towards a theory for earth’s climate sensitivity (ecs) · instability in current climates. in...

Thorsten Mauritsen Max Planck Institute for Meteorology

Towards a theory for Earth’s Climate Sensitivity (ECS)

40 years of Consensus-building

1860 1880 1900 1920 1940 1960 1980 2000 2020

1.5 1.5

3.0 3.0

4.5 4.5

6.0 6.0

ECS(K

)

Stefan (1879),Boltzmann (1884)

Arrhenius (1896)

Callendar (1938)

Manabe and Wetherald(1967)

Augustsson andRamanathan (1977)

”We believe, therefore, that...”

Charney

FAR

SAR

TAR

AR4

p < 5%

p < 10%

AR5

Likely:p>

66%

Ansatz

1. Define a best estimate 2. Pose arguments why other best estimates are consistent 3. Explain what it would take for it to be wrong

1. Define a best estimate 2. Pose arguments why other best estimates are consistent 3. Explain what it would take for it to be wrong

�5 5 10

Approximate temperature relative to present (K)

2

4

6

8

10

ECS(K

)

Schmittner et al. (2011), Last glacial maximumHargreaves et al. (2012), Last glacial maximumMauritsen and Pincus (2017), Instrumental record warmingOngoing work, Instrumental record variabilityHargreaves and Annan (2016), PlioceneSha↵er et al. (2016), Late PaleoceneSha↵er et al. (2016), PETMRohling et al. (2012), LGM onlyCMIP5, Climate modelsBrient and Schneider (2016), low cloudsCharney report (1979)

Bloch-Johnsonetal.

(2015)

Meraner etal. (2013

)

Cloudy futuresScientists have good reasons to believe that changesto water in response to a given radiative forcing ac-count for more than half of Earth’s average surfacetemperature change. But estimating the climate sen-sitivity with greater precision remains difficult. Models that encapsulate the basic properties of waterproduce a wide range of estimates (see figure 4). Mostof the imprecision in climate sensitivity and re-gional patterns of rainfall changes can be related toa poor understanding of how clouds change in awarming climate15 and how changing clouds affectatmospheric circulations.8

Although clouds have long been recognized ascrucial for Earth’s radiation budget, only in the pastfew decades have researchers appreciated thatclouds can both warm and cool the atmosphere andthe surface. Early models of the climate system, to theextent that they considered clouds at all, assumedthat their effect on the enthalpy budget was not afunction of the climate state. But RCE models devel-oped in the early 1970s and later general-circulationmodels demonstrated that clouds exert a marked in-fluence on climate sensitivity.8,16

In addition to the idea of a positive feedback as-sociated with changes in the cloud-greenhouse effect,other ideas have begun to emerge as to why cloudi-ness might depend on the working temperature ofthe atmosphere. In most cases the ideas stem from thefundamental properties of water. For instance, be-cause the lapse rate of air that remains saturated as itrises is a function of temperature, warmer climatesmight be characterized by more condensate-ladenclouds; the larger optical depth increases the cloud- albedo effect and thereby moderates the warming. Incontrast, warming is also expected to be accompa-nied by increased evaporation, which drives moremixing in the lower atmosphere and may lead tofewer clouds, enhancing warming.17

As the singular challenge clouds pose to ourunderstanding of climate and climate change hasbecome better appreciated, research on clouds hasintensified. In recent years detailed experimentationand analyses of climate models have demonstratedwhich cloud regimes and processes are critical to ex-plaining intermodel differences in the projections offuture climate.15 Recent research also shows thatclouds directly mediate the response of the atmos-phere to an external forcing, and they do so on time

scales as short as a few hours.18 More generally, sostrong is the coupling between clouds and circula-tion systems, from thunderstorms to monsoons,that advancing our understanding of regional cli-mate change rests firmly on advancing our under-standing of clouds and cloud processes.

Despite imperfect models, our understanding ofthe behavior of the climate system is so deeply rootedin the basic physicochemical properties of the watermolecule that we can confidently conclude that globalwarming from anthropogenic emissions of long-livedgreenhouse gases poses serious risks. And yet we’rehampered by an inability to clearly pin down the paceof that warming and the nature of regional changes theplanet is likely to experience. A grasp of both is crucialfor adaptation measures. That fact highlights the ur-gent need to better understand the ways in whichwater couples to the atmosphere’s circulation systems.

We thank Kerry Emanuel, Isaac Held, John Mitchell, andRaymond Pierrehumbert for their extensive and thoughtfulcomments on an early version of this manuscript, and AikoVoigt for contributions to our discussion of RCE.

References1. K. P. Shine, I. V. Ptashnik, G. Rädel, Surv. Geophys. 33,

535 (2012).2. R. T. Pierrehumbert, Principles of Planetary Climate,

Cambridge U. Press, New York (2010).3. S. Manabe, R. T. Wetherald, J. Atmos. Sci. 24, 241 (1967).4. K. A. Emanuel, J. D. Neelin, C. S. Bretherton, Q. J. R.

Meteorol. Soc. 120, 1111 (1994).5. D. Popke, B. Stevens, A. Voigt, J. Adv. Model. Earth

Syst. (in press), doi:10.1002/jame.20009.6. B. Stevens, S. E. Schwartz, Surv. Geophys. 33, 779 (2012).7. G. L. Stephens et al., Nat. Geosci. 5, 691 (2012).8. A. Slingo, J. M. Slingo, Q. J. R. Meteorol. Soc. 114, 1027

(1988).9. D. L. Hartmann, K. Larson, Geophys. Res. Lett. 29, 1951

(2002).10. J. F. B. Mitchell, C. A. Wilson, W. M. Cunnington,

Q. J. R. Meteorol. Soc. 113, 293 (1987).11. S. C. Sherwood et al., J. Geophys. Res. 115, D09104 (2010).12. S. Bony et al., in Climate Science for Serving Society:

Research, Modelling, and Prediction Priorities, G. Asrar,J. W. Hurrell, eds., Springer, Berlin (in press).

13. I. M. Held, B. J. Soden, J. Climate 19, 5686 (2006).14. S. Bony et al., Nat. Geosci. (in press), doi:10.1038/ngeo1799. 15. S. Bony et al., J. Climate 19, 3445 (2006).16. V. Ramanathan, J. Coakley Jr, Rev. Geophys. Space Phys.

16, 465 (1978).17. M. Rieck, L. Nuijens, B. Stevens, J. Atmos. Sci. 69, 2538

(2012).18. J. Gregory, M. Webb, J. Climate 21, 58 (2008). ■

34 June 2013 Physics Today www.physicstoday.org

Water

SURFACE TEMPERATURE CHANGE K)(20 3

3.45

1.15

4

2.67

1

CMIP5 modeling

Robust feedbacks

a b cΔTd

ΔTwater

Figure 4. How much does the temperature of Earth’s surface changefrom doubling the carbon dioxide in the atmosphere? Comprehensiveclimate models from the coupled-model intercomparison project(CMIP5) yield a median estimate of 3.45 K bounded in the orange boxby the 25%–75% spread over the total range of values. Shown in blue arethe estimates of the temperature change based on well-understoodfeedback processes. In the absence of the effects of water, one expects awarming ΔTd of about 1 K. Water in the atmosphere increases that dry response by an additional 1.5 K. The amplification includes contributionsfrom processes described in the text: the combined watervapor andlapse- rate feedbacks (a), the cloud- greenhouse feedback (b), and the surfacealbedo feedback (c).

Downloaded 31 May 2013 to 136.172.75.107. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://www.physicstoday.org/about_us/terms

Robust understanding: 2.6 K Assumed unbiased best estimates (squares): 2.2-2.8 K

Stevens and Bony (2013)Schmittner et al. (2011), Hargreaves et al. (2012),

Hargreaves and Annan (2016), ongoing work

Ansatz

“I believe, therefore, that ECS is 2.6 K”

Best estimates of ECS vary

ECS ~ 4-5 K

ECS ~ 2-3 KECS ~1.6-2.0 K

Illustration modified from Glen Fergus

CMIP5 models: 3.4 K Emergent constraints: ~ 4 K

Instrumental Record ECS

Committed warming inferred from observations Mauritsen and Pincus

Methods147

Using an energy balance model two measures of the climate response to doubled CO2 concentrations,148

transient climate response (TCR) and equilibrium climate sensitivity (ECS), can be estimated18149

from observations of changes between two epochs in global-mean temperature �T and planetary150

imbalance �Q, as well as estimates of e↵ective radiative forcing F and the e↵ective radiative forcing151

at doubled CO2 (F2⇥) as152

TCR = F2⇥�T

�F(6)

ECS = F2⇥�T

�F ��Q(7)

where e↵ective radiative forcing, hereafter forcing, accounts for rapid adjustments27, i.e. responses153

of the climate system that a↵ect radiative balance but do not scale with temperature.154

In this work the present-day epoch estimates of temperature and planetary imbalance are com-155

puted over the years 2005-2015, as coincident with the latest planetary imbalance estimate10, while156

the reference epoch values are computed over the period 1859-1882; a period which, like the present-157

day epoch has seen little influence of volcanic eruptions on the global energy balance20. Estimates158

of annual, global mean surface temperature are taken from HadCRUT49 with uncertainty in �T159

set to 0.08 K20. Planetary imbalance is estimated10 as 0.71 Wm�2 with 5-95% confidence intervals160

of 0.10 Wm�2, and the corresponding values during the baseline period are estimated20 at 0.15 ±161

