In situ aircraft measurements of cloud microphysical properties and aerosol during the 1st phase of the Cloud Aerosol Interaction and Precipitation Enhancement EXperiment (CAIPEEX-I) over the Indian sub-continent provided initial opportunities to investigate the dispersion effect and its implications for estimating aerosol indirect effects in continental cumuli. In contrast to earlier studies on continental shallow cumuli, it is found that not only the cloud droplet number concentration but also the relative dispersion increases with the aerosol number concentration in continental cumuli. The first aerosol indirect effect estimated from the relative changes in droplet concentration and effective radius with aerosol number concentration are 0.13 and 0.07, respectively. In-depth analysis reveals that the dispersion effect could offset the cooling by enhanced droplet concentration by 39% in these continental cumuli. Adiabaticity analysis revealed aerosol indirect effect is lesser in subadiabatic clouds possibly due to inhomogeneous mixing processes. This study shows that adequate representation of the dispersion effect would help in accurately estimating the cloud albedo effect for continental cumuli and can reduce uncertainty in aerosol indirect effect estimates.
 A major uncertainty in estimation of climate sensitivity to increased anthropogenic aerosol arises from uncertainty in estimating the aerosol indirect effect (AIE). As a consequence of increased cloud condensation nuclei (CCN) concentrations and their effect on cloud droplet dispersion, the Twomey effect (cooling) may be significantly offset over continental polluted clouds. There are several theoretical and observational studies of aerosol-cloud interactions and AIE estimates on maritime stratocumuli [Lu et al., 2007; Brenguier et al., 2000].
 Cumuli cover a significant fraction (>1%) of the earth surface [Albrecht, 1989]. Although fractional coverage of cumuli is small, they play key roles in maintaining the energy and moisture budgets of the tropics [Neggers et al., 2009] and the lower tropospheric thermodynamic structure over extensive areas of the earth's surface [Kollias and Albrecht, 2010]. Deep cumuli tend to be the source of the most intense precipitation because of their greater geometrical thickness and strong vertical air velocity, which tends to support high liquid water contents (LWC), promoting the rapid growth of precipitation sized particles by the accretion of droplets. Compared to maritime stratocumuli, continental cumuli are more susceptible to mixing processes due to their greater thickness, strong convection and entrainment, they undergo large changes in microphysical properties and limited cloud lifetime. Convective cumuli exhibit smaller cloud droplet sizes and are less effective for warm rain initiation over land than over ocean [Rosenfeld and Lensky, 1998]. However, systematic analysis of aerosol-cloud relationships for continental convective cumuli is sparse.Lu et al. reported aerosol-cloud relationships from fourteen scattered and isolated warm continental cumuli sampled over the Houston region during Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS) campaign.Hudson and Yum  were the first to demonstrate that in theory and in some limited measurements, higher CCN concentrations cause ‘slightly’ broader cloud droplet spectra. Later Liu and Daum  showed that anthropogenic aerosol exert an additional effect on cloud properties, derived from changes in the spectral shape of the size distribution of cloud droplets in polluted air.
 Increase in ambient aerosol concentrations due to anthropogenic activities can modify the microphysical properties of clouds, thereby affecting the climate system [Intergovernmental Panel on Climate Change, 2007; Ramanathan et al., 2001]. Anthropogenic aerosol acting as CCN can increase cloud droplet number concentration (Nc), which thereby enhances cloud albedo [Twomey, 1974]. This process is usually referred to as the Twomey effect or cloud albedo effect. The resulting smaller cloud droplets also suppress the collision-coalescence process and thereby inhibit rainfall and enhance cloud lifetime [Albrecht, 1989]. This process is known as second AIE or cloud lifetime effect. Even though many in situ and satellite remote sensing studies have shown observational evidence of Twomey's hypothesis; the uncertainty in AIE estimates is still large [Feingold et al., 2003; McComiskey and Feingold, 2008]. Shao and Liu  made a critical examination of the observed AIE estimates and explained the discrepancies in the first AIE from different methods and on different scales and presented an improved parameterization of the first AIE that can be used in global climate models.
