1. Introduction
The Madden–Julian oscillation (MJO; Madden and Julian 1971), with a period of 20–100 days, is the dominant component of intraseasonal variability in the tropical atmosphere (Majda and Biello 2004; Zhang 2005). Atmospheric overturning in the MJO is organized over a broad range of spatial and temporal scales within a large-scale envelope (predominantly of zonal wavenumber 2) that propagates eastward at an average speed of 5 m s−1 across the warm waters of the Indian Ocean and the Western Pacific (Hendon and Liebmann 1994; Majda et al. 2007; Chen et al. 2014). The MJO exerts pronounced influences on monsoon systems, tropical cyclogenesis, El Niño, and the Southern Oscillation and has broad impacts on global climate and weather systems around the globe (Tyrrell et al. 1996; Bergman et al. 2001; Maloney and Hartmann 2001; Zhang 2005; Lorenz and Hartmann 2006; He et al. 2011; Pai et al. 2011; Klotzbach 2014; Chi et al. 2015). Though the MJO is a major source of intraseasonal predictability and has prominent impacts on climate, it is still an unmet challenge for global climate models to simulate and predict accurately (Slingo et al. 1996; Lin et al. 2006; Hung et al. 2013; Jiang et al. 2015). This difficulty exposes a gaping hole in our knowledge of tropical dynamics and, in particular, of the interactions between convection and atmospheric motions at larger scales (Zhang 2005; Zhang et al. 2013). The purpose of this paper is to diagnose the atmospheric overturning associated with a MJO event, to assess the contributions of the various scales of motions, and ultimately to seek better understanding of the multiscale interactions that are driving the MJO.
The international field campaign Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY)/Dynamics of the Madden–Julian Oscillation (DYNAMO) was conducted in and around the tropical Indian Ocean from October 2011 to March 2012. Three MJO events (the October, November, and December MJO events) were captured by the sounding, ground-based radar, ship/mooring, and airborne (aircraft did not sample the October event) observational networks during the field campaign (Yoneyama et al. 2013; Zhang et al. 2013). A number of studies documented various aspects of these MJO events based on the collected in situ observations. For example, Johnson and Ciesielski (2013) diagnosed the large-scale kinematic and thermodynamic properties of the October and November MJO events based on the sounding array observations. Using shipborne radar, Xu and Rutledge (2014) investigated the convective population and atmospheric conditions over the central Indian Ocean in the three MJO events. Rowe and Houze (2014) compared the microphysical characteristics of convective systems observed by the dual-polarimetric Doppler S-band radar between the MJO active and inactive phases during October, November, and December. Using the same dual-polarimetric radar observations, Barnes and Houze (2014) also studied the microphysical characteristics of mature near-equatorial oceanic mesoscale convective systems during the MJO active phases. Moum et al. (2014) analyzed the air–ocean interactions from westerly wind burst in the November MJO event based on research vessel observations. The budget of moist static energy of the three MJO events was analyzed by Sobel et al. (2014) with the sounding array data.
Besides these observational studies, forecasting and simulating skills of global and regional models on the MJO events observed during CINDY/DYNAMO have also been examined in a variety of research works (Fu et al. 2013; Kerns and Chen 2014; Ling et al. 2014; Takemi 2015; S. Wang et al. 2015, hereinafter W15; W. Wang et al. 2015; Xiang et al. 2015; Hagos et al. 2016; Janiga and Zhang 2016; Pilon et al. 2016; Powell 2016). W15 simulated the October and November MJO events using a convection-permitting regional model with 9-km grid spacing. The authors compared the simulated atmospheric circulation, rainfall intensity and propagation, precipitable water, wavenumber-frequency distributions of surface precipitation, radiative fluxes, and the budget of moist static energy with multiple observational datasets. It is shown that the model successfully captured many aspects of the two simulated MJO events, especially for the October MJO event. In particular, the evolutions of large-scale circulation, the convective activity, and the cloud–radiative feedback, which are important to the MJO dynamics (Wang et al. 2016), are faithfully reproduced in the simulation.
