Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207

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Journal of Atmospheric and Solar-Terrestrial Physics

1364-68

doi:10.1

n Corr

Physiqu

E-m

journal homepage: www.elsevier.com/locate/jastp

A correlation of mean period of MJO indices and 11-yr solar variation

Elena Blanter a,b,n, Jean-Louis Le Mouel a, Mikhail Shnirman a,b, Vincent Courtillot a

a Geomagnetism and Paleomagnetism, Institut de Physique du Globe de Paris, 1 rue Jussieu, Paris, Franceb Institution of Russian Academy of Sciences – Institute of Earthquake Prediction Theory and Mathematical Geophysics, Profsoyuznaya str. 84/32, Moscow 117997, Russia

a r t i c l e i n f o

Article history:

Received 20 June 2011

Received in revised form

25 January 2012

Accepted 25 January 2012Available online 4 February 2012

Keywords:

Madden–Julian oscillation

MJO spectral properties

11-yr solar cycle

Sun–climate interaction

26/$ - see front matter & 2012 Elsevier Ltd. A

016/j.jastp.2012.01.016

esponding author at: Geomagnetism and P

e du Globe de Paris, 1 rue Jussieu, Paris, Fran

ail address: blanter@ipgp.fr (E. Blanter).

a b s t r a c t

This paper focuses on the decadal to multi-decadal evolution of the spectral properties of the Madden–

Julian Oscillation (MJO). Guided by former studies, we test whether the �11-yr (Schwabe) cycle of solar

activity could be reflected in the spectral features of MJO indices: namely, we study the evolution of

MJO mean period within different period ranges and compare these with the evolution of solar activity.

We focus on solar proxies best linked to UV emission and cosmic rays: sunspot number WN, F10.7 flux,

core-to-wing ratio MgII, and galactic cosmic rays (GCR). A clear solar signature in MJO spectral

properties is indeed found and shown to be both statistically significant and robust. UV proxies are

found to be better correlated with MJO mean period than GCR, thus supporting rather the ozone

mechanism of solar impact on MJO. The overall correlation with solar activity is found to be stronger in

the Indian Ocean. Long periods (e.g. 50–80 day) are better correlated with solar activity than shorter

periods (e.g. 30–60 day). A marked change in the relationship between MJO mean period and solar

activity takes place in the declining phase of solar cycle 23, adding to its unusual character.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The Madden Julian Oscillation (MJO) has been much studiedsince it was discovered in 1971 (Madden and Julian, 1971, 1972,1994). Despite progress in modeling (e.g. Raymond, 2001; Majdaand Biello, 2004; Majda and Stechmann, 2011), this complexphenomenon is far from being sufficiently well understood (e.g.Zhang, 2005; CLIVAR Madden–Julian Oscillation Working Group,2009). MJO originates in the near-equatorial zone of the Pacifichemisphere and forms the dominant mode of tropical atmo-spheric variability on an intra-seasonal time scale. MJO eventsconsist primarily in large-scale (�1000 km across) deep convec-tive rainfall anomalies that propagate eastward from the IndianOcean, through Indonesia, into the western Pacific where theydecay around the dateline. The typical lifetime for MJO events isaround 45–50 day and is generally comprised between 30 and 60day (Zhang, 2005). The mean lifetime of MJO events showssignificant intra-annual variations from 30–35 day (Shaik, 2009)to 50–55 day (Shaik and Cleland, 2004), or even 60–70 day (Shaikand Bate, 2003). Pohl and Matthews (2007) have shown that MJOlifetime in the equinoctial seasons depends on the state of the ElNino-Southern Oscillation (ENSO).

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Zhang (2005) reviewed potential physical mechanisms of MJOgeneration, none of which are unequivocally accepted. There aretwo main schools of thought regarding the energy source of MJO:some consider it as a response of the atmosphere to an indepen-dent external forcing mechanism, whereas others think that MJOgenerates its own energy source through some atmosphericinstability. Besides generation mechanisms, there are forcingfactors and conditions that influence the MJO life cycle and partlydetermine its seasonal variations; solar activity may be oneof them.

There are several ways in which solar activity may impactMJO: one may suggest two possible mechanisms. First, solar

irradiance (at various wavelengths) can play a role in determiningwarm pool conditions and maintaining local, stationary intra-seasonal oscillations in deep convection. Second, cloud formation,which might also be modulated by solar activity, could play a rolein MJO through its contribution to the vertical heating profile ofthe atmosphere.

Interest in MJO has further increased in the past decade, whenit was found that MJO influences atmospheric circulation welloutside of the tropics (e.g. Mo and Higgins, 1998; Jones, 2000;Cassou 2008). Vecchi and Bond (2004) identified a systematiceffect of MJO phase on intra-seasonal variability in wintertimesurface air temperature through the global Arctic. Donald et al.’s(2006) near-global analysis demonstrated that MJO influencesdaily rainfall patterns up to high latitudes. MJO has also beenfound essential for ENSO dynamics (e.g. Hendon, 2005; Zhang,2005; Hendon et al., 2007). So, as a main mode of tropical

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207196

convection, MJO is closely related with the Earth’s climate at aplanetary scale (e.g. Zhang, 2005). Evidence of these diverseimpacts of MJO on the global climate system warrant furtherinvestigation of the phenomenon and its possible role in climateforcing.

In previous papers, we have been able to identify a solarsignature in the long-term evolution of seasonal temperaturedisturbances of the European and North Pacific regions (Le Mouelet al., 2009; Courtillot et al., 2010). These are known to beinfluenced by MJO activity during the same seasons (Winter inEurope and Late Fall in the North Pacific) in which we evidenced asolar signature (e.g. Higgins and Mo, 1997; Bond and Vecchi,2003; Vecchi and Bond, 2004; Cassou, 2008) and it is reasonableto expect that MJO could impart a significant contribution tothese regional disturbances of temperature. However, to ourknowledge, the �11-yr solar cycle has not yet been found inMJO evolution.

Recent papers (e.g. Gray et al., 2010) suggest two main sourcesof solar influence on the Earth’s climate as manifested by the11-yr solar cycle. The first one is related to the response of climateto variations in solar irradiance: this response can be amplified bythe capacity of the ocean to integrate small long-term variationsin heat input and by an important feedback mechanism involvingozone production (Frohlich and Lean, 2004). Changes in the UVpart of the solar irradiance spectrum alter the ozone concentra-tion and temperature of the upper stratosphere, therefore thermalgradients and wind systems, leading to changes in the verticalpropagation of planetary waves that drive global circulation(Labitzke and van Loon, 2006; Gray et al., 2010; Haigh et al.,2010). The solar cycle, which modulates UV and EUV emissions,also modulates ozone concentration in the middle atmosphereand tropospheric density and mean temperature (e.g. Calisesi andMatthes, 2006). A second family of mechanisms involves ener-getic particles, mainly galactic cosmic rays (GCR), interacting withcloud formation through cloud condensation nuclei or the iono-sphere and the global electric circuit (e.g. Svensmark and Friis-Christensen, 1997; Svensmark, 1998, 2000; Marsh andSvensmark, 2000a, b; Solanki and Krivova, 2003; Stott et al.,2003; Usoskin et al., 2005, 2006; Tinsley et al., 2007).

