Will global warming modify the activity of the Madden–Julian Oscillation?

Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: 544–552, January 2011 B

Notes and CorrespondenceWill global warming modify the activity of the Madden–Julian

Oscillation?

Charles Jonesa* and Leila M. V. Carvalhoa,b

aEarth Research Institute, University of California, Santa Barbara, California, USAbDepartment of Geography, University of California, Santa Barbara, California, USA

*Correspondence to: Dr Charles Jones ERI, University of California, Santa Barbara, CA 93106, USA.E-mail: [email protected]

The Madden–Julian Oscillation (MJO) is the most prominent form of tropicalintraseasonal variability in the climate system. Observations suggest that warmingin the tropical Indian and Pacific Oceans in recent decades may have contributed toincreased trends in the annual number of MJO events. A stochastic model is used toproject changes in MJO activity under a global warming scenario. The mean numberof events per year may rise from ∼3.9 (1948–2008) to ∼5.7 (2049–2099) and theprobability of very active years (5 or more events) may significantly increase from0.51 ± 0.01 (1990–2008) to 0.75 ± 0.01 (2010–2027) and 0.92 ± 0.01 (2094–2099).Copyright c© 2011 Royal Meteorological Society

Key Words: intraseasonal variability; MJO; climate change

Received 2 June 2010; Revised 3 December 2010; Accepted 7 December 2010; Published online in Wiley OnlineLibrary 28 February 2011

Citation: Jones C, Carvalho LMV. 2011. Will global warming modify the activity of the Madden–JulianOscillation?. Q. J. R. Meteorol. Soc. 137: 544–552. DOI:10.1002/qj.765

1. Introduction

The Madden–Julian Oscillation (MJO) is the mostprominent form of tropical intraseasonal variability inthe climate system (Madden and Julian, 1994; Zhang,2005). The influential nature of the MJO has been notedon monsoon systems (Carvalho et al., 2002a,b; Lau andWaliser, 2005), occurrences of extreme precipitation (Jones,2000; Jones et al., 2004a), weather forecast accuracy (Joneset al., 2004a,b, 2011), interactions with El Nino/SouthernOscillation (McPhaden, 1999; Lau, 2005), deep oceanvariability (Matthews and Meredith, 2004; Matthews et al.,2007), distributions of tropical cyclones and hurricanes(Maloney and Hartmann, 2000; Kim et al., 2008) andsurface chlorophyll variations in tropical oceans and coastalareas (Waliser et al., 2005; Isoguchi and Kawamura, 2006).The oscillation exhibits important seasonal changes andpronounced interannual variations (Jones and Carvalho,2006, 2011; Pohl and Matthews, 2007).

While progress to understand the mechanisms of theMJO has improved over the years, global climate models

still do not realistically reproduce all characteristics of theMJO (Zhang, 2005; Lin et al., 2006). Therefore, the questionof how global warming will further impact the MJO hasnot been explored. The objective of this note is to showprojections of possible changes in the activity of the MJOunder one particular climate warming scenario. We refer toactivity as the number of MJO events occurring in a periodof time. The approach used here is probabilistic and employspreviously published stochastic models of the MJO. Section2 provides an overview of the stochastic models. Section 3discusses the activity of the MJO in the current climate andpresents projections of changes in the activity of the MJO.Section 4 presents the conclusions.

2. Stochastic models of the MJO

Two stochastic models have been developed to simulate thevariability of the MJO. An overview of the methodology andmain model features are summarized here, while additionaldetails can be found in Jones (2009) and Jones and Carvalho(2011); some figures are reproduced here for completeness.

Copyright c© 2011 Royal Meteorological Society

Global Warming and the MJO 545

The stochastic models were built from observations ofMJO occurrences. To identify MJO events, daily averages ofzonal wind components at 850 hPa (U850) and 200 hPa(U200) from the National Centers for EnvironmentalPrediction/National Center for Atmospheric Research(NCEP/NCAR) reanalysis (Kalnay et al., 1996) were used(1 January 1948–31 December 2008). Daily averages ofoutgoing long-wave radiation (OLR; Liebmann and Smith,1996) were used to characterize the convective signalassociated with the MJO (1 January 1979–31 December2008)

To isolate the MJO signal, the seasonal cycle was removedand the time series were detrended and filtered in frequencydomain to retain intraseasonal variations (20–200 days)(Matthews, 2000; Jones, 2009). MJO events were identifiedwith combined empirical orthogonal function (EOF)analysis of equatorially averaged (15◦S–15◦N) U200 andU850. The phase diagram of the first two normalizedprincipal components (PC1, PC2) approximately followsthe convention of Wheeler and Hendon (2004) and was usedto identify MJO events according to the following criteria:(i) the phase angle between PC1 and PC2 systematicallyrotated anti-clockwise indicating eastward propagation atleast to phase 5 (maritime continent), (ii) the amplitude(PC12 + PC22)0.5 was always larger than 0.35, (iii) the meanamplitude during the event was larger than 0.9, and (iv) theentire duration of the event lasted between 30 and 90 days. Atotal of 239 MJO events were identified during 1948–2008.The overall conclusions in this study are not sensitive tothe criteria defined above. Figure 1 shows the canonical lifecycle of the MJO based on composites of OLR anomaliesfrom events during 1979–2008.

