1. Introduction

Among possible radiative forcings that can cause long-term climate change, the effect of changing tropospheric aerosols on cloud properties (called the aerosol indirect effect) is the most uncertain (0 to −1.5 W m⁻²) relative to the other known forcings (IPCC 1996, 115). Most estimates assume that this forcing will be negative, though that is not necessarily so. However, even this range of uncertainty in the forcing implies such a large range of climate sensitivities, that are all consistent with the observed temperature changes responding to increasing greenhouse gas abundances, that policymaking is difficult (Schwartz and Andreae 1996).

The aerosol indirect effect refers to the influence of aerosols on cloud properties when they act as cloud condensation nuclei (CCN). Essentially, cloud droplets form in two nearly separate stages: a very short nucleation stage at the beginning, where cloud droplet number density increases rapidly (preexisting water-containing aerosols are “activated”), but there is little increase in droplet size, followed by a much longer growth stage, where droplet number density remains relatively constant and droplet size increases (Rossow 1978). In the nucleation stage, cloud droplet number density is influenced by CCN concentration and updraft velocity, but in the usual case of hydrophilic CCN with a broad size distribution, the influence of CCN concentration predominates (Twomey 1977). In the droplet growth stage, droplet number density will also be altered by droplet evaporation and collision-coalescence. Thus, an increase in aerosol concentration (N_a) is expected to increase cloud droplet number density (N) and, consequently, cloud albedo (a), thereby offsetting part of the greenhouse warming (Twomey 1977; Twomey et al. 1984). Although an increase in N, by itself, would increase cloud albedo, this hypothesis usually includes the additional assumptions that the cloud liquid water content (LWC) and geometric layer thickness (h) are also constant (i.e., the cloud liquid water path, LWP = LWC × h, is constant) because they are presumed to be little affected by changes in CCN concentrations. Thus, a constant LWP is widely assumed in estimating the aerosol indirect effect (e.g., Charlson et al. 1987, 1992; Slingo 1990; Jones et al. 1994; Boucher and Lohmann 1995;Jones and Slingo 1996). Based on these assumptions and the distribution of cloud optical thicknesses, a relationship between cloud albedo (at the top of the atmosphere) and cloud droplet concentration can be inferred: Δα ≈ 0.066ΔN/N for 0.3 ⩽ α ⩽ 0.6 (Twomey et al. 1984). Twomey (Twomey 1991; Platnick and Twomey 1994) later suggested an expression, Δτ/τ = Δα/[α(1 − α)] = ΔN/(3N), which gives Δα ≈ 0.08ΔN/N for 0.3 < a < 0.6. Schwartz and Slingo (1996) derived a similar relationship for albedo at cloud top, Δα ≈ 0.075ΔN/N for 0.28 < α < 0.72.

Another consequence of the assumption that LWP remains constant while N_c is increased by increasing N_a is that the mean cloud droplet radius (r) decreases. Aircraft observations have indeed shown that N_c is generally larger and r generally smaller over land than ocean (e.g., Twomey 1977), qualitatively consistent with generally larger values of N_a over land than ocean and with the assumption that LWP is about the same. The dataset of Leaitch et al. (1992) has been cited by Boucher and Lohmann (1995) and others as support for the assumption that LWP is constant even though N_c and r are changing. Satellite observations of ship tracks also focused attention on aerosol-induced changes in cloud droplet radius (Coakley et al. 1987). A satellite survey has shown that the aircraft observations are true globally: cloud droplet effective radius (r_e, see section 2) for low-level clouds is generally smaller over land than over ocean and smaller in the Northern Hemisphere than in the Southern Hemisphere (Han et al. 1994). Thus, the aerosol indirect effect has sometimes been formulated as “an increase of N_a decreases cloud droplet sizes and increases cloud albedo,” but this is misleading because a reduction in droplet size by itself will, in fact, cause a decrease in scattering cross section and cloud albedo (despite the slightly larger scattering efficiency of smaller droplets). For example, for a factor of 2 change in droplet radius relative to 10 μm, the scattering cross section changes by 400%, whereas the scattering efficiency changes in the opposite direction by only about 15% (cf. Rossow et al. 1989; Nakajima et al. 1991). However, the constant LWP hypothesis predicts an overall increase in cloud albedo because the effect of increasing N_c outweighs the effect of decreasing droplet size.