Early papers (Djurovic and Paquet, 1988; Djurovic et al., 1994)proposed a link between characteristic times of MJO and specificperiodicities in solar variations, but have not been confirmed bylater studies. Had clear correlations between MJO amplitude andthe solar cycle existed, they would have likely been uncovered forsome time. Our working hypothesis is therefore that solar activitymay influence the spectral characteristics of MJO rather than itsamplitude. In this paper, we compare the evolution of MJOspectral properties with different solar proxies, in the hope ofcontributing to the detection of a possible link between solaractivity and MJO.

We investigate the spectral properties of daily series of MJOindices, which are constructed from the anomalies of zonal wind,outgoing long wave radiation (OLR) and pressure fields. Weanalyze them using the wave-packet technique, which we suc-cessfully applied in previous work (Shnirman et al., 2010). In thepresent paper, we study the evolution of the mean period in agiven spectral domain rather than that of energy, which has beeninvestigated in previous studies. An advantage is that the meanperiod is little affected by a baseline change nor by some possibleamplification (or reduction) of signal amplitude due to satelliteplatform changes (despite the facts that the mean period is apriori less stable than mean energy and that the influence ofdifferent waves contributing to the MJO spectral domain—e.g.equatorial Rossby ER waves (Roundy et al., 2009) cannot beproperly estimated). In order to try and see which mechanismmight be responsible for any observed relationship between solar

activity and MJO spectral properties, we consider different indicesof solar activity. The F10.7 radio flux and MgII index, on one hand,monitor the evolution of UV/EUV emission, related to the ozonemechanism, whereas GCR, on the other hand, monitors energeticparticles potentially affecting cloud formation.

2. Data

Daily MJO indices used in this study are available through theKNMI access point http://climexp.knmi.nl/). In this section wegive a brief description of each index we use, focusing on featuresmost important to our approach.

2.1. MJO indices

We consider two sets of MJO daily indices.The first one contains 10 MJO indices (MJO1–MJO10) relevant

to 801E, 1001E, 1201E, 1401E, 1601E, 1201W, 401W, 101W, 201E,and 701E longitudes, respectively, which are provided by theNational Center for Environmental Prediction, Climate PredictionCenter NCEP/CPC. These indices are built through an ExtendedEmpirical Orthogonal Function (EEOF) analysis from pentad(5 day) 200-hPa velocity potential anomalies equator-ward of301N. Anomalies are relative to 1979–1995, and each index isnormalized by its standard deviation computed during ENSO-neutral and weak ENSO winters (November–April) in this timeinterval. A short description of the indices and original pentadvalues is available at: http://www.cpc.noaa.gov/products/precip/CWlink/daily_mjo_index/pentad.shtml.

Five out of the ten MJO indices (MJO10, MJO1, MJO2, MJO3, MJO4)are relevant to the zone of MJO convection (e.g. Zhang, 2005); eachone of the other five indices forms a pair with one of the first five anddisplays very similar spectral properties (MJO1 and MJO6, MJO2 andMJO7, etc y See Figs. A1 and A2 in the Appendix). The MJOconvection zone covers the equatorial parts of the Indian and westernPacific Oceans. MJO10 and MJO1 are relevant to the Indian Ocean,where MJO events usually start, whereas MJO4 is relevant to thewesternmost Pacific where they end. Several authors have noted thatfeatures of MJO activity in the Indian Ocean differ from those in thePacific (e.g. Hendon et al., 2007; Cassou, 2008; Mori and Watanabi,2008; Johnson and Feldstein, 2010). Pairs of MJO indices (MJO1 andMJO6, MJO2 and MJO7 etc) are highly anticorrelated (Table 1) due tospatial patterns of anomalies measured by these indices (see e.g. firstfigure of http://gcmd.nasa.gov/records/GCMD_NOAA_NWS_CPC_MJO.html).

The second set contains two daily series: RMM1 and RMM2,provided by the Center for Australian Weather and ClimateResearch http://cawcr.gov.au/staff/mwheeler/maproom/RMM/.These two indices rely on the first two Empirical OrthogonalFunctions (EOFs) of the field based on a combination of near-equatorial averages of the 850 hPa zonal wind, the 200 hPa zonalwind and satellite-based OLR data (see Wheeler and Hendon,2004, for a detailed description). The annual cycle and thecomponents of inter-annual variability have been removed fromthe combined field series, yielding the real-time multivariate MJOseries RMM1 and RMM2.

The Fourier spectra of several MJO indices are shown in Fig. 1.There are no simple, sharp spectral lines; the smoothed spectra(red curves in Fig. 1) actually illustrate the wide distribution ofMJO characteristic (pseudo-) periods. Note that the filtering usedin the construction of EOFs (Maloney and Hartmann, 1998)reduces the contribution of shorter periods. The main parts ofthe spectra are concentrated in the 30–60 day band, withmaximum amplitude in the 40–50 day range. However, there is

Table 1Correlation coefficients between 12 series of MJO indices themselves without averaging (above main diagonal), and between MJO series prior to averaging and MJO 4-yr

running means (below main diagonal, italic). Bold values in the upper part of the Table underline correlation coefficients between two MJO series whose absolute value is

larger without averaging than after taking 4-yr running means; bold values in the italicized bottom part correspond to the opposite.

4-yr running means No averaging

MJO1 MJO2 MJO3 MJO4 MJO5 MJO6 MJO7 MJO8 MJO9 MJO10 RMM1 RMM2

MJO1 1.00 0.85 0.49 �0.11 �0.81 �0.99 �0.77 �0.29 0.50 0.98 �0.28 0.75MJO2 0.87 1.00 0.88 0.42 �0.39 �0.91 �0.99 �0.75 �0.02 0.73 �0.65 0.48MJO3 0.45 0.84 1.00 0.81 0.11 �0.60 �0.93 �0.97 �0.50 0.31 �0.83 0.11

MJO4 �0.29 0.23 0.72 1.00 0.67 0.01 �0.54 �0.92 �0.91 �0.31 �0.76 �0.37MJO5 �0.89 �0.54 0.44 0.69 1.00 0.73 0.26 �0.33 �0.91 �0.91 �0.24 �0.77MJO6 �0.98 �0.93 �0.57 0.15 0.82 1.00 0.85 0.40 �0.40 �0.95 �0.63 �0.39MJO7 �0.77 �0.99 �0.92 �0.38 0.40 0.86 1.00 0.83 0.15 �0.63 0.72 �0.39MJO8 �0.15 �0.62 �0.95 �0.90 �0.31 0.29 0.74 1.00 0.68 �0.09 0.84 0.06

