Cloud condensation nuclei (CCN) and cloud microphysics measurements with various levels of pollution over the Indian Ocean showed roughly linear relationships. Estimates of adiabatic cloud droplet concentrations make more useful comparisons than average droplet concentrations, which are reduced by entrainment and averaging artifacts. Adiabatic cloud droplet estimates indicate higher cloud supersaturations. As predicted, the supersaturations were suppressed by higher CCN and cloud droplet concentrations. However, the actual suppression of cloud supersaturations was not as great as these comparisons indicated because many small cloud droplets were below the detection limit of the Forward Scattering Spectrometer Probe (FSSP), especially in the polluted air. Predictions of droplet concentrations based on CCN spectra and updraft velocities matched estimates of adiabatic cloud droplet concentrations in the clean air but overpredicted adiabatic estimates of polluted cloud droplet concentrations largely because of the undercounting of smaller droplets in polluted air masses. Thus, when all things were considered, a reasonable level of closure was found between predictions of droplet concentrations and adiabatic estimates of cloud droplet concentrations.
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 There have been only a few near-simultaneous observations of cloud condensation nuclei (CCN) and cloud droplets over wide ranges of concentrations [Twomey and Warner, 1967; Hudson and Yum, 2001]. Although often assumed, there have been only a few observations of somewhat linear relationships between CCN and cloud droplet concentrations [e.g., Hegg et al., 1991; Yum et al., 1998; Snider and Brenguier, 2000; Yum and Hudson, 2001] over somewhat limited ranges of concentrations. Leaitch et al.  and others have suggested that there is a saturation effect of CCN; i.e., that cloud droplet concentrations do not always respond to higher CCN concentrations even accounting for the suppression of cloud supersaturations (S) at high concentrations [e.g., Twomey, 1959]. The paucity of CCN-cloud droplet closure over wide ranges of concentrations has helped to feed speculation that other aerosol characteristics than nuclei critical supersaturations (Sc) also affect the nucleation and growth of cloud droplets [e.g., Chuang et al., 2000]. This has led to several challenges to the conventional wisdom of a linear relationship between CCN and cloud droplets, especially in polluted environments [Kulmala et al., 1993, 1997; Shulman et al., 1996, 1997; Chuang et al., 1997; Laaksonen et al., 1998; Facchini et al., 1999; Nenes et al., 2001]. More specifically this pertains to the relationship between measurements and predictions of cloud droplet concentrations. Therefore, we present comparisons between CCN and cloud droplet spectra in three Indian Ocean Experiment (INDOEX) flights that each displayed similar wide ranges of CCN and cloud droplet concentrations.
 The measurements presented here were obtained during three of eighteen research flights of the NCAR C-130 during INDOEX in February and March 1999 [Ramanathan et al., 2001]. These “gradient flights” of 20 and 24 February and 4 March began at the Maldives Island base at 4° North Latitude. The aircraft then flew south at altitudes below 850 mb for 3 to 4 hours to approximately 8° South Latitude. Throughout all of the INDOEX flights the air over the northern Hemisphere Indian Ocean was very polluted, mainly due to advection of material from the Indian Subcontinent [e.g., Ramanathan et al., 2001]. However, as the aircraft moved across the Intertropical Convergence Zone (ITCZ) the particle concentrations gradually decreased to that characteristic of clean maritime air. Very small shallow sparse boundary layer trade wind cumulus clouds were penetrated during these transects. These clouds were seldom more than a few hundred meters in either horizontal or vertical extent. The aircraft was in cloud less than 10% of the time during these flights.
 The featured measurements here are from the Desert Research Institute (DRI) CCN spectrometers [Hudson, 1989]. Also presented are measurements of the total particle concentrations with a model 3010 TSI condensation nuclei (CN) counter. These instruments obtained continuous samples from an inlet similar to that used by Hudson et al.  and Yum and Hudson . We also present cloud droplet (2–50 μm diameter) data obtained with the Forward Scattering Spectrometer Probe (FSSP) 100 [e.g., Hudson and Yum, 2001].
 Like the work by Yum and Hudson  INDOEX CCN spectra also needed an inversion correction because the calibration spectra were wider than those that were observed in earlier projects. Without the inversion correction, the lower concentration channels (usually at lower S) would be overestimated by as much as a factor of three at the lowest S of 0.02%. At S above 0.08% these inversion corrections made imperceptible changes. Since these inversion corrections are subject to uncertainty, CCN concentrations (NCCN) at S below 0.07% should be regarded with caution. As with all previously presented DRI CCN data the measurements that were obtained within the clouds were excluded.
