1. Introduction
The Indian summer monsoon features large spatial and temporal variations in precipitation (Chang et al. 2017). Among the transient features that grow in this region are synoptic-scale disturbances that are often referred to as monsoon low pressure systems. These systems are characterized by slow westward and northward propagation and a horizontal radius of ~2000 km (Godbole 1977; Krishnamurti et al. 1975, 1976; Sikka 1977; Lau and Lau 1990). The India Meteorological Department (IMD) categorizes monsoon low pressure systems according to the strength of surface wind speed. The weakest systems are defined as lows, stronger systems with surface winds between 8.5 and 16.5 m s−1 are defined as monsoon depressions, and the strongest systems are referred to as cyclonic storms (Saha et al. 1981; Krishnamurthy and Ajayamohan 2010; Hunt et al. 2016). Anomalous anticyclones are also observed during the Indian monsoon, which have structures similar to the low pressure systems but with reversed polarity (Krishnamurthy and Ajayamohan 2010). This study focuses on the weaker lows, depressions, and the anomalous anticyclones, which we will collectively refer to as synoptic-scale monsoonal disturbances (SMDs; Krishnamurthy and Ajayamohan 2010; Ditchek et al. 2016).
During their life cycle, monsoon low pressure systems often make landfall over the Indian subcontinent, producing up to half of the total monsoon rainfall received by India (Stano et al. 2002; Ding and Sikka 2006; Yoon and Chen 2005; Yoon and Huang 2012). Conversely, anomalous anticyclones are associated with breaks in the monsoon, with little or no rainfall occurring during the passage of these systems. Thus, understanding SMDs is of critical importance to our understanding of the Indian monsoon and its variability.
In spite of the important role that SMDs have in the monsoon’s hydrologic cycle, very few studies have analyzed how these systems modulate rainfall. Many studies have assumed that SMDs are a result of a variant of baroclinic instability called moist baroclinic instability [Salvekar et al. 1986; Krishnakumar et al. 1992; Krishnamurti et al. 2013; see also Cohen and Boos (2016) for a review on the topic], with precipitation being a result of large-scale quasigeostrophic (QG) ascent in these disturbances (Shukla 1978; Mak 1983; Sanders 1984). Other studies have included moist convection in the form of frictional convergence feedbacks (Goswami 1987).
To the best of our knowledge, the first study to examine the water vapor budget of SMDs was Yoon and Chen (2005). They found that the leading balance in SMDs involves import of moisture through convergence and loss of moisture through condensation and precipitation. Their study, however, only considered the Eulerian temporal tendency in moisture over a limited domain near the center of the vortex. Thus, their study does not take into account the propagation of the moisture anomalies. However, recent studies have shown that SMDs are characterized by large specific humidity anomalies on the order of 0.3 g kg−1 (Krishnamurthy and Ajayamohan 2010) and lower-tropospheric relative humidity values of over 80% (Hunt et al. 2016). The large amplitude of specific humidity together with the ~5-day time scale of SMDs suggests that the temporal tendency in moisture may not be negligible. Understanding the evolution of moisture may lead to novel insights into the dynamics of SMDs. Moreover, while several studies have analyzed the thermodynamic budget of SMDs (Saha and Saha 1988; Sørland and Sorteberg 2015), no study has looked at this budget in the context of moist processes, nor has any study looked at both the moisture and thermodynamic budgets within the context of moist static energy (MSE).
The goal of this study is to analyze the moisture and MSE budgets of SMDs. To carry out this analysis, we will make use of daily fields from GFDL’s atmospheric general circulation model (AGCM). We use this model because it captures the main features of SMDs and because it does not exhibit the large residuals in moisture/MSE budgets that reanalysis products have as a result of the data assimilation process (Mapes and Bacmeister 2012). Additionally, previous studies have shown that models are able to simulate SMDs reasonably well (Ashok et al. 2000; Sabre et al. 2000; Stowasser et al. 2009; Sørland et al. 2016; Hunt and Turner 2017). We will show that the propagation of the moisture anomalies is governed by vertical moisture advection while propagation of the MSE anomalies is predominantly due to horizontal MSE advection. While these two processes may seem distinct, we will show that horizontal dry static energy advection can induce vertical motion, which in turns induces a moisture tendency through vertical moisture advection. Ascent driven by radiative heating, in turn, plays a key role in maintaining the moisture anomalies.
