The spatiotemporal structure of precipitation in Indian monsoon depressions

Indian monsoon depressions are synoptic‐scale events typically spun up in the Bay of Bengal. They usually last 4–6 days, during which they propagate northwestward across the Indian subcontinent before dissipating over northwest India or Pakistan. They can have a significant effect on monsoon precipitation, particularly in primarily agrarian northern India, and therefore quantifying their structure and variability and evaluating these in numerical weather prediction (NWP) models and general circulation models (GCMs) is of critical importance. In this study, satellite data from CloudSat and recently concluded Tropical Rainfall Measuring Mission (TRMM) missions are used in conjunction with an independently evaluated tracking algorithm to form a three‐dimensional composite image of cloud structure and precipitation within monsoon depressions. The composite comprises 34 depressions from the 1998–2014 TRMM mission and 12 from the 2007–present CloudSat mission and is statistically robust enough to allow significant probing of the spatiotemporal characteristics of moisture and hydrometeor fields. Among the key results of this work are the following: the discovery and characterization of a bimodal, diurnal cycle in surface precipitation; the first picture of the structure of cloud type and density in depressions, showing that deep convection dominates south of the centre and prominent cirrus throughout; the first composite picture of vertical hydrometeor structure in depressions, showing significant precipitation for hundreds of kilometres outside the centre and well past the mid‐troposphere; and a novel discussion of drop‐size distributions (showing significant uniformity across the depression) and the resulting latent heat profiles, showing that average heating rates near the centre can reach 2 K h‐1.


Introduction
Indian monsoon depressions (MDs) are synoptic-scale disturbances that originate near the head of the Bay of Bengal or in the Indian monsoon trough region (Sikka, 1977;Krishnamurthy and Shukla, 2007;Hurley and Boos, 2015;. With a typical frequency of 2-5 per summer and an average duration of 4-6 days (Godbole, 1977;Saha et al., 1981;Sarker and Choudhary, 1988;Hurley and Boos, 2015;, they are an important feature of the Indian monsoon, capable of providing very heavy precipitation across much of northern India (Godbole, 1977;Stano et al., 2002;, which, as a predominantly agrarian society, relies prominently on rainfall. It is therefore crucial to have a clear understanding of the hydrometeor structure and moist thermodynamic processes of these events. Short and Nakamura (2000) and Fu and Liu (2001) provided the first analyses of the vertical structure of rainfall rates in the tropics using satellite data, preceding the case study of the three 1999 depressions by Stano et al. (2002). Since then, there have been numerous further studies using the Tropical Rainfall Measuring Mission (TRMM), but none exploiting the depth of such satellite data on the nearly 40 MDs that have occurred since the launch of TRMM. Recently, Bowman and Fowler (2015) used TRMM to examine the diurnal structure of tropical cyclones, showing that precipitation within 500 km of the centre had a diurnal cycle with a maximum in the early morning.
We remain, therefore, without even a basic understanding of the moist processes that occur in MDs. Whilst it has been known for some time that the maximum surface precipitation is to be found several hundred kilometres southwest of the depression Gridded global precipitation Huffman et al. (1995Huffman et al. ( , 1997Huffman et al. ( , 2007Huffman et al. ( , 2010; Huffman (1997) centre (Roy and Roy, 1930;Ramanathan and Ramakrishnan, 1933;Mull and Rao, 1949;Desai, 1951;Petterssen, 1956;Mooley, 1973;Godbole, 1977;Daggupaty and Sikka, 1977;Stano et al., 2002;Yoon and Chen, 2005;, there is no certainty on the generating mechanism and several prevailing theories result: the westward axial tilt of the core with height, collocation with a lower-troposphere convergence maximum, cyclonic mixing of cool monsoon circulation with warm, moist southwesterlies from the Bay of Bengal, or even some combination of these. Most recently, Yoon and Chen (2005) suggested that this asymmetry was a consequence of MD water-vapour flux convergence coupling with longer-period modes of monsoon variability, but showed only that these (10-20 and 30-60 days) modes could enhance or suppress the MD rainfall, not that they were necessarily the reason for the location of its maximum. Sørland and Sorteberg (2015) tracked 39 monsoon lowpressure systems (LPSs) associated with daily extreme rainfall events as given by the gridded gauge precipitation dataset of the India Meteorological Department (Rajeevan et al., 2005(Rajeevan et al., , 2006; they attempted to correlate precipitation rates in these LPSs with prognostic parameters, finding the most significant correlation was with 750 hPa vertical velocity. They also posited that a strong negative correlation between surface rain rate and 950 hPa temperature indicated that evaporative cooling from precipitation was responsible for the lower tropospheric cold core (e.g. Godbole, 1977;Hurley and Boos, 2015; of MDs.
This study comprises three main parts: after discussing the data and methodology in section 2, we will look at TRMM and CloudSat-derived composites in section 3, compare these with a specific case study in section 4 and then explore the diurnal pattern in section 5, before concluding in section 6.