2.1. A homogenous stochastic model of the MJO

Jones (2009) introduced a homogeneous stochastic modelcapable of simulating the temporal and spatial variabilityof the MJO. In this study, only the temporal componentis relevant and additional details about other aspects ofthe model can be seen in Jones (2009). The temporalvariability of the MJO uses the observed time series of phases,which consists of nine possible states S = 0, 1, 2, . . .8. S = 0corresponds to days when the MJO is quiescent andS = [1, 8] when it is active and in one of the eight phases ofthe PC1–PC2 diagram. According to observations of MJOevents, phases increase from low to high values indicatingeastward propagation. An event may propagate up to phase8 or end prematurely before that (phases 4–7). Moreover,the MJO may persist in the same phase for several days(typically 5–8 days) and even retrograde to a lower phasefor a few days (usually 1–2 days) before it continues eastwardpropagation. A primary MJO is defined when the oscillationinitiates from a quiescent state, whereas a successive eventoccurs when one MJO initiates right after a previous event,i.e. the phase diagram shows a continuous evolution fromphase 8 to phase 1 (Matthews, 2008).

Jones (2009) used a homogenous nine-state first-orderMarkov Chain approach (Wilks, 2006) and the time series ofphases to model the temporal variability of the MJO. Eighty-one conditional probabilities are involved and correspondto all possible transitions: Pji, j = [0, 8] and i = [0, 8], wherethe first subscript indicates the state at time t and thesecond subscript the state at time t + 1 (Wilks, 2006).The conditional probabilities determine transitions from

situations of non-MJO to MJO (and vice versa) andtransitions through the eight phases that characterize itslife cycle. The conditional probabilities of initiation of MJOsare given by P01, P02, P03 and P04 indicating that the MJO inthis model can start in phases 1, 2, 3 and 4 (i.e. ‘primary’event). The conditional probability of a successive event isP81 indicating transition from phase 8 to phase 1. In addition,Pji is always higher for eastward propagation than westwardpropagation. The westward propagation simply indicatesthat the MJO can retrograde to lower phases usually fora few days. Pji values equal to zero indicate that the MJOcannot ‘jump’ across non-adjacent phases. The conditionalprobabilities of termination of MJOs are P40, P50, P60, P70

and P80. Figure 2 schematically shows all possible phasetransitions.

The estimation of Pji in the homogeneous model is doneusing the time series of phases (61 years at daily values). Forinstance, P01 is estimated as: P01 = (number of 1s following0s)/(total number of 0s), and likewise for other conditionalprobabilities (Wilks, 2006). Jones (2009) discussed in detailthe estimation of Pji and how to minimize systematic errorsin the MJO simulations. The optimal estimation for thehomogeneous stochastic model was the mean Pji valuesestimated in 30-year windows (Table II in Jones, 2009). Themodel is called homogeneous because, once estimated, thetransition probabilities are constants.

The simulation of temporal variability of the MJO isaccomplished with the following procedure. The modeluses a daily time step and is initialized at phase S = 0 (i.e.quiescent MJO). An algorithm for uniform random numbers(r) continuously generates r ∈ [0, 1], which is compared tothe conditional probabilities until an MJO event initiates,i.e. a transition occurs from S = 0 to S = [1, 2, 3 or 4](Figure 2). Once an event starts, a duration Tk ∈ [30, 90]days is randomly generated from a gamma probabilitydistribution function (p.d.f.) fitted to observed durations ofMJOs. This step specifies that the given event will last Tk days.Random numbers r are generated and compared against Pji

values. The system then follows transitions through the eightMJO phases until the duration of Tk is reached. If a transitionattempts to terminate the event before the duration Tk isreached, new r values are picked until it continues thetransitions through the eight phases. If the duration Tk isreached and the system is in phase S = 4, 5, 6 or 7, thesystem returns to S = 0, since these are the only possibilities(Figure 2). If the system is in phase S = 8 when Tk is reached,the system may change to S = 0 or S = 1 depending on thevalue of r. This situation may initiate a successive MJO event.

