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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, D17204, doi:10.1029/2005JD006097, 2006

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ArticleSatellite-based assessment of marine low cloud variability associatedwith aerosol, atmospheric stability, and the diurnal cycle
Toshihisa Matsui,1 Hirohiko Masunaga,1 Sonia M. Kreidenweis,1 Roger A. Pielke Sr.,1
Wei-Kuo Tao,2 Mian Chin,2 and Yoram J. Kaufman2
Received 16 April 2005; revised 21 April 2006; accepted 16 May 2006; published 9 September 2006.

[1] This study examines variability in marine low cloud properties derived fromsemiglobal observations by the Tropical Rainfall Measuring Mission (TRMM) satellite, as
linked to the aerosol index (AI) and lower-tropospheric stability (LTS). AI is derived from
the Moderate Resolution Imaging Spectroradiometer (Terra MODIS) sensor and the
Goddard Chemistry Aerosol Radiation and Transportation (GOCART) model and is used
to represent column-integrated aerosol concentrations. LTS is derived from the NCEP/
NCAR reanalysis and represents the background thermodynamic environment in which
the clouds form. Global statistics reveal that cloud droplet size tends to be smallest in
polluted (high-AI) and strong inversion (high-LTS) environments. Statisticalquantification shows that cloud droplet size is better correlated with AI than it is with LTS.
Simultaneously, the cloud liquid water path (CLWP) tends to decrease as AI increases.
This correlation does not support the hypothesis or assumption that constant or increased
CLWP is associated with high aerosol concentrations. Global variability in corrected
cloud albedo (CCA), the product of cloud optical depth and cloud fraction, is very well
explained by LTS, while both AI and LTS are needed to explain local variability in
CCA. Most of the local correlations between AI and cloud properties are similar to theresults from the global statistics, while weak anomalous aerosol-cloud correlations
appear locally in the regions where simultaneous high (low) AI and low (high) LTS
compensate each other. Daytime diurnal cycles explain additional variability in cloudproperties. CCA has the largest diurnal cycle in high-LTS regions. Cloud droplet size and
CLWP have weak diurnal cycles that differ between clean and polluted environments.
The combined results suggest that investigations of marine low cloud radiative forcing and
its relationship to hypothesized aerosol indirect effects must consider the combined
effects of aerosols, thermodynamics, and the diurnal cycle.
Citation: Matsui, T., H. Masunaga, S. M. Kreidenweis, R. A. Pielke Sr., W.-K. Tao, M. Chin, and Y. J. Kaufman (2006), Satellitebased assessment of marine low cloud variability associated with aerosol, atmospheric stability, and the diurnal cycle, J. Geophys. Res.,
111, D17204, doi:10.1029/2005JD006097.

1. Introduction[2] Global low cloud properties critically control the
Earth’s radiation budget and hydrological cycle. Marine
low clouds have been extensively observed in the descending branch of the Hadley Circulation, where large-scale
subsidence occurs [Klein and Hartmann, 1993]. Marine low
clouds have an annually and globally averaged net cooling
effect of 15 (W/m2) [Hartmann et al., 1992]. A 4%
increase in low cloud cover could offset the anthropogenic
greenhouse gas warming due to a doubling of CO2 [Slingo,
1990]. The National Research Council [2005] highlighted
1
Department of Atmospheric Science, Colorado State University, Fort
Collins, Colorado, USA.
2
Laboratory for Atmospheres, NASA Goddard Space Flight Center,Greenbelt, Maryland, USA.

Copyright 2006 by the American Geophysical Union.
0148-0227/06/2005JD006097$09.00

the importance of cloud radiative effects within the climate
system. Variability in global low cloud fields modulates thewarm rain rate, which is estimated to account for 31% of thetotal surface precipitation over the tropics [Lau and Wu,
2003]. This large effect on the Earth’s climate prompts
scientists to examine the variability of low cloud properties
as linked to various meteorological parameters, such as sea
surface temperature (SST), relative humidity (RH) nearcloud layers, and lower-tropospheric stability (LTS) [e.g.,
Weare, 1994; Klein and Hartmann, 1993; Park and Leovy,
2004; Klein, 1997]. Comparisons of different parameters
used in cloud models show that no single meteorologicalparameter explains more than 13% of the variance in lowcloud amounts, and that multiple regressions using a combination of different parameters do not increase theexplained variance [Klein, 1997].
[3] Marine low clouds have a strong diurnal cycle due toradiation-driven turbulence in the cloud-capped marine
boundary layer [e.g., Driedonks and Duynkerke, 1989]. In

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the early morning, solar radiation starts heating the subcloudlayer, while longwave emission cools the cloud top. The
combination of longwave cooling and shortwave heating
drives turbulent mixing that (1) destabilizes the cloudlayer separately from the rest of the boundary layer and(2) induces entrainment of dry air that thins the cloud layer
in a complex manner. The isolated layer progressively thins
the cloud during the late morning and into the afternoon(see the review given by Driedonks and Duynkerke [1989]).
This diurnal cloud cycle was captured in the Atlantic
Stratocumulus Transition Experiment (ASTEX) [Cieselski
et al., 2001], in the First International Satellite Cloud
Climatology Project Regional Experiment (FIRE) [Hignett,
1991], and in observations from the California coastal
region [Betts, 1990]. Wood et al. [2002] showed the semiglobal-scale diurnal cycle of the cloud liquid water path
(CLWP) using a 2-year data set from the Tropical Rainfall
Measuring Mission (TRMM) satellite. They demonstrated
that the diurnal cycle generally peaked early in the morning,but that the timing of those peaks varied slightly in different
geographic regions.
[4] In recent decades, advanced space-borne satellites andglobal modeling systems investigated the global distributionof aerosol concentrations [Kaufman et al., 2002]. Hygroscopic aerosol particles serve as cloud condensation nuclei(CCN) that initiate the formation of cloud droplets. Higher
concentrations of submicron aerosols are expected to reduce
the average size of cloud droplets, in turn increasing thecloud albedo under the assumption of constant liquid watercontent [Twomey et al., 1984], and could enhance the cloudliquid water path by inhibiting the precipitation initiation
process [Albrecht, 1989]. These aerosol-cloud-climate linkages are called the aerosol indirect effects. Many studies
show a reduction of cloud droplet size associated with highaerosol concentrations observed in ground-based experiments [e.g., Feingold et al., 2003; Penner et al., 2004] aswell as in satellite imagery [e.g., Kaufman and Fraser,
1997; Nakajima et al., 2001; Bréon et al., 2002; Matsui etal., 2004a; Kaufman et al., 2005]. Some of the studies
capture rainfall inhibition due to air pollution [Rosenfeld,
1999; Matsui et al., 2004a]. Although many researchers
show links between small cloud droplets and high aerosol
concentrations in the ambient air, they do not consistently
find a dramatic increase in cloud albedo as initially hypothesized, probably because of the complicated feedbacks
involving thermodynamics and below-cloud turbulent mixing processes [Jiang et al., 2002].
[5] Another important aspect of the aerosol effect is thataerosol particles absorb and scatter radiation, which isdenoted as the aerosol direct effect. Absorbing aerosols,
such as black carbon and mineral dust, could contribute tohigh diabatic heating in the atmosphere that often enhances
cloud evaporation (the semidirect effect) [Ackerman et al.,
2000; Koren et al., 2004; Krüger and Graßl, 2004].
Atmospheric diabatic heating could strengthen inversions,which could inhibit the cyclogenesis process and consequently constrain hurricane tracks [Dunion and Velden,
2004]. Ramanathan et al. [2001] suggested that a combination of the aerosol direct and indirect effects could
weaken the hydrological cycle, which could be a major
environmental issue in this century.

