Madden-Julian Oscillation in a climate model with a well-resolved stratosphere



[1] This work evaluates how well a coupled ocean-atmospheric climate model with a well-resolved stratosphere captures the observed Madden-Julian Oscillation (MJO) signal in the upper troposphere and lower stratosphere. The model is the Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC) coupled modeling system (CMCC-CMS) with 95 atmospheric levels. CMCC-CMS produces MJO composites of precipitation that are very similar to those of the observations and the ERA-40 reanalysis product. Furthermore, model precipitation is found to propagate eastward near the observed speed. There is also strong agreement in the tropics and subtropics in the temperature and flows at 100 and 200 hPa upon comparing the composites based on the full 340 years of model output and those for the past 20 years of the model output with those of the ERA-40 reanalysis. At the 100 hPa level the temperature anomalies in the model output and reanalysis propagate eastward at about 7 m s–1 at the equator, 25°N and 65°N. Longitude and height cross sections at 25°N suggest vertically propagating Rossby waves up to near the 10 hPa level in both the model and observations. Latitude and height cross sections of temperature and zonal and meridional winds indicate strong vertical propagation in the tropics in both the model and reanalysis. Overall, the CMCC-CMS model shows MJO characteristics in the tropical and subtropical troposphere and lower stratosphere that are in very good agreement with observed analyses.

1. Introduction

[2] The Madden-Julian Oscillation (MJO) was identified by Madden and Julian [1972, 1994] as a slow eastward-propagating anomaly in tropical winds and surface pressure having a period of around 45 days [Zhang, 2005]. Since its discovery, the MJO has evoked a great deal of interest in part because of its potential use as a forecast tool for such diverse situations as the timing of the Indian monsoon depressions [Yasunari, 1981], the occurrence of intense winter rains in California [Jones, 2000], and the frequency and intensity of hurricanes in the eastern Pacific and Caribbean [Maloney and Hartmann, 2000a, 2000b]. The influence on hurricanes appears to be communicated by way of upper tropospheric wind and wind shear anomalies.

[3] Recently, a number of studies of models, which contributed to the most recent Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), have investigated the quality of MJO simulations in coupled ocean-atmosphere global climate models. Lin et al. [2006] conclude that the total intraseasonal variance in precipitation is too weak and the phase speeds are too fast in most models. Kim et al. [2009] find that most models produce a propagating mode of precipitation and wind that is too weak relative to observations. These failures are associated with many possible causes, but are generally thought to be related to deficiencies in model moist convection parameterizations [e.g., Gualdi et al., 1997; Deng and Wu, 2010]. Both papers conclude that recent versions of the ECHAM4/ECHAM5 models from the Max Planck Institute for Meteorology (MPI) are among the few that reasonably reproduce the MJO.

[4] In a recent paper, Weare [2010a] showed composites of observed MJO-associated changes in ERA-40 [Uppala et al., 2005] winds, temperature, and ozone in the tropics for the upper troposphere and lower stratosphere. Evidence is presented for significant and coherent MJO departures throughout the lower stratosphere. In a follow-up paper, Weare [2010b] used Extend (three-dimensional) Eliassen-Palm flux estimates to show how MJO signals can propagate both poleward and deep into the stratosphere.

[5] The primary goal of this work is to evaluate how well a coupled ocean-atmosphere climate model with a well-resolved stratosphere captures the observed MJO signal in the upper troposphere and lower stratosphere. The chosen model is the Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC) coupled model with 95 atmospheric levels with a top at 80 km. The methods used will follow those of Weare [2010a].

2. Data, Model, and Statistics

2.1. ERA-40

[6] ERA-40 [Uppala et al., 2005] involves comprehensive use of traditional observations and satellite data in state-of-the-art forecast model-derived gridded data fields. The current analysis follows that of Weare [2010a] and uses 6 h values of total precipitation, zonal (u) and meridional (v) winds, and temperature (T) at 10, 20, 30, 50, 70, 100, 150, and 200 hPa on a 2.5° × 2.5° grid for 1980–2001. It should be noted that precipitation is not directly assimilated into the ERA-40; it is the model calculation that is consistent with the observed thermodynamic and motion fields. To identify the MJO, the 22 year daily means of these data at every grid point are first removed. Then, these anomalies are filtered using a 150 point Lanczos band-pass filter [Duchon, 1979], capturing well the 20–90 day periodicities.