Tropical Rainfall Measuring Mission
This study makes substantial use of data from the TRMM satellite mission, which was operational between December 1997 and October 2014 (Simpson et al., 1988(Simpson et al., , 1996Kummerow et al., 1998Kummerow et al., , 2000. It accommodated five instruments: the TRMM Microwave Imager (TMI); the Precipitation Radar (PR); the Visible Infrared Radiometer (VIRS); the Cloud and Earth Radiant Energy Sensor (CERES); and the Lightning Imaging Sensor (LIS). Throughout, we will be concerned with data output products that inherits from the first three. The PR was a Ku-band radar working at 13.8 GHz (Kawanishi et al., 1993(Kawanishi et al., , 2000 that provided high spatiotemporal resolution three-dimensional precipitation measurements over both land and ocean and is the primary source of these datasets; for a summary of which TRMM data are used in this study, see Table 1. The level-2 algorithms (those prefixed with '2') retain  Haynes et al. (2009) the resolution and footprint of the original satellite swath, a 220 km wide track at 4 km × 4 km × 250 m (80 vertical levels) * ; in contrast, the level-3 algorithm used here has global coverage between the 50th parallels and is a multi-satellite product, also comprising inputs from GMS, . This surface precipitation product has a resolution of 0.25 • × 0.25 • .

CloudSat
CloudSat is a National Aeronautics and Space Administration (NASA) polar-orbiting A-Train satellite primarily equipped with a 94 GHz cloud-profiling active reflectivity radar , which measures the backscattered energy from clouds and precipitation. It has been in almost continuous operation since June 2006 and, via the CloudSat Data Processing Centre at Colorado State University, the mission releases numerous cloud quantification and thermodynamic datasets. A summary of those datasets used in this study is given in Table 2. The radar measures nadir only and therefore the output swaths have zero width; the along-track resolution is 1.7 km and there are 125 vertical levels at a resolution of 250 m.

ERA-Interim
We will make occasional use of the European Centre for Medium-Range Weather Forecasts (ECMWF) authored ERA-Interim (ERA-I) reanalysis product. This has six-hourly global coverage at T255 (∼ 77 km at the equator) resolution (Dee et al., 2011). Quite a number of products are available on a global Gaussian grid, either at the surface, on pressure levels (37 in total, from 1000 to 1 hPa) or at sigma or potential vorticity levels. There are also some precipitation-related datasets within ERA-I, but, as a prognostic variable, it has poor skill when compared with satellite observations (Liu et al., 2014).  outlined a wind-thresholded vorticity-pressure feature-tracking algorithm applied to ERA-Interim reanalysis data over the Indian subcontinent for the period 1979-2014, wherein they identified and corroborated 106 MDs with genesis over either the Bay of Bengal or the subcontinent itself; we shall be using the relevant subset of that data for the TRMM (CloudSat) operation period: 34 (12) depressions during 1998-2014 (2007-present). Furthermore, in some instances (usage of the 3B42 data) we replicate the rotation-composition method of  (also used in e.g. Catto et al. 2010): for each MD time step, the depression heading is calculated; the data are then reoriented, centralized and composited on to a new grid such that the composite heading is due north and the 850 hPa relative vorticity maximum lies above the latitude-longitude origin.

Compositing
Where data are sparser, compositing the data in this manner is not statistically robust. Instead we can boost the sample size artificially by collapsing the azimuthal dimension and treating the composite data as a function only of radius and height. This introduces a degeneracy that we can exploit to examine an asymmetry of our choice. The largest mode of spatial asymmetry in MDs is caused by the presence of the Himalayas  and so we shall henceforth define the pseudoradial coordinate, with magnitude equal to the radius and the sign of the normalized latitude; for example, a point 440 km westsouthwest (or any bearing between 90 • and 270 • ) of the centre would have a pseudoradius of −440 km (or −4 • using the 111 km per degree employed in this study). This method was developed with CloudSat data in mind, but for consistency has been extended to discussions of vertical structure derived from TRMM products.

Composite structure
Firstly, we shall build a three-dimensional composite in the manner outlined in section 2.2. It is important to gauge the mean structure of precipitation and cloud attributes for two reasons: so that we have a fundamental base for further analysis and because, as the leading-order moment, this is what any model should primarily be tested against.

Hydrometeor distributions
Arguably the outright most important feature of an MD is surface precipitation, so we shall open our discussion of mean structure with this field. Figure 1 presents this in two ways: (i) rotated, i.e. the data from each time step are rotated such that the depression propagates along zero bearing, and (ii) unrotated.
Note that Figure 1(a) comprises the same data as Figure 4(a) from . The most striking difference between the two, noting the different colour scales, is the magnitude of the central maximum; there are two factors causing it to be reduced in the rotated composite: implicit smoothing during interpolation on to the rotated grid and the temporal variability of the location of the maximum precipitation in the rotated coordinates (providing extra variance associated with the spread of headings). We should note that both of these factors are unique to precipitation fields, which have categorically the highest variance of any common meteorological variable and which uniquely do not have composite extrema collocated with the depression centre. As discussed previously, we see the maximum surface precipitation located several hundred kilometres southwest; it has a maximum magnitude of over 70 mm day −1 at 1.4 • S, 1.7 • W and falls away quickly except for a band in the east representing orographic rainfall along the coast of the Bay of Bengal.
