The formation of first raindrops in deep convective clouds is investigated. A combination of observational data analysis and 2D and 3D simulations of deep convective clouds suggests that the first raindrops form at the top of undiluted or slightly diluted cores. It is shown that droplet size distributions in these regions are wider and contain more large droplets than in diluted volumes. The results of the study suggest that the initial raindrop formation is determined by the basic microphysical processes within ascending adiabatic volumes. It allows one to predict the height of the formation of first raindrops considering the processes of cloud condensation nuclei activation, droplet diffusion growth, and coalescence growth. The results obtained in the study explain observational results through which the in-cloud height of first raindrop formation depends linearly on the droplet number concentration at cloud base. The results also explain why a simple adiabatic parcel model can reproduce this dependence. The present study provides a physical basis for retrieval algorithms of cloud microphysical properties and aerosol properties using satellites. The study indicates that the role of mixing and entrainment in the formation of the first raindrops is not of crucial importance. It is also shown that low variability of effective and mean volume radii along horizontal traverses, as regularly observed by in situ measurements, can be simulated by high-resolution cloud models in which mixing is parameterized by a traditional 1.5 order turbulence closure scheme.
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 Observational studies [e.g., Rosenfeld and Gutman, 1994; Freud et al., 2008; Rosenfeld et al. 2008; Freud et al., 2011; Prabha et al., 2011] as well as numerical simulations [e.g., Pinsky and Khain, 2002; Benmoshe et al., 2012] suggest that rapid formation of raindrops in convective clouds begins when the effective radius exceeds a certain threshold value reff _ c. Depending on the cloud type and the droplet concentration, reff _ c varies from about 11 to 15 µm. Freud and Rosenfeld  found that in developing convective clouds, the effective radius reff is related to the mean volume radius rv as reff ≈ 1.08 ⋅ rv, and therefore the beginning of raindrop formation can also be characterized by the threshold value of the mean volume radius rv _ c. Another finding of that study was that the height Hp of first raindrops formation above cloud base increases nearly linearly as droplet number concentration N increases. The linear dependence Hp(N) was confirmed for different environmental conditions and diverse geographical locations such as India and Israel, suggesting that this linear (or nearly linear) dependence is a common characteristic of deep convective clouds with warm base. The observed dependence Hp(N) is shown in Figure 1a. The level of raindrop formation was determined by Freud and Rosenfeld  using threshold values of rain water mixing ratio qPc, namely, 0.01 gkg− 1 and 0.03 gkg− 1. Most estimations were performed using qPc of about 0.03 gkg− 1. The values of the mean volume radii rv _ c corresponding to these thresholds were evaluated using measured drop size distributions (DSDs). Figure 1b shows dependence Hp(N) obtained in simulations by two spectral bin microphysical (SBM) models: the adiabatic parcel model [Pinsky and Khain, 2002] and 2D Hebrew University Cloud Model (HUCM) [Benmoshe et al., 2012]. In the simulations, the time instance of the beginning of raindrop formation was determined using the same threshold values of qPc as in the observations. Then, the values of the mean volume radii rv _ c, at which first raindrops formed were determined and compared with the observations.
 One can see that both the adiabatic parcel model and HUCM reproduce the nearly linear dependence of Hp(N) and have slopes close to the observed ones. The nearly linear dependence Hp(N) at which rv reaches its threshold value directly follows from the theory of diffusion drop growth in an ascending adiabatic parcel. According to the theory, with the proportionality coefficient depending slightly on the temperature [Pinsky et al., 2012].
 There is a good agreement between Hp(N) derived from in situ measurements and the results obtained using an adiabatic parcel model. Moreover, there is a good agreement between the results obtained using a dynamically simple parcel model and those obtained with the multidimensional cloud model. These findings raise an important question: “Why a dynamically simple adiabatic parcel model is able to reproduce the height of the first raindrops formation in a dynamically complicated nonadiabatic convective cloud involved in mixing with the drop free environment?”
 To answer the question, we will show that: (1) among a great number of cloud volumes, there are some that remain undiluted or are diluted only slightly, at least up to heights where the formation of first raindrops takes place; and (2) drop collisions are the most intense in these slightly diluted cloud volumes.
 We address these questions by analyzing observational data and supporting numerical simulations using 2D and 3D cloud models with spectral bin microphysics.
2 Observational Data Sets
 The instruments and techniques of the Cloud Aerosol and Precipitation Enhancement EXperiment (CAIPEEX-2009) measurements are described by Prabha et al.  and Kulkarni et al. . CAIPEEX is an airborne observational campaign which is investigating the aerosol-cloud interaction primarily over continental Indian region. The first phase of CAIPEEX in 2009 carried out observations over several locations in India, investigating the aerosol and cloud microphysics. A suite of instruments onboard the CAIPEEX aircraft is provided in Table 1. In the present study, we used data from 11 flights of deep convective (congestus type) clouds within a wide range of thermodynamical and aerosol conditions, from highly polluted dry super continental conditions during the premonsoon to relatively clean and wet monsoon conditions. A Cloud Droplet Probe (CDP; Droplet Measurement Technologies DMT, Inc.) and a Cloud Imaging Probe were used to measure the drop size distribution (DSD) within the diameter range between 2 and 50 µm. The cloudy volumes were defined as zones where the cloud droplet number concentration N exceeded 10 cm−3. Liquid water content (LWC) was also measured by the HotWire LWC probe and was used to correct the LWC measured by CDP.
Table 1. List of Instruments on Board the CAIPEEX Aircraft With Data Sampling Detailsa
(PCASP is the Passive Cavity Aerosol Spectrometer Probe, CIP is the Cloud Imaging Probe, CDP is the Cloud Droplet Probe, DMT is Droplet Measurement Technologies, AIMMS is Air Data Probe, CCN is Cloud Condensation Nuclei).