 The ratio of standard deviation (σ) to mean radius (rm) represents the relative dispersion (ε = σ/rm) of cloud droplet size distribution. A large value of σ indicates a mixture of large and small cloud droplets, while a small value indicates all droplets of approximately the same size. The dispersion effect can either offset or enhance the Twomey cooling effect and it is proportional to the Twomey effect in magnitude [Liu and Daum, 2002]. In general, AIE is mainly depicted as a relative change in Nc for relative changes in aerosol or CCN concentrations, ignoring the effect of dispersion on cloud droplet size distribution. Assuming a constant effective radius ratio (β = effective radius/mean volume radius) for cloud effective radius (Reff) parameterization had been a common practice and was used for evaluation of AIE. Recent studies have shown that enhanced aerosol loading enhances ε and β and the enhanced ε exerts a warming effect (Dispersion Effect, hereafter referred to as DE) that tends to offset the Twomey effect by 10–80% depending on the relationship between β(ε) and Nc [Liu and Daum, 2002; Rotstayn and Liu, 2003; Peng and Lohmann, 2003]. By combining detailed cloud microphysical observations from several field experiments, Liu et al.  demonstrated that DE could offset the Twomey effect by as much as 42% and also emphasized that practice of describing the Twomey effect as first AIE is no longer valid as AIE is an algebraic sum of both the Twomey and dispersion effects [Liu and Daum, 2002]. On the contrary, Martins and Silva Dias suggested that an increase in CCN concentrations from biomass-burning aerosol might lead to an additional effect caused by a decrease inε.Lu et al.  noted that there are no discernible effects on droplet spectral dispersion in shallow continental cumuli. Berg et al.  also report that dispersion is not a strong function of pollutant loading in shallow cumuli and does not offset the Twomey effect. Hence, there is a need to establish the relation between εand sub-cloud aerosol concentration (Nacc) for polluted continental cumuli, and examine their effects on AIE.
 Including the DE in global climate models (GCM) may reduce the global mean AIE [Peng and Lohmann, 2003; Rotstayn and Liu, 2003]. Liu et al.  have shown that using an unrealistically small ε, such as assuming a mono-disperse cloud, can lead to significant overestimation of cloud albedo by climate models, resulting in a negative bias of global mean estimates of shortwave cloud radiative forcing that is comparable to the warming caused by doubling the CO2concentration. They suggested that dispersion bias may be one of the reasons for overestimation of shortwave radiative cooling in many climate models. However, the main difficulty is that the factors that determine DE are poorly understood. A better understanding of DE may improve aerosol-cloud interactions in GCMs, which in turn reduces the uncertainty in AIE estimates.
 Relative dispersion (ε) is a measure of the relative width of the cloud droplet distribution. It is also reported that, theory predicts broader cloud drop spectra (σ) for continental clouds [Hudson and Yum, 1997; Miles et al., 2000], while in the observations cleaner clouds show broader spectra and continental clouds show narrower spectra, i.e., σ is larger for maritime clouds [Yum and Hudson, 2005]. It is expected that Nc increases with Nacc and as a result droplet mean radius is smaller for larger Nc, i.e., at larger Nc the competition for available water vapor among the activated droplets is higher, so the droplets cannot grow very large. Polluted clouds show a smaller Reff throughout the cloud [Lu et al., 2008]. In most of the studies, aerosol-cloud interaction is explained by considering only changes in Nc and rm, neglecting changes in the spectral shape of the cloud droplet size distribution. However, it has been shown that ε has a significant role in determining cloud radiative properties [Liu et al., 2008]. Hence, this topic needs further research with detailed analysis of observations under different atmospheric dynamical conditions and cloud types.
 Over the Indian sub-continent, information on AIE and DE from direct observations is almost nonexistent till now. This study focuses on this aspect by providing direct estimates ofεand its relationship with aerosol concentrations from in situ measurements for the first time. The main objective of this study is to present the cloud-aerosol relationships in warm continental cumuli during pre-monsoon and monsoon seasons over the Indian region using data sets from CAIPEEX-I campaign. In this context, this study addresses the following objectives: (i) to investigate observational evidence of the effect of aerosol on Nc and Reffin continental warm cumuli, (ii) to estimate AIE, (iii) to examine the relation between sub-cloud aerosol concentration (Nacc) and ε, (iv) to estimate DE and the resultant AIE in continental warm cumuli and (v) the effect of adiabaticity on cloud microphysics (LWC, Nc and Reff) and AIE estimates.