The main objective of this study is to assess the variations in the atmospheric overturning of the MJO using convection-permitting simulations as in W15. While the convective mass transport can be easily obtained in a general circulation model owing to its reliance on convective parameterization, a particular challenge in using a high-resolution model lies in assessing the mass transport and the contribution of individual scales as the model simulates a broad range of motions. In this study, we apply the isentropic analysis framework introduced by Pauluis and Mrowiec (2013) in which the vertical mass transport is sorted out in terms of the equivalent potential temperature of the air parcels. This technique has the advantages of 1) identifying the atmospheric overturning associated with upward transport of warm moist air and downward transport of colder dryer air and 2) systematically filtering gravity waves. Vertical mass transport contributed by different scales of motions can thus be more easily identified (Slawinska et al. 2016). In this study, we systematically apply the isentropic analysis to investigate the evolution of the atmospheric overturning during the October MJO event using the same simulations as in W15. The experimental setup and analysis methodology are described in section 2. Section 3 analyzes the atmospheric mass transport associated with multiple scales. As mentioned above, the actual behavior of MJO is complex owing to a wide range of scales involved. Time filtering is usually needed to be applied to precipitation or OLR observations to capture the eastward propagation of the MJO. In this study, the eastward propagation of the MJO as an envelope of the convective-scale overturning characterized by isentropic analysis will be discussed in section 4 to see if this technique can capture the propagation of the MJO without any time filtering. This approach allows us not only to assess the evolution of convective mass transport over different subregions but also to assess the changes in the thermodynamic properties of the updrafts and downdrafts. Section 5 gives the concluding remarks of the study.
2. Experimental setup and methodology
a. WRF Model setup
The model configuration here is the same as the one used in W15. The Advanced Research version of WRF (Skamarock et al. 2008), version 3.4.1, is used to simulate the atmosphere over the whole equatorial Indian Ocean, from 20°S to 20°N and from 48° to 120°E (Fig. 1). The horizontal grid spacing is 9 km and there are 45 vertical levels with 9 levels in the lowest 1 km and a nominal top at 20 hPa. Vertically propagating gravity waves have been suppressed in the top 5 km of the model with the implicit damping scheme (Klemp et al. 2008). The 6-hourly ERA-Interim (Dee et al. 2011) is used as the initial and boundary conditions for the WRF simulation, and SST is updated every 6 h using the ERA-Interim SST data. The simulation employs the unified Noah land surface physical scheme (Tewari et al. 2004), the Yonsei University (YSU) boundary layer scheme (Hong et al. 2006), the GCM version of the Rapid Radiative Transfer Model (RRTMG) longwave radiation scheme (Iacono et al. 2008), and the updated Goddard shortwave scheme (Shi et al. 2010). The WRF double-moment (WDM) microphysics scheme (Lim and Hong 2010) from WRF3.5.1 with an update on the limit of the shape parameters and terminal speed of snow is used in this simulation. No cumulus scheme has been used. The model integration starts from 0000 UTC 1 October 2011. For the first 3 days, a spectral nudging is used to relax the horizontal wind with a zonal wavenumber 0–4 and a meridional wavenumber 0–2, which constrains the large-scale flow and convergence in the domain and allows the mesoscale to saturate in the spectral space. More details on the model configurations and descriptions can be found in W15.
Spatial distribution of the accumulated rainfall in the WRF simulation (color shading; from 4 Oct to 14 Nov 2011). Different subregions (450 km × 450 km) are indicated by the black rectangles. Coastlines are shown by the gray lines.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
The simulation is integrated until 14 November 2011 without any further nudging after the first 3 days. The analysis focuses on the free run period from 4 October to 14 November. Figure 2 shows the Hovmöller diagrams of the 3-hourly rainfall averaged between the equator and 4.5°N from the WRF simulation and the TRMM observation. The WRF simulation reproduces both the intensity and the propagation of the surface rainfall, as previously discussed in W15. The observation and simulation clearly show that the October MJO event is initiated in the western Indian Ocean (~60°E) around 14 October (shown by the red dashed line) and propagates eastward with a speed around 5 m s−1. The eastward propagation is disrupted near the Maritime Continent (~100°E) around 6 November (disrupted date herein). We also observe a westward propagation for each rainfall episode within the MJO envelope, which may be related to the propagations of equatorial Rossby waves and mixed Rossby–gravity waves (Wheeler and Kiladis 1999; Zuluaga and Houze 2013). The simulated surface rainfall intensity of several episodes is slightly stronger than that in the TRMM observations, while the WRF simulation captures the mean strength of these westward-propagating episodes. Precipitation over the Maritime Continent is little influenced by the MJO event, and a prominent diurnal cycle of precipitation is evident over Indonesia and Borneo. More details on the atmospheric environment and energy budgets of this MJO event can be found in W15.