Cloud droplet spectra
2 to 50 µm, 1 to 2 µm, 30 bins
Cloud particle spectra
25 to 1550 µm, 25 µm, 62 bins
Liquid water content
0 to 3 g m−3, 0.05 g m−3, 0.01 g m−3
DMT CCN counter
0.5–10 µm (0.1% to 1.2% SS)/0.5 µm
PMS PCASP SPP 200
0.1 to 3 µm, 0.02 µm, 30 bins
U,W: 0.01 m s−1
0–2000 ft/0.15 m
 The Aircraft Integrated Meteorological Measurement System was used to measure the air temperature, the relative humidity, and the winds. The concentration of cloud condensation nuclei (CCN) was measured using DMT CCN counter. Subcloud observations of CCN were carried out for three supersaturation settings (0.2%, 0.4%, and 0.6%). The Passive Cavity Aerosol Spectrometer Probe (PCASP) was used for aerosol measurements (size distribution, effective radius, and concentration). Subcloud aerosol data were also considered. All measurements were carried out at 1 Hz sampling frequency, i.e., were averaged over approximately 100 m of horizontal distance. Instruments used in this study and their parameters are listed in Table 1 [see also Prabha et al., 2011]. Observations were carried out over Pathankot (32.28°N, 75.65°E) on 24 and 28 May 2009: over Hyderabad (17.45°N, 78.46°E) on 15–17 and 20–22 June 2009 and over Bareilly (28.22°N, 79.27°E) on 23–28 August 2009. Some of the characteristics of microphysical observations over Pathankot and Bareily are described in Prabha et al. . Observations over Hyderabad and over Bareilly were taken from polluted dry conditions to relatively cleaner and wetter monsoon conditions as monsoon conditions advanced over these locations. On 22 June and 25 August, the aerosol concentrations were considerably lower above the boundary layer due to increased rainfall.
 Dynamical and microphysical characteristics observed at the cloud base and in the mixed layer are presented in Table 2. In some cases, the measured CCN concentration is higher than the aerosol concentration. This is attributed to the fact that the PCASP instrument did not measure the fine-mode particles (< 0.1 µm). Monsoon cases (such as of 22 June and 25 August) are characterized by a significant reduction in the droplet number concentration and increase in the mean radius, in comparison to the premonsoon cases. Maximum droplet number concentration (CDNC) exceeds 1000 cm−3 during the premonsoon cloud samples (e.g., 16 June). The conditions on 23 and 24 August may be considered as polluted monsoon conditions. 24 and 28 May are supercontinental conditions with elevated aerosol layers (also discussed in Prabha et al. ). Cloud microphysics data during both ascents and descents through tops (100–200 m below cloud top) of growing convective clouds were used in the present analysis. During the profiling, clouds developed at certain levels showed some precipitation. Once precipitation was detected, further profiling was not carried out. The methodic of successive cloud penetrations just below the ascending cloud top of developing clouds allows tracking time and height evolution of cloudy parcels ascending from cloud base and located at the cloud top during cloud development. This methodic allows the comparison of results of observations with those obtained using a parcel model, in which parcel represents a cloudy volume ascending in the cloud top.
Table 2. Summary of Observations Used in the Present Study, Including Cloud Base Height (m), Cloud Top Height (m), the Mean Drop Radius at Cloud Base, Spectral Width at Cloud Base, Number Concentration of Activated Droplets (CDNC), Cloud Base Updraft in an Area of 50 km x 50 km, Boundary Layer (BL; in the Mixed Layer) Aerosol Number Concentration, BL Number Concentration of Cloud Condensation Nuclei (NCCN), Subcloud Aerosol Concentration, Subcloud NCCN, and Maximum CDNCa
Cloud Base Height (m)
Cloud Top Height (m)
Mean Radius (µm)
Spectral Width (µm)
Cloud Base CDNC (cm− 3)
Cloud Base Updraft (ms− 1)
BL Na (cm− 3)
BL NCCN (cm− 3)
Subcloud Na (cm− 3)
Subcloud CCN (cm− 3)
Maximum CDNC, (cm− 3)
Aerosol concentration and CCN concentration at 0.4% (for 24 May averaged at 0.5%) supersaturation in the mixed layer and just below the cloud base during the CCN cycle and maximum CDNC is also shown.
24 May *
3.26 ± 0.50
1.34 ± 0.16
519.91 ± 422.39
0.79 ± 3.10
2579 ± 745
1610 ± 307
2.46 ± 0.17
1.16 ± 0.09
192.45 ± 157.14
0.64 ± 0.84
2194 ± 956
2001 ± 984
2.99 ± 0.18
1.15 ± 0.06
230.51 ± 76.24
0.59 ± 1.09
955 ± 103
1148 ± 298
3.37 ± 0.53
1.30 ± 0.19
340.01 ± 225.61
3.91 ± 1.89
1274 ± 196
1446 ± 331
2.23 ± 0.26
0.99 ± 0.17
113.82 ± 93.66
2.31 ± 1.70
962 ± 171
157 ± 146
2.60 ± 0.54
0.97 ± 0.23
109.80 ± 128.62
2.02 ± 2.00
1276 ± 271
2922 ± 923
3.24 ± 0.36
1.24 ± 0.13
389.00 ± 293.95
2.55 ± 1.67
969 ± 188
1272 ± 398
2.16 ± 0.30
0.86 ± 0.12
64.57 ± 45.16
0.67 ± 0.92
334 ± 48
469 ± 133
2.93 ± 0.18
1.32 ± 0.16
104.47 ± 110.69
1.05 ± 0.80
1449 ± 143
4975 ± 1819
3.96 ± 0.89
1.50 ± 0.24
185.26 ± 167.20
1.42 ± 0.73
2043 ± 148
6054 ± 2197
3.89 ± 0.98
1.40 ± 0.20
232.45 ± 180.84
3.69 ± 2.40
648 ± 106
2252 ± 882
3 Analysis of Measurements
3.1 Adiabatic Fraction
 The effect of cloudy air dilution will be characterized by the adiabatic fraction (ADF), defined as the ratio LWC/LWCad, where LWCad is the adiabatic liquid water content. LWCad is determined as the LWC in a nonprecipitating adiabatic parcel ascending from the cloud base.
 Figures 2-4 (left panels) show the LWC, the effective radius, and the vertical velocity measured on 22 June 2009 along horizontal aircraft traverses at levels 1.2 km, 3.4 km, and 4.7 km above the cloud base, respectively (some details of this monsoon case are presented in Prabha et al. ). At 3.4 km, the effective radius reaches 15 µm that can serve as an indication of the beginning of raindrop formation. One can see that the ADF changes from the value close to zero to one along the traverses. Analysis of these results further shows that close to adiabatic (slightly diluted) cloud volumes exist even at the distances as high as 4.7 km above cloud base. These volumes exist both in updrafts and in downdrafts. The DSDs presented in these figures also show multiple modes in DSDs. The formation of multimodal DSDs in monsoon cloud is probably related to in-cloud activation of small aerosol (interstitial) particles ascending from cloud base together with cloud drops. This process is discussed in Prabha et al.  in detail. Figure 5 shows an example of a 66 s cloud pass in the premonsoon cloud observed on 16 June at 7.1 km. The effective radius is nearly constant (10.8 µm) along the traverse. The CDNC in this region exceeds 600 cm−3 and LWC is ≈ 3 gm− 3. However, at the cloud edges, CDNC reduced to <100 cm− 3. The entrainment mixing effect on the DSD is not seen beyond 300 m from the cloud edge, and there are clear indications of a wide adiabatic cloud volume. These wide adiabatic regions are also seen in the cloud samples at 6.1 km. There are slightly diluted regions in the cloud samples at 5.75 km and 4.75 km, and there are oscillations in vertical velocity as illustrated earlier for monsoon cloud. Similar observations are also noted in other premonsoon cloud samples.