 Geographical locations of the experimental regions including research flight paths and wind fields at 850 hPa during different months in pre-monsoon and monsoon seasons are given insection 2. A brief description of data is given in section 3. Section 4 deals with the AIE estimation using flight averaged data. Also in section 4, we examine the relationship between ε and Nacc and quantify DE using effective radius ratio (β) and water per droplet (L/Nc) and its influence on AIE estimates.
2. Experimental Regions and Meteorology
 The objective of CAIPEEX-I was to document and understand aerosol, CCN concentrations and cloud microphysical properties such as Nc, Reff, and LWC over different regions during pre-monsoon and summer monsoon seasons. A detailed description of the above CAIPEEX project can be found on the Web page:http://www.tropmet.res.in/∼caipeex/. The scientific objectives, instruments used in the aircraft and data quality are described in Kulkarni et al. . CAIPEEX-I was conducted for intensive cloud and aerosol observations using an instrumented Piper Cheyenne aircraft over different parts of India during the period May–September 2009, which includes pre-monsoon, active and break monsoon conditions. Used in the present study were data from aircraft missions conducted over different regions from the following base locations in India namely Pathankot (PTK) (32.2°N, 75.6°E), Hyderabad (HYD) (17.5°N, 78.4°E), Bareilly (BLY) (28.4°N, 79.4°E) and Pune (PNE) (18.5°N, 73.8°E). Aircraft measurement strategy was to make aerosol and CCN sampling almost at constant flight level below cloud base and ascend to do cloud profiling at several vertical levels covering the entire cloud. Cloud passes were made at 300 m intervals and the aircraft was kept straight and level during each cloud pass and was allowed to ride with the updrafts and downdrafts. Some of the cloud profiling was done from cloud top to cloud base and CCN sampling was done below cloud base just before landing. Maps of the four base stations PTK, HYD, BLY and PNE, where mainly continental cumulus clouds were sampled, and the flight paths are shown inFigure 1. For background, monthly averages of Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) averaged for the corresponding months are shown. There were higher AODs in northern India, especially over the Indo-Gangetic Plains and relatively lower AODs in the southern latitudes.
Figure 2shows NCEP/NCAR reanalysis wind fields at the 850 hPa level and MODIS Level 3 cloud water effective radius (MOD08) during May, June, August and September 2009. In the month of May, heat wave conditions prevailed over northern India and winds were northerly, which brought in dust aerosol from desert regions. In addition, forest fires were also observed over PTK during pre-monsoon season. The clouds were mainly convective super-continental cumuli over PTK and the cloud base height and temperature was 3 to 4 km and 10°C. As the analysis was restricted to warm clouds, few cloud samples were available from PTK. Monsoon rains usually begin over the Indian subcontinent during the first week of June, however the monsoon was delayed in HYD by at least a week. Although a weak trough oriented west southwest-east northeast continued to lie across South Central India, the weather in the trough region continued to be dry, hot and hazy. In HYD, cloud base height and temperature was 1.5–2.5 km and 14–21°C. In August, the monsoon rainband extended from northeast India to the southwest, leaving northwest India without cloud cover. A light westerly wind at all altitudes existed over BLY and the wet surface sustained very high moisture at low-levels resulting in large haze particles. Cloud base height and temperature ranges were 0.8–1.2 km and 22–25°C over BLY. In September, the northern limit of the monsoon front crossed the region of PNE and the winds were weak. The weak monsoon circulation, which allowed the development of a thick haze layer with its influence on continental cumuli were observed. Over PNE, the cloud base height and temperature was 2.5 km and 15°C.
