 024 plusmn 000 852 01598 3 065 plusmn 004 072 plusmn 011 045 plusmn 015 044 plusmn 010 142 plusmn 002 023 plusmn 000 636 01399 4 031 plusmn 005 101 plusmn 012 072 plusmn 017 028 plusmn 011 136 plusmn 002 022 plusmn 000 621 014100 5 045 plusmn 005 099 plusmn 012 028 plusmn 017 019 plusmn 011 129 plusmn 002 017 plusmn 000 449 013

101 GISS-E2-H-CC p1 0 037 plusmn 004 077 plusmn 011 043 plusmn 016 050 plusmn 011 160 plusmn 002 023 plusmn 000 1277 016

102 GISS-E2-R p1 0 019 plusmn 004 021 plusmn 011 030 plusmn 015 019 plusmn 010 097 plusmn 002 015 plusmn 000 439 011103 1 031 plusmn 004 103 plusmn 011 076 plusmn 015 032 plusmn 010 110 plusmn 002 017 plusmn 000 302 010104 2 051 plusmn 004 061 plusmn 010 020 plusmn 015 043 plusmn 010 102 plusmn 002 016 plusmn 000 184 009105 3 049 plusmn 004 071 plusmn 011 086 plusmn 016 054 plusmn 011 109 plusmn 002 017 plusmn 000 170 010106 4 027 plusmn 004 105 plusmn 011 078 plusmn 016 036 plusmn 011 115 plusmn 002 018 plusmn 000 339 011107 5 032 plusmn 005 083 plusmn 012 046 plusmn 017 058 plusmn 011 096 plusmn 002 015 plusmn 000 233 012

108 GISS-E2-R p2 0 042 plusmn 004 048 plusmn 011 026 plusmn 016 041 plusmn 011 088 plusmn 002 014 plusmn 000 265 011109 1 063 plusmn 004 -052 plusmn 011 023 plusmn 016 050 plusmn 011 072 plusmn 002 012 plusmn 000 497 013110 2 017 plusmn 004 034 plusmn 011 115 plusmn 016 061 plusmn 011 078 plusmn 002 013 plusmn 000 500 012111 3 058 plusmn 005 068 plusmn 012 080 plusmn 017 055 plusmn 012 065 plusmn 002 010 plusmn 000 432 014112 4 021 plusmn 004 086 plusmn 011 047 plusmn 016 033 plusmn 011 072 plusmn 002 012 plusmn 000 554 013113 5 039 plusmn 004 080 plusmn 011 050 plusmn 015 036 plusmn 010 071 plusmn 002 011 plusmn 000 497 012

114 GISS-E2-R p3 0 031 plusmn 005 078 plusmn 012 046 plusmn 017 028 plusmn 011 095 plusmn 002 015 plusmn 000 270 012115 1 024 plusmn 004 056 plusmn 011 051 plusmn 016 088 plusmn 011 119 plusmn 002 018 plusmn 000 398 011116 2 056 plusmn 005 073 plusmn 012 074 plusmn 018 070 plusmn 012 124 plusmn 002 019 plusmn 000 244 012117 3 045 plusmn 004 129 plusmn 012 063 plusmn 016 001 plusmn 011 117 plusmn 002 019 plusmn 000 312 011118 4 017 plusmn 005 102 plusmn 012 033 plusmn 017 001 plusmn 012 108 plusmn 002 017 plusmn 000 404 012119 5 037 plusmn 004 117 plusmn 012 061 plusmn 016 084 plusmn 011 114 plusmn 002 018 plusmn 000 240 011

120 GISS-E2-R-CC p1 0 027 plusmn 004 052 plusmn 011 045 plusmn 015 038 plusmn 010 109 plusmn 002 015 plusmn 000 338 011

121 HadGEM2-AO 0 122 plusmn 005 156 plusmn 014 156 plusmn 020 038 plusmn 013 080 plusmn 002 010 plusmn 001 169 013

122 HadGEM2-CC 0 098 plusmn 005 077 plusmn 014 021 plusmn 020 049 plusmn 013 030 plusmn 002 003 plusmn 001 1209 019

123 HadGEM2-ES 0 103 plusmn 005 065 plusmn 014 -016 plusmn 020 053 plusmn 013 048 plusmn 002 006 plusmn 001 733 016124 1 076 plusmn 006 109 plusmn 015 006 plusmn 022 065 plusmn 015 049 plusmn 002 006 plusmn 001 630 019125 2 104 plusmn 005 146 plusmn 013 070 plusmn 018 033 plusmn 012 065 plusmn 002 008 plusmn 000 375 013126 3 040 plusmn 006 094 plusmn 015 059 plusmn 021 -044 plusmn 014 068 plusmn 002 009 plusmn 001 497 017