Events generated by the homogeneous stochastic modeloccur irregularly in time and can appear as isolated eventsor successive MJOs in agreement with observations. Theoscillations in the model can last between 30 and 90 days,have different zonal propagation characteristics and theeastward propagation is consistent with observations ofthe MJO.

2.2. A non-homogenous stochastic model of the MJO

Jones and Carvalho (2011) extended the homogeneousversion to a non-homogeneous stochastic model in whichthe probabilities of MJO initiation vary in time. An overviewof the main formulation is provided here and additionaldetails are discussed therein.

Copyright c© 2011 Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: 544–552 (2011)

546 C. Jones and L. M. V. Carvalho

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Figure 1. Phase composites of OLR anomalies. Light (dark) shading indicates positive (negative) anomalies. The contour interval is 2.5 W m−2 and zerocontours are omitted (after Jones, 2009; Jones and Carvalho, 2011).

Western Pacific MJO starts

7 6 Eastwardpropagation

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Figure 2. Schematic diagram showing all possible phase transitions in the homogeneous stochastic model of the MJO. Phase S = 0 corresponds toinactive MJO. Curved arrows indicate that the system remains in the same phase (after Jones, 2009; Jones and Carvalho, 2011).



First, the homogenous stochastic model provides theprobabilities of primary and successive MJO initiations(Table II in Jones 2009). A constant parameter is defined asPHMG = P01 + P02 + P03 + P04, i.e. the sum of conditionalprobabilities of primary events in the homogeneous model.PHMG = 0.015649 is the average value estimated in 30-yearsamples. The conditional probability of a successive MJOwas estimated as P81 = 0.084706. (Note that the stochasticmodels need probabilities estimated in double precision butare shown rounded to six decimal digits.)

Next, to represent the non-stationarity of the MJO,the conditional probabilities of primary and successiveevents were estimated in shorter intervals throughoutthe time series of observed phases. A variable was thendefined as KNHM(t) = K01(t) + K02(t) + K03(t) + K04(t)which represents the sum of conditional probabilitiesof primary events estimated in 3-year moving windows.Likewise, the conditional probability of a successive MJOestimated in 3-year moving windows is K81(t). The 3-yearwindow size was deemed optimal and reproduces someimportant multi-year variations in the activity of the MJOduring 1948–2008.

The non-stationarity of the MJO is represented by theratios KNHM(t)/PHMG and K81(t)/P81, which show how theprobabilities of primary and successive MJO initiations varyin time relative to a homogeneous stochastic process. Thepositive trend in KNHM(t)/PHMG (Figure 3(a)) indicates anincrease in MJO activity after the 1970s. Moreover, multi-annual changes in KNHM(t)/PHMG suggest low-frequencyvariations in the MJO; those changes are more noticeableafter removing the trend. Jones and Carvalho (2011)showed that the long-term trend and multi-annual changesin KNHM(t)/PHMG are significantly correlated with long-term warming and low-frequency changes in sea surfacetemperature (SST) anomalies in the Indian and westernPacific warm pool. Likewise, K81(t)/P81 (Figure 3(b)) showsa positive trend to high values indicating an increase insuccessive MJO occurrences; if K81(t)/P81 = 0 in a 3-yearinterval, it means that there was no successive MJO inthat period, although isolated MJOs could have occurred.K81(t)/P81 suggests that a change in the MJO occurred afterthe early 1970s such that the probability of successive MJOinitiation is considerably higher than in the early part of therecord.

Jones and Carvalho (2011) showed that the non-stationarity of the MJO during 1948–2008 can be empiricallyrepresented by a regression that expresses KNHM(t)/PHMG

as a function of low-frequency SST changes in the tropicalIndian and western Pacific warm pool:

KNHM

PHMG(t) = 1.25 +

4∑

j=0

ajMSST(t − jτj)

+4∑

j=0

bjVSST(t − jγj) + 0.48Tr30(t), (1)

where aj, bj are regression coefficients, MSST and VSST

are detrended 3-year running means and variances ofSST anomalies averaged over the warm pool (15◦S–15◦N;50◦E–150◦W); τj (0, 156, 312, 468 and 624 days) and γj

(0, 300, 600, 900 and 1200 days) are time lags; Tr30 is anon-dimensional 30-year running mean of SST anomaliesto account for the long-term trend in the warm pool region.

Tr30 is used (as opposed to a simple linear trend) to make thenon-homogeneous stochastic model stable if large negativeSST anomalies are used in the regression equation. Theempirical constants (1.25 and 0.48) keep the bias in themodel to a minimum.