 Figure 6 presents the vertical distribution of LWC and adiabatic LWC for the different observations considered. One can see that adiabatic or close to adiabatic volumes were registered in premonsoon clouds developing in extremely polluted and dry atmosphere (16 June), in clouds during the transition period 21 June and in monsoon clouds on 22 June developing in moist and relatively less polluted air. Since clouds measured in CAIPEEX premonsoon were extremely polluted, the first raindrops formed at several kilometers above cloud base.
 The existence of close to adiabatic volumes near cloud top was reported earlier by Heymsfield et al. , Paluch , Jensen et al. , Gerber , and in several other studies. Gerber et al.  did not find adiabatic volumes at altitudes higher than about 1000 m above cloud base in shallow maritime cumulus clouds observed in the RICO experiment. At the same time, at this altitude, rv already exceeded 12–14 µm and the clouds began drizzling [Gerber et al., 2008]. Thus, the first drizzle drops could still have formed at heights where nearly undiluted cloudy volumes exist.
 The decrease in the horizontally averaged ADF with increasing the height above cloud level is usually attributed to the effects of mixing with the environment. This effect should be especially pronounced in small clouds like those observed in RICO. There are several physical mechanisms that can decrease ADF with height that are not related to mixing. Sun et al.  note that ascending cloud volumes push the neighboring air volumes upward. These volumes may contain lower water vapor mixing ratios and, therefore, have higher lifting condensation levels than those ascending from the cloud base level. Thus, the ADF evaluated as the ratio LWC/LWCad, where the adiabatic liquid water content LWCad is determined as LWC in a nonprecipitating adiabatic parcel ascending from the cloud base, underestimates the fraction of undiluted volumes.
 Another reason that can lead to subadiabatic contents in clouds measured in CAIPEEX is a comparatively low sampling frequency that corresponds to spatial resolution of about 100 m. Gerber  and Gerber et al.  demonstrated that utilization of higher frequency reveals the existence of higher number of undiluted volumes. We came to a similar conclusion by analysis of observations carried out at 10 Hz sampling rate (not shown here) using a combination of instruments such as two Forward Scattering Spectrometer Probes (FSSP) and Cloud Aerosol Spectrometer (CAS). It is noted that droplet number concentration remained high and did not show diluted cloud volumes in the penetrations that indicates similarity to cloud cores.
 Finally, we note that at levels higher than about 3 km above the cloud base in a warm environment such as during CAIPEEX, the adiabatic liquid water content almost certainly exceeds the value that can be reliably measured with the DMT LWC probe. This is another reason for possible underestimation of the ADF in in situ measurements.
 Despite the likely underestimation of ADF in deep convective clouds, the analysis of many cloud samples from Ganges Valley during the transition to monsoon with very high aerosol loading and under moist conditions suggests that up to 30% of cloud parcels at elevated layers are only slightly diluted, with ADF > 0.7.
 Therefore, it seems that the question whether undiluted or slightly diluted cloudy volumes exist at the level of first raindrop formation can be answered positively. It is especially true for deep convective clouds because the dilution decreases the buoyancy which would prevent cloud development.
3.2 Conditions for Raindrop Formation
 Another question to be answered is whether undiluted or slightly diluted cloudy volumes have advantages for raindrop formation. In convective clouds, the effective and the mean volume radii increase with height, at least up to the level of raindrop formation [Freud et al., 2008; Freud and Rosenfeld, 2012; Benmoshe et al., 2012]. At the same time, Figures 2-5 (left panels) show that the effective radius (or the mean volume radius) remains nearly constant along the horizontal traverses despite substantial variations of CWC (liquid water content of cloud droplets with radii below 40–50 µm) and ADF (from near zero to about 1). The low variability of the effective radius horizontally (along the aircraft pass lengths) was found previously in observations [e.g., Paluch, 1986; Gerber, 2000; Gerber et al., 2008; Freud et al., 2008; Prabha et al., 2011; Freud and Rosenfeld, 2012] and in numerical simulations [Benmoshe et al., 2012]. The low variability of reff horizontally allows one to represent the effective radius -altitude diagram as nearly functional dependence reff (z) with low dispersion. Rosenfeld and Gutman , Freud et al. , and Freud and Rosenfeld  relate the formation of raindrops with the altitude, where the effective radius reaches its critical value of 12–15 µm. Using the observational dependence of the altitude (over cloud base) at which reff reaches its critical value on droplet concentration, Rosenfeld et al.  proposed a new method to retrieve drop concentration and aerosols from satellites.
 The low variability of the effective radius in the horizontal means that threshold value of the effective radius can be achieved at a level where the drop concentration and mass content values may significantly differ in the horizontal direction. Thus, achieving the threshold value of effective radius cannot be a sufficient condition for raindrop formation. Indeed, where the CWC and the droplet concentrations are low, the formation of raindrops is hardly possible. Thus, formation of the DSDs with reff (or rv) equal to or exceeding their threshold values is a necessary (beneficial), but not the sufficient condition for raindrop formation. As shown by Freud and Rosenfeld , the collision kernel is proportional to . As follows from the stochastic collision equation, the collision rate is proportional to the product of the collision kernel and the square of the droplet concentration. Taking into account that reff is nearly constant along the horizontal traverses, it is reasonable to assume that for a given reff exceeding the critical value, the formation of first raindrops takes place in cloudy volumes with the maximum droplet concentration. Indeed, variations of effective radius, say by ≈10%–20%, lead to the change of the collision kernel by factor of 1.6–2.5. At the same time, variations of square of droplet concentration can easily change collision rate by two orders of magnitude. Thus, if variations of the effective radius do not exceed 20% of its maximum value, it is reasonable to expect that the maximum of collision rate will be reached in volumes with the maximum droplet concentration. Assuming a similar mean volume radius, these are also volumes with the maximum CWC. The role of CWC in rain formation is well recognized and used in many bulk parameterization schemes where the rate of raindrop formation is proportional to the CWC [e.g., Kessler, 1969]. Even when not stated explicitly, such parameterizations are based on the assumption that the first raindrops form in undiluted or slightly diluted volumes.