Hovmöller diagrams of 3-hourly surface precipitation from (a) the WRF simulation and (b) TRMM observations averaged over latitudes 0°–4.5°N. The onset (14 Oct) and disrupted (6 Nov) date of the MJO event are shown by the red dashed lines. The black dashed lines are longitude grid lines.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
b. Isentropic analysis
The isentropic analysis technique developed by Pauluis and Mrowiec (2013) is applied in this study to investigate the mean properties of atmospheric overturning across multiple scales during this MJO event. The isentropic analysis relies on sorting the vertical mass transport in terms of the equivalent potential temperature θe of air parcels and computes the atmospheric overturning in isentropic coordinates (z, θe). Compared with the Eulerian analysis, isentropic analysis filters out reversible oscillatory motions associated with gravity waves and emphasizes the fact that the vertical mass transport in convection (Pauluis and Mrowiec 2013; Pauluis 2016; Slawinska et al. 2016), mesoscale systems (Mrowiec et al. 2012, 2015, 2016), and global atmospheric circulations (Pauluis et al. 2008, 2010; Yamada and Pauluis 2016) are all due to the combinations of ascending air parcels with high entropy and descending air parcels with low entropy.
c. Multiscale decomposition of mass flux
3. Atmospheric overturning across multiple scales
This section studies the multiscale atmospheric overturning in the October MJO event as described by the isentropic analysis. Figure 3 shows the isentropic streamfunctions associated with multiple scales averaged over all 120 subregions from 4 October to 14 November 2011. Figure 3a shows the convective-scale isentropic streamfunction. The solid black line is the horizontal-mean profile of equivalent potential temperature. Because air parcels with low θe are on average subsiding in convection, given the definition of Eq. (3), the convective-scale streamfunction at each given height are first decreasing with θe. The vertical mass flux changes from negative to positive when the streamfunction reaches its minimum value at each level. The streamfunction is negative throughout the troposphere, indicating that the rising air parcels have higher θe than the subsiding air parcels on average which leads to a net upward transport of θe for the summed convective-scale circulation. In the streamfunction, isolines associated with deep convective drafts connect the surface with the upper troposphere (shown by the black dashed contour in Fig. 3a). The equivalent potential temperature θe of air parcels being lifted by deep convection drops from near the surface to the melting level (around 6 km), which is due to the entrainment of drier air in the updrafts. Above the melting level, the streamlines are almost vertical, reflecting that deep convective updraft can transport mass and energy upward without significant dilution above the freezing level. From the upper troposphere to the surface, the averaged potential temperature of the subsiding air parcels surrounding deep convective updrafts (shown by the left part of the black dashed contour in Fig. 3a) first decrease by 25 K from 14 to 1.5 km, which is induced by the radiative cooling effect, then increase by 15 K in the lowest 1.5-km level, which is closely related to the mixing between the subsiding environmental air and the detrained cloudy air that has a higher θe (Pauluis and Mrowiec 2013). When compared with the deep convective overturning that can transport mass from the surface to the upper troposphere, shallow convective-scale overturning is much more prominent (around one order magnitude greater) in the convective-scale streamfunction with a center located around 1–3 km and a top below 5 km (or melting level). It corresponds to the fact that shallow convective overturning dominates the mass transport in lower troposphere and produces the most precipitation over the tropical Indian Ocean (Liu et al. 2008). In shallow convective overturning, the θe of the air parcels is much higher than the mean profile of θe (~10 K), which shows air parcels in shallow cumulus are much warmer and moister than the environment [refer to Pauluis and Mrowiec (2013)].
Isentropic streamfunctions (color shading; kg m−2 s−1) associated with the (a) convective scale, (b) regional scale, (c) meridional scale, and (d) basin scale averaged over 120 subregions from 4 Oct to 14 Nov 2011. The x axis is equivalent potential temperature (K) and the y axis is height (km). The black solid line shows the horizontal-mean profile of equivalent potential temperature averaged over 120 subregions. Isolines of streamfunction are shown as red contours with a −0.001 kg m−2 s−1 interval in (a) and a −0.0002 kg m−2 s−1 interval in (b)–(d). The black dashed lines in (a)–(c) show the isolines of 0 kg m−2 s−1. The black dashed line in (d) shows the lowest θe above which the basin-scale streamfunction is constant for each height level.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
The regional-scale isentropic streamfunction is presented in Fig. 3b, which indicates the collective contribution of organized mesoscale convective systems to the whole atmospheric overturning in this MJO event. When compared with the convective-scale streamfunction, the regional-scale streamfunction is shallower in the vertical and wider in the lower troposphere, which corresponds to weaker vertical motions at this scale. The isolines of the regional-scale streamfunction are closely aligned with the horizontal-mean profile of θe, showing the bulk of the regional-scale descending motions occurs at θe closer to the horizontal-mean atmospheric state than that of the convective-scale overturning. In the subsiding part of the regional-scale streamfunction, with slower vertical motions, both the reduction of θe above 1.5 km induced by the radiative cooling and the increase of θe in the lowest 1.5 km due to the mixing with detrained cloudy air are more prominent than those in the convective-scale streamfunction, which are 32 and 26 K, respectively. The regional-scale streamfunction peaks at around 4–9 km, which might correspond to the distinctive overturning in the anvil clouds that usually exist at the rear of mesoscale systems extending hundreds of kilometers (DePasquale et al. 2014; Slawinska et al. 2016).