0.075 Wm�2. We take the forcing from greenhouse gases, aerosols, and a range of other sources162

(ozone, stratospheric water vapor, land use, contrails, solar variability, and black carbon on snow)163

from Annex II of the IPCC Fifth Assessment11. The F2⇥ is set to 3.71 Wm�2 which is consistent164

with the tabulated forcing. Uncertainty in each component is also taken from the assessment re-165

port21 and uncertainty in F2⇥ is set proportional to that of greenhouse gas forcing. The results are166

insensitive to the value of and amount of uncertainty in F2⇥ because �F appearing in the denomi-167

nator is dominated be greenhouse gas forcing and so random errors roughly cancel in the estimates168

of TCR and ECS. Forcing is evaluated at the center of the present-day epoch, year 2010, because169

the time series ends in 2011. All input to the analysis is tabulated in Table S1.170

Uncertainty in Equation 7 can be represented by treating each term as a probability distribu-171

tion18;19;20;14. Even symmetric uncertainty in forcing and, for ECS, in ocean heat uptake, creates172

skewed distributions18 of TCR and ECS because the terms appear in the denominator. Uncertainty173

Page 8

Zero-layer diagnostic model:


Figure 2: Estimates of committed warming under five di↵erent sets of assumptions as described in the

text. Displayed numbers are the median and 5-95 percentiles of the respective distribution. Also shown

in gray is the instrumental temperature record9, and black horizontal lines indicate the reference periods

used to estimate TCR and ECS (Figure 1). All temperatures are relative to the 1850-1899 mean, which is

here taken to be the pre-industrial reference temperature (Methods).

The result is a slight reduction in equilibrium committed warming (Figure 2 case c).65

Estimating the amount of warming to be realized in the current century requires accounting for66

the multiple timescales of equilibration in the climate system. These time scales – in an idealized67

view, a yearly to decadal time scale associated with equilibration of the atmosphere, upper soil and68

ocean mixed-layer, and a centennial to millennial time scale associated with the overturning of the69

deep oceans – imply that the temporal response of surface temperature is sensitive to the history70

of the applied forcing. An abruptly applied positive forcing, such as that arising from the cessation71

of anthropogenic aerosol emissions (�Faero

), is associated primarily with a fast warming near the72

surface, followed by slow warming, while equilibration with remnant planetary energy imbalance due73

to past forcing (Q) involves mainly a slow warming of the deep oceans. The fraction of equilibrium74

warming on centennial time scales may be estimated using ocean models of varying complexity2275

but these are poorly constrained by observations. Instead, we assume that the centennial response76

to present-day forcing will be consistent with the present response to historical forcing, and so77

Page 4

Gregory et al. (2002), Otto et al. (2013), Lewis and Curry (2015), Mauritsen and Pincus (2017)

0 1 2 3 4 5 6

Equilibrium Climate Sensitivity [K]

ECS: 1.79 [1.08 - 4.44]

Instrumental Record ECS


Methods147

Using an energy balance model two measures of the climate response to doubled CO2 concentrations,148

transient climate response (TCR) and equilibrium climate sensitivity (ECS), can be estimated18149

from observations of changes between two epochs in global-mean temperature �T and planetary150

imbalance �Q, as well as estimates of e↵ective radiative forcing F and the e↵ective radiative forcing151

at doubled CO2 (F2⇥) as152

TCR = F2⇥�T

�F(6)

ECS = F2⇥�T

�F ��Q(7)

where e↵ective radiative forcing, hereafter forcing, accounts for rapid adjustments27, i.e. responses153

of the climate system that a↵ect radiative balance but do not scale with temperature.154

In this work the present-day epoch estimates of temperature and planetary imbalance are com-155

puted over the years 2005-2015, as coincident with the latest planetary imbalance estimate10, while156

the reference epoch values are computed over the period 1859-1882; a period which, like the present-157

day epoch has seen little influence of volcanic eruptions on the global energy balance20. Estimates158

of annual, global mean surface temperature are taken from HadCRUT49 with uncertainty in �T159

set to 0.08 K20. Planetary imbalance is estimated10 as 0.71 Wm�2 with 5-95% confidence intervals160

of 0.10 Wm�2, and the corresponding values during the baseline period are estimated20 at 0.15 ±161

0.075 Wm�2. We take the forcing from greenhouse gases, aerosols, and a range of other sources162

(ozone, stratospheric water vapor, land use, contrails, solar variability, and black carbon on snow)163

from Annex II of the IPCC Fifth Assessment11. The F2⇥ is set to 3.71 Wm�2 which is consistent164

with the tabulated forcing. Uncertainty in each component is also taken from the assessment re-165

port21 and uncertainty in F2⇥ is set proportional to that of greenhouse gas forcing. The results are166

insensitive to the value of and amount of uncertainty in F2⇥ because �F appearing in the denomi-167

nator is dominated be greenhouse gas forcing and so random errors roughly cancel in the estimates168

of TCR and ECS. Forcing is evaluated at the center of the present-day epoch, year 2010, because169

the time series ends in 2011. All input to the analysis is tabulated in Table S1.170

Uncertainty in Equation 7 can be represented by treating each term as a probability distribu-171

tion18;19;20;14. Even symmetric uncertainty in forcing and, for ECS, in ocean heat uptake, creates172

skewed distributions18 of TCR and ECS because the terms appear in the denominator. Uncertainty173

Zero-layer diagnostic model:


Figure 2: Estimates of committed warming under five di↵erent sets of assumptions as described in the

text. Displayed numbers are the median and 5-95 percentiles of the respective distribution. Also shown

in gray is the instrumental temperature record9, and black horizontal lines indicate the reference periods

used to estimate TCR and ECS (Figure 1). All temperatures are relative to the 1850-1899 mean, which is

here taken to be the pre-industrial reference temperature (Methods).

The result is a slight reduction in equilibrium committed warming (Figure 2 case c).65

Estimating the amount of warming to be realized in the current century requires accounting for66

the multiple timescales of equilibration in the climate system. These time scales – in an idealized67

view, a yearly to decadal time scale associated with equilibration of the atmosphere, upper soil and68

ocean mixed-layer, and a centennial to millennial time scale associated with the overturning of the69

deep oceans – imply that the temporal response of surface temperature is sensitive to the history70

of the applied forcing. An abruptly applied positive forcing, such as that arising from the cessation71

of anthropogenic aerosol emissions (�Faero

), is associated primarily with a fast warming near the72

surface, followed by slow warming, while equilibration with remnant planetary energy imbalance due73

to past forcing (Q) involves mainly a slow warming of the deep oceans. The fraction of equilibrium74

warming on centennial time scales may be estimated using ocean models of varying complexity2275

but these are poorly constrained by observations. Instead, we assume that the centennial response76

to present-day forcing will be consistent with the present response to historical forcing, and so77

Page 4

Gregory et al. (2002), Otto et al. (2013), Lewis and Curry (2015), Mauritsen and Pincus (2017)

0 1 2 3 4 5 6


ECS: 1.79 [1.08 - 4.44]

• Aerosol forcing (Marvel et al. 2015) • Time-dependent feedback (Armour 2017) • Observational issues (Richardson et al. 2016) • Early period heat uptake (Huybers, in prep)

Underestimated Aerosol Cooling?

�1.5 �1.0 �0.5 0.0

Aerosol forcing wrt 1750 (W m�2)

1

2

3

4

ECS(K

)

• It will take about -1.3 Wm-2 to get ECS = 2.6 K • Such strong cooling is being contested

Time Dependent Feedback less Effective

0.0 0.5 1.0 1.5 2.0 2.5Ocean heat uptake e�cacy, ✏

0

1

2

3

4

5

ECS

CMIP5 model range, Geo↵roy et al. 2013

Zero-layer assumption

Two-layer assumption

NATURE GEOSCIENCE | ADVANCE ONLINE PUBLICATION | www.nature.com/naturegeoscience 1

news & views

Climate scientists broadly agree that Earth’s equilibrium climate sensitivity — the global warming that occurs

a long time after the atmospheric carbon dioxide has been doubled — is likely to be between 1.5 and 4.5 K. Estimates based on climate models often favour the upper end of the range1,2, whereas estimates based on instrumental-record warming tend to arrive at the lower end3,4. This apparent discrepancy is currently the subject of intense research efforts and a number of explanations have been proposed. Writing in Nature Geoscience, Zhou and colleagues5

show that the cloud response to a peculiar pattern of sea surface temperature warming could be the cause of the difference.

Climate sensitivity is determined by two factors: the radiative forcing from the increase in atmospheric carbon dioxide concentrations, which is fairly well known, and the less certain climate change feedback. Feedback is the rate of change in the Earth’s radiation budget with global mean surface warming, and is made up of contributions from infrared emissions to space due to the warming itself, as well as changes in atmospheric water vapour, surface

reflectivity and clouds. Cloud feedbacks are usually identified as the main source of uncertainty.

