the mechanism of ﬁrst raindrops formation in deep ...€¦ · parcels ascending from cloud base...

The mechanism of first raindrops formation in deepconvective clouds

A. Khain,1 Thara V. Prabha,2 Nir Benmoshe,1 G. Pandithurai,2 and M. Ovchinnikov3

Received 24 November 2012; revised 6 July 2013; accepted 9 July 2013.

[1] The formation of first raindrops in deep convective clouds is investigated. Acombination of observational data analysis and 2D and 3D simulations of deep convectiveclouds 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 largedroplets than in diluted volumes. The results of the study suggest that the initial raindropformation is determined by the basic microphysical processes within ascending adiabaticvolumes. It allows one to predict the height of the formation of first raindrops consideringthe processes of cloud condensation nuclei activation, droplet diffusion growth, andcoalescence growth. The results obtained in the study explain observational results throughwhich the in-cloud height of first raindrop formation depends linearly on the droplet numberconcentration at cloud base. The results also explain why a simple adiabatic parcel modelcan reproduce this dependence. The present study provides a physical basis for retrievalalgorithms of cloud microphysical properties and aerosol properties using satellites. Thestudy indicates that the role of mixing and entrainment in the formation of the first raindropsis not of crucial importance. It is also shown that low variability of effective and meanvolume radii along horizontal traverses, as regularly observed by in situ measurements, canbe simulated by high-resolution cloud models in which mixing is parameterized by atraditional 1.5 order turbulence closure scheme.

Citation: Khain, A., T. V. Prabha, N. Benmoshe, G. Pandithurai, and M. Ovchinnikov (2013), The mechanism of firstraindrops formation in deep convective clouds, J. Geophys. Res. Atmos., 118, doi:10.1002/jgrd.50641.

1. Introduction

[2] Observational studies [e.g., Rosenfeld and Gutman,1994; Freud et al., 2008; Rosenfeld et al. 2008; Freudet al., 2011; Prabha et al., 2011] as well as numerical simu-lations [e.g., Pinsky and Khain, 2002; Benmoshe et al., 2012]suggest that rapid formation of raindrops in convectiveclouds begins when the effective radius exceeds a certainthreshold value reff _ c. Depending on the cloud type and thedroplet concentration, reff _ c varies from about 11 to 15 μm.Freud and Rosenfeld [2012] found that in developingconvective clouds, the effective radius reff is related to themean volume radius rv as reff≈ 1.08 � rv, and therefore thebeginning of raindrop formation can also be characterizedby the threshold value of the mean volume radius rv _ c.Another finding of that study was that the height Hp of firstraindrops formation above cloud base increases nearly line-arly as droplet number concentration N increases. The lineardependenceHp(N) was confirmed for different environmental

conditions and diverse geographical locations such as Indiaand Israel, suggesting that this linear (or nearly linear)dependence is a common characteristic of deep convectiveclouds with warm base. The observed dependence Hp(N) isshown in Figure 1a. The level of raindrop formation wasdetermined by Freud and Rosenfeld [2012] using thresholdvalues of rain water mixing ratio qPc, namely, 0.01 gkg� 1

and 0.03 gkg� 1. Most estimations were performed usingqPc of about 0.03 gkg

� 1. The values of the mean volume radiirv _ c corresponding to these thresholds were evaluated usingmeasured drop size distributions (DSDs). Figure 1b showsdependence Hp(N) obtained in simulations by two spectralbin microphysical (SBM) models: the adiabatic parcel model[Pinsky and Khain, 2002] and 2D Hebrew University CloudModel (HUCM) [Benmoshe et al., 2012]. In the simulations,the time instance of the beginning of raindrop formationwas determined using the same threshold values of qPc as inthe observations. Then, the values of the mean volume radiirv _ c, at which first raindrops formed were determined andcompared with the observations.[3] 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 lineardependence Hp(N) at which rv reaches its threshold value di-rectly follows from the theory of diffusion drop growth in anascending adiabatic parcel. According to the theory,Hper3v_ c Nwith the proportionality coefficient depending slightly on thetemperature [Pinsky et al., 2012].

1Department of Atmospheric Sciences, Hebrew University of Jerusalem,Jerusalem, Israel.

2Indian Institute of Tropical Meteorology, Pune, India.3Pacific Northwest National Laboratory, Richland, WA.

Corresponding author: A. Khain, Department of Atmospheric Sciencesof the Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904,Israel. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.2169-897X/13/10.1002/jgrd.50641

1

JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 1–18, doi:10.1002/jgrd.50641, 2013

[4] There is a good agreement betweenHp(N) derived fromin situ measurements and the results obtained using an adia-batic parcel model. Moreover, there is a good agreementbetween the results obtained using a dynamically simple par-cel model and those obtained with the multidimensionalcloud model. These findings raise an important question:“Why a dynamically simple adiabatic parcel model is ableto reproduce the height of the first raindrops formation in adynamically complicated nonadiabatic convective cloudinvolved in mixing with the drop free environment?”[5] To answer the question, we will show that: (1) among

a great number of cloud volumes, there are some that remainundiluted or are diluted only slightly, at least up to heightswhere the formation of first raindrops takes place; and(2) drop collisions are the most intense in these slightlydiluted cloud volumes.[6] We address these questions by analyzing observational

data and supporting numerical simulations using 2D and 3Dcloud models with spectral bin microphysics.

2. Observational Data Sets

[7] The instruments and techniques of the Cloud Aerosoland Precipitation Enhancement EXperiment (CAIPEEX-2009) measurements are described by Prabha et al. [2011]and Kulkarni et al. [2012]. CAIPEEX is an airborne observa-tional campaign which is investigating the aerosol-cloudinteraction primarily over continental Indian region. The firstphase of CAIPEEX in 2009 carried out observations overseveral locations in India, investigating the aerosol and cloudmicrophysics. A suite of instruments onboard the CAIPEEXaircraft is provided in Table 1. In the present study, we useddata from 11 flights of deep convective (congestus type)clouds within a wide range of thermodynamical and aerosolconditions, from highly polluted dry super continental condi-tions during the premonsoon to relatively clean and wetmonsoon conditions. A Cloud Droplet Probe (CDP; DropletMeasurement Technologies DMT, Inc.) and a Cloud ImagingProbe were used to measure the drop size distribution (DSD)

within the diameter range between 2 and 50μm. The cloudyvolumes were defined as zones where the cloud droplet numberconcentration N exceeded 10 cm�3. Liquid water content(LWC) was also measured by the HotWire LWC probe andwas used to correct the LWC measured by CDP.[8] The Aircraft Integrated Meteorological Measurement

System was used to measure the air temperature, the relativehumidity, and the winds. The concentration of cloud conden-sation nuclei (CCN) was measured using DMTCCN counter.Subcloud observations of CCN were carried out for three su-persaturation settings (0.2%, 0.4%, and 0.6%). The PassiveCavity Aerosol Spectrometer Probe (PCASP) was used foraerosol measurements (size distribution, effective radius,and concentration). Subcloud aerosol data were also consid-ered. All measurements were carried out at 1Hz samplingfrequency, i.e., were averaged over approximately 100m ofhorizontal distance. Instruments used in this study andtheir parameters are listed in Table 1 [see also Prabha et al.,

Figure 1. (a) The relationship between the height of the first raindrop formation and concentration ofactivated CCN, i.e., droplet concentration (in units (mg)�1) as follows for analysis of in situ measurements.(b) The same relationship obtained using simulations with cloud parcel model (solid lines). The values ofthe mean volume and effective radii corresponding to the threshold values of qPc are presented in the rightbottom corner table. The equations of the best linear fits are taken from a study by Freud and Rosenfeld[2012]. Dashed line with asterisks denotes the results of HUCM.