3. Data and Methods
 Data presented here were obtained using aircraft mounted aerosol and cloud probes from Droplet Measurement Technologies (DMT Inc.) such as the Passive Cavity Aerosol Spectrometer Probe (PCASP) for the particle size range of 0.10 to 3.0 μm, a CCN counter, a Cloud Droplet Probe (CDP) measured the cloud droplet size distribution from 2 to 50 μm, a Hot-Wire Liquid Water Content sensor (LWC-100, range 0.0 to 5 g/m3) and an Airborne Integrated Meteorological Measurement System (AIMMS-20) probe for temperature, humidity, wind speed and direction. The present analysis was restricted to warm cloud parcels (cloud parcel temperature, T > 0°C) and droplet diameter for modal liquid water content (DL) with a threshold of less than 24 μm [Andreae et al., 2004] to restrict the analysis to non-precipitating cloud samples. All the instruments PCASP, CDP, AIMMS were factory calibrated at DMT in April 2009 just before the campaign. LWC was measured by the two Hotwire probes, HW-DMT and HW-CIP (Cloud imaging probe). During the flight, zero offset (baseline) changed from time to time and was corrected for each of the probes by calculating a 2–5 min running average (averaging length is based on maximum cloud penetration length) of LWC. Further it was checked with the CDP derived LWC and the correlation coefficient values with CDP data are 0.95 for both the HW probes. The CDP sizing calibration was validated from time to time during the campaign period, by running PSL (Polystyrene Latex) and glass beads of known sizes through its sampling volume. The results showed agreement within a sizing precision of ±1.5μm during this campaign period. The aerosol concentration used in the study is derived from the PCASP constant altitude flight legs below cloud base. Since the PCASP predominantly covered the aerosol accumulation mode size range these measurements are henceforth referred to as sub-cloud accumulation mode aerosol concentration (Nacc).
 Reffis one of the important parameters for deriving cloud optical properties in large-scale models. Most of the general circulation models use a 1/3 power law to parameterize Reff as a function of LWC (L) and Nc [Slingo, 1990; Bower et al., 1994; Liu et al., 2006]. Reff was calculated using the ratio between third and second moment of the cloud droplet size distribution measured by CDP. Reff is commonly parameterized as,
where Rv is mean volume radius, ρw is the density of water, and β (=Reff/Rv) is the effective radius ratio, which is a dimensionless parameter that depends on spectral shape of the cloud droplet size distribution. Most general circulation models use β as a constant value (β = 1, monodisperse size distribution). Liu and Daum  used different distribution functions to calculate β. They compared the expressions with observations and concluded that a Gamma distribution is the best to describe the dependence of Reff on ε. Using a Gamma distribution, β can be expressed as
 AIE is difficult to quantify as it depends on interactions between aerosol, CCN and cloud properties. According to Twomey's hypothesis, cloud droplet size reduces with increase in aerosol loading for a cloud under similar liquid water path (LWP) conditions [Twomey, 1974]. This has ample support from in situ as well as satellite observations [Feingold et al., 2003; Penner et al., 2004; Pandithurai et al., 2009]. Recently, AIE estimates over the Indian region were made using MODIS data sets [Massie et al., 2007; Ravi Kiran et al., 2009; Panicker et al., 2010]. Two fundamental relationships characterize AIE: the dependence of Nc on Nacc and the dependence of Reff on Nacc [Shao and Liu, 2009]. These parameters in turn depend on the L, vertical velocity, and CCN spectra. In general, aerosol-cloud interactions or AIE can be quantified by using the following equation [Feingold et al., 2003]
where ΔNaccis the relative change in sub-cloud aerosol number concentration and ΔReff is the relative change in cloud droplet effective radius. AIEn and AIEs are aerosol indirect effect in terms of number and size effects.