 This assumption is further analyzed on the basis of the right panels of Figures 2-5 showing the DSDs. These figures indicate a similarity in the shapes of the first mode of DSDs with peaks at the drop diameter of about 21 µm independently on the ADF values. The fluctuations of the concentration of the smallest droplets (forming the second DSD mode) can be attributed to in-cloud activation of CCN in parcels ascending from the cloud base, or to partial drop evaporation in downdrafts [Prabha et al., 2011]. Formation of small droplets can be also caused by nucleation of CCN in air volumes in which ascent is triggered by pressure fluctuations atop of ascending volumes [Sun et al., 2012]. Here, we are interested in the larger droplets belonging to the first mode, because collisions among these droplets lead to raindrop formation. One can see that the change in the “amplitude” of the DSD correlates well with the ADF changes. This finding illustrates the point that undiluted or slightly diluted cloudy volumes have not only the largest CWC, but also the widest DSDs with a higher concentration of the largest droplets. To illustrate this point, we define the drop diameter D10 chosen by counting 10 largest droplets at the tail of the DSD and the corresponding size is D10. Drop diameter D10 thus characterizes the tail of largest droplets, the larger the D10, the longer the tail. Hobbs and Rangno  used a similarly defined measure, which they called a threshold diameter, to characterize the broadness of the DSD. The relationship between the concentration of small droplets and D10 is shown in Figure 7. All the cloud base data were screened out from this analysis. Small droplet number concentration is the concentration of droplets with diameters below 20 µm. The color map denotes the ADF. The relationships are shown for both premonsoon and monsoon clouds. There are several points to emphasize:
Both the values of D10 and the concentration of small droplets are low in diluted volumes. For instance, in the premonsoon case (Figure 7d), all cloudy volumes with droplet concentration lower than 500 cm−3 are diluted. It is a natural result of cloudy volume dilution by cloud free air.
In most cases, large droplets are not observed in strongly diluted volumes, except when droplet concentration is extremely low. For instance, Figure 7c (monsoon) shows that if droplet concentration is below 100 cm−3, all drops are comparatively large.
At a given concentration of small droplets, undiluted and slightly diluted parcels have larger value of D10 as compared to diluted volumes, which is in agreement with Figures 2-5. Undiluted and slightly diluted volumes may contain droplets with diameters exceeding 40 µm. These largest droplets in ascending adiabatic volumes can form as a result of droplet collisions. Such drops are able to trigger rapid collisions and raindrop formation in the presence of significant CWC [Khain et al., 2000; Pinsky and Khain, 2002]. This indicates that collision process in adiabatic parcels is substantially much more efficient than in diluted ones.
Another important feature of Figure7is the trend of the decrease of both the concentration of small droplets and D10 with the decrease of ADF (see Figures 7a, 7b, and 7d). This feature is also seen in the examples of DSDs presented in Figures 2-5.
 Thus, formation of the first raindrops should be expected in undiluted or in slightly diluted cloud volumes due to the specific features of their DSDs (large LWC, larger concentration, and the existence of large droplets).
 Besides, Prabha et al.  showed that the many cases spectrum width of the DSD is the highest in undiluted or slightly diluted cloud volumes. The mechanisms underlying the appearance of undiluted and slightly diluted volumes are investigated with numerical modeling.
4 Numerical Simulations
 Determination of the exact location of first raindrops using in situ measurements in a deep convective cloud is a difficult if not impossible task because raindrops detected along a traverse can be produced at a different level and transported to the observed location by sedimentation or advection. This is why the combination of observations and numerical modeling applied in this study is of high importance. To simulate deep convective clouds with parameters similar to those observed in CAIPEEX, two numerical models with similar SBM schemes were used: the 2D mixed-phase HUCM [Khain et al., 2011; Benmoshe et al., 2012] and the 3D System for Atmospheric Modeling (SAM) [Khairoutdinov and Randall, 2003; Fan et al., 2009a, 2009b]. The SBM in the SAM is based on the original microphysical scheme by Khain et al. , modified by Fan et al. [2009a]. In both models, the SBM is based on solving an equation system for eight size distributions for water drops, ice crystals (columnar, plate like, and dendrites), snowflakes, graupel, hail/frozen drops, and CCN. Each size distribution is represented by a 33 (in the SAM) and 43 (in the HUCM) mass doubling bins, i.e., the mass of a particle mk in the k − th bin is determined as mk = 2mk − 1. All relevant microphysical processes and interactions of warm and ice processes are included in the models. Since the focus of this study is on the formation of raindrops due to warm processes, the description of ice processes is not addressed here. The details of model treatment of ice can be found in the references cited above. In both models, DSD contains drops of all sizes with the radii range 2 µm to 0.33 cm in SAM and from 2 µm to ~1 cm in HUCM. Drops with the radii larger than 40–50 µm are assigned to raindrops. The dependence of the collision efficiencies on height is taken into account. The HUCM contains detailed description of the effect of turbulence on collision of cloud droplets. Turbulence is characterized using the turbulence kinetic energy (TKE) dissipation rate and the Taylor microscale Reynolds number. Using these parameters, look-up tables of turbulence-induced enhancement factors are applied to the collision kernel for cloud droplets [Pinsky et al. 2008; Benmoshe et al., 2012]. The turbulent diffusion coefficients are calculated using 1.5 order closure scheme (the K-theory) that includes solving the nonstationary equation for the TKE. These coefficients are applied to describe the mixing of all thermodynamic quantities and size distributions. The detailed description of the model is presented in Benmoshe et al. .
 Dynamically, both HUCM and SAM are based on the anelastic equations. Dynamical frameworks of the HUCM and SAM are described by Khain and Sednev  and Khairoutdinov and Randall , respectively. In both models, a high spatial resolution of 50 m was used in all directions. This high-resolution allows models to resolve fine cloud structure and microphysical processes related to the formation of droplets and first raindrops. The computational domain of HUCM was 25 km × 16 km in the horizontal and vertical directions, respectively. The SAM computational domain is 12.5 km × 12.5 km × 14 km.