Feedback may not be constant over time: in climate models that use sea surface temperatures that were observed while keeping the atmospheric composition constant6, feedback rapidly becomes more negative by up to about a factor two from the 1950–1970s until now; a change that corresponds to a halving of the climate sensitivity. This is a puzzling result: it is unclear how climate sensitivity in a model could be so crucially different depending

GLOBAL WARMING

Clouds cooled the EarthThe slow instrumental-record warming is consistent with lower-end climate sensitivity. Simulations and observations now show that changing sea surface temperature patterns could have affected cloudiness and thereby dampened the warming.

Thorsten Mauritsen

Temperature trend 1980–2005 (K per year)

Remote warmingof troposphere

Strengthening inversion

–0.08 –0.06 –0.04 –0.02 0.00 0.02 0.04 0.06 0.08

More low-level clouds

a

b

c

Figure 1 | Schematic of the proposed mechanism for increasing low-level cloudiness with observed non-uniform sea surface temperature pattern. a–c, In areas of sea surface warming, strong updrafts in convectively precipitating areas lead to a fairly homogeneous vertical temperature profile warming (west Pacific, the black and red curves are idealized vertical temperature profiles before and after warming, respectively). Where sea surface temperatures are relatively cool, the lowermost mixed-layer of the atmosphere is also cool, but a sharp rise in temperature (inversion) occurs at 1–2 km height and stratocumulus clouds form below this temperature inversion. In the mid- and upper parts of the tropical troposphere the horizontal temperature gradients are kept weak by various atmospheric motions (red curly symbols). Therefore, when the warmest regions warm more than the colder regions (a), then the inversion becomes stronger (b), and more low-level clouds form (c). Zhou and colleagues5 show that this mechanism is responsible for the influence of sea surface temperature patterns on climate sensitivity. The map shows the trend in annual mean sea surface temperature for the period 1980–2005 from the HadSST3 dataset.

State Dependent Feedback

abrupt4xCO2

MPI-ESM-LRIPSL-CM5A-LRHadGEM2-ESCSIRO-Mk3.6.0CNRM-CM5BCC-CSM1.1

Surface temperature change (K)

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Meraner, Mauritsen and Voigt (2013)ECHAM6.0, mixed-layer ocean


Meraner, Mauritsen and Voigt (2013)

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ty (K

)

2xCO2

4xCO2

8xCO2

16xCO2

Fixed tropopause temperature

Fixed tropopause pressure

0 10 20 30 40 500

2

4

6

8

10

Glo

bal c

ontr

ol

Surface temperature ( C)o

TropicsExplanatory model (green):

• Constant RH

• Moist adiabat (RCE)

• Constant tropopause temperature


�5 5 10


2

4

6

8

10

ECS(K

)


Bloch-Johnsonetal.

(2015)

Meraner etal. (2013

)

I believe, therefore, that… ECS is 2.6 K (2.0-3.5)

The hypothesis requires the following to be consistent with current evidence:

• ECS rises in a warmer climate • Feedback must be highly time-dependent

and/or • Aerosol cooling strongly negative • Climate models miss negative feedback(s)

I believe, therefore, that… ECS is 2.6 K (2.0-3.5)

1.5 3.0 4.5 9.0


0

2

4

6

8

10

12

14Proba

bility,

Num

berofmodels

Process-level approach: ECS = �F2x/P�i

Zero cloud feedback

Multiple Lines of Evidence

Knutti et al. (2017)

4 NATURE GEOSCIENCE | ADVANCE ONLINE PUBLICATION | www.nature.com/naturegeoscience

REVIEW ARTICLE NATURE GEOSCIENCE DOI: 10.1038/NGEO3017

Cons

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Equilibrium climate sensitivity (°C)

Revi

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ned

lines

of e

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nce

Arrhenius (1896); best estimate for different regions Hulburt (1931); best estimate Callendar (1938); best estimate Plass (1956); best estimate Möller (1963); best estimate Augustsson and Ramanathan (1977); range of experiments Charney et al. (1979); best estimate Lorius et al. (1990); best estimate IPCC FAR Houghton (1990) IPCC SAR Houghton (1995) Idso (1998); best estimate IPCC TAR Houghton (2001); likely Hegerl et al. (2006); median and 90% Annan and Hargreaves (2006); maximum likelihood and 95% Edwards et al. (2007) IPCC AR4 Solomon et al. (2007); best estimate and 66% Knutti and Hegerl (2008); best estimate and 66% Palaeosens (2012); mean and 90% Skinner (2012); best estimate and ballparkIPCC AR5 Stocker et al. (2013); 66% Annan and Hargreaves (2015); best estimate and 90% Heydt et al. (2016); range of best estimatesForster (2016); mean and 90% Loeb et al. (2016); range of estimates Specht et al. (2016); best estimate Stevens et al. (2016); 94% Lewis and Grünwald (2017); median and 90% Harde (2017); best estimate

Andronova and Schlesinger (2001); median and 90% Kaufmann and Stern (2002); plausible range Harvey and Kaufmann (2002); most likely and favoured Gregory et al. (2002); mode see paper for uncertaintyKnutti et al. (2002); median and 90% Forest et al. (2002); mean and 90% Frame et al. (2005); median and 90% Tsushima et al. (2005); mean and standard error Andreae et al. (2005); supported range Stern et al. (2006); best estimate Forest et al. (2006); mean and 90% Forster and Gregory (2006); median and 95%Schwartz (2007/08); mean and 1σ based on time constant and heat capacity Chylek et al. (2007); 95%Tomassini et al. (2007); mean and 90% Forest et al. (2008); mean and 90% Sanso et al. (2008); mean and 90% Sanso and Forest (2009); mean and 90% Lindzen and Choi (2009); mean and standard error Meinshausen et al. (2009); mode and 90% Murphy et al. (2009); supported range from short-term observations Bender et al. (2010); mean and 95%Lin et al. (2010); best estimate see paper for uncertainty Roe and Armour (2011); median and 90% Lindzen and Choi (2011); mean and 95% Huber et al. (2011); median and likely range Libardoni and Forest (2013); median and 90% Schwartz (2012); range consistent with observations and forcing estimatesAldrin et al. (2012); mean and 90% Olson et al. (2012); mode and 95% van Hateren (2013); mean and standard error, see paper for definitionsBengtsson and Schwartz (2013); best estimate and 1σ for lower limit of sensitivityLewis (2013); median and 90% Otto et al. (2013); median and 90% for 1970–2009Otto et al. (2013); median and 90% for 2000sHarris et al. (2013); median and 90% Donohoe et al. (2014); best estimate Masters (2014); median and 90% Bodman et al. (2013); median and 90%Lewis (2014); median and 90% Schwartz et al. (2014); range consistent with observations and AR5 likely forcing range Urban et al. (2014); median and 90% Lovejoy (2014); mean and standard error Kummer and Dessler (2014); central value and 90% see paper for uncertainty Skeie et al. (2014); mean and 90% Lewis and Curry (2015); median and 90% Loehle (2014); best estimate and 95% Cawley et al. (2015), correcting Loehle (2014); 95% Loehle (2015); best estimate Marvel et al. (2015); mean and 90% Johansson et al. (2015); mode and 90% for data until 1986 Johansson et al. (2015); mode and 90% for data until 2011 Monckton et al. (2015); mean and consistent model parameterLewis (2016); median and 90% Bates (2016); "in the neighborhood" Armour (2017); best estimate and 90%

0 2 4 6 8 10

Figure 2 | Overview of published best estimates and ranges for equilibrium climate sensitivity constrained by different lines of evidence. As with Fig. 1, but the grey shaded range marks the 1.5 °C to 4.5 °C range within which the IPCC have assessed that ECS is ‘likely’ to lie (probability >66%), the grey vertical lines indicate a value of 1 °C below which ECS is ‘extremely unlikely’ (<5%), and a value of 6 °C above which ECS is ‘very unlikely’ (<10%). Details and assumptions are given in the text, Methods section and the Supplementary Table. Supplementary Figure 1 provides a combination of Figs 2 and 3.