Table 1. List of Instruments on Board the CAIPEEX Aircraft WithData Sampling Detailsa

Variable Instrument Range/Resolution/Accuracy

Cloud droplet spectra DMT CDP 2 to 50μm, 1 to 2μm, 30 binsCloud particle spectra DMT CIP 25 to 1550μm, 25μm, 62 binsLiquid water content DMT LWC-

1000 to 3 gm�3, 0.05 gm�3, 0.01 gm�3

CCN DMT CCNcounter

0.5–10μm (0.1% to 1.2% SS)/0.5μm

Aerosol PMS PCASPSPP 200

0.1 to 3μm, 0.02μm, 30 bins

Temperature AIMMS T: �30�50°C/0.01°CWinds U,W: 0.01m s�1

Relative humidity RH: 0–100%/0.1%Altitude Radar

Altimeter0–2000 ft/0.15m

a(PCASP is the Passive Cavity Aerosol Spectrometer Probe, CIP is theCloud Imaging Probe, CDP is the Cloud Droplet Probe, DMT is DropletMeasurement Technologies, AIMMS is Air Data Probe, CCN is CloudCondensation Nuclei).

KHAIN ET AL.: RAIN ONSET

2

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 overBareilly (28.22°N, 79.27°E) on 23–28 August 2009. Some ofthe characteristics of microphysical observations overPathankot and Bareily are described in Prabha et al.[2012]. Observations over Hyderabad and over Bareilly weretaken from polluted dry conditions to relatively cleaner andwetter monsoon conditions as monsoon conditionsadvanced over these locations. On 22 June and 25 August,the aerosol concentrations were considerably lower abovethe boundary layer due to increased rainfall.[9] Dynamical and microphysical characteristics observed

at the cloud base and in the mixed layer are presented inTable 2. In some cases, the measured CCN concentration ishigher than the aerosol concentration. This is attributed tothe fact that the PCASP instrument did not measure thefine-mode particles (< 0.1μm). Monsoon cases (such as of22 June and 25 August) are characterized by a significantreduction in the droplet number concentration and increasein the mean radius, in comparison to the premonsoon cases.Maximum droplet number concentration (CDNC) exceeds1000 cm�3 during the premonsoon cloud samples (e.g., 16June). The conditions on 23 and 24 August may be consid-ered as polluted monsoon conditions. 24 and 28 May aresupercontinental conditions with elevated aerosol layers(also discussed in Prabha et al. [2012]). Cloud microphys-ics data during both ascents and descents through tops(100–200m below cloud top) of growing convective cloudswere used in the present analysis. During the profiling,clouds developed at certain levels showed some precipita-tion. Once precipitation was detected, further profiling wasnot carried out. The methodic of successive cloud penetra-tions just below the ascending cloud top of developingclouds allows tracking time and height evolution of cloudyparcels ascending from cloud base and located at the cloudtop during cloud development. This methodic allows thecomparison of results of observations with those obtainedusing a parcel model, in which parcel represents a cloudyvolume ascending in the cloud top.

3. Analysis of Measurements

3.1. Adiabatic Fraction

[10] The effect of cloudy air dilution will be characterizedby 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 adia-batic parcel ascending from the cloud base.[11] Figures 2–4 (left panels) show the LWC, the effective

radius, and the vertical velocity measured on 22 June 2009along horizontal aircraft traverses at levels 1.2 km, 3.4 km,and 4.7 km above the cloud base, respectively (some detailsof this monsoon case are presented in Prabha et al. [2011]).At 3.4 km, the effective radius reaches 15 μm that can serveas an indication of the beginning of raindrop formation.One can see that the ADF changes from the value close tozero to one along the traverses. Analysis of these resultsfurther shows that close to adiabatic (slightly diluted) cloudvolumes exist even at the distances as high as 4.7 km abovecloud base. These volumes exist both in updrafts and indowndrafts. The DSDs presented in these figures also showT

able2.

Sum

maryof

Observatio

nsUsedin

thePresent

Study,Including

Cloud

BaseHeight(m),Cloud

Top

Height(m),theMeanDropRadiusatCloud

Base,SpectralW

idth

atCloud

Base,

Num

berC

oncentratio

nof

Activated

Droplets(CDNC),Cloud

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CCN),SubcloudAerosol

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n,SubcloudNCCN,and

Maxim

umCDNCa

Date

Cloud

Base

Height(m)

Cloud

Top

Height(m)

MeanRadius

(μm)

SpectralW

idth

(μm)

Cloud

BaseCDNC

(cm

�3)

Cloud

BaseUpdraft

(ms�

1)

BLNa

(cm

�3)

BLNCCN

(cm

�3)

SubcloudNa

(cm

�3)

SubcloudCCN

(cm

�3)

Maxim

umCDNC,

(cm

�3)

24May

*3403

7287

3.26

±0.50

1.34

±0.16

519.91

±422.39

0.79

±3.10

2768.13

976.14

2579

±745

1610

±307

1396

28May

4500

7484

2.46

±0.17

1.16

±0.09

192.45

±157.14

0.64

±0.84

1428.28

1285.66

2194

±956

2001

±984

2776

15June

3158

7129

2.99

±0.18

1.15

±0.06

230.51

±76.24

0.59

±1.09

916.5

1045.00

955±103

1148

±298

1035

16June

2709

7116

3.37

±0.53

1.30

±0.19

340.01

±225.61

3.91

±1.89

1200.42

1447.75

1274

±196

1446

±331

1455

17June

3326

7150

2.23

±0.26

0.99

±0.17

113.82

±93.66

2.31

±1.70

1046.59

631.29

962±171

157±146

1251

20June

1958

7006

2.60

±0.54

0.97

±0.23

109.80

±128.62

2.02

±2.00

1150.89

2836.17

1276

±271

2922

±923

1073

21June

2452

7137

3.24

±0.36

1.24

±0.13

389.00

±293.95

2.55

±1.67

102.85

232.66

969±188

1272

±398

1188

22June

2062

7085

2.16

±0.30

0.86

±0.12

64.57±45.16

0.67

±0.92

655.35

1151.28

334±48

469±133

419

23Aug.

1180

4948

2.93

±0.18

1.32

±0.16

104.47

±110.69

1.05

±0.80

1494.17

6088.47

1449

±143

4975

±1819

1135

24Aug.

735

5561

3.96

±0.89

1.50

±0.24

185.26

±167.20

1.42

±0.73

3326.74

17884

2043

±148

6054

±2197

1143

25Aug.

650

7560

3.89

±0.98

1.40

±0.20

232.45

±180.84

3.69

±2.40

805.17

4919.89

648±106

2252

±882

884

a Aerosol

concentrationandCCNconcentrationat0.4%

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3

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10

12

14

r eff(

µm)

0

2

4LWC LWCadi

LWC

(gm

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95703 95705 95707 95709 957193.0

3.2

3.4

Alti

tude

(km

)

Time (UTC,Hmmss)

-12-6w

(m

s-1)

Figure 2. Left: Changes of LWC and LWCad, the effective radius, vertical velocity, and flight level as afunction of time over 1 km length traverse through the cloud at 3.1 km altitude (1.2 km above cloud base) inresearch flight on 22 June 2009. The zone of analysis of DSDs is denoted by the red box. Right: the DSDs atdifferent points of the traverse. Time in UTC, droplet concentration (cm�3), mean volume radius (μm),spectral width (μm), the quasi-steady supersaturation (%), adiabatic fraction, and temperature (°C) alongthe aircraft traverses are presented in the right panel.