2.2. GPCP Rainfall

[7] The Global Precipitation Climatology Project (GPCP) [Huffman et al., 2001] merges daily rain gauge and infrared and microwave-based satellite rainfall estimates to create daily precipitation maps at 0.5° × 0.5° resolution. These estimates have been available since October 1996. The period January 1997 through December 2010 was used for comparison. After linearly interpolating these data to the 2.5° ERA-40 grid, filtered departures were created in the manner described above.


[8] The Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC) coupled ocean-atmosphere-ice climate model with a well-resolved stratosphere, labeled CMCC-CMS, is based on the middle atmosphere version of the fifth-generation MPI-European Centre, Hamburg (ECHAM) global atmospheric model (MA-ECHAM5) [Roeckner et al., 2006; Manzini et al., 2006], the Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) OASIS3 coupler [Valcke, 2006; Fogli et al., 2009], the OPA8.2 parallel ocean model [Madec et al., 1999], and the LIM sea-ice model [Fichefet and Morales-Maqueda, 1997]. This atmospheric model has T63 horizontal resolution and 95 levels with a top at 80 km (0.01 hPa). It includes a parameterization of momentum-conserving orographic and nonorographic gravity wave drag. Giorgetta et al. [2006] show that a similar 90 level atmospheric model internally generates the quasi-biennial oscillation (QBO) in the equatorial stratosphere; preliminary analyses of a fully coupled CMCC-CMS model also show a clear QBO with a period of around 24 months. The oceanic and sea-ice components have a resolution of about 2° in the horizontal with 31 ocean levels; there is no flux adjustment. The available output covers about 340 years with preindustrial values of greenhouse gases (CO2, N2O, and CH4) and prescribed tropospheric and stratospheric ozone [Kiehl et al., 1999]. Only temperature and wind at the 100 and 200 hPa levels are employed from the full model output (labeled CMS:340). In addition, the same variables as those obtained from ERA-40 are chosen for the last 20 years of the model output (labeled CMS:20) for more detailed analyses. All output is MJO filtered in a manner identical to that of the ERA-40.

2.4. Compositing

[9] Weare [2010a] developed an MJO index, which is based on filtered equatorially symmetric variations in 200 hPa zonal winds between 10°S and 10°N over the Indian Ocean (60°E−90°E). The procedure identifies time periods in which each region has relatively strong easterlies that are symmetric about the equator. Weare [2010a] defined the index as “the symmetric component zonal wind, when the velocity is at least one standard deviation less than the mean and when at the same time the ratio of the antisymmetric to symmetric components is at least one standard deviation less than the mean of that ratio.” Unfortunately, on rare occasions this results in a division by zero. To eliminate this possibility, the final part of this step was replaced by one that tests whether a particular difference between the antisymmetric and symmetric components is larger than 1.5 standard deviations of that difference. As in the study by Weare [2010a], this procedure identifies time periods in which a region has relatively strong easterlies that are symmetric about the equator. The current index using the ERA-40 reanalysis is very similar to that illustrated by Weare [2010a, Figure 1]. This index is used to calculate zero lag composite means and for these periods of strong symmetric easterlies in the reference region and for times lagging and leading those central times by up to 25 days.