We are now in a position to explore the composite vertical structure of precipitation. The simplest manifestation of this is rain rate, shown in Figure 2; ground clutter returns and any missing data are not included in the composite, therefore any part of the composite with no useful data is shown as the background grey colour. The seemingly very high rainfall rates shown near the surface are an artefact of this process: there, only very high radar reflectivities can surpass ground clutter. The general structure is what we might expect on consideration of the surface precipitation shown in Figure 1; indeed, the data from (b) of that figure are collapsed on to the pseudoradius coordinate for illustration. Here, the asymmetry is stark: the strongest rains both at the surface and aloft are found several hundred kilometres away from the centre, in the southern half. We note also that the rainfall rates in the upper mid-troposphere (∼ 7 km) are proportional to those much nearer the surface, implying that most surface rainfall is the result of deep convective processes. The effect of the Himalayas in the northern half can also be seen: the ratio of rainfall aloft to that near the surface is higher in the south (e.g. 10-15 • ) than the north, implying orographic forcing there. Now we have an idea of the rainfall rates throughout the composite MD, we can use data from TRMM 2B31 to estimate raindrop size distributions (DSDs); doing so will further assist our investigation into the physics driving hydrometeors in MDs. We obviously cannot show the varying DSDs throughout the composite, so instead a figure showing the modal raindrop size throughout the MD with some selected DSDs is given ( Figure 3). Calculating these distributions is non-trivial and it is beyond the scope of this study to describe the full calculation here; for a full derivation, the reader is encouraged to visit Haddad et al. (1997a). What the figure shows us is that there is a well-defined area where the TRMM 2B31 algorithm believes that there is rain and within it the modal drop size has fairly low variance. It is  Composite vertical profile of rain rate (mm day −1 , coloured contours) from TRMM 2A25 as a function of pseudoradius. Overlaid as a dark grey line for illustration is the (unrotated) composite surface rain rate (mm day −1 , right axis) from TRMM 3B42 (see Figure 1(a)), also as a function of pseudoradius. Note that the lowest contour is coloured white and the background grey. particularly interesting to note that, whilst the highest rainfall rates (see Figure 2) and highest raindrop number densities are found to the south of the centre, the largest drops tend to be found at the centre itself. Raindrop size appears, at least south of the centre, to be fairly uniform with height until within a kilometre or so of the apparent cloud top. This uniformity indicates that these southern areas are well mixed in depth, in contrast with the centre itself, where the drop size generally increases with height, implying strong ascent there. Finally, we can complete our discussion on the composite hydrometeor structure by considering the distribution of frozen water in MDs. Figure 4 shows the expected densities of snow and graupel in the composite MD, as well as the average freezing, bright band and storm heights. The maxima for snow and graupel densities are to be found directly above the highest rain rates, indicating that an area of deep convection is responsible for both. This is supported by the graupel having a comparable (or even greater) density to snow, indicating the presence of some mixing process allowing the aggregation and refreezing of the latter into the former. One might be surprised to see that there is a very low frozen hydrometeor density in the north around the Himalayas, but this is simply explained: the climatological freezing height in the Himalayan foothills is over 5 km, but almost all rainfall there is orographic and happens below this altitude, resulting in very little ice formation. The height of the bright band gives us an indication of where extant falling snow is melting most rapidly -we do not expect this to be necessarily at the freezing height, because there is a fairly shallow temperature gradient and ice has a finite heat capacity. The difference between the bright band and freezing heights can be interpreted as a weak metric for vertical wind speed.

Cloud scenario
The importance of classifying clouds in a hydrometeor-based compositing study such as this is clear: the presence of different types of cloud represent the dominance of crucially different precipitating and non-precipitating mechanisms in the atmosphere. If we can constrain the types most likely to be present throughout the MD, we can evaluate the physics behind their representation in GCMs and NWPs better.
The CloudSat 2B-CLDCLASS product classifies cloud types by using constraints such as spatial cloud properties, cloud temperature, the existence of precipitation and radiance measurements from other A-Train satellites (Wang and Sassen, 2007). The category bins are as follows: clear, cirrus, altostratus, altocumulus, stratus, stratocumulus, cumulus, nimbostratus and deep convection, all of which can be found in the Tropics (Sassen and Wang, 2008) and indeed over India. Regridding discrete, qualitative data must be done carefully: we cannot simply compute an interpolating function or calculate distribution moments; instead we must consider the mode. Heeding this, the modal cloud-type composite is given in Figure 5. Here, the hue is a function of the most common type (excluding clear sky); the transparency is zero (i.e. fully opaque) if the ratio of the modal frequency (including clear sky) is greater than or equal to 0.5; Differing hues represent varying cloud types, with the transparency in each case proportional to the ratio of the modal value and the number of overpasses up to a value of 0.5. Parts of the composite not comprising at least ten satellite overpasses are not shown here. We remind the reader that CloudSat height is referenced above the geoid, rather than necessarily the Earth's surface. below this value they are directly proportional. For example, if the modal cloud type in a particular instance was altostratus and it was present in 30% of the composite, it would be represented in the figure as a red hue with 60% opacity (40% transparency).