 The thermodynamical profiles and CCN size distribution were chosen close to those observed in polluted premonsoon clouds from CAIPEEX described in Prabha et al. . The CCN concentration was assumed constant within the lower 2 km layer and then decreasing exponentially with altitude. To keep the cloud within the computational domain during the simulations, the wind shear was assumed weak in simulations with HUCM (2 ms− 1 per 10 km in the lowest 10 km, and zero above the 10 km level). No wind shear was included in the SAM simulations. During CAIPEEX, a strong easterly jet was observed at heights above 7 km [Prabha et al., 2011]. Since we are interested in the first rain formation taking place below this level, using a weak wind shear seems to be a reasonable compromise.
 Note that turbulence (and related turbulent mixing) within deep convective clouds is caused to a large extent by strong gradients of vertical velocity, arising due to the work of buoyancy force. In simulated clouds, the maximum values of the dissipation rate may exceed 2000 cm2s− 3, i.e., very high values [Benmoshe et al., 2012]. Thus, the utilization of the weak horizontal wind shear in the simulations does not necessarily decrease the rate of turbulent mixing.
 In HUCM, the convection was triggered by a 1 km wide thermal bubble imposed near the surface for the first 10 min of the simulation. The amplitude of the temperature perturbation was varied randomly over time and space within the “heating zone.” More details of the initial conditions are described in Benmoshe et al. . In SAM simulations, the cloud was triggered by adding random fluctuations to the initial temperature field in the boundary layer as described by Ovtchinnikov and Kogan . Different approaches used in the HUCM and SAM simulations to trigger convection affect the timing of cloud formation: utilization of a comparatively weak but prolonged heating in the HUCM leads to later cloud formation than a stronger instantaneous temperature perturbation used in SAM. As soon as cloud forms, however, its further development and vertical velocity is largely determined by the stability of the atmosphere.
 Note that the observed clouds contained ice at high levels [Prabha et al., 2011]. Ice processes are also included in the models. However, ice crystal number and mass concentrations are low near the level of interest (~5.5 km) around the time of the first raindrop formation and have little on cloud dynamics and liquid-phase microphysics. In regard to graupel and hail, these hydrometeors form by freezing/riming of raindrops or though the long process of riming at high levels. Consequently, these processes do not affect the early rain formation. The amount of graupel and hail was negligibly small during the developing stage of cloud evolution. Therefore, the ice processes play very little, if any, role in the formation of first raindrops in both real clouds and simulations. These processes can, of course, be very important in the subsequent cloud development and precipitation production.
4.1 Two-Dimensional Simulations
 To illustrate the reliability of the DSD shapes simulated using the HUCM, Figure 8 shows the relationship between the effective radii and the mean volume radii at the instance before and several minutes after the formation of first raindrops (panels a and b). One can see that at the nonprecipitating stage, the ratio reff/rv ≈ 1.08, which in exact agreement with the in situ measurements (panel c) [Freud and Rosenfeld, 2012].
 Formation of raindrops leads to an increase of the ratio reff/rv because the effective radius is determined by higher moments of DSD than the mean volume radius and increases faster with the formation of raindrops. Our supplemental simulations of deep convective clouds under different aerosol conditions showed that this relationship between the mean volume radius and the effective radius is valid for deep convective clouds with aerosol loadings within a wide range. CAIPEEX observations also confirm this relationship for a wide range of aerosol pollution.
 For detection of first rain, we kept the same threshold that was used by Freud and Rosenfeld  (see Figure 1), i.e., rain water content (RWC) ~ 0.03 gkg− 1. Figure 9 shows the fields of CWC, RWC, the turbulent kinetic energy dissipation rate, and the mean volume radius near the top of a developing convective cloud. The cloud top zone shown in Figure 9 contains three turrets (or bubbles). The mean volume radius reaches ≈9.3–9.5 µm at the tops of the bubbles. The effective droplet radius is equal to ≈10–11 µm at this height, which is in agreement with the observations in premonsoon clouds [Prabha et al., 2011]. The first raindrops form near the top of a decaying bubble B where high LWC is accompanied by enhanced turbulence (note high dissipation rate) that intensifies collisions. This result agrees well with those reported in detailed studies of the first raindrop formation in turbulent clouds [Benmoshe et al., 2012 and Seifert et al., 2010]. The CWC at the turret tops is as high as 3.5–4 gm− 3, which is close to the adiabatic value. Figure 10 shows the field of ADF corresponding to the CWC field in Figure 9. The zones of relatively larger ADF exist near the tops of the turrets. One can see a slightly diluted core in turret A. In order to understand why the highest values of ADF (and CWC) are reached at the turret tops or cores, it is necessary to trace back the history of a turret's development. At each time instance, turrets are at different stages of their development. In Figure 9, turret A is developing, while turret B is decaying. The history of formation and evolution of bubbles A, B, and C is illustrated in Figure 11, where the CWC fields are presented with a time increment of 2 min. All the bubbles develop from the same stream that starts developing from the cloud base. This stream then splits into several streams giving raise to formation of different bubbles (plumes, jets). The common source near cloud base leads to a situation when each bubble (especially near the tops) contains large CWC, comparatively close to the adiabatic value. Bubble B develops first and reaches the maximum height at t = 66 min (Figures 9 and 11). Later on, bubble B starts descending with velocity of 4 ms− 1 until its dissipation, while its core near the top remains diluted only slightly (Figure 10). The first raindrops are produced at the top of bubble B. After a delay, bubble A starts developing rapidly (with maximum updraft velocity in it of 15 ms− 1), producing the first raindrops within a few minutes. From the cloud top, the first raindrops spread along the edges of the bubbles where downdrafts take place (Figure 12).
 Analysis of time changes of elevation levels of different bubbles indicates the existence of both ascending and descending volumes in clouds in agreement with observations (see Figures 2-5). For instance, cloud volume B reaches its maximum height of 6 km (panel d), and then it descends (panels e and f). Parcel C reaches 5 km level (panel d) and descends to about 4 km level during several minutes. These downdrafts can be a part of in-cloud oscillations driven by buoyancy or can be explained by considerations of continuity, when downward motion of parcels reached their maximum height is forced by continuously ascending new parcels. The mechanisms leading to such downdrafts require special investigation.
 Note that the formation of first raindrops takes place at heights of about 5.5 km, i.e., about 1.3 km above the freezing level. Further cloud evolution in the model is accompanied by formation of ice, and cloud top reaches of about 10 km.