3. CCN Spectra
 The most significant feature of the spatial distributions of CCN concentrations (NCCN) and other aerosols in INDOEX [e.g., Heymsfield and McFarquhar, 2001; Ramanathan et al., 2001] is shown in Figure 1, where the high concentrations over the northern Hemisphere Indian Ocean give way to clean maritime air of the southern Hemisphere. These horizontal gradients were nearly identical for the three flights considered here. All of the CN and CCN measurements throughout INDOEX, north and south of the ITCZ, were similar to the respective extremes shown in Figure 1. We have participated in only one previous flight (17 June 1992; Atlantic Stratocumulus Transition Experiment [ASTEX]) that displayed both clean and polluted CCN spectra and clouds [Hudson and Li, 1995]. However, these INDOEX flights are unique in that not only were extreme clean and polluted air masses and clouds encountered during the same flights, but so were all intermediate particle (Figure 1) and cloud droplet concentrations.
Figure 2 shows average boundary layer spectra in the clean, transition, and polluted air masses during these three flights. Figure 3 [from Yum and Hudson, 2002] shows average boundary layer spectra that have been obtained in other parts of the world with the same instrument. At S near 1% the polluted INDOEX concentrations are similar to the other two continental/polluted spectra (ASTEX and Small Cumulus Microphysics Study [SCMS]). At intermediate S (i.e., 0.1%) INDOEX polluted is higher but at S below 0.06% INDOEX polluted has lower concentrations than these other two polluted/continental measurements. The clean INDOEX measurements are very similar to the other clean maritime measurements in other parts of the world.
 As has generally been the case in previous measurements of CCN spatial variations the concentrations were generally vertically uniform within the boundary layer [Hudson and Frisbie, 1991; Hudson, 1993; Hudson and Li, 1995; Hudson et al., 1998; Hudson and Xie, 1999; Hudson and Yum, 2001; Yum and Hudson, 2002]. The small sizes of the clouds and the cloud droplets and the sparseness of the clouds precluded significant cloud scavenging that could inhomogeneously alter boundary layer CCN concentrations. Vertical soundings immediately at the beginning and end of each of the three horizontal gradient legs displayed vertical uniformity in CCN concentrations within the boundary layer. This is quantified by standard deviations that were less than 15% of the mean boundary layer concentrations in these soundings. At the middle of two of the legs partial soundings within the boundary layer showed standard deviations of less than 10% of the mean. Most of the measurements were made at pressure altitudes between 900 and 950 mb. The average pressure altitude of the CCN measurements was 941 ± 29 mb while the average pressure altitude of the cloud measurements was 925 ± 19 mb.
4. Considerations for Comparisons With Clouds
Hudson and Yum  noted that much of the observed variability in cloud droplet concentrations (Nc) and sizes, even in the same air masses, is due to the variability of entrainment. Entrainment reduces Nc by diluting cloud parcels with cloud-free air and by evaporating some cloud droplets to sizes below the threshold of the FSSP. Apparent, but artifactual, reductions of Nc also occur when measurement intervals (1s used here, which corresponds to 100 m) include both cloudy and cloud-free volumes; these are essentially cloud edge (or hole) effects. As pointed out by Yum et al.  and Hudson and Yum  these factors complicate comparisons of Nc with CCN spectra. Coalescence among cloud droplets and drops can also reduce Nc. However, this was not a complication here because the clouds and the cloud droplets were so small that there was little coalescence and no measurable precipitation.
 Cloud droplet-CCN comparisons are more useful when cloud droplet concentrations (Nc) are not reduced by entrainment, artifact, or coalescence. That is, the most appropriate CCN comparisons are with adiabatic Nc, which we refer to as Na. These Na should produce more useful estimates of effective supersaturations (Seff), which are the supersaturations (S) for which the cumulative CCN concentrations equal Nc [e.g., Hudson, 1984]. Therefore, Seff reveals which particles are actually CCN. Due mainly to variations in updraft velocity (W), Seff can vary even within each cloud. Nonetheless, CCN that have individual critical supersaturations (Sc) less than Seff form activated cloud droplets and CCN with Sc above Seff remain unactivated haze droplets. However, evaporation of activated cloud droplets can release CCN with Sc less than Seff and therefore evaporation may be related to the Sc of the nuclei upon which the droplets formed [e.g., Hudson and Rogers, 1986; Twohy and Hudson, 1995]. It is usually difficult to find adiabatic cloud parcels for which measured cloud droplet concentrations can be assured to be equal to Na. This was especially true in INDOEX where there were more than typical variations of measured Nc due to the small sizes of the clouds and the cloud elements, which then resulted in lower measured Nc because of entrainment and artificial reductions because of the prevalence of cloud edges. For these reasons average Nc [Nc(ave)] are less appropriate for estimating Seff. Nonetheless, Nc(ave) is still important for macroscopic considerations such as cloud albedo.