[10] The statistical assessment as to whether a composite mean inline imageat each point is different from zero is based on the two-sided t test [Von Storch and Zwiers, 1999]:

display math

where N is the effective number of samples in the composite mean and σX is the standard deviation of X over the domain. For the ERA-40 and CMS:20 outputs, the standard deviations are based on the variability within the approximately 20 year composites of the filtered data. Since these means are calculated from data that are highly filtered and thus have substantial autocorrelations, N is smaller than the number of days contributing to the means. As in an earlier study by Weare [2010a], this N is estimated using the procedure described by Leith [1975]. The statistical significance of the full 340 year CMS:340 output is analyzed differently. In this case fifteen 8000 day (∼22 year) composites are calculated for each variable. The standard deviation in equation (1) is determined from the variability of these 15 means; N is15. In all cases absolute values of t greater than 2 are judged to be statistically different than zero at approximately the 95% significance level.

[11] As an index of CMCC-CMS agreement with the ERA-40 reanalysis or the GPCP observations we have followed Sato et al. [2009], who employ the skill score of Taylor [2001]. This score S is defined as

display math

where R is the spatial correlation between model and observed or reanalysis composite fields and σr is the ratio of the standard deviation over the domain of the model relative to that of reanalysis or observations.

3. Results

[12] Prior to examining the traits of the MJO in CMCC-CMS, we discuss a few basic aspects of the climatology of the model stratosphere. Figure 1 shows the zonal mean temperature, zonal wind, and meridional wind for January in the last 20 years of model output and the ERA-40 reanalysis. Although the profiles are very similar, the tropical temperatures of the model are up to about 5°C lower and the model subtropical jets are a few degrees closer to the equator than in the analysis. The departures of the January mean 100 hPa temperatures and velocities from the January zonal means in Figure 1 are illustrated in Figure 2. Outside the high latitudes of the Southern Hemisphere the patterns are very similar. For instance, all of the major cyclonic and anticyclonic centers in the model have very similar locations and magnitudes to those in the reanalysis. The primary disagreement in temperature is in the higher latitudes of the Northern Hemisphere, where the model east-west differences are too weak by ∼2 K. One of the important features of this stratosphere-resolving model is that it reproduces a realistic QBO. Figure 3 shows downward propagation from the mesosphere of the mean zonal wind averaged between 5°N and 5°S, yielding very realistic QBO variations in the stratosphere. The mean period of the model's QBO is about 24 months, compared with about 28 months for observations [Baldwin et al., 2001].

Figure 1.

January mean 100 hPa temperature (green; K-195), u (black; m−s), and v (red; m−s × 10); CMS:20 (heavy) and ERA-40 (light).

Figure 2.

January mean 100 hPa temperature (K) and velocity streamline departures from the zonal means in Figure 1 for (a) CMS:20 and (b) ERA-40.

Figure 3.

Zonally averaged 5°S–5°N CMCC-CMS zonal wind speed (ms−1) for 10 arbitrarily chosen model years.

[13] In order to give a general assessment of the quality of the primary MJO signal in the CMCC-CMS model, MJO composite results for CMS:20, GPCP, and ERA-40 total precipitation are illustrated in Figure 4. The zero-lag composite precipitation patterns (Figures 4a–4c) are similar to those of analyses of estimated precipitation by Sato et al. [2009, Figure 1] and observed outgoing longwave radiation (OLR) for Northern Hemisphere summers, as illustrated by Sperber and Annamalai [2008, Figures 5c and 5d]. The primary difference is that the current results have large anomalies south as well as north of the equator. Significant signals in the observations in the western Pacific occur around 5°N and 5°S of the equator. The standard deviations of the MJO composite means averaged over the area shown in Figures 4a–4c are nearly equal, being about 0.56 mm/day for the model, 0.58 mm/day for the GPCP, and 0.57 mm/day for ERA-40. The Taylor skill score S for this domain is 0.78 using either GPCP or ERA-40 as the reference. This is nearly identical to that for a somewhat different domain for the 19 layer INGV-SXG model, which is a predecessor of the CMCC-CMS and has one of the highest scores in the model comparison by Sato et al. [2009].

Figure 4.