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Equilibrium climate sensitivity (°C)

Covey et al. (1996); plausible range Lea (2004); mean and standard error Annan et al. (2005); mean and standard deviation Schneider von Deimling et al. (2006); 90% Royer et al. (2007); mean and 90% see paper for definitions Chylek and Lohmann (2008); mean and 95% Dunkelye Jones et al. (2010); best estimate Köhler et al. (2010); most likely and 90% Holden et al. (2010); mode and 90%Rohling et al. (2012); mean and uncertainty, see paper for aerosol forcing uncertainty Hargreaves et al. (2012); median and 90% Schmittner et al. (2011); median and 90% Caballero and Huber (2013); range of simulations Kutzbach et al. (2013); model range warm Pleistocene Kutzbach et al. (2013); model range cold Pleistocene Heydt et al. (2014); best estimate, see paper for uncertainty Harrison et al. (2015); best estimate Köhler et al. (2015); mean and 68% for cold Pleistocene Köhler et al. (2015); mean and 68% for warm Pleistocene Martínez-Botí et al. (2015); 68% Shaffer et al. (2016); preferred value PETM, see paper for uncertainty Shaffer et al. (2016); preferred value pre-PETM, see paper for uncertaintyHargreaves and Annan (2016); best estimate Anagnostou et al. (2016); mode and 66% for one proxyFriedrich et al. (2016); mean and likely range for cold Pleistocene Friedrich et al. (2016); mean and likely range for warm Pleistocene

Murphy et al. (2004); median and 90% Knutti et al. (2006); median and 90% Huber and Knutti (2011); mean and 90% Loutre et al. (2011); range of parameter settings Sexton et al. (2012); mean and 90% Fasullo and Trenberth (2012); constraint model rangeTett et al. (2013); best estimate and 95% Masson and Knutti (2013); best estimate and 95% Su et al. (2014); lower bound Sherwood et al. (2014); best estimate and plausible rangeTian (2015); best estimateSanderson (2015); mean and 90% Zhai et al. (2015); mean and standard deviation Brient and Schneider (2016); most likely and 90% Tan et al. (2016); best estimate Siler et al. (2017); most likely and 90%

Manabe and Wetherald (1967); best estimate and range for different assumptions Manabe and Wetherald (1975); best estimate Ramanathan et al. (1979); range of different models, Northern Hemisphere only Piani et al. (2005); median and 90% Räisänen (2005); median and 90% Stainforth et al. (2005); median and 90% Forster and Taylor (2006); mean and standard deviation Soden and Held (2006); mean and range of all models CMIP3 median and range of all models CMIP5 median and range of all models Sanderson et al. (2011); mean and 90% for one ensemble Andrews et al. (2012); mean and range of all models Olivié et al. (2012); mean and range of all models Geoffroy et al. (2013b); mean and range of all models Geoffroy et al. (2013a); mean and range of all models Dessler (2013); best estimate and standard deviation of model ensemble Sanderson (2013); most likely and 90%Forster et al. (2013); mean and 90% Chung and Soden (2015); range of all models Andrews et al. (2015); mean and range of all models Zelinka et al. (2016); null hypothesis Caldwell et al. (2016); mean and range of all modelsRagone et al. (2016); best estimate without ocean heat transport Lucarini et al. (2017); best estimate with ocean heat transport by diffusion Proistosescu and Huybers (2017); median and 90%

0 2 4 6 8 10

Figure 3 | Overview of published best estimates and ranges for equilibrium climate sensitivity constrained by different lines of evidence. Continued from Fig. 2. Supplementary Figure 1 provides a version where Figs 2 and 3 are combined.



The use of the recent warming as a constraint is attractive, as greenhouse gases have ‘likely’ caused 0.5 °C to 1.3 °C of warming (>66% probability) over the period 1951−2010, whereas there is

also ‘very likely’ a human contribution to upper-ocean warming7. However, estimating ECS and TCR from the instrumental record requires a conceptual or physical model10. In the simplest form, the

Schneider von Deimling et al. (2006); 90% Friedrich et al. (2016); mean and likely range

IPCC TAR Houghton et al. (2001) IPCC AR4 Solomon et al. (2007); 80% Knutti and Hegerl (2008); 90% Meinshausen et al. (2009); 90% IPCC AR5 Stocker et al. (2013); 66%

Loutre et al. (2011); range of parameter sets Harris et al. (2013); median and 90% van Hateren (2013); mean and standard error Hawkins et al. (2014); median and 90% see paper for uncertainty estimates Shindell (2014); best estimate and 95% Millar et al. (2015); mean and 90% Sanderson (2015); best estimate and 90%

Raper et al. (2002); best estimate Räisänen et al. (2005); median and 90% Collins et al. (2006); best estimate CMIP3 range of all models CMIP5 range of all models Forster et al. (2013); mean and 90% Marvel et al. (2015); mean and 90% Ragone et al. (2016); best estimate = 7.2° C without ocean heat uptake Lucarini et al. (2017); best estimate with ocean heat uptake by diffusion

Stern et al. (2006); best estimate Stott et al. (2006); ref. 222, mean and 90% Frame et al. (2006); mode and 90% Forest et al. (2008); mode and full range Tung et al. (2008); best estimate Gregory and Forster (2008); median and 90% Knutti and Tomassini (2008); median and 90% Bender et al. (2010); 95% Schwartz (2012); range consistent with observations and forcing estimates Gillett et al. (2012); 90% for 1900–2000 Gillett et al. (2012); 90% for 1850–2010 Rogelj et al. (2014); median and 90% Bengtsson and Schwartz (2013); best estimate and 1σ for lower limit of sensitivityPadilla et al. (2011); most likely and 90% Libardoni and Forest (2013); median and 90%Otto et al. (2013); median and 90% for 1970–2009 Otto et al. (2013); median and 90% for 2000s Gillett et al. (2013); mean and 90%van der Werf and Dolman (2014); mean and 90% Skeie et al. (2014); mean and 90% Merlis et al. (2014); median and 50% Rypdal and Rypdal (2014); best estimate Ollila (2014); best estimate Loehle (2014); best estimate and 95% Cawley et al. (2015), correcting Loehle (2014); 95% Cawley et al. (2015); mode and 95% Myhre et al. (2015); best estimtate and 90% Loehle (2015); best estimate Lewis and Curry (2015); median and 90% Lewis (2016); median and 90% Ollila (2016); best estimate Storelvmo et al. (2016); best estimate and 95% Richardson et al. (2016); best estimate and 90% Jones et al. (2016); best estimate

Transient climate response (°C)

Cons

train

ts fr

om th

e ob

serv

ed w

arm

ing

in re

spon

se to

forc

ing

Infe

rred

from

GCM

sCo

nstra

ined

with

clim

atol

ogy

Revi

ews

Pala

eocl

imat

em

odel

ling

0 1 2 3 4

Figure 1 | Overview of published best estimates and ranges for the transient climate response constrained by different lines of evidence. Different colours represent different studies. Dots mark means, medians or best estimates; lines mark different percentile ranges. The grey shaded range marks the 1 °C to 2.5 °C range within which the TCR is ‘likely’ to lie (probability >66%) as assessed by the IPCC, the grey vertical line indicates a value of 3 °C above which TCR is ‘extremely unlikely’ (<5%). Details and assumptions are given in the text, the Methods section and Supplementary Table 1.

Time- and State Dependence

0 5 10 15 20

Temperature (K)

0

5

10

15

Imblance

(Wm�2)

0 5 10 15 20

Temperature (K)

0

5

10

15

Imblance

(Wm�2)

Low-level cloud emergent constraints

than that of interannual variability so that the deseason-alized variability that we used above provides more ro-bust constraints on ECS than seasonal variability.Of course, all of these posterior ECS estimates are

conditional on the range of ECS simulated by the CMIP5models. They merely indicate which ECSs in the modelrange are more plausible than others, given the observa-tions. They do not rule out ECSs entirely outside the rangeindicated by current climatemodels: that is, that allmodelsare wrong. We found our information-theoretic weightingof climate models to give more robust posterior ECS es-timates than methods that are based, for example, onestimating regression lines between ECS and present-day

dac/dhTi from climate simulations and that then use theestimated regression lines for inferences about the pos-terior ECS. Such methods can underestimate theweight of LS models that are consistent with the data weconsidered; they thus can lead to unrealistically narrowposterior ECS estimates. By contrast, our information-theoretic weighting yields more realistic posterior esti-mates for the mode and confidence bounds of the ECS.

4. Influence of inversion strength

Other environmental factors besides the surfacetemperature may influence TLCs: for example, vertical

FIG. 6. Constraining ECS using the covariance of deseasonalized TLC reflection with SST.(a) Scatterplot of ECS vs deseasonalized dac/dhTi in CMIP5 models (numbered in order ofincreasing ECS; Table 1). Gray lines represent the robust regression line (solid; r520.67) andthe 90% bootstrap confidence interval (dashed). The green line at the lower axis indicates thePDF of the deseasonalized dac/dhTi inferred from observations. (b) Posterior PDF of ECS(orange) obtained by a weighted average of the climate models, given the observed desea-sonalized dac/dhTi. The bars with circles represent themode and confidence intervals (66%and90%) implied by the posterior (orange) PDF and the prior (gray) PDF.

TABLE 4. Posterior ECS estimate given observations. The ECS estimates and 90% confidence interval (in square brackets) are based on thepriorECSestimate given by 29CMIP5models,with thepriormost likely value 3.6Kandprior 90%confidence interval [1.86, 4.80]. The estimatesare weighted by (columns from left to right) howwell models reproduce the univariate regression coefficient of TLC reflection onto temperature(b1), how well they reproduce the bivariate regression coefficients of TLC reflection onto temperature (~b1) or onto inversion strength (~b2), orhow well they simultaneously reproduce both regression coefficients (~b1, ~b2). Boldface numbers represent ECS estimates for which the cor-relation coefficients between ECS and the corresponding regression coefficient in climate models are relatively high (jrj . 0.65).