 All existing estimates of DE were based on empirical β(ε)-Nc relationships, which have large uncertainties. In order to reduce the uncertainties and better estimate of DE, Liu et al.  examined the dependence of β on (L/Nc) (i.e., water per droplet or specific cloud water content) and described the dependence of β on (L/Nc) with the following expression,
 Log-log Plot betweenβ and (L/Nc) shows generally that β decreases with (L/Nc) and the exponent bβ can be obtained by a linear fit between log β and log (L/Nc). Here bβ is the dispersion factor, which is defined as the percentage of offset/enhancement to the Twomey cooling effect due to the dispersion of cloud droplet distributions. The above relationship includes the fact that droplet distributions narrow as droplets grow according to adiabatic theory. The advantage of equation (4) for representing DE is that it accounts for L variations. By substituting equation (4) into equation (1), the new parameterization for Reff is given by,
 A bβ value of 0.1 can offset the Twomey cooling by 30% (i.e., 3 times bβ) as explained in Liu et al. . According to Liu et al. , the resultant AIE is the sum of AIEn and DE,
where AIEn = b/3 and DE is the warming dispersion effect associated with enhanced ε and can be calculated from DE = -bβb, where bβ can be estimated from equation (4). b is the exponent to the power law fit between Nc and Nacc and can be obtained from,
4. Results and Discussion
4.1. Aerosol and Cloud Microphysics Over Different Regions of India
Figure 3shows the Box and Whiskers plot for sub-cloud Naccand in-cloud Nc, Reff and LWC of warm continental cumuli. The top and bottom of Boxes represents the 75th and 25th percentiles and the band near the middle of the box is the median; the Whiskers are 95 and 5 percentile values of the data set and the circle represents the mean value. Aerosol concentrations below cloud base range from 200–2700 cm−3 indicating a wide range of clean and polluted environments. Also, the latitudinal gradient shows lower aerosol concentrations in southern latitudes and higher aerosol concentrations in northern latitudes. Continental cumuli cloud type clouds were observed in PTK, HYD, BLY and PNE. The flight averaged Nc observed in warm parts of the clouds are 680, 349, 331, and 551 cm−3 over PTK, HYD, BLY and PNE, respectively. The flight averaged LWC from all the research flights is 0.34, 0.36, 0.74, 0.38 gm−3 over PTK, HYD, BLY and PNE, respectively. Higher Reffover BLY is due to higher LWC. Summary of subcloud aerosol and continental warm cloud measurements for fourteen continental cloud cases including cloud- base and top heights are given inTable 1. It can be noted that over BLY, cloud base heights were low and greater cloud depths were sampled compared to other regions. CCN spectra were typically measured at 0.2, 0.4 and 0.6% supersaturations (S) and Nacc were measured below cloud base for about 7–10 min. CCN spectra observed on three days at PTK, HYD and PNE are shown in Figure 4a. The relationship between the flight averaged CCN concentration at 0.2% S and Nacc from the flights considered was found to show a positive correlation coefficient of 0.7 (Figure 4b). Adiabatic LWC was estimated using observed cloud base height, pressure and temperature. Adiabatic fraction is the ratio of observed LWC to that of adiabatic LWC. Some of the key microphysical signatures of pre-monsoon and monsoon clouds observed during CAIPEEX can be found inPrabha et al. .
Table 1. Summary of Selected Research Flights and Observed Aerosol-Cloud Properties During CAIPEEX-I
 Previous studies report effective radius ratios (β) of 1.14 and 1.22 by Martin et al.  and Deng et al. for warm continental clouds, respectively, which is an important parameter for effective radius parameterization schemes. However, such information is sparse for tropical continental cumuli, that are influenced by anthropogenic aerosol. The above pre-factor ‘β’ was estimated using CAIPEEX-I data for continental clouds.Figure 5a shows the scatterplot of all individual observations of Rv and Reff for the above fourteen flight cases. This is fitted with a linear regression that is forced to zero intercept and yields a slope (β = Reff/Rv) of 1.18 (correlation coefficient = 0.97). The k value (k = Rv3/Reff3 = β−3) estimated from CAIPEEX-I for continental cumuli is 0.61, which is also in agreement withMartin et al.  and Hudson and Yum . Polluted continental cumuli have lower k values compared to clean maritime clouds. Figure 5b illustrates the frequency distribution of relative dispersion observed for continental cumuli. From Table 1, it can be noted that the PTK region is influenced by higher Nacc and average ε is 0.362 ± 0.033. Other continental cloud regimes observed from HYD (ε = 0.363 ± 0.021), BLY (ε = 0.354 ± 0.032) and PNE (ε = 0.34 ± 0.011) regions also indicated narrow frequency distributions of relative dispersion compared to maritime clouds observed over the Mangalore coast during July 5 (BLR1) and July 7 (BLR2), 2009 shown in Figure 5b. Coastal maritime clouds have higher rm and σ and exhibit a greater range of ε.