The land–water and hemispheric differences of cloud droplet sizes are qualitatively consistent with the expected changes induced by the land–water and hemispheric differences of N_a if LWP is about the same. However, the corresponding hemispheric difference of cloud albedos is not found (Schwartz 1988), so LWP may not be unaffected by aerosol concentration changes. We suggested that the effect of aerosol-induced changes in cloud droplet size on cloud albedo (changed scattering cross section and scattering efficiency) might be offset by other aerosol-induced changes of cloud optical thickness (e.g., cloud droplet number density), but did not check this quantitatively (Han et al. 1994).

Since the nucleation of CCN quickly begins consuming all of the water vapor in excess of saturation in a cooling (ascending) air parcel, subsequent cloud droplet growth occurs with an approximate balance between the rates of vapor supply (continued cooling) and consumption; however, because the growth rate of the droplets increases with increasing size (surface area), the vapor supersaturation declines slowly during the growth phase. Thus, the condensation growth rate of cloud droplets is controlled by the cloud dynamics, that is, the cooling rate that determines the maximum vapor supersaturation attained, but is not directly affected by changes in N_c. The ultimate size attained by the droplets depends, therefore, on the processes that limit cloud water content; these include a finite duration of the updraft, droplet sedimentation, or the onset of collisional growth leading to precipitation (Rossow 1978).

If droplet size is limited either by the time available for growth or by sedimentation, then N_c and r are effectively independent: increasing either would increase cloud albedo, but would also increase LWP. In this case, the aerosol indirect effect would be even simpler: an increase of N_a would increase N_c producing a direct increase in albedo because cloud droplet size might remain unchanged. The albedo change in this case would be much larger than in the case of constant LWP, because there would be no offsetting decrease in albedo with decreasing droplet size. However, if there are feedbacks between the microphysical processes and the cloud dynamics, the behavior could be more complicated. Ackerman et al. (1995) argue, for example, that a reduction of cloud droplet sizes would lead to a reduction of LWC because evaporation at the cloud base stabilizes the boundary layer, decoupling the cloud from the subcloud vapor supply. Considine (1997) illustrates the effects of the decoupling by comparing two cases with different updraft velocities at cloud base: a larger updraft nucleates more droplets, leading to smaller droplets for the same LWC, but LWC is smaller at the same height above cloud base and the cloud layer is much deeper. If cloud droplet growth is limited by the onset of droplet collisions (precipitation), then the size of cloud droplets will be affected directly by changes in N_c. For the same LWC, increasing N increases the droplet collision rate (the collision rate also depends on the size dispersion), but the associated decrease in r decreases the collision rate even more (Rossow 1978); thus, because a larger value of LWC is required to attain the same precipitation efficiency, both the average LWC (as well as LWP) and the cloud lifetime are increased (e.g., Albrecht 1989). All of these theoretical considerations suggest, in fact, that LWC, and thus LWP, will not remain constant if N changes. Hence, we cannot determine how cloud albedo will change unless we also know how either LWP or cloud droplet size responds to changing aerosol concentrations.

The dataset of Leaitch et al. (1992), which is a regional composite of 92 observations from several seasons and years, is cited as support for the assumption of constant LWP. However, Nakajima et al. (1991) argue that averaging the data for different cases may hide the detailed behavior. They show, for example, that cloud optical thicknesses, τ; droplet effective radii, r_e; and LWP values, derived from four days of MCR (multispectral cloud radiometer) data during the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE), exhibit little correlation if all of the data are averaged together; but that two different relationships appear in data for individual cases: for optically thinner clouds (τ ⩽ 15, LWP ⩽ 120 g m⁻²), LWP and τ increase with increasing cloud droplet radius and, for thicker clouds, τ increases as r_e decreases. Rawlins and Foot (1990) found in their aircraft measurements that cloud optical thickness increases with increasing cloud droplet size. Han et al. (1994) found the same relation as Nakajima et al. (1991) in a global survey of τ and r_e for liquid water clouds obtained from 2 yr of ISCCP satellite data, with the turning point at τ ≈ 15–20.