MJO9 0.69 0.26 �0.30 �0.87 �0.95 �0.60 �0.10 0.59 1.00 0.67 0.55 0.62MJO10 0.97 0.79 0.34 �0.40 �0.93 �0.96 �0.69 �0.03 0.79 1.00 �0.11 0.78RMM1 �0.28 �0.26 �0.17 0.02 0.21 0.27 0.23 0.10 �0.14 �0.25 1.00 0.00

RMM2 �0.21 �0.33 �0.37 �0.24 �0.04 0.23 0.34 0.33 0.08 �0.15 �0.03 1.00

20 30 40 50 60 70 80 900

1

2

3

4

5

6x 10−3 x 10−3

x 10−3 x 10−3

Period (day)

Pow

er

20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

Period (day)

Pow

er

20 30 40 50 60 70 80 900

1

2

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6

Period (day)

Pow

er

20 30 40 50 60 70 80 900

1

2

3

4

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6

7

8

9

Period (day)

Pow

er

Fig. 1. Fourier power spectra for four indices characterizing the Madden–Julian oscillation (see text): MJO1 (a), MJO4 (b), RMM1 (c) and RMM2 (d) time series are

computed over the 1980–2009 time span (blue curves) and their running averages taken over 20 frequencies (bold, red curves). Periods in days. (For interpretation of the

references to colour in this figure legend, the reader is referred to the web version of this article.)

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207 197

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207198

significant power at 70–80 day, comparable to that in the 40–50day range for RMM1 and even slightly larger for RMM2.

2.2. Solar indices

We use four indices as proxies of solar activity: they arerelated to the two most probable mechanisms of solar cycleinfluence on MJO, i.e. ozone balance and cloud formation. In thefirst group we have sunspot number WN, F10.7 radio flux F andMgII index, all characteristic of (or influenced by) UV/EUV emis-sions. In the second group, we have the series of galactic cosmicray (GCR) measurements.

Sunspot number (WN). The sunspot or Wolf number (WN)series is the best-known and most commonly used solar proxy.Daily data are available from 1850 onwards at ftp://ftp.ngdc.org.Sunspot number is correlated with total solar irradiance (TSI) andEUV irradiance and is the reference series used to characterizesolar activity in long-term climate simulations.

Radio Flux F10.7 (F). The decimetric F10.7 index is a dailymeasurement of the radio flux at 10.7 cm made at PentictonObservatory, available since 1947 (ftp://ftp.ngdc.noaa.gov). F is nowconsidered to be better correlated with EUV irradiance than WN

(Donnelly et al., 1983; Floyd et al., 2005; Dudok de Wit et al., 2009).Magnesium core-to-wing ratio index (MgII). The MgII index is

constructed from the ratio of the irradiances of the highly variableMgII h and k emission cores near 280 nm to those of the weaklyvariable nearby wings (Heath and Schlesinger, 1986). It has beenrecorded by different satellites and a uniform composite of dailyrecords is available from 1979 onwards. We use the LASP,University of Colorado composite of the core-to-wing ratio,available at http://lasp.colorado.edu/lisird/mgii/mgii.html, whichuses SORCE satellite observations (Snow et al., 2005) and is freefrom calibration problems reported for the NOAA MgII index inthe declining phase of the 23rd solar cycle (Lukianova andMursula, 2011). This index is known to provide a good represen-tation of FUV (130–170 nm) and is the best proxy for UV emission(Dudok de Wit et al., 2009).

Galactic cosmic rays (GCR). It is well established that the flux ofgalactic cosmic rays (GCR) reaching the Earth is anti-correlatedwith solar activity, with a variable lag on the order of 1yr (Usoskinet al., 1997). The evolution of the amplitude of the six-monthcomponent of series of length of day (LOD) measurements showsa good correlation with GCR evolution (Le Mouel et al., 2010). Asin Le Mouel et al. (2010), we use monthly GCR series availablefrom ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/COSMIC_RAYS/STATION_DATA/MOSCOW/docs/moscow.tab.

3. Properties of MJO indices uncovered by the wave-packettechnique

MJO indices, like MJO events, do not display sharp periodi-cities. Such time series are usually investigated using waveletanalysis. However powerful, wavelet analysis is too complexwhen one wants to compare integral characteristics of such timeseries. We use here a wave-packet technique that combines theadvantages of the wavelet representation of the time evolution ofthe spectral properties of a time series with the simplicity ofFourier transforms.

3.1. The wave-packet technique: amplitude and mean period

The wave-packet technique is particularly useful when thetime series under consideration does not have sharp, definitespectral lines (such as a daily or an annual line linked to theEarth’s rotation about itself and around the Sun) but rather

significant energy over a range of a frequencies (i.e. characteristictimes such as the �11-yr solar cycle or the 40–50 day range ofthe Madden–Julian Oscillation). Courtillot et al. (1977) forinstance have emphasized this difference between ‘‘astronomical’’and ‘‘astrophysical’’ lines in a study of the aa geomagnetic index.The wave-packet technique has previously been applied toinvestigations of solar activity (Le Mouel et al., 2007; Shnirmanet al., 2009, 2010). It consists in the determination of theamplitude and mean period of a given time series calculatedwithin a sliding window T with a length that is much longer thanthe characteristic periods one wants to estimate. The resultingamplitude and mean period, which vary as a function of time (i.e.the center of the sliding window), are the output of a sort of filterwhich emphasizes the amplitude, the spectral characteristics ofthe time series in a given period range and their time evolution.

The wave-packet procedure is simple and is reminiscent of theFast Fourier Transform. Indeed, Fourier harmonics with a uniformspacing in frequency, namely ð1=TÞ,ð2=TÞ,. . ., are considered in asliding time interval of length T. These frequencies form anorthogonal basis of the Fourier spectra and all waves in thisfrequency domain may be represented as their linear combina-tion. The packet of power peaks corresponding to the period range[ymin,ymax] contains the lines (harmonics) with periodsyn(n¼ 1,. . .,N) such that yminrynrymax. In the present study,periods ymin and ymax are always within the usual range of MJOenergy (i.e. 30–90 day; see above and Fig. 1). The number N oflines in the packet is fixed by the choice of the limits yminand ymax

and of the length T of the sliding window. Let FðtÞ be any of theMJO indices, then the energy EDðtÞ of the wave-packet is deter-mined from the amplitudes of orthogonal waves with angularfrequencies on ¼ ð2p=ynÞ:

EDðtÞ ¼XN

n ¼ 1

ðA2nðtÞþB2

nðtÞÞ ð1Þ

where:

AnðtÞþ iBnðtÞ ¼1

T

XtþT=2

t ¼ t�T=2

FðtÞðcosontþ isinontÞ ð2Þ

Index D in EDðtÞ denotes the period interval D¼ ½ymin,ymax�. Theamplitude is simply the square root of wave-packet energy EDðtÞ.The mean period PDðtÞ of the wave-packet is determined as theweighted sum of periods of orthogonal components yn:

PDðtÞ ¼1

EDðtÞ

XN

n ¼ 1

ynðA2nðtÞþB2

nðtÞÞ ð3Þ

3.2. Wave-packet energy of MJO and LOD series.

In order to illustrate the wave packet technique describedabove, let us consider the LOD data provided by the ParisObservatory and available at http://hpiers.obspm.fr/iers/eop/eopc04 05/eopc04.62-now. The daily LOD series starts in 1962and is known to be closely related to the Atmospheric AngularMomentum (AAM) for periods shorter than one year (e.g. Hideand Dickey, 1992). Perturbations in the AAM are related toequatorial and tropical atmospheric circulation. Because MJO isthe leading mode of tropical circulation, its evolution is reflectedin the relevant spectral domain of the LOD and AAM series (e.g.Hendon, 1995). Fig. 2 shows the wave-packet energies of LOD andthree MJO indices for periods between 35 and 60 day: there is asimilarity in the evolution of energy, in agreement with previousstudies (e.g. Magana, 1993; Weickmann and Sardeshmukh, 1994;Hendon, 1995; Feldstein, 1999).

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 20100.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4E

(t)

Fig. 2. Evolution of the energy of the 35–60 day wave-packet for the length of day

(LOD—blue curve, multiplied by 5� 107), and three Madden–Julian oscillation

indices: MJO1 (green), RMM1 (red) and RMM2 (cyan) series. (For interpretation of

the references to colour in this figure legend, the reader is referred to the web

version of this article.)

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207 199

3.3. Two distinct period domains in MJO indices

The full spectral range of MJO periods extends from 20 to 90day (e.g. Zhang, 2005). The spectra of indices MJO1 and MJO4have their main energy located between 40 and 60 day, but theamplitude in the 70–80 day range is comparable or even larger forMJO indices RMM1 and RMM2 (Fig. 1). When analyzing theinfluence of Universal time (UT) and Atmospheric AngularMomentum (AAM) on the spectral properties of MJO, Djurovicet al. (1994) distinguish two domains of periods (22–56 day and50–80 day) and conclude that MJO consists of at least threeoscillations (or lines) with periods of 40, 50 and somewherebetween 60 and 80 day, the first two in the first period domain,the third one in the second period domain. In the present workwe consider two period domains: D1 ¼ ½30,60� days andD2 ¼ ½50,80� days. The first interval covers the main spectral partof MJO and corresponds more or less to the first period interval ofDjurovic et al. (1994), the second interval being the same astheirs. We can therefore build on the conclusions of previousstudies and be confident that both intervals of the MJO spectrumyield a significant signal and that their spectral power does notresult from noise or spurious pseudo-periodicity. In the followingsection, we analyze how the mean periods of MJO indices dependon the choice of interval of periods D1 or D2.

3.4. Wave-packet filtering and correlation between MJO indices

Being non-orthogonal projections of the same space–timefield, indices MJO1 to MJO10 are not independent, even at zerolag. Table 1 shows the correlation coefficients between dailyseries (non-italicized triangle above the main diagonal) and thecorrelation coefficient between these series before and after 4-yraveraging (italicized triangle below the main diagonal). The 4-yrrunning averaging of MJO series does not increase significantlythe overall correlation: only geographically close or pairs of

associated indices are related (MJO1 with MJO6, MJO2 withMJO7, etc y see Table 1, italicized values). Bold values in theupper triangle indicate correlation coefficients between raw timeseries in which the absolute value is larger than after taking the4-yr running mean; bold values in the lower triangle indicate theopposite.

Considering the 30–60 (‘‘short’’; Table 2) and 50–80 (‘‘long’’;Table 3) day period bands, we perform a filtering of the MJOsignal that emphasizes a signal that is common to all MJO indices.Both amplitudes and mean periods in these bands are muchbetter correlated with each other for all MJO series than the seriesthemselves or their running means (Tables 2 and 3 vs Table 1). Letus note that the change of satellite platform of OLR affecting thecorrelation of running means of RMM indices (Table 1) is notmanifested in the wave packet (Tables 2 and 3). In the ‘‘short’’period domain, amplitudes are better correlated than meanperiods (Table 2) whereas in the ‘‘long’’ period domain theopposite holds (Table 3).

3.5. Choice of parameters

In order to estimate mean periods, we use two sets ofparameters: the period interval D (e.g. 30–60 day) and slidingtime window T (4 or 2-yr in the present study). The interval ofperiods D has to be chosen within the MJO range (20–90 day) andcannot be too short, in order to have a sufficient number ofFourier lines in the wave packet. Enlarging D ensures higherstability of the mean period but diminishes its sensitivity tovariations of the spectrum. Sliding window T should be chosenlarge enough to have a sufficient number of Fourier lines in thewave packet and maximally suppress short-term variabilityunrelated to the solar cycle (e.g. seasonal variations) but shortenough to preserve decadal variations. To simplify comparisonand estimation of correlation coefficients between MJO meanperiods and solar proxies, we consider running means of solarseries performed with the same averaging window T as the slidingtime window used for the mean periods.

4. Results

We now study the evolution of the MJO mean period in the‘‘short’’ and ‘‘long’’ period domains and compare it with that ofthe �11-yr cycle of solar activity. Statistical significance of allcorrelations is estimated through 5000 Monte-Carlo simulationsof synthetic series having the same power spectrum as the realMJO series for periods 20–80 day. An example of the typicaldistribution of correlation coefficients between mean period and�11-yr solar cycle is given in the Appendix (Fig. 3A; dashed linesindicate the 1% and 5% levels for positive and negative correla-tions, i.e. the same values used for confidence levels in the mainbody of the paper. For a two-sided statistical test, which we use,correlation values exceeding 1% and 5% levels are significant at98% and 90% confidence levels, respectively.

4.1. Solar cycle

The mean periods P½30,60� and P½50,80� are roughly anti-corre-lated (Fig. 3 and Table 4). This anti-correlation fails only in theyears 1991 to 1994 and, with an abrupt change, after 2005(Fig. 3). Before 2005, we see three almost complete, clear Schwabecycles in the evolution of both mean periods. However, all 144correlation coefficients in Table 4 are less than 0.8 and only 13 arebetween 0.7 and 0.8. Fig. 4 illustrates the good correlationbetween the two mean periods estimated over a 4-yr slidingwindow and the 4-yr running means of two solar indices, MgII

1980 1985 1990 1995 2000 2005 201040

41

42

43

44

45

46

47

48

P[3

0,60

]

54

56

58

60

62

64

66

68

70

P[5

0,80

]

Fig. 3. Evolution of MJO1 mean periods in the [30 day–60 day] (P½30,60�—blue

curve) and 50 day–80 day] (P½50,80�—red curve, sign reversed) period ranges,

estimated over a 4-yr running window. The vertical dashed line shows the

approximate time when the sign of correlation changes. Window is centered.

