Cloud optical thickness and the effective radius of cloud droplets were derived by a combined use of the precipitation radar and visible and infrared scanner onboard the Tropical Rainfall Measuring Mission satellite to study the effect of precipitation on the relationship between cloud optical thickness (τ) and the effective radius (re) on a global scale. Whether τ and re correlate positively or negatively is a key to finding evidence of the indirect effects of aerosols, but up to now this has been a subject of considerable debate. No clear correlation has been reported on a global scale because τ is affected by many factors, among which the effect of precipitation is one of the most uncertain. To study the effect of precipitation, we assessed the relationship between τ and re in terms of the critical radius of cloud droplets (rc), below which precipitation hardly forms. In our analysis, there was no clear correlation between τ and re in water clouds which is consistent with many previous studies. However, interesting features of the relationship were revealed that are related to rc. Cloud optical thickness is a maximum for clouds with re around the value of rc. On a global average, cloud optical thickness tends to increase with re (positive correlation) for re < rc and to decrease (negative correlation) for re > rc. A change in the sign of the relationship was clearly observed at re ∼ rc on a global scale. These features were observed typically for non-precipitating clouds and clouds with weak rain. The relationship is strongly affected by precipitation which should be carefully considered when using it to find evidence of the indirect effects of aerosols.
 The cloud feedback problem is considered to be the largest source of uncertainty in climate studies. This is because the behavior of clouds is linked to aerosols and precipitation. Atmospheric aerosols act as cloud condensation nuclei (CCN) and influence cloud properties. An increase in aerosol concentration results in a decreased drop size and modifies the cloud radiative forcing, which is known as the “first indirect effect” of aerosols [Coakley and Walsh, 2002]. Decreased drop size may also suppress precipitation, which is known as the “second indirect effect” of aerosols [Albrecht, 1989; Rosenfeld, 2000]. The signature of these indirect effects is expected to appear in the relationships between τ and re [Han et al., 1994]. Extensive studies, therefore, have been made of this relationship by using numerical models and observations [e.g., Lohmann et al., 2000; Boers and Rotstayn, 2001]. However, no clear correlation has been observed between τ and re [e.g., Harshvardhan et al., 2002; Nakajima and Nakajima, 1995]. This is because the correlation is affected by many factors. In addition to aerosols, various thermodynamic conditions of the environment, and the growth and dissipation of clouds and precipitation can affect this relationship. Both positive and negative correlations have been observed depending on the particular interaction of these factors.
 One of the key factors for improving our understanding of the correlation is precipitation, which controls the amount of clouds. Precipitation not only produces cloud droplets by breakup of rain drops [Kobayashi and Adachi, 2001] but also removes cloud droplets. Drizzle, for instance, reduces τ by 18% on average [Boers et al., 1996]. Increased aerosols may suppress precipitation, leading to enhance cloud lifetime and consequently to a negative feedback for global warming. Moreover, drop spectral broadening generated by drizzle formation can modify cloud optical properties [Hudson and Yum, 1997; Liu and Daum, 2002]. Through these processes, it has been reported that precipitation can reduce or otherwise modify the correlation [Boers and Rotstayn, 2001]. Measurements to examine how precipitation affects the correlation are critical for detecting the indirect effects of aerosol on the relationship between τ and re. Little, however, is known regarding the degree to which precipitation modifies this relationship. It is difficult to distinguish the effect of precipitation on the relationship from other effects such as liquid water path (LWP), which is the primary determinant of τ.
 Recent studies have suggested that there are significant differences in cloud drop size between precipitating and non-precipitating clouds [Kobayashi, 2007]. Cloud droplets cannot grow to raindrops until they exceed rc. This suggests that there should be also some changes in τ at the critical size if precipitation really affects the correlation. The changes in τ that are associated with condensation and coalescence are closely related to drop size, whereas, changes in LWP that result from sub-adiabatic processes like entrainment are not clearly related to re. These different features enable us to detect the expected changes in τ at re = rc from statistical studies using satellite data. The objective of the present study is to reduce the uncertainty in the mechanisms that determine the relationship between τ and re by examining how precipitation affects the relationship.