It is opportune to mention that the relationship betweenK81(t)/P81 and SST changes in the warm pool is noteasily represented. During some decades, an increase in thenumber of successive MJOs leads warming in the warm poolby 1–2 years, whereas the relationship is not systematicallyseen in other decades. To simplify the problem, Jonesand Carvalho (2011) used the fact that K81(t)/P81 andKNHM(t)/PHMG are correlated (0.51) and defined K81(t)/P81

as:

K81

P81(t) = 0.4 + 0.56

KNHM

PHMG(t), (2)

where P81 is the conditional probability in the homogeneousmodel (i.e. average value of 30-year samples) and K81(t) isestimated in 3-year moving windows.

In the non-homogeneous stochastic model, only theprobabilities of MJO initiation vary in time and theremaining ones are kept constant during the simulations.This simplifies the formulation and allows investigating thehypothesis that multi-annual to long-term changes in SSTanomalies in the warm pool drive variations in the activity ofthe MJO. Another important feature is that uncertainties inSST anomalies in the warm pool and errors in the regressionmodel are taken into account in the ensemble simulations.

An overview of the non-homogenous stochastic simula-tions for the observational record is as follows. The first stepis to construct time series of KNHM(t)/PHMG and K81(t)/P81.Mean monthly SST anomalies averaged over the warm poolfrom four different datasets are used in Eqs (1) and (2).Uncertainties in SST anomalies are represented by the stan-dard deviation of the datasets. Upper and lower boundsfor KNHM(t)/PHMG and K81(t)/P81 are constructed usingEqs (1) and (2) with SST anomalies expressed as SSTA ± δ,where SSTA is the mean anomaly and δ is the standard devi-ation. Errors associated with regression Eqs (1) and (2) areadded to the upper and lower bounds of KNHM(t)/PHMG andK81(t)/P81. (Jones and Carvalho, 2011, provide full detailson the error analysis.)

The non-homogeneous stochastic model is initialized atS = 0 (i.e. quiescent MJO) and observed mean SST anomalyin the warm pool on 1 January 1948. The probabilityratios of primary and successive MJOs for that day aredetermined by Eqs (1) and (2). However, random Gaussianerrors ε with zero mean and bounded by the upper andlower bounds of the KNHM(t)/PHMG and K81(t)/P81 curvesare added to the value specified by Eqs (1) and (2) forthat day: KNHM(t)/PHMG + ε, K81(t)/P81 + ε. This processensures that KNHM(t)/PHMG and K81(t)/P81 are randomlydrawn between possible values that take into considerationuncertainties associated with SST anomalies in the warmpool and errors due to the regression models (Figure 6below gives an example).

Next, since KNHM(t)/PHMG and K81(t)/P81 are specifiedfor that day, and PHMG and P81 are constants, KNHM(t)and K81(t) are also known which determine K01(t),K02(t), K03(t), K04(t) and K81(t) for that day. Forinstance, if KNHM(t)/PHMG is 1.2 on that day, it meansthat KNHM(t) = K01(t) + K02(t) + K03(t) + K04(t) has toincrease by 20% and K00(t) decrease by 20% (K00(t) +



Figure 3. (a) Time series of KNHM(t)/PHMG which indicates changes in the probability of initiation of primary MJO events relative to the homogeneousstochastic model (after Jones and Carvalho, 2011). (b) Time series of K81(t)/P81 which indicates changes in the probability of initiation of successiveMJO events relative to the homogeneous stochastic model. Smooth curves were obtained with a 365-day moving average. Period: 1948–2008.

K01(t) + K02(t) + K03(t) + K04(t) = 1) since these are theonly possible transitions when the system is at state 0 attime t (Figure 2 also Table II in Jones, 2009). The increase(decrease) in each individual term is done maintaining thesame relative ratios of the probabilities in the homogeneousstochastic model (likewise for the conditional probabilityof successive events). Since all conditional probabilities arethen specified for that day, the model proceeds with thesame rules described in the homogenous stochastic modelsimulation (section 2.1). Lastly, the simulation continueswith a daily time step until the end of the observed recordof KNHM(t)/PHMG and K81(t)/P81. The end result is a timeseries of phases in which MJO occurrences behave as in theobservations.

3. The activity of the MJO in the present climate andstochastic projections

Observed multiannual changes and long-term trends in theactivity of the MJO were investigated by computing thenumber of events in 5-year running windows (Figure 4).Variations in the MJO (solid curve with circles) show lowactivity (∼18 events in 5 years) until about 1972, when aregime shift appears to have occurred leading to a systematiclong-term increase. In addition, multi-annual periods ofhigh and low MJO activity are noticed throughout therecord.