This study is structured as follows. The next section describes GFDL’s AGCM, version 4.0 (AM4.0), and the methods of analysis. Section 3 describes the Indian monsoon mean state and variability as simulated by AM4.0. Sections 4 and 5 discuss the moisture and MSE budgets of SMDs, respectively. Section 6 synthesizes the results from the two budgets. A concluding discussion is offered in section 7.
2. Data and methods
a. Model description
Most of the analysis presented here is made using daily output data from AM4.0 (Zhao et al. 2018a,b). AM4.0 uses a finite-volume, cubed-sphere topology with ~100-km resolution per cube face. The output resolution used here is on a 1.25° × 1° longitude–latitude grid. The model contains 33 vertical hybrid sigma–pressure levels (Simmons and Burridge 1981) extending from the surface to 1 hPa. Convection is parameterized in terms of a double plume scheme, which is similar to the shallow convection scheme described in Bretherton et al. (2004a) but extended to include an additional plume to represent deep convection. Further details about the model configuration and its initial performance have been documented by Zhao et al. (2018a,b).
The simulations presented here are made using prescribed present-day sea surface temperature boundary conditions (Zhao et al. 2018a). The experiments are run for 1 year as spinup and then run for an additional 10 years. We analyze the last 10 years of the simulation. Because we are mainly interested in the dynamics of SMDs in this model, we restrict our analysis to the boreal summer months of June–September (JJAS).
The following AM4.0 fields are used in this study: the horizontal winds u and υ, geopotential height Z, specific humidity q, precipitation P, dry static energy s, frozen moist static energy h, surface and top of the atmosphere shortwave (SW) and longwave (LW) radiative fluxes, and surface sensible H and latent heat fluxes E. In addition to daily data from AM4.0, two other datasets are used in this study. We make use of the 1.5° × 1.5° horizontal resolution, daily geopotential height and wind data from ERA-Interim (Dee et al. 2011) for the 33-yr time period of 1979–2011. Rainfall data from the Tropical Rainfall Measuring Mission product 3B42 (TRMM-3B42; Huffman et al. 2007) from 1998 to 2011 are also used in this study.
b. Methods
Many of the results shown in the following sections are obtained through linear regression analysis, following the method described in Adames and Wallace (2014). We create a time series that describes the evolution of SMDs over the Bay of Bengal. Daily precipitation data, filtered to retain time scales shorter than 15 days and westward-propagating zonal wavenumbers 3–25 using the method of Hayashi (1979), are used to create this index. We chose this time scale and these zonal wavenumbers so that it fully captures the spectral signal associated with these disturbances, as will be shown in the next section. While we have verified that our results are reproducible using a 10- or 20-day high-pass filter, it is possible that our regression maps also contain a signal in the 10–20-day time scale of intraseasonal variability in this region (Annamalai and Slingo 2001).
The filtered data were averaged over the longitude–latitude box of 85°–90°E, 15°–20°N, where SMD activity is strongest (Sikka 1977; Godbole 1977; Boos et al. 2015). This method is similar to the method employed by Yoon and Chen (2005) and Chen et al. (2005). The index is standardized, and the anomaly patterns correspond to a one-standard-deviation anomaly of the precipitation time series. The statistical significance of the regression patterns was tested via a two-tailed t test, and the contour and shading intervals are selected to roughly represent the 95% confidence interval.
