1. Introduction
The Madden–Julian oscillation (MJO) is the most prominent mode in the tropics on intraseasonal time scales. It is featured by an eastward propagation along the equator at a phase speed of around 5 m s−1 and a planetary-scale convection–circulation coupled structure (e.g., Madden and Julian 1972; Kiladis et al. 2005; Li and Zhou 2009). The characterized circulation pattern associated with the MJO is a Rossby wave–Kelvin wave (R-K) coupled structure that is similar to the solution of Gill’s model (Gill 1980): to the east of the MJO convection, an easterly (westerly) anomaly is seen near the equator in the lower (upper) troposphere; and to the west of the MJO convection, a westerly (easterly) anomaly is near the equator and a pair of cyclonic (anticyclonic) gyres is off the equator in the lower (upper) troposphere (e.g., Hendon and Salby 1994). Although this observed circulation pattern has been known for many years, what role it plays in the eastward propagation of the MJO is under debate so far (see Li 2014 for a review).
Historically, many MJO theories have considered the MJO as a moist Kelvin-like wave mode, and it propagates slowly eastward with the presence of interactions with diabatic heating and boundary layer processes (e.g., Wang 1988). More recently, a theory in which the MJO is regarded as a moisture mode has emerged, and the MJO convection anomaly is assumed to follow the anomalous column-integrated moist static energy (MSE) under the weak temperature gradient (WTG) approximation (e.g., Maloney 2010; Hsu and Li 2012; Sobel and Maloney 2013; Hsu et al. 2014; Li and Hsu 2018).
How the Rossby wave component of the MJO flow affects the MJO eastward propagation is an open question. One school of thought proposed that the slow eastward propagation of the MJO is a consequence of a balance between fast eastward-moving Kelvin waves and slower westward-moving Rossby waves to a large extent (e.g., Kang et al. 2013; Wang and Chen 2017). From this view, the Rossby wave component hinders the eastward propagation of the MJO (hereinafter referred to as “drag effect”). By contrast, the other school of thought argued that the east–west asymmetry of column MSE tendency is essential to the eastward propagation of the MJO and the Rossby wave component acts to enhance the zonal asymmetry of the horizontal MSE advection (e.g., Sobel et al. 2014; Wang et al. 2017). Thus, from the MSE point of view a stronger Rossby wave component is in favor of the eastward propagation of the MJO (hereinafter referred to as “acceleration effect”).
The present study was partially motivated by idealized aquaplanet experiments of Kang et al. (2013, hereinafter K13), who found that the MJO eastward propagation speed is slower in a “broad SST experiment” than a “narrow SST experiment.” The former one has a smaller near-equator curvature than the latter one. Without a detailed diagnosis of the model outputs, K13 argued that the broad SST experiment would produce a stronger Rossby wave component because a larger off-equatorial SST would favor a stronger Rossby wave development. But, as discussed in section 3, such an argument is incorrect. Furthermore, the change in the meridional SST distribution may not only modify the Rossby and Kelvin wave component but also the background mean state. Therefore, the change in the eastward propagation is possibly attributed to other factors. In fact, the broad SST experiment reproduced by this study simulates a mean moisture field that peaks at off-equatorial regions in both the Northern and the Southern Hemisphere that is different from the observed winter mean moisture field over the warm ocean that peaks approximately at the equator. The reversed meridional gradient of the mean moisture near the equator would lead to different MSE advection effects for the Rossby wave component, as further elaborated in section 3.
This work was also motivated by recent studies of Wang and Chen (2017) and Wang and Lee (2017), who found that the eastward propagation speeds of the MJO modes are inversely related to a ratio between the Rossby wave and the Kelvin wave strength in a theoretical model with two cumulus parameterizations and simulations from 24 general circulation models (GCMs). They noted that a greater ratio is associated with slower eastward propagation. This prompted them to support the Rossby wave drag effect. But as we know, the change in the ratio cannot be simply interpreted as an indicator of change in the Rossby wave intensity because the Kelvin wave component also changes. Moreover, Wang et al. (2017) pointed out that vertically integrated horizontal MSE advection is primarily determined by circulation in the lower troposphere around 700 hPa. This motivates us to further explore relationships between the simulated eastward propagation and the Rossby and Kelvin wave components at different vertical levels.
In the present study, we first reexamine aquaplanet experiments with an in-depth diagnosis. Then we further diagnose simulations from 26 models that participated in the MJO Task Force/GEWEX Atmospheric System Studies (MJOTF/GASS) project (Jiang et al. 2015). We strive to reveal a more robust relationship between the simulated eastward propagation features and the strength of Rossby wave component by analyzing both the aquaplanet and multimodel simulations. We will also pay attention to the changes in the strength of the Kelvin wave component and the basic state.
Note that in the standard solution of the Gill model, Kelvin wave response is purely zonal, without a meridional wind component. This is because in this simplified framework, Kelvin wave is only a response to a given stationary heating, and there is no interactive heating allowed. When considering circulation induced heating, say, in a full-physics atmospheric general circulation model (AGCM), one may expect the occurrence of a negative heating anomaly at the equator to the east of the specified heating center that is a result of Kelvin wave–induced low-level (upper level) zonal wind divergence (convergence). The negative heating anomaly favors low-level anomalous anticyclonic flow with a poleward component to the east of the MJO convective center. Therefore, the observed anomalous anticyclonic gyres at low levels to the east of MJO convection are fundamentally caused by Kelvin wave response, an extended version of the Gill solution, when an interactive heating is considered. To the first order of approximation, throughout the paper we regard the circulation anomalies to the east of the MJO center as a Kelvin wave component.