 Figure 13 shows an example of DSDs calculated in a developing convective cloud whose structure is shown in Figures 9 and 11. The DSDs are presented at the points located near the top of the cloud at the times corresponding to the beginning of raindrop formation. These points are marked by asterisks in Figure 9. Comparison with Figure 2 reveals a similarity between the simulated and measured DSDs: in both cases, the DSD maximum of about 40 cm− 3µm− 1 is located at the drop diameter of 20 µm. The cloudy volume located near the cloud edge (x = 9.25 km) contains a larger amount of small droplets, possibly as a result of partial droplet evaporation in cloud downdrafts. The largest droplets exist in the undiluted volume with maximum CWC (x = 10.25 km).
4.2 Three-Dimensional Simulations
 Results obtained using 3D SAM simulations not only support the results of the 2D HUCM simulations but also provide new information concerning the cloud structure and the formation of first raindrops. Figure 14 shows fields of CWC and RWC at the time period during the beginning of the process of raindrop formation. One can see that at t = 30 min, first raindrops form at the top of the tower where the CWC is high, i.e., in volumes, which are diluted only slightly. Such positive correlation between CWC and RWC remains at t = 31 min. After this short period, the increase in RWC leads to corresponding decrease in the CWC, so that at t = 33 min high, RWC is observed in regions where CWC is comparatively low. Thus, it is possible to see the zones of the first raindrop formation only in high time resolution model output. By looking at the instantaneous fields of CWC and RWC at t = 33 min and for later times, one could jump to a wrong conclusion that rain forms at cloud edges, where CWC and droplet number concentration are low, and look for a different explanation of this effect, such as invoking specific types of cloud mixing with surrounding. At the same time, the increase in the RWC along cloud edges is caused by the raindrop transport from the cloud top by downdrafts. This is illustrated in Figure 15, where horizontal cross sections in the fields of W, CWC, RWC, and droplet concentration at z = 6 km are presented for a time period from 33 to 37 min. During this time period, the CWC is well correlated with vertical velocity, and its maximum is in the updraft. At the same time, RWC is maximum in zones of downdrafts largely near cloud edges. Droplet concentration is also minimum near cloud edges. This decrease can be caused by many reasons: evaporation in downdrafts, collection by raindrops, and mixing of cloudy air with environment droplet free air.
 Figure 16 (top panels) shows PDFs of the cloud water at all levels above the cloud base. Similar to the observations, the model-predicted CWC at any given level changes within a wide range, from zero to the adiabatic or close to adiabatic values. One can see that just at the moment t = 30 min, that can be considered as the time of the formation of first raindrops, the maximum of LWC is close to LWCad. Formation of raindrops, their settling, as well as possible mixing with the surrounding dry air decrease the maximum LWC values. Deviations of maximum values of CWC from the corresponding adiabatic values begin at levels above 5 km. It is interesting that at height of ≈5 km, the maximum values of CWC sharply decrease. Such decrease of maximum values of CWC at ≈5 km takes place in the 2D HUCM simulations (not shown) as well. Such decrease possibly reflects the transition of the largest cloudy droplets to raindrops with the radii exceeding 50 µm. This zone increases with time reflecting increase of RWC. Entrainment of environmental air may also contribute to the CWC decrease near 5 km level. Note, however, that cloudy volumes with LWC close to LWCad remain at the higher levels. We interpret this effect in the same way as in case of the 2D HUCM simulations: despite the fact that the roots of the ascending turrets can mix with the surrounding air, the tops of the turrets contain close to adiabatic volumes.
 The 3D simulations indicate good agreement with observations as regards to the vertical profiles of the effective radius. Figure 16 (bottom) shows the vertical profiles of the probability distribution function of effective radius at the time period of first raindrop formation. One can see several specific features of the profiles discussed both in the observational section of this study, as well as reported in other observational studies [e.g., Freud et al., 2011; Freud and Rosenfeld, 2012]: in spite of very high variability of the CWC at each level, the variation of the effective radius is comparatively small; and the first raindrops form at the level where the effective radius reaches 10–11 µm. The observations of effective radius from a cloud observed during the high aerosol pollution and transition from premonsoon to monsoon on 20 June is compared with the simulations. It may be noted that there is close agreement between the observations and the simulations both in the mean vertical profiles and the spatial variations in the simulation. The analysis of the numerical results and observations explain why a dynamically simple adiabatic parcel model is able to reproduce well the height of the first raindrop formation: the evolution of the DSD within undiluted or slightly diluted cores of developing clouds unfolds similarly to that in adiabatic volumes and does not depend on the trajectory of volume ascent.
5 Discussion and Conclusions
 The main conclusion of this study is that the first raindrops form in undiluted or slightly diluted volumes near the cloud top where the CWC reaches its maximum. This conclusion suggests the following conceptual scheme of convective cloud dynamics. At the stage of development, convective clouds contain many rising plumes. During their motion, these plumes mix with the surrounding cloudy plumes and sometimes with environment air, while in the largest plumes undiluted or slightly diluted cores remain. At a certain stage of a plume evolution, its roots may disappear, so the instant image of the CWC field may not reveal the roots of such cores at the cloud base. DSDs in the cloud cores evolve like those in ascending adiabatic parcels. These phenomena explain the ability of a dynamically simple spectral bin microphysics parcel model to simulate the height of the formation of the first raindrops. Correspondingly, it explains the nearly linear dependence of the altitude of the first rain formation on the droplet concentration, as follows from the theory of diffusion growth in adiabatic updrafts. Measurements and simulations were performed for clouds with warm cloud bases. We believe that in case when first raindrops form due to warm processes, our conclusions remain valid in case of colder cloud bases. For instance, Freud and Rosenfeld  found linear dependence of height of first raindrop formation on drop concentration for India, Israel, California, Texas, and Europe.
 Note that it is quite natural to expect the existence of undiluted (or slightly diluted) volumes in updrafts of deep convective clouds. For instance, a widely accepted method to evaluate the maximum of the updraft velocity using the CAPE is fully based on the concept of the ascending adiabatic parcel. Strongly diluted volumes have no buoyancy and would hardly allow convective clouds to reach heights of 10–12 km.