4.2. Aerosol Indirect Effect in Continental Cumuli
 From the CAIPEEX research flights, fourteen continental flights conducted from PTK, HYD, BLY and PNE listed in Table 1 were selected for indirect effect analysis. It can be noted from Figure 6 that of these flights, the average LWC on nine days had similar values ranging from 0.32 to 0.44 except flights over BLY region, which had higher LWC values. Hence, the analyses of BLY flights were restricted to lower cloud depths so as to have similar LWC values for AIE analysis. Figure 6 includes the cloud base and cloud top heights probed of each flight considered in the analysis. Figure 7ashows the scatterplot between flight-averaged sub-cloud Nacc and Nc. Nc is proportional to Nacc and this can be expressed by equation (7).
 Nc is found to increase with increase in Nacc with a correlation coefficient of 0.54. The exponent ‘b’ of the power law fit between Nc and Nacc is found to be 0.39. Shao and Liu  has shown that the exponent b values from several reports were found to range from 0.25 to 0.85 all influences on Nc are contained in b, including those of aerosol characteristics and dynamics and are as follows: i) activation effect which is primarily determined by the size distribution of aerosol, ii) adiabaticity, which is a proxy for entrainment. It may be noted that the cloud samples considered here came from different environments.
 The activation ratio (ratio of average Ncduring updraft conditions to total aerosol concentration) depends on the chemical composition and size distribution of sub-cloud aerosol, and vertical velocity. AIEn is proportional to the ratio of the relative change in Nc with respect to relative change in Nacc. From equations (3), (7) and (8), AIEn estimated over Indian region during CAIPEEX campaign is 0.13 which is b/3 (b = 0.39). Lu et al.  reported similar relation Nc = 15.3Nacc0.43, (Corr. Coefft. = 0.77) from GoMACCS for continental shallow cumuli. It is very difficult to get a similar activation ratio over different geographical regions, as it depends on several factors mentioned above such as aerosol chemical composition, size distribution, and other environmental mixing conditions and cloud base vertical velocity.
 Aerosol 1st indirect effect (AIEs) also refers to changes in Reff for different aerosol environments. The flight averaged Reff is plotted against Nacc and is shown in Figure 7b. The increase in Nacc increases the CCN and hence higher Nc with smaller droplet sizes. Reff clearly decreases with increase in Naccand the linear fit to the log-log plot exhibits a correlation coefficient of −0.47. The slope of the above plot is found to be −0.07 and is also termed as AIEs (equation 3). Ncis proportional to the sub-cloud Nacc, however it does not account for DE, whereas Reff might be affected by dispersion. The difference between AIEn and AIEs estimates from Nc and Reff is possibly that the droplet dispersion effect on cloud droplet spectra is implicitly included in Reff whereas the increase in Ncdoes not include dispersion influence. Assuming a 100% plane-parallel cloud cover,McComiskey and Feingold  reported that an increment of 0.05 in AIE could lead to local aerosol indirect forcing of −3 to −10 Wm−2 depending on the anthropogenic aerosol perturbation of CCN ranging from 300 to 2500 cm−3 relative to a background value of 100 cm−3. The present study shows that AIEs is 0.07, and the radiative forcing can range from −4.2 to −14.0 Wm−2.
4.3. Effect of Aerosol on Cloud Droplet Dispersion
Figure 7c shows the scatterplot between flight averaged Nacc and ε. This clearly indicates an increase in ε with increase in Nacc in these continental cumuli. A high correlation coefficient of 0.82 is noted. The power law fit to the above plot yields a relation as follows:
Lu et al.  also observed that increase in ε with Naccfor maritime clouds and pointed out that sub-cloud aerosol may be a better surrogate rather than Nc for dispersion correlation. Previous studies by Liu and Daum  and Pawlowska et al.  used Nc instead of aerosol number concentration as the basis for the dispersion correlation. Lu et al.  showed that ε in continental shallow cumuli observed in GoMACCS campaign did not show any discernible aerosol effects on relative dispersion. On the contrary, we observed that there is a strong influence of aerosol on cloud droplet dispersion and the relative dispersion (and β shown in Figure S1 of the auxiliary material) increases with aerosol in this study.