The rest of the paper is organized as follows. Section 2 describes the designs of the aquaplanet experiments and the multimodel datasets used in current study. Section 3 examines the relationship between the MJO eastward propagation and the Rossby and the Kelvin wave components in a set of aquaplanet experiments. Section 4 diagnoses the correlation relationship between the MJO eastward propagation skill and the Rossby and the Kelvin wave intensities among 26 state-of-art GCMs. Section 5 discusses the propagation characteristics of aquaplanet MJOs. Section 6 gives concluding remarks of this study.
2. Experiments and datasets
a. Aquaplanet experimental design
The model used in the aquaplanet experiments is a full-physics atmospheric GCM—ECHAM, version 4.6 (Roeckner et al. 1996)—at a horizontal resolution of spectral T42 with 19 vertical levels extending from the surface to 10 hPa. This AGCM is among one of the best models in simulating the MJO properties (Lin et al. 2006) and was previously used to study the northward propagation of the intraseasonal oscillation (ISO; Jiang et al. 2004) and real-case MJO prediction (Fu and Wang 2009).
Meridional profiles of SST forcing (°C) used in the aquaplanet experiments of KS (red), WS (green), and NS (blue).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
b. Multimodel climate simulations and observational data
The multimodel dataset used in this study is from the climate simulation component of the MJOTF/GASS MJO global model comparison project (Jiang et al. 2015); they are the same data analyzed in Wang and Lee (2017). We analyze 26 simulations from the dataset (see Table 1 for details of the models). All of the participating models were integrated for 20 years, either with atmosphere–ocean coupling or forced by the weekly SST and sea ice concentrations based on the NOAA Optimum Interpolation SST, version 2, product (Reynolds et al. 2002) during 1991–2010. All datasets are archived using daily means and horizontal resolution of 2.5°×2.5°.
List of 26 GCMs from the MJOTF/GASS project. [Acronym expansions are available online at http://www.ametsoc.org/PubsAcronymList, and also see Table 1 in Wang et al. (2017).]
The observational data used in this study includes the daily precipitation data from 1° daily (1DD) Global Precipitation Climatology Project (GPCP; Huffman et al. 2001) dataset, version 1.1, and daily three-dimensional data from European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011) from 1997 to 2010. Both datasets are archived using horizontal resolution of 2.5°×2.5°.
3. Relationship between MJO eastward propagation and the Rossby–Kelvin wave intensity in aquaplanet simulations
a. Eastward propagation characteristics
We first compare the dominant eastward-propagating mode simulated in each experiment. Figure 2 shows the zonal wavenumber–frequency spectra of 850-hPa zonal wind and precipitation merged data, averaged over 10°S–10°N. Each variable has been removed of climatology and normalized by its zonal-mean magnitude before merging. As one can see, all three runs simulate a dominant eastward-propagating mode of planetary zonal scale (zonal wavenumbers 1–3). The maximum spectral power in the KS run appears within the periods of 30–80 days, and that in the WS run occurs within the periods of 20–30 days. The NS run produces two spectral centers; one is at the wavenumber 1 and the period of 20 days and the other is at the wavenumber 2 and the period of 15 days.
Zonal wavenumber–frequency power spectrum of 850-hPa zonal wind and precipitation merged data averaged over 10°S–10°N from (a) KS, (b) WS, and (c) NS.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Then, we extract the dominant wave mode from each simulation. First, daily precipitation fields are filtered onto east wavenumbers 1–3 and period of 18–80 days with a space–time filter (Wheeler and Kiladis 1999). The period range is chosen to cover the maximum spectral powers on intraseasonal time scale in all cases. The following results based on the filtered precipitation would not change if we modified the filter domain to east wavenumbers 1–3 and period of 20–80 days (figures not shown). Second, a reference time series is obtained by averaging the filtered precipitation anomaly over a small box over the equator (5°S–5°N, 160°–170°E). Note that longitudinal variations of the reference box would not affect the results since the boundary forcing is zonally symmetric. Third, all unfiltered daily fields are regressed onto the precipitation index that has been normalized to 3 mm day−1. The regressed fields are used as composite results.
Figure 3 displays lagged time–longitude plots of regressed precipitation and 850-hPa zonal wind anomaly averaged over 10°S–10°N from day −20 to day +20 for the aquaplanet simulations. Day 0 is when the precipitation anomaly center is at 5°S–5°N, 160°–170°E. All three runs display a significant eastward propagation of precipitation and low-level wind, with easterly anomaly leading the positive rainfall anomaly at quadrature phase. Then we estimated the eastward propagation phase speed of different variables based on their lagged time–longitude diagram. Taking the precipitation anomaly, for instance, we first obtained daily tracking of longitude of maximum rainfall anomaly from day −10 to day +10, and then calculated the regression line of the tracking (see green lines in Fig. 2). The slope of the regression line corresponds to the phase speed. Table 2 presents the estimated phase speeds of precipitation, OLR, and 850-hPa zonal wind anomaly (u850) for the three runs. The averaged speeds of the eastward propagation variables in KS, WS, and NS are 8, 11, and 14 m s−1, respectively. It suggests that a wider meridional SST-forced experiment tends to simulate a slower eastward-propagating mode than a narrower meridional SST-forced experiment does. This is consistent with the finding from K13.