93335 93500 93503 93506 93509

5.1

5.4

5.7

6.0

-12-8-404

12

14

16

0

2

4

LWC LWCadi

Time (UTC,Hmmss)

r eff(

m)

LWC

(gm

-3)

w (

ms-1

)A

ltitu

de (

km)

ADF=0.72

ADF=0.1

ADF=0.82

ADF=0.23

Figure 3. Left: Changes of LWC and LWCad, the effective radius, vertical velocity, and flight level as afunction of time over a traverse through the cloud at 5.45 km altitude (3.4 km above cloud base) in researchflight on 22 June 2009. The zones of analysis of DSDs are denoted by the red and blue boxes. Right: theDSDs at different zones of the traverse. Time in UTC, droplet concentration (cm�3), mean volume radius(μm), spectral width (μm), the quasi-steady supersaturation (%), adiabatic fraction, and temperature (°C)along the aircraft traverses are presented in the right panels.


4

multiple modes in DSDs. The formation of multimodalDSDs in monsoon cloud is probably related to in-cloudactivation of small aerosol (interstitial) particles ascendingfrom cloud base together with cloud drops. This process isdiscussed in Prabha et al. [2011] in detail. Figure 5 showsan example of a 66 s cloud pass in the premonsoon cloudobserved on 16 June at 7.1 km. The effective radius is nearlyconstant (10.8 μm) along the traverse. The CDNC in thisregion exceeds 600 cm�3 and LWC is ≈ 3 gm� 3. However,at the cloud edges, CDNC reduced to <100 cm� 3. The en-trainment mixing effect on the DSD is not seen beyond300m from the cloud edge, and there are clear indicationsof a wide adiabatic cloud volume. These wide adiabatic re-gions are also seen in the cloud samples at 6.1 km. Thereare slightly diluted regions in the cloud samples at 5.75 kmand 4.75 km, and there are oscillations in vertical velocityas illustrated earlier for monsoon cloud. Similar observationsare also noted in other premonsoon cloud samples.[12] 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 wereregistered in premonsoon clouds developing in extremelypolluted and dry atmosphere (16 June), in clouds during thetransition period 21 June and in monsoon clouds on 22June developing in moist and relatively less polluted air.Since clouds measured in CAIPEEX premonsoon wereextremely polluted, the first raindrops formed at severalkilometers above cloud base.[13] The existence of close to adiabatic volumes near cloud

top was reported earlier by Heymsfield et al. [1979], Paluch

[1986], Jensen et al. [1985], Gerber [2000], and in severalother studies. Gerber et al. [2008] did not find adiabaticvolumes at altitudes higher than about 1000m above cloudbase in shallow maritime cumulus clouds observed in theRICO experiment. At the same time, at this altitude, rvalready exceeded 12–14 μm and the clouds began drizzling[Gerber et al., 2008]. Thus, the first drizzle drops couldstill have formed at heights where nearly undiluted cloudyvolumes exist.[14] The decrease in the horizontally averaged ADF with

increasing the height above cloud level is usually attributedto the effects of mixing with the environment. This effectshould be especially pronounced in small clouds like thoseobserved in RICO. There are several physical mechanismsthat can decrease ADF with height that are not related tomixing. Sun et al. [2012] note that ascending cloud volumespush the neighboring air volumes upward. These volumesmay contain lower water vapor mixing ratios and, therefore,have higher lifting condensation levels than those ascendingfrom the cloud base level. Thus, the ADF evaluated as theratio LWC/LWCad, where the adiabatic liquid water contentLWCad is determined as LWC in a nonprecipitating adiabaticparcel ascending from the cloud base, underestimates thefraction of undiluted volumes.[15] Another reason that can lead to subadiabatic contents

in clouds measured in CAIPEEX is a comparatively lowsampling frequency that corresponds to spatial resolution ofabout 100m.Gerber [2000] andGerber et al. [2008] demon-strated that utilization of higher frequency reveals the exis-tence of higher number of undiluted volumes. We came to

LWC LWCad

ADF=0.55

ADF=0.1

ADF=0.93

ADF=0.51

91610 91612 91614 91616 91618 916206.3

6.6

6.9

-12-8-404

12

14

16

0

2

4

Time (UTC,Hmmss)

r eff(

m)

LWC

(gm

-3)

w (

ms-1

)A

ltitu

de (

km)

Figure 4. Left: Changes of LWC and LWCad, the effective radius, vertical velocity, and flight level as afunction of time over a traverse through the cloud at 6.75 km altitude (4.7 km above cloud base) in researchflight on 22 June 2009. The zones of analysis of DSDs are denoted by the red and blue boxes. Right: theDSDs at different zones of the traverse. Time in UTC, droplet concentration (cm�3), mean volume radius(μm), spectral width (μm), the quasi-steady supersaturation (%), adiabatic fraction, and temperature (°C)along the aircraft traverses are presented in the right panels.


5

a similar conclusion by analysis of observations carried out at10Hz sampling rate (not shown here) using a combination ofinstruments such as two Forward Scattering SpectrometerProbes (FSSP) and Cloud Aerosol Spectrometer (CAS). Itis noted that droplet number concentration remained highand did not show diluted cloud volumes in the penetrationsthat indicates similarity to cloud cores.[16] Finally, we note that at levels higher than about 3 km

above the cloud base in a warm environment such as duringCAIPEEX, the adiabatic liquid water content almost cer-tainly exceeds the value that can be reliably measured withthe DMT LWC probe. This is another reason for possibleunderestimation of the ADF in in situ measurements.[17] Despite the likely underestimation of ADF in deep

convective clouds, the analysis of many cloud samples fromGanges Valley during the transition to monsoon with veryhigh aerosol loading and under moist conditions suggeststhat up to 30% of cloud parcels at elevated layers are onlyslightly diluted, with ADF> 0.7.[18] Therefore, it seems that the question whether undiluted

or slightly diluted cloudy volumes exist at the level of first rain-drop formation can be answered positively. It is especially truefor deep convective clouds because the dilution decreases thebuoyancy which would prevent cloud development.

3.2. Conditions for Raindrop Formation

[19] Another question to be answered is whether undilutedor slightly diluted cloudy volumes have advantages for

raindrop formation. In convective clouds, the effective andthe mean volume radii increase with height, at least up tothe level of raindrop formation [Freud et al., 2008; Freudand Rosenfeld, 2012; Benmoshe et al., 2012]. At the sametime, Figures 2–5 (left panels) show that the effective radius(or the mean volume radius) remains nearly constant alongthe horizontal traverses despite substantial variations ofCWC (liquid water content of cloud droplets with radii below40–50 μm) and ADF (from near zero to about 1). The lowvariability of the effective radius horizontally (along theaircraft 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 andRosenfeld, 2012] and in numerical simulations [Benmosheet al., 2012]. The low variability of reff horizontally allowsone to represent the effective radius -altitude diagram asnearly functional dependence reff (z) with low dispersion.Rosenfeld and Gutman [1994], Freud et al. [2008], andFreud and Rosenfeld [2012] relate the formation of raindropswith the altitude, where the effective radius reaches its criticalvalue of 12–15 μm. Using the observational dependence ofthe altitude (over cloud base) at which reff reaches its criticalvalue on droplet concentration, Rosenfeld et al. [2012]proposed a new method to retrieve drop concentration andaerosols from satellites.[20] The low variability of the effective radius in the hori-

zontal means that threshold value of the effective radius canbe achieved at a level where the drop concentration and mass

Figure 5. Left: Changes of LWC and LWCad, the effective radius, vertical velocity, and flight level as afunction of time over a traverse through the cloud at 7.1 km altitude (5.1 km above cloud base) in researchflight on 16 June 2009 (premonsoon transition period). The zones of analysis of DSDs are denoted by letterfrom Figures 5b to 5e. The zone of downdrafts is marked by a box. Right: the DSDs at different zones of thetraverse. Time in UTC, droplet concentration (cm�3), mean volume radius (μm), spectral width (μm), thequasi-steady supersaturation (%), adiabatic fraction, and temperature (°C) along the aircraft traverses arepresented in the right panels.