 Unlike the stratocumulus clouds investigated during the First Aerosol Characterization Experiment (ACE 1) [Yum et al., 1998] but like SCMS [Hudson and Yum, 2001] these INDOEX cloud measurements did not present any periods of constant cloud droplet concentrations (Nc) that would suggest near-adiabatic parcels. Adiabatic cloud droplet concentrations (Na), however, could be estimated from Nbinmax, which is obtained by sorting measured cloud droplet concentration (Nc) frequency distributions into concentration bins and then choosing the highest Nc bin with at least three data points [Yum et al., 1998].
Hudson and Yum  also presented other methods of estimating Na based upon distributions of measured Nc versus the ratio of measured cloud droplet liquid water content (Lc) to estimated adiabatic cloud liquid water content (La). This analysis was straightforward and accurate for SCMS because of the constancy of cloud base height and temperature. However, the INDOEX clouds were spread over long horizontal distances that made it more difficult to always accurately estimate cloud base altitude. In spite of these complications, the patterns that emerged from analyses such as Figure 4 are similar to those usually found in SCMS [Hudson and Yum, 2001]. Cloud droplet concentration (Nc) at Lc/La = 1 in such diagrams should represent adiabatic droplet concentrations (Na). The most significant feature of these diagrams is the straight line border of data points that usually extends from the origin toward the upper right. Points along this border should represent dilution or the artifacts caused by measurements that include out-of-cloud parcels. Both of these processes should reduce Nc and Lc in the same proportions. The complete evaporation of some cloud parcels while other parcels are not evaporated at all would also produce data along the same straight lines between Na and the origin. This latter process is referred to as inhomogeneous mixing [e.g., Baker et al., 1980]. Since there are almost never any data points in the lower right of these distributions (high Lc/La and low Nc), diluted parcels did not seem to produce large droplets, as had been hypothesized by Telford and Chai . Data points to the left or above the origin-to-upper-right border represent either parcels with higher updraft velocity (W) that result in higher Na, and/or homogeneous mixing [Warner, 1973; Mason and Jonas, 1974] where all droplets in a parcel are reduced in size by similar amounts. Homogeneous evaporation is suggested by the typical triangular pattern of data with a horizontal top (Figure 4) because homogeneous evaporation would shift data points from the lower right border to the left. This partial evaporation of droplets reduces liquid water content (Lc) but does not reduce Nc, unless some of the smallest droplets shrink below the threshold of the FSSP-100. If variations of W were the dominant process then there would be various Na, which would produce a triangular pattern of data points with a vertical right-hand border near Lc/La = 1, or perhaps a semicircular or angled upper right-hand border. The typically observed flat horizontal upper border is more suggestive of homogeneous evaporation moving data horizontally to the left from the aforementioned origin-to-upper-right-hand data boundary.
 One way to estimate adiabatic cloud droplet concentrations (Na) is the intersection of that lower right-hand borderline of the data points with Lc/La = 1. We refer to this droplet concentration as Namin because it seems to be a lower bound of Na because it assumes a single updraft velocity (W). A more objective estimate of Na is obtained from the intersection of the linear regression of all of the data points (i.e., in Figure 4) with the vertical line, Lc/La = 1. This Nareg probably overestimates average Na because it does not account for homogeneous evaporation. The usual pattern of the data points, either a straight line from the origin toward the upper right or the triangular pattern with a horizontal upper boundary (e.g., Figure 4) seems to suggest that there is only one W, which produces a single Na, and that the mixing is homogeneous.
5. Comparisons with Clouds
Heymsfield and McFarquhar  showed the marked differences between clouds formed in the polluted and clean air north and south of the ITCZ, respectively, during INDOEX. Table 1 shows averages of CN, CCN, and cloud microphysics in the three air mass regimes. Each piece of data in Table 1 is the average of the three flights. The first seven rows show the tendency for particle and cloud droplet concentrations to increase toward the northern Hemisphere where the pollution sources are located [e.g., Ramanathan et al., 2001].