Longitude–time evolution of rainfall anomalies (shaded; mm day−1) and 850-hPa zonal wind (contour with an interval of 4 m s−1, zero contour omitted, negative contours dashed) averaged over 10°S–10°N by lag regression against a reference rainfall time series over 5°S–5°N, 160°–170°E for (a) KS, (b) WS, and (c) NS. The reference time series is obtained by filtered precipitation anomaly onto east wavenumbers 1–3 and frequency domain corresponding to period of 18–80 days. The slope of the green dashed line in each panel corresponds to the estimated phase speed of the positive rainfall anomaly.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Estimated phase speed (m s−1) of the intraseasonal eastward-propagating mode represented by the precipitation, OLR, and u850 for KS, WS, and NS experiments.
b. Basic-state characteristics simulated in aquaplanet experiments
The basic state in the experiments is summarized in Fig. 4. The NS and WS runs exhibit an equator-peak structure of precipitation (or moisture), associated with low-level convergence at the equator induced by equatorward meridional wind in the Northern Hemisphere and Southern Hemisphere. In contrast, the precipitation (or moisture) in KS peaks off the equator, near 12°S and 12°N, consistent with the meridional wind converging in both hemispheres. It is clear that the mean precipitation (or moisture) magnitude at the equator is greatest in NS and lowest in KS. All three runs simulate an easterly wind at low levels in the tropics, with the strongest wind in NS and the weakest wind in KS. The pattern of intraseasonal precipitation anomaly amplitude in the experiments (Fig. 5) looks very similar to the pattern of mean precipitation (or moisture); the intraseasonal rainfall anomaly at the equator is greatest in NS and weakest in KS. The result is understandable, because a large mean precipitation area is usually associated with strong ascending motion, and the latter would induce abundant mean moisture in the column through vertical advection. Given a perturbation of convergence on the intraseasonal time scale, the moisture-convergence anomaly tends to be stronger in the region where the mean moisture is more abundant, and thus generating larger intraseasonal precipitation anomaly.
Time-mean zonal-mean (a) precipitation, (b) 1000–700-hPa-averaged specific humidity, (c) meridional wind, and (d) zonal wind for KS (red), WS (green), and NS (blue).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Zonal-averaged standard deviation of 20–100-day-filtered precipitation anomaly for KS (red), WS (green), and NS (blue).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
It is interesting to note from Fig. 4 that the basic state of KS is dramatically different from those of WS and NS with only a little change in the SST forcing profiles. Actually, Neale and Hoskins (2000) have pointed out that the mean states in aquaplanet simulations are very sensitive to the SST forcing profiles; the split of moisture (or precipitation) maximum tends to occur with small near-equator SST gradient while a single maximum in moisture (or precipitation) on the equator tends to occur with large SST gradient. The meridional distribution of mean moisture fields suggest that the Rossby wave component would result in a negative meridional MSE advection west of the MJO convection in the NS and WS runs but a positive meridional MSE advection in the KS run. The latter is unrealistic compared to the observed MSE tendency (e.g., Wang et al. 2017). Given the unrealistic mean state and the horizontal MSE advection in KS, in the following we only focus on the diagnosis of the Rossby and Kelvin wave components and their roles in the eastward propagation in WS and NS.
c. Comparisons of Rossby and Kelvin wave intensities
Figure 6 presents the horizontal patterns of regressed day-0 700-hPa wind anomaly for WS and NS. Both experiments simulate a clear Rossby–Kelvin wave coupled structure. The Kelvin wave component is associated with strong easterly anomaly at the equator and poleward meridional wind anomaly off the equator (Zhang and Ling 2012; Kim et al. 2014; Wang et al. 2018). The Rossby wave component is associated with a strong westerly anomaly at the equator and equatorward meridional wind anomaly converging at the equator. As the simulated mean moisture for the two runs maximizes at the equator, the Rossby–Kelvin wave structure would generate a positive meridional MSE advective tendency to the east and a negative meridional MSE advective tendency to the west.
Horizontal patterns of regressed day-0 700-hPa wind anomalies (vectors; m s−1), meridional wind component (shaded; m s−1), and rainfall anomalies (contours with an interval of 0.5 mm day−1, zero contour omitted, and negative contours dashed) for (a) WS and (b) NS. The rectangles in (a) mark the region for defining the Rossby wave index (10°S–10°N, 80°–150°E) and the region for defining the Kelvin wave index (10°S–10°N, 150°W–30°W), respectively.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Next, we define various strength indices of the Rossby (Kelvin) wave component by 700-hPa zonal wind anomaly, meridional wind anomaly and vorticity anomaly over a rectangular region located west (east) of the simulated MJO’s rainfall maximum bounded by 10°S−10°N, 80°−150°E (10°S−10°N, 150°−30°W). The two domains are selected since they cover the major part of the Rossby wave and the Kelvin wave circulations (see boxes in Fig. 6a). The zonal wind index is calculated by its average over 5°S–5°N. Since the meridional wind/vorticity anomalies are opposite to the north of the equator and to the south of the equator, the meridional wind/vorticity index is defined by its difference between the 0°–10°N average and the 10°S–0° average. Note that an absolute sign is added to each index so that we only consider the amplitude of the Rossby or Kelvin wave component. Table 3 displays the ratio of each index in the NS run to the WS run. The ratios for all indices are greater than 1, indicating that NS has a stronger Rossby wave component and a stronger Kelvin wave component than WS. The occurrence of a stronger Rossby wave component in the presence of a narrower meridional SST is against the argument suggested by K13.
Ratio of the Rossby and Kelvin wave strength in the NS run to the WS run.