Figure 3c shows the isentropic streamfunction associated with the meridional overturning over the Indian Ocean. The Hadley circulation is associated with ascending motions over the equatorial ITCZ and descending motion in the subtropics. When diagnosed through the isentropic streamfunction, the Hadley circulation shows up as rising motion of warm, moist air and subsiding motion of colder dryer air. Compared to the regional-scale counterpart, the streamfunction associated with the meridional scale is 1–2 km shallower, which reflects that the averaged depth of the meridional circulation is shallower than that of the organized mesoscale convective systems. The tilt of the streamfunction in the lower troposphere is also more prominent in the meridional-scale circulation, which indicates that the impacts of entrainment are stronger within the meridional circulation, which may be related to weaker vertical motions at this scale. The minimum of the meridional-scale streamfunction is located around 6 km, showing that the vertical mass transport of the meridional circulation is strongest in the middle troposphere.
Figure 3d shows the isentropic streamfunction associated with the basin scale. The dashed black line is the lowest θe above which the streamfunction is constant for each height level. The basin-scale streamfunction differs from those associated with other scales in that it does not vanish at high θe and therefore does not have a closed contour. This arises from the fact that the large-scale boundary conditions used in the simulations impose large-scale ascent over the entire basin, which is compensated by subsidence outside of the simulated domain. Similar to the meridional scale, the basin-scale streamfunction also peaks around 6 km.
Evolution of isentropic upward mass transports (color shading; kg m−2 s−1) associated with (a) all scales, (b) convective scale, (c) regional scale, (d) meridional scale, and (e) basin scale averaged over 120 subregions. The black dashed lines show the onset and disrupted dates of the MJO event.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
The convective mass transport peaks in the lower troposphere, indicative of the preponderance of shallow convective-scale overturning (Fig. 4b). During the suppressed phase, the convective activity is comparatively weak, especially above the freezing level. During the MJO active phase, the convective-scale overturning is reinforced considerably and becomes much deeper, with the strength of convective upward mass transport increases more than 50% in lower troposphere and reaches the strength around 0.5 kg m−2 s−1 between 5- and 10-km altitude (Fig. 4b), which is consistent with Del Genio et al. (2012) and many other studies that found an enhancement of the tropical convective activity during the MJO. However, the convective overturning is still more prominent in the lower troposphere during the active phase, which indicates that both shallow and deep convection increase during the MJO active phase. The statistical significance of the differences in the convective-scale overturning for the active and suppressed MJO phases is tested using the t test. Results show that the increase in convective-scale overturning during the MJO active phase is statistically significant at the 99% confidence level.
The mass transports associated with the regional, meridional, and basin scales (Figs. 4c, 4d, and 4e) are one order of magnitude smaller than that associated with the mass transport by convective scale (Fig. 4b). The meridional and basinwide overturning also increase significantly during the MJO active phase (Figs. 4d and 4e; around 3 times stronger than the suppressed phase, statistically significant at the 99% confidence level), reflecting that the Hadley circulation is reinforced by the MJO heating; stronger basin-scale updraft is imposed by the lateral boundary (Fig. 4e). Similar to the analysis of the streamfunctions in Figs. 3c and 3d, both the meridional and basinwide upward mass transports peak at around 6 km, which considerably enhances the total upward mass transport in the middle troposphere (~34%) during the active phase of the MJO (Fig. 4a). In contrast, the contribution from the regional overturning to the mass transport shows a weak enhancement near the end of the MJO active phase but it is otherwise small (Fig. 4c). Several studies (e.g., Tromeur and Rossow 2010; Virts and Houze 2015) have pointed out the fact that the MJO corresponds to increased activity at the synoptic and mesoscales. However, such increases in synoptic and mesoscale activity do not correspond to an increase in the atmospheric overturning. A possible explanation is that the isentropic analysis filters out the reversible oscillatory motions like gravity waves. For gravity waves, the ascending and subsiding motions are out of phase with the perturbations in both temperature and θe, so that their net contribution to the isentropic mass transport is small when averaged over the entire basin. Thus, if the mesoscale and synoptic-scale structures in the tropics fit the broader concept of convectively coupled gravity waves (Emanuel et al. 1994; Wheeler and Kiladis 1999), a majority of their contribution to the isentropic overturning will be filtered out and should be small when compared to other scales of motions, though the contribution from the nonlinear convectively coupled gravity waves with significant irreversible diabatic process cannot be purely removed by the isentropic analysis.