Table 1. Averages and Standard Deviations of Aerosol and Cloud Microphysics for Each Air Mass
N is the concentration. The first three rows are aerosol particles and the next four rows (4–7) are cloud droplet concentrations (Nc). Rows 5–7 are estimates of adiabatic Nc (Na) (see text). Lc is cloud droplet liquid water content and La is the adiabatic Lc. MD is mean cloud droplet diameter, Dv is cloud droplet mean volume diameter, De is cloud droplet effective diameter, which is the third moment divided by the second moment.
361 ± 31
910 ± 177
1808 ± 41
176 ± 25
577 ± 120
1190 ± 128
78 ± 8
289 ± 39
580 ± 194
68 ± 46
131 ± 40
181 ± 71
189 ± 64
335 ± 91
478 ± 114
200 ± 85
482 ± 126
598 ± 115
289 ± 95
662 ± 209
862 ± 290
0.12 ± 0.08
0.12 ± 0.09
0.12 ± 0.04
0.16 ± 0.07
0.16 ± 0.05
0.17 ± 0.03
0.32 ± 0.09
0.27 ± 0.05
0.30 ± 0.06
0.22 ± 0.10
0.21 ± 0.06
0.21 ± 0.06
13.7 ± 5.7
10.5 ± 4.1
8.9 ± 1.1
15.2 ± 6.4
11.5 ± 4.3
10.0 ± 0.8
16.7 ± 7.2
12.6 ± 4.6
11.2 ± 0.4
K = Dv3/De3
0.76 ± 0.08
0.75 ± 0.09
0.72 ± 0.09
 One type of estimate of adiabatic cloud droplet concentrations (Na), Nbinmax, is usually lower than but within 30% of one of the other types of estimates of Na, Namin (e.g., Table 1). The consistency between these two types of Na estimates suggests that they may both be reasonably good estimates of true Na. Nareg is significantly higher than Nbinmax and Namin and thus Nareg is probably an overestimate of true Na (section 4). Note that the differences in condensation nuclei concentrations (NCN) and CCN concentrations (NCCN) (rows 1–3) among the three air masses are greater than the corresponding differences in any of the cloud droplet concentrations (rows 4–7). Quantitatively, whereas the ratios of polluted to clean NCN and NCCN are more than 5, all of the ratios of polluted to clean Nc are less than 3. Likewise, the polluted to transition NCN and NCCN ratios are 2 while the polluted to transition Nc ratios are less than 1.5. Furthermore, the transition to clean NCN and NCCN ratios are at least 2.5 while the transition to clean Nc ratios are less than 2.5.
 There were no discernable visual differences in the clouds along the tracks of any of the three flights. The frequency of clouds was also similar in the three regimes. The similarity of the cloud liquid water contents (Lc) among the three air masses is shown by the similarities of the three columns of row 8, Table 1. The similarities among the three columns of each of rows 9–11, Table 1 (starting with Lc/La) suggests similar levels of entrainment in the three air masses. Entrainment is the major factor in reducing Lc below adiabatic values (La). Entrainment reduces cloud droplet concentrations (Nc) by dilution or evaporation and/or by reducing droplet sizes by evaporation. The higher ratios of average cloud droplet concentrations [Nc(ave)] to adiabatic cloud droplet concentrations [Na] in rows 10 and 11 compared to the ratio of measured liquid water content [Lc] to adiabatic liquid water content [La] in row 9 for each column suggest that there is some homogeneous evaporation because homogeneous evaporation should reduce Lc more than Nc. This is in contrast with dilution, edge effects, and inhomogeneous evaporation, all of which reduce Nc in the same proportion as Lc is reduced. If there were no homogeneous evaporation, rows 9–11 should be identical in each column.
 Rows 12–14 of Table 1 (starting with MD the mean diameter of the cloud droplets) show that the air mass differences in Nc caused by the air mass differences in NCCN also affect droplet size. These air mass differences in MD are consistent with the air mass differences in Nc and the air mass similarities of liquid water content (Lc). The factor of 3 higher Nc of polluted clouds over clean clouds is consistent with the 50% larger MD in clean clouds. This is because Lc should be proportional to Nc and the cube of MD, since the cube root of 3 is 1.44. The ratio (K) of the cubes of average volume mean diameter (Dv) to effective diameter (De) in the last row of Table 1 displays similar averages to those found in maritime and continental air masses, respectively, by Martin et al.  and Hudson and Yum . At least the sense of these K differences is identical—lower values in more polluted air masses.