D17204[6] To summarize, the large-scale thermodynamic field,
the radiation-driven diurnal cycle, and aerosol-cloud interactions are all critical in understanding the variability of
global marine low cloud properties. This study attempts toincorporate these aspects together to arrive at a deeper
understanding of marine low cloud variability. This study
extends the analysis by Matsui et al. [2004a] to anannual cycle (section 2), includes different aerosol data sets
(section 2.1), examines not only cloud droplet size but also
cloud liquid water path and cloud albedo (section 2.3),
statistically quantifies the relationship on the global scale(section 3.1) and local scale (section 3.2), and examines thediurnal cycle in regions with different thermodynamic
environments and aerosol concentrations (section 3.3).

2. Data Sets and Method
2.1. Lower-Tropospheric Stability (LTS) From the
NCEP/NCAR Reanalysis[7] A large amount of latent heat release over the warm
sea surface drives upward motion in the equatorial regions
and large-scale subsidence in the subtropics. The large-scale
subsidence over cold sea surface temperatures (SST) createsa strong inversion in the lower troposphere. Consequently,
cool, moist air below the inversion layer supports anincrease in the relative humidity (RH) and, thus, frequent
cloudiness. The magnitude of the inversion strength can bemeasured as the potential temperature difference between
the atmosphere at the 700-mb level and the surface, denoted
as lower-tropospheric stability (LTS) [Klein and Hartmann,
1993].
[8] Klein [1997] found that LTS is highly correlated withcloud amount, although other parameters such as lowertropospheric relative humidity are important as well. This
study focuses on LTS as an indicator of the thermodynamic
environment, as was done in the previous study [Matsui etal., 2004a], where low-cloud properties were investigated interms of aerosols and LTS. While the role of other parameters is certainly important, their impact on low clouds is notconsidered in the present paper, as we wanted to focus
specifically on LTS. LTS is also more readily derived fromremote sensing soundings or objective analyses, in comparison with subgrid parameters, such as cloud updraft velocity
or turbulent kinetic energy. In this study, LTS is derived
from the NCEP/NCAR reanalysis data set (2.5  2.5 grid
space) [Kalnay et al., 1996]. Although LTS can be correlated with aerosols on the regional scale, these correlations
tend to be canceled out on the global scale. For example,
global linear correlations between AI and LTS are 0.016
and 0.024 for the MODIS and GOCART cases. respectively.
These values are significant at 0.05 level, but are very small.
Regional correlations of LTS with AI can account forregional anomalies in the dependence of cloud properties
on AI and LTS, as discussed later.
[9] Figure 1 shows the annual mean and standard deviation of the global distribution of LTS sampled from March
2000 to February 2001 at the same sampling rate as that of
the cloud data set. LTS varies season-by-season and yearby-year. Regions with high LTS (strong inversions) arefrequently observed off the coast of California, Namibia,
and Chile. Those areas are located in the eastern parts ofmajor oceans (Figure 1). Low-LTS regions are found in the

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Figure 1. (top) Annual mean and (bottom) standard deviation of lower-tropospheric stability (LTS),
sampled from March 2000 to February 2001. High-LTS (strong inversion) regions are located in theeastern parts of major oceans.
tropics over warm SSTs, where surface energy flux andmass convergence create strong vertical mixing in theboundary layer. LTS exhibits large standard deviations in
midlatitude regions, in comparison to those in seen in thetropics (Figure 1), because of propagating synoptic fronts
and seasonal shifts of the Hadley cell.
2.2. Aerosol Index From MODIS and GOCART[10] In this study, aerosol concentration is represented by
the Aerosol Index (AI), which is the product of aerosol
optical depth (AOD) and the Ångstrom exponent. AI isbetter correlated with column aerosol concentrations andcloud properties than is AOD alone [Nakajima et al., 2001;
Bréon et al., 2002]. Global aerosol distributions fromsatellite retrievals and global chemistry transport model
calculations are used in this study, since both data havedifferent advantages and disadvantages [Yu et al., 2003;
Chin et al., 2004; Matsui et al., 2004b]. The satellite data
set used to compute AI is the Moderate Resolution Imaging
Spectroradiometer (Terra MODIS) Level-3 (collection 4)
instantaneous AOD at 0.55 mm and Ångstrom exponent
between 0.55 mm and 0.87 mm, which are archived on a
global 1  1 latitude-longitude grid. A comprehensive
description of the algorithm, sensor specification,
validation, and data sets is summarized by Remer et al.
[2005]. The other data set used to compute AI is from the
Goddard Chemistry Aerosol Radiation and Transportation(GOCART) model, which is a global chemical-aerosoltransport model driven by the Goddard Earth Observing
System Data Assimilation System (GEOS DAS) global
analysis (2  2.5 grid space). It prognoses a global
distribution of sulfate and its precursors, organic carbon,
black carbon, mineral dust, and sea salt (see details given by
Chin et al. [2002, 2004]). This study computes AI from
GOCART predictions of daily AOD at 0.55 mm andÅngstrom exponent between 0.55 mm and 0.90 mm. The
AODÅngstrom exponent ( d log
d log l , where l is the wavelength
at which AOD is determined) is an indicator of the size
distribution of aerosols; e.g., fine-mode particulate matter,such as sulfate and organic carbon, tend to be associatedwith high Ångstrom exponents, whereas the size distributions of coarse-mode particles, such as large sea salt anddust, tend to have low (near-zero) Ångstrom exponents.
[11] While satellite estimates of AOD are based on themeasured instantaneous top-of-atmosphere (TOA) radiance,
estimates of AOD from global chemistry transport models
are calculated on the basis of aerosol and precursor emissions inventories, atmospheric objective analysis, and simulated aerosol optical and microphysical properties.
Intercomparison of AOD at 0.55 mm between MODIS
retrievals and GOCART simulations has been reported for
global and regional scales [Yu et al., 2003; Chin et al., 2004;
Matsui et al., 2004b]. Figure 2a shows the global distribution of GOCART and MODIS AI integrated from 1 March

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Figure 2. (a) Annual average of MODIS and GOCART AI. (b) Local linear correlation coefficient (in 4  4 grid boxes)
between daily GOCART AI and MODIS AI. All data are sampled from March 2000 to February 2001.