The figure shows that despite all clouds types being present, there are three distinct domains of cloud structure. In the far south, there is the stratification one might expect in a typical tropical environment (Stein et al., 2011): convective clouds in the lower troposphere, becoming altostratus in the mid-troposphere and cirrus tending towards the tropopause; as we move closer to the centre, the initially low-level convective clouds suddenly dominate throughout the height of the troposphere, even rising higher than the cirrus further afield. In the north, however, whilst there is some deep convection much closer to the centre, it tends to be much more mixed: there is some mid-level stratus present, indicating that the Himalayas are forcing orographic cloud there. We might suppose that if the height coordinate were measured from the actual surface, rather than the geoid, in the north we would recover dominant stratus at/near the surface; this is indeed the case, although it is not shown here.
We can use these data to explore a little further: by considering the fraction of overpasses that detect cloud (as opposed to clear sky) to generate a cloud-cover variable; the result is shown in Figure 6. Here, both the composite from CloudSat overpasses and an equivalently constructed composite from ERA-I are shown. Both have clearly captured some structure, but there are stark differences: the ERA-I composite has substantially less cloud in the mid-troposphere, where it suggests almost no cover at all, and in the lower troposphere, where the deep convection is poorly resolved. The ERA-I derived composite does, however, capture the asymmetry and the high-level cloud structure well compared with CloudSat. Unfortunately, since the comparison of the global all-year climatologies of satellite and reanalysis cloud cover by Jakob (1999), there has been no further research on comparison of these cloud products in the tropics. Now, we wish to explore the convective and non-convective spatial regimes of the composite MD. Such analysis has been done before using contoured frequency by altitude diagrams (CFADs), for single events (e.g. Yuter and Houze, 1995), domain composites (e.g. Liu et al., 2010) and system composites (e.g. Hence and Houze, 2011). CFADs display normalized histograms of radar reflectivities as a function of height and have specifically been used for cloud-type analysis with both the 13.8 GHz TRMM PR (Houze et al., 2007) and the 94 GHz CloudSat radar (Young, 2015). We hypothesize three distinct regimes from , we see that the CFAD at a pseudoradius of −4 • has a very strong resemblance to their composite of convective cloud structure. Conversely, the CFAD at 10 • pseudoradius has a clearly stratiform structure, as we might expect from our earlier analysis. Finally, at a pseudoradius of −10 • , we note more of a mixed regime, with a slight preference for convective structure, albeit with a less common occurence than that observed nearer the centre. Repeating this analysis for Figure 8 by comparison with the 94 GHz reflectivity CFAD composites over Africa from Young (2015), we build a very simlar picture: mixed with occasional convection at −10 • ; common convection at −4 • ; and common stratiform at 10 • . Here we also note the strong attentuation in the higher frequency CloudSat radar reflectivity, particularly below 4 km, as also noted by Sindhu and Bhat (2013).
We can attempt to delineate these regimes further by considering the 'rain type' product from TRMM 2A23 alongside the simultaneous estimated surface rainfall rate to explore any spatial coherence in precipitation attributable to convective and stratiform processes, respectively. The TRMM 2A23 rain-type algorithm uses a combination of two methods (Awaka et al., 2007) to determine what type of process rain, if existent, is likely to be have been generated by. The first, the V-method, determines that precipitation is stratiform if a bright band exists and convective if there is no bright band but the radar reflectivity is above a threshold of 39 dBZ; otherwise, it determines it to be 'other'. The second, the H-method (based on Steiner et al., 1995), requires several criteria (39 dBZ reflectivity threshold, high signal-to-noise ratio) to make the determination of convective precipitation; if these criteria are not met but rain is still certain, it is determined to be stratiform; if the signal-to-noise ratio is too weak but rain is possible, it is assigned 'other'. Subsequently, the 2A23 rain-type algorithm determines that precipitation is definitely stratiform if it is V-stratiform or H-stratiform/other and correspondingly convective if it is V-convective/other or Hconvective. If the H-method and V-method explicitly disagree, preference is given to the V-method; this, with other sensible combinations comprise the maybe and probable levels of each type. If neither method can make a determination, but rain is certain, it is given the 'other' category. Figure 9 shows the composite proportion of TRMM 2A25 estimated surface precipitation rate definitely attributable to convective and stratiform systems according to the TRMM 2A23 rain-type algorithm, as well as the remainder. Overall, approximately half of the rainfall is attributed, but the algorithm struggled considerably around the Himalayas and south of the peninsula. There is an arguably greater propensity for convective precipitation in the northwest, as the MD starts to push into the drier desert environment of Pakistan; there is significant area of more likely stratiform precipitation southwest of the centre, a little further out than the location of the precipitation maximum. Figure 10 shows the composite proportion of surface precipitation that is at least maybe attributable to convective and stratiform systems, again with the remainder on the right. This time, almost all rainfall events have been assigned a type, bar a handful of outliers. This looks much like an amplification  of the signals in Figure 9, except that the rainfall over/around the Himalayas has mostly been designated as stratiform (as we would expect). It is not obvious why we see the high (∼ 50% definite, ∼ 80% maybe) stratiform allocation covering a significant area approximately 500 km southwest of the centre, as we might expect this to be quite convective. Given that the stratiform allocation relies strongly on bright band detection and we know one can exist there, even in the clearly convective regime closer to the centre (cf. Figures 4 and 5), this could be tricking the algorithm into the wrong diagnosis. Houze (1997) discussed this apparent problem in some detail, but it is clear we should interpret the results displayed in Figures 9 and 10 with due caution.