It is worth mentioning that the Rossby (Kelvin) wave strength calculated above can be only referred to as “relative strength,” because before the calculation all fields were regressed onto a fixed 3 mm day−1 rainfall anomaly. By doing so, one may better compare MJO-related circulation patterns among different simulations. In the following, we compare “absolute strength” of the Rossby (Kelvin) wave component, which can be inferred from Fig. 5. As the NS run exhibits the strongest intraseasonal precipitation amplitude at the equator in the three runs (see blue line in Fig. 5), it also simulates the strongest Rossby (Kelvin) wave component. Furthermore, the absolute strength of the Rossby wave component in the KS run is the weakest among the three runs (figure not shown). The results indicate that a wider (narrower) meridional SST distribution experiment tends to simulate a weaker (stronger) Rossby wave component and a slower (faster) eastward propagation speed.
d. Comparisons of horizontal MSE advection
Figures 7a and 7b show horizontal distributions of column-integrated MSE tendency at day 0 for NS and WS. As expected, positive (negative) MSE tendency anomaly is seen to the east (west) of the rainfall center. Figure 7c displays the difference of MSE tendency between the two runs over the east box and the west box, respectively. Apparently, larger zonal asymmetry in the column MSE tendency is seen in NS, consistent with that NS simulates a faster and stronger eastward propagation. Then we examined the column-integrated horizontal advection of MSE (Figs. 7d–f). As shown in Fig. 7f, the zonal asymmetry of horizontal MSE advection is enhanced in NS relative to WS. As the zonal advection component is near zero (figure not shown), the horizontal advection is dominated by the meridional advection component. The MSE budget diagnosis confirms that a stronger Rossby wave component and a stronger Kelvin wave component in NS indeed increase the zonal asymmetry of MSE tendency that is in favor of eastward propagation. This supports the Rossby wave acceleration effect.
Horizontal patterns of column-integrated (a),(b) MSE tendency (W m−2) and (d),(e) horizontal MSE advection (W m−2) at day 0. (c) The difference of the column-integrated MSE tendency between NS and WS over the east box (10°S–10°N, 150°W–30°W) and the west box (10°S–10°N, 80°–150°E). (f) As in (c), but for horizontal MSE advective tendency. The rectangles are the same as in Fig. 6a.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
It is worth mentioning that the enhanced meridional MSE advection in NS relative to WS is also contributed by the increase in meridional gradient of mean moisture, as shown in Fig. 4. The difference between Figs. 7c and 7e suggests that the other MSE tendency terms, such as vertical MSE advection, may also play a role in the MSE tendency change, and this will be discussed in section 5.
4. Relationship between MJO eastward propagation and the Rossby–Kelvin wave intensity in 26 climate models
a. Relative role of the Rossby and Kelvin wave component
Wang and Lee (2017) revealed a significant relationship between the simulated MJO eastward propagation and the ratio of Rossby wave strength to Kelvin wave strength (R/K) in multimodel simulations. Does a greater R/K represent a stronger Rossby wave component in these models? Here we intend to address this question. Furthermore, Wang and Lee (2017) only discussed the relationship at the 850-hPa level. It is desirable to reveal the relationships between the eastward propagation and individual Rossby or Kelvin wave components at different vertical levels.
Following Wang and Lee (2017), the MJO propagation is measured by lagged time–longitude variations of intraseasonal precipitation anomalies during the boreal winter season (November–April) with respect to two reference locations, the eastern Indian Ocean (EIO; 5°S–5°N, 75°–85°E) and western Pacific (WP; 5°S–5°N, 130°–150°E). For each reference location, we calculated lead–lag regression patterns of precipitation against the reference time series, which is 20–100-day-filtered (Duchon 1979) precipitation anomaly averaged over the reference box. For each simulation, the magnitude of a regression field is determined by one standard deviation of the reference time series of precipitation.
Figures 8a and 8b display the lagged time–longitude diagrams with reference to the EIO and WP for observation and simulations. For brevity, the model simulations are shown only for the two best and two worst models. The skill scores are calculated based on the pattern correlation coefficients (PCC) (50°E–180°, from day −20 to day 20) between each model and the observations. Different from the conventional PCC skill scores, we remove the subregions at the reference center (70°–90°E and 130°–150°E) in the calculation (marked by rectangles). This is because even poor models can simulate standing oscillations at the reference center that contaminate the eastward propagation skill score (Wang et al. 2017). The bars in Fig. 8c display the PCC skill scores of each model averaged for the two key reference regions. The averaged score is highly correlated with that obtained from conventional PCC skill (i.e., Jiang et al. 2015) [correlation coefficient (CC) = 0.91], but presents a greater contrast in the good and the poor models. Furthermore, it is highly correlated with that measured at EIO (CC = 0.97) and with that measured at WP (CC = 0.86). Overall, higher-averaged PCC skill corresponds to more systematic eastward propagation of both the wet and dry anomalies and better propagation speeds over the equatorial Indo-Pacific warm pool regions. Hereafter, the averaged PCC skill score is referred to as the overall MJO PCC skill.