Several studies explicitly illustrate the complexity of cloud property changes with changing aerosol concentration (e.g., Hobbs et al. 1970; Fitzgerald and Spyers-Duran 1973; Dytch 1975). Measurements of clouds upwind and downwind of St. Louis on two days in 1971 showed larger cloud droplets and smaller droplet concentrations upwind than downwind, consistent with an aerosol effect; but the liquid water content behaved differently in the two cases (Fitzgerald and Spyers-Duran 1973). In one case the liquid water content downwind was only half of the upwind value, so that the downwind cloud optical thickness (τ ≈ 11.2) was smaller than that of the upwind clouds (τ ≈ 15.2), despite smaller droplets and larger droplet concentrations. In the other case, where the liquid water content is about the same downwind and upwind, the downwind optical thickness (τ ≈ 18.0) is larger that the upwind value (τ ≈ 16.5). Even ship tracks turned out to involve changes of LWC (Radke et al. 1989; King et al. 1993). Stephens (1978) summarized a range of aircraft observations of cloud droplet size distributions for different cloud types over midlatitude continents (from Carrier et al. 1967) by suggesting a monotonic relationship between τ and LWP, which implies that LWP increases with increasing r_e when LWP ≥ 50 g m⁻². This relationship has been used in GCM studies (e.g., Fouquart et al. 1990; del Genio et al. 1996).

Satellite observations also suggest that both cloud liquid water path and cloud droplet size change when aerosol concentration changes. Minnis et al. (1992) reported a diurnal variation of cloud liquid water content, optical thickness, and cloud droplet sizes during the FIRE experiment in July 1986. The decrease of cloud droplet size, optical thickness and cloud liquid water content from morning through late afternoon can be explained by diurnally changing wind direction bringing air from the continent with larger aerosol concentrations during the afternoon and from the ocean in the morning with smaller aerosol concentrations. Twohy et al. (1995) described observations of two stratiform clouds, one pristine and one polluted, at the same location on two different days. They found that the sulfate concentration, cloud droplet concentration, and droplet sizes in the polluted cloud compared with the pristine cloud were consistent with an aerosol effect, but that the albedo difference of these two clouds was negligible because of a smaller liquid water path in the polluted cloud.

Thus, even though the available aircraft and satellite studies show the expected changes in cloud droplet sizes that could be induced by changes in aerosol concentration, they do not appear to show the corresponding changes in cloud albedo. Moreover, many of these studies suggest that LWP might not remain constant with changes in aerosol concentration. In this study, we use our near-global, multiyear dataset of cloud optical thicknesses and droplet radii (Han et al. 1994) to quantify the direct correlation of global changes of effective droplet size (r_e) and cloud albedo. This is presented in section 4a after definitions and equations are given in section 2 and the satellite datasets and retrieval methodology are briefly described section 3. The results show two different relationships: for most continental clouds and all optically thick clouds (τ > 15) over most of the world, cloud albedo increases with decreasing r_e; however, for optically thin clouds (τ < 15) over oceans and tropical rain forest areas, cloud albedo decreases with decreasing r_e. To find out the underlying reason, we examine the correlation of global changes of r_e and LWP in section 4b. The results show that for clouds over most regions of the world and for all seasons, LWP decreases with decreasing r_e. Thus, a decrease of r_e does not necessarily lead to a more reflective cloud as predicted by the original hypothesis. The fact that LWP is not always constant implies that cloud dynamic feedbacks may affect the magnitude of the indirect effect of aerosols. In section 5, we summarize these results and outline a different approach to determining the effects of aerosols on clouds from observations.