127 inmcm4 0 036 plusmn 003 017 plusmn 009 021 plusmn 012 001 plusmn 008 102 plusmn 001 016 plusmn 000 419 008

128 IPSL-CM5A-LR 0 089 plusmn 006 025 plusmn 015 073 plusmn 021 021 plusmn 014 160 plusmn 002 025 plusmn 001 893 018129 1 106 plusmn 005 067 plusmn 013 -033 plusmn 019 -011 plusmn 013 165 plusmn 002 026 plusmn 000 1223 018130 2 112 plusmn 005 093 plusmn 013 068 plusmn 019 037 plusmn 013 152 plusmn 002 024 plusmn 000 714 015131 3 053 plusmn 006 094 plusmn 014 061 plusmn 020 024 plusmn 014 167 plusmn 002 026 plusmn 001 1169 018132 4 065 plusmn 006 019 plusmn 015 089 plusmn 021 057 plusmn 014 155 plusmn 002 025 plusmn 001 785 017133 5 092 plusmn 005 135 plusmn 014 -006 plusmn 019 008 plusmn 013 136 plusmn 002 021 plusmn 001 431 014

134 IPSL-CM5A-MR 0 055 plusmn 005 096 plusmn 013 065 plusmn 018 042 plusmn 012 130 plusmn 002 021 plusmn 000 357 012135 1 063 plusmn 005 091 plusmn 014 062 plusmn 019 -002 plusmn 013 154 plusmn 002 024 plusmn 001 852 016136 2 086 plusmn 005 047 plusmn 013 044 plusmn 018 016 plusmn 012 166 plusmn 002 026 plusmn 000 1271 017

137 IPSL-CM5B-LR 0 004 plusmn 005 010 plusmn 013 088 plusmn 019 017 plusmn 013 143 plusmn 002 024 plusmn 000 919 016

138 MIROC5 0 088 plusmn 006 001 plusmn 016 125 plusmn 022 015 plusmn 015 070 plusmn 002 007 plusmn 001 294 014139 1 062 plusmn 006 080 plusmn 014 036 plusmn 020 061 plusmn 014 081 plusmn 002 010 plusmn 001 159 013140 2 083 plusmn 005 095 plusmn 014 089 plusmn 020 025 plusmn 013 088 plusmn 002 010 plusmn 001 84 011141 3 052 plusmn 006 024 plusmn 015 106 plusmn 021 024 plusmn 014 068 plusmn 002 007 plusmn 001 374 014142 4 059 plusmn 006 020 plusmn 014 041 plusmn 020 072 plusmn 014 079 plusmn 002 010 plusmn 001 213 014

143 MIROC-ESM 0 084 plusmn 005 049 plusmn 013 035 plusmn 018 080 plusmn 012 115 plusmn 002 018 plusmn 000 108 011144 1 028 plusmn 005 -021 plusmn 014 -070 plusmn 019 016 plusmn 013 112 plusmn 002 018 plusmn 001 455 015145 2 062 plusmn 005 077 plusmn 014 -004 plusmn 019 037 plusmn 013 106 plusmn 002 016 plusmn 001 127 013

146 MIROC-ESM-CHEM 0 049 plusmn 004 136 plusmn 011 -052 plusmn 016 072 plusmn 011 105 plusmn 002 016 plusmn 000 221 010

147 MPI-ESM-LR 0 011 plusmn 006 011 plusmn 015 017 plusmn 022 070 plusmn 015 144 plusmn 002 022 plusmn 001 761 018148 1 009 plusmn 005 041 plusmn 014 057 plusmn 020 107 plusmn 013 154 plusmn 002 024 plusmn 001 1052 016149 2 041 plusmn 006 088 plusmn 014 092 plusmn 020 -081 plusmn 014 131 plusmn 002 020 plusmn 001 563 014

150 MPI-ESM-MR 0 058 plusmn 005 041 plusmn 013 -042 plusmn 019 -051 plusmn 013 140 plusmn 002 021 plusmn 000 722 015151 1 010 plusmn 005 113 plusmn 013 086 plusmn 019 077 plusmn 013 140 plusmn 002 021 plusmn 000 731 014152 2 054 plusmn 005 072 plusmn 012 -002 plusmn 018 060 plusmn 012 139 plusmn 002 020 plusmn 000 543 014

