The layer-mean radar reflectivity e observed by CloudSat and the columnar effective particle radius Re obtained from a combined microwave-shortwave analysis are combined to investigate the joint relationships between e and Re for warm clouds. Global statistics for seasonally averaged data reveals that radar reflectivities e less than about −10 dBZ tend to relate to the effective radius via a sixth-power dependency, corresponding to a constant number concentration implying that the condensation particle growth process mainly takes place within the cloud layer for e < −10 dBZ. For e > −10 dBZ, e depends on Re through a cubic relation, corresponding to a constant mass concentration implying coagulation as the dominant particle growth process. These microphysical regimes so identified are shown to be consistent with CloudSat-inferred rainfall rate.
 Cloud feedback processes are recognized as one of the main sources of uncertainty in understanding and predicting the global climate [e.g., Stephens, 2005]. Warm clouds play a fundamental role in Earth's climate through their radiative and hydrological effects. These effects of the clouds are strongly regulated by their microphysical structure formed through particle growth processes from micron-sized cloud droplets to millimeter-sized rain drops. The liquid cloud particles are considered to grow through condensation process for early stage of cloud development and through coagulation in mature stages especially with significant concentrations of drizzle particles [e.g., Rogers and Yau, 1989]. It is important to understand how these processes indeed take place in real atmosphere and how they influence the optical and microphysical properties of clouds.
 Recent progress in satellite remote sensing techniques provides us with cloud optical and microphysical properties on the global scale. Notable is the launch of CloudSat on April 2006 bringing new observations of clouds with Cloud Profiling Radar (CPR) operating at 94 GHz. The CloudSat satellite flies as part of a constellation of satellites referred to as the A-Train [Stephens et al., 2002] that includes the Earth Observing System (EOS) Aqua satellite. The Aqua spacecraft is equipped with MODIS (MODerate resolution Imaging Spectroradiometer) visible radiometers and AMSR-E (Advanced Microwave Scanning Radiometer for the Earth Observing System) microwave imagers. These active and passive sensors of the A-Train provide a unique ability to simultaneously observe various aspects of cloud-to-precipitation processes on the global scale.
 This study aims to categorize the warm cloud microphysical regimes according to particle growth processes by combining analysis of active and passive global cloud observations provided by the A-Train. We make use of the CPR data of CloudSat, microwave of AMSR-E data in the form of cloud liquid water path and shortwave reflected radiances measured by MODIS, and combine them to identify cloud particle growth regimes. CloudSat provides the radar reflectivity factor Ze as a main observable that detects the micron-sized cloud particles to millimeter-sized rain drops. The AMSR-E microwave radiometer is sensitive to the presence of drizzle particles and produces a liquid water path W that includes the contribution from drizzle-sized particles. This information of the liquid water path, when combined with cloud optical depth τc retrieved by shortwave analysis from MODIS, leads to an estimate of a layer-mean effective particle radius Re as proposed by Masunaga et al. [2002a, 2002b] and Matsui et al. . This columnar effective radius Re is a measure of particle size that includes cloud to drizzle particles, and can then be used for comparison with the radar reflectivity Ze to investigate the dependency of radar observations on particle radius. In combining these data we show in this paper that there exist coherent relationships between the layer-mean radar reflectivity and the columnar effective radius on global scale. We further show that these relationships identify the processes of particle growth by condensation and coagulation.
2. The Data
2.1. Cloudsat Radar Reflectivity
 The first parameter analyzed in this study is the radar reflectivity Ze observed by CloudSat. We employ the CloudSat Geometrical Profiling Product (Geoprof), which is one of the standard data products by the CloudSat project [Mace et al., 2007]. The Geoprof data provides the radar reflectivity profiles observed by CPR onboard CloudSat. The profile is vertically averaged for the warm cloud columns determined by cloud top temperature higher than 273.15 K from MODIS measurement matched to CloudSat CPR footprint.
Figure 1a shows the global distribution of the layer-mean radar reflectivity e of warm cloud averaged over the summer season of June-July-August (JJA) in 2007 for 2.5 degree grid boxes. The geographical pattern of the radar reflectivity tends to be similar to the warm rain climatology [e.g., Schumacher and Houze, 2003]. Small values are found over several coastal regions and continental areas except for northern Amazon and central Africa, where significant rainfall occurs similar to oceanic tropical regions characterized by large values of radar reflectivity.