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2000 to 28 February 2001, whenever MODIS retrievals and
GOCART outputs are simultaneously available. MODIS
and GOCART AI exhibit high spatial coherence on global
scales (correlation: 0.83). High values of AI appear along
the coastlines of Asia, India, eastern United States, and West
Africa. Very small values of AI appear in the remote Indianand Pacific Oceans. However, local correlations (daily
correlation in 4  4 grid boxes) are highly variable indifferent regions (Figure 2b). Remote oceans, particularly
the southern portions of the Indian and Pacific Oceans, havecorrelations less than 0.2 between MODIS and GOCART
AI, probably because of the low, and therefore more
uncertain, AI values.
[12] The GOCART model explicitly simulates different
aerosol species in four-dimensional fields. When weconvert the GOCART-predicted AOD to AI, the summation of the contributions of sulfate, organic carbon, andblack carbon represents approximately 97% of the total
AI. Dust and sea salt together represent about 3% of thetotal AI, because the Ångstrom exponents of the assumed
size distributions for those species are close to zero.
Large particles of sea salt and sulfate-coated dust serveas giant cloud condensation nuclei (GCCN). GCCN
potentially enhance the cloud drizzle process in environments characterized by high CCN concentrations, but
probably have little effect in low-CCN-concentration
environments where drizzle is active regardless of thepresence of GCCN [Feingold et al., 1999]. However, it is
not possible using AI to explicitly investigate the potential role of GCCN, as investigated by Feingold et al.
[1999]. Emissions of sulfate and sulfate precursors and oforganic carbon are primarily from industrial and agricultural activities. Therefore AI derived from multispectral
AOD allows us to focus on the anthropogenic aerosol
impact on marine low cloud. Although the size distributions assumed in the MODIS retrievals are slightly
different from those used in GOCART, the correspondence between aerosol types and concentrations and
MODIS AI can be similarly interpreted.
[13] The vertical distribution of AI remains uncertainin satellite-based aerosol-cloud interaction studies [Matsui
et al., 2004a; Bréon et al., 2002; Nakajima et al., 2001;
Sekiguchi et al., 2003]. More accurate assessments will
be available when the multisatellite A-Train platform isestablished [Stephens et al., 2002; Kaufman et al.,2003].
2.3. Marine Low Cloud Properties From the
TRMM Satellite[14] Masunaga et al. [2002a] proposed a new algorithm
that simultaneously derives different cloud properties
through a combined use of data from the TRMM Microwave Imager (TMI) and Visible/Infrared Radiance Imager(VIRS). First, VIRS radiances at 0.63 micron, 3.7 micron,and 10.8 micron are used to derive low-cloud opticaldepths, cloud top droplet effective radius (Re(top)), andcloud top temperature [Kawamoto et al., 2001; GTR 1.0
package from T. Y. Nakajima, personal communication,
2003]. Second, TMI brightness temperatures at 10.65 GHz,
19.35 GHz, and 37.0 GHz yield the column water vapor andcloud liquid water path (CLWP) for the VIRS-derived cloud
top temperatures and cloud fractions. We updated the look-

D17204up table used by the microwave algorithm so that itallows realistic variability of the water vapor and temperature profiles to improve the products obtained by
Masunaga et al. [2002a] and Matsui et al. [2004a]. The
TMI-derived CLWP (CLWPTMI) with the VIRS-derived
optical thickness (tVIRS) provide the cloud droplet effective radius (Re) via
ReðcolumnÞ ¼

1:5 CLWPTMI;
rw tVIRS

where rw represents water density. Re(column) represents
column-integrated Re, since microwave brightness temperature and visible radiance do not suffer from saturation
within any cloud thickness of marine low clouds (seethe details of the algorithm given by Masunaga et al.
[2002a]). Simultaneous analysis of Re(top) and Re(column)
provides more information to examine warm rain processes[Masunaga et al., 2002b; Matsui et al., 2004a].
[15] Klein and Hartmann [1993] showed that the lowcloud fraction is the primary parameter controlling thesurface cooling effect. While many studies focus on thechange in cloud optical depth and cloud fraction separately,
this study uses cloud amount defined by the corrected cloud
albedo, CCA:
CCA ¼ Acloud * CF;

where CF is the low-cloud fraction in a 1  1 box
derived from VIRS 2km-footprint pixels, and Acloud is thecloud albedo, which is expressed for a plane-parallel
cloud in a two-stream radiative transfer model [Hobbs,
1993] as,Acloud ¼

tVIRS:tVIRS þ 6:7

CCA accounts for cloud radiative forcing as the
combined effect of the cloud optical depth and cloud
fraction.
[16] To define a VIRS 2km-footprint pixel that is overcast, the following criteria must be satisfied simultaneously[Kawamoto et al., 2001]: (1) Radiances in channel 1 (l =0.623 mm), channel 2 (l = 1.610 mm), and channel 3 (l =3.784 mm) are all positive; (2) solar zenith angle must bewithin 0  60; (3) reflectance in channel 1 is greater than
the sum of 0.1 and the ocean albedo value; (4) brightness
temperature of channel 4 (l = 10.826 mm) is less than thesea surface temperature; (5) brightness temperature ofchannel 4 (l = 10.826 mm) is greater than brightness
temperature of channel 5 (l = 12.028 mm); and (6) 3 
3-window standard deviations of channel 1 is less than
100 Wm2ster1mm1, and 3  3-window standard deviations of brightness temperature of channel 5 is also lessthan 100 K, indicating a horizontally homogeneous pixel.
Cloud pixels with high ambient aerosols were removed
from the analysis by taking the 95% of the total PDF(Figure 3). These data screening procedures should ensure