Figure 5 shows the relationship between local NCCN(1%) and peak measurements of cloud droplet concentrations [Nc(peak)] for each of the individual cloud penetrations during these three flights. Table 2 displays the linear regressions for this and other aerosol-cloud droplet (Nc) relationships for all of these individual cloud penetrations. NCCN(1%) has a better correlation with droplet concentrations (Nc) than NCN or NCCN at all of the lower supersaturations (S). Maximum droplet concentrations [Nc(peak)] are better correlated with the aerosol than average droplet concentrations [Nc(ave)]. The last column shows that NCN are much higher than both Nc, and that NCCN are much higher than Nc(ave) but similar to Nc(peak). Thus Nc(peak) seems to have a better connection with the CCN concentrations. This is perhaps because Nc(peak) is a better approximation of true adiabatic cloud droplet concentrations (Na).
Table 2. Linear Regressions of NCN and NCCN Versus Cloud Droplet Concentrations (Nc) and Average Ratios for Each Individual Cloud
The number of data points (clouds) is n, the intercept is b, the slope is a, and r is the correlation coefficient.
 The INDOEX clouds were too small to find near-adiabatic parcels but estimates of adiabatic cloud droplet concentration (Na) (section 4) are possible for large enough groups of these clouds. Therefore, as mentioned in section 3, the cloud and aerosol data from each flight were naturally divided into three spatially distinct groups. The maritime and polluted groups are defined by the rather consistent concentrations that were found toward the northern (e.g., prior to 0350 in Figure 1) and southern extremes (e.g., after 0500 in Figure 1). The transition air mass was then defined to be between these two regimes. This division allows the more sophisticated estimates of Na but limits the number of data points to 9 instead of 37. This more complex analysis is presented in Table 3 and Figure 6, which are analogous to Table 2 and Figure 5, respectively. Again for all of the various cloud droplet concentration estimates (average, binmax, adiabatic minimum, and adiabatic regression), NCCN(1%) show better correlations than NCN or lower S NCCN. Again Nc(ave) has the worst correlations of any of the cloud droplet representations. The best correlations are for Nbinmax and Namin. The ratios of aerosol to cloud droplet concentrations (Nc) (last column) for average and binmax (first 6 rows, Table 3) are almost identical to these ratios for Nc(ave) and Nc(peak), respectively, in Table 2. The aerosol to droplet concentration ratios for adiabatic minimum and adiabatic regression are then progressively lower.
Table 3. Linear Regressions of NCN and NCCN Versus Cloud Droplet Concentrations (Nc) and Average Ratios for Each Air Mass of Each of the Three Flightsa
 Next we tried to predict cloud droplet concentrations from the CCN spectra and measured updraft velocities (W). It was not possible to measure the very most appropriate W for this purpose, which is W at or just above cloud base when the clouds were forming. We instead had to use the measured W within the clouds. However, this is not such a serious shortcoming for such thin clouds as the within cloud measurements were seldom very far from the bases of these clouds anyway because these clouds were never more than a few hundred meters thick. Although W was positive for the broad majority of the in-cloud measurements, we used two different representations of W — the average for all of the cloud penetrations and the average for only positive W. The adiabatic condensation model of Robinson  was used to calculate predictions of Nc from W and CCN spectra [e.g., Hudson and Yum, 1997; Yum et al., 1998; Hudson et al., 2000]. We used the same two commonly accepted values for the condensation coefficient of water droplets —1.0 (which is the maximum possible value) and 0.036 [e.g., Hudson et al., 2000]. Thus, we made four different cloud droplet concentration predictions (Np) for each of the three air masses of each of the three flights (thus 9 for each type of prediction, each row of Table 4). Table 4 then displays the linear regressions of each of these four Np against each of the four representations of Nc. Again we note that Nc(ave) has the worst correlations and the highest ratios (first 4 rows). This further substantiates that Nc(ave) significantly underestimates adiabatic cloud droplet concentrations (Na). Correlations for the three Na representations are similar to each other but the predicted to measured ratios for the adiabatic regressions (Nareg; last four rows) are very low; this again suggests that the adiabatic regressions overestimate true Na. In all cases, except Nc(ave), Np based on positive W yield better correlations and higher Np to Nc ratios. However, the superior correlations for Nc(ave) when all (including negative) values of W are included in the predictions (rows 1 and 2 compared to rows 3 and 4 of Table 4) suggest perhaps that downdrafts reduce Nc, which is reasonable. Note that Np based on the smaller condensation coefficient (0.036) is always higher because a lower condensation coefficient retards condensation and thus allows cloud supersaturation (S) to increase so that more CCN can become activated droplets.