Diabatic heating: latent and radiative
Whilst much of the thermodynamics in the atmosphere are dominated by adiabatic processes, in the tropics, and particularly in cyclonic tropical systems where precipitation and cloud cover are appreciably increased, we must also consider diabatic processes in order to form a complete picture. MDs have dense cloud cover at all levels (Godbole, 1977;, resulting in complicated radiative heating/cooling profiles, which, in this study, we will attempt to demonstrate. Further, the constant flux and phase changing of atmospheric moisture in MDs results in widespread latent heating/cooling. By far the most most important phase transition in MDs is lower-tropospheric condensation of warm, water-vapour laden air rising from near the surface (with a secondary contribution from freezing in the mid-troposphere). It has long been proposed that this latent heat release is intrinsic to conditional instability of the second kind and is a potential source of energy for MDs moving over the ocean (Shukla, 1978). The CloudSat-derived radiative heating profile is shown in Figure 11 and looks as we might naively expect from inspection of the cloud cover in Figure 6: substantial short-wave heating at and slightly beneath the cloud tops (particularly the thicker convective clouds) and long-wave cooling elsewhere. The composite heating rates in the upper troposphere south of the centre can reach over 0.2 K h −1 ; this value is more than an order of magnitude less than what one might expect at the top of a tropical anvil (Ackerman et al., 1988), but still considerably more than the summer monsoon climatology (not shown). The small magnitude arises because, while the MD is dominated by instances of deep convection, the cloud tops of which are strongly heated, these vary in height and precise location and are thus smoothed out in the composite. We will later evaluate this discussion in the context of a case study, in particular diagnosing the features of a large anvil structure. We can use data from TRMM to inspect the composite latent heating profile, which is given in Figure 12. This figure also shows two 1D profiles through selected pseudoradii. We can instantly deduce that latent heating is the larger of the two diabatic heat sources in MDs, as it is in the tropics in general (Roca et al., 2010): the intense convective rain south of centre leads to a composite mean latent heating rate of as much as 1.8 K h −1 in the mid-troposphere, supporting the warm core found there in other studies (e.g. Godbole, 1977, and many others).

Reanalysis composite
We can use ERA-Interim reanalysis data to construct a few more useful composites and complete our discussion. Figure 13 shows the structures of (a) temperature anomaly, (b) vertical velocity and (c) divergence, respectively, and we can use these to develop the ideas introduced in this section so far. These reanalysis composites are constructed in the same way as those previously derived from satellite data in this study. The similarity of all three panels to those computed from the full three-dimensional composite technique used for MDs in  is a useful indicator that the pseudoradial method used here is robust. Summarizing briefly, we have found that the region of maximum rainfall in MDs is collocated with a significant area of deep convection and intense low-tropospheric latent heating rates. There is no clear significant cloud structure to the north of the depression, other than the presence of orographically induced stratus, which are also associated with increased rainfall. Figure 13(a) shows the composite vertical temperature structure, taken as an anomaly to the June-September summer climatology. It bears some horizontal resemblance to the two diabatic heating fields discussed in the previous section, but this semblance is lost in the vertical. Monsoon depressions are roughly in thermal wind balance, so we should not expect to be able to explain the gross thermal structure in terms of local heating rates (especially radiative); however, it is not implausible that the strong latent heating in the lower middle troposphere warms air that is subsequently lifted by the deep convection in which it generally sits. Figure 13(b) shows vertical velocity; this is provided by ERA-Interim as ω (= ∂P/∂t) and has been converted to w (= ∂h/∂t) here for convenience. There is a fairly strong similarity between this field and the observed cloud-cover structure shown in Figure 6, indicating (as expected) that much of this cloud is convective; we can support this assertion further by noting that the maximum upward speed in the lower troposphere is collocated with the maximum rainfall rates (see Figure 2) at each height. Finally, in Figure 13(c), a composite of divergence is shown. Given the results so far and in particular bearing in mind the theory suggested by Yoon and Chen (2005) that  the rainfall asymmetry in a depression is controlled by lowlevel moisture convergence modulated by larger-scale monsoon variability, the fact that the rainfall and convergence maxima are not collocated is perhaps surprising. Given that the gradient of specific humidity across the depression is not steep enough to shift the moisture flux convergence maximum far from the air convergence maximum, moisture convergence is not the mechanism responsible for the asymmetry, in accord with the moisture trajectory analysis of , who found that the dominant moisture flux convergence terms in MDs were slightly asymmetrical but not off-centre enough to explain the precipitation maximum correctly. Recalling, then, the three suggested theories for the precipitation southwest maximum in Mooley (1973), we can now rule out the hypothesis that the asymmetry is caused by an off-centre moisture-flux convergence maximum. Further, inspection of Figure 6 very strongly suggests that this phenomenon is not due to the westward axial tilt observed in some fields of the MD with height. Ruling these out leaves us with the hypothesis that this activity peaks southwest of the centre due to the cyclonic mixing (and subsequent forced ascent) of warm, humid air from the Arabian Sea with the cooler, drier, continental air mass. If this is correct, this feature would be unique to the monsoon depressions of India; unfortunately, a detailed study of rainfall in global monsoon depressions has not yet been carried out, but some case-study analysis of Australian monsoon depressions by Zhao and Mills (1991) and a more recent study by Berry et al. (2012) of objectively tracked Australian monsoon disturbances suggest that this is indeed the case.