Band ECS (b1) ECS (~b1) ECS (~b2) ECS (~b1, ~b2)

Deseasonalized 3.98 [2.25, 4.96] 3.92 [2.36, 4.96] 3.87 [1.99, 4.72] 3.98 [2.43, 4.84]Intra-annual 4.04 [1.98, 4.85] 3.81 [2.03, 4.87] 4.04 [1.96, 4.81] 4.10 [1.95, 4.85]Seasonal 4.09 [2.42, 4.90] 2.94 [2.01, 4.52] 2.77 [1.95, 4.51] 2.65 [1.78, 3.65]Interannual 3.58 [2.16, 4.75] 3.87 [2.34, 4.89] 3.37 [1.93, 4.74] 3.81 [2.29, 4.81]

5830 JOURNAL OF CL IMATE VOLUME 29

Brient and Schneider (2016)Sherwood et al. (2014)

Climate Dynamics Course Notes Mauritsen

feedback), is found in climate models to be about +1.2 Wm�2K�1, and so is not su�cient to causeinstability in current climates. In warmer climates the positive water vapor feedback is thoughtto increase faster than the negative Planck feedback and so could aid in destabilising the system.Finally, the first term on right hand side of Eq. 3.2 is the planetary albedo feedback, which is dueto clouds, surface albedo as well as absorption by the atmosphere foremost water vapor. It is leftas an exercise to estimate the criterion for instability when considering planetary albedo feedback.

3.2 Feedback mechanisms

Above we calculated the feedback parameter for the general case (Eq. 3.2) and identified threeterms, one related to how planetary albedo changes with temperature, one related to how thee↵ective emissivity changes and one which is directly related to the Planck feedback. Now, if wewant to go about understanding and quantifying the feedback it is more convenient to make anotherdivision. For instance the planetary albedo is controlled by changes in surface albedo, cloudiness andwater vapor, as well as some other factors such as aerosol particles and ozone that we shall ignorehere as feedbacks. As a first step let us divide � into contributions due to changes in temperature,water vapor, clouds and surface albedo:

� = �T

+ �W

+ �C

+ �A

+ ... (3.4)

where there are a number of additional terms due to interactions between e.g. clouds and watervapor changes as well as other factors that we have ignored. As long as we consider relativelysmall perturbations then the interactions between feedbacks are of secondary importance. For largeperturbations, however, it is easy to appreciate that this will no longer be the case. For instanceat high latitudes cloudiness tends to increase in a warming climate, and so a decreasing surfacealbedo will have less of an impact on the energy imbalance than in a colder case. Or if the verticaltemperature structure is substantially altered due to a rising tropopause, then the impacts of cloudsand water vapor changes on the greenhouse e↵ect may be di↵erent.

It turns out to be meaningful to divide the temperature feedback parameter into two contributions(Figure 3.3). The Planck feedback is that which would occur if the entire troposphere would warm atthe rate of the surface temperature (gray shading). The lapse-rate feedback is that due to deviationsfrom vertically uniform warming. In a later chapter we shall study stratospheric adjustment as aresponse to changing CO

2

which is not considered a feedback, and so ignoring the stratospherictemperature changes, we can write the temperature feedback as:

�T

⇡ �P

+ �LR

. (3.5)

The planck feedback is therefore always negative, whereas the lapse-rate feedback could be eitherpositive or negative: If the troposphere warms faster than the surface temperature then the systemcan radiate more to space relative to the case where warming was vertically uniform. This is thecase in the tropics where the troposphere is vertically mixed by deep convective clouds (as in Figure3.3). At high latitudes, however, the surface may well warm faster than the troposphere such thatthe lapse-rate feedback is a positive feedback mechanism acting to amplify regional warming (Pithanand Mauritsen5). However, because the tropics cover a much larger area the lapse-rate feedback isthought to be on average negative.

It is worth noting that the division of feedback parameters chosen here is only one of manypossible divisions, a few of which makes sense. A powerful recent development has been to includesome of the water vapor feedback into the temperature feedback, namely that which would occurif relative humidity stayed fixed (Held and Shell7). This is e↵ective since, as we shall argue next,changes in relative humidity tend to be small in climate models.

respectively). These correlations suggest that the predictive skill ofLTMI arises from both subsidence and other regions; further workis needed to better assess this. Cloud amount reduces more in high-LTMI models both at low and mid-levels (Extended Data Fig. 3),although the greater net radiative impact of low cloud makes its effectdominant16. Previously reported water vapour and lapse-rate feed-backs17 are, in contrast, not correlated with the LTMI.

Is the imputed lower-tropospheric mixing impact on low cloudsstrong enough to explain the approximately 1.5 W m22 K21 spread ofcloud feedbacks seen in GCMs?4 One recent study18 imposed increasedsurface latent heat fluxes in a large region typified by shallow clouds,finding an increase in cloud-related net cooling of about 1 W m22 for a2–3 W m22 increase in the surface flux, other things held fixed. Aneven larger sensitivity, nearly 1:1, has been reported in a differentmodel for advective changes in moisture input19. If a similar but oppositecloud response occurred for moisture removal by lower-troposphericmixing, then to explain the feedback spread, the boundary-layer dryingresponses would need to span a range across models of about 3 W m22

per K of surface warming. This roughly matches the contribution to thespread from Msmall alone (Fig. 2b). The additional drying responsefrom MLT, large was about 0.6 W m22 K21 greater in the high-D models(mean D of 0.34) than in the low-D ones (mean 0.24), which, if rescaledby the full spread of D in the full GCM ensemble, implies a furthersource of spread in drying response of about 2 W m22 K21. We con-clude that, even if not all low clouds are as sensitive as the ones exam-ined in the cited studies, the lower-tropospheric mixing response isstrong enough to account for the cloud feedback spread and its typ-ically positive sign5.

Why does moisture transport increase so strongly with warming?The magnitude of these increases, typically 5%–7% per K of surfacewarming, is roughly what would be expected if the circulations remainedsimilar against a Clausius–Clapeyron increase in moisture gradients20,as indeed it does, at least for the large-scale part21 (Extended Data Fig. 4).Further study is needed to understand why this is so, and to examine ingreater detail how clouds respond to changing moisture transports;changes in low cloud amount may for example help the atmosphererestore imbalances in boundary layer moist enthalpy such as those causedby lower-tropospheric mixing19. Because LTMI ignores any informationon clouds, it is likely that additional measures of cloud characteristics22

could explain some of the variations in low-cloud feedback not yetexplained here.

We end by considering observational estimates of S and D (seeFig. 5). These show an S near the middle of the GCM range, but aD close to the top end, as hinted already by Fig. 3. D may not be wellconstrained because v must be inferred from observational reana-lyses, although available horizontal wind observations support theexistence of strong mid-level outflows13, and the result is consistentacross both reanalyses examined. The reanalysis estimates of S are lessconsistent but this quantity can be fairly well constrained by radio-sonde observations.

Taking the available observations at face value implies a most likelyclimate sensitivity of about 4 uC, with a lower limit of about 3 uC.Indeed, all 15 of the GCMs with ECS below 3.0 uC have an LTMIbelow the bottom of the observational range. Further work may beneeded to better constrain these indices, and to test whether theirrelationship to ECS is robust to design factors common to all models.For example, this should be tested in global cloud-resolving models.

–0.8 –0.6 –0.4 –0.2 0.0 0.2

Large-scale source (g kg–1 day–1)

1,000

800

600

400

200

Pre

ssur

e (h

Pa)

High D

Low D

High D, +4 K

Low D, +4 K

Figure 4 | Estimated water vapour source MLT, large due to large-scale lower-tropospheric mixing and its response to warming. See Methods forcalculation details. Data are from ten atmosphere models, averaged from 30u Sto 30uN over oceans, with the average of the four models having the largest Dshown in magenta and the average of the four models with the smallest Dshown in blue. Dashes show results in 14 K climate. Changes at 14 K arenearly identical whether or not land areas are included.

0.2 0.3 0.4 0.5 0.6 0.7S

1

2

3

4

5

Clim

ate

sens

itivi

ty

a

r = 0.50

0.1 0.2 0.3 0.4 0.5D

1

2

3

4

5

Clim

ate

sens

itivi

ty

b

r = 0.46

0.4 0.5 0.6 0.7 0.8 0.9 1.0

LTMI, (S + D)

1

2

3

4

5

Clim

ate

sens

itivi

ty

c

r = 0.68/0.70

MERRA

ERAi

Figure 5 | Relation of lower-tropospheric mixing indices to ECS. ECS versusS (a), D (b) and LTMI 5 S 1 D (c) from the 43 coupled models with knownECS. Linear correlation coefficients r are given in each panel (r 5 0.70 in c is thecorrelation to the total system feedback). Error bars shown near panel axesindicate 2s ranges of the direct radiosonde estimate (a) and the S value fromradiosondes added to the D value from each of the two reanalyses (c). ERAi andMERRA are the two monthly reanalysis products.

RESEARCH ARTICLE

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A missing iris-effect

NATURE GEOSCIENCE | VOL 8 | MAY 2015 | www.nature.com/naturegeoscience 347

strength of the net temperature restoration depends on atmospheric feedback mechanisms. In the case of open domains such as the one analysed here, lateral fluxes of energy out of the domain can change.

Satellite data from the Clouds and the Earth’s Radiant Energy System (CERES) instruments show a strong negative longwave regression close to the Planck feedback in the tropics16, and a weak positive shortwave regression to yield a net regression of −3.2 ± 1.0 W m−2 K-1 (Fig. 2, Supplementary Table 2). The ensemble mean of the climate models of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) matches the observed relation-ship between temperature and net shortwave radiation, albeit with considerable scatter, but systematically exhibits a longwave regres-sion that is too weak (Fig. 2b, Supplementary Table 3). Analysis of irradiances measured in cloud-free regions reveals that the dis-crepancy in the longwave radiation is due to both water vapour and clouds, with the latter dominating. The regression coefficients are sensitive to methodological details, for instance the treatment of vol-canoes7,15, or the lag (or no lag) in the radiative response relative to temperature changes8, but the discrepancy between the observations on the one hand and the models on the other is robust.