2.2. Columnar Effective Particle Radius
 The second parameter for analysis is a columnar effective particle radius that is estimated from shortwave-retrieved cloud optical depth τc and microwave-derived liquid water path W according to the method proposed by Masunaga et al. [2002a]. The latter only exists over oceans and thus our analysis is restricted to oceans. We use the data of MODIS cloud optical depth and AMSR-E liquid water path for warm clouds matched to CloudSat CPR footprint. The columnar effective radius Re is defined in terms of τc and W as
where ρw denotes the liquid water density. The difference in the spatial resolution between the shortwave and microwave radiometers should be properly taken into account [Masunaga et al., 2002a]. Since the footprint of the microwave instrument exceeds either the CloudSat radar or the MODIS footprint, then partially cloudy footprints will be smoothed in the AMSR-E and the cloud water content will be undersampled in these circumstances. To avoid these beam-filling problems we analyze only the data with MODIS cloud fractions within the AMSR-E footprint larger than 0.9. The effective radius defined by (1) includes the contribution from drizzle particles since the microwave is sensitive to drizzle-sized particles [Masunaga et al., 2002a].
Figure 1b shows the global distribution of Re seasonally averaged over the same period as e in Figure 1a also for 2.5 degree grid boxes. The columnar effective radii are generally larger than those derived from MODIS corresponding to particles near cloud-top especially over regions of significant rainfall [Masunaga et al., 2002b; Matsui et al., 2004]. The difference in those two effective radii reflects the vertical inhomogeneity of particle size induced by particle growth from cloud to drizzle particles. The columnar effective radius tends to be small over the same regions where the radar reflectivity is small (Figure 1a). The columnar effective radii are also found to be systematically smaller than cloud-top values in these regions, indicating the suppression of vertical particle growth due to large static stability and/or large aerosol abundance [Masunaga et al., 2002b; Matsui et al., 2004]. Large values of Re are found mainly over tropical rainfall regions where e is also large (Figure 1a).
3. Microphysical Regimes
Figures 1a and 1b illustrate the similarity of features between e and Re. This similarity suggests that these two quantities obtained from independent measurements may represent the warm rain formation processes in different ways. The radar reflectivity Ze is a parameter that includes information on both water concentration and particle size, and can then be theoretically related with the effective radius Re through number and mass concentrations in different manners.
 Assuming that the droplet size distribution of liquid cloud is given as modified-Gamma function
the radar reflectivity Ze for Rayleigh region and the effective radius Re are given as
where r0, N and μ denote the characteristic radius, total number concentration and the shape parameter, respectively. These parameters fully specify the distribution function (2). Eliminating r0 from (3) and (4) leads to the relationship between Ze and Re through N (in cm−3) as
We interpret the sixth-power relationship (5) as representing particle growth by condensation process that operates in a manner that conserves the total number concentration N since each cloud particle tends to grow by absorbing water vapor without interactions among cloud particles in the condensation process.
 It also follows from (3) and (4) that Ze varies with a cubic dependency on Re as
for a constant mass concentration q (in gm−3) given by
The cubic relation (6) occurs under the dominance of the coagulation process where particle size (and Ze) grow under the condition that the total mass concentration q is conserved since the cloud particles collide and coalesce with each other without changing the total mass. In this way we associate both the sixth-power and cubic dependencies of the radar reflectivity on particle radius specifically in terms of microphysical growth processes. A typical value of shape parameter μ in modified-Gamma function (2) is about 2 [Duda et al., 1991] (fitted by Miles et al. ), and μ tends to range between 1 and 3 [Meyers et al., 1997].
Figure 2 shows the joint probability distribution of seasonally averaged e and Re during 2007 JJA over the ocean of 60°S−60°N for 2.5 degree grid boxes. The theoretical relationships (5) and (6) with μ assumed to be 2 are also shown for reference for specified values of the number concentration N (solid lines) and the mass concentration q (dashed lines), respectively. Figure 2 illustrates that the observed radar reflectivity e varies with the columnar effective radius Re roughly following the solid lines for e smaller than about −10 dBZ. This suggests that the condensational growth process is dominant in these cases and implies that clouds observed for this part of the diagram are developing without significant drizzle particles. In this region of the diagram, the data cross the dashed lines and the mass concentration q is increasing with increasing the effective radius Re, indicating that the water amount increases with particle growth by the condensation process. The labeled values of solid lines provide a hint at the column averaged number concentrations N ranging from about 10 cm−3 to 100 cm−3 implied from the majority of the observations presented in Figure 2 for e < −10 dBZ. Although the labeled values designating the number concentration N slightly vary with the choice of the shape parameter μ, the change is within the factor of about 1.3 for the range of μ = 1 ∼ 3. The implied range of number concentration agrees with previously observed values summarized by Miles et al.  and recent global statistics by Hu et al. .