In section 3, we make use of space–time spectral analysis, following the methods of Wheeler and Kiladis (1999) and Hendon and Wheeler (2008). To extract the signal of SMDs, the time series of precipitation is divided into 60-day segments that overlap by 30 days. The segments are tapered to zero through the use of a Hanning window. We also use a Hanning window in longitude to emphasize tropical wave activity occurring over the longitude range of 50°–130°E. After tapering, complex fast Fourier transforms (FFTs) are computed in longitude and then in time. Finally, the power spectrum is averaged over all segments and over the 10°–25°N latitude belt. The number of degrees of freedom is calculated to be ~40 [2 (amplitude and phase) × 10 (years) × 122 (days in JJAS)/60 (segment length)]. We calculate the signal as 
Additionally, in sections 4–6, we employ a compositing technique in space that smooths out small-scale noise in the moisture and MSE budget terms so that the synoptic-scale structure of the SMD-related processes can be brought out more clearly. We will refer to this technique as an SMD composite. In this procedure, we generate multiple maps by shifting the longitude–latitude box of the SMD index (85°–90°E, 15°–20°N) by up to 2° north or south and/or west or east. For example, regression maps are generated by using indices centered on 85°–90°E, 14°–19°N or 85°–90°E, 16°–21°N. Each of these maps is then shifted such that the center of the moisture/MSE anomalies is centered over the 85°–90°E, 15°–20°N box. The SMD composite is then obtained by averaging all of the regression maps.
3. Monsoonal mean state and variability in AM4.0
Figure 1 shows the JJAS-mean 850-hPa geopotential height and horizontal winds for AM4.0 and ERA-Interim. AM4.0 captures the main features of the monsoonal circulation. The simulated monsoon trough is situated over northeast India, with the corresponding increase in height southward toward the Indian Ocean. A low-level westerly jet is seen in the area where the height gradient is strongest. There are also some differences with respect to ERA-Interim. AM4.0 exhibits stronger westerlies that extend farther eastward past the Philippines, and the geopotential height gradient is stronger. The difference in the westerly jet is further shown in Fig. 2, along with moisture, precipitation, and its variability. Mean precipitation (Figs. 2a,b) in AM4.0, while of similar magnitude to TRMM, occurs at different locations with respect to observations. TRMM shows rainfall maxima along the western coast of India and over the northeastern Bay of Bengal. AM4.0 exhibits a broader region of rainfall over northwest India that extends eastward and merges with a second region of maximum rainfall that is centered over the Bay of Bengal. The standard deviation of JJAS precipitation, shown in Fig. 2b, exhibits similar spatial patterns. Additionally, it is clear that TRMM precipitation exhibits a larger variance than the model does. This may be related to the inability of coarse-resolution GCMs to fully represent the topographic features of South Asia, thus not adequately representing their effects on precipitation.
Mean JJAS 850-hPa geopotential height (shading) and horizontal flow (arrows) for (a) AM4.0 and (b) ERA-Interim. The longest arrows correspond to winds of ~15 m s−1. White areas in (a) correspond to regions where the Z field is beneath the surface.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Mean JJAS 850-hPa zonal wind (contours) and (a) mean JJAS precipitation, (b) standard deviation of JJAS precipitation, (c) JJAS column-integrated water vapor 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Column-integrated water vapor, shown in Fig. 2c, exhibits horizontal pattern in AM4.0 that is consistent with reanalysis, although AM4.0 slightly overestimates column water in comparison to ERA-Interim. Column dry static energy, shown in Fig. 2d, exhibits slightly smaller values in AM4.0 than ERA-Interim. Nonetheless, the two datasets exhibit similar horizontal patterns, revealing that dry static energy (DSE) increases with latitude during JJAS over southern Asia. It will be shown in subsequent sections that this positive meridional DSE gradient plays a central role in the propagation of the SMDs. Column MSE, shown in Fig. 2e, is similar to column moisture except the MSE maximum is shifted northward.