(For interpretation of the references to colour in this figure legend, the reader is

referred to the web version of this article.)

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207200

and GCR; the correlation fails after 2005 (although the data seriesafter that date is quite short). Fig. 5 confirms these results when2-yr sliding window and running means are used.

4.2. Short and long MJO periods

Table 5 lists the correlation coefficients between both meanperiods of all 12 MJO indices and the solar indices WN, F, MgII andGCR. For the ‘‘short’’ period domain (30–60 day), UV proxies arebetter correlated with the mean period than GCR, and the MgII

index is the best correlated for all MJO indices (Table 5, left part).All correlation coefficients have the same sign and values relevantto MJO1, MJO5, MJO6, MJO9, MJO10 and RMM2 are above the 1%confidence level. For the ‘‘long’’ period domain (50–80 day), GCR

is better correlated with the mean period than UV proxies(Table 5, right part). Correlation coefficients of indices MJO1,MJO5, MJO6, MJO10 and RMM2 are above the 1% confidence level.

4.3. Change of correlation in 2005

It is clear from Fig. 4 (and also Fig. 5) that correlations (or anti-correlations) between mean periods and solar activity changearound 2005. When considering the time span 1979–2004 (ratherthan 1979–2009 as in Table 5), the correlation coefficientsbetween MJO mean periods in the ‘‘long’’ period domain increaseand exceed the 1% confidence level for all solar proxies (Table 6).They average �0.80 for all 12 MJO indices vs MgII and �0.76,

Table 2Correlation properties of MJO series in the ‘‘short’’ period domain (30–60 day). Correla

Bold values above the main diagonal (non-italicized) indicate when amplitudes of two

main diagonal (italicized) correspond to the opposite.

Period Amplitude

MJO1 MJO2 MJO3 MJO4 MJO5 MJO6

MJO1 1.00 0.97 0.94 0.93 0.96 0.99

MJO2 0.93 1.00 0.99 0.93 0.90 0.99MJO3 0.83 0.94 1.00 0.97 0.90 0.96MJO4 0.79 0.80 0.92 1.00 0.96 0.93MJO5 0.93 0.81 0.80 0.90 1.00 0.94MJO6 0.99 0.96 0.86 0.77 0.90 1.00

MJO7 0.91 1.00 0.97 0.82 0.80 0.94

MJO8 0.80 0.89 0.98 0.97 0.84 0.81

MJO9 0.84 0.77 0.84 0.97 0.97 0.81

MJO10 0.99 0.89 0.81 0.82 0.97 0.98

RMM1 0.87 0.92 0.96 0.92 0.86 0.88RMM2 0.96 0.92 0.87 0.84 0.92 0.95

Table 3Same as Table 2 in the ‘‘long’’ period domain (50–80 day).

Period Amplitude

MJO1 MJO2 MJO3 MJO4 MJO5 MJO6

MJO1 1.00 0.97 0.81 0.57 0.84 0.99

MJO2 0.95 1.00 0.90 0.64 0.81 0.98

MJO3 0.87 0.96 1.00 0.89 0.88 0.82

MJO4 0.86 0.88 0.95 1.00 0.87 0.55

MJO5 0.96 0.88 0.86 0.93 1.00 0.81

MJO6 0.99 0.98 0.90 0.87 0.94 1.00

MJO7 0.92 1.00 0.98 0.89 0.87 0.96

MJO8 0.86 0.93 0.99 0.98 0.89 0.88MJO9 0.90 0.86 0.90 0.98 0.98 0.89MJO10 0.99 0.94 0.88 0.89 0.98 0.99RMM1 0.84 0.90 0.96 0.96 0.88 0.86RMM2 0.97 0.91 0.85 0.87 0.95 0.95

�0.78 and �0.76, respectively vs WN, F and GCR. Such anincrease is not so clear for the correlation coefficients in the‘‘short’’ period domain, where average values of correlationcoefficients are only marginally larger (Table 6) than in the

tion coefficients between amplitudes and mean period of 12 series of MJO indices.

MJO series are better correlated than their mean periods, bold values below the

MJO7 MJO8 MJO9 MJO10 RMM1 RMM2

0.95 0.93 0.93 0.99 0.84 0.85

1.00 0.97 0.90 0.95 0.87 0.88

0.99 1.00 0.91 0.93 0.92 0.87

0.94 0.98 0.98 0.94 0.94 0.83

0.88 0.92 0.99 0.98 0.87 0.77

0.98 0.95 0.92 0.99 0.86 0.86

1.00 0.98 0.89 0.94 0.89 0.88

0.91 1.00 0.94 0.93 0.93 0.870.77 0.90 1.00 0.95 0.91 0.78

0.87 0.80 0.88 1.00 0.86 0.82

0.94 0.95 0.87 0.86 1.00 0.80

0.91 0.85 0.86 0.95 0.89 1.00

MJO7 MJO8 MJO9 MJO10 RMM1 RMM2

0.94 0.70 0.59 0.86 0.62 0.86

0.99 0.79 0.62 0.94 0.69 0.87

0.94 0.97 0.85 0.84 0.87 0.82

0.70 0.97 0.98 0.66 0.90 0.64

0.83 0.88 0.92 0.91 0.83 0.80

0.96 0.70 0.57 0.98 0.61 0.86

1.00 0.84 0.67 0.93 0.74 0.87

0.95 1.00 0.93 0.75 0.91 0.74

0.86 0.93 1.00 0.70 0.89 0.64

0.92 0.88 0.94 1.00 0.68 0.87

0.91 0.97 0.93 0.87 1.00 0.76

0.88 0.85 0.90 0.96 0.84 1.00

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207 201

1979–2009 case (Table 5). Once again, values of correlationachieved for MJO1, MJO5, MJO6 and MJO10, which are relevantto the Indian Ocean zone where MJO events originate, are higherthan for other MJO indices (Table 6).