MJO mean precipitation (mm/day). Zero-lag maps: (a) GPCP, (b) CMS:20, and (c) ERA-40; 5°N lags, −25:25 days, Hovmöller diagrams (d) GPCP, (e) CMS:20, and (f) ERA-40. Heavy lines in Figures 4d–4f represent propagation speeds of 7 m s–1. Only composites with t values greater than 1 are plotted; regions significant at the 95% level are enclosed in the black contours. The green rectangle in Figure 4a shows the area of the composting center.

Figure 5.

MJO mean temperature (K) and stream function for the composite departures based on the Indian Ocean region for the 200 hPa level for (a) CMS:340, (b) CMS:20, and (c) ERA-40. The green A and C define the centers of anticyclonic and cyclonic flows, respectively. The violet rectangles show the regions of the mean wind used to make the composites. For the CMS:340 analysis, only composites that are significant at 95% are plotted. For the other two analyses, only temperature composites with t values greater than 1 are plotted; regions significant at the 95% level are enclosed in the green contours. Gray areas on all three plots show areas in which the CMS:340 flow composites are not significant at the 95% level.

[14] Figures 4d–4f show time longitude plots of MJO composite precipitation at 5°N for lags between 25 days preceding the easterly maxima to 25 days following. These are comparable to the OLR plots of Kim et al. [2009, Figure 9], Sperber and Annamalai [2008, Figure 6], and Lin et al. [2006, Figure 11]. Unlike many of the models described in those papers, the CMS:20 results indicate a slow eastward propagation of both positive and negative precipitation anomalies across the Indian and western Pacific oceans. From 60°E to 120°E, the propagation speed of the model, the GPCP observations, and ERA-40 are all about 4 m s–1. Farther to the east, precipitation shows faster propagation, such that the speed for the entire domain is near 7 m s–1. Lin et al. [2006] estimate a comparable propagation speed for the satellite precipitation observations and the most realistic of the 14 models that they analyzed. Overall, the MJO composite precipitation of the CMCC-CMS appears to replicate the tropical MJO signal as well as most, if not all, of the models described in the earlier model comparison papers.

Figure 6.

MJO mean temperature (K) and stream function for the composite departures based on the Indian Ocean region for the 100 hPa level for (a) CMS:340, (b) CMS:20, and (c) ERA-40. Other notation is the same as that in Figure 5.

[15] Figures 5 and 6 illustrate zero-lag Indian MJO composite mean departures of T and stream function, based on the u and v composite means, for 100 and 200 hPa for the CMS:340 and CMS:20 output and the ERA-40 reanalysis. Overall, broad areas of significant and coherent MJO departures are observed for both sets of model output and reanalysis for both levels. The maximum amplitudes of the ERA-40 and CMS:20 composites are very comparable; those of the CMS:340 output are slightly smaller. Furthermore, there is a great deal of similarity between the patterns developed by the model and reanalysis. For instance the identified cyclones (C) and anticyclones (A) are in very similar locations in all three analyses. It should also be noted that the regions in which the velocity composites in the CMS:340 are not significant at the 95% levels are often in the regions in which the ERA-40 and CMS:20 results differ substantially. Nevertheless, Table 1 shows that the CMS:20 MJO composites for the globe are generally in excellent agreement with observations in terms of the magnitude of the variability and the pattern of the anomalies. This leads to skill scores, which are greater than 0.84 for temperature and zonal wind at the 200 and 100 hPa levels. The scores for the region between 45°N and 45°S are between 0.02 and 0.05 higher (not shown).

Table 1. Statistics Contributing to Skill Scores S (Equation (2)) for Global CMS:20 MJO Composites (See Figures 5 and 6)

[16] Not surprisingly, at 200 hPa near the Indian reference region there is a strong easterly flow, which extends westward into the Atlantic region in all three composites. The easterly departures exceed 3 m s–1 near the composite centers. These equatorial easterlies are associated with a zone of significant negative temperature anomalies in CMCC:340 outputs and observations. North and south of the composite centers all three composites show warm anticyclonic anomalies with positive temperature departures of more than 1°C. To the east of these anticyclones are broad and cool cyclonic anomalies. The locations and amplitudes of these anomalies are very similar in both model composites and the observations. Poleward of about 45° the model outputs and observations differ considerably, even for regions that are judged to be significant at the 95% level for the 20 year analyses.