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Figure 3. Probability density function (PDF) of (a) AI and LTS and (b) cloud properties. Variability of
95% of the total PDF is shown for each variable.
separation between cloudy pixels and pixels with very
high aerosol concentrations.
2.4. Method of Analysis[17] This section describes the various statistical method
and results. The sampling and statistical methods are as
follows.
[18] 1. Sample the TRMM-derived low cloud properties,
MODIS AI, GOCART AI, and NCEP LTS, only when they
are simultaneously available. Note that the NCEP LTS is
temporally interpolated to coincide with the TRMM satellite
overpasses. MODIS AI values are instantaneous values atapproximately 10:30 am local time, and GOCART AI
values are daily averages. Although a time lag up to ±5 hourexists between the MODIS and TRMM overpasses, temporalautocorrelations of aerosol extinction are still very high in thisrange [Anderson et al., 2003].
[19] 2. Generate the probability density function (PDF) of
MODIS AI, GOCART AI and NCEP LTS from the total
samples (Figure 3).
[20] 3. Select 95% of the most frequent ranges from thetotal PDF by removing ±2.5% of the smallest and largest
values for MODIS AI, GOCART AI and NCEP LTS. For anormal distribution, 95% of the total PDF is equivalent to
the range of four standard deviations (4s). These ranges are
represented as dAI 95% (0.41 for MODIS; 0.26 for
GOCART) and dLTS95% (10.5K), respectively (Figure 3).
[21] 4. Similarly, select 95% of the most frequent ranges
for Re(column), CLWP, and CCA. These ranges are

represented as dRe(column)95% (50.0 mm), dCLWP 95%(188.0 g/m2), and dCCA95% (0.37) (Figure 3). These values
are used to examine how well AI and LTS can explain thevariability of cloud properties.
[ 22 ] 5. Select the sampling bins for MODIS AI,
GOCART AI and NCEP LTS as 10% of dAI95% anddLTS95%, respectively. These are represented as dAIbin(0.04 for MODIS; 0.026 for GOCART) and dLTSbin(1.05 K).
[23] 6. Compute mean values of Re(column), CLWP, and
CCA for each bin (dAIbin and dLTSbin) of the MODIS AI,
GOCART AI and NCEP LTS. Mean values are represented
as ReðcolumnÞ, CLWP, and CCA.
[24] The above symbols and variables are summarized in
the Notation section. The TRMM overpasses include theannual cycle from March 2000 to February 2001. Samplingis significantly concentrated in the subtropics because of thelarge amount of marine low cloud in those regions and theunique overpass pattern of the TRMM satellite (Figure 4).
The sampling weights are identical between the GOCART
and MODIS cases. Sampling was restricted to low clouds,
defined as those which have a cloud top temperature above
273 K.
[25] It is worthwhile to note that Re(top) is generally
larger than Re(column) for nonprecipitating clouds, while
Re(top) can be smaller than Re(column) for precipitating
clouds [Masunaga et al., 2002a; Matsui et al., 2004a].
Figure 3b shows the mode of Re(column) appear to be

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Figure 4. Global distribution of sampling number. Sampling numbers are significantly concentrated in
the subtropics because of the large amount of marine low cloud and the unique overpass pattern of the
TRMM satellite.
greater than the Re(top). This is possibly explained by the
sampling biases in precipitating clouds and/or algorithm
biases. We must reexamine Re(column)-Re(top) relationship and algorithm for different types of clouds in different
climatological regions, when the global-scale vertical profile of cloud properties become available [Stephens et al.,2002]. Nevertheless, this uncertainty fundamentally does
not affect our analysis, since this study does not focus on thecomparison between Re(top) and Re(column).

3. Results
3.1. Global Statistics Among Cloud Properties, LTS,
and AI[26] Figure 5a shows the variability of ReðcolumnÞ as afunction of LTS and AI. Clean (low-AI) environments inregions with low LTS tend to have the largest ReðcolumnÞ,while polluted (high-AI) environments with high LTS tend
to have the smallest ReðcolumnÞ. Table 1 shows the changes
in cloud properties for dAI95% and dLTS95%. For example,dReðcolumnÞ95% for dAI95% and dLTS95% are defined as

17.5% and 16.6% respectively of dRe(column)95% (50.0 mm)(Table 1). Note that relationships between LTS and cloudproperties appear to be slightly different between the
MODIS and GOCART cases, although LTS is independentof AI in the global sampling. This is because differences in
global distribution of AI between MODIS and GOCART
cause slightly different sampling of background LTS. In
both cases, however, the global distribution of cloud droplet
size is correlated better with AI than it is with LTS. This
result can be applied to the warm rain process, since theprocess can be diagnosed by the droplet effective size
[Matsui et al., 2004a].
[28] Figure 5a shows that the relationships between
Re(column) and AI are nonlinear, whereas the Re-LTS
slopes are approximately linear. For example, ReðcolumnÞ
appears to decline more rapidly with increases in AI for
small AI, whereas increases in AI at high AI do not reducethe cloud droplet size effectively. This trend for small AI isimportant, because small values of AI are much more
frequent than high values (Figure 3a). Thus we additionallydefine changes in ReðcolumnÞ between neighboring bins

8 P 

>
>
ReðcolumnÞlow AIbin  ReðcolumnÞhigh AIbin * sampling#LTSbin>>>
LTSbin>P>>>sampling#LTSbin<
LTSbindReðcolumnÞ95% ¼
P>>ReðcolumnÞlow LTSbin  ReðcolumnÞhigh LTSbin * sampling#AIbin
>
>
>
AIbin
>
P
>
>
>
sampling#AIbin
:

ð1Þ

AIbin

where ReðcolumnÞlow_AIbin is the ReðcolumnÞ in the lowest
bin of AI, ReðcolumnÞhigh_AIbin is the ReðcolumnÞ in thehighest bin of AI, ReðcolumnÞlow_LTSbin is the ReðcolumnÞ
in the lowest bin of LTS, and ReðcolumnÞhigh_LTSbin is theReðcolumnÞ in the highest bin of LTS. Similar definitions
are applied to CLWP and CCA.
[27] This result shows that an increase in dAI95% corresponds to a reduction of 12.24 mm in ReðcolumnÞ in the
MODIS case and 12.19 mm in the GOCART case, explaining 24.4% and 24.3% respectively of dRe(column)95%(50.0 mm) (Table 1). Similarly, an increase in dLTS95%
corresponds to a reduction of 8.77 mm in ReðcolumnÞ in the
MODIS case and 8.35 mm in the GOCART case, explaining(dAIbin and dLTSbin), weighted by the frequency distributionof the sampling number, which is strongly peaked near themean value of the LTS PDF and low AI values (Figure 3a):PPdReðcolumnÞ * sampling#bindReðcolumnÞfreq ¼ LTSbin AIbinP P
ð2Þ
sampling#bin
LTSbin AIbin