2. Definitions and equations

The basic equation that links cloud effective droplet radius (r_e), LWP, and optical thickness (τ) comes from the definition of r_e (Hansen and Travis 1974):

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where the density of water is taken to be unity and the extinction efficiency, Q_ext ≈ 2 for wavelengths much less than r_e. Changes in these three quantities are then related by

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The liquid water path can be approximated as

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where water density ρ_w is unity and r_υ and N_c are the volume-mean droplet radius and droplet number density, both averaged over the cloud layer of geometrical thickness, h. If the cloud droplet size distribution follows a gamma distribution (Hansen and Travis 1974),

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where a = r_e and b is the effective variance of the size distribution, then the effective droplet size is related to the volume-mean radius by

r³_ebbr³_υ(5)

Aircraft measurements suggest values of b for different cloud types ranging from 0.111 for fair weather cumulus to 0.193 for stratus (Hansen 1971); thus, r_υ ≈ 0.85r_e within about 5%. This linear relationship between r_e and r_υ, also suggested by others (Martin et al. 1994; Fouquart et al. 1990), implies

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where we assume that b does not vary much compared with variations (at most a 15% error).

The relative variation of LWP and T can now be expressed as

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and

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Since we have already averaged the droplet radius and number density over the depth of the cloud layer, we replace Nh by the mean “column” density, N_c. The advantage of this parameter is that it can be estimated from remote sensing data (Han et al. 1997, manuscript submitted to Geophys. Res. Lett.). If the cloud layer thickness is nearly constant, the relative change of N_c is the same as that of N—that is, dN/N = dN_c/N_c—which is usually assumed in model studies. Then the relative changes of LWP and T become

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If d(LWP)/LWP = 0 is assumed as in many model studies, then dN_c/N_c = −3dr_e/r_e and dτ/τ = −dr_e/r_e; hence cloud optical thickness and albedo increase even though droplet size decreases. Another equivalent formulation used is that dτ/τ = (1/3)dN_c/N_c (e.g., Platnick and Twomey 1994). If no constant LWP is assumed, and dN_c/N_c = −βdr_e/r_e is used, then Eq. (10) implies that

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so that cloud albedo will increase as long as β > 2 for dr_e/r_e < 0 or β < 2 for dr_e/r_e > 0.

3. Satellite data and retrieval method

Liquid cloud droplet sizes are retrieved by extending the ISCCP analysis of NOAA-9 Advanced Very High Resolution Radiometer (AVHRR) data for January, April, July, and October 1985–88. The original ISCCP analysis separates cloudy and clear image pixels (area about 4 km × 1 km sampled to a spacing of about 30 km) and retrieves cloud optical thickness and top temperature (T_c) from radiances measured by AVHRR at wavelengths of 0.54–0.80 μm (channel 1) and 10.0–11.6 μm (channel 4), assuming r_e = 10 μm. Results for individual pixels form the ISCCP CX dataset (Rossow et al. 1991). The analysis uses the NOAA TIROS Operational Vertical Sounder (TOVS) products to specify atmospheric temperature, humidity, and ozone abundance and also retrieves the surface temperature (T_s).

The ISCCP analysis is extended by retrieving r_e from AVHRR radiances at wavelengths of 3.44–4.04 μm (channel 3) and revising the values of τ to be consistent for clouds with T_c ≥ 273 K (Han et al. 1994, 1995). Only liquid water clouds are considered in this study because 90% of the tropospheric aerosol are distributed below 3-km altitude (Griggs 1983). Moreover, aerosol effects on ice clouds may be different than on liquid water clouds. The radiances are modeled as functions of illumination–viewing geometry by including the effects of Lambertian reflection–emission from the surface (the ocean reflectance is anisotropic, see Rossow et al. 1989); absorption–emission by H₂O, CO₂, O₃, O₂, N₂O, CH₄, and N₂ with the correlated k-distribution method (Lacis and Oinas 1991); and Rayleigh scattering by the atmosphere and Mie scattering–absorption by horizontally homogeneous cloud layers using a 12-Gauss point doubling–adding method. The droplet size distribution is assumed to the gamma distribution. Error sources are discussed and validation studies are reported in Han et al. (1994, 1995). Note that the satellite-measured radiation is sensitive only to the droplet sizes in the topmost part of the clouds; therefore, the values of LWP obtained by this analysis may be biased if r_e at cloud top is systematically different from the vertically averaged value (Nakajima et al. 1991). For nonprecipitating clouds (LWP ⩽ 150 g m⁻²), the results of this method agree well with ground-based microwave radiometer measurements (Han et al. 1995). Lin and Rossow (1994, 1996) show excellent agreement of microwave (from SSM/I) determinations of LWP over the global ocean with those obtained from the ISCCP results, assuming 10-μm droplets, and Greenwald et al. (1997) compare microwave retrievals of LWP from SSM/I and from GOES-8 over the Pacific Ocean.