[17] The flow anomalies at 100 hPa are very similar to those at 200 hPa in the model and observations. The maximum easterlies are near the reference regions with magnitudes greater than 3 m s–1. Most strikingly, the temperature anomalies at 100 hPa are nearly the inverse of those at 200 hPa such that the pattern correlations between 100 and 200 hPa for temperatures between 45°N and 45°S are −0.54 for the observations and −0.59 for the CMS:20 output. At 100 hPa the anticyclones poleward of the composite centers are cold and the cyclones to the east are warm. The temperature amplitudes are about 1°C for both the model and observations. A similar temperature reversal was also observed for El Niño–Southern Oscillation (ENSO) composites of the ERA-40 analyses [Weare, 2009; Calvo Fernández et al., 2004].

[18] Figure 7 illustrates time longitude samples of 100 hPa temperature MJO departures at three latitudes for lags between −25 and +25 days for both the CMS:340 and CMS:20 output and ERA-40 reanalysis. At all three latitudes there is evidence of eastward propagation in both the two model runs and observations. The amplitudes of the anomalies in the CMS:340 are slightly smaller than those for CMS:20 or ERA-40 reanalysis. Figures 4d–4f and the equatorial results in Figure 7 show in both the model and reanalysis the strong coupling between precipitation and the upper troposphere that is a defining factor of the MJO [Zhang, 2005]. Along the equator the negative anomalies proceed across the Indian Ocean into the western Pacific at a propagation speed of around 5 m s–1 in the CMS:340 output and observations; that of CMS:20 is slightly slower. This speed is slightly slower than the 5–7 m s–1 for the precipitation anomalies, shown in Figure 4. At 25°N the propagation speed is also around 5 m s–1 for both model analyses and somewhat faster for the ERA-40 reanalysis. At 65°N all three analyses suggest eastward propagation speeds of about 5 m s–1. However, the phases differ considerably in the three analyses. Thus, Figure 7 shows that there is strong evidence that eastward propagating MJO signals in the tropical troposphere are associated with similar propagation in the lower stratosphere and at higher latitudes.

Figure 7.

Sample MJO longitude-time mean temperature (K) composite departures for lags from 25 days before to 25 days after the peak days based on the Indian Ocean region at the 100 hPa level for (a) CMS:340, (b) CMS:20, and (c) ERA-40. Heavy lines identify propagation speeds of approximately 5 m s–1. Only temperature composites with t values greater than 1 are plotted; regions significant at the 95% level are enclosed in the black contours.

[19] Figure 8 shows sample longitude-height and latitude-height cross sections for the zero-lag composites of T, u, and v from the CMS:20 and reanalysis for 25°N and 80°E. In the longitude-height cross sections at 25°N (Figure 8a) there is good agreement between the model and analysis temperature and meridional velocity composites between 200 and about 50 hPa, which runs eastward from the prime meridian to about 120°W. The zonal wind composites for both the model and reanalysis composites suggest significant MJO signals up to about 10 hPa. However, the phases differ considerably. Similar profiles at 30°N and 35°N (not shown) suggest that the phase differences are not directly related to the slight error in the model jet in this region (Figure 1). Nevertheless, these anomalies have a distinct westward tilt that may be associated with Rossby waves [Lindzen, 1967]. The u composites suggest propagation across the Pacific associated with such waves up to nearly the 10 hPa level in both model and reanalysis.

Figure 8.

(a) Height-longitude composites at 25°N and (b) height-latitude composites at 80°E of temperature, zonal wind, and meridional wind for the CMS-20 output and ERA-40 reanalysis. The green lines in Figure 8a identify the tilt consistent with upward propagating Rossby waves. The t values greater than 1 are plotted; regions significant at the 95% level are enclosed in the contours.