153 MPI-ESM-P 0 039 plusmn 005 071 plusmn 013 117 plusmn 019 005 plusmn 013 146 plusmn 002 023 plusmn 000 751 015154 1 033 plusmn 006 067 plusmn 014 -013 plusmn 020 034 plusmn 014 147 plusmn 002 022 plusmn 001 757 017

155 MRI-CGCM3 0 013 plusmn 005 029 plusmn 012 033 plusmn 017 017 plusmn 012 072 plusmn 002 011 plusmn 000 638 012156 1 042 plusmn 005 060 plusmn 013 039 plusmn 019 046 plusmn 013 052 plusmn 002 008 plusmn 000 763 015157 2 052 plusmn 005 036 plusmn 013 016 plusmn 018 045 plusmn 013 070 plusmn 002 011 plusmn 000 397 013

158 MRI-ESM1 0 054 plusmn 005 056 plusmn 014 -014 plusmn 019 052 plusmn 013 089 plusmn 002 013 plusmn 001 177 011

159 NorESM1-M 0 072 plusmn 005 043 plusmn 012 000 plusmn 018 039 plusmn 012 082 plusmn 002 013 plusmn 000 202 010160 1 042 plusmn 005 063 plusmn 012 -002 plusmn 017 080 plusmn 012 087 plusmn 002 013 plusmn 000 234 011161 2 032 plusmn 005 049 plusmn 013 076 plusmn 018 030 plusmn 012 086 plusmn 002 013 plusmn 000 293 011

162 NorESM1-ME 0 055 plusmn 005 103 plusmn 014 058 plusmn 020 064 plusmn 013 087 plusmn 002 012 plusmn 001 134 011

average 058 plusmn 030 068 plusmn 042 048 plusmn 048 039 plusmn 037 109 plusmn 036 016 plusmn 006 5130 014

45

Table 3 See Sections 32 and 33 The regression coefficients φ usingEq 10 for band-pass frequency scales S1 S2 S3 and S4 for allavailable 162 GCM simulations and for their ensemble mean (whichis numbered -0- in the list) The χ2 test values were calculatedusing Eq 9 Last two columns report the correlation coefficientsbetween the GST power spectrum (periodogram and MEM) andthe correspondent GCM power spectra See also Figures 13 14and 15

model simulation S1 S2 S3 S4 χ2 Corr Coeff Corr Coeff 05-7 years 7-14 years 14-28 years 28-104 years Periodogram MEM

0 ensemble mean 005 036 081 063 86 079 -002

1 ACCESS1-0 0 -005 053 091 051 69 034 008

2 ACCESS1-3 0 006 012 122 055 153 048 -0073 1 -003 -011 114 077 194 063 0124 2 003 -003 122 078 171 081 028

5 bcc-csm1-1 0 003 037 121 108 67 097 0366 1 005 063 092 079 27 079 0197 2 006 062 133 070 51 093 032

8 bcc-csm1-1-m 0 002 057 118 023 120 025 -0119 1 009 100 091 063 21 021 -00610 2 000 083 175 020 183 050 -008

11 BNU-ESM 0 002 029 156 078 128 084 -003

12 CanESM2 0 -006 024 122 075 102 079 00213 1 -002 057 112 111 31 087 00914 2 -003 060 057 087 53 079 00015 3 005 007 086 090 133 077 -00416 4 -001 055 082 111 37 089 025

17 CCSM4 0 008 038 126 068 81 093 00118 1 -001 048 113 061 65 094 04219 2 010 057 067 049 82 093 01120 3 013 069 074 052 58 088 -00821 4 009 030 097 048 113 094 01322 5 003 041 150 049 128 084 004

23 CESM1-BGC 0 002 072 088 051 49 096 -003

24 CESM1-CAM5 0 004 047 068 025 140 081 04025 1 013 057 091 097 29 097 00326 2 003 053 058 111 59 087 006

27 CESM1-CAM5-1-FV2 0 009 037 041 077 118 085 -01128 1 005 028 057 101 105 097 -00229 2 009 -006 026 072 260 098 04530 3 000 034 069 059 103 064 009