Table 4. Linear Regressions of Predictions (Np) of Droplet Concentrations Versus Measured or Estimated Droplet Concentrations (Nc) and Ratios, which are also Divided by Air Massesa
 In the last three columns of Table 4 we divide the average ratios of Np to Nc according to air masses. This displays the striking result that in all rows there is a progressively greater relative apparent overprediction for the transition over clean and then polluted over transition air masses. A major reason for these apparent relative overpredictions in the polluted and transition air masses is shown in Figure 7. The relatively high droplet concentrations in the lowest size channels for the transition and especially the polluted clouds suggest that many activated cloud droplets were too small to be detected by the FSSP-100. This flight shown in Figure 7 was the most extreme example; nonetheless the polluted concentrations but not the transition concentrations seemed to also be significantly underestimated in the other two flights.
 In Table 4 correlation coefficients that exceed 0.9 and Np/Nc that approach 1.0 for the clean air masses, in which there apparently was little undercounting of Nc, are found for binmax (Nbinmax) and adiabatic minimum (Namin) for predictions (Np) with W > 0 (rows 7 and 8 and 11 and 12). These four rows suggest a high degree of closure between Np and Na. Furthermore, when we boosted Na for the transition and polluted clouds by ratios approaching those in the last columns of Table 4, as is certainly suggested by Figure 7, we found even higher linear regression correlation coefficients, intercepts closer to zero, slopes closer to 1.0, and lower overall ratios of Np to Na. These results tend to support conventional cloud condensation theory rather than some of the speculations that were noted in section 1. We note, however, that Np (Table 4) have approximately the same correlation coefficients as NCCN(1%) have with the corresponding representations of cloud droplet concentrations (Nc) in Table 3. The ratios of Np to Nc are, however, lower than the NCCN(1%) ratios, and the slopes (a) and intercepts (b) of the Np-Nc linear regressions are lower than the NCCN(1%)-Nc regressions. NCCN at lower S also have lower average ratios with Nc that are also closer to 1.0. Moreover, these linear regressions have lower slopes and intercepts than NCCN(1%) (Table 3, rows 6 and 9 compared to rows 5 and 8). However, the correlation coefficients for these lower S NCCN are lower than the correlations for NCCN(1%)! This perhaps suggests that the initial cloud supersaturations (S) may be rather high (i.e., 1%).
7. Cloud Supersaturations
Table 5 shows average effective supersaturations (Seff) based upon average cloud droplet concentrations [Nc(ave)], and the three estimates of adiabatic cloud droplet concentrations (Na) as well as the four corresponding predictions of droplet concentrations (Np). As predicted by Twomey , in general, Seff decreases for more polluted air masses because of the competition among droplets for available condensate. The reduction of cloud supersaturations (S) by higher NCCN is probably the chief reason that there is less of a difference in Nc (factor of 2.5–3.5 for polluted to clean) than NCCN (factor of 7–9 for polluted to clean) in Table 1. The estimates of Seff based on estimates of Na (rows 2–4, Table 5) are much higher than Seff based on Nc(ave) (row 1, Table 5). This further illustrates how misleading Nc(ave) can be for estimating Seff. Evaporation may or may not be related to the critical supersaturations (Sc) of the nuclei upon which the droplets formed [e.g., Yum et al., 1998]. Nonetheless, it is significant that Tables 2 and 3 show that entrainment does not completely wash out the relationship between CCN and Nc(ave). The greater differences in Seff among the different air masses for measured cloud droplet concentrations (rows 1–4, Table 5) compared to predicted cloud droplet concentrations (Np) (rows 5–8, Table 5) probably again reflects the fact that many of the smaller activated cloud droplets in the polluted clouds were not measured. If these droplets had been measured then Seff based on Nc(ave) and Na would have been higher in the polluted and transition clouds and there would have been smaller differences in Seff among the various air masses. Thus the air mass differences in Seff based on cloud droplet concentration measurements (rows 1–4, Table 5) would be more similar to the differences in Seff based on cloud droplet concentration predictions (Np) (rows 5–8, Table 5).