Figure 7d shows the scatterplot between water per droplet (L/Nc) and effective radius ratio (β) on all 14 days considered. It can be noted that β decreases with (L/Nc) and the linear fit to the flight averaged data yield
 The uncertainty in the quantitative estimate of AIEn is significantly larger under low Nc as compared to high Nc conditions [Zhao et al., 2006]. The relation between Nc and ε indicates that the dispersion shows a wide range of values when Nc is low. As Nc increases, ε converges to a narrow range. Most of the studies use equation (1) to estimate AIE [Feingold et al., 2003]. AIEnestimated for the Indian region during CAIPEEX-I campaign is found to be 0.13 (Figure 7a; AIEn = b/3 = 0.39/3). From the above, DE (i.e., −b*bβ) for continental clouds is found to be −0.051 (Figure 7d; bβ = 0.13) and the dispersion effect can offset the AIEn effect by 39% over Indian region and the resultant AIEnis 0.079 for continental cumuli during the CAIPEEX-I campaign. The resultant AIEn is found to be closer to the AIEs estimated using Reff and this suggests that DE is implicitly included when AIE estimates are made using relative changes in Reff with relative changes in Nacc. Some of the AIEn and AIEs values reported in the literature and dispersion offset values are listed in Table 2.
Table 2. Some of the AIE and Dispersion Offset Values Reported in the Literature
 In general, clean maritime clouds have larger droplets and higher σ whereas polluted continental clouds have smaller droplets and lower σ. The relationship between flight averaged Nc and σ (Figure 8a) for entire warm cloud depth of similar LWC shows that cloud with higher Nc have lower σ and vice versa in this study. Usual observation is that σ increases with rm (Figure 8b) and with altitude above cloud base. Hudson and Yum (1997) predicted decrease of σ with rm for specific cloud parcels moving upward adiabatically with a constant updraft. The larger dispersion observed in continental cloud types were possibly due to smaller droplets (rm) rather than broader droplet distributions (σ) [Yum and Hudson, 2005]. Instead of flight averaged data, Nc versus σ for a fixed mean radius (rm) for two narrow range of values a) 3–4 μm, b) 4–5 μm (Figures 9a and 9b) suggest that σ increases with Nc. For a fixed lower mean radius σ increases with Nc, which is similar to that reported by Hudson and Yum  and Miles et al.  (Figure 9a). Thus, determination of differences in σ caused by CCN had to be restricted to cloud parcels with rather small mean diameters for two reasons: (1) the polluted clouds never achieved any larger mean diameters because the competition among droplets restricted droplet sizes, and (2) the effect of the aerosol tends to get overwhelmed by dynamic effects at larger mean droplet sizes [Hudson and Yum, 1997]. The continued presence of small droplets in the droplet spectrum and possible dynamic effect was discussed in Prabha et al. . The effective radius ratio (β = Reff/Rv) is also found to increase with Nc, which is consistent with Martin et al. . This suggests that new Reff parameterizations need to be developed which includes σ.
4.4. Effect of Adiabaticity on Cloud Microphysical Properties and AIE
 AIEn estimated from the relationship between Nacc and Nc for continental cumuli is generally influenced by strong convection and different degrees of entrainment mixing. Continental cumuli tend to entrain faster because they originate over a warmer land surface and they have shorter lifetimes compared to marine cumuli. Being warmer they tend to rise higher and thus form ice earlier, which leads to precipitation and evaporation before liquid drop coalescence processes develop [Telford, 1987]. Further mixing of the cloudy air with the entrained air leads to dilution of LWC and Nc [Kim et al., 2005; Chin et al., 2000; Miller et al., 1998]. Shao and Liu examined the influence of mixing on the evaluation of the first AIE and attributed difference to evaporation associated with entrainment-mixing processes. The variation of LWC due to these non-adiabatic processes would induce uncertainty in AIE estimates. Therefore, the subadiabatic character of the clouds, or adiabaticity [AFL=LWC/LWCad] is used to characterize the entrainment-mixing processes [Kim et al., 2008]. Box plots of cloud microphysical properties (Figure 10) for subadiabatic (AFL < 0.7) and adiabatic (0.7 < AFL < 1.2) indicate consistently higher values of LWC and Nc for adiabatic clouds. Reff could either increase or decrease, depending on inhomogeneous or heterogeneous mixing conditions by several possible mechanisms as demonstrated by Kim et al. . Recent analysis by Freud and Rosenfeld  shows that Reff in convective clouds do not deviate much from the adiabatic Reff, despite undergoing considerable entrainment of surrounding air and due to the apparent tendency of the mixing to be dominated by inhomogeneous mixing. They also suggested that when the observed clouds are subadiabatic, the details of the mixing process may be important in determining the radiative impact of the clouds and may, in some circumstances be the controlling factor. Figure 11 shows the relation between adiabaticity (AFL) and cloud microphysical parameters Nc and σ. Decrease in Nc for lower AFL indicate dilution and droplet evaporation due to stronger entrainment mixing, which results in lower Nc, which is consistent with that of inhomogeneous mixing [Baker et al., 1980]. Using CAIPEEX-I data,Nair et al.  suggested a simple formulation from the linear relation between Nc and AFL, that will be useful for large scale models to predict Nc, when only LWC is diagnosed. They have also shown that the simple formulation was found to improve the skill of parameterized Reff for monsoon clouds. The AIE calculated from data sets of both adiabatic and subadiabatic samples shown in Table 3 indicates the reduction in AIE for subadiabatic case. The reductions in AIEn and AIEsfor subadiabatic clouds as compared to adiabatic clouds are 58% to 44%, respectively. The dispersion offset is higher in adiabatic clouds (66%) as compared to sub-adiabatic clouds (39%).