 The most important observational and numerical result obtained in the study is that DSDs in undiluted volumes are larger and wider compared to those in diluted volumes. So, the measurements clearly indicate that process of collisions is more intense in undiluted volumes. We postulate, however, that the location of the first raindrop formation can hardly be detected in measurements. As numerical simulations show, the formation of first raindrops (in a very small amount) occurs in the zones of high CWC very rapidly, over a few minutes. This process can easily be masked by the subsequent appearance of raindrops at cloud edges where CWC is low. A great number of in situ measurements in clouds, as well as measurements from satellites, show that first raindrops form when the droplet effective radius reaches a critical value. However, these measurements do not allow to determine the location of the first raindrop formation since the effective radius changes horizontally only slightly. Only numerical simulations performed with high spatial (~50 m) and temporal (few seconds) resolutions allow to track cloud evolution in detail and to determine the zones of the formation of first raindrops.
 The concept that the first raindrops form in the adiabatic (or nearly adiabatic) volumes is supported by the results of numerous observations and numerical simulations, showing that an increase in the droplet concentration (caused for instance by an increase in CCN concentration), leads to a decrease in supersaturation that hinders formation of large drops and delays raindrop formation [e.g., Khain, 2009]. This CCN effect can be distinctly seen only in the adiabatic ascending volumes where all growing droplets compete for a certain amount of available water vapor. As we saw from Figures 2-5, in nonadiabatic volumes, an increase in droplet concentration is often accompanied by increase in size and concentration of large droplets.
 The results of the present study explain the decrease of the threshold value of reff from ~15 µm to ~10–11 µm when droplet concentration increases from clean maritime to very polluted continental clouds, as found in the numerical simulations [Benmoshe et al., 2012] and in situ observations [Prabha et al., 2011]. The collision rate is proportional to the product of the collision kernel and the square of droplet concentration. According to Freud and Rosenfeld , the value of the collision kernel is proportional to . Thus, the “threshold values” of the collision kernel in clean and polluted air differ by the factor of ≈7. This difference can be compensated by a corresponding increase in droplet concentration in polluted clouds.
 According to the observations and numerical results presented here, the dynamical structure of convective clouds can be conceptually represented as a tree with many branches rooted near the cloud base. Thus, a convective cloud may have many plumes containing undiluted or slightly diluted cores surrounded by the more diluted cloud air. One possible mechanism of plume formation is cloud-entrainment interface instability [Grabowski and Clark, 1991, 1993]. According to these studies, a characteristic linear scale of a plume is about one tenth of the cloud radius. In deep convective clouds, the bubbles can be large enough to be resolved in observations at 100 m sampling intervals. This means that even the sampling at 1 s interval can identify unique signatures of slightly mixed regions of the deep convective cloud. The observations at higher resolution may be useful in the investigation of mixing in pockets. According to the results of the numerical simulations, the maximum values of LWC in deep convective clouds can be as high as 3–4 gm− 3 and even higher.
 The fine dynamical structure of convective clouds characterized by the existence of many evolving plumes can be resolved by models with a high spatial resolution, for instance using a 50 m grid size as in the present study. Similar simulations with a coarser grid spacing of 350 m show a formation of a cloud with a single main core [Khain et al., 2004, 2005, 2008]. The cloud structure simulated using such a coarse resolution agrees well with the traditional concept assuming that a cloud has single undiluted core surrounded by diluted cloud air [Riehl and Malkus, 1958; Riehl and Simpson, 1979]. At the same time, both conceptual schemes of the cloud dynamical structure are similar in regard to the mechanism of the first raindrop formation, as in both schemes raindrops form in adiabatic (or nearly adiabatic) updrafts. Indeed, the simulations of rain formation using 350 m horizontal grid spacing [Khain et al., 2004, 2008] and the 50 m grid spacing used in the present study yield similar heights of raindrop formation and a similar response of the height of the rain formation to aerosol concentration variations.
 It is well known that according to the theory of the drop diffusional growth, the DSDs tend to narrow with height (in the space of drop radii) in ascending adiabatic parcels. A question arises, why the widest DSD form in slightly diluted cloud volumes? This problem was investigated by Pinsky and Khain  in detail. It was shown that despite the fact that diffusion drop growth dominates in the DSD formation at the developing stage, collisions between droplets play a very important role producing the largest “superadiabatic” droplets in the droplet spectra. The smallest droplets may form due to in-cloud nucleation of CCN, which were not activated near cloud base and ascended together with droplets to regions of strong updrafts, where supersaturation exceeds its value near cloud base. This process of formation of new droplets inside clouds at altitudes of several kilometers above cloud base was investigated numerically by Pinsky and Khain , Segal et al. , Khain et al. , and others. Observations illustrating this phenomenon are described in the study by Prabha et al. . Cloud volumes at the cloud base have different updraft velocities, which leads to different droplet concentrations as well as different heights above cloud base where in-cloud nucleation takes place. In-cloud mixing between these low-diluted volumes having, however, different DSDs may also lead to DSD broadening and high variation of concentration of the smallest droplets [Khain et al., 2000; Segal et al., 2003].
 In the light of the conclusion that the first raindrops form in slightly diluted cloud volumes, another question arises concerning the role of mixing between cloud volumes and the dry environment (cloud free air) in the formation of first raindrops. The role of mixing and entrainment in DSD formation was discussed in numerous observational and numerical studies. A detailed survey of these studies is presented in a review by Devenish et al. . Despite significant efforts, many problems remain unresolved due to the complexity of the entrainment and mixing process. The 1 Hz frequency measurements discussed in the present study, as well as numerical simulations performed using HUCM and SAM in their current configurations are not sufficient for investigating this process in detail.
 However, it is to be mentioned that 10 Hz observations (not presented) during the second phase of CAIPEEX observations illustrate that main DSD features found in 1 Hz observations and discussed here remain valid for 10 Hz observations as well.