 In this paper, we examined the cloud-precipitation interaction in warm rain process from the viewpoint of the critical radius by using precipitation radar and visible and infrared scanner onboard the Tropical Rainfall Measuring Mission (TRMM) satellite. In particular, we focused on marine water clouds, which have strong negative feedbacks that could offset warming effects resulting from CO2 doubling by small changes in the cloud amount [Albrecht, 1989; Randall et al., 1984], and we analyzed how cloud optical thickness varies in the conversion process from cloud droplets to rain drops in terms of rc.
 The TRMM is equipped with a precipitation Radar (PR). The PR is a unique space-borne sensor used to measure three-dimensional rain structure with a horizontal resolution of 5 km at nadir and a swath width of 245 km. The vertical resolution is 125 m. TRMM is also equipped with a visible and infrared scanner (VIRS). The VIRS has five channels and measures visible and infrared radiance with a horizontal resolution of 2.4 km at nadir and a swath width of 830 km. Both sensors sample almost simultaneously with similar spatial resolutions. Consequently, the combined use of the PR and VIRS is well suited for studies of cloud-precipitation interactions. The TRMM orbit has an inclination of 35° and the observed area is from −35° to +35° in latitude. We selected VIRS data for which the center position of the PR is within the footprint of the VIRS and made match-up datasets from data for 11 days in December 2002 and 10 days in June 2003. The swath of the VIRS is wider than that of the PR, so VIRS data extending beyond the swath of the PR were excluded. Ultimately, we generated four global-segmented datasets, each with data for 5 or 6 days. One segment box has a 0.5° × 0.5° latitude-longitude spatial resolution. Data exist for at least 100 pixels in each grid box. The pixel for precipitating at the highest rain rate or for the highest reflection at Ch1 (0.63 μm) when no precipitating pixels occur in a box was selected. For this process, we used rain rates near the surface measured with the PR. In the analysis, pixels for which the brightness temperature at Ch4 (10.8 μm) of the VIRS ranged from 273 to 290K and the brightness temperature difference between Ch4 and Ch5 (12 μm) was less than 1 K were furthermore selected to remove erroneous data of optically thin, cold clouds and subpixel clouds [Rosenfeld and Gutman, 1994].
 The reflected radiances at Ch1 (0.63 μm) and Ch3 (3.80 μm) measured with the VIRS were used to derive the cloud optical thickness and effective radius of droplets near the cloud tops [Han et al., 1994; Nakajima and Nakajima, 1995]. The retrieval is based on the difference in water absorbing characteristics between solar reflectance at Ch1 and Ch3. Ch3 includes contributions of thermal emissions from the atmosphere and ground surface. A lognormal size distribution of cloud droplets with a standard deviation of 0.35 was assumed. The undesired thermal emissions from the cloud tops were removed from the measured radiance at Ch3. The cloud top temperature was determined from the Ch4 radiance using LOWTRAN-7 assuming a tropical model for the atmosphere above the cloud top. This assumption leads to some error in the derived re. However, a difference of 4 K between the model and the actual temperature profile causes an error of less than 0.7 μm in the retrieved re [Han et al., 1994]. Use of the mid-latitude summer model for the atmosphere above the cloud top instead of the tropical model results in a difference of 0.8 μm in the mean re. Because we applied the method over a limited range of latitude, this error is not serious. Absorption by various gas components is also corrected at Ch1 and Ch3. We ignored the thermal emission from the ground surface because we examined optically thick clouds [King, 1987].