[20] For the latitude-height composites at 80°E (Figure 8b) there is broad agreement between the model and observations below about 50 hPa in the tropics. There is also clear evidence in the ERA-40 reanalysis of a propagation of an MJO signal deep into the stratosphere for both temperature and meridional wind near 25°N and 25°S of the equator. The model results suggest propagation up to only about the 50 hPa level at these latitudes. Both the model output and the reanalysis imply vertical propagation of meridional wind perturbations near the equator to near the top of the domain analyzed. These plots and those for other latitudes and longitudes (not shown) suggest that there are preferred locations for the strong vertical propagation associated with the MJO.

4. Conclusions and Discussion

[21] MJO composites of winds and temperature in the upper troposphere and stratosphere in the CMCC-CMS coupled ocean-atmosphere climate model are compared to those derived from the ERA-40 reanalysis. The CMCC-CMS climate model has a well-resolved stratosphere with high atmospheric vertical resolution and a good representation of the stratospheric mean state and variability. Thus, CMCC-CMS is well suited for studying the stratosphere-troposphere two-way coupling involving dynamical links between the stratospheric circulation and the tropospheric circulation, including vertically propagating tropical waves.

[22] The model MJO composites of precipitation are very similar to those of the composite station-satellite observations and reanalysis and are consistent with previously published MJO precipitation and OLR analyses. At 200 hPa the MJO departures for both the model and reanalysis show easterlies and cool anomalies in the equatorial regions of the compositing center, nearly symmetric warm anticyclonic zones at 25° poleward of those centers, and cold cyclonic regions to the east of the anticyclonic sites. At 100 hPa there is a near reversal of the temperature anomalies in the subtropics. Longitude-height and latitude-height cross sections suggest vertical propagation from the troposphere well into the stratosphere in parts of the tropics and subtropics. At 25°N the longitude-height westward tilt is consistent with wave-one Rossby waves in both the model output and reanalysis.

[23] One of the most interesting aspects of these results is the dramatic reversal in temperature anomalies between the 200 and 100 hPa levels in the subtropics of the Eastern Hemisphere, shown in Figures 5, 6, and 8. The simple model by Gill [1980] helps to explain this feature. In this model, positive precipitation anomalies in the broad region straddling the equator near 100°E (Figures 4a–4c) lead to low-level convergence and upward motion centered about the equator. The low-level flow is associated with divergent anticyclonic flows at upper levels, as is seen in Figures 5 and 6. The rising air in this broad region is superimposed on a mean vertical structure in which the tropopause is between 200 and 100 hPa. Near 200 hPa, latent heat release associated with the precipitation more than offsets the adiabatic cooling of the rising air, leading to a warm perturbation. Above the tropopause at 100 hPa, adiabatic cooling with latent heating leads to a cold perturbation.

[24] The localized interactions away from the equator, illustrated in Figure 8, are qualitatively consistent with the linear theory for vertical propagation in complex three-dimensional background fields recently developed on a beta plane and demonstrated with idealized flows [Nathan and Hodyss, 2010]. This theory shows that vertical propagation is possible over limited longitudes even where the classical theory of Charney and Drazin [1961] precludes propagation in zonally averaged flows. This theory also indicates that vertical propagation is sensitively related to details in the background potential vorticity gradient. Unfortunately, the current theory, based on the beta-plane approximation, is not directly relatable to observations. Nevertheless, these results suggest that the lower stratosphere may play a role in some important higher-latitude teleconnections in a way suggested by the transmission of ENSO signals to high latitudes [Ineson and Scaife, 2009; Manzini, 2009].


[25] ERA-40 data were provided by the European Centre for Medium-Range Weather Forecasting from their web site at The GPCP data were available at This work was partially supported by NSF grant ATM0733698. The first author received partial support from CMCC under the PISAC program, which was funded by the Bank Foundation CARISBO of Bologna, Italy. This research was also funded in part by the European Commission's 7th Framework Programme COMBINE project 226520.