 We limit the discussion to three specific issues that may be useful for better understanding the role of mixing of cloudy volumes with dry and droplet-free environment during the formation of first raindrops. The first comment concerns the possibility of existence of undiluted volumes in turbulent convective clouds. The distance at which environmental air penetrates the cloudy air due to turbulent diffusion can be evaluated as , where k is a turbulent diffusion coefficient. In highly turbulent deep convective clouds k ~ 50 m2s− 1 [Benmoshe et al., 2012]. The time needed for a growing thermal to reach the altitude where first raindrops form is about 5 min., yielding L ≈ 120 − 150 m. Thus, plumes that are over several hundred meters in width are likely to contain undiluted or slightly diluted cores. It is especially true for deep convective clouds where updrafts are surrounded by saturated or supersaturated cloudy air. In small clouds such as in RICO, entrainment and mixing can eliminate undiluted cores, thus decreasing the probability of raindrop formation. An indirect evidence of the fact that mixing of cloudy air with the environment has a smaller effect on formation of the first raindrops was obtained in a supplemental numerical simulation in which the CCN concentration was initially assumed constant in the height. In this simulation, significant amounts of CCN penetrate updrafts within a wide range of heights. The results (not shown here) indicate that due to mixing with the environment, a significant increase in CCN concentration at high levels leads to an increasing concentration of small droplets at the lateral edges of a cloud. These droplets form by activation of aerosols entrained into cloud updrafts. At the same time, the CCN from the environment do not entrain into the undiluted cloud cores. Thus, droplets nucleated at the upper levels do not affect (or affect only slightly) the formation of first raindrops. Figure 17 shows a similarity between the accumulated rain amounts in simulations with an exponential decrease of CCN concentration with altitude and those in which CCN concentration is constant with height. A low sensitivity of precipitation to CCN entering into clouds at upper levels was also reported by Fan et al. , who used a high-resolution 3D SAM model with spectral bin microphysics.
The second comment relates to the fact that the size and concentration of the largest droplets in the diluted cloudy volumes are found to be substantially lower than those in undiluted or slightly diluted volumes. Since entrainment of dry drop-free air from environment increases the rate of dilution, the role of the entrainment in the acceleration of raindrop formation can be questioned. The results obtained in the present study regarding the process of entrainment and mixing are in agreement with those from Paluch : “Since such process does not affect the large end of the droplet spectrum, then entrainment and mixing has little immediate effect upon collection efficiencies of hydrometeors growing by accreting the cloud droplets. If mixing does not greatly influence (reduce) the local cloud droplet concentrations and sizes, then the onset of the coalescence process will be relatively uninfluenced by entrainment.” This conclusion actually means that the process of the first rain formation is determined largely by the basic condensation and collisions mechanisms in ascending near adiabatic volumes.
The third comment concerns the numerical representation of turbulent mixing in the numerical models used in the study. As seen in Figures 2-5, the effective radius changes only slightly (by about 10%–15% of its maximum value) along the horizontal traverses of a nonprecipitating cloud, despite the substantial changes in the adiabatic liquid water fraction, LWC, and the droplet concentration. The low variability of the effective radius along the horizontal traverses was reported in many studies [e.g., Paluch and Knight, 1984; Paluch, 1986; Gerber, 2000; Gerber et al., 2008; Freud et al., 2008; Freud and Rosenfeld, 2012]. The low variability is often interpreted as a consequence of either extreme inhomogeneous mixing or homogeneous mixing at high relative humidity [e.g., Gerber et al., 2008; Freud and Rosenfeld, 2012]. At the same time, Figure 9d of this study, as well as the vertical profiles of effective radius calculated for deep convective clouds with different aerosol loadings (Figure 16 in this study) [see also Benmoshe et al., 2012], shows that both HUCM and SAM models reproduce well this low variability of the effective radius within clouds at any specific level, as well as the vertical profiles of the effective radius. Note that in these models turbulent mixing is parameterized using a standard 1.5 closure scheme based on the K-theory, according to which subgrid turbulent fluxes are proportional to the gradients of grid resolvable values. In this approach, changes of all variables in model grid points are considered uniformly distributed over the air volumes represented by the grid points. Such mixing can be rather attributed to homogeneous, or “mechanical.” The models used in the present study do not include additional terms used in several studies [e.g., Grabowski, 2007; Morrison and Grabowski, 2008] to adjust droplet concentrations according to the inhomogeneous mixing scenario. Thus, the traditional approach to parameterization of turbulent mixing allows high-resolution models to successfully reproduce the features typically attributed to the effects of inhomogeneous mixing. We hypothesize that this is because the internal cloud structure forms largely by mixing of saturated or very close to saturation volumes, in which case inhomogeneous and homogeneous mixings turn out to be undistinguishable. This problem will be considered in more detail in a separate study.
 Note that the results concerning the microphysical and dynamical cloud properties (such as DSDs, LWC values, vertical profiles of the effective radius, the relationship between the effective radii and the mean volume radii, the height of the first raindrop formation, etc.) obtained in simulations with the 2D HUCM and 3D SAM models turned out to be quite similar. The difference in the heights of first rain formation of about 400 m (6.1 km in SAM and 5.7 km in HUCM) can be attributed to a more detailed description of turbulent effects on drop collisions in HUCM accelerating collisions near the cloud top, to a utilization of different convection initialization procedures and different wind shears and, of course, to the difference in the dimensionality of the models. Thus, in spite of limitations of the 2D geometry in simulations of cloud dynamics discussed in detail by Benmoshe et al. , the 2D geometry can be successfully used for analysis of microphysical processes in clouds.
 The main practical importance of the study indicating that process of raindrop formation is determined by basic microphysical processes within ascending adiabatic volumes is that we can predict the height of the formation of first raindrops considering the processes of nucleation (including in-cloud nucleation), diffusion growth, and collisions. In our opinion, the belief in the possibility of such a prediction was lost to a large extent when the mechanism of inhomogeneous mixing was considered as the main cause of formation of large droplets and first raindrops (see overview by Devenish et al. ). The result that first raindrops form near cloud top explains why the process of rain formation can be investigated from satellites that measure the effective radii only within the narrow cloud top layer [Rosenfeld and Lensky, 1998]. The results obtained in this study provide a physical basis for retrieval algorithms of cloud microphysical properties and aerosol properties using satellites [e.g., Rosenfeld et al., 2012] and can be useful in the parameterization of autoconversion in numerical cloud models.
 This research was supported by the U.S. Department of Energy's Atmospheric Science Program Atmospheric System Research, an Office of Science, Office of Biological and Environmental Research program, under grant DE-SC0006788, and the Binational US-Israel Science Foundation (grant 2010446). The CAIPEEX project and IITM are fully funded by the Ministry of Earth Sciences, the Government of India, New Delhi. The authors acknowledge with gratitude that the team effort and the dedication of the IITM scientists made CAIPEEX a great success. The Pacific Northwest National Laboratory (PNNL) is operated by Battelle for the DOE under contract DE-AC06-76RLO 1830. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-05CH11231.
 The authors express their gratitude to Rosenfeld for his interest in the study and useful discussions. Thoughtful comments from Andrew Heymsfield and two anonymous reviewers helped substantially to improve the manuscript.