The relationship between the slope of the regression of net radia-tion against temperature and ECS is not strong. Reference 8 pro-vides estimates of ECS from a set of 11 previous-generation CMIP3 models, as well as the actual ECS based on CO2-doubling experi-ments. Omitting one model with infinite estimated ECS, a dissat-isfying correlation between estimated and actual ECS of −0.11 is found, making it difficult to argue that a more negative regression coefficient between monthly anomalies of net radiation and tem-perature per se implies a smaller ECS. In the analysis of the CMIP5 ensemble presented here, we obtain stronger correlations of +0.38 and +0.32 between net regression and the inverse ECS for the Atmospheric Model Intercomparison Project (AMIP) and historical experiments, respectively (Supplementary Table 3). Of the eleven models that match CERES net regression in either experiment, four have ECS above 3 K and seven below. When run with a prescribed evolution of sea surface temperatures (AMIP) only the two versions of the Beijing Climate Center (BCC) model match observations in the slope of the regression between net, longwave and shortwave radiation with temperature. If run in coupled mode (historical) only one version of the Goddard Institute for Space Studies (GISS-E2-H) model matches CERES data.

Thus, whereas the discrepancy between the model ensemble and observations is suggestive of missing processes, the analysis of monthly variability in the tropical radiation budget poses at best weak constraints on global ECS.

Convective aggregation as a possible mechanismOne objection to the idea of an iris effect is that it is not clear what the physical mechanism might be. An iris effect could result if the efficiency of precipitation within deep convective cloud tow-ers increased with warming, leading to less detrainment into their anvils5,17. This could occur if aggregation of convective clouds into large clusters is temperature-dependent. Aggregation is due to an instability of radiative-convective equilibrium, whereby relatively dry regions cool radiatively, resulting in local subsidence and fur-ther suppression of convection, ultimately leading to an aggregated state with localized convective clusters18. The cooling of the dry and clear regions is expected to increase with warmer temperatures and hence promote aggregation19. In addition, in a warmer climate convective clouds may further be invigorated by enhanced latent heat release20.

As larger convective clouds dilute less by lateral mixing they pre-cipitate more of their water during ascent, and fewer large clusters can provide the necessary latent heating to sustain atmospheric radi-ative cooling (Fig. 1). Both cloud-resolving simulations21 and obser-vations22 confirm that outgoing longwave radiation does increase as a consequence of a drying environment in more aggregated states. Shortwave absorption also increases, which tends to cancel some of the effect. All in all, however, we conclude that it is plausible that con-vective aggregation constitutes a negative longwave feedback on cli-mate change — and to our understanding, the underlying processes are not explicitly represented in climate models.

In principle, the problem of convective aggregation lends itself to fine-scale simulations that explicitly resolve the dynamics of indi-vidual convective clouds. In small-domain simulations, however, whether or not convection will aggregate depends critically on reso-lution, domain-size and initial conditions23. This complicates the interpretation of possible temperature dependencies. Pioneering work to simulate convective clouds at the global scale has suggested a somewhat puzzling combined upper-level reduction in cloud ice with an increase in cloud cover in response to warming24. But the model’s feedback is highly sensitive to the representation of physical processes that remain unresolved. Cloud microphysics, in particular, represents a challenge to the application of fine-scale simulations25.

Climate model test with a simple parameterization Convective processes that could give rise to an iris effect are crudely represented in most global climate models. Despite some progress in understanding how convective aggregation could be enhanced at warmer temperatures, knowledge of how to incorpo-rate such processes remains primitive. For this reason, we simply scale the conversion rate from cloud water to rain (Cp) in convec-tive clouds in the ECHAM6 atmosphere general circulation model (Supplementary Methods) with local surface temperature, similar to a previous approach17:

Cp(Ts) = Co (1 + Ie) (1)Ts − To

where Co = 2 × 10−4 s−1 is the default conversion rate in ECHAM6, Ts is surface temperature, and To is a reference temperature set to 25 °C — a value typically found in the tropics. The parameter Ie is included to control the strength of the iris effect, and is here set to 0.2, 0.5 and 1.0, corresponding in the most extreme case to a doubling of the conversion rate per degree warming. Because the rate at which cloud water is converted to precipitation in convective clouds is not a directly observable quantity, but is important for the behaviour of the parameterization, it is frequently used as a tuning

Dry and cleary and cl Moist and cloudy

Iris expansions expans

Radi

ative

cool

ing

Late

nt h

eatin

g

Strong OLR Weak OLR

ing tropopauseropoRisi u

Figure 1 | Illustration of the tropical atmospheric circulation.

PERSPECTIVENATURE GEOSCIENCE DOI: 10.1038/NGEO2414

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Mauritsen and Stevens (2015)

A missing iris-effect

Mauritsen and Stevens (2015)

348 NATURE GEOSCIENCE | VOL 8 | MAY 2015 | www.nature.com/naturegeoscience

parameter, and as such has been varied by almost two orders of magnitude26. By comparison, the changes introduced through our simple parameterization, equation (1), are small. With these set-tings, in particular the choice of To, the present-day mean climate of ECHAM6-Iris is not appreciably different from that of the origi-nal model (Supplementary Figs 1–5 and Supplementary Table 1). Moreover, because precipitation outside the tropics is foremost carried by the large-scale cloud scheme, mid-latitude storms and

circulation are not directly affected much by the modification. The approach is clearly simplistic, but allows an exploration of the impli-cations of an iris effect in a simple and controllable way. Indeed, we find that whereas ECHAM6 was among the largest outliers in its representation of month-to-month tropical co-variability in radiation and surface temperature (Fig. 2), all three settings of Ie yield longwave regression coefficients in statistical agreement with the data.

The tropical atmosphere consists of moist and cloudy regions asso-ciated with large-scale rising motion, convective storms and pro-nounced precipitation on the one hand, and dry and clear regions with subsiding motion on the other hand (Fig. 1). The atmos-pheric circulation maintains an approximate balance between radiative cooling, which occurs preferentially in the dry and clear regions, and latent heating from the condensation of water vapour in precipitating clouds. As a conceptual starting point, convection occurs in a narrow intertropical convergence zone (ITCZ) near the Equator and subsidence is predominant in the subtropics, although the reality is, of course, more complicated.

Shifts in the tropical circulation in a warming climate can act either to amplify or to dampen the temperature change through feedback mechanisms. Positive and well-understood feedbacks arise; for example, specific humidity increases in a warmer cli-mate, and the altitude of convective cloud tops rises. Both these feedbacks act to reduce the outgoing longwave radiation (OLR), and thereby amplify surface warming.

The controversial ‘iris hypothesis’ proposes that the frac-tion of the dry and clear regions could increase with warming1 and exert a negative feedback: a larger extent of the dry and clear regions would lead to a less cloudy upper troposphere and hence an increase in OLR. Such an effect could mitigate against climate

change. But a drier upper troposphere would also allow more solar radiation to be absorbed by the Earth and atmosphere, rather than reflected back to space by the clouds, so that the net effect of reducing high clouds is not obvious12,13. On balance, the effect is thought to be negative.

Evidence for an iris effect is found in observations of tropical variability of upper-level cloud cover, precipitation and the radia-tion balance co-varying with natural variations of the surface tem-perature. These findings have led to estimates1,8 of the sensitivity of surface temperature to a doubling of atmospheric CO2 concentra-tions of only about 1 K, much lower than the broadly accepted range of 1.5–4.5 K (ref. 11). The estimate of ECS with an iris effect, however, depends not only on the rate of reduction of high-level clouds, but also on the cloud optical properties of the most sensi-tive clouds. If the thinnest clouds are preferentially removed, the effect on outgoing longwave radiation is stronger than that on reflectivity, and the iris effect is stronger. On the other hand, if the reduction in cloud cover affects thicker clouds more strongly, the loss in reflectivity plays a more important role, and the iris effect is less pronounced.

Notwithstanding its exact strength, the evidence for an iris effect has been contested, and the lack of a clear physical mechanism has caused widespread scepticism.

Box 1 | The tropical circulation and the iris effect.

Obs: CERES-EBAF 2.8CMIP5 historical

CMIP5 AMIPECHAM6

Ie = 0.2Ie = 0.5Ie = 1.0

Temperature (K)

Obs

Obs

Zero net regression

Shortwave regression (W m–2 K–1)

Net radiation (W m–2)

Longwave regression (W m–2 K–1)

CERES

net regression

a b

–2.0

–4.0

–6.0

2.0 4.0

4.0

1.0–1.0

–4.0

6.00.0

Figure 2 | Regression lines calculated from anomalies of top of atmosphere radiation versus surface temperature in the tropics (20° S to 20° N). a, De-trended monthly mean de-seasonalized anomalies (shown as black dots) of observed net radiation (CERES-EBAF 2.8) against surface temperature (HadCRUT4) for the full years 2001–2013. The black line shows a linear regression on the data, and orange is the 5–95% confidence interval obtained from a two-sided t-test. Regressions from models are shown as grey and coloured lines according to the legend and are performed for the period 1995–2005 to avoid the influence of the Pinatubo eruption. b, The relation between the shortwave and longwave contributions to net regression. Error bars indicate 5–95% confidence intervals on the regression coefficients. In the t-test we account for temporal autocorrelation in the surface temperature record of about 10 months. Longwave Planck feedback (green) of –3.94 W m−2 K−1 and Planck feedback plus water vapour feedback evaluated at constant relative humidity (pink) of –2.12 W m−2 K−1 for the tropical region, 20° N to 20° S, are obtained from ref. 16.