31 CESM1-FASTCHEM 0 005 053 130 056 75 087 00632 1 006 063 089 071 34 093 00133 2 003 076 124 044 63 091 001

34 CESM1-WACCM 0 -001 063 143 050 84 090 029

35 CMCC-CESM 0 -004 003 -016 041 389 071 013

36 CMCC-CM 0 004 038 -053 040 459 034 003

37 CMCC-CMS 0 -005 -019 011 036 388 001 -004

38 CNRM-CM5 0 002 062 102 045 67 015 00139 1 -004 062 098 070 34 088 -00140 2 004 041 107 078 59 069 -00141 3 008 060 096 099 24 087 04442 4 009 064 118 053 57 078 00643 5 011 052 097 064 54 046 01344 6 004 054 103 104 32 098 06345 7 000 029 097 054 106 025 -01046 8 007 055 030 063 122 094 01947 9 003 030 092 110 76 088 046

48 CSIRO-Mk3-6-0 0 004 070 107 080 20 022 -01249 1 005 026 066 115 102 057 -01050 2 008 035 066 110 81 090 04651 3 -002 032 148 110 104 057 -00652 4 -003 014 096 122 118 042 -01053 5 007 011 075 085 131 034 -00954 6 008 026 043 054 160 050 -00355 7 004 060 061 117 50 066 -00756 8 004 015 007 048 275 017 00157 9 -006 031 028 062 169 016 -008

58 EC-EARTH 0 003 034 091 045 111 076 -00559 1 007 047 098 002 185 068 02360 2 001 005 089 053 167 087 00861 3 004 034 090 013 178 077 -00862 4 010 059 061 034 113 081 01163 5 001 006 101 081 138 094 00164 6 005 021 084 048 136 083 -00465 7 005 057 060 063 72 081 01466 8 001 075 130 057 51 089 -004

67 FGOALS-g2 0 000 006 019 021 320 048 -00768 1 -003 -004 034 056 252 090 07469 2 -001 -005 -006 046 372 078 08670 3 -001 020 024 033 247 083 -00371 4 -002 003 026 035 284 065 044

72 FIO-ESM 0 003 004 026 019 314 068 -01273 1 001 031 035 017 236 044 -00774 2 005 012 -007 021 377 053 001

75 GFDL-CM3 0 -003 033 106 163 125 087 -00676 1 002 070 082 127 29 098 01177 2 -003 062 052 100 55 055 -01278 3 010 044 094 128 57 058 00279 4 007 032 083 141 98 076 014

80 GFDL-ESM2G 0 005 009 126 081 138 063 01881 1 -002 016 119 031 180 -002 -00282 2 007 025 086 039 142 011 -003

83 GFDL-ESM2M 0 015 035 079 029 143 029 -011

84 GISS-E2-H p1 0 001 037 070 041 123 033 00685 1 005 049 082 036 102 047 02886 2 004 052 062 041 107 037 -00887 3 010 017 066 042 169 072 01688 4 005 053 077 042 92 083 -00689 5 007 047 095 045 88 069 000

90 GISS-E2-H p2 0 003 045 088 057 75 045 -01191 1 006 057 074 037 96 006 -01492 2 004 039 104 057 83 050 00793 3 004 036 109 057 90 029 -01394 4 002 053 080 054 71 053 -003

95 GISS-E2-H p3 0 003 049 091 056 69 057 -007

46

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion

Table 3 See Sections 32 and 33 The regression coefficients φ usingEq 10 for band-pass frequency scales S1 S2 S3 and S4 for allavailable 162 GCM simulations and for their ensemble mean (whichis numbered -0- in the list) The χ2 test values were calculatedusing Eq 9 Last two columns report the correlation coefficientsbetween the GST power spectrum (periodogram and MEM) andthe correspondent GCM power spectra See also Figures 13 14and 15

model simulation S1 S2 S3 S4 χ2 Corr Coeff Corr Coeff 05-7 years 7-14 years 14-28 years 28-104 years Periodogram MEM

0 ensemble mean 005 036 081 063 86 079 -002

1 ACCESS1-0 0 -005 053 091 051 69 034 008

2 ACCESS1-3 0 006 012 122 055 153 048 -0073 1 -003 -011 114 077 194 063 0124 2 003 -003 122 078 171 081 028

5 bcc-csm1-1 0 003 037 121 108 67 097 0366 1 005 063 092 079 27 079 0197 2 006 062 133 070 51 093 032

8 bcc-csm1-1-m 0 002 057 118 023 120 025 -0119 1 009 100 091 063 21 021 -00610 2 000 083 175 020 183 050 -008

11 BNU-ESM 0 002 029 156 078 128 084 -003

12 CanESM2 0 -006 024 122 075 102 079 00213 1 -002 057 112 111 31 087 00914 2 -003 060 057 087 53 079 00015 3 005 007 086 090 133 077 -00416 4 -001 055 082 111 37 089 025