6

content values may significantly differ in the horizontaldirection. Thus, achieving the threshold value of effectiveradius cannot be a sufficient condition for raindrop forma-tion. Indeed, where the CWC and the droplet concentrationsare low, the formation of raindrops is hardly possible. Thus,formation of the DSDs with reff (or rv) equal to or exceedingtheir threshold values is a necessary (beneficial), but not thesufficient condition for raindrop formation. As shown byFreud and Rosenfeld [2012], the collision kernel is propor-tional to r4:8eff . As follows from the stochastic collision equa-tion, the collision rate is proportional to the product of thecollision kernel and the square of the droplet concentration.Taking into account that reff is nearly constant along the hor-izontal traverses, it is reasonable to assume that for a givenreff exceeding the critical value, the formation of first rain-drops takes place in cloudy volumes with the maximumdroplet concentration. Indeed, variations of effective radius,say by ≈10%–20%, lead to the change of the collision kernelby factor of 1.6–2.5. At the same time, variations of square ofdroplet concentration can easily change collision rate by twoorders of magnitude. Thus, if variations of the effectiveradius do not exceed 20% of its maximum value, it is reason-able to expect that the maximum of collision rate will bereached 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 rainformation is well recognized and used in many bulk parame-terization schemes where the rate of raindrop formation isproportional to the CWC [e.g., Kessler, 1969]. Even whennot stated explicitly, such parameterizations are based onthe assumption that the first raindrops form in undiluted orslightly diluted volumes.

[21] This assumption is further analyzed on the basis of theright panels of Figures 2–5 showing the DSDs. These figuresindicate a similarity in the shapes of the first mode ofDSDs with peaks at the drop diameter of about 21 μm inde-pendently on the ADF values. The fluctuations of the concen-tration of the smallest droplets (forming the second DSDmode) can be attributed to in-cloud activation of CCN in par-cels ascending from the cloud base, or to partial drop evapo-ration in downdrafts [Prabha et al., 2011]. Formation ofsmall droplets can be also caused by nucleation of CCN inair volumes in which ascent is triggered by pressure fluctua-tions atop of ascending volumes [Sun et al., 2012]. Here, weare interested in the larger droplets belonging to the firstmode, because collisions among these droplets lead to rain-drop formation. One can see that the change in the “ampli-tude” of the DSD correlates well with the ADF changes.This finding illustrates the point that undiluted or slightly di-luted cloudy volumes have not only the largest CWC, but

Figure 6. LWC values measured at different heights in developing cumulus clouds observed during6 days of CAIPEEX 2009: premonsoon clouds developing in extremely polluted and dry atmosphere(16 June); transition period (21 June) monsoon clouds developing in moist and less polluted air(22 June). The lower panel shows the gradual transition of polluted clouds to clean monsoon clouds overBareilly in Ganges Valley. Color indicates the temperature measured at different vertical levels. Profilesof adiabatic LWC (in g m�3) are plotted with open circles. The decrease of this quantity above a certainlevel is related to the decrease in air density.


7

also the widest DSDs with a higher concentration of the larg-est droplets. To illustrate this point, we define the drop diam-eter D10 chosen by counting 10 largest droplets at the tail ofthe DSD and the corresponding size is D10. Drop diameterD10 thus characterizes the tail of largest droplets, thelarger the D10, the longer the tail. Hobbs and Rangno[1985] used a similarly defined measure, which they calleda threshold diameter, to characterize the broadness of theDSD. The relationship between the concentration of smalldroplets and D10 is shown in Figure 7. All the cloud basedata were screened out from this analysis. Small dropletnumber concentration is the concentration of droplets withdiameters below 20 μm. The color map denotes the ADF.The relationships are shown for both premonsoon and mon-soon clouds. There are several points to emphasize:[22] 1. Both the values of D10 and the concentration of

small droplets are low in diluted volumes. For instance, inthe premonsoon case (Figure 7d), all cloudy volumes withdroplet concentration lower than 500 cm�3 are diluted. It isa natural result of cloudy volume dilution by cloud free air.[23] 2. In most cases, large droplets are not observed in

strongly diluted volumes, except when droplet concentrationis extremely low. For instance, Figure 7c (monsoon) showsthat if droplet concentration is below 100 cm�3, all dropsare comparatively large.[24] 3. At a given concentration of small droplets, undiluted

and slightly diluted parcels have larger value of D10 as com-pared to diluted volumes, which is in agreement with

Figures 2–5. Undiluted and slightly diluted volumes may con-tain droplets with diameters exceeding 40μm. These largestdroplets in ascending adiabatic volumes can form as a resultof droplet collisions. Such drops are able to trigger rapid colli-sions and raindrop formation in the presence of significantCWC [Khain et al., 2000; Pinsky and Khain, 2002]. This indi-cates that collision process in adiabatic parcels is substantiallymuch more efficient than in diluted ones.[25] 4. Another important feature of Figure 7 is the trend of

the decrease of both the concentration of small droplets andD10 with the decrease of ADF (see Figures 7a, 7b, and 7d).This feature is also seen in the examples of DSDs presentedin Figures 2–5.[26] Thus, formation of the first raindrops should be

expected in undiluted or in slightly diluted cloud volumesdue to the specific features of their DSDs (large LWC, largerconcentration, and the existence of large droplets).[27] Besides, Prabha et al. [2012] showed that the

many cases spectrum width of the DSD is the highest inundiluted or slightly diluted cloud volumes. The mechanismsunderlying the appearance of undiluted and slightly dilutedvolumes are investigated with numerical modeling.

4. Numerical Simulations

[28] Determination of the exact location of first raindropsusing in situ measurements in a deep convective cloud is adifficult if not impossible task because raindrops detected

Figure 7. The relationship between concentration of cloud droplets with diameter smaller than 20μm,and D10, a droplet diameter such that the cumulative concentration of droplets with diameters exceedingD10 is equal to 10 cm�3. These relationships are obtained from in situ observations under different mete-orological and aerosol conditions. Color scale indicates adiabatic fraction (ADF) with blue (red) circlesrepresenting weakly (strongly) diluted volumes.


8

Figure 8. (a) The relationships between the effective and the mean volume radii in a numerically simu-lated deep convective cloud at the developing nonprecipitating stage and (b) several minutes after raindropformation. The solid straight lines show the approximation of the relationship by linear dependencesobtained using the least root square method. (c) The relationship between the effective and the mean vol-ume radius obtained for 1 Hz averaged DSDs measured in various locations, cloud types, and by differentcloud droplet probes. The color coding denotes different field campaigns and location data: red forCAIPEEX, blue for the Israeli rain enhancement program; purple for Suppression of PrecipitationExperiment in California, green for the Southern Plains Experiment in Cloud seeding of Thunderstormsfor Rainfall Augmentation; and grey for European Integrated project on Aerosol Cloud Climate and AirQuality interactions performed over the Netherlands and the North Sea. Numbers in the legend denotethe number of measurements that were used to calculate the linear best fit for each location [from Freudand Rosenfeld, 2012].

Figure 9. The fields of (a) CWC, (b) RWC, (c) dissipation rate, and (d) mean volume radius near the topof the developing convective cloud simulated using HUCM, t = 66min. Asterisks show the points whereDSD are plotted in Figure 13.