Figure 5 shows the scatterplots of total upward versus downward isentropic mass fluxes at different altitudes over all 120 subregions. The total upward (downward) mass fluxes shown here is the average of ascending (subsiding) air parcels at all equivalent potential temperatures on different altitudes. We observe a strong correlation between the upward and downward mass fluxes, meaning that regions of strong updrafts are typically associated with stronger downdrafts. Note that the boundary conditions impose a large-scale ascent over the entire basin in the simulation (Fig. 3d), so that the upward mass flux is typically larger than the downward mass flux at all altitudes, and the linear regression coefficient between the two fluxes is smaller than 1.0 for the entire troposphere (Fig. 5). From a physical point of view, the ratio of the downward mass flux to the upward mass fluxes account for the ability of convective updrafts to generate convective downdrafts.
Scatterplots of total upward vs downward mass fluxes (kg m−2 s−1) at different altitudes over 120 subregions [from (a) 3 to (d) 9 km]. The black solid line in each panel represents the linear fit of the scatterplot. The linear regression coefficient and its 95% confidence interval are shown in the upper-right corner of each panel. The black dashed line in each panel shows a straight line with a slope of 1.0.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
Figure 5 also shows that the ratio between the downward and upward mass fluxes decreases substantially with height. The linear regression coefficient between the downward and upward mass fluxes is high under the melting layer (0.545 at 3 km, with a 95% confidence interval from 0.544 to 0.547), showing that convective updrafts can generate a substantial amount of downdraft. The regression coefficient however decreases substantially above the freezing level, (0.374 at 9 km, with a 95% confidence interval from 0.373 to 0.375). This is consistent with the analysis of Fig. 4, which shows that convective mass transport peaks below the melting layer. The linear regression coefficient between the downward to upward mass flux can be physically interpreted in terms of the evaporation efficiency of the atmospheric overturning (Mrowiec et al. 2012). Thus, the isentropic analysis in our simulation is consistent with an evaporation efficiency of about 54% in the lower troposphere that gradually decreases to 37% in the upper troposphere. When compared to the tropic inland regions, for example sub-Saharan Africa (the evaporation efficiency is close to 1.0; Geerts and Dejene 2005), the evaporation efficiency in the MJO is much lower because of the moister large-scale environment over the tropic oceans.
As mentioned above, the direct contribution from the large scales (basin, meridional, and regional scales) to the total atmospheric overturning is one order of magnitude smaller than that from the convective activity. However, the large-scale flow can still essentially influence the total atmospheric overturning indirectly, since it provides the environment for the initiation and development of convection. To assess the convective-scale overturning under different large-scale regimes, we divide all convective-scale vertical mass transports into nine regimes based on the strength of 
Isentropic streamfunction (kg m−2 s−1) of convective-scale overturning in different regimes of 
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
In the subsiding regimes (Figs. 6a–e), the average strength of the convective overturning is weak. Convection is shallower and is dominated by warm-rain processes with its vertical circulation limited under the melting level. Though deep convective-scale ascent can still be found over the subsiding regimes, the strength is weak, reflecting that the large-scale subsidence suppresses the development of deep convective overturning. As mentioned above, the tilt of the streamfunction in the lower troposphere is closely related to the mixing between rising clouds and the environmental air, which results both in a reduction of θe inside clouds and in an increase of the θe in the environment. The tilt of the streamlines increases with the strength of the large-scale subsidence, which indicates that entrainment has a strong impact on the behavior of rising plumes (from Fig. 6e to Fig. 6a). Equivalent potential temperature θe of descending air parcels is also low in the subsidence regimes, with the lowest θe at about 317 K located at around 1.5 km. It should be noted that the spatial resolution of 9 km in our simulation is insufficient to accurately resolve the entrainment process. More pronounced entrainment should be expected in simulations with even higher spatial resolution.