PERSPECTIVE NATURE GEOSCIENCE DOI: 10.1038/NGEO2414

© 2015 Macmillan Publishers Limited. All rights reserved

Tropics: 20S-20N

− 0.6 − 0.4 − 0.2 0.0 0.2Missing feedback parameter (Wm− 2K − 1)

1

2

3

4

5

6ECS (K)

Candidates for biased/missing feedbacks are:

• Ozone feedback, about -0.1 Wm-2/K • Iris-effect, about -0.3 Wm-2/K

Together is enough to move CMIP5 model collection mean:

Nowack et al. (2014), Chiodi and Polvani (2016) Mauritsen and Stevens (2015), Williams and Pierrehumbert (2017)

3.4 K → 2.5 K

Climate Dynamics Course Notes Mauritsen

feedback), is found in climate models to be about +1.2 Wm�2K�1, and so is not su�cient to causeinstability in current climates. In warmer climates the positive water vapor feedback is thoughtto increase faster than the negative Planck feedback and so could aid in destabilising the system.Finally, the first term on right hand side of Eq. 3.2 is the planetary albedo feedback, which is dueto clouds, surface albedo as well as absorption by the atmosphere foremost water vapor. It is leftas an exercise to estimate the criterion for instability when considering planetary albedo feedback.

3.2 Feedback mechanisms

Above we calculated the feedback parameter for the general case (Eq. 3.2) and identified threeterms, one related to how planetary albedo changes with temperature, one related to how thee↵ective emissivity changes and one which is directly related to the Planck feedback. Now, if wewant to go about understanding and quantifying the feedback it is more convenient to make anotherdivision. For instance the planetary albedo is controlled by changes in surface albedo, cloudiness andwater vapor, as well as some other factors such as aerosol particles and ozone that we shall ignorehere as feedbacks. As a first step let us divide � into contributions due to changes in temperature,water vapor, clouds and surface albedo:

� = �T

+ �W

+ �C

+ �A

+ ... (3.4)

where there are a number of additional terms due to interactions between e.g. clouds and watervapor changes as well as other factors that we have ignored. As long as we consider relativelysmall perturbations then the interactions between feedbacks are of secondary importance. For largeperturbations, however, it is easy to appreciate that this will no longer be the case. For instanceat high latitudes cloudiness tends to increase in a warming climate, and so a decreasing surfacealbedo will have less of an impact on the energy imbalance than in a colder case. Or if the verticaltemperature structure is substantially altered due to a rising tropopause, then the impacts of cloudsand water vapor changes on the greenhouse e↵ect may be di↵erent.

It turns out to be meaningful to divide the temperature feedback parameter into two contributions(Figure 3.3). The Planck feedback is that which would occur if the entire troposphere would warm atthe rate of the surface temperature (gray shading). The lapse-rate feedback is that due to deviationsfrom vertically uniform warming. In a later chapter we shall study stratospheric adjustment as aresponse to changing CO

2

which is not considered a feedback, and so ignoring the stratospherictemperature changes, we can write the temperature feedback as:

�T

⇡ �P

+ �LR

. (3.5)

The planck feedback is therefore always negative, whereas the lapse-rate feedback could be eitherpositive or negative: If the troposphere warms faster than the surface temperature then the systemcan radiate more to space relative to the case where warming was vertically uniform. This is thecase in the tropics where the troposphere is vertically mixed by deep convective clouds (as in Figure3.3). At high latitudes, however, the surface may well warm faster than the troposphere such thatthe lapse-rate feedback is a positive feedback mechanism acting to amplify regional warming (Pithanand Mauritsen5). However, because the tropics cover a much larger area the lapse-rate feedback isthought to be on average negative.

It is worth noting that the division of feedback parameters chosen here is only one of manypossible divisions, a few of which makes sense. A powerful recent development has been to includesome of the water vapor feedback into the temperature feedback, namely that which would occurif relative humidity stayed fixed (Held and Shell7). This is e↵ective since, as we shall argue next,changes in relative humidity tend to be small in climate models.

Page 20

highECS Part B1 Mauritsen

It is fair to ask at what point the uncertainty on ECS is su�ciently low? The answer depends on thequestion asked, of course, whether it is to estimate impacts of changing the atmospheric composition, or ifone is trying to reconcile theory with evidence from past climates. For certain purposes the current level ofuncertainty is fully su�cient [101], in other estimates the economic value could be tremendous [about 10trillion US$, 5]. With time, uncertainty derived from the observed warming [16, 18, 19, 62] will naturallyreduce as the signal becomes stronger relative to noise and observations more accurate; with a sit-and-waitstrategy we can expect uncertainty on TCR to halve in about 15 years time [39]. Still, this method is basedon simplistic framework, in which we lack confidence in underlying assumptions, and further if ECS is highit will take longer time than TCR to reveal itself [7].

I firmly believe we should be more ambitious than this, and, rather than waiting for climate change tounfold, take this opportunity to challenge our scientific understanding of how the climate system works, andluckily I am not alone in thinking so: A group of about forty scientists, myself included, gathered for a weekto identify the Grand Challenges of Clouds, Circulation and Climate Sensitivity [3] arguing that a focus oncloud feedbacks and convective cloud organization could lead to a substantial reduction in uncertainty ofECS within the next 5-10 years is indeed feasible due to recently gained insights, and a rapidly growingcapacity to observe and simulate the atmosphere and oceans.

2 METHODOLOGY

My project aims to bound the risk of high ECS, and the work is organized into three work packages asfollows:

WP1: Confront hypotheses of high ECS with past climates – build alternative climate modelsthat match instrumental record warming and expose them to the past

WP2: Time- and state-dependent feedbacks – the foundation of a new physics-based frameworkto combine di↵erent lines of evidence

WP3: Understanding deep convective cloud feedbacks – quantify missing upper-level cloudcover feedback and investigate the signature on past climates

In part B2 of this proposal each work package is described in detail, and in this part, below, I provide furthermotivation for my methodology. Building on the results, I will develop a new physics-based framework tocombining di↵erent lines of evidence of ECS. This new methodology is distinct from, yet inspired by, thatproposed by Stevens et al. [65] which was based on bayesian statistics. I am convinced that an eventualscientific consensus on reducing uncertainty in ECS must build on a physical understanding.

2.1 Clouds are the culprit

Climate sensitivity is determined by a series of processes in the Earth system [20]. A forced system willwarm and therefore radiate more to space eventually achieving a new equilibrium that can be estimated as:

ECS =�F2x

�, (1)

where F2x is the forcing from a doubling of atmospheric CO2, and the negative feedback parameter can beapproximately split into individual contributions by a linear sum: � = �

p

+ (�wv

+ �lr

) + �a

+ �c

, wherethe terms are the Planck, water vapor, lapse-rate, albedo and cloud feedback parameters. Water vaporand lapse-rate feedbacks are usually treated together as they are physically anti-correlated [107]. I appliedEquation (1) and used means and standard deviations of each term Monte Carlo sampling from gaussiandistributions to obtain probabilities of ECS in light of current CMIP5 climate models (Figure 1). Myresult is consistent with independent estimates (Masahiro Watanabe, personal communication). We noticehow the distribution is asymmetric as a consequence of most uncertainty arising from the denominator ofEquation (1), and that there is considerable overlap of this process-based approach with the IPCC consensusrange, but in particular high ECS values are hard to rule out. These high values of ECS are entirelydue to cloud feedbacks which can be realized by setting �

c

= 0 (blue). That is not to say that otherfeedbacks are not important, for instance surface albedo feedbacks are key to understanding colder climates

Page 3

A Statistics Approach

Annan and Hargreaves (2006), Stevens et al. (2016), Knutti et al. (2017), Sherwood et al, in preparation

precisely f(Ojx), which is the likelihood of x given O. So wecan iteratively combine new information with a priorprobabilistic estimate simply by multiplying the prior pdfwith the likelihood function arising from the new data, andrenormalising appropriately, as Forest et al. [2002] did forseparate records of 20th century temperature change.