The similar definition is applied to CLWP and CCA. Thisvalue represents the frequency weighted mean values of thechange in clouds properties over the globe. Table 2 showsdReðcolumnÞfreq (1.80 and 0.94, respectively) as afunction of dAIbin and dLTSbin. dAIbin explains twice the7 of 16

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Figure 5. Global statistics of mean warm cloud properties ((a) column droplet effective radius, (b) cloudliquid water path, and (c) corrected cloud albedo) as functions of LTS and AI.
variability in ReðcolumnÞ that is attributed to dLTSbin forboth the MODIS and GOCART cases, showing consistently
that cloud droplet size is correlated better with AI than it iswith LTS by using the definition (1) and (2).

[29] Figure 5b shows the variability of CLWP as afunction of NCEP LTS and AI. While higher LTS corresponds to slightly lower CLWP for all AI bins, it is clearthat AI is more strongly correlated with CLWP. An increase

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Table 1. Mean Changes in Cloud Properties With Increases in dAI95% and dLTS95%jdReðcolumnÞj

dReðcolumnÞ95%, mm (d ReðcolumnÞ
Forcing

MODIS

dAI95%
dLTS95%

12.24 (24.4%)
8.77 (17.5%)* 100)

95%

GOCART12.19 (24.3%)
8.35 (16.6%)

jdCLWPj

dCLWP 95%, g/m2 (dCLWP

95%* 100)

jdCCAjdCCA95%(dCCA

95%

*100)

MODIS

GOCART

MODIS

GOCART39.24 (20.8%)
8.51 (4.5%)

42.56 (22.6%)
5.04 (2.6%)

0.039 (10.6%)
0.115 (31.2%)

0.026 (7.1%)
0.117 (31.8%)

in dAI95% corresponds to a reduction of 39.2 g/m2 of CLWP
in the MODIS AI case and 43.56 g/m2 in the GOCART case,
explaining 20.8% and 22.6% of dCLWP95% (188.0 g/m2)(Table 1). On the other hand, an increase in dLTS95%
corresponds to a reduction of 8.51 g/m2 of CLWP in the
MODIS case and 5.04 g/m2 in the GOCART case, which
explains only 4.5% and 2.6% of dCLWP95% (188.0 g/m2),
respectively (Table 1). Table 2 also shows that CLWP is
more strongly correlated with the AI than it is with LTS byusing the definition (2). Note that we also tested the VIRSderived CLWP and found similar results (not shown here).
Han et al. [1998] examined data from the Advanced VeryHigh Resolution Radiometer (AVHRR) with the same
273 K cloud top temperature threshold for low cloud
sampling, and also found that the liquid water pathdecreases with decreasing cloud droplet size. On the other
hand, Sekiguchi et al. [2003] examined AVHRR data
corresponding to a different low cloud top temperaturethreshold (below 257 K), and found that the liquid water
path increases with decreasing cloud droplet size. These
different results suggest that different sampling criteria interms of cloud top temperature could be a key issue
leading to qualitative differences in the relationships between liquid water path and cloud droplet size.
[30] Twomey et al. [1984] assumed that liquid water pathremained constant as aerosol concentrations increased,
while Albrecht [1989] hypothesized that high aerosol concentrations could increase CLWP via a less efficient precipitation process. Originally both hypotheses were built
assuming that only microphysical processes affect cloudproperties. The aerosol semidirect effect [Ackerman et al.,
2000; Koren et al., 2004; Krüger and Graßl, 2004] is one
possible reason for the low CLWP with high aerosol
concentrations that we observed in this analysis. Somemodel studies proposed microscale dynamic processes that
qualitatively explain this result. For example, Jiang et al.
[2002], using a nonhydrostatic two-dimensional eddyresolving model with an explicit microphysics parameterization, found that drizzle inhibition due to air pollution
results in a stable boundary layer below cloud, which
reduces the moisture supply and leads to low CLWP. In
the clean environment, enhanced drizzle evaporation below

the cloud destabilizes the boundary layer, which results inpenetrating cumuli, leading to high CLWP. These relationships must be further tested with different observations anda number of simulation studies.
[31] Finally, Figure 5c shows variations in CCA with LTS
and AI. There is a strong, linear correlation with LTS. An
increase in dLTS95% corresponds to an increase of CCA by
0.115 in the MODIS case and by 0.117 in the GOCART
case, which explains 31.2% and 31.8% respectively ofdCCA95% (0.37) (Table 1). On the other hand, the AICCA relationship appears to be nonlinear and different
between the MODIS and the GOCART cases. An increase
in dAI95% corresponds to a very slight increase of CCA(about 0.039 in the MODIS case and 0.026 in the GOCART
case), and explains 10.6% and 7.1% respectively ofdCCA95% (0.37) (Table 1). For high-AI bins, CCA-AI
correlation slopes are nearly zero and/or slightly negative,
while positive CCA-AI correlation slopes exist for low-AI
bins. Although we used CCA instead of cloud opticaldepth, this result is similar to that inferred from satellite
measurements of cloud optical depth over the Amazon basin[Kaufman and Fraser, 1997]. By using the definition (2),the correlation slope of MODIS AI with CCA is comparable
to the correlation of LTS with CCA (Table 2), suggestingthat the aerosol-CCA correlation can be captured frequently
over the globe. However, this is not captured in the
GOCART case; that is, AI has a weak correlation with the
CCA by using both the definition (1) and (2). We conduct
further tests of these relationships on a local scale in thenext section.
[32] Note that partially cloudy VIRS pixels could result inbiases in the retrieved cloud properties. Cloud optical depth
and cloud top temperature could have a negative bias, whilecloud droplet radius can be overestimated, from a partiallycloudy VIRS pixel. Variation of AI in a partially cloudy
pixel can affect the values of estimated cloud properties tosome degree that has not yet been quantified.
3.2. Local Statistics Between Cloud Properties, AI,
and LTS[33] In the previous section, we found strong relationships between cloud properties, AI, and LTS on the global

Table 2. Frequency Weighted Mean Values of the Change in Cloud Properties With Increases in dAIbin and dLTSbin Over the Globea
dCLWP freq, g/m2dReðcolumnÞfreq, mm

dCCAfreq

Forcing

MODIS

GOCART

MODIS

GOCART

MODIS

GOCARTdAIbindLTSbin

1.80
0.94

1.58
0.85

3.85
0.62

5.04
0.37

0.01360.01350.00160.0133aChanges in cloud properties are weighted by the sampling number as described in the text.