4.4. UV and GCR

In order to see which solar proxy is better correlated with theMJO mean periods and then have some indications about thephysical processes involved, let us consider Fig. 5 in which a 2-yrsliding window has been used. The corresponding correlationcoefficients for the period 1979–2004 prior to the breakdown incorrelation are given in Table 7. Correlation values for all solarindices are very close but occur in monotonic order withCðP,GCRÞrCðP,WNÞrCðP,FÞrCðP,MgIIÞ. The best values of corre-lation coefficients (above the 1% confidence level) are againobtained for indices in the Indian Ocean: MJO1, MJO5, MJO6and MJO10. The lower values of correlation coefficients between

Table 4Correlation between P½30,60� and P½50,80� of different MJO series. All correlation coefficien

Mean period in

50–80 day range

Mean period in 30–60 day range

MJO1 MJO2 MJO3 MJO4 MJO5 M

MJO1 0.59 0.68 0.64 0.52 0.51 0

MJO2 0.52 0.69 0.67 0.50 0.43 0

MJO3 0.49 0.68 0.71 0.55 0.43 0

MJO4 0.52 0.65 0.70 0.61 0.49 0

MJO5 0.59 0.67 0.66 0.59 0.55 0

MJO6 0.57 0.69 0.65 0.51 0.49 0

MJO7 0.52 0.69 0.69 0.52 0.43 0

MJO8 0.51 0.68 0.71 0.58 0.46 0

MJO9 0.56 0.65 0.67 0.60 0.53 0

MJO10 0.59 0.68 0.65 0.54 0.53 0

RMM1 0.58 0.73 0.75 0.61 0.52 0

RMM2 0.49 0.64 0.62 0.48 0.42 0

1980 1990 200040

42

44

46

48

P[3

0,60

]

20100.26

0.265

0.27

0.275

0.28

0.285

0.29

MgI

I

40

42

44

46

48

P[3

0,60

]

1980 1990 2000 2010

8000

8200

8400

8600

8800

9000

9200

9400

CR

(rev

erse

d)

Fig. 4. Evolution of the mean periods P½30,60� (blue curves, a and c) and P½50,80� (blue curve

running mean of solar index MgII (red curves, a and b) and the flux of galactic cosmic ray

and c. (For interpretation of the references to colour in this figure legend, the reader i

mean periods and UV proxies are due to an increased noise/signalratio when passing from a 4-yr to a 2-yr sliding window. Thechanges in the confidence levels in model simulations whenpassing from a 4-yr to a 2-yr window are in the same order(see Appendix, Fig. A3). The overall correlation of mean periodswith GCR is significantly lower than with UV proxies due to thewell-known delay of the GCR �11-yr cycle with respect tosunspot numbers (e.g. Usoskin et al., 1997, and Fig. 5c and d).The correlation increases strongly and becomes significant whenthis 1-yr lag is introduced (e.g. the correlation for MJO1 vs GCR

changes from 0.36, given in Table 7, to 0.69).

4.5. Mean period domain

We next analyze the stability of our results with respect to achange of the mean period domain. Fig. 6 shows how thecorrelation between the mean period of MJO1 and the two solarindices MgII and GCR depends on the center of the mean period

ts are negative: their absolute values are given in the table.

JO6 MJO7 MJO8 MJO9 MJO10 RMM1 RMM2

.64 0.69 0.60 0.50 0.58 0.56 0.53

.60 0.71 0.61 0.44 0.52 0.59 0.47

.57 0.71 0.66 0.47 0.49 0.65 0.46

.56 0.68 0.68 0.54 0.52 0.67 0.50

.63 0.68 0.64 0.56 0.59 0.61 0.56

.63 0.70 0.60 0.48 0.57 0.57 0.52

.60 0.71 0.63 0.45 0.52 0.61 0.48

.57 0.71 0.68 0.51 0.51 0.67 0.49

.59 0.67 0.66 0.56 0.56 0.64 0.54

.64 0.69 0.61 0.52 0.59 0.58 0.55

.64 0.76 0.71 0.55 0.58 0.70 0.55

.56 0.66 0.58 0.43 0.49 0.55 0.46

1990 200055

60

65

70

P[5

0,80

]

1980 2010

0.26

0.265

0.27

0.275

0.28

0.285

0.29

MgI

I (re

vers

ed)

1980 1990 2000 201055

60

65

70

P[5

0,80

]

8000

8200

8400

8600

8800

9000

9200

9400

CR

s, b and d) for MJO1 estimated over a 4-yr sliding window compared with the 4-yr

s GCR (red curves, c and d). Window is centered. Ordinates are reversed in panels b

s referred to the web version of this article.)

1980 1985 1990 1995 2000 2005 201036

38

40

42

44

46

48

P[3

0,60

]

76007800800082008400860088009000920094009600

GC

R (r

ever

sed)

1980 1985 1990 1995 2000 2005 20103839404142434445464748

P[3

0,60

]

0.265

0.27

0.275

0.28

MgI

I

1980 1985 1990 1995 2000 2005 201054565860626466687072

P[5

0,80

]

0.260.2620.2640.2660.2680.270.2720.2740.2760.2780.28

MgI

I (re

vers

ed)

1980 1985 1990 1995 2000 2005 201054565860626466687072

P[5

0,80

]76007800800082008400860088009000920094009600

GC

R

Fig. 5. Same as Fig. 4 but with a 2-yr sliding window and running mean.

Table 5Correlation coefficients between MJO mean periods in the ‘‘short’’ (left 4 columns)

and ‘‘long’’ (right 4 columns) period domains and solar activity represented by the

WN, F, MgII and GCR series, computed with a 4-yr sliding window over the 1979–

2009 time span (see text).

P[30,60] WN F MgII GCR P[50,80] WN F MgII GCR

MJO1 0.60 0.65 0.69 �0.59 MJO1 �0.53 �0.55 �0.54 0.68

MJO2 0.40 0.45 0.50 �0.38 MJO2 �0.48 �0.51 �0.52 0.57

MJO3 0.35 0.38 0.43 �0.24 MJO3 �0.41 �0.44 �0.46 0.45

MJO4 0.50 0.50 0.53 �0.31 MJO4 �0.39 �0.43 �0.44 0.49

MJO5 0.68 0.71 0.73 �0.57 MJO5 �0.47 �0.50 �0.50 0.65

MJO6 0.56 0.61 0.65 �0.55 MJO6 �0.51 �0.54 �0.53 0.64

MJO7 0.38 0.43 0.49 �0.34 MJO7 �0.46 �0.49 �0.50 0.51

MJO8 0.40 0.42 0.46 �0.26 MJO8 �0.39 �0.43 �0.45 0.45

MJO9 0.62 0.62 0.64 �0.46 MJO9 �0.42 �0.46 �0.46 0.58

MJO10 0.65 0.69 0.73 �0.61 MJO10 �0.50 �0.53 �0.53 0.67

RMM1 0.47 0.51 0.56 �0.38 RMM1 �0.34 �0.39 �0.41 0.46

RMM2 0.54 0.57 0.62 �0.48 RMM2 �0.50 �0.52 �0.50 0.67

Table 6Same as Table 5 but over the 1979–2004 time span.