Eastward propagation of MJO in observations and model simulations as shown by the lead–lag regression of 20–100-day bandpass-filtered precipitation averaged over 10°S–10°N with reference to itself over the (a) EIO (5°S–5°N, 75°–85°E) and (b) WP (5°S–5°N, 130°–150°E), during boreal winter (November–April). The dashed lines mark the domain of 70°–90°E, from day −20 to day 20, for the EIO reference, and the domain of 130°–150°E, from day −20 to day 20, for the WP reference. (c) The bars represent the overall MJO PCC skill and the line denotes the overall MJO speed skill.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Then, we calculate the correlation coefficients of the MJO PCC skill with R/K, as well as the intensity of the individual Rossby (Kelvin) wave component by using all the 26 GCMs (see Fig. 9). Following Wang and Lee (2017), the Rossby (Kelvin) wave intensity is estimated by equatorial (5°S–5°N) maximum westerly (minimum easterly) speed. Here, the wind speed is obtained basing on day-0 regressed wind anomaly with respect to the EIO index. Note that an absolute sign is added to each index so that a positive correlation for the Rossby (Kelvin) wave index indicates a positive relationship between the MJO eastward propagation and the Rossby (Kelvin) wave strength. As shown in Fig. 9, the correlations for R/K (black line) are significantly negative at nearly all levels, consistent with Wang and Lee (2017). However, it is interesting to note that the correlations for the Rossby wave index (red line) are statistically insignificant at 850 hPa and below, indicating that the significant relationship revealed by Wang and Lee (2017) is attributed to the Kelvin wave component (blue line) rather than the Rossby wave component. Furthermore, a significant positive correlation for the Rossby wave index appears in the lower free atmosphere (between 600 and 700 hPa), suggesting that a stronger Rossby wave component at these levels favors a better eastward propagation.
Correlation coefficients of MJO PCC skill with Rossby wave strength (i.e., equatorial westerly maximum; red) and with Kelvin wave strength (i.e., equatorial easterly maximum; blue) and with R/K (black). The black dashed lines denote the 95% confidence level for the correlation coefficients (i.e., ±0.39).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
One may wonder how sensitive the result above is to the Rossby and Kelvin wave intensity definition. To check the result sensitivity, we introduce various strength indices in the following. Figures 10a and 10b display horizontal patterns of regressed wind anomaly at 700 hPa composite for six best models (good models) and six poorest models (poor models) selected according to the PCC skill, respectively. The good (poor) models are CNRM-CM, ECHAM5-SIT, GISS_ModelE, SPCAM3_AMIP, SPCCSM, and TAMU_CAM4 (CanCM4, CFSv2AMIP, CWBGFS, MIROC5, NavGEM01, and UCSD_CAM3). Both groups display a Rossby–Kelvin wave couplet pattern. But the good model group shows a stronger Rossby wave component and a Kelvin wave component as well than the poor model group, as seen from the meridional wind anomalies (shaded), which is consistent with Fig. 9.
Horizontal patterns of regressed 700-hPa wind anomalies (vectors; m s−1) and the associated meridional wind component (shaded; m s−1) composited for the (a) good MJO models and (b) poor MJO models. The rectangles in (a) mark the region for defining the Rossby wave indices (10°S–10°N, 40°–70°E) and the region for defining the Kelvin wave indices (10°S–10°N, 90°–160°E), respectively.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Based on the above circulation characteristics, the strength of Rossby (Kelvin) wave component may be measured by indices 1) area-averaged zonal wind anomaly (uwind), 2) north–south difference of meridional wind anomaly (vwind), and 3) north–south difference of vorticity anomaly over a west (east) box (see red boxes in Fig. 10). The definition of these indices is the same as used in section 3. An additional Rossby wave index is defined by the meridional wind anomaly average over 0°–10°N, 40°–70°E based on the argument by Wang et al. (2017) that the background MSE gradient is near zero south of the equator over the Indian Ocean so that anomalous meridional MSE advection vanishes. For all the indices above, an absolute sign is added so that we only consider the amplitude of the Rossby (Kelvin) wave component.
Figure 11a shows the correlation coefficients of each of the Rossby wave strength indices [i.e., indices (1–3) in the west box] with the PCC skill from 1000 to 500 hPa. The results are generally consistent with that based on the Rossby wave westerly index shown in Fig. 9 (red line). The correlation coefficients are insignificant below 800 hPa but become larger with height. Three of the four indices show significantly positive correlations above 800 hPa, indicating a positive relationship between the MJO eastward propagation and the Rossby wave strength.
(a) Correlation coefficients of MJO PCC skill with each of the Rossby wave indices, i.e., zonal wind index (green), meridional wind index (red solid), vorticity index (blue), and Northern Hemisphere meridional wind anomaly (red dashed). (b) Correlation coefficients of MJO PCC skill with each of the Kelvin wave indices, i.e., zonal wind index (green), meridional wind index (red), and vorticity index (blue). The black dashed lines denote the 95% confidence level for the correlation coefficients (i.e., ±0.39).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Figure 11b displays the correlations of each of the Kelvin wave indices [i.e., indices (1–3) in the east box] with the PCC skill from 1000 to 500 hPa. Interestingly, the indices all show significantly positive correlation coefficients above 800 hPa; but they become complicated below 800 hPa. In particular, the correlations even turn significantly negative for the meridional wind index (red line). Such an opposite relationship is attributed to the observational fact that there is pronounced poleward flow in the lower troposphere in response to a negative heating anomaly east of the MJO convection (Kim et al. 2014; Wang et al. 2017) while there is equatorward flow in the boundary layer resulting from boundary layer convergence in response to the Kelvin wave–induced low pressure anomaly east of the MJO convection.
In the correlation analysis above we use PCC skill, which is not necessarily related to the actual phase speed of simulated MJO in these models. A parallel calculation is done, as shown in Fig. 11, in which we replace the PCC skill with the MJO phase speed in each model. Below is the calculation procedure. First, we estimate the phase speed of simulated MJO with respect to two reference locations, EIO and WP. For each reference location, we calculate lead–lag correlation pattern of 20–100-day-filtered precipitation anomaly against itself averaged over the reference box. We obtain daily tracking of longitude of maximum correlation coefficient, which should be greater than 0.2, from day −10 to day +10 and calculate the regression line of the tracking. The phase speed at each reference location is represented by the slope of the regression line. Then, the average of the estimated phase speeds over the two reference locations is referred to as the overall MJO phase speed and is shown by line in Fig. 8c. The correlation coefficient between the overall MJO PCC skill and the overall MJO phase speed is 0.8.