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scale, and the correlation slopes are quantified by thedefinition (1) and (2). In this section, we examine how
those relationships vary in different geographical regions.
Sekiguchi et al. [2003] examined local correlations using the
AVHRR and the POLarization and Directionality of the
Earth’s Reflectances (POLDER) instrument, and showedthat strong correlation between aerosols and cloud properties exist along coastlines where continental air masses meet
maritime clean air. We derive the linear correlation coefficient in each 4 box on a global grid for the same annual
sampling period used in the previous section. The variability of local positive or negative correlation reported by
Sekiguchi et al. [2003] is seen in this study to depend on
both aerosol and thermodynamic variability. Positive (negative) correlations are showed in red (blue) shades, andstatistically insignificant correlations (approximately, jrj <0.05) with t-distribution critical level set to 0.05 are shownin white (Figure 6).
[34] Figure 6a shows the correlation map between
Re(column) and MODIS AI (left), GOCART AI (center),and NCEP LTS (right). Strong negative correlations (blue)
appear in the subtropics in the Northern Pacific Ocean, in
the Indian Ocean, and in most of the Atlantic Ocean.
Correlation maps for the MODIS and GOCART cases show
general agreement with the global statistics discussed in
section 3.1. Weak correlations (white) and slightly positive
correlations (red) appear in the remote Southern Pacific
Ocean in the MODIS case, in the middle of the Pacific
Ocean in the GOCART case, and off the west coast of
Africa. In the remote ocean, the correlation coefficient may
be very small because of the small variability in AI and thelow sampling number. Overall correlations are negative,
which was captured in the global statistics (section 3.1).
The LTS-Re(column) correlation also appears to be highly
positive in the subtropics and weak or slightly negative in
the Pacific Ocean. This is because, in subtropical regions,
LTS varies substantially because of propagating midlatitude
fronts and the seasonal shift of the large-scale circulation(Figure 1). These considerations also explain the weakcorrelation in the equatorial regions, where LTS does notchange substantially throughout the year (Figure 1).
[35] Figure 6b shows the local correlation map between
CLWP and MODIS AI (left), GOCART AI (center), and
NCEP LTS (right). Negative correlations (blue) in the
MODIS case appear in the northern subtropics in the Pacific
Ocean, in the coastal zones around the Indian Ocean andSouth Africa, and for the northern part of the Atlantic
Ocean. The GOCART case has a slightly larger area of
negative correlations than the MODIS case, which isconsistent with the result discussed in the previous section.
The geographical locations of the negative correlations are,apparently, coherent with those of Re(column) (Figure 6a).
This suggests that a reduction in cloud droplet size andcloud liquid water associated with high concentrations ofaerosols occurs simultaneously on a local scale over theocean.
[36] Figure 6c shows the local correlation map between
CCA and MODIS AI (left), GOCART AI (center), and
NCEP LTS (right). The MODIS case shows positive correlations over almost the entire domain; that is, the aerosol
indirect effect exists over almost the entire ocean. The
GOCART case shows positive correlations in the northern

D17204part of the Pacific Ocean and off the east coast of North
America, while negative correlations appear off the east
coast of Australia and Africa and in some remote ocean
areas. This result is consistent with the global statistics; the
MODIS case shows stronger correlation between AI and
the CCA than the GOCART case does (section 3.1). Boththe MODIS and the GOCART cases show that the strongest
positive correlation appears in the Northern Pacific, where a
combination of industrial and dust aerosols from East Asia
advect over the ocean. LTS also has a consistently positive
correlation with CCA over the global ocean.
[37] In section 3.1, we found that increases in AI as wellas LTS are accompanied by decreases in cloud droplet size,
decreases in liquid water path, and increases in CCA.
However, in a marine environment, if AI becomes high,but LTS becomes low, changes in cloud properties can beoffset or very small because of the competition between AI
and LTS. Jiang et al. [2002] and Takemura et al. [2005] also
found that a change in simulated CLWP could depend upon
the large-scale thermodynamic feedback. In section 1, we
stated that AI and LTS are independent on the global scale.
In contrast, they are usually correlated either positively or
negatively on a local scale (Figure 7). In the MODIS case,negative correlations appear in a large portion of thesouthern Pacific Ocean, and positive and negative correlations appear in the Atlantic Ocean. In the GOCART case,negative and positive correlations also appear in different
regions. Positive AI-LTS correlations mean that high (low)AI appears with high (low) LTS. For positively correlated
regions, both factors tend to reduce Re(column) and CLWP,
while increasing CCA (Figure 6). On the other hand,negative AI-LTS correlations mean that high (low) AI
appears with low (high) LTS, which has the opposite effecton cloud properties (Figure 6). Comparing Figures 6 and 7,
the regions with negative AI-LTS correlations are coherent
with the regions with weak AI-cloud properties correlationin Figure 6, such as the southern Pacific Ocean and off thewest coast of West Africa. This implies that the global
distribution of local aerosol-cloud relationship could be
modulated by feedback from the large-scale thermodynamic
field. The importance of the large-scale feedback on aerosol
direct and indirect effects is investigated and discussed in
the global modeling study presented by Takemura et al.
[2005].
3.3. Diurnal Cycle of Cloud Properties in Different
LTS and AI Regions[38] As introduced in section 1, marine low clouds haveradiation-driven strong diurnal variability [e.g., Driedonks
and Duynkerke, 1989]. The TRMM sun-asynchronous orbit
allows us to examine the daytime diurnal cycle ofReðcolumnÞ, CLWP, and CCA in regions with different
LTS and AI. For clarity, LTS and AI bins are assigned to be
twice as large as those in the previous sections. The LTS
and AI contours in the figures are labeled by the mean valueof each LTS and AI bin, respectively.
[39] Figure 8a shows the daytime diurnal cycle of various
cloud properties in different LTS bins. ReðcolumnÞ appears
to be higher in lower-LTS bins, while CCA appears to belarger in higher-LTS bins over most of the diurnal cycle.
ReðcolumnÞ reaches its maximum from 10 am to 1 pm anddecreases toward evening, with consistent behavior for any

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Figure 6. Linear correlation coefficient in each 4 box on a global grid for the same annual sampling period as in Figures 1
and 2. Nonsampled grids (over land) and statistically insignificant correlations (approximately, jrj < 0.05) with thet-distribution critical level set to 0.05 are shown in white. (a) Re (columns), (b) CLWP, and (c) CCA are linearly correlatedwith MODIS AI, GOCART AI, and LST.