Figure 3a shows the JJAS signal strength of precipitation in AM4.0 averaged over the 10°–25°N latitude belt. Variability in the South Asian monsoon region is governed by westward-propagating synoptic-scale disturbances (zonal wavenumbers 3–25) with time scales between 3 and 15 days. This range of zonal and temporal scales is consistent with the documented scale of SMDs (Sikka 1977; Godbole 1977; Stano et al. 2002; Hunt et al. 2016). A weaker signal is also seen at eastward-propagating zonal wavenumbers 1–20 and time scales longer than 30 days, likely in association with the boreal summer intraseasonal oscillation (BSISO). In comparison, the signal strength for TRMM-3B42 rainfall, shown in Fig. 3b, is slightly weaker but shows a nearly identical signal, with peak strength also occurring near zonal wavenumber 10 and 5-day time scales.
Signal strength of (left) AM4.0 and (right) TRMM-3B42 precipitation. The signal was obtained from data around the 10°–25°N latitude belt and longitudinally tapered to emphasize the Asian monsoon region over 50°–130°E. The dashed lines highlight the box used to define the filter used to analyze SMDs in this study.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Based on the space–time variability in Fig. 3, we construct an SMD index by filtering daily precipitation in order to retain westward-propagating zonal wavenumbers 3–25 and time scales of 15 days and shorter (dashed box in Fig. 3). We have verified that our results are robust to different choices of the filter as long as the frequencies and wavenumbers where SMD activity is strongest are included (see Fig. 3). The filtered precipitation field is then averaged over the 85°–90°E, 15°–20°N box. Regression maps of the horizontal structure of SMDs is shown in Fig. 4. At lag day −2, an anticyclonic feature is seen over northeast India, with negative precipitation anomalies centered near and to the west of the maximum height anomalies. This anticyclone reaches a peak amplitude over India and dissipates as it reaches the Arabian Sea at lag day 1. The anomalous anticyclone is followed by a cyclonic anomaly coupled to enhanced precipitation. The region of enhanced rainfall is first seen developing near the coast of Myanmar at lag day −2. At lag day −1, the precipitation anomalies have amplified and propagated west toward the Bay of Bengal. These anomalies are centered between the minimum height anomalies and anomalous northerly flow, consistent with observations (Warner 1984; Chen et al. 2005; Hunt et al. 2016) and previous modeling studies (Ashok et al. 2000; Sabre et al. 2000; Stowasser et al. 2009; Hunt and Turner 2017). In subsequent days, the region of enhanced precipitation follows a pattern similar to the anticyclone that preceded it. The horizontal structure and propagation of the depressions in Fig. 4 are similar to those seen in Fig. 2 of Daggupaty and Sikka (1977) and Fig. 4 of Yoon and Chen (2005).
Five-panel sequence of AM4.0 anomalous precipitation (shading), 850-hPa 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
We can obtain some insights into the vertical structure of the simulated SMDs by analyzing longitude–height cross sections. Figure 5 shows a cross section of anomalous geopotential height 
Longitude–height cross section of a monsoon low pressure system at lag day 0 averaged over the 10°–25°N latitude belt. (a) Meridional wind (shading) and geopotential height (contours) anomalies. Contour interval is 1.5 m. (b) Specific humidity q (shading) and vertical velocity (contours). Contour interval is 5 hPa day−1. The zonal mass circulation averaged over the 10°–25°N latitude belt is shown as arrows in (a) and (b). The largest zonal flux vector is about 0.5 kg m−2 s−1, and the largest vertical flux vector is about 0.001 kg m−2 s−1. (c) Anomalous column-averaged vertical velocity, precipitation, and column water vapor averaged over the 10°–25°N latitude belt. The fields have been normalized by their standard deviation to facilitate comparison.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
An interesting feature about the cross sections in Figs. 5a and 5b is the phasing between the fields. Both 
Figure 6 shows a time–longitude diagram of anomalous precipitation associated with SMDs. It is clear from this diagram that the SMDs are arranged into a packet of three to four westward-propagating vortices. Each anomaly propagates westward with a phase speed of ~−4 m s−1. The maximum amplitude of the enhanced and/or suppressed anomalies progressively shifts eastward, indicating that the wave train might be characterized by an eastward group velocity.