9

along a traverse can be produced at a different level andtransported to the observed location by sedimentation oradvection. This is why the combination of observations andnumerical modeling applied in this study is of high importance.To simulate deep convective clouds with parameters similar tothose observed in CAIPEEX, two numerical models with

similar SBM schemes were used: the 2D mixed-phaseHUCM [Khain et al., 2011; Benmoshe et al., 2012] and the3D System for Atmospheric Modeling (SAM)[Khairoutdinov and Randall, 2003; Fan et al., 2009a,2009b]. The SBM in the SAM is based on the original micro-physical scheme by Khain et al. [2004], modified by Fanet al. [2009a]. In both models, the SBM is based on solvingan 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 isrepresented by a 33 (in the SAM) and 43 (in the HUCM) massdoubling bins, i.e., the mass of a particle mk in the k� th bin isdetermined as mk=2mk� 1. All relevant microphysical pro-cesses and interactions of warm and ice processes are includedin the models. Since the focus of this study is on the formationof raindrops due to warm processes, the description of ice pro-cesses is not addressed here. The details of model treatment ofice can be found in the references cited above. In both models,DSD contains drops of all sizes with the radii range 2 μm to0.33 cm in SAM and from 2 μm to ~1 cm in HUCM. Dropswith the radii larger than 40–50 μm are assigned to raindrops.The dependence of the collision efficiencies on height is takeninto account. The HUCM contains detailed description of theeffect of turbulence on collision of cloud droplets. Turbulence

Figure 10. The field of adiabatic fraction corresponding tothe CWC field shown in Figure 9.

Figure 11. Fields of CWC plotted with time increment of 2min showing the evolution of bubbles A, B,and C. Figure 11d corresponds to time instance t = 66min as Figure 9.


10

is characterized using the turbulence kinetic energy (TKE) dis-sipation rate and the Taylor microscale Reynolds number.Using these parameters, look-up tables of turbulence-inducedenhancement factors are applied to the collision kernel forcloud droplets [Pinsky et al. 2008; Benmoshe et al., 2012].The turbulent diffusion coefficients are calculated using 1.5 or-der closure scheme (the K-theory) that includes solving thenonstationary equation for the TKE. These coefficients are ap-plied to describe the mixing of all thermodynamic quantitiesand size distributions. The detailed description of the modelis presented in Benmoshe et al. [2012].[29] Dynamically, both HUCM and SAM are based on the

anelastic equations. Dynamical frameworks of the HUCMand SAM are described by Khain and Sednev [1996] andKhairoutdinov and Randall [2003], respectively. In bothmodels, a high spatial resolution of 50m was used in all di-rections. This high-resolution allows models to resolve finecloud structure and microphysical processes related to theformation of droplets and first raindrops. The computationaldomain of HUCM was 25 km× 16 km in the horizontal andvertical directions, respectively. The SAM computational do-main is 12.5 km× 12.5 km× 14 km.[30] The thermodynamical profiles and CCN size distribution

were chosen close to those observed in polluted premonsoonclouds from CAIPEEX described in Prabha et al. [2011]. TheCCN concentration was assumed constant within the lower 2km layer and then decreasing exponentially with altitude. Tokeep the cloud within the computational domain during thesimulations, the wind shear was assumed weak in simulationswith HUCM (2 ms� 1 per 10 km in the lowest 10 km, and zeroabove the 10km level). No wind shear was included in theSAM simulations. During CAIPEEX, a strong easterly jetwas observed at heights above 7 km [Prabha et al., 2011].Since we are interested in the first rain formation taking placebelow this level, using a weak wind shear seems to be a reason-able compromise.[31] Note that turbulence (and related turbulent mixing)

within deep convective clouds is caused to a large extent bystrong gradients of vertical velocity, arising due to the workof buoyancy force. In simulated clouds, the maximum valuesof the dissipation rate may exceed 2000 cm2s� 3, i.e., veryhigh values [Benmoshe et al., 2012]. Thus, the utilization ofthe weak horizontal wind shear in the simulations does notnecessarily decrease the rate of turbulent mixing.[32] In HUCM, the convection was triggered by a 1 km

wide thermal bubble imposed near the surface for the first

10min of the simulation. The amplitude of the temperatureperturbation was varied randomly over time and space withinthe “heating zone.” More details of the initial conditions aredescribed in Benmoshe et al. [2012]. In SAM simulations,the cloud was triggered by adding random fluctuationsto the initial temperature field in the boundary layer asdescribed by Ovtchinnikov and Kogan [2000]. Differentapproaches used in the HUCM and SAM simulations to trig-ger convection affect the timing of cloud formation: utiliza-tion of a comparatively weak but prolonged heating in theHUCM leads to later cloud formation than a stronger instan-taneous temperature perturbation used in SAM. As soon ascloud forms, however, its further development and vertical ve-locity is largely determined by the stability of the atmosphere.[33] Note that the observed clouds contained ice at high

levels [Prabha et al., 2011]. Ice processes are also includedin the models. However, ice crystal number and mass con-centrations are low near the level of interest (~5.5 km) aroundthe time of the first raindrop formation and have little on clouddynamics and liquid-phase microphysics. In regard to graupeland hail, these hydrometeors form by freezing/riming of rain-drops or though the long process of riming at high levels.Consequently, these processes do not affect the early rain for-mation. The amount of graupel and hail was negligibly smallduring the developing stage of cloud evolution. Therefore,

Figure 12. The fields of RWC at t = 68 and 70min. The left and right panels correspond to the CWC fieldsshown in Figures 11e and 11f.

Figure 13. The DSD in the points located near cloud top(marked by asterisks) at t = 66min (the very beginning ofraindrop formation). The largest droplets form in the volumeswith maximum CWC and intense turbulence.


11

the ice processes play very little, if any, role in the formation offirst raindrops in both real clouds and simulations. These pro-cesses can, of course, be very important in the subsequentcloud development and precipitation production.

4.1. Two-Dimensional Simulations

[34] To illustrate the reliability of the DSD shapes simu-lated using the HUCM, Figure 8 shows the relationship be-tween the effective radii and the mean volume radii at theinstance before and several minutes after the formationof first raindrops (panels a and b). One can see that atthe nonprecipitating stage, the ratio reff /rv ≈ 1.08, which inexact agreement with the in situ measurements (panel c)[Freud and Rosenfeld, 2012].[35] Formation of raindrops leads to an increase of the ratio

reff /rv because the effective radius is determined by highermoments of DSD than the mean volume radius and increasesfaster with the formation of raindrops. Our supplemental sim-ulations of deep convective clouds under different aerosolconditions showed that this relationship between the meanvolume radius and the effective radius is valid for deep con-vective clouds with aerosol loadings within a wide range.CAIPEEX observations also confirm this relationship for awide range of aerosol pollution.[36] For detection of first rain, we kept the same threshold

that was used by Freud and Rosenfeld [2012] (see Figure 1),i.e., rain water content (RWC) ~ 0.03 gkg� 1. Figure 9 showsthe fields of CWC, RWC, the turbulent kinetic energy dissi-pation rate, and the mean volume radius near the top of adeveloping convective cloud. The cloud top zone shown inFigure 9 contains three turrets (or bubbles). The mean

volume radius reaches ≈9.3–9.5 μm at the tops of the bub-bles. The effective droplet radius is equal to ≈10–11 μm at thisheight, which is in agreement with the observations inpremonsoon clouds [Prabha et al., 2011]. The first raindropsform near the top of a decaying bubble B where high LWC isaccompanied by enhanced turbulence (note high dissipationrate) that intensifies collisions. This result agrees well withthose reported in detailed studies of the first raindrop forma-tion in turbulent clouds [Benmoshe et al., 2012 and Seifertet al., 2010]. The CWC at the turret tops is as high as 3.5–4gm� 3, which is close to the adiabatic value. Figure 10 showsthe field of ADF corresponding to the CWC field in Figure 9.The zones of relatively larger ADF exist near the tops of theturrets. One can see a slightly diluted core in turret A. In orderto understand why the highest values of ADF (and CWC)are reached at the turret tops or cores, it is necessary to traceback the history of a turret’s development. At each timeinstance, 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 Cis illustrated in Figure 11, where the CWC fields are presentedwith a time increment of 2min. All the bubbles develop fromthe same stream that starts developing from the cloud base.This stream then splits into several streams giving raise toformation of different bubbles (plumes, jets). The commonsource near cloud base leads to a situation when each bubble(especially near the tops) contains large CWC, comparativelyclose to the adiabatic value. Bubble B develops first andreaches the maximum height at t = 66min (Figures 9 and11). Later on, bubble B starts descending with velocity of4 ms� 1 until its dissipation, while its core near the top remains