Figures 12a and 12b present the correlations of each Rossby and Kelvin wave index with the phase speed from 1000 to 500 hPa, respectively. The results are very similar to those obtained based on the PCC skill. The correlation coefficients are significantly positive above 800 hPa for both the Rossby and the Kelvin wave indices, and they become complicated below. Therefore, the MJO propagation speed is positively related to both the Rossby wave component strength and the Kelvin wave component strength in the lower troposphere, which supports the Rossby wave acceleration effect hypothesis.
As in Fig. 11, but for correlation coefficients with MJO overall phase speed skill.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Given the positive correlation of Rossby and Kelvin wave strength with the MJO eastward phase speed or PCC skill, R/K is not proper to measure the propagation. A better index is either the sum of the strength of the Rossby wave and the Kelvin wave component (denoted as R+K) or the product of them (denoted as R*K). Figures 13a and 13b show the correlations between the speed skill and the R+K and R*K from 1000 to 500 hPa, respectively. The correlations for all the indices increase as expected and reach as large as 0.8, which is apparently larger than that obtained from R/K (black line in Fig. 9). The results obtained based on the PCC skill are generally the same (figure not shown).
Correlation coefficients of MJO phase speed with (a) R+K and (b) R*K. The Rossby and Kelvin wave strength is measured by zonal wind (black), meridional wind (red), vorticity (blue), or maximum westerly or easterly index (green). The black dashed lines denote the 95% confidence level for the correlation coefficients (i.e., ±0.39).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
It is worth mentioning that the Rossby (Kelvin) wave indices calculated above represent the absolute strength. A parallel calculation was done for the relative strength based on wind fields regressed onto a fixed 3 mm day−1 rainfall anomaly. The result is essentially same (figures not shown).
b. Horizontal MSE advections
Because the Rossby and Kelvin wave components mainly contribute to anomalous horizontal MSE advection, in this subsection we further examine the relationship between the MJO eastward propagation and the horizontal MSE advection. Figures 14a and 14b display the correlation coefficients between the PCC skill and the horizontal MSE advection anomaly (blue line) from 1000 to 500 hPa to the west and to the east of the MJO convection center, respectively. As expected, the PCC skill is significantly related to both positive MSE advection anomaly to the east and negative MSE advection anomaly to the west, especially in the lower troposphere. It suggests that enhanced zonal asymmetry of the horizontal MSE advection anomaly could contribute to the eastward propagation of the MJO.
(a) Correlation coefficients of MJO PCC skill and west-box- (10°S–10°N, 40°–70°E) averaged horizontal MSE advection (blue) and its zonal (green) and meridional component (red). (b) As in (a), but for the east box (10°S–10°N, 90°–160°E) average. The black dashed lines denote the 95% confidence level for the correlation coefficients (i.e., ±0.39).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Furthermore, the significant correlations primarily arise from the correlations for the meridional advection component (red line), while the correlations for the zonal advection component (green line) are near zero. This is consistent with the hypothesis that enhanced meridional wind anomalies associated with the intensified Rossby (Kelvin) wave component could lead to larger zonal asymmetry of horizontal MSE advection, and thus stronger and faster eastward propagation of MJO. The result is consistent with Wang et al. (2017), who conducted a detailed MSE budget analysis for the 26 GCMs and showed that the advection of mean MSE by MJO meridional wind anomaly is the primary contributing term to the horizontal MSE advection.
5. Discussion: What determines the eastward propagation speeds in the aquaplanet simulations?
In section 3, we revealed the role of the Rossby wave component on the eastward phase propagation of MJO through comparing the NS run and the WS run. An interesting question is, what causes the different propagation speeds in the three aquaplanet simulations? Here we intend to address this question through an MSE budget analysis using Eq. (4).
Figure 15 displays the horizontal patterns of column-integrated MSE tendencies in the three aquaplanet simulations. The result is essentially the same as Figs. 7d–f, except that the magnitude of regressed fields is not normalized to a 3 mm day−1 rainfall anomaly, rather regressed based on the precipitation anomaly at each run. All the three runs show a clear east–west asymmetry of MSE tendency, which agrees well with their eastward phase propagation characteristics.
Horizontal patterns of column-integrated MSE tendency (W m−2) for (a) KS, (b) WS, and (c) NS. The magnitude of regressed fields is determined by precipitation anomaly at each run, rather than a fixed 3 mm day−1 rainfall anomaly as shown in Figs. 7a,b. The east and west boxes are the same as in Fig. 6a.
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
Figure 16a displays the MSE budget results for the NS run. Each bar in Fig. 16a denotes the zonal difference of MSE budget between an east box average and a west box average (east minus west). Here the same east and west boxes are used for all the cases as shown in Fig. 7. A positive difference denotes that it favors the eastward phase propagation. As one can see, vertical MSE advection (Wadv), horizontal MSE advection (Hadv), and surface heat flux (Qt) all act to promote the eastward phase propagation, wherein the vertical advection term plays a leading role. The radiation term (Qr) acts to hinder the eastward phase propagation. The similar conclusion can be found in the WS and KS runs (figure not shown).
(a) Zonal asymmetry of each MSE budget quantity for the NS run, calculated by difference between the east box average and the west box average (east minus west). The gray bars from left to right represent column-integrated MSE tendency (dmdt), Wadv, Hadv, Qt, Qr, and sum of budget terms (sum). (b) MSE budget differences between NS and WS (NS minus WS) and (c) between WS and KS (WS minus KS).
Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0749.1
It is worth mentioning that the surface heat flux in the real world acts against the eastward propagation. In the aquaplanet, it acts oppositely because the mean wind is easterly in the tropics (Fig. 4d). By contrast, the mean wind is westerly in observations over the tropical Indian and western Pacific Oceans.
The difference in the MSE budget results between NS and WS (NS minus WS, Fig. 16b) shows that the NS run has a larger east–west asymmetry in the MSE tendency, agreeing with the simulation result that NS simulates a faster eastward phase speed than WS. As one can see, the difference in the MSE tendency is primarily attributed to the difference in the horizontal advection term, while the other three terms play a minor role.
What causes the difference in the horizontal advection term between NS and WS? The first factor is the mean moisture gradient. As revealed by section 3, differing horizontal advective tendencies between NS and WS result from different mean moisture meridional gradients. In response to a narrower meridional SST forcing (NS run), more mean moisture is produced at the equator (Fig. 4b). This results in a larger meridional gradient of mean moisture off the equator. The second factor is the perturbation strength. A greater mean moisture near the equator may strengthen the MJO heating, even though initial MJO perturbation strength is same. Figure 5 shows clearly that the MJO rainfall anomaly is greater in NS than in WS (and KS as well). The stronger MJO heating further causes a stronger meridional wind component in both east and west of the MJO convective center. Therefore, both the change in the mean moisture gradient and the MJO meridional wind strength contribute to the difference in the meridional MSE advection, which is a dominant term of the horizontal MSE advection.
Then, why does the WS run simulate a faster eastward propagation speed than the KS run? The comparison of the MSE east–west tendency between the two runs (WS minus KS, Fig. 16c) shows that WS has a larger east–west asymmetry of MSE tendency. It appears that the vertical MSE advection, the horizontal MSE advection, and the surface heat flux terms all contribute to the change in MSE tendency. The difference in the horizontal advection term is largely due to contrasting mean states in the two simulations, as discussed in section 3. In response to a wider meridional SST forcing (KS run), the mean moisture maximizes off the equator, which leads to a reversed meridional gradient of the mean moisture compared to the WS run (Fig. 4b). As a result, the meridional MSE advection contributes negatively to the MJO eastward phase propagation in KS, while it plays a positive role in WS. Previous studies have suggested that the vertical MSE advection term is dominated by advection of mean MSE profile by MJO vertical velocity perturbation (e.g., Wang et al. 2017). Since the mean MSE profiles are similar in the two runs, the weakened zonal difference of vertical MSE advection in KS is primarily attributed to weaker vertical velocity perturbation to the east and west of the MJO convection center (figure not shown). The suppressed vertical motion anomalies in KS are further related to weaker MJO heating.
Since the phase speed of the eastward propagation mode in KS is closest to the observed MJO among the three aquaplanet simulations, one may consider that the KS run produces more realistic MJOs. But it is worth mentioning that one should not compare the aquaplanet MJOs directly with the real-world MJOs, because the mean states in an aquaplanet world are significantly different from the real world. For instance, the mean zonal wind at the equator is easterly in aquaplanet simulations but is westerly in the real world (over the equatorial Indian Ocean, Maritime Continent, and western Pacific). Therefore, the surface heat flux term acts to promote the eastward propagation of aquaplanet MJOs, but acts to hinder the eastward propagation of the observed MJOs. This may be one reason for the systematically faster propagation speed of aquaplanet MJOs relative to the real-world MJOs. Another factor that would be worth mentioning is the existence of the Maritime Continent that cause stationary oscillation and stagnant behavior of MJO convection in the real atmosphere.
Thus, one cannot simply judge which of the three cases in the aquaplanet simulations is more realistic based on the simulated phase speed (or period). One needs to include at least the comparison of simulated mean state and MJO perturbation structures. If one agrees with the physical principal that an east–west asymmetry in the MSE tendency results in eastward propagation, then diagnosing the MJO structure and processes that cause the MSE zonal asymmetry becomes a good way to judge which case is more realistic in generating MJO. Because the observed mean MSE gradient is toward the higher latitudes, a poleward (equatorward) flow to the east (west) of MJO convection strengthens the east–west asymmetry of MSE tendency. But a mean state with an opposite mean MSE meridional gradient in the KS run would reduce the east–west asymmetry. While the offsetting effect of the surface heat flux and the meridional MSE gradient may lead to a “realistic” phase speed that is close to the observed, the physics behind that is not real.
Another point worth noting is that although the simulated eastward propagation modes in the NS and WS runs are faster than the observed MJO, they are not convectively coupled Kelvin waves because their structures resemble well that of the observed MJO. We examined the phase relationship between the boundary layer convergence and the convective center and found that the boundary layer convergence in the simulations leads the convective center (figure not shown), as in the observed MJO. The poleward meridional wind anomaly east of the convective center does not appear in a convectively coupled Kelvin wave, but is seen in the observed MJO (e.g., Kim et al. 2014).
6. Concluding remarks
In this study, through the in-depth analysis of aquaplanet experiments and 26 climate model simulations, we investigate contrasting views concerning Rossby wave effect on MJO eastward propagation (i.e., the “drag effect” versus the “acceleration effect”). The drag effect hypothesis argued that, because Rossby waves favor westward propagation, a stronger Rossby wave component slows down the eastward propagation of MJO. The acceleration effect hypothesis suggested that a stronger Rossby wave component enhances the east–west asymmetry of MSE tendency and thus favors the eastward propagation of MJO. Both the diagnosis of the aquaplanet experiments and 26 GCM simulations support the acceleration effect hypothesis.