Time–longitude diagram of anomalous precipitation obtained from a lag regression of the SMD index described in section 2. The fields have been averaged over the 10°–25°N latitude belt. The contour interval is 0.2 mm day−1. The dotted lines that slant westward with increasing time represent constant phase speeds of −4 m s−1. The lines that slant eastward correspond to phase speeds of 2 m s−1.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
4. Column-integrated moisture budget
In the previous section, we analyzed the mean state and variability in the South Asian monsoon as simulated by AM4.0. Precipitation variability in this region is found to be predominantly due to synoptic-scale features that resemble SMDs. In this section, we will seek to understand the evolution of the precipitation anomalies in these systems by analyzing the evolution of column-integrated moisture. Figure 7a shows column-integrated moisture and precipitation in an SMD composite. The two fields are spatially correlated, with enhanced precipitation located in regions of enhanced moisture and vice versa for regions of suppressed precipitation. The correlation is clearer in Fig. 8, which shows the two fields in a scatterplot. A robust correlation of 0.84 is observed, further suggesting a strong coupling between the two fields. We can thus relate 
SMD composite at lag day 0 of anomalous column-integrated water vapor (contours) and (a) anomalous precipitation (shading) and (b) column-integrated vertical moisture advection (shading). The contour interval is 0.25 × 106 J m−2. The SMD composite is constructed by generating multiple regression maps from SMD indices that are slightly shifted in space (see section 2b). Each of these maps is then shifted such that the center of the moisture/MSE anomalies is centered over the 85°–90°E, 15°–20°N box. The SMD composite is an average of all the regression maps. The terms are multiplied by Lυ = 2.5 × 106 J kg−1 to facilitate comparison with the MSE budget. The 850-hPa anomalous horizontal winds are shown as arrows in (a) and (b). The longest arrows correspond to wind anomalies of ~2 m s−1.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Scatterplot of anomalous column-integrated water vapor 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
The contribution of each term in Eq. (2) to the propagation of the moisture anomalies is shown in Figs. 7 and 9. Precipitation (Fig. 7a) and vertical moisture advection (Fig. 7b) are the leading-order terms and largely cancel one another. The sum of the two terms (Fig. 9b) is ~15% as large as the individual terms that compose it. It moistens the atmosphere in regions of anomalous northerly flow and dries in regions of southerly flow. We see that 
SMD composite at lag day 0 of the (a)–(d) column-integrated moisture and (e)–(h) MSE budgets. In (a)–(d) column moisture is the contoured field, and (a) moisture tendency, (b) sum of vertical moisture advection and precipitation, (c) horizontal moisture advection, and (d) surface latent heat fluxes are the shaded fields. In (e)–(h) column MSE is the contoured field, and (e) the column MSE tendency, (f) vertical MSE advection, (g) horizontal MSE advection, and (h) longwave radiative heating are the shaded fields. Shading is in units of W m−2. The contour interval is 0.25 × 106 J m−2. The 850-hPa anomalous horizontal winds are shown as arrows. The longest arrows correspond to wind anomalies of ~2 m s−1.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
In comparison, horizontal moisture advection is largely in phase with the moisture anomalies and acts to damp them, with an additional component that shifts the moisture tendency poleward. Surface evaporation anomalies, shown in Fig. 9d, contribute little to the propagation of the moisture anomalies, only exhibiting significant anomalies over the Bay of Bengal.
Normalized contribution of the individual terms in the (a) column-integrated moisture and (b) MSE budgets to the (top) maintenance and (bottom) propagation of the regressed SMDs. The terms are obtained by projecting (top) 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Our results are qualitatively consistent with the analysis of Yoon and Chen (2005), who looked at the moisture budget of SMDs in ERA-40. They also found that the leading terms are vertical moisture advection (moisture convergence in their framework) and precipitation. However, they found that the total moisture tendency in SMDs was small. This may be largely explained by the small 10° × 10° box centered on the center of the vortex. Comparing with Fig. 9, it is clear that the use of this box tends to cancel out the positive moisture tendency to the west of the region of maximum anomalous precipitation and negative moisture tendency to the east. Yoon and Chen (2005) also found that surface evaporation anomalies play a larger role in SMDs than what is found here.