Figure 14. Fields of CWC and RWC in the vertical cross section thorough the center of the computationalvolume at the time period during the beginning of the process of raindrop formation.


12

diluted only slightly (Figure 10). The first raindrops are pro-duced at the top of bubble B. After a delay, bubble A startsdeveloping rapidly (with maximum updraft velocity in it of15 ms� 1), producing the first raindrops within a few minutes.From the cloud top, the first raindrops spread along the edgesof the bubbles where downdrafts take place (Figure 12).[37] Analysis of time changes of elevation levels of differ-

ent bubbles indicates the existence of both ascending anddescending volumes in clouds in agreement with observa-tions (see Figures 2–5). For instance, cloud volume B reachesits maximum height of 6 km (panel d), and then it descends(panels e and f). Parcel C reaches 5 km level (panel d) anddescends to about 4 km level during several minutes. Thesedowndrafts can be a part of in-cloud oscillations drivenby buoyancy or can be explained by considerations of con-tinuity, when downward motion of parcels reached theirmaximum height is forced by continuously ascendingnew parcels. The mechanisms leading to such downdraftsrequire special investigation.[38] Note that the formation of first raindrops takes place at

heights of about 5.5 km, i.e., about 1.3 km above the freezinglevel. Further cloud evolution in the model is accompaniedby formation of ice, and cloud top reaches of about 10 km.

[39] Figure 13 shows an example of DSDs calculated in adeveloping convective cloud whose structure is shown inFigures 9 and 11. The DSDs are presented at the pointslocated near the top of the cloud at the times correspondingto the beginning of raindrop formation. These pointsare marked by asterisks in Figure 9. Comparison withFigure 2 reveals a similarity between the simulated andmeasured DSDs: in both cases, the DSD maximum of about40 cm� 3μm� 1 is located at the drop diameter of 20 μm. Thecloudy volume located near the cloud edge (x = 9.25 km)contains a larger amount of small droplets, possibly as aresult of partial droplet evaporation in cloud downdrafts.The largest droplets exist in the undiluted volume with max-imum CWC (x = 10.25 km).

4.2. Three-Dimensional Simulations

[40] Results obtained using 3D SAM simulations not onlysupport the results of the 2DHUCM simulations but also pro-vide new information concerning the cloud structure and theformation of first raindrops. Figure 14 shows fields of CWCand RWC at the time period during the beginning of the pro-cess of raindrop formation. One can see that at t = 30min, firstraindrops form at the top of the tower where the CWC is high,

Figure 15. The fields of the vertical velocity, CWC, RWC, and droplet concentration at z = 6 km duringthe process of rain evolution. One can see that after the formation of first raindrops near cloud tops withinthe areas of high CWC, mass of raindrops increases along cloud edges, where downdrafts take place. Inthese zones, droplet concentration decreases.


13

i.e., in volumes, which are diluted only slightly. Such positivecorrelation between CWC and RWC remains at t = 31min.After this short period, the increase in RWC leads to corre-sponding decrease in the CWC, so that at t = 33min high,RWC is observed in regions where CWC is comparativelylow. Thus, it is possible to see the zones of the first raindropformation only in high time resolution model output. Bylooking at the instantaneous fields of CWC and RWC att = 33min and for later times, one could jump to a wrongconclusion that rain forms at cloud edges, where CWCand droplet number concentration are low, and look for adifferent explanation of this effect, such as invoking spe-cific types of cloud mixing with surrounding. At the sametime, the increase in the RWC along cloud edges is causedby the raindrop transport from the cloud top by downdrafts.This is illustrated in Figure 15, where horizontal cross sec-tions in the fields of W, CWC, RWC, and droplet concentra-tion at z = 6 km are presented for a time period from 33 to37min. During this time period, the CWC is well correlatedwith vertical velocity, and its maximum is in the updraft. Atthe same time, RWC is maximum in zones of downdraftslargely near cloud edges. Droplet concentration is also min-imum near cloud edges. This decrease can be caused bymany reasons: evaporation in downdrafts, collection by

raindrops, and mixing of cloudy air with environment drop-let free air.[41] 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 withina wide range, from zero to the adiabatic or close to adiabaticvalues. One can see that just at the moment t = 30min, thatcan be considered as the time of the formation of first rain-drops, the maximum of LWC is close to LWCad. Formationof raindrops, their settling, as well as possible mixing withthe surrounding dry air decrease the maximum LWC values.Deviations of maximum values of CWC from the corre-sponding adiabatic values begin at levels above 5 km. It isinteresting that at height of ≈5 km, the maximum values ofCWC sharply decrease. Such decrease of maximum valuesof CWC at ≈5 km takes place in the 2D HUCM simulations(not shown) as well. Such decrease possibly reflects the tran-sition of the largest cloudy droplets to raindrops with the radiiexceeding 50 μm. This zone increases with time reflecting in-crease of RWC. Entrainment of environmental air may alsocontribute to the CWC decrease near 5 km level. Note, how-ever, that cloudy volumes with LWC close to LWCad remainat the higher levels. We interpret this effect in the sameway as in case of the 2D HUCM simulations: despite the fact

Figure 16. Upper row: PDF of cloud water content at different time instances. Red curves denote adia-batic LWCad. Lower row: Vertical profiles of probability distribution function of effective radius at the timeperiod of first raindrop formation. Height is measured from the surface. Observations of effective radiusduring a transition (premonsoon to monsoon) period with high aerosol concentrations are shown with blacksymbols. The points of low effective radii at height of about 6 km did not belong to the deep convectivecloud under investigation.


14

that the roots of the ascending turrets can mix with thesurrounding air, the tops of the turrets contain close to adia-batic volumes.[42] The 3D simulations indicate good agreement with ob-

servations as regards to the vertical profiles of the effectiveradius. Figure 16 (bottom) shows the vertical profiles ofthe probability distribution function of effective radius atthe time period of first raindrop formation. One can seeseveral specific features of the profiles discussed both in theobservational section of this study, as well as reported inother observational studies [e.g., Freud et al., 2011; Freudand Rosenfeld, 2012]: in spite of very high variability ofthe CWC at each level, the variation of the effective radiusis comparatively small; and the first raindrops form at thelevel where the effective radius reaches 10–11 μm. Theobservations of effective radius from a cloud observed duringthe high aerosol pollution and transition from premonsoon tomonsoon on 20 June is compared with the simulations. Itmay be noted that there is close agreement between theobservations and the simulations both in the mean verticalprofiles and the spatial variations in the simulation. The anal-ysis of the numerical results and observations explain why adynamically simple adiabatic parcel model is able to repro-duce well the height of the first raindrop formation: theevolution of the DSD within undiluted or slightly dilutedcores of developing clouds unfolds similarly to that inadiabatic volumes and does not depend on the trajectory ofvolume ascent.