P[30,60] WN F MgII GCR P[50,80] WN F MgII GCR

MJO1 0.62 0.66 0.70 �0.57 MJO1 �0.83 �0.84 �0.83 0.85

MJO2 0.46 0.49 0.55 �0.37 MJO2 �0.76 �0.78 �0.80 0.73

MJO3 0.39 0.42 0.48 �0.27 MJO3 �0.69 �0.73 �0.77 0.64

MJO4 0.49 0.52 0.57 �0.37 MJO4 �0.70 �0.75 �0.78 0.71

MJO5 0.66 0.69 0.73 �0.59 MJO5 �0.80 �0.82 �0.82 0.84

MJO6 0.59 0.63 0.67 �0.53 MJO6 �0.81 �0.82 �0.83 0.81

MJO7 0.45 0.48 0.54 �0.34 MJO7 �0.73 �0.76 �0.79 0.69

MJO8 0.43 0.45 0.51 �0.30 MJO8 �0.68 �0.73 �0.77 0.66

MJO9 0.60 0.62 0.66 �0.51 MJO9 �0.74 �0.78 �0.80 0.78

MJO10 0.66 0.69 0.73 �0.60 MJO10 �0.82 �0.84 �0.84 0.85

RMM1 0.55 0.58 0.64 �0.43 RMM1 �0.65 �0.70 �0.76 0.67

RMM2 0.52 0.55 0.60 �0.47 RMM2 �0.86 �0.86 �0.85 0.89

Table 7Same as Table 6 but with a 2-yr sliding window.

P[30,60] WN F MgII GCR P[50,80] WN F MgII GCR

MJO1 0.53 0.56 0.59 �0.36 MJO1 �0.67 �0.69 �0.69 0.57

MJO2 0.44 0.47 0.51 �0.24 MJO2 �0.59 �0.62 �0.64 0.45

MJO3 0.41 0.43 0.46 �0.18 MJO3 �0.51 �0.55 �0.58 0.41

MJO4 0.47 0.48 0.50 �0.23 MJO4 �0.51 �0.54 �0.55 0.48

MJO5 0.58 0.60 0.62 �0.38 MJO5 �0.65 �0.67 �0.67 0.62

MJO6 0.52 0.56 0.59 �0.34 MJO6 �0.65 �0.67 �0.68 0.53

MJO7 0.44 0.47 0.50 �0.23 MJO7 �0.57 �0.59 �0.62 0.43

MJO8 0.43 0.44 0.47 �0.19 MJO8 �0.49 �0.53 �0.56 0.41

MJO9 0.54 0.55 0.56 �0.31 MJO9 �0.58 �0.60 �0.61 0.55

MJO10 0.57 0.60 0.62 �0.39 MJO10 �0.67 �0.69 �0.70 0.59

RMM1 0.52 0.53 0.57 �0.30 RMM1 �0.58 �0.61 �0.63 0.50

RMM2 0.47 0.50 0.53 �0.33 RMM2 �0.61 �0.60 �0.60 0.60

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207202

domain ½ymin,ymax�. We consider three examples with ymax�

ymin ¼ 25, 30 and 35 day. The abscissa x indicates the center ofinterval ½ymin,ymax�. Dashed and dotted horizontal lines correspond to

5% and 1% confidence levels, respectively. In all cases, there is good (atleast better than 5% level) correlation (or anti-correlation) betweenx¼40 and 50 day, followed by good anti-correlation (or correlation)between x¼60 and 70 day. Correlation breaks down around x¼55day and after x¼75 day. The two period domains of 30–60 day and50–80 day that we have considered above are clearly inside theintervals with significant correlation (Fig. 6, blue curves). A sharpchange in the correlation between mean period and solar activityhappens around 55 day, which is a rather clear minimum in thespectra of Fig. 1.

5. Summary and discussion

The main hypothesis underlying this work has been vindi-cated: we have been able to demonstrate a clear solar signature inthe spectral characteristics of the Madden–Julian oscillation andhave shown it to be both statistically significant and robust. Wecan summarize our findings as follows:

(1)

The three UV proxies used in this study may be rankedaccording to the degree in which they represent UV

30 40 50 60 70 80−1

−0.5

0

0.5

1

Cor

rela

tion

coef

ficie

nt

30 40 50 60 70 80−1

−0.5

0

0.5

1

Cor

rela

tion

coef

ficie

nt30 40 50 60 70 80

−1

−0.5

0

0.5

1

Cor

rela

tion

coef

ficie

nt

30 40 50 60 70 80−1

−0.5

0

0.5

1

Cor

rela

tion

coef

ficie

ntFig. 6. Correlation coefficients between MJO1 mean period and MgII (a and b) and GCR (c and d) as a function of the position of the center of the period domain for domain

widths of 25 day (green curves), 30 day (blue curves) and 35 day (red curves). Sliding window is 4-yr in a and c and 2-yr in b and d. (For interpretation of the references to

colour in this figure legend, the reader is referred to the web version of this article.)

1980 1990 2000 20100.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

Time (years)

Ene

rgy

1980 1990 2000 20100.05

0.1

0.15

0.2

0.25

0.3

Time (years)

Ene

rgy

1980 1990 2000 20100.08

0.1

0.12

0.14

0.16

0.18

0.20.22

0.24

0.26

0.28

Time (years)

Ene

rgy

1970 1980 1990 2000 20100.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (years)

Ene

rgy

Fig. A1. Evolution of the energy of the 30–60 day interval wave packet for paired indices (a) MJO1 (blue) and MJO6 (red); (b) MJO4 (blue) and MJO9 (red); (c) MJO5 (blue) and

MJO10 (red); (d) RMM1 (blue) and RMM2 (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207 203

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207204

emissions. The MgII series is the best but the shortest one; thesunspot number series is the longest, but its relationship withUV is weaker than for F10.7 or MgII. Comparing correlationcoefficients between MJO mean period and UV solar proxies,we see that there is a systematic increase in correlation whengoing from sunspot number to MgII index. This implies thatthe correlation is best for the best UV proxy.

(2)

The correlation between MJO mean period and GCR is lessgood than that with UV proxies when there is no lag betweenseries. However, it increases strongly when a 1-yr lag isintroduced. This suggests that UV emission rather than GCRis at the origin of the Schwabe-like cycle in MJO ‘‘short’’periods (e.g. 30–60 day).

(3)

There is no significant phase drift between MJO mean periodand solar cycle. However, it is difficult to propose a morequantitative test due to the irregularity of the solar cycle,which is far from being a pure 11-yr sine wave. One could askwhat changes in MJO occur across a solar cycle: could space–time differences between MJO events near the maximum vsminimum of a solar cycle be evidenced? Do MJO spectralcharacteristics relate in a simple way to space–time features?The answer appears to be negative. MJO is a nonlinearphenomenon and there is no one-to-one correspondencebetween its power spectral properties and space–time fea-tures. In addition, our treatment of data series is also non-linear. As a result the dynamics of MJO mean period, though

1980 1990 2000 201039

40

41

42

43

44

45

46

47

48

Time (years)

Mea

n pe

riod

140

41

42

43

44

45

46

47

48

49

Mea

n pe

riod

1980 1990 2000 201040

41

42

43

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49

Time (years)

Mea

n pe

riod

139

40

41

42

43

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46

47

48

49

Mea

n pe

riod

Fig. A2. Same as Fig. 1 but for

of course related with MJO events, cannot be interpreted in asimple way in geographical space.