The observed activity of the MJO was compared againstsimulations from the homogeneous and non-homogeneousstochastic models in the following way (Figure 4). Anensemble run of 1000 members was performed with thehomogeneous stochastic model and the number of MJO

events in 5-year moving windows was computed. Thisensemble run provides frequency distributions of activityof the MJO in each year. Since the transition probabilitiesin the homogeneous stochastic model are constant in time,the MJO in this model behaves as a stationary process. Forthis reason, trends and low-frequency changes cancel out inthe computation of the ensemble mean, which is indicatedby the horizontal dashed line (18 events in 5 years). Theother two horizontal dashed lines show the 5th and 95thpercentiles of the frequency distribution and indicate thespread of possible values in the homogeneous model.

Similarly, an ensemble run of 1000 members wasperformed with the non-homogeneous stochastic modeland the solid smooth curve shows the ensemble mean(Figure 4). The ensemble mean from non-homogeneousstochastic simulations follows the observed trends in theMJO. The shaded region indicates the spread in thefrequency distribution of number of events in 5 years.As discussed in detail by Jones and Carvalho (2011), theensemble simulations with the non-homogeneous stochasticmodel are significantly correlated (0.68) with the observedlong-term changes in the MJO (correlations greater/less than±0.66 are significant at 5% level).

Probabilistic projections of changes in the activityof the MJO were investigated in the context of non-homogeneous stochastic model simulations. The focuswas on the A1B global warming scenario (IPCC, 2007),which assumes balanced usage of fossil intensive andnon-fossil energy sources in a future world of rapideconomic growth and a global population that peaks inmid-century and declines thereafter. Projections of SSTfrom coupled climate models for the period 2010–2099



Figure 4. MJO activity during 1948–2008. The black solid curve shows ensemble mean number of events in 5-year moving windows obtained withnon-homogeneous stochastic model simulations (1000 members). The shaded region indicates the 5th–95th percentile spread. The observed numberof MJO events in 5-year moving windows is shown by the black curve with circles. Horizontal dashed lines indicate 5th and 95th percentiles (13 to 22events in five years) and the ensemble mean number of events (18 events in five years) obtained with a homogeneous stochastic model. (After Jones andCarvalho, 2011.)

were used to drive the non-homogeneous stochasticmodel of MJO activity. The following models were used:ECHAM5/MPI-OM (two runs), BCCR-BCM2.0 (BjerknesCentre for Climate Research, Norway), CCSM3 (NationalCenter for Atmospheric Research, USA), GFDL-CM2.1 (USDept. of Commerce/NOAA/Geophysical Fluid DynamicsLaboratory, USA) and MRI-CGCM2.3.2 (MeteorologicalResearch Institute, Japan). Monthly SST anomalies averagedover the Indian Ocean and western Pacific warm pool wereused in the regression equations of conditional probabilitiesof MJO initiation (section 2).

Figure 5 shows each projection of SST anomalies and theensemble mean (bold solid line). The ensemble mean SSTanomaly in the warm pool increases from about 0.6◦C in2010 to 2.8◦C in 2099. Although all models show systematicwarming trends during 2010–2099, there is also a largespread among the model runs, particularly in the magnitudesof decadal variations. This uncertainty in changes in SSTanomalies in the warm pool was represented as the standarddeviation from the ensemble mean and used in the stochasticsimulations of the MJO.

To derive projections of probabilities of primary andsuccessive MJO initiations, the ensemble mean SST anomalywas used in Eqs (1) and (2) and upper/lower boundscalculated to account for uncertainties in projections ofSST anomalies in the warm pool and errors associatedwith the regression model. The mean KNHM(t)/PHMG

(Figure 6) starts from about 2.1 in the present climateand systematically increases to 3.7 by 2099. KNHM(t)/PHMG

also shows periods of high and low activity and reflectsthe spread of decadal variations in SST anomalies projectedby the coupled model runs. Projections of K81(t)/P81 showlong-term increases as well, since they were determined fromEq. (2) (not shown).

An ensemble of 1000 members was constructed such thateach member runs for 90 years at daily resolution. Eachsimulation resulted in a time series of phases and representssituations of active MJO (S = [1, 8]) and quiescent periods(S = 0). Next, we computed the number of MJO eventsper calendar year (2010–2099) (each year has a frequencydistribution of 1000 data points). We note that thenon-homogenous stochastic model simulates primary andsuccessive MJOs. For simplicity, the results are presentedhere in terms of total (primary plus successive) events.

Moreover, a statistical test (Rodionov, 2004) was performedto detect change points in the ensemble mean number ofevents per year.

Figure 7 displays the results as decadal shifts in theprojected changes in the mean number of MJO events. Thesimulations suggest progressive increases from the currentmean of 4.6 events year−1 to about 5.7 events year−1 by2094–2099. It is interesting to note that, although the 95thpercentiles of the distributions remain virtually unchangedin the projections, the 5th percentiles increase from 3 events(2010–207) to 4 events by 2038–2049.