In the ascending regimes (Figs. 6f–i), the convective overturning intensifies (5 times stronger than the convective overturning in the subsiding regimes on average). Shallow convective overturning is still prominent and an overturning mass transport peaks at around 1–4 km. Regions of large-scale ascent typically correspond to a moister (and slightly warmer) environment, which reduces the negative impacts of entrainment. This appears in the isentropic analysis as a reduction of the tilt of streamlines in the ascending regimes. The isentropic mass transport increases with the strength of the large-scale upward mass transport, which confirms that convective overturning is enhanced in regions of large-scale ascent. The isentropic mass transport is however systematically larger than the magnitude of the large-scale mass transport itself, which implies that convective motions tend to amplify the large-scale ascent.
To sum up, in comparison with the convective-scale circulation, the direct contribution from the large-scale circulations to the atmospheric overturning is relatively weak during the MJO event (Figs. 3 and 4). However, the large-scale circulations modulate the convective activity (Fig. 6). The large-scale upward motion and the associated low-level convergence and high-level divergence provide favorable atmospheric environment for the initiation and development of convective overturning. Similar results can also be found in the previous literatures (e.g., Johnson and Ciesielski 2013; Powell and Houze 2015; Ruppert and Johnson 2015). For example, in Powell and Houze (2015), they found that the large-scale circulation is instrumental to the onset of MJO events. In addition, large-scale motions appear to play a more substantial role in the isentropic mass transport in the middle to upper troposphere and may, thus, play a substantial role in increasing the depth of the atmospheric overturning.
4. Propagation of MJO as a convective envelope
As mentioned in the introduction, the MJO event is characterized as a large-scale envelope of enhanced convective activity which propagates eastward across the equatorial Indian and west Pacific Oceans at an average speed of 5 m s−1. In this section, the detailed spatial, vertical, and temporal variations of the convective-scale atmospheric overturning in the October MJO event will be investigated in the context of isentropic analysis, with a special emphasis on features associated with the MJO’s eastward propagation.
a. Mass transport at different altitudes
Figure 7 shows the Hovmöller diagrams of the convective-scale isentropic upward mass transport (color shadings) and the mean vertical mass fluxes (black contours) averaged over subregions 61–75 at 2-, 5-, and 10-km altitudes, respectively. The x axis is the longitude (from the western equatorial Indian Ocean to the island of Borneo) and the y axis shows the dates. The onset and disrupted dates of the October MJO event are shown by the two white dashed lines. Both the convective-scale upward mass transports and the mean vertical mass fluxes are enhanced considerably after the onset of the MJO, indicating that the convective activity and the atmospheric overturning are enhanced during the active phase of this MJO event. The eastward propagation of the MJO is clearly captured by the convective-scale upward mass transports and the mean vertical mass fluxes at different levels. As for the surface rainfall field (Fig. 2), the eastward propagation of enhanced convective-scale upward mass transport is also disrupted near the Maritime Continent (~100°E). During the active phase of the MJO event, the mean vertical mass flux is enhanced on the middle and upper troposphere (Figs. 7b and 7c), which is closely related to the strengthening of the basin- and meridional-scale atmospheric overturning during this period (Figs. 4d and 4e). Both shallow and deep convective-scale upward mass transports are enhanced during the MJO active phase (more than 50%, statistically significant at the 99% confidence level) while the mass transport in the lower troposphere is more prominent than that in the middle and upper troposphere (Figs. 7a–c). The enhancement of the deep convective-scale upward mass transport occurs simultaneously with the onset of the MJO, while the reinforcement of the shallow convective-scale upward mass transport occurs a few days earlier (Figs. 7a and 7c). This strongly suggests that preconditioning by shallow congestus clouds might play an important role in the initial development of the MJO over the Indian Ocean. Previous studies show that preceding shallow or moderately deep convective activity can enhance the low-level mass convergence, moisten the lower troposphere, and produce a favorable environment for the initiation of deep convection (Zhang and Song 2009; Powell and Houze 2013; Chikira 2014; Xu and Rutledge 2014; Bellenger et al. 2015; Powell and Houze 2015; Ruppert and Johnson 2015; Takemi 2015; Powell 2016).
Hovmöller diagrams of isentropic upward mass transport (kg m−2 s−1) associated with the convective-scale (color shading) and mean mass flux (black contours; solid contours represent upward mean mass flux and dashed ones are downward mean mass flux; the interval is 1 kg m−2 s−1) at (a) 2-, (b) 5-, and (c) 10-km altitudes. The white dashed lines show the onset and disrupted dates of the MJO event. The reinforcement of shallow upward mass transport is highlighted by the red arrow in (a).