Case study
The nature of this research prompts a validation of the satellite products, both with each other and with independent data. For this purpose, we carry out a case study, which benefits us further with some validation of the composite discussed previously. We select an event where TRMM and CloudSat overpasses intersect near an MD centre within a short time frame. The best such example was the MD of early July 2007; see Figure 14: the overpass intersection was separated by 62 minutes at a distance of just 96 km from the depression centre. This figure also shows the locations of the sixteen gauge sites used for TRMM validation later in this section, as well as the total accumulated rainfall (if > 20 mm) for the UTC day 7 July 2007, for which the depression started on the yellow marker and progressed westward by four markers. This shows well the propensity for an MD rainfall maximum to be southwest of the centre, which is in fact where almost all the heavy rainfall is; recall that the central India average daily rainfall in July is approximately 10 mm day −1 and so even the lowest contour here is twice that value. Note also the presence of an unrelated storm over northeast India and the coastal rainfall associated with southeast Asia, as well as significantly enhanced rainfall over the Western Ghats as a result of the MD enhancing westerlies there. This pattern agrees with , who found that depressions result in enhanced rainfall along the Western Ghats and along the coast of southeast Asia (among other areas). The July 2007  and Chittagong (C). Overlaid (coloured contours, mm) is the total precipitation for the UTC day 7 July.
the Bay of Bengal before making landfall in Bangladesh/northeast India, propagating parallel to the Himalayas before dissipating over northwest India. This makes it a good candidate for this case study, in that there is nothing unusual we should be aware of. We now have an idea of the basic footprint of this particular MD and are in a position to look at the respective TRMM and CloudSat overpasses. Selected data from each are shown in Figure 15, with TRMM in the top three panels, CloudSat in the next three and ERA-Interim (following the CloudSat trajectory, but approximately 3 h earlier). Each panel is directly analogous to a figure discussed in the previous section, with the exception of the third-from-bottom subfigure, which shows the reflectivity (dBZ) measured by CloudSat. For each satellite, the data are represented as projections on to the longest global coordinate axis for the overpass in question: latitude for the polar-orbiting CloudSat and longitude for the 35 • inclination TRMM. Since TRMM data are from finite-width swaths, these are meridionally averaged before projection. The location of the centre of the depression at the time of the overpasses was 22.5 • N, 81.6 • E, and these values on their respective axes in Figure 15 should be taken as such -they are marked with a 'C'. Both overpasses indicate that there is some activity directly over the centre, but that there is more intense activity several hundred kilometres away (distinct for each overpass). The data from CloudSat indicate that the centre sits under the edge of a very large anvil cloud, the shape of which is well captured; large radiative heating across the top and a strong (subsequently attenuated) reflectivity indicate the presence of dense, tall cloud here. There is also evidence of some activity in the north too, with stratiform and orographic cloud present around the Himalayas. The TRMM overpass was slightly less fortunate with positioning, but still captured some interesting features: a convective bloom approximately 500 km to the west of the depression, some activity associated with the centre and an area to its north, and the coastal rainfall of southeast Asia. All three areas demonstrate convective activity, but the area north of the MD centre has the weakest: we might expect this, given the previous analysis, but even so, there are rainfall rates here of up to 10 mm h −1 driving latent heating of the order of 10 K h −1 .
We cannot say with certainty that the deepest convection (in the northwest) is necessarily associated with the depression, but inspection of Figure 14 suggests that it is probable. The inclusion of some almost contemporaneous ERA-Interim data, nearest-neighbour-interpolated to the CloudSat ground track, permits us to make some general comments on the thermodynamical interpretation of these fields. Firstly, we must note that ERA-Interim has a fairly coarse spatial and temporal resolution: the latter constraint requires us to choose the 1200Z fields, nearly three hours after the relevant CloudSat overpass; this discrepancy will cause some apparent displacement when comparing fields from both. Secondly, we also note that the temperature field is taken as an anomaly to the June-September climatology, computed on a grid point by grid point basis. In both reanalysis fields presented in Figure 15, the form quite closely resembles the gross composite structure computed by ; however, there are also some distinctive features to remark upon.
With some confidence, we can associate the strong vertical lifting at approximately 22 • N with the deepest convection, but we also note that much of that same anvil is collocated with lifting confined to the lower troposphere and is flanked by large areas of upper/mid-tropospheric subsidence that appear to be suppressing convection; there is also a deep anomalously warm core aloft with large spatial extent, overlapping both the deep convection and the surrounding area of descent. The large spatial extent of the depression -examination of the anomalous zonal wind (not shown) indicates that 10 m s −1 isosurfaces reach beyond the 15th and 30th parallels -makes it highly plausible that the anomalous ascent at the Himalayan foothills and resulting cloud structure there are also directly related to the circulation of the MD.