An interesting feature of the stochastic model approachis the possibility of computing probabilistic projections ofchanges in the activity of the MJO. Jones and Carvalho(2011) derived cumulative probability curves of number ofMJO events per year during 1880–2008. For the period ofavailable observations, the probability of 5 or more eventsin a year was 0.19 in 1948–1972, 0.33 in 1973–1989 and0.51 in 1990–2008. The same approach was applied tothe projections of changes in the MJO (Figure 8). Notethat the probability curves in any two adjacent periods arestatistically different from each other at the 5% confidencelevel, since they were obtained after the identification ofchangepoints in the time series of number of events peryear. For comparison with present climate, the probabilityof 5 or more events in a year increases as: 0.75 (2010–2027),0.78 (2028–2037), 0.82 (2038–2049), 0.88 (2050–2093) and0.92 (2094–2099).

4. Conclusions

The MJO is the most important mode of tropicalintraseasonal variability. Observational studies based onreanalysis data indicate that the MJO shows regime changeson low-frequency time-scales (i.e. variations longer than∼2 years) (Jones and Carvalho, 2006, 2011). In addition,the MJO exhibits a long-term trend in activity (Jones, 2009)including a trend toward greater event frequency after themid-1970s (Jones and Carvalho, 2006; Pohl and Matthews,2007). These changes in the MJO coincide with the long-term warming in the Indian Ocean and western Pacific warmpool. A possible linkage between increased MJO activity andwarming in the tropical oceans is in agreement with the study



Figure 5. Projections of monthly SST anomalies in the Indian and western Pacific warm pool region (2010–2099). Thin solid curves were obtained fromsix coupled general circulation model simulations and the bold black curve is the ensemble mean.

Figure 6. Projections of probability ratios of initiation of primary MJO events (2010–2099). The shaded region indicates upper/lower confidence levelsgiven uncertainties in projections of SST anomalies and errors in the empirical regression model (see text for additional details).

Figure 7. Projected changes in MJO activity during 2010–2099. Each bar summarizes statistics obtained with stochastic simulations: mean number ofevents year−1 (circles), 95% confidence level (horizontal ticks), and 5th and 95th percentiles (tips of the bars). Changes between adjacent time periodsindicated on the bottom axis are significant at the 5% level.



Figure 8. Cumulative probabilities of number of MJO events year−1. Each curve represents cumulative probabilities in the indicated decades. The x-axisdenotes n or more events year−1. Differences in probability curves between two adjacent time periods are significant at the 5% level.

of Slingo et al. (1999), although dynamical mechanismsneed yet to be demonstrated. Slingo et al. (1999) performedgeneral circulation model experiments forced with observedSSTs and partially reproduced the positive trends in tropicalintraseasonal amplitudes since the mid-1970s.

This is the first study to derive quantitative projections ofchanges in MJO activity in the A1B global warming scenario.A non-homogeneous stochastic model was developed basedon the empirical evidence that the probability of MJOinitiation is associated with multi-annual changes andpositive trend in SST anomalies in the Indian Ocean andwestern Pacific. Projections of SST anomalies in the warmpool from IPCC coupled models were used to drive theprobabilities of MJO initiation in the non-homogeneousstochastic model. The results suggest decadal shifts in thenumber of MJO occurrences per year and the probability ofvery active years (5 or more events) significantly increasesfrom the values in the present climate.

One significant challenge in the development of acomprehensive theory of the MJO has been to determinewhat dynamical mechanisms control the initiation of theoscillation. Kemball-Cook and Weare (2001), for instance,analyzed radiosonde data in the Indian Ocean, MaritimeContinent and western Pacific Ocean to investigate threepossible mechanisms of MJO initiation: (i) extratropicaltriggering, (ii) tropical circumnavigating triggering and(iii) recharge–discharge. They used an instability indexdefined as moist static energy (h) at 1000 hPa minus that at500 hPa. (h = cpT + Lq + gz; cp = specific heat at constantpressure, T = temperature, L = latent heat of condensation,g = gravity acceleration, z = geopotential height). Theyshowed that the instability index was well correlated withconvective available potential energy (CAPE) and foundsupport for the recharge–discharge mechanism. In thiscase, the initiation of organized convection during the MJOis initiated by a combination of low-level moist static energybuild-up and concurrent drying of the mid-troposphereassociated with subsidence from a previous cycle of MJOconvection.