Table 5. Averages of Effective Supersaturations (Seff) Based on Various Representations of Droplet Concentrations (Nc) and Predictions of Nc (Np) for the Three Air Mass Regimes
Np(1.0) (W > 0)
Np(0.036) (W > 0)
 One reason that Seff based on Np are lower than binmax and adiabatic minimum Seff for the clean air masses (column 1) was that these adiabatic cloud droplet concentrations (Na) sometimes exceeded NCCN(1%). This made it impossible to match these Na with any NCCN and all we could conclude in those cases was that Seff exceeded 1%.
8. Discussion and Comparisons with Previous Work
 The undercounting of cloud droplets in the polluted clouds due to droplets below the FSSP-100 threshold is another reason for the apparently greater air mass difference in CCN concentrations (NCCN) compared to the air mass differences in cloud droplet concentrations (Nc) that were discussed at the beginning of section 5 (i.e., Table 1). Similar results were also found for a similar wide range of concentrations in Atlantic stratus clouds [Yum and Hudson, 2001]. Figure 8 displays averages of the three flights for each of the three INDOEX air mass regimes and compares these with other overall averages from previously published data from other projects. Like INDOEX two of the other projects also had different air mass regimes (two instead of three). Table 6 shows the linear regressions and ratios of this relationship among these air mass/project averages as well as other air mass/project average relationships for these same nine air mass/project regimes. In spite of differences in cloud types the correlations are reasonably good. The clean SCMS data point shows the greatest deviation from the regression line because the higher W of these cumulus clouds produced relatively more cloud droplets per CCN. Moreover the greater thickness of the SCMS clouds produced significantly larger droplets that were not subject to being missed by the size threshold of the FSSP. The polluted SCMS data point is not as much of an outlier because those droplets were larger and thus not subject to being missed by the FSSP. Curiously the CN concentrations seem to show better correlations with Nc than NCCN although the NCN/Nc ratios are much too high to suggest that all particles (CN) are capable of producing cloud droplets. Furthermore, like Tables 2 and 3, the correlation coefficients seem to be worse for NCCN at lower S where the ratios of NCCN to Nc and the regression slopes and intercepts are lower. These results further suggest that cloud supersaturations are higher than previously thought [e.g., Hudson, 1984; Hudson and Svensson, 1995]; i.e., sometimes greater than 1%. This is consistent with the works of Hegg et al. , Yum et al. , Hudson and Yum , and Yum and Hudson  who found Seff approaching and exceeding 1% in maritime clouds.
Table 6. Linear Regressions of Project Averages of NCN and NCCN Versus Nc for INDOEX, FIRE 1, ASTEX, ACE 1, and SCMSa
 The binmax Seff for the clean INDOEX clouds of 0.80% is virtually identical to the binmax Seff of 0.89% in ACE 1, which was also in the southern Hemisphere [Yum et al., 1998] and binmax Seff > 1% in northern Hemisphere ASTEX maritime clouds (eastern Atlantic) but greater than binmax Seff of 0.48% in FIRE (eastern north Pacific maritime clouds) [Yum and Hudson, 2001]. The polluted binmax Seff of 0.09% is lower than the binmax Seff of 0.17% in ASTEX continental. Seff from Nc(ave) in the clean INDOEX regime of 0.11% is right between the Nc(ave) Seff of 0.15% in ACE 1 [Yum et al., 1998] and 0.08% in FIRE but lower than 0.20% in the cleaner SCMS clouds [Hudson and Yum, 2001] and 0.31% in ASTEX maritime [Yum and Hudson, 2001]. The higher values for ASTEX and SCMS may be due to higher updrafts (W) of those stratocumulus and cumulus clouds. Likewise the INDOEX polluted Nc(ave) Seff of 0.05% is nearly identical to ASTEX continental — 0.04% — and somewhat similar to the polluted SCMS Nc(ave) Seff of 0.12%. This last difference may also be due to the more vigorous clouds of SCMS (higher W). Furthermore, the adiabatic minimum INDOEX clean Seff of 0.60% is between the 0.48% Seff that was calculated for near-adiabatic parcels in ACE 1 and > 1% for ASTEX maritime. The average W in INDOEX clean and ACE 1 was similar, 31 and 25 cm s−1, respectively. Adiabatic estimates of Seff in SCMS were somewhat higher even though the NCCN were higher in SCMS than in INDOEX clean and ACE 1. This was again because of the higher W in the cumulus clouds of SCMS. Higher adiabatic Seff in polluted SCMS than polluted INDOEX was also probably due to higher W in SCMS.