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
b. Mass flux in different subregions
The temporal and spatial evolutions of the vertical structure of convective-scale mass fluxes are further investigated. Figure 8 presents the isentropic distributions of the convective-scale vertical mass fluxes averaged over different periods and subregions. As mentioned in section 3, the convective-scale atmospheric overturning is a combination of ascending air parcels with high potential temperature and descending air parcels at low potential temperature. For each subregion over the equatorial Indian Ocean (subregions 61–68), the convective-scale mass flux is weak (with the maximum vertical mass flux weaker than 0.003 kg m−2 s−1 K−1) and shallow (below melting level) during the suppressed phase of the MJO event. While, during the active phase of the MJO event, it becomes much stronger (with the maximum vertical mass flux stronger than 0.008 kg m−2 s−1 K−1) and deeper that connects the air from near the surface to the upper troposphere. The enhancements of the convective-scale mass flux in all subregions during the active phase of the MJO are statistically significant at the 99% confidence level (the statistical significances are tested using the t test). Strong convective-scale mass fluxes are mainly concentrated in the lower troposphere which corresponds to the analysis of Figs. 3 and 4, indicating that shallow convective overturning dominates the mass transport in lower troposphere over the tropical Indian Ocean. The eastward propagation of the MJO event can be clearly captured by the strongest value of the convective-scale vertical mass flux in each equatorial subregion: from subregions 61–62 (15–19 October), to subregions 64–65 (20–24 October), to subregions 67–68 (25–29 October), and to subregions 70–71 (30 October–3 November), which corresponds to the eastward propagation of the convective-scale upward mass transports shown in Fig. 7. Because of the stronger convective heating, the environmental equivalent potential temperature also becomes higher in the lower and middle troposphere (shown by the black solid lines in Fig. 8) during the active phase of the MJO event. Over the Maritime Continent (subregions 74–75), the convective-scale mass flux, however, has been influenced little by the MJO event. The average rainfall rate in each subregion during different periods has also been given in Fig. 8, showing that the rainfall rate varies directly with the vertical convective-scale mass flux: a stronger convective activity produces stronger surface precipitation during the active phase of the MJO.
Isentropic distributions of convective-scale vertical mass flux (kg m−2 s−1 K−1; color shading) averaged over different subregions (columns) and different periods (rows). For each panel, the x axis is equivalent potential temperature (K) and the y axis is height (km). The black solid line shows the mean profile of equivalent potential temperature. The mean surface rain rate over the subregion is shown in the upper-right corner of each panel. The number of subregions and their longitude ranges are shown at the top of each column. Time period (month day–month day) is shown in each panel of the first column.
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
c. Vertical entropy transport
The isentropic analysis can also be used to assess the vertical transports of energy and entropy. As shown in Fig. 3a, on average, the potential temperature of ascending air parcels is higher than that of descending air parcels in the convective-scale overturning, which leads to an upward entropy transportation for the whole convective overturning.
(a) Evolution of perturbation isentropic-mean equivalent potential temperature (K) in the mean convective-scale updraft. (b) As in (a), but for the mean convective-scale downdraft. (c) Evolution of the isentropic-mean equivalent potential temperature difference (K) between the mean convective-scale updraft and downdraft 
Citation: Journal of the Atmospheric Sciences 75, 2; 10.1175/JAS-D-17-0060.1
The evolution of equivalent potential temperature of the mean downdraft 
The evolution of isentropic-mean equivalent potential temperature differences between the mean convective-scale updraft and downdraft is shown in Fig. 9c. As mentioned before, rising air parcels have higher equivalent potential temperature than the subsiding air parcels on average, indicating that there has an upward entropy transport in the convective-scale atmospheric overturning. The equivalent potential temperature differences between the mean updraft and downdraft decreases with the height and changes sign near the tropopause. The entropy transport by convection is upward through the troposphere and reverses direction near the tropopause. The equivalent potential temperature differences between the mean updraft and downdraft become smaller in the lower troposphere during the active phase of the MJO event, which reflects a moister environment. The largest difference in equivalent potential temperature between updraft and downdraft is about 15 K which occurs between 5 and 10 October. This difference gradually decreases before the onset reaching its lowest value of about 10 K between 20 and 25 October. The active phase of the MJO thus corresponds to a period of reduced thermodynamic difference between updraft and downdraft. This means that convection is less efficient at reducing the equivalent potential temperature of the lower troposphere, so that more convective mass transport is necessary to compensate for a given surface heating.
5. Summary and discussion
In this study, we analyze the atmospheric overturning across multiple scales during the October MJO event observed by the CINDY/DYNAMO campaign. The MJO event is simulated with the WRF Model under the same configuration as W15. Isentropic analysis proposed by Pauluis and Mrowiec (2013) is applied in this study, for the first time for such a purpose, to investigate the contributions of individual scales to the total atmospheric overturning of the MJO. The framework of isentropic analysis analyzes the atmospheric overturning by conditionally averaging vertical mass transport in terms of the equivalent potential temperature and describes the flow in a height–entropy (z–θe) coordinate. This approach makes it possible to unambiguously extract the mass transport associated with different scales in the high-resolution simulation.