In aquaplanet experiments, wider and narrower zonally symmetric SST meridional profiles are specified and the two experiments (i.e., the WS run and the NS run) simulate realistic mean states. Comparisons in the wavenumber–frequency power spectra and time–longitude diagrams suggest that the NS run, which is forced by a narrower meridional SST profile, has stronger and faster eastward propagation (14 m s−1) than the WS run does (11 m s−1). Meanwhile, the NS run is shown to have a stronger Rossby wave component as well as a stronger Kelvin wave component relative to the WS run by various strength indices. As the mean moisture in the two runs maximizes at the equator, the enhanced meridional wind anomaly associated with the Rossby and Kelvin wave components enhance the positive (negative) horizontal MSE advection and MSE tendency to the east (west) of the MJO convection center in the NS run relative to the WS run. The comparisons between WS and NS support the acceleration effect hypothesis.
A caution is needed in interpreting the Rossby and Kelvin wave effect based on another aquaplanet experiment (i.e., KS) that produces an unrealistic mean moisture distribution with a maximum specific humidity in off-equatorial regions. Under such a mean state, Rossby waves would result in a positive MSE tendency to the west of MJO convection that is opposite to the observed MSE tendency pattern. It suggests that the basic state from an aquaplanet experiment is very sensitive to the SST meridional profiles and reminds us of the necessity of checking the simulated basic state from an aquaplanet experiment.
Through the analysis of the 26 GCM simulations, we examined the relationship of strength of individual Rossby and Kelvin wave component at different pressure levels with the MJO eastward propagation skill. The MJO eastward propagation skill was represented by either pattern correlation coefficients of simulated precipitation anomaly with the observed precipitation anomaly on a lead–lag regression diagram (i.e., PCC skill) or the phase speed of the precipitation anomaly from a lead–lag correlation map (i.e., speed skill). Thus a higher skill corresponds to more robust and faster eastward propagation. It was found that the strength of Rossby or Kelvin wave component is positively correlated to the MJO eastward propagation skill above 800 hPa. In other words, models that simulate realistic eastward-propagating MJOs tend to have a stronger Rossby as well as a stronger Kelvin wave component, whereas the models that produce nonpropagation tend to have a weaker Rossby and a weaker Kelvin wave component. Furthermore, the MJO eastward propagation skill is significantly correlated with positive (negative) horizontal MSE advection anomalies to the east (west), indicating the role of zonal asymmetry of horizontal MSE advection anomaly in contributing to the eastward propagation of the MJO. The significant correlations primarily arise from the correlations for the meridional advection component. These results agree with the Rossby wave acceleration effect hypothesis.
A significant distinction can be seen in the boundary layer below 800 hPa, where the strength of the Rossby and Kelvin wave component are poorly correlated with the MJO eastward propagation skill. This is attributed to the distinctive structures of MJO winds below and above the top of the boundary layer, especially in the meridional wind field (Wang et al. 2017).
Since the strength of Rossby and Kelvin wave components above 800 hPa are both positively correlated to the MJO eastward propagation skill, it is reasonable to use the sum of the strength indices of the Rossby and Kelvin wave components (i.e., R+K) or the product of them (i.e., R*K) as a structure parameter measuring the MJO eastward propagation, rather than using R/K (Wang and Lee 2017). The correlation coefficients between the MJO eastward propagation skill and R+K or R*K are larger than those for R/K or individual Rossby or Kelvin wave component.
It is worth mentioning that the original Gill model solution has a simpler horizontal structure with a pure zonal wind Kelvin wave response to the east of a specified heating. Such a structure is not consistent with the observations that show a negative heating to the east of MJO convection and a marked meridional wind component. We argue that such an observed MJO wind structure is essentially an extended version of the Gill solution, because the negative heating anomaly to the east is the result of the Kelvin wave induced low-level (upper level) zonal wind divergence (convergence). In other words, the observed meridional wind is a result of the Kelvin wave response, when considering circulation induced interactive heating. The cause of this negative heating anomaly was investigated by Wang et al. (2017) through a set of idealized AGCM experiments. In response to an MJO-like heating anomaly, which consists of a deep convective heating and a stratiform-like heating in its rear, a zonally asymmetric vertical overturning flow resembling the observed is simulated, with a strong subsidence anomaly and a negative heating anomaly to the east. The so-induced negative heating anomaly further generates a pair of anticyclonic gyres and poleward meridional flow in the lower troposphere to its west. Note that a stationary heat source and a large dissipation rate were specified in the original Gill model. A recent study by Kacimi and Khouider (2018) showed that the standard Gill solution pattern may alter to a certain extent when a moving heat source is specified and a smaller dissipation rate is assumed. Thus a caution is needed to interpret the observed MJO circulation structure using a simple Gill model framework.
Another point worth noting is that the propagation of MJO convection in aquaplanet experiments depends not only on the specified SST meridional distribution, but also on cumulus convection parameterization scheme (e.g., Blackburn et al. 2013). Further investigation using various types of convective representation such as the explicit convection scheme (e.g., Nasuno et al. 2007, 2008; Yoshizaki et al. 2012; Takasuka et al. 2015) is needed.
Acknowledgments
This work was supported by NSFC Grants 41630423 and 41705059; National Key R&D Program 2015CB453200; NSF Grant AGS-1643297; NSFC Grants 41475084 and 41575043; Jiangsu Project BK20150062; JAMSTEC JIJI Theme 1 Project; and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD; R2014SCT00). This is SOEST contribution 10380, IPRC contribution 1323, and ESMC contribution 217.
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