17 CCSM4 0 008 038 126 068 81 093 00118 1 -001 048 113 061 65 094 04219 2 010 057 067 049 82 093 01120 3 013 069 074 052 58 088 -00821 4 009 030 097 048 113 094 01322 5 003 041 150 049 128 084 004

23 CESM1-BGC 0 002 072 088 051 49 096 -003

24 CESM1-CAM5 0 004 047 068 025 140 081 04025 1 013 057 091 097 29 097 00326 2 003 053 058 111 59 087 006

27 CESM1-CAM5-1-FV2 0 009 037 041 077 118 085 -01128 1 005 028 057 101 105 097 -00229 2 009 -006 026 072 260 098 04530 3 000 034 069 059 103 064 009

31 CESM1-FASTCHEM 0 005 053 130 056 75 087 00632 1 006 063 089 071 34 093 00133 2 003 076 124 044 63 091 001

34 CESM1-WACCM 0 -001 063 143 050 84 090 029

35 CMCC-CESM 0 -004 003 -016 041 389 071 013

36 CMCC-CM 0 004 038 -053 040 459 034 003

37 CMCC-CMS 0 -005 -019 011 036 388 001 -004

38 CNRM-CM5 0 002 062 102 045 67 015 00139 1 -004 062 098 070 34 088 -00140 2 004 041 107 078 59 069 -00141 3 008 060 096 099 24 087 04442 4 009 064 118 053 57 078 00643 5 011 052 097 064 54 046 01344 6 004 054 103 104 32 098 06345 7 000 029 097 054 106 025 -01046 8 007 055 030 063 122 094 01947 9 003 030 092 110 76 088 046

48 CSIRO-Mk3-6-0 0 004 070 107 080 20 022 -01249 1 005 026 066 115 102 057 -01050 2 008 035 066 110 81 090 04651 3 -002 032 148 110 104 057 -00652 4 -003 014 096 122 118 042 -01053 5 007 011 075 085 131 034 -00954 6 008 026 043 054 160 050 -00355 7 004 060 061 117 50 066 -00756 8 004 015 007 048 275 017 00157 9 -006 031 028 062 169 016 -008

58 EC-EARTH 0 003 034 091 045 111 076 -00559 1 007 047 098 002 185 068 02360 2 001 005 089 053 167 087 00861 3 004 034 090 013 178 077 -00862 4 010 059 061 034 113 081 01163 5 001 006 101 081 138 094 00164 6 005 021 084 048 136 083 -00465 7 005 057 060 063 72 081 01466 8 001 075 130 057 51 089 -004

67 FGOALS-g2 0 000 006 019 021 320 048 -00768 1 -003 -004 034 056 252 090 07469 2 -001 -005 -006 046 372 078 08670 3 -001 020 024 033 247 083 -00371 4 -002 003 026 035 284 065 044

72 FIO-ESM 0 003 004 026 019 314 068 -01273 1 001 031 035 017 236 044 -00774 2 005 012 -007 021 377 053 001

75 GFDL-CM3 0 -003 033 106 163 125 087 -00676 1 002 070 082 127 29 098 01177 2 -003 062 052 100 55 055 -01278 3 010 044 094 128 57 058 00279 4 007 032 083 141 98 076 014

80 GFDL-ESM2G 0 005 009 126 081 138 063 01881 1 -002 016 119 031 180 -002 -00282 2 007 025 086 039 142 011 -003

83 GFDL-ESM2M 0 015 035 079 029 143 029 -011

84 GISS-E2-H p1 0 001 037 070 041 123 033 00685 1 005 049 082 036 102 047 02886 2 004 052 062 041 107 037 -00887 3 010 017 066 042 169 072 01688 4 005 053 077 042 92 083 -00689 5 007 047 095 045 88 069 000

90 GISS-E2-H p2 0 003 045 088 057 75 045 -01191 1 006 057 074 037 96 006 -01492 2 004 039 104 057 83 050 00793 3 004 036 109 057 90 029 -01394 4 002 053 080 054 71 053 -003

95 GISS-E2-H p3 0 003 049 091 056 69 057 -007

46

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion

96 1 006 053 082 043 86 054 00797 2 004 038 085 055 91 035 03798 3 004 051 084 072 51 081 04199 4 005 040 110 047 98 050 -007100 5 006 040 103 063 73 048 -006