The overturning circulation of the MJO event is decomposed into four contributions: a basinwide ascent (basin scale), a zonally symmetric meridional overturning (meridional scale), zonal asymmetries on scales larger than 450 km (regional scale), and a convective contribution associated with all scales less than 450 km (convective scale). Our analysis shows that the atmospheric overturning over the Indian Ocean is dominated by the contribution from the convective scale. The overturning associated with other scales of motion is at least one order magnitude smaller than that owing to convection. However, the vertical mass transport by the convective scale peaks in the lower troposphere, while the transport by the larger scales reaches its maximum in the midtroposphere. This indicates that while the atmospheric overturning is dominated by the smaller scales, the larger scales enable the atmospheric overturning to reach a higher altitude than it would owing to the influence of convection alone.
We also analyze the evolution of the upward mass transport. During the active phase of the MJO, the atmospheric overturning associated with all scales becomes significantly stronger. This increase of mass transport is most pronounced for the contributions from the convective scales. The large-scale overturning is also important because it can significantly enhance the vertical mass transport in the middle to upper troposphere and modulate the convective activity. Notably, the convective mass transport intensifies in the lower troposphere a few days before the initiation of the MJO event. This strongly indicates that preconditioning by shallow congestus clouds plays an important role in the development of the MJO over the Indian Ocean.
In contrast to the previous studies based on coarse-resolution models or large-scale atmospheric datasets that do not resolve the convective scale and only capture the atmospheric overturning by the large-scale atmospheric motion (e.g., Kiladis et al. 2005; Johnson and Ciesielski 2013), the isentropic analysis based on cloud-permitting simulation shows that convective scale dominates the atmospheric overturning of the MJO and strongly interacts with the large scales. The contribution of convective scale to the total atmospheric overturning is much larger in the isentropic analysis than that in the traditional Eulerian averaging, because the conditional averaging based on equivalent temperature can better extract the vertical mass flux associated with convective scale.
The eastward propagation of the MJO is clearly captured by the eastward propagation of the convective-scale vertical mass transport. Prior to initiation of the MJO, there is a noticeable increase in shallow convective overturning in the equatorial Indian Ocean. The initiation itself corresponds to the intensification and deepening of convection which then slowly propagates eastward. The convective-scale vertical mass transport over the Maritime Continent, however, has been influenced little by the MJO event. In our simulation, the MJO propagation can be unequivocally identified from the propagation of the convective mass transport, without applying any additional filtering which is usually needed to be done for the precipitation or OLR fields.
Isentropic analysis also offers an efficient way to divide the upward and downward mass transports in the convective-scale overturning and characterize the thermodynamic properties of convective-scale updraft and downdraft separately. The convective-scale vertical entropy transport in the MJO event has been studied in this paper. In the mean convective-scale updraft, the averaged equivalent potential temperature becomes higher in the troposphere while lower above the tropopause during the active phase of the MJO, which is related to stronger and deeper convective activity during this period. Similar evolution can also be found in the mean convective-scale downdraft. In the boundary layer, the averaged equivalent potential temperature is decreased in the mean convective-scale downdraft during the active phase of the MJO, which is related to the stronger convective downdraft and cold pools. In general, the increase of equivalent potential temperature of convective-scale overturning during the MJO active phase is not significant, especially when compared to the variations of other strong tropic atmospheric systems like hurricane (Mrowiec et al. 2016).
With the isentropic analysis technique, detailed thermodynamic cycles and energy transport of multiscale atmospheric overturning in the MJO can also be investigated based on the mean airflow as Lagrangian dynamics approximation (Pauluis 2016), which would be interesting to study in the future. Using cloud-resolving models with parameterized large-scale dynamics, several recent studies have investigated the interactions between convection development and large-scale overturning in the tropics (e.g., Wang et al. 2013, 2016). These modeling results are also deserving of further analysis using the isentropic analysis technique.
Acknowledgments
Authors Xingchao Chen and Olivier Pauluis are supported by the New York University Abu Dhabi Research Institute under Grant G1102. This research is also partially sponsored by NSF Grant 1305798. The computations were carried out on the High Performance Computing resources at NYUAD. We acknowledge the support from Dr. Yue Ying and Dr. Sourav Taraphdar for providing the WRF Model setup.
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