5. Frozen moist static energy budget
The column frozen MSE anomalies along with their tendency are shown in Fig. 9e. The 
The leading terms in the 
As in Fig. 9, but the shaded fields show (a) horizontal advection of low-frequency MSE by the high-frequency winds, (b) horizontal advection of high-frequency MSE by the low-frequency winds, (c) horizontal advection of high-frequency MSE advection by the high-frequency winds, and (d) the sum of (a)–(c). The 850-hPa anomalous horizontal winds are shown as arrows. The longest arrows correspond to wind anomalies of ~2 m s−1.
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
The contribution of each term to the propagation and maintenance of MSE is shown in Fig. 10b. It is clear that horizontal MSE advection is the largest contributor to the propagation of the MSE anomalies, with some offset from vertical MSE advection. Longwave radiative heating maintains MSE against vertical MSE advection.
6. Bridging the budgets
By combining Eqs. (2) and (8), it becomes clear that different processes contribute to vertical motion: convective and radiative heating, horizontal DSE advection, and the DSE tendency. The 
(a) As in Fig. 5c, but showing column-averaged 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
We can further investigate the contributions of the aforementioned components of vertical motion to the vertical moisture advection. Figure 13a shows that vertical moisture advection from 
SMD composite of (a) 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
(a) As in Fig. 10, but showing the contributions by, from left to right, 
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
Thus, that horizontal DSE advection contributes the most to the propagation of the MSE anomalies is consistent with the propagation of the moisture anomalies being predominantly due to the residual between the sum of vertical moisture advection and precipitation. Similarly, anomalous radiative heating induces vertical motion that supplies additional moisture to the region of anomalous precipitation in SMDs, acting to maintain it 
7. Concluding discussion
In this study we analyzed the column moisture and MSE budgets of synoptic-scale monsoon disturbances (SMDs) as simulated by GFDL’s AM4.0. AM4.0 captures a mean JJAS flow and horizontal distributions of moisture, DSE, and MSE that are consistent with those of ERA-Interim. However, the model fails to accurately describe the distribution of climatological-mean precipitation. In spite of this caveat, the model captures SMDs that are consistent with observations (Daggupaty and Sikka 1977; Chen et al. 2005). This result suggests that SMDs might not be sensitive to the details of the climatological-mean distribution of precipitation. A schematic summarizing the main results of this study is shown in Fig. 15.
Schematic describing the structure and propagation of an SMD as inferred from results of this study. (top) A longitude–height cross section and (bottom) a latitude–height cross section corresponding to the left side of the top panel (~83°E). The anomalous northerly winds (solid contours in top panel; arrow in bottom panel) advect warm air from the Indian subcontinent. This warm air ascends along lines of constant potential temperature θ (QG ascent; red vertical arrow), which moistens the free troposphere. This moistening creates a more favorable environment for deep convection (blue vertical arrows), which reaches a maximum amplitude to the west of the center of low pressure. The maximum in ascent (mixed blue and red arrow) is due to the sum of adiabatic ascent and convectively driven ascent. The rain area is maintained by the moist environment augmented by ascent driven by radiative heating (light orange arrows); L depicts the center of the low pressure system, and J represents the center of the low-level westerly jet. Flow out of the page is depicted by solid lines, and flow into the page is depicted by dashed lines. Liquid water content and ice crystals are depicted with circles, as in Janiga and Zhang (2016).
Citation: Journal of the Atmospheric Sciences 75, 6; 10.1175/JAS-D-17-0309.1
The simulated SMDs are found to exhibit a life cycle where they develop over the Bay of Bengal, attain a maximum amplitude as they make landfall over India, and then dissipate as they reach the Arabian Sea. While this life cycle is consistent with previous studies (Krishnamurthy and Ajayamohan 2010; Yoon and Chen 2005), it may also be due to our choice of index, which is centered near the coastline. A lag regression analysis reveals that these systems are arranged into wave trains of three to four events that propagate westward.