The individuality of this MD shows that the results of section 2.2 should be treated as a composite, not a 'mean-state' depression, as can be done for less spatially variable fields . We can, however, create a composite representation showing the mean when the field is non-zero alongside the probability that that is the case (e.g. the mean rain rate when there is rain and the overall probability of rain for that location). If we do this, we find two things: firstly, that the shape is very similar, with the small exception of a more prominent local extremum at the centre; secondly, the magnitude of all hydrometeor and diabatic heating fields is roughly doubled. The first point supports usage of the composite in the form given throughout this study, as the main source of structure in it is the magnitude of the fields, not the probability of activity at that location. Now that we have an instantaneous snapshot of this depression, we can further our understanding by examining how its passage affects the atmosphere around it using observational data. Such analysis is fairly rife in literature on a case study by case study or small composite basis (e.g. Koteswaram and George, 1960;Krishnamurti et al., 1975Krishnamurti et al., , 1976Daggupaty and Sikka, 1977;Godbole, 1977) and aids understanding of the dynamics involved. The MD in question passed almost directly over a sounding station at Ranchi (see Figure 14), for which daily soundings are observed at 0000 UTC. Tephigrams presenting these data are displayed in Figure 16. As expected, they show a typically warm, moist, tropical atmospheric profile with strong vertical wind shear. As the MD passes overhead, the winds strengthen and moisture is carried a lot higher in the troposphere -the entire profile is almost saturated -and significant instabilities have developed, evidenced by the numerous inversions throughout. † Note that the superadiabatic layer between 850 and 800 hPa in Figure 16   the morning after the MD passed overhead (July 8) possesses the strongest winds (agreeing with the composite in , but is also several degrees warmer, since the moisture packed into the column during the previous day rains out and the thick cloud clears. We conclude this section with a brief validation of the TRMM 3B42 surface rainfall product against some station gauge data. This will, in general, help validate the composite image developed by providing some assurance that the presence of the depression does not cause TRMM to misestimate the rainfall wildly. Such evaluation has been covered in much greater detail for tropical cyclones by Chen et al. (2013) and over orography by Dinku et al. (2007Dinku et al. ( , 2008Dinku et al. ( , 2010; the former found that TRMM underestimated rainfall in tropical cyclones, particularly over land or near orography, the latter found that TRMM performed well over most orography, but with decreasing skill as the topography became more complex. For our evaluation, we will consider the mean and variance of both TRMM 3B42 and gauge-measured rainfall at the 16 stations presented in Figure 14 over the first half of July 2007. To use TRMM to estimate the daily rainfall accumulated at each station (reproducing the daily gauge data), we took the appropriate pixel (0.25 • ×0.25 • ) from TRMM 3B42 and averaged over the eight relevant three-hourly values. This and the gauge rainfall are shown in Figure 17. Further, as not all stations reported rainfall (zero or otherwise) on all days, the equivalent data were also masked in TRMM. Assuming the gauge data are true, the pattern and variance is captured well by TRMM, however the magnitude is underestimated by as much as 30% on average during the most intense rainfall. This value is in close agreement with that found by Pokhrel and Sikka (2013) for gridded TRMM PR values over the whole peninsula and surrounding ocean. The data from a selection of individual stations along the MD path are presented in Figure 18; they show both the clear westward propagation of the system and the consistency of rainfall underestimation by TRMM.

Diurnal variability
It is well known that the day-night cycle drives marked changes in the atmosphere and it is reasonable therefore to surmise that there will be some diurnal cycle in the thermodynamics of MDs. The better we can quantify this finer-scale variability, the more we can design our NWP models to provide higher quality forecasts. Yet, surprisingly, discussion on the diurnal variability of MDs is almost non-existent in the literature.  showed that there is a significant contrast between depressions during the day and at night: during the day, MDs are warmer and drier throughout, with a sizeable reduction in low-level cloud cover at the centre. Gauge values are given in green, TRMM 3B42 estimates are given in blue. Each is shown with a 1σ band. Where gauge measurements were missing, TRMM data were also omitted from the average. Recently Bowman and Fowler (2015) used surface rainfall data from TRMM 3B42 to perform a detailed investigation the diurnal cycle of precipitation in a global catalogue of tropical cyclones (IBTrACS, Knapp et al., 2010). They found the amplitude to vary unimodally over the diurnal cycle, with a maximum 7% greater than the mean centred at approximately 0600 local time. We are now in a position to repeat this analysis for the composite MD, as shown in Figure 19. This is performed on the rotated composite, because this filters out the diurnally varying land/seabreeze related coastal rainfall contribution from southeast Asia. The most immediate feature in Figure 19 is the diurnal cycle of the central maximum, which has a peak at 0000 UTC (0530 IST ‡ ). The ‡ Indian Standard Time surrounding rainfall also varies diurnally, but out of phase with the central maximum, similarly to the land-ocean contrast in the cycles displayed by the rain resulting from tropical convection (Nesbitt and Zipser, 2003;Kikuchi and Wang, 2008).
The thermodynamics behind both types of diurnal cycle are already well understood. Tropical convective precipitation peaks in the late afternoon as the result of a number of coupled processes, but can be thought of most simply as cumulative surface heating from insolation generating maxima in sensible and latent surface heat fluxes, promoting static destabilization (e.g. Byers and Braham, 1948;Ogura and Takahashi, 1971;Bechtold et al., 2004;Hirose and Nakamura, 2005). In contrast, the diurnal cycle of tropical cyclone precipitation is a result of the enhanced nocturnal radiative cooling of anvil cloud tops destabilizing the upper troposphere (e.g. Kraus, 1963;Tripoli, 1992), an effect with magnitude peaking around local dawn.