Table 3. Summary of Aerosol Indirect Effect and Dispersion Offset for Adiabatic and Subadiabatic Clouds
Adiabatic (0.7 < AF < 1.2)
Subadiabatic (0.0 < AF < 0.7)
5. Summary and Conclusions
 We report aerosol-cloud relationships from warm continental cumuli observed over the Indian region during 2009 May–September CAIPEEX-I campaign. The effective radius ratio (β) and kvalues are found to be 1.18 and 0.61, respectively for continental cumuli, which are important inputs to the cloud parameterization schemes in large-scale models. The continental cumuli observed under a wide range of aerosol concentrations enabled us to investigate the effect of aerosol on cloud droplet number concentrations and effective radius. AIE is quantitatively estimated for the first time over the Indian sub-continent using sub-cloud aerosol number concentrations and in-cloud droplet number concentrations and droplet effective radius data sets from research flights having similar flight averaged LWC. As a consequence of increased CCN and its influence on cloud droplet dispersion, AIE (cooling) may be significantly offset over continental clouds. AIE estimates made using two different methods giving close values of 0.13 and 0.07, respectively. From the CDP observed cloud droplet size distribution, relative dispersion is estimated. The flight averaged relative dispersion in these continental cumuli is found to increase with sub-cloud aerosol concentration in contrast to previous studies on maritime stratocumulus and continental shallow cumuli. The DE is estimated using effective radius ratio (β) and water per droplet (L/Nc) and the in depth analysis shows that the Twomey cooling may get offset by 39%. Adiabaticity analysis revealed aerosol indirect effect is lesser in subadiabatic clouds possibly due to inhomogeneous mixing processes.
 Over India, significant continued dimming is observed under all sky conditions [Padma Kumari et al., 2007; Padma Kumari and Goswami, 2010; Soni et al., 2012], where aerosol and clouds together contribute to the annual trend. This observation of significant decreasing trend of global solar radiation has important implications on the role of aerosol relative to that of greenhouse gases on the regional monsoon climate especially in the context of observed increasing trend of surface temperatures over the region [Kothawale and Rupa Kumar, 2005]. To understand these trends, it is essential to estimate the aerosol indirect effects accurately. Our results indicate that models must take into account the effect of DE adequately in order to be able to estimate climate sensitivity due to aerosol-cloud interactions. Accurate estimate of AIE is possible only if the cloud droplet dispersion is taken into account in models and may be important for improving the accuracy of simulating aerosol indirect effects in climate models.
 The CAIPEEX project and IITM are fully funded by Ministry of Earth Sciences (MoES), Government of India, New Delhi. The authors express their gratitude to D. Rosenfeld, E. Freud, D. Axisa and W. Woodley for their contribution on the data and quality checks. Authors acknowledge with gratitude that several scientists at IITM, their team effort and dedication made CAIPEEX a grand success. MODIS AOD, DER data obtained from Giovanni and NCEP/NCAR reanalysis wind fields are greatly acknowledged. S. Dipu gratefully acknowledges CSIR, Government of India for Research Fellowship. Authors would like to thank three anonymous reviewers for constructive comments which helped in improving the manuscript considerably.