Figure 2 also demonstrates that e tends to behave more like the cubic dependence on Re following the dashed lines for e larger than about −10 dBZ. This tendency implies that coagulation is the dominant particle growth process as is typical of more mature stage of cloud development. It is also noteworthy that the observed plot for this range crosses the solid lines indicating a decrease in number concentration N with increasing Re, again supporting the notion that the coagulation process is taking place in this regime with decreasing number populations of particles. The labeled values of dashed lines indicate a range in q between about 0.1 gm−3 to 1 gm−3 for the majority of observation over e > −10 dBZ. The labeled values too can vary within the factor of about 1.7 depending on μ ranging from 1 to 3. This range of mass concentration is also consistent with those in previous observations summarized by Miles et al.  and global analysis recently obtained by Hu et al. . It should also be noted that the value of the mass concentration is consistent with rough estimate independently obtained by AMSR-E-derived liquid water path divided with CloudSat-observed cloud layer depth, which provides q = 0.15 ± 0.087 gm−3 as global mean and standard deviation for 2007 JJA seasonal average.
4. Consistency with Rainfall
Figure 2 reveals a coherent transition in particle growth from condensation to coagulation around e ∼ −10 dBZ and Re ∼ 20 μm. Matrosov et al.  found that the drizzle tended to contaminate interpretation of the radar reflectivity when larger than −15 dBZ. The value of e ∼ −10 dBZ is reasonable compared to this value although somewhat larger given that e is a layer average quantity. The value of Re ∼ 20 μm is also consistent with the study of Jonas  who suggests that this size is a boundary between condensation and coagulation processes.
 The transitional change in e − Re dependency around those values is expected to coincide with the presence and absence of rainfall. Figure 3 shows the e − Re plot separately according to liquid rainfall rate retrieved from attenuation of CloudSat radar signal [Haynes and Stephens, 2007]. The plots for the regions of seasonally averaged rainfall rate smaller and larger than 0.1 mmhour−1 are referred to as a light drizzle (Figure 3a) and rain (Figure 3b), respectively. Observations in light drizzle regions (Figure 3a) roughly follow the sixth-power dependency (solid lines) and, as expected, coincide with the condensation regimes. The majority of the data that correspond to raining regions (Figure 3b), on the other hand, coincides with the coagulation regime following the cubic relationship (dashed lines). These results clearly suggest that the condensation and coagulation regimes appear in consistent manner with rainfall on the global scale.
 This study makes use of radar reflectivity, liquid water path and optical thickness independently observed by CloudSat, AMSR-E and MODIS, respectively, as part of the A-Train satellite constellation. These observations are used to investigate the relationship between the layer-mean radar reflectivity e and the columnar effective particle radius Re derived from microwave-sensed liquid water path and shortwave-retrieved optical thickness. Global statistics for seasonally composited data reveals that the radar reflectivity tends to relate with the effective radius according to the sixth-power under conditions of condensation growth and cubic dependencies under conditions of coagulation and rain formation. There is a distinct difference in the dependency of e on Re occurring at about e ∼ −10 dBZ and Re ∼ 20 μm, which, we interpret, illustrates the transitional change in dominant particle growth process from condensation to coagulation. The condensation and coagulation regimes are also found to correspond to small and large amounts of rainfall, respectively, suggesting that the microphysical regime identified are robust in describing warm rain formation processes.
 This study introduces the method to observe, for the first time, the condensation and coagulation processes. The proposed method will be further used in future studies to investigate how the particle growth processes are influenced by other factors such as dynamical static stability and aerosol abundance. Observational description of microphysical processes shown in this study also provides a new way to validate and evaluate the cloud parameterizations employed in current climate and cloud models.
 We are grateful to John M. Haynes for providing the data set of MODIS and AMSR-E matched to CloudSat CPR footprint, and the rainfall data retrieved from CloudSat. We also acknowledge Hirohiko Masunaga and Toshihisa Matsui for their valuable comments on earlier version of this paper. This study was supported by NASA grant NNX07AR11G.