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Figure 7. Linear correlation coefficient between AI and LTS in each 4 box on a global grid for thesame annual sampling period as in Figure 6. Positive AI-LTS (red) correlations mean that high AI appears
with high LTS, while negative AI-LTS correlations mean that high AI appears with low LTS, which has
opposite effect on cloud properties. Therefore negative-correlation regions appear to be coherent with the
weak-correlation regions in Figure 6.

LTS. The largest LTS regions (19.6) exhibit a slightly
different pattern in CLWP from the other regions. CLWP
stays at its maximum from 7 am to 12 pm and then rapidly
decreases in the afternoon. In particular, times of peak
CLWP in high-LTS bins (highest three bins of LTS) appear
to be in the early morning between 7 am and 9 am, while
peak times in the lowest two LTS bins are in the latemorning between 9 am and 1 pm. The diurnal cycles ofcloud top height varies with LTS, but generally decline ( afew hundred meters) from the morning to the evening.
These patterns are similar to observations from the FIRE
intensive observation period [Hignett, 1991]. The diurnal
cycle of CCA depicts a strong contrast between daytime
diurnal variability in high- and low-LTS regions. HigherLTS bins tend to have larger morning/evening peaks and thelargest diurnal variability. In the highest-LTS (19.6 K)
regions, CCA declines about 50% from its peak value inthe morning. For all LTS bins, except the lowest (=11.2), thediurnal minima appear to be at noon. Morning maxima areslightly larger than those in the evening.
[40] Figure 8b shows the daytime cloud diurnal cycle fordifferent AI. ReðcolumnÞ and CLWP are generally higher
for lower-AI (clean) environments over most of the diurnal
cycle. Note that the sampling is unbiased with the background LTS values. Both the MODIS and GOCART relationships show distinctly different diurnal cycles between
high- and low-AI bins. In the polluted environment cases(the highest three bins of AI), ReðcolumnÞ and CLWP have
sharp rises in the early morning between 7 am and 9 am in
the MODIS case, and between 7 am and 12 pm in the
GOCART case. On the other hand, the clean environmental
cases (lowest two bins of AI) show consistently high valuesof ReðcolumnÞ and CLWP between 7 am and 1 pm. In all
the cases, ReðcolumnÞ and CLWP show a rapid decrease in
the late afternoon. Cloud top height gradually declines fromthe morning to midafternoon, and slightly increases between
3 pm and 5 pm. The diurnal cycle of cloud top height
exhibits substantial diversity between the high- and low-AI
regions in the GOCART case, but this feature is not seen in
the MODIS case. CCA has a strong diurnal cycle, but does
not have any discernible variation with AI.
[41] While data from the TRMM satellite showed thedaytime diurnal cycle of ReðcolumnÞ, CLWP, and CCA, theexact mechanism that drives different daytime diurnal

cycles is still unknown. One possible explanation could
be solar heating. As explained in section 1, absorption ofsolar radiation in the middle of the cloud layer and longwave cooling at cloud top drive turbulent mixing in thecloud layer [e.g., Driedonks and Duynkerke, 1989]. The
degree of solar heating may change for different droplet size
spectra. Water clouds could absorb up to 15– 20% of theincident solar radiation, with the largest values arising fromthe thickest clouds with large cloud droplets [King et al.,1990]. On the other hand, small, narrowly concentrated
cloud droplet spectra tend to have less absorption of solar
radiation. Therefore thin clouds with smaller droplet size
forming in polluted environments could reduce evaporation
due to solar heating in the morning, supporting increases thecloud droplet size and liquid water that persist later in themorning as compared with thicker clouds having larger
mean droplet sizes. However, this discussion is only speculative. More intensive measurements will be required toestablish the mechanisms involved.
[42] An important implication of the daytime diurnal
cycle is that satellite-based assessments of the aerosol
indirect effect could appear to be slightly different depending on the local time of satellite overpass. Unlike the
TRMM satellite, all of the polar orbiting environmental
satellites (POES) have a constant local time of satellite
overpass. Differences in ReðcolumnÞ and CLWP between
the highest-AI bin and the lowest-AI bin are largest in theearly morning (Figure 8b). If one measures ReðcolumnÞ and
CLWP early in the morning, the correlation slope between
aerosols and cloud properties could be larger than the daily
mean, whereas the correlation could be smaller aroundnoon. Moreover, the CCA-LTS correlation slope could
become much larger for morning/evening-time sampling,
and vice versa for noontime sampling. This daytime diurnal
cycle must be incorporated into the estimation of cloudradiative forcing and the aerosol indirect effect estimatedfrom the POES.

4. Summary[43] This study examines links between variability inmarine low cloud properties derived from the TRMM
satellite, MODIS/GOCART-derived aerosol index (AI),and lower-tropospheric stability (LTS) derived from the

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Figure 8. Diurnal cycles of cloud properties in different (a) LTS and (b) AI regions. Contours of LTS
and AI represent
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the mean values of the LTS and AI bins, respectively. Error bars represent standard
errors (s/ n  2, where n and s are the number of quasi-coincident measurements for each bin andstandard deviation, respectively).

NCEP/NCAR reanalysis. AI and LTS are used to represent
column-integrated aerosol concentrations and backgroundthermodynamic environments, respectively. Results are
summarized as follows.
[44] 1. Cloud droplet sizes tend to be smallest in polluted
and strong-inversion environments. Cloud droplet size
decreases linearly with increasing LTS, while AI has evenstronger anticorrelations with cloud droplet size, especiallyin clean environments. Statistical quantification shows thattwice as much variability in cloud droplet size is explainedby AI than by LTS.