3. Observational Constraints3.1. 20th Century Warming

[5] Many studies have attempted to estimate climatesensitivity using the overall warming trend of the lastseveral decades or century, using a range of models,methods and prior assumptions [Knutti et al., 2002;Gregory et al., 2002; Andronova and Schlesinger, 2001;Forest et al., 2002]. The resulting pdfs have generallyshown that the recent warming does not provide a usefulconstraint when compared to the long-established (albeitsubjective) estimate of 1.5–4.5!C. One fundamental rea-son for this is that the net forcing is itself not wellconstrained, and in particular is not constrained well awayfrom zero, due to the possibility of sulphate aerosolssubstantially cancelling out the greenhouse gas forcing. Ifthe net forcing is small, then climate sensitivity wouldhave to be very high to explain the observed warming.Nevertheless, the results rarely assign a high probabilityto values in excess of 10!C, and they generally point to amaximum likelihood value well within the conventionalrange. We use as a typical representative of this class ofconstraints a probabilistic estimate of (1, 3, 10) where inthis notation, used throughout this paper, the central valueindicates the maximum likelihood estimate in degreesCelsius and the outer values represent the limits of the95% confidence interval for a pdf, or 95% of the areaunder the curve for a likelihood function. Since thisdistribution is strongly asymmetric, we use the gamma

distribution as a parsimonious representation, using shapeand scale parameters 3.2 and 1.36 (see Figure 1). We takethis distribution as our prior with which additionalinformation in the form of likelihood functions will becombined.

3.2. Volcanic Cooling

[6] The short-term large-scale cooling following volcaniceruptions has also recently been used to estimate climatesensitivity [Wigley et al., 2005; Frame et al., 2005;Yokohata et al., 2005]. Although it might appear that thisinformation is already implicit in the 20th century recon-structions, those papers generally did not consider the short-term temperature changes in detail, instead relying largelyon a long-term energy balance. Therefore we consider itreasonable to treat this constraint as a physically andobservationally independent one. The impact of this as-sumption is discussed further in Section 4. Wigley et al.[2005] use a simple energy balance model (MAGICC) witha variable climate sensitivity parameter, and simulate theeruptions of Agung, El Chichon and Pinatubo. A compar-ison with the observed cooling produces a plausible rangefor each individual eruption which in each case gives a highlikelihood to values close to 3!C, with an upper limitranging from 5.2–7.7!C and a lower limit of 0.3–1.8!C.In principle, the three estimates could themselves be com-bined into an estimate which has significantly tighter limitsof about (1.8, 2.8, 4.4). However, their analysis does notconsider the issue of model error, which suggests they mayhave overestimated the precision of their estimates, andmoreover implies that the uncertainties on the three esti-mates may not be wholly independent. On the other hand,theoretical considerations and simulations with a range ofdifferent models [Frame et al., 2005; Yokohata et al., 2005]confirm that a sensitivity in the region of 6!C or moreimplies a long cool period over several years which is notseen in the observational record. Although as Frame et al.[2005] remark, natural variability could potentially opposeand obscure this forced response for a single eruption, it ishighly unlikely for this to have happened for each eruptionin the historical record. We therefore use a gamma functionwith shape and scale parameters 8.5 and 0.40 as ourlikelihood function (see Figure 1). The shape of thisfunction is described by (1.5, 3, 6).

3.3. Last Glacial Maximum

[7] Temperatures at the Last Glacial Maximum (LGM)were substantially lower than the modern pre-industrial statefor an extended period. However, temperature estimates areimprecise and rely on interpretation of proxy data. Recentsyntheses of tropical data [Ballantyne et al., 2005] indicate acooling in this region of about 2.7!C relative to the pre-industrial state for sea surface temperatures, and 5!C overland. The cooling increases at higher latitudes, giving anaverage of 5.7–8.7!C over the northern hemisphere con-tinents [Bintanja and de Wal, 2005]. Given this evidence, arange of (3, 6, 9) for the globally-averaged cooling is surelyrobust, with the true value likely to be near the middle ofthis the range. The main changes in radiative forcing at theLGM are due to lower GHG levels and large ice sheets overthe northern hemisphere, which each account for about!3Wm!2 [Taylor et al., 2000] but changes in vegetation

Figure 1. Pdfs and likelihood functions for climatesensitivity based on various observational constraints. Bluedashed line: 20th century warming (1, 3, 10). Blue dottedline: volcanic cooling (1.5, 3, 6). Blue dot-dashed line:LGM cooling (!0.6, 2.7, 6.1). Red solid line: combinationof the three constraints (1.7, 2.9, 4.9). Thin red dashed line:combination of three copies of widest constraint (1.5, 3.0,6.3). Thin red dotted line: five constraints (2.0, 3.0, 4.3).See text for details.

L06704 ANNAN AND HARGREAVES: MULTIPLE OBSERVATIONAL CONSTRAINTS L06704

2 of 4

A Mechanistic View

• How does ECS depend on State? • How do feedbacks vary with Time? • What are models missing?

�5 5 10


2

4

6

8

10

ECS(K

)


Bloch-Johnsonetal.

(2015)

Meraner etal. (2013

)

Pliocene – Model constraint

Hargreaves and Annan (2016)

J. C. Hargreaves and J. D. Annan: Pliocene and climate sensitivity 1595

underestimate spatial variation to some extent, it seems rea-sonable to conclude that much of the model–data discrepancyhere is due to uncertainties in the analysis of the data points.Furthermore, we do not expect models to be able to reli-ably simulate spatial anomaly patterns skilfully at the mPWP,since they fail to do this for other time periods of palaeocli-matic interest where sufficient data have been assembled totest this rigorously (Hargreaves et al., 2013). We therefore donot think it is meaningful to constrain the models in this caseby a small number of irregularly sampled points and preferto focus on averages over larger spatial scales where we canreasonably expect the models to have some skill (Hargreavesand Annan, 2014).

3.4 Climate sensitivity estimate

To calculate an estimate for equilibrium climate sensitivity,we combine the model estimates for climate sensitivity andthe warming at the mPWP, together with the PRISM3 es-timate of tropical ocean temperature change, using the ap-proach described in Hargreaves et al. (2012). For consis-tency with the data, we use sea surface temperature from theclimate models, which are of course very close to SAT atthe same locations. The interpolated PRISM3 data indicatea warming of 0.8 �C for the SST integrated over 30� S to30� N. The calculation of climate sensitivity involves sam-pling from the uncertain temperature distribution and, foreach sample, generating a prediction of the associated sen-sitivity taking account of the uncertainty in the linear rela-tionship. The PRISM3 reconstruction does not include an es-timate of uncertainty in the reconstruction. Initially we takea value of 0.4 �C (at 1 standard deviation), based on the hopeboth that the signal was at least as large as than the noise andthat it might come close to matching the value of 0.7 �C (at 2standard deviations) which was obtained for a recent recon-struction of the LGM tropics (Annan and Hargreaves, 2013).It is of course essential to test the sensitivity of our result tothis assumed uncertainty, and we discuss this further below.Figure 2 shows the result. The regression model generates anestimate for the equilibrium climate sensitivity of 1.9–3.7 �C.Only the models with weaker tropical warming are consistentwith the data; as these tend to be low sensitivity models, theresulting estimate for S is at the low end of (and extendingto values outside) the full range of models that contributed toPlioMIP.

4 Uncertainties

4.1 Data uncertainty

Proxy-based reconstructions of past climates are, of course,uncertain. As mentioned above, however, the size of the un-certainty in the PlioMIP Experiment 1 SST field has notbeen objectively estimated, and our initial value of 0.4 �C issimply an assumption based in part on previous work fo-

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Mid−Pliocene Tropical ocean SST anomaly

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Observed value (5−95 %)

Estim

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(5−9

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)

Figure 2. Estimating equilibrium climate sensitivity using themPWP. Red dots represent model values; solid and dashed red linesindicate regression relationship and its uncertainty respectively.Blue arrows show proxy-based reconstruction of tropical temper-ature change over ocean, together with uncertainty of 0.1 (dashed),0.4 (solid), and 1.0 (dot-dashed). Black arrows of the correspondingtype show the resulting sensitivity estimates.

cussing on the LGM. It would be reasonable to assume thatthe Pliocene temperature estimate is in fact more uncertain,so we tested the sensitivity of our result to this. The dashedand dot-dashed blue and black lines in Fig. 2 show the effecton the estimate of replacing the original estimate of 0.4 �Cwith values of 0.1 and 1 �C (all at 1 standard deviation) re-spectively. It is apparent that reducing the uncertainty even toan extremely low value has relatively little effect on the re-sulting sensitivity estimate (which only narrows marginallyto 2.1–3.6 �C), as in this case the spread around the regres-sion line makes a dominant contribution to the total uncer-tainty. However, none of the models are consistent with thistemperature estimate, as all warm by more than 0.8 �C in theregion, many by a substantial margin. If we increase the SSTuncertainty estimate substantially to 1 �C, then the uncer-tainty of the overall result does increase more noticeably to1.3–4.2 �C. At this point, even the models with the strongestwarming are consistent with the data, and thus the estimatedsensitivity range covers the full range of model values withan extension also to lower values. Note that, at this level ofuncertainty, the data would no longer give us confidence eventhat the mPWP was warmer than the pre-industrial period,at least in the tropics. It would be very useful to have morecomplete understanding of the uncertainties of temperaturereconstructions for the mPWP.

4.2 Forcing uncertainty

A major issue in simulating the mPWP is that the atmo-spheric CO2 level corresponding to interglacial peaks is notprecisely known. Furthermore, there is hypothesised to beadditional forcing due to methane which cannot be directlyinferred from proxy data but which has instead been assumed

www.clim-past.net/12/1591/2016/ Clim. Past, 12, 1591–1599, 2016

ECS

(K)

towards a theory for earth’s climate sensitivity (ecs) · instability in current climates. in...

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