Thus, a possible hypothesis for the observed positivetrend in MJO activity is that warming of the tropical IndianOcean and western Pacific increases the background CAPEnecessary for triggering MJO events. The instability indexdescribed above was computed with NCEP/NCAR reanalysis

(not shown) and it clearly shows significant (5% level)positive trends in intraseasonal variance averaged over thewarm pool during 1948–2008. However, Kemball-Cookand Weare (2001) warned that near-surface NCEP/NCARreanalysis may be more influenced by model physicsthan station data over that region and may not beable to accurately represent the timing of MJO events.Nevertheless, the trend in the instability index is consistentwith trends in CAPE and Convective Inhibition (CIN)discussed by Riemann-Campe et al. (2009) who analyzedERA-40 reanalyses of the European Centre for Medium-Range Weather Forecasts for the period 1958–2001.

However it is important to mention other possible impactsthat global warming might have on the MJO. These mightinclude changes in longitudinal gradients of SST in thetropical Indian and Pacific Oceans, modifications in themean state (Inness et al., 2003) or changes in extratropicalstochastic forcing on the MJO (Ray and Zhang, 2010).

Lastly, it is relevant to note that this study investigated oneaspect of a very complicated problem (i.e. number of MJOevents). Additional studies need to be developed to examinelikely modifications in amplitude, structure and differencesin mechanisms associated with primary and successive MJOevents. New reanalysis products and improved global climatemodels might bring new insights on the variability of theMJO in the present climate and how it might change in thefuture.

Acknowledgements

NCEP/NCAR reanalysis and OLR data were providedby the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA,from their web site at http://www.cdc.noaa.gov. SSTprojections were obtained from the World Climate ResearchProgramme’s (WCRP’s) Coupled Model IntercomparisonProject phase 3 (CMIP3) multi-model dataset. Weacknowledge the modelling groups, the Program for ClimateModel Diagnosis and Intercomparison (PCMDI) and theWCRP’s Working Group on Coupled Modelling (WGCM)for their roles in making available the WCRP CMIP3multi-model dataset. Support of that dataset is providedby the Office of Science, US Department of Energy. Thisresearch was funded by NOAA Office of Global Programs(NOAA/NA05OAR4311129, NA07OAR4310211).



References

Carvalho LMV, Jones C, Liebmann B. 2002a. Extreme precipitationevents in southeastern South America and large-scale convectivepatterns in the South Atlantic convergence zone. J. Climate 15:2377–2394.

Carvalho LMV, Jones C, Silva Dias MAF. 2002b. Intraseasonal large-scale circulations and mesoscale convective activity in tropical SouthAmerica during the TRMM-LBA campaign. J. Geophys. Res.-Atmos.107(D20): DOI:29/2001JD000745.

Inness PM, Slingo JM, Guilyardi E, Cole J. 2003. Simulation of theMadden–Julian oscillation in a coupled general circulation model.Part II: The role of the basic state. J. Climate 16: 365–382.

IPCC. 2007. Climate Change 2007: The Physical Science Basis.Contribution of Working Group I to the Fourth Assessment Reportof the Intergovernmental Panel on Climate Change. Solomon S, Qin D,Manning M, Chen Z, Marquis M, Averyt K, Tignor MMB, Miller HL.(eds.) Cambridge University Press: London and New York.

Isoguchi O, Kawamura H. 2006. MJO-related summer cooling andphytoplankton blooms in the South China Sea in recent years. Geophys.Res. Lett. 33: L16615, DOI: 10.1029/2006GL027046.

Jones C. 2000. Occurrence of extreme precipitation events in Californiaand relationships with the Madden–Julian oscillation. J. Climate 13:3576–3587.

Jones C. 2009. A homogeneous stochastic model of the Madden–JulianOscillation. J. Climate 22: 3270–3288.

Jones C, Carvalho LMV. 2006. Changes in the activity of theMadden–Julian Oscillation during 1958–2004. J. Climate 19:6353–6370.

Jones C, Carvalho LMV. 2011. Stochastic simulations of theMadden–Julian Oscillation activity. Clim. Dyn. 36: 229–246. DOI:10.1007/s00382-009-0660-2.

Jones C, Waliser DE, Lau KM, Stern W. 2004a. Global occurrencesof extreme precipitation and the Madden–Julian oscillation:Observations and predictability. J. Climate 17: 4575–4589.

Jones C, Waliser DE, Lau KM, Stern W. 2004b. The Madden–JulianOscillation and its impact on Northern Hemisphere weatherpredictability. Mon. Weather Rev. 132: 1462–1471.

Jones C, Gottschalck J, Carvalho LMV, Higgins WR. 2011. Influence ofthe Madden–Julian Oscillation on forecasts of extreme precipitationin the contiguous United States. Mon. Weather Rev. DOI:10.1175/2010MWR3512.1. In press.