Cloud spherical albedo at 0.6-μm wavelength, calculated from the retrieved values of τ and r_e using the same radiative transfer model (including the global average effects of ozone and water vapor absorption), is used for a simple comparison of cloud effects on solar radiation. Using visible spherical albedo allows us to compare any two clouds on an equal basis, but this neglects systematic variations of reflected sunlight with solar zenith angle (latitude and time of day) and absorption of sunlight by clouds. The calculated values of cloud albedo for different combinations of r_e and LWP are shown in Fig. 1. If τ is held constant by varying N_c proportionally to r⁻²_e [cf. Eq. (10)], a cloud with smaller r_e would have a larger albedo because of a small increase of scattering efficiency with decreased r_e (since there is no significant absorption at 0.6-μm wavelength, the scattering efficiency is indicated by Q_ext, which varies from 2.16 to 2.05 as r_e varies from 5 to 30 μm). If LWP is held constant by varying N_c proportionally to r⁻³_e [cf. Eq. (9)], then cloud albedo increases as r_e decreases because τ varies proportionally to r⁻¹_e.

We look for correlated regional and seasonal variations of τ (converted to cloud albedo, α) and LWP versus variations of r_e. All of the individual pixel values are collected for each 2.5° × 2.5° map grid cell for each month, representing both spatial variations at scales ∼10–100 km and daily variations over each month. A linear regression of the scattered values is used to determine correlations. Typically, about 100 samples per map grid cell per month are available; results are not reported if there are fewer than 10 samples. If, for example, ΔLWP ≈ 0, then the correlation coefficient between r_e and LWP should be approximately zero and the correlation between r_e and τ (or α) should be negative.

4. Results

a. Correlation of cloud albedo a and r_e variations

Cloud spherical albedo (α) at visible wavelengths is dependent on cloud optical thickness (or LWP) and droplet size. The global satellite survey by Han et al. (1994) confirmed results from aircraft studies (Nakajima et al. 1991) showing τ and r_e variations that are correlated differently in two ranges of τ divided at a value of about 15–20. Therefore, we examine the variations of α and r_e for these same two ranges. Figure 2 shows the correlation coefficients between a and r_e of liquid water clouds with τ ⩽ 15 for each 2.5° × 2.5° map grid cell in January, April, July, and October 1987. Figure 3 shows the correlation coefficients for liquid water clouds with τ > 15. These figures show a complicated relationship. Thinner clouds (τ ⩽ 15) over most ocean areas and the tropical rain forests show a positive correlation between α and r_e, while over most continental areas this correlation is negative. In the former case, since α increases as r_e increases, Eq. (11) implies that β < 2; in the latter case α decreases as r_e increases with 2 < β < 3. Thicker clouds (τ > 15) show a negative correlation of α and r_e over most of the world with 2 < β < 3. Albrecht et al. (1995) observed the same behavior in thicker marine stratus clouds during the ASTEX experiment.

Since the aerosol loading in the Northern Hemisphere is about three times larger than in the Southern Hemisphere, the usual hypothesis for the aerosol indirect effect predicts a systematically larger cloud albedo in the Northern Hemisphere; however, Schwartz (1988) showed that satellite albedo data exhibit little hemispheric albedo contrast, possibly even a higher albedo in the Southern Hemisphere. Slingo (1988) attributed this to variations of cloud amount and cloud water path between the two hemispheres that mask the effect of aerosols on cloud droplet number density and size. In addition, hemispheric differences in high-level cloud albedo (either unrelated to or differently related to aerosol changes) may further disguise the aerosol–cloud interaction in clouds at low altitudes (Langner et al. 1992; Kaufman and Nakajima 1993) where most of the aerosols are found (Griggs 1983). Our study overcomes these limitations because we isolate low-level clouds from all others, determine τ and r_e directly from observations, and calculate the cloud albedos from their properties. Since the pixel area is about 4 km², there is little effect of cloud cover variations within pixels [cf. Wielicki and Parker 1992, they show little change of cloud cover fraction up to a pixel size of about 1 km (note change from 2 km)] and no effect of larger-scale cloud cover on total albedo.