[45] 2. Higher values of AI tend to be associated withsignificantly lower cloud liquid water path (CLWP), while
higher LTS is linked with a slightly lower CLWP. Statisticalquantification showed that the global variability of CLWP is
more strongly correlated with AI than it is with LTS. These
results do not support the hypotheses or assumption of
constant or increased LWP of warm clouds associated withhigh aerosol concentrations [Twomey et al., 1984; Albrecht,
1989].
[46] 3. High LTS, i.e., strong inversions, result in extensive cloud cover and high regional albedo. LTS is linearlycorrelated with the corrected cloud albedo (CCA: product of

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cloud optical depth and cloud fraction), while the AI-CCA
relationship is nonlinear and is different for the MODIS AI
and the GOCART AI cases. In clean environments, small
increases in AI can enhance CCA; however, this enhancement was not observed in already polluted (high-AI) environments. For the MODIS data set, statistical quantificationsuggests that global variability in CCA is well explained by
LTS, while both AI and LTS are needed to explain local
variability of CCA.
[47] 4. Most of the local correlations between AI andcloud properties agree with the results from the global
statistics; that is, higher AI or higher LTS is associated withsmaller cloud droplet size and lower CLWP, and higher
CCA. On the other hand, weak local aerosol-cloud correlations appear in the regions where high (low) AI and low(high) LTS occur simultaneously, thereby offsetting eachother.
[48] 5. Daytime diurnal cycles can explain additionalvariability in cloud properties; none of the cloud properties
is constant through the daytime. CCA has the largest diurnal
cycle in high-LTS regions, such as off the coasts ofCalifornia, Namibia, and Chile. Cloud droplet size and
CLWP have slightly different diurnal cycles between clean
and polluted environments. Reasons for this behavior remain uncertain. This daytime diurnal cycle should beincorporated into the estimation of cloud solar radiative
forcing and aerosol indirect effects produced using datafrom Polar Orbiting Environmental Satellites (POES).
[49] These findings should be tested with data fromdifferent satellite platforms and with various numericalmodeling experiments. Remaining uncertainties and proposed future directions for analyses are summarized asfollows.
[50] 1. The statistical quantification may vary for adifferent choice of thermodynamic (e.g., turbulent kinetic
energy or updraft velocity) and aerosol parameters (e.g.,
AOD and the Ångstrom exponent derived at different
wavelengths).
[51] 2. Our statistical sampling and analysis is limited towarm clouds with cloud top temperatures greater than
273 K. Analyses must be extended to ice and mixed phase
clouds in future work. Such studies [e.g., Koren et al., 2005;
Lin et al., 2006] have shown different relationships forcloud-aerosol interactions than were seen in this work.
[52] 3. Observations of the vertical distribution of AI are
required on a global scale. Kaufman et al. [2003] proposed
multisensor satellite retrievals of coarse- and fine-mode
aerosol optical depth and vertical distribution by utilizing
space-borne LIDAR measurements in addition to MODIS
radiances in the inversion. These techniques and data sets
will be available in the near future.
[53] 4. The role of GCCN is largely ignored by the use of
AI as the aerosol variable. A study examining the role of
GCCN more explicitly is possible by investigating therelative roles of the fine- and coarse-mode aerosol fractions
available in the MODIS aerosol products.
[54] 5. The VIRS footprint size may be too coarse toresolve the properties of highly broken clouds, leading to
unknown biases in the quantitative analysis. The TMI-VIRS
combined algorithm used in this study can be applied to the
combination of the Advanced Microwave Scanning Radiometer (AMSR) and MODIS sensors on the Aqua satellite

D17204platform. MODIS has a much smaller footprint than VIRS,
while AMSR has microwave channels similar to those of
TMI.

NotationAI
dAI95%
dAIbinLTS
dLTS95%
dLTSbinRe(column)dRe(column)95%
ReðcolumnÞ
dReðcolumnÞ95%dReðcolumnÞfreqCLWP
dCLWP95%
CLWP
dCLWP95%
dCLWPfreq
CCA
dCCA95%CCA
dCCA95%dCCAfreq

Aerosol index: the product of aerosol
optical depth and the Ångstrom exponent.
95% of the most frequent AI out of total
probability density function (0.41 for
MODIS; 0.26 for GOCART).
Size of sampling bin: 10% of dAI95%(0.04 for MODIS, 0.026 for GOCART).
Lower-tropospheric stability (or inversion strength): potential temperature at
700 mb – surface potential temperature.
95% of the most frequent LTS out of total
probability density function (10.5 K).
Size of sampling LTS bin: 10% of
dLTS95% (1.05 K).
Column integrated cloud droplet effective radius (mm).
A range of 95% of the most frequent( 4s) Re(column) out of total probability density function (50.0 mm).
Re(column) averaged for each bin (dAIbin
and dLTSbin).
Mean change in ReðcolumnÞ with increase in dAI95% and dLTS95%.
Frequency weighted mean values of thechange in ReðcolumnÞ with increase indAIbin and dLTSbin over the globe.
Cloud liquid water path (g/m2).
A range of 95% of the most frequent( 4s) CLWP values out of total probability density function (188.0 g/m2).
CLWP averaged for each bin (dAIbin anddLTSbin).
Mean change in CLWP with increase indAI95% and dLTS95%.
Frequency weighted mean values of thechange in CLWP with increase in dAIbin
and dLTSbin over the globe.
Corrected cloud albedo: the product ofcloud optical depth and cloud fraction in1 box.
A range of 95% of the most frequent( 4s) CCA out of total probability
density function (0.37).
CCA averaged for each bin (dAIbin anddLTSbin).
Mean change in CCA with increase indAI95% and dLTS95%.
Frequency weighted mean values of thechange in CCA with increase in dAIbin
and dLTSbin over the globe.

[55] Acknowledgments. This work is funded by NASA CEAS fellowship, NAG5-12105, and NASA Radiation Project, NNG04GB87G.
VIRS (1B01) and TMI (1B11) data were provided by NASA GSFC DAAC.
T. Jackson, H. Rui, J. R. Vanderpool, and W. Berg helped the author to readthe tape-archived TRMM data set. NCEP/NCAR Reanalysis data were
provided by NOAA CDC. The authors would like to thank T.Y. Nakajima

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at NASDA/EORC for providing the GTR 4.1 packages; NASA GSFC
code 613.1 Mesoscale Atmospheric Processes Branch for providing computer resources; Bill Cotton for the notes from the ‘‘Thermodynamics andCloud Physics’’ course at Department of Atmospheric Science, Colorado
State University; and a reviewer for his/her detailed comments andsuggestions.

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M. Chin, Y. J. Kaufman, and W.-K. Tao, Laboratory for Atmospheres,NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA.
S. M. Kreidenweis, H. Masunaga, T. Matsui, and R. A. Pielke Sr.,
Department of Atmospheric Science, Colorado State University, Fort
Collins, CO 80523-1371, USA. (matsuit@atmos.colostate.edu)

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