Kalnay E, Kanamitsu M, Kirtler R, Collins W, Deaven D, Gandin L,Iredell M, Saha S, White G, Woollen J, Zhu Y, Chelliah M, Ebisuzaki W,Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Leetma A,Reynolds R, Jenne R, Joseph D. 1996. The NCEP–NCAR 40-yearreanalysis project. Bull.Amer. Meteorol. Soc. 77: 437–471.

Kemball-Cook SR, Weare BC. 2001. The onset of convection in theMadden–Julian oscillation. J. Climate 14: 780–793.

Kim J-H, Ho C-H, Kim H-S, Sui C-H, Park SK. 2008. Systematic variationof summertime tropical cyclone activity in the western North Pacific inrelation to the Madden–Julian Oscillation. J. Climate 21: 1171–1191.

Lau WKM. 2005. El Nino Southern Oscillation connection. In:Intraseasonal Variability in the Atmosphere–Ocean Climate System,Lau WKM, Waliser DE. (eds.) Springer Praxis: Chichester, UK.

Lau WKM, Waliser DE. 2005. Intraseasonal Variability in theAtmosphere–Ocean Climate System. Springer: Chichester, UK.

Liebmann B, Smith CA. 1996. Description of a complete (interpolated)outgoing longwave radiation dataset. Bull. Amer. Meteorol. Soc. 77:1275–1277.

Lin JL, Kiladis GN, Mapes BE, Weickmann KM, Sperber KR, Lin W,Wheeler MC, Schubert SD, Del Genio A, Donner LJ, Emori S,Gueremy J-F, Hourdin F, Rasch PJ, Roeckner E, Scinocca JF. 2006.Tropical intraseasonal variability in 14 IPCC AR4 climate models.Part I: Convective signals. J. Climate 19: 2665–2690.

Madden RA, Julian PR. 1994. Observations of the 40–50-day tropicaloscillation – A review. Mon. Weather Rev. 122: 814–837.

Maloney ED, Hartmann DL. 2000. Modulation of hurricane activity inthe Gulf of Mexico by the Madden–Julian Oscillation. Science 287:2002–2004.

Matthews AJ. 2000. Propagation mechanisms for the Madden–JulianOscillation. Q. J. R. Meteorol. Soc. 126: 2637–2651.

Matthews AJ. 2008. Primary and successive events in the Madden–JulianOscillation. Q. J. R. Meteorol. Soc. 134: 439–453. DOI: 10.1002/qj.224.

Matthews AJ, Meredith MP. 2004. Variability of Antarctic circumpolartransport and the Southern Annular Mode associated withthe Madden–Julian Oscillation. Geophys. Res.Lett. 31: DOI:10.1029/2004GL021666.

Matthews AJ, Singhruck P, Heywood KJ. 2007. Deep ocean impact ofa Madden–Julian Oscillation observed by Argo floats. Science 318:1765–1769.

McPhaden MJ. 1999. Genesis and evolution of the 1997–98 El Nino.Science 283: 950–954.

Pohl B, Matthews AJ. 2007. Observed changes in the lifetimeand amplitude of the Madden–Julian Oscillation associated withinterannual ENSO sea surface temperature anomalies. J. Climate 20:2659–2674.

Ray P, Zhang CD. 2010. A case study of the mechanics of extratropicalinfluence on the initiation of the Madden–Julian Oscillation. J. Atmos.Sci. 67: 515–528.

Riemann-Campe K, Fraedrich K, Lunkeit F. 2009. Global climatologyof Convective Available Potential Energy (CAPE) and ConvectiveInhibition (CIN) in ERA-40 reanalysis. Atmos.Res. 93: 534–545.

Rodionov SN. 2004. A sequential algorithm for testingclimate regime shifts. Geophys. Res. Lett. 31: L09204, DOI:09210.01029/02004GL019448.

Slingo JM, Rowell DP, Sperber KR, Nortley E. 1999. On the predictabilityof the interannual behaviour of the Madden–Julian Oscillation andits relationship with El Nino. Q. J. R. Meteorol. Soc. 125: 583–609.

Waliser DE, Murtugudde R, Strutton P, Li JL. 2005. Subseasonalorganization of ocean chlorophyll: Prospects for prediction basedon the Madden–Julian Oscillation. Geophys. Res. Lett. 32: L23602,DOI: 23610.21029/22005GL024300.

Wheeler MC, Hendon HH. 2004. An all-season real-time multivariateMJO index: Development of an index for monitoring and prediction.Mon. Weather Rev. 132: 1917–1932.

Wilks DS. 2006. Statistical Methods in the Atmospheric Sciences. (seconded.) International Geophysics Series. Academic Press: San Diego andLondon.

Zhang CD. 2005. Madden–Julian Oscillation. Rev. Geophys. 43: 1–36.


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