We propose that these fields can be simply modelled by fitting a sum of two arbitrarily phased two-dimensional Gaussian functions with some climatological offset (or residual), of the form P(x, y) = P residual (x, y) where P is the observed spatial distribution of the precipitation, P residual is the difference between the observed rainfall and the fitted function, n is an index for the two Gaussian functions, σ x and σ y refer to the standard deviation of the Gaussian along the x and y axes respectively, (x o , y o ) are the coordinates of the centre of the Gaussian and θ is its rotational phase. We can fit these parameters to our rotated ( 2016) data using the Levenberg-Marquadt algorithm (Levenberg, 1944;Marquadt, 1963), which interpolates between the gradientdescent and Gauss-Newton methods and is a common algorithm for least-squares curve fitting. Although rotation smooths the precipitation pattern (reducing derived intensities, see Figure 1), there is no significant dependence of MD propagation direction on the time of day, so calculations of the relative diurnal cycle will not be affected. Performing this analysis on the rotated composite yields a stable convergence for the fitting algorithm and a robust final fit; indeed, we recover both modes of the diurnal cycle ( Figure 20). The distribution given by this fitted function passes a Pearson's chi-squared goodness-of-fit test at a 95% confidence interval when compared with the observations. It is evident that the two modes are very much in antiphase and that the central mode is always responsible for the more intense rainfall: it has a mean value of 25.0 mm day −1 compared with 12.1 mm day −1 for the outer mode. However, both modes have a similar variability: 70% and 64% peak-to-trough for the central and outer modes, respectively. These values are markedly larger than that quoted by Bowman and Fowler (2015) for tropical cyclones, because we are considering two distinct modes varying in antiphase, but even if we only fit one Gaussian across the cycle we still recover a diurnal cycle with peak-to-trough variability of 36% and a maximum at 0000 UTC. We have shown, therefore, that MDs exhibit substantially greater diurnal variability in surface rainfall than tropical cyclones and that there are two main processes responsible for this precipitation. Further work is needed to determine to what extent these modes are coupled.
Analysis of the unrotated composite by empirical orthogonal function (EOF) decomposition shows that the diurnal cycle discussed here is the principal mode of variability; the second most dominant mode manifests as an east-west translation of the location of maximum rainfall that also varies on a diurnal cycle: eastmost at 0000 UTC, westmost at 1200 UTC. This could be due to the zonal gradient of heat flux from the ground as maximum insolation moves westward throughout the day, or some more complicated Rossby-wave dynamics via land-sea thermal contrast.

Conclusions
Indian monsoon depressions are relatively long-lived tropical lows that usually cross central India several times each summer. They are exceptionally moist synoptic-scale systems that often increase precipitation in north and central India drastically during their passage across the subcontinent. A description of the precipitating processes and moist thermodynamics of MDs is therefore important for scientific understanding and the evaluation of climate models and NWPs, so that their potential impact on the urban and agrarian cultures in flood-susceptible areas can be better constrained. The method presented here provides a basis whereby MDs in NWP models and GCMs can also be composited and subsequently evaluated. This is the first such detailed study to use satellite data to bring forward a composite image of these processes and therefore it provides a number of novel results to this field. We have confirmed the long-known presence of a surface rainfall maximum several hundred kilometres southwest of the centre and attributed it to collocated deep convection. We have shown that this area of convection is substantial, both in the composite and in a case study, extending for upwards of 500 km from near the centre towards the south(west). We have also shown that the hydrometeor structure is far less symmetric than previously assumed: rain to the north of the centre is up to an order of magnitude less than can be found at the same radius to the south of the centre and deep convection is entirely absent as a significant process in the north: almost all precipitation is stratiform, driven by interaction with the orography of the Himalayan foothills.
We have shown that MDs have consistently deep convection collocated with the area of maximum precipitation, covering a significant region. Within this, the highest raindrop density is found, directly beneath the highest densities of snow and graupel. The largest raindrops, however, are found at the centre, where, in the comparatively uncommon event of convection occurring, the highest rainfall rates can also be found. Outside the centre, the raindrop size distributions tend to be uniform with height up to about 5 km, implying that these areas are well mixed. To the south of this deep convection, we have shown the cloud structure to be typically tropical, whereas to the north of the centre it is far more orographically driven.
Our case study shows that the presence of an MD sets up multiple instabilities in the atmosphere and saturates the troposphere up to 600 hPa. Using this example, we also compared TRMM-based surface rainfall estimates with station gauge-based estimates along the MD track, finding that TRMM 3B42 can significantly underestimate the higher rainfall rates associated with MDs: the highest rainfall rates were underpredicted by 30%.
We discovered and quantified a bimodal diurnal rainfall cycle in MDs: an uncoupled, antiphase cycle with a central mode (associated with the maximum precipitation in the southwest, peak-to peak variation 70%) and an outer mode (associated with the general convective precipitation across the MD, peak-to-peak variation 64%). A full understanding of these dynamical features will require detailed regional simulations with high-resolution models.
Further work is now needed to look at the mechanisms responsible for the decay and ultimate dissipation of depressions and investigate what is responsible for the zonal shift of the precipitation maximum across the diurnal cycle and how convection parameters in numerical models affect their propagation and duration.