5. Discussion and Conclusions

[43] The main conclusion of this study is that the first rain-drops form in undiluted or slightly diluted volumes near thecloud top where the CWC reaches its maximum. This conclu-sion suggests the following conceptual scheme of convectivecloud dynamics. At the stage of development, convectiveclouds contain many rising plumes. During their motion,these plumes mix with the surrounding cloudy plumes andsometimes with environment air, while in the largest plumesundiluted or slightly diluted cores remain. At a certain stageof a plume evolution, its roots may disappear, so the instantimage of the CWC field may not reveal the roots of suchcores at the cloud base. DSDs in the cloud cores evolve likethose in ascending adiabatic parcels. These phenomenaexplain the ability of a dynamically simple spectral binmicrophysics parcel model to simulate the height of the forma-tion of the first raindrops. Correspondingly, it explains thenearly linear dependence of the altitude of the first rain forma-tion on the droplet concentration, as follows from the theory ofdiffusion growth in adiabatic updrafts. Measurements andsimulations were performed for clouds with warm cloud ba-ses. We believe that in case when first raindrops form due towarm processes, our conclusions remain valid in case ofcolder cloud bases. For instance, Freud and Rosenfeld[2012] found linear dependence of height of first raindrop for-mation on drop concentration for India, Israel, California,Texas, and Europe.[44] Note that it is quite natural to expect the existence of

undiluted (or slightly diluted) volumes in updrafts of deepconvective clouds. For instance, a widely accepted methodto evaluate the maximum of the updraft velocity using theCAPE is fully based on the concept of the ascending

adiabatic parcel. Strongly diluted volumes have no buoyancyand would hardly allow convective clouds to reach heightsof 10–12 km.[45] The most important observational and numerical re-

sult obtained in the study is that DSDs in undiluted volumesare larger and wider compared to those in diluted volumes.So, the measurements clearly indicate that process of colli-sions is more intense in undiluted volumes. We postulate,however, that the location of the first raindrop formationcan hardly be detected in measurements. As numerical simu-lations show, the formation of first raindrops (in a very smallamount) occurs in the zones of high CWC very rapidly, overa few minutes. This process can easily be masked by the sub-sequent appearance of raindrops at cloud edges where CWCis low. A great number of in situ measurements in clouds, aswell as measurements from satellites, show that first rain-drops form when the droplet effective radius reaches a criticalvalue. However, these measurements do not allow to deter-mine the location of the first raindrop formation since theeffective radius changes horizontally only slightly. Onlynumerical simulations performed with high spatial (~50m)and temporal (few seconds) resolutions allow to track cloudevolution in detail and to determine the zones of the forma-tion of first raindrops.[46] The concept that the first raindrops form in the adia-

batic (or nearly adiabatic) volumes is supported by the resultsof numerous observations and numerical simulations, show-ing that an increase in the droplet concentration (caused forinstance by an increase in CCN concentration), leads to adecrease in supersaturation that hinders formation of largedrops and delays raindrop formation [e.g., Khain, 2009].This CCN effect can be distinctly seen only in the adiabaticascending volumes where all growing droplets compete for acertain amount of available water vapor. As we saw fromFigures 2–5, in nonadiabatic volumes, an increase in dropletconcentration is often accompanied by increase in size andconcentration of large droplets.[47] The results of the present study explain the decrease of

the threshold value of reff from ~15 μm to ~10–11 μm whendroplet concentration increases from clean maritime to verypolluted continental clouds, as found in the numerical simu-lations [Benmoshe et al., 2012] and in situ observations[Prabha et al., 2011]. The collision rate is proportional tothe product of the collision kernel and the square of dropletconcentration. According to Freud and Rosenfeld [2012],the value of the collision kernel is proportional to r4:8eff .Thus, the “threshold values” of the collision kernel in cleanand polluted air differ by the factor of ≈7. This differencecan be compensated by a corresponding increase in dropletconcentration in polluted clouds.[48] According to the observations and numerical results

presented here, the dynamical structure of convective cloudscan be conceptually represented as a tree with many branchesrooted near the cloud base. Thus, a convective cloud may havemany plumes containing undiluted or slightly diluted coressurrounded by the more diluted cloud air. One possible mech-anism of plume formation is cloud-entrainment interface insta-bility [Grabowski and Clark, 1991, 1993]. According to thesestudies, a characteristic linear scale of a plume is about onetenth of the cloud radius. In deep convective clouds, the bub-bles can be large enough to be resolved in observations at


15

100 m sampling intervals. This means that even the samplingat 1 s interval can identify unique signatures of slightly mixedregions of the deep convective cloud. The observations athigher resolution may be useful in the investigation of mixingin pockets. According to the results of the numerical simula-tions, the maximum values of LWC in deep convective cloudscan be as high as 3–4 gm� 3 and even higher.[49] The fine dynamical structure of convective clouds

characterized by the existence of many evolving plumescan 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 350mshow a formation of a cloud with a single main core [Khainet al., 2004, 2005, 2008]. The cloud structure simulated usingsuch a coarse resolution agrees well with the traditional con-cept assuming that a cloud has single undiluted coresurrounded by diluted cloud air [Riehl and Malkus, 1958;Riehl and Simpson, 1979]. At the same time, both conceptualschemes of the cloud dynamical structure are similar inregard to the mechanism of the first raindrop formation, as inboth schemes raindrops form in adiabatic (or nearly adiabatic)updrafts. Indeed, the simulations of rain formation using 350mhorizontal grid spacing [Khain et al., 2004, 2008] and the 50mgrid spacing used in the present study yield similar heights ofraindrop formation and a similar response of the height of therain formation to aerosol concentration variations.[50] It is well known that according to the theory of the

drop diffusional growth, the DSDs tend to narrow withheight (in the space of drop radii) in ascending adiabatic par-cels. A question arises, why the widest DSD form in slightlydiluted cloud volumes? This problem was investigated byPinsky and Khain [2002] in detail. It was shown that despitethe fact that diffusion drop growth dominates in theDSD formation at the developing stage, collisions betweendroplets play a very important role producing the largest“superadiabatic” droplets in the droplet spectra. The smallestdroplets may form due to in-cloud nucleation of CCN, whichwere not activated near cloud base and ascended together withdroplets to regions of strong updrafts, where supersaturationexceeds its value near cloud base. This process of formationof new droplets inside clouds at altitudes of several kilometers

above cloud base was investigated numerically by Pinsky andKhain [2002], Segal et al. [2003], Khain et al. [2012], andothers. Observations illustrating this phenomenon are de-scribed in the study by Prabha et al. [2011]. Cloud volumesat the cloud base have different updraft velocities, which leadsto different droplet concentrations as well as different heightsabove 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 broadeningand high variation of concentration of the smallest droplets[Khain et al., 2000; Segal et al., 2003].[51] In the light of the conclusion that the first raindrops

form in slightly diluted cloud volumes, another questionarises concerning the role of mixing between cloud volumesand the dry environment (cloud free air) in the formation offirst raindrops. The role of mixing and entrainment in DSDformation was discussed in numerous observational andnumerical studies. A detailed survey of these studies ispresented in a review by Devenish et al. [2012]. Despite sig-nificant efforts, many problems remain unresolved due to thecomplexity of the entrainment and mixing process. The 1 Hzfrequency measurements discussed in the present study, aswell as numerical simulations performed using HUCM andSAM in their current configurations are not sufficient forinvestigating this process in detail.[52] However, it is to be mentioned that 10 Hz observa-