 The position of the INDOEX polluted data point in Figure 8 tends to further support the undercounting of cloud droplets in INDOEX. The apparent linearity of the overall project averages (Figure 8 and Table 6) and the linearity of Figures 5 and 6 and Tables 2 and 3, suggests a lack of support for the concept of a saturation of the effects of CCN on clouds [e.g., Leaitch et al., 1986; Martin et al., 1994]. This saturation effect suggests that contrasts in cloud droplet concentrations (Nc) are less than contrasts in NCCN, even apart from the differences due to the reduction of S due to competition in more polluted air masses. The results presented here suggest that perhaps the apparent saturation of the effect of CCN on clouds may have been due to the undercounting of Nc in polluted atmospheres. This deduction agrees with the work of Bower et al. , who showed linearity between total aerosol particle concentrations and Nc even for concentrations exceeding 2000 per cm−3. Nonetheless, in effect, the apparent “saturation” of the indirect effect may in a sense be real if these small droplets that cannot be detected by the FSSP-100 also do not substantially contribute to the reflection of solar radiation.
 The apparent undercounting of the FSSP-100 prompted us to consider the FSSP-300, which extends down to 0.3 μm diameter. However, the concentration ratios of the FSSP-300 to FSSP-100 in the 2–5 μm diameter overlap region ranged from 10 to 0.4! As was indicated from the FSSP-100 measurements, the FSSP-300 did show considerable concentrations of droplets below 2 μm in the polluted and transition air masses. However, it also even showed substantial concentrations of sub-2 μm droplets in the clean clouds. This is inconsistent with the FSSP-100 and CCN measurements. Other than the first gradient flight shown in Figure 7, the FSSP-100 found very few droplets smaller than 10 μm in the clean air masses. Considering that Seff of these clouds was at least 0.4% and that the maximum haze droplet size for 0.4% Sc particles is 0.35 μm it is unlikely that there would be appreciable concentrations of 1–2 μm droplets in these clouds. For each of these reasons we could not take the FSSP-300 data seriously. We are not aware of previous FSSP-300 comparisons with FSSP-100 in cloud. On the other hand even accurate measurements of cloud droplets below 2 μm diameter might still be inconclusive because of the difficulty of separating haze droplets from activated cloud droplets in polluted clouds with low Seff and small activated cloud droplets. For instance the maximum haze droplet (unactivated droplets that have not exceeded the peak of the Kohler curve) sizes for Sc of 0.1% is 1.4 μm.
9. Summary and Conclusions
 CCN and cloud droplet concentrations showed similar variations during three transects though considerable air mass differences over the Indian Ocean. A more-or-less linear relationship seemed to exist between CCN concentrations and cloud droplet concentrations. Various estimates of adiabatic cloud droplet concentrations were considerably higher than average cloud droplet concentrations and somewhat consistent with each other. These yielded better correlations with CCN spectra and average concentration ratios closer to 1.0. This suggests that these adiabatic cloud droplet concentration estimates are more appropriate for comparing with CCN spectra.
 Many activated droplets in the polluted clouds were not counted by the FSSP-100. This may be a reason for some previous observations of an apparent saturation effect of CCN on cloud droplet concentrations. Future investigations of polluted clouds should require measurements of droplets smaller than 2 μm diameter.
 The linear relationships between CCN and cloud droplets in INDOEX and other projects and the agreement between predictions of cloud droplet concentrations and inferred adiabatic cloud droplet concentrations, especially those that are “corrected” for undercounting seem to support the validity of conventional diffusional cloud droplet growth theory. Linearity between predictions and measurements of cloud droplet concentrations was also observed by Snider and Brenguier  and Yum and Hudson . Unlike some previous CCN-cloud droplet comparisons [e.g., Chuang et al., 2000] these results do not suggest large corrections to Kohler theory.
 This work was supported by the Department of Energy through the Cooperative Institute for Atmospheric Sciences and Terrestrial Applications (CIASTA), contract number NA67RJ0146. The Research Aviation Facility of the National Center for Atmospheric Research, which provided the aircraft and cloud microphysical data, are commended.