It is worth noting that the mean state in AM4.0 is characterized by excess precipitation over the tropical western North Pacific. This region was referred to in Fig. 10 of Zhao et al. (2018a) as the “Philippine hot spot.” This may increase the number of lows that propagate into the Bay of Bengal, contributing to the higher SMD spectral variance that AM4.0 exhibits with respect to TRMM-3B42 (see Fig. 3).
The column-integrated moisture and MSE budgets of the simulated SMDs are analyzed and compared in this study. In the moisture budget, it is found that the sum of vertical moisture advection and precipitation is the largest contributor to both the propagation and maintenance of the column moisture anomalies. This moisture tendency results from anomalous vertical moisture advection slightly leading the precipitation anomalies as the SMD propagates westward, indicating that vertical moisture advection from deep ascent moistens the troposphere prior to the maximum in anomalous precipitation, as summarized in Fig. 15. Similarly, vertical moisture advection maintains the precipitation anomalies against damping by horizontal advection.
The column MSE budget reveals that the processes that maintain the moisture anomalies in SMDs differ from those that induce its propagation. Horizontal MSE advection governs the propagation of the MSE anomalies. Because the horizontal structure of MSE advection differs from that of horizontal moisture advection, it is inferred that it is predominantly due to horizontal DSE advection. When both MSE and moisture budgets are considered together, we find that horizontal DSE advection induces vertical motion. This ascent, in turn, moistens the atmosphere to the west of the maximum precipitation anomalies (red arrow in Fig. 15). Ascent associated with horizontal DSE advection corresponds to lifting occurring along isentropic surfaces.
In contrast, it is found that longwave radiative heating maintains the MSE anomalies against dissipation from horizontal MSE advection. This anomalous heating induces vertical motion, which supplies the precipitation anomalies with additional water vapor (orange arrows in Fig. 15). The same mechanism is suggested to play a key role in the maintenance of the MJO (Andersen and Kuang 2012; Chikira 2014; Sobel et al. 2014; Wolding et al. 2016) and in convective self-aggregation (Bretherton et al. 2005; Wing and Emanuel 2014). The anomalous circulations associated with radiative heating have also been shown to play a role in maintaining breaks in the Indian monsoon (Prasanna and Annamalai 2012).
Many studies have used the quasigeostrophic (QG) omega equation to diagnose the region of anomalous precipitation (Mak 1982; Sanders 1984) in SMDs. In this study, QG vertical motion approximately corresponds to isentropic ascent 
The results shown in this study contrast to those presented by Boos et al. (2015). In their analysis of the vorticity budget of monsoon depressions, they found that the nonlinear horizontal vorticity advection, or “beta drift,” is responsible for the propagation of the vortex. For the moisture and MSE budgets considered here, we found that nonlinear terms contribute little to these budgets. These differences may be attributed to the choice of index. The index used by Boos et al. (2015) is based on stronger monsoon depression, while our linear regression index may be more representative of the weaker monsoon lows. It would be interesting to repeat the analysis presented here with an index such as the one used by Boos et al. (2015).
The results presented in this study indicate that analyzing moisture and MSE budgets provide useful insights into dynamics of SMDs. It would be interesting to compare these budgets to those of easterly waves both in the Pacific and over Africa. Furthermore, incorporating these equations into a linear theoretical framework for monsoon depressions may also shed light on our understanding of these systems. Such a framework is presented in a companion paper (Adames and Ming 2018).
Acknowledgments
This work was supported by the National Oceanic and Atmospheric Administration (NOAA) Grant NA15OAR4310099. We thank Isaac Held, Kuniaki Inoue, Brian Mapes, H. Annamalai, and an anonymous reviewer for comments that have helped improve the manuscript. We would also like to thank Ming Zhao for making the AM4.0 data available to us.
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