Figure 4 shows the zonal, annual mean values of a and r_e averaged over 1985–88 for the four months (January, April, July, and October). The values of α are calculated from the retrieved values of r_e and τ, thus, LWP ≈ τr_e/1.5 [from Eq. (4)] and from Eqs. (9) and (10)

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Figure 4 reveals that Northern Hemisphere clouds have smaller droplet sizes and larger albedos than Southern Hemisphere clouds for April, July, and October outside the tropical zone, qualitatively consistent with the albedo contrast expected assuming constant LWP. In the Tropics, except in October, the cloud albedos are similar in the two hemispheres. In January, α is larger in the northern subtropics but smaller in the Tropics and midlatitudes. However, Fig. 5 shows that LWP is not actually constant with latitude (or longitude): the hemispheric contrast of LWP values varies from zone to zone and season to season. Figure 6 shows values of α calculated from the same retrieved values of r_e, but assuming that LWP is fixed at its value at the equator. Comparing Figs. 4 and 6 shows that with fixed LWP the northern cloud albedos would generally be larger than the southern cloud albedos, except in the Tropics;however, LWP variations offset this effect in some latitude zones and seasons and enhance it in others. Thus, regional and interhemispheric LWP variations affect cloud albedo variations nearly as much as do variations of r_e, as Slingo (1988) cautioned.

Table 1 is a summary of cloud effective radius (r_e, in μm), LWP (in g m⁻²), and albedo values for continental and maritime clouds in the two hemispheres, for 1988. This is a summary from about 2.8 million Global Area Coverage (GAC) pixels of AVHRR data. It shows that cloud droplet sizes and LWP of clouds in the Northern Hemisphere (NH) are both slightly smaller than those values in the Southern Hemisphere (SH). The resulting cloud albedos in the two hemispheres are almost the same as found by Schwartz (1988).

5. Discussion and conclusions

The primary effect on cloud properties of changing aerosol concentrations is expected to be changes in cloud droplet number density (N_c). Thus, an anthropogenic increase in near-surface aerosol concentrations would cause an increase of N_c and, all other things remaining constant, an increase of cloud albedo. However, there is plenty of theoretical and observational evidence that the interactions of the microphysical and dynamical processes that form and destroy clouds might couple changes of N_c to changes in droplet sizes (and hence cloud water content) and to changes in vertical and horizontal extent. Lack of a comprehensive understanding of these processes has limited consideration of the aerosol effect on clouds to the case where cloud water content and vertical extent are held constant—that is, that cloud liquid water path is constant while N_c varies. This approach is consistent with the current state of the art in climate GCM representations of cloud processes where only cloud liquid water content and horizontal extent are determined prognostically and either N_c or r_e (or some droplet size parameter) and vertical extent are specified (e.g., Smith 1990; Tiedke 1993; Fowler et al. 1996). Notable differences are the scheme described by del Genio et al. (1996) that determines cloud vertical extent as well and the scheme described by Ghan et al. (1997) that treats the dependence of effective radius on LWC and N. To complete the cloud microphysical feedbacks in climate models, the dependence of r_e on cloud liquid water content and/or cloud droplet concentrations must be represented (Schwartz and Slingo 1996).

Large systematic differences in aerosol concentration caused by human activities and natural differences in climate are known to exist between land and ocean areas and between the Northern and Southern Hemispheres, so there have been many attempts to determine the nature of a possible aerosol effect on clouds by finding observable differences in cloud properties that could be caused by these aerosol concentration differences. Schwartz (1988) searched satellite albedo data for a systematically larger planetary albedo in the Southern Hemisphere but did not find it. However, as pointed out by Slingo (1988), this approach could have been confused by other interhemispheric differences in total cloud cover, liquid water content in low-level clouds (actually water path), and high-level cloud properties (as well as surface albedos). Since an aerosol-induced increase of N_c implies a decrease in cloud droplet radius (r_e), if LWP is approximately constant, as found in many aircraft studies, Han et al. (1994) looked for and found the expected systematic decreases of r_e over land compared with over ocean and in the Northern Hemisphere compared with the Southern Hemisphere; however, they also noticed systematic differences in cloud optical thicknesses (τ). In fact, they found that the values of τ and r_e varied together systematically, but with different relations in two regimes.