tions (not presented) during the second phase of CAIPEEXobservations illustrate that main DSD features found in1 Hz observations and discussed here remain valid for 10Hz observations as well.[53] We limit the discussion to three specific issues that

may be useful for better understanding the role of mixing ofcloudy volumes with dry and droplet-free environmentduring the formation of first raindrops. The first commentconcerns the possibility of existence of undiluted volumesin turbulent convective clouds. The distance at which envi-ronmental air penetrates the cloudy air due to turbulent diffu-sion can be evaluated as L≈

ffiffiffiffikt

p, where k is a turbulent

diffusion coefficient. In highly turbulent deep convectiveclouds k ~ 50 m2s� 1 [Benmoshe et al., 2012]. The timeneeded for a growing thermal to reach the altitude where firstraindrops form is about 5min., yielding L ≈ 120� 150 m.Thus, plumes that are over several hundred meters in widthare likely to contain undiluted or slightly diluted cores. It isespecially true for deep convective clouds where updraftsare surrounded by saturated or supersaturated cloudy air. Insmall clouds such as in RICO, entrainment and mixing caneliminate undiluted cores, thus decreasing the probability ofraindrop formation. An indirect evidence of the fact thatmixing of cloudy air with the environment has a smallereffect on formation of the first raindrops was obtained in asupplemental numerical simulation in which the CCN con-centration was initially assumed constant in the height. In thissimulation, significant amounts of CCN penetrate updraftswithin a wide range of heights. The results (not shown here)indicate that due to mixing with the environment, a signifi-cant increase in CCN concentration at high levels leads toan increasing concentration of small droplets at the lateraledges of a cloud. These droplets form by activation of aero-sols entrained into cloud updrafts. At the same time, theCCN from the environment do not entrain into the undilutedcloud cores. Thus, droplets nucleated at the upper levels

Figure 17. Time dependence of accumulated rain in simu-lation with exponential decrease in CCN concentration andwith CCN= const with height at t = 0.


16

do not affect (or affect only slightly) the formation of firstraindrops. Figure 17 shows a similarity between the accumu-lated rain amounts in simulations with an exponential de-crease of CCN concentration with altitude and those inwhich CCN concentration is constant with height. A low sen-sitivity of precipitation to CCN entering into clouds at upperlevels was also reported by Fan et al. [2010], who used ahigh-resolution 3D SAMmodel with spectral bin microphysics.[54] The second comment relates to the fact that the size

and concentration of the largest droplets in the diluted cloudyvolumes are found to be substantially lower than those inundiluted or slightly diluted volumes. Since entrainment ofdry drop-free air from environment increases the rate of dilu-tion, the role of the entrainment in the acceleration of rain-drop formation can be questioned. The results obtained inthe present study regarding the process of entrainment andmixing are in agreement with those from Paluch [1986]:“Since such process does not affect the large end of the drop-let spectrum, then entrainment and mixing has little immedi-ate effect upon collection efficiencies of hydrometeorsgrowing by accreting the cloud droplets. If mixing does notgreatly influence (reduce) the local cloud droplet concentra-tions and sizes, then the onset of the coalescence process willbe relatively uninfluenced by entrainment.” This conclusionactually means that the process of the first rain formationis determined largely by the basic condensation and colli-sions mechanisms in ascending near adiabatic volumes.[55] The third comment concerns the numerical represen-

tation of turbulent mixing in the numerical models used in thestudy. As seen in Figures 2–5, the effective radius changesonly 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 waterfraction, LWC, and the droplet concentration. The low vari-ability of the effective radius along the horizontal traverseswas 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 lowvariability is often interpreted as a consequence of eitherextreme inhomogeneous mixing or homogeneous mixing athigh relative humidity [e.g., Gerber et al., 2008; Freud andRosenfeld, 2012]. At the same time, Figure 9d of this study,as well as the vertical profiles of effective radius calculatedfor 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 wellthis low variability of the effective radius within clouds atany specific level, as well as the vertical profiles of the effec-tive radius. Note that in these models turbulent mixing isparameterized using a standard 1.5 closure scheme basedon the K-theory, according to which subgrid turbulent fluxesare proportional to the gradients of grid resolvable values. Inthis approach, changes of all variables in model grid pointsare considered uniformly distributed over the air volumesrepresented by the grid points. Such mixing can be ratherattributed to homogeneous, or “mechanical.” The modelsused in the present study do not include additional terms usedin several studies [e.g., Grabowski, 2007; Morrison andGrabowski, 2008] to adjust droplet concentrations accordingto the inhomogeneous mixing scenario. Thus, the traditionalapproach to parameterization of turbulent mixing allowshigh-resolution models to successfully reproduce the features

typically attributed to the effects of inhomogeneous mixing.We hypothesize that this is because the internal cloudstructure forms largely by mixing of saturated or very closeto saturation volumes, in which case inhomogeneous and ho-mogeneous mixings turn out to be undistinguishable. Thisproblem will be considered in more detail in a separate study.[56] Note that the results concerning the microphysical and

dynamical cloud properties (such as DSDs, LWC values, ver-tical profiles of the effective radius, the relationship betweenthe effective radii and the mean volume radii, the height ofthe first raindrop formation, etc.) obtained in simulationswith the 2D HUCM and 3D SAM models turned out to bequite similar. The difference in the heights of first rain forma-tion of about 400m (6.1 km in SAM and 5.7 km in HUCM)can be attributed to a more detailed description of turbulenteffects on drop collisions in HUCM accelerating collisionsnear the cloud top, to a utilization of different convectioninitialization procedures and different wind shears and, ofcourse, to the difference in the dimensionality of the models.Thus, in spite of limitations of the 2D geometry in simula-tions of cloud dynamics discussed in detail by Benmosheet al. [2012], the 2D geometry can be successfully used foranalysis of microphysical processes in clouds.[57] The main practical importance of the study indicating

that process of raindrop formation is determined by basicmicrophysical processes within ascending adiabatic volumesis that we can predict the height of the formation of first rain-drops considering the processes of nucleation (including in-cloud nucleation), diffusion growth, and collisions. In ouropinion, the belief in the possibility of such a predictionwas lost to a large extent when the mechanism of inhomoge-neous mixing was considered as the main cause of formationof large droplets and first raindrops (see overview byDevenish et al. [2012]). The result that first raindrops formnear cloud top explains why the process of rain formationcan be investigated from satellites that measure the effectiveradii only within the narrow cloud top layer [Rosenfeldand Lensky, 1998]. The results obtained in this study providea physical basis for retrieval algorithms of cloud microphys-ical properties and aerosol properties using satellites[e.g., Rosenfeld et al., 2012] and can be useful in the param-eterization of autoconversion in numerical cloud models.

[58] Acknowledgments. This research was supported by the U.S.Department of Energy’s Atmospheric Science Program Atmospheric SystemResearch, an Office of Science, Office of Biological and EnvironmentalResearch program, under grant DE-SC0006788, and the Binational US-IsraelScience Foundation (grant 2010446). The CAIPEEX project and IITM arefully funded by the Ministry of Earth Sciences, the Government ofIndia, New Delhi. The authors acknowledge with gratitude that the teameffort and the dedication of the IITM scientists made CAIPEEX a greatsuccess. The Pacific Northwest National Laboratory (PNNL) is operatedby Battelle for the DOE under contract DE-AC06-76RLO 1830. Thisresearch used resources of the National Energy Research ScientificComputing Center, which is supported by the Office of Science of theU.S. Department of Energy under contract DE-AC02-05CH11231.[59] The authors express their gratitude to Rosenfeld for his interest in

the study and useful discussions. Thoughtful comments from AndrewHeymsfield and two anonymous reviewers helped substantially to improvethe manuscript.

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