(4)

The correlation of MJO spectral properties with solar activityis better in the Indian Ocean. Although it is clear that highamplitude events of MJO convection originate there, MJOcirculation signals can originate from any longitude range.The base state of the Indian basin supports convection betterthan many other regions, so that a circulation feature thatdevelops farther west can become associated with betterorganized deep convection over the Indian basin.

Altogether, these findings tend to support the ozone mechan-ism of solar impact on MJO rather than GCR modulation of clouds.We observe a change of correlation between solar activity andMJO mean period around 2005. A possible explanation may befound in the extremely low UV/EUV emission during the recentsolar minimum (Solomon et al., 2010). Daily measurements of thesolar spectrum made by the Spectral Irradiance Monitor (SIM)instrument on the Solar Radiation and Climate Experiment(SORCE) satellite since April 2004 show an important change inthe solar irradiance spectrum with respect to previous modelsduring this declining phase (Lean, 2000, Krivova et al., 2003;Krivova et al., 2006). Particularly, the decrease of the UV part ofthe solar spectrum is 4 to 6 times larger than expected (Haighet al., 2010). An anomalous evolution of total solar irradiance andits UV/EUV part for solar cycle 23 is also reported by Lukianova

980 1990 2000 2010Time (years)

970 1980 1990 2000 2010Time (years)

the mean period.

−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

correlation coefficient

conf

iden

ce le

vel

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

corr

elat

ion

coef

ficie

nt

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207 205

and Mursula (2011). The ozone altitude profile modeled by Haighet al. (2010) based on SIM data is different from the one based onLean’s model and does suggest that radiative forcing of surfaceclimate by the Sun should be out of phase with respect to solaractivity over the declining phase of solar cycle 23 (Haigh et al.,2010). This deviation from the expected scenario may be a reasonfor the decorrelation between MJO mean period and solar activityobserved since 2005. Unfortunately, the MJO series are too shortto allow a firm conclusion.

The ‘‘short’’ and ‘‘long’’ periods of the MJO spectrum display anopposite correlation with respect to solar activity. This differencemight be due to a mixing of MJO events with Kelvin waves, whosecharacteristic times peak around 70 day (Hendon et al., 1998). Thespectral filtering used in the construction of MJO indices does notprevent a contamination from the Kelvin wave component in theMJO spectrum (Zhang, 2005). This anti-correlation between themean periods in the two domains can be reproduced by simplemodels (e.g. when the amplitude of a spectral line or lines at theedge between the two domains is modulated by the solar cycle). Ifthe two domains (30–60 and 50–80 day) were consideredtogether (as interval 30–80 day), the modulation of the meanperiod would disappear. We note that there are very few MJOevents with lifetime greater than 60 day. The origin of ‘‘long’’periods in the MJO spectral range is not clear. It could be theresult of nonlinearity of MJO, reflect complex dynamics of MJO lifecycle (e.g. Majda and Stechmann, 2011) or an influence ofconvectively coupled Kelvin waves (e.g. Weeler and Kiladis,1999; Roundy et al., 2009; Ridout and Flatau, 2011). We suggestthat both period domains represent MJO phenomena in twodifferent ways, because our methods do not allow to separateMJO waves from others (e.g ER waves) that could contaminateMJO indices (e.g. Roundy et al., 2009).

35 40 45 50 55 60 65 70 75−0.8

center of period segment (days)

Fig. A3. (a) Distribution of correlation coefficients of the mean period of simu-

Acknowledgements

We thank two anonymous referees for useful comments on thefirst draft of this manuscript. IPGP Contribution NS 3258.

lated series (based on MJO1 spectrum) in the 30–60 day range and sunspot

number WN. 4-yr (blue), 2-yr (red) and 1-yr (green) sliding windows are

considered. Dashed lines correspond to the 1% and 5% confidence levels.

(b) Correlation of mean period range and MgII for the same simulated series vs

center of 30-day segment of the mean period estimation. Mean value (black,

dashed), 1% (red), 2% (magenta) and 5% (blue) confidence levels. (For interpreta-

tion of the references to color in this figure legend, the reader is referred to the

web version of this article.)

Appendix A

A.1. Similarity of spectral properties between different MJO indices

The evolutions of the energy and the mean period (Eqs. (1) and(2)) of the wave packets within the 30–60 day MJO main perioddomain are the same for geographically paired indices (e.g. MJO1and MJO6, MJO2 and MJO7, etc y) (Figs. A1 and A2). Despitesome differences in the amplitude of variations, there is a verygood similarity between the evolution of energy all MJO indices(Fig. A1). However, there is an increased difference between theevolution of energies of RMM1 and RMM2 after 2005 (Fig. A1, d).Multiple gaps in the RMM data series may explain the differencesobserved around 1980, but not the differences after 2005, whendata are continuous and there is no reported change in therecording methods. The evolutions of mean period for differentMJO series are less similar than those of amplitudes; however, theclose similarity of pairs of indices remains valid (Fig. A2).

A.2. Properties determined by the MJO spectrum

In order to test the significance of observed correlationcoefficients, we performed 5000 simulations of the model series,with a spectrum in the 20–90 day band given by the smoothedspectrum of MJO indices in the same range of periods. The lengthof each simulated series is the same as the length of MJO indices.

Part (a) of Fig. A3 presents the distribution of correlation coeffi-cients between the mean period in the 30–60 day range and WN

as the probability p that the correlation coefficient be larger thanC for �1rCr1. Averaging windows of 4-yr, 2-yr and 1-yr areconsidered. The 1% and 5% confidence levels for positive andnegative correlation are shown by horizontal dashed lines. Part(b) of Fig. A3 shows that positive and negative correlations ofmean period of simulated series with the MgII index havepractically equal probabilities. Confidence levels are almost inde-pendent of the chosen period range (see the 1%, 2% and 5%confidence levels in Fig. A3, b). We conclude that the spectra ofMJO indices do not determine the appearance of the �11-yr solarcycle in the MJO mean period for any period range.

A.3. Correlation between solar proxies.

Most solar indices are naturally closely related, as a result ofsolar dynamo evolution. However, their correlation depends ontime and performed smoothing or time lag. Table A1 shows thatusing annual means improves the correlation between UV proxies

Table A1Correlation coefficients between different solar proxies in the 1979–2009 time

span italicized cells correspond to daily values, non-italicized cells correspond to

annual means.

WN F10.7 MgII GCR GCR with 1-yr lag

WN 1.000 0.988 0.978 �0.813 �0.869

F10.7 0.855 1.000 0.994 �0.838 �0.866

MgII 0.917 0.870 1.000 �0.844 �0.864

E. Blanter et al. / Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012) 195–207206

(compare non-italicized cells with italicized ones) and 1-yr back-ward phase shift of GCR series gives higher values of correlationwith UV proxies (compare the two columns on the right). If weassume that the MgII index is the best UV measure, then itscorrelation coefficients with other solar proxies (Table A1) may beused as a rough measure of their closeness to UV emissions.

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