To reconcile these results, we examine the geographic and seasonal variations of cloud albedo (α) and r_e and their correlation to see what relationship appears. If LWP is constant [d(LWP)/LWP = 0] while N changes, then the column number density, N_c = Nh, changes as dN_c/N_c = −βdr_e/r_e with β = 3. Consequently, the cloud optical thickness varies as dτ/τ = 2 dr_e/r_e + dN_c/N_c = (2 − β)dr_e/r_e, which means τ and α increase with decreasing r_e if β > 2. Our results show that this prediction is true for thicker (τ > 15) clouds over oceans and all clouds over most land areas, although 2 < β < 3, indicating other influences at work. However, for thinner clouds (τ ⩽ 15) over oceans and tropical rain forests, we find that τ and α decrease with decreasing r_e—that is, β < 2—contrary to the assumption that LWP is constant. The underlying reason for this more complicated behavior is that cloud liquid water generally increases with increasing r_e, which appears to overwhelm changes in N_c for optically thinner clouds.

Table 2 lists the seasonal variation and the annual mean of the percentage of thin clouds (τ ⩽ 15) in all water clouds in 1988. This table shows more thin clouds over oceans than over land. The annual mean values show that about 79% of water clouds are thin clouds (τ ⩽ 15) for both hemispheres. Interannual variations do not significantly change this value.

Since 79% of all low-level clouds have τ < 15, the land–water and interhemispheric changes in LWP appear to dominate over possible aerosol-induced differences in N_c.

The situation is even more complicated than this summary, exhibiting regional and zonal mean differences in the relative magnitudes of the variations of τ and r_e and, consequently, differences in the variations of LWP and α. Even for most clouds over land that exhibit a correlation of α and r_e that is consistent in sign with the assumption of constant LWP, the magnitude of the difference is, in fact, altered by changing LWP values. For most clouds over ocean, except for the optically thicker clouds, the differences in LWP appear to dominate. In other words, where aerosol concentrations are already high (over land), cloud albedo and droplet size appear to vary consistently with the expectation that LWP is approximately constant, despite some actual variation of LWP; however, where aerosol concentrations are still low (over ocean), cloud albedo and droplet size do not vary consistently with this expectation.

We have shown that the correlated variations of cloud albedo and droplet size vary with geographic (hence circulation) regime, with cloud type—optically thin or thick—and with aerosol concentration. Moreover, we have shown that these variations are not always consistent with the assumption that LWP is constant. Thus, these results are sufficient to cast doubt on previous estimates of the aerosol indirect effect by suggesting that LWP may not remain constant because cloud processes may link aerosol-induced changes in N_c to changes in other cloud properties. However, these results are not sufficient to determine what the actual effect of a systematic change in aerosol concentration would be for two reasons. First, we have determined the correlated changes of cloud properties using their day-to-day variability, which may not represent their changes under the influence of systematic aerosol changes. Second, we have not actually correlated these cloud changes with changes of aerosol concentration, rather we have shown that the correlations in day-to-day cloud property changes are different in some regions where aerosol concentrations are known to be different (however, we cannot say that aerosol concentration differences explain all of the differences in cloud behavior that we find).

As one approach to make further progress, it is necessary to derive a “column” cloud droplet number density that can be observed from satellites and examine its variability, together with that of droplet size, to see how this quantity varies when average aerosol concentration varies. Using a modified definition of “cloud susceptibility,” which is valid under the condition of changing LWP, it is necessary to compare its values for clouds over ocean and land and between clouds in the Northern and Southern Hemispheres. Finally, it is necessary to combine a method for estimating variations in aerosol column concentrations from the same AVHRR observations to compare with nearby changes in cloud droplet concentration, droplet size (and LWP), and cloud albedo. This may provide the most direct assessment of the nature of aerosol effects on clouds that is possible with today’s satellite observations.