101 GISS-E2-H-CC p1 0 005 045 098 042 94 066 022

102 GISS-E2-R p1 0 006 025 041 024 221 035 -007103 1 003 041 090 031 123 044 -007104 2 003 029 083 045 124 069 016105 3 003 039 081 052 95 072 -005106 4 003 043 095 023 137 090 -007107 5 006 038 085 045 105 037 -008

108 GISS-E2-R p2 0 004 036 079 053 100 044 -009109 1 001 023 010 062 231 045 025110 2 003 062 049 028 138 005 -014111 3 006 054 088 074 43 052 013112 4 -001 025 084 035 150 025 -013113 5 -003 043 080 041 105 059 005

114 GISS-E2-R p3 0 005 032 097 040 122 026 001115 1 003 052 088 024 122 062 009116 2 001 069 108 056 44 091 -006117 3 009 041 115 049 95 060 046118 4 012 021 094 025 177 -020 -017119 5 005 060 106 026 106 067 001

120 GISS-E2-R-CC p1 0 007 045 071 031 127 032 -007

121 HadGEM2-AO 0 007 036 127 132 86 080 040

122 HadGEM2-CC 0 000 015 045 101 153 080 029

123 HadGEM2-ES 0 012 024 054 102 117 075 -011124 1 004 030 108 099 73 040 -011125 2 002 013 106 113 116 067 -004126 3 010 -010 095 058 207 028 -011

127 inmcm4 0 -005 001 026 034 290 095 063

128 IPSL-CM5A-LR 0 000 048 033 097 107 078 002129 1 009 030 113 096 75 084 049130 2 002 065 110 107 20 091 067131 3 005 064 083 047 66 075 008132 4 004 045 064 063 84 068 002133 5 000 015 130 073 130 084 028

134 IPSL-CM5A-MR 0 000 058 107 059 53 074 -006135 1 004 033 108 071 79 066 005136 2 000 004 065 082 159 077 065

137 IPSL-CM5B-LR 0 004 048 021 015 238 067 -011

138 MIROC5 0 010 059 -005 103 187 071 050139 1 -003 037 081 073 75 052 -006140 2 -003 018 081 094 105 076 -001141 3 008 044 027 058 152 049 -008142 4 002 067 058 079 49 035 -013

143 MIROC-ESM 0 002 063 072 092 33 082 060144 1 002 -007 035 055 264 028 -012145 2 003 021 110 078 102 051 -008

146 MIROC-ESM-CHEM 0 002 036 139 052 117 065 004

147 MPI-ESM-LR 0 003 058 096 -005 190 084 -003148 1 009 030 081 021 171 067 007149 2 004 042 095 035 113 081 -010

150 MPI-ESM-MR 0 005 -001 077 062 182 085 002151 1 012 082 090 014 116 005 -010152 2 001 034 051 053 133 075 003

153 MPI-ESM-P 0 004 023 097 047 131 062 045154 1 010 038 087 022 149 064 -012

155 MRI-CGCM3 0 000 015 034 020 266 035 038156 1 -004 008 054 055 187 050 -004157 2 003 019 049 065 153 039 -013

158 MRI-ESM1 0 005 012 082 062 141 057 -008

159 NorESM1-M 0 004 040 044 068 114 090 -001160 1 -004 040 067 043 119 076 -001161 2 000 014 059 040 189 058 -002

162 NorESM1-ME 0 009 069 093 055 45 071 -005

average 003 plusmn004 038 plusmn022 080 plusmn036 061 plusmn030 126 plusmn 80 063plusmn025 008plusmn 021

47

• 1 Introduction
• 2 Simple analysis of GST and the CMIP5 ensemble mean simulations
• 3 Scale-by-scale comparison between GST and the CMIP5 simulations
• • 31 Scale-by-scale harmonic decomposition comparison
  • 32 Scale-by-scale band-pass filter decomposition comparison
  • 33 Direct power spectrum comparison
  • • 4 Visual examples of CMIP5 GCM deficiencies
    • • 41 Example 1 the GCM simulations significantly diverge from the GST record since 2000
      • 42 Example 2 a detailed qualitative visual study of the CanESM2 GCM simulations
      • • 5 Discussion
        • 6 The astronomically-based empirical harmonic model
        • • 61 Millennial solar cycle paleoclimatic temperature reconstructions and their interpretation
          • 62 Construction of the astronomicalsolar harmonics
          • 63 The six-harmonic astronomicalsolar model for climate change
          • • 7 Conclusion