Figure 1 shows scatter-plots of cloud optical thickness versus effective radius for non-precipitating clouds (Figure 1a) and precipitating clouds (Figure 1b) derived from the datasets for June. There seem to be no clear correlations which is consistent with many previous studies [e.g., Harshvardhan et al., 2002]. The relationship between τ and re depends on various parameters of aerosols, mixing, clouds, and precipitation [Boers and Rotstayn, 2001] and can result in either positive or negative correlations. A positive correlation is expected for thin clouds [Han et al., 1994]. In the condensation process, τ increases with re assuming a constant number of cloud condensation nuclei [Considine and Curry, 1996]. A negative correlation is expected for polluted air conditions such as clouds in ship-tracks. For collision-coalescence processes, cloud droplets grow rapidly to form drizzle when they exceed rc. Drizzle has a role to remove small cloud drops and consequently results in a negative correlation [Nakajima and Nakajima, 1995], which may explain the negative correlation observed for optically thicker clouds [Lohmann et al., 2000]. The data in Figure 1 reflect various thermodynamics conditions of the environment, growing/dissipating stages of clouds and precipitation, CCN concentrations, and so on, and thus exhibit considerable spread. However, there are some interesting features revealed by Figure 1. The largest τ appears at re ∼ 16 μm which almost corresponds to rc. It should be noted that re of 16 μm corresponds to 11.7 μm in the mode radius of a lognormal distribution of cloud droplets. In rain formation processes, cloud droplets grow by condensation for re < rc. When the radii of droplets exceed rc, they grow by collision-coalescence. A previous study shows that there are significant differences of re between non-precipitating clouds (NPCs) and precipitating cloud (PRCs) that are related to rc of cloud droplets [Kobayashi, 2007]. Condensation/evaporation growth of cloud droplets is a continuous process, while growth of cloud drops by coalescence is a discontinuous process in which cloud droplets cannot grow until they exceed the critical size [Houze, 1993]. Consequently, the relationship between τ and re can also be expected to be different for re < rc than for re > rc. Cloud optical thickness increases with drop size in the initial stages of cloud formation and decreases in the initial stages of rain formation. The important feature suggested from Figure 1 is not how τ and re correlate, but that the maximum τ is around at re ∼ rc.
 We may have observed a thin, high-altitude cirrus clouds overlying lower water clouds, which results in lower optical thickness and larger drop size. In retrieving re from space, the effects of cirrus contamination cannot be neglected. To avoid cirrus contamination, we selected clouds with a brightness temperature (Bt) larger than 273K. This criterion may not enough to avoid cirrus contamination. Therefore, we derived re for clouds with Bt larger than 280k and compared it to the re for clouds with Bt larger than 273K [Han et al., 1994]. Essentially similar results were obtained which suggests that cirrus contamination is likely removed. In addition, essentially similar results were obtained from data of each 0.1 × 0.1 grid box in which a few pixels exist.
Figure 2 shows the global mean relationships between τ and re for NPCs (solid line) and PRCs (dotted line). It is clearly shown that cloud optical thickness is maximum for clouds with re around the value of rc. Cloud optical thickness can be approximately as
where, ρ is density of water. Cloud optical thickness decreases with re monotonically if LWP is constant. The tendency to increase in τ for re < rc for both NPCs and PRCs indicates, therefore, increases in LWP and is likely associated with condensation or evaporation processes as mentioned earlier. Deeper clouds associated with strong convection also result in the tendency to increase in τ. In the present study, this effect is not significant. Deep convective clouds with cloud top temperature (Tc) colder than 273K were excluded in our analysis. In addition, clouds of Tc ranging from 280 to 285K showed almost the same features as in Figure 2.
 When the effective radius exceeds rc, τ begins decreasing for NPCs, suggesting a small change or slight increase in LWP, which is likely associated with the growth of cloud droplets to drizzle by collision-coalescence processes. A change in sign of the relationships for NPCs is clear at re ∼ rc on a global scale. For PRCs, on the other hand, τ remains almost constant for re > rc, suggesting considerable increases in LWP with re, which probably result from changes in the thermodynamics conditions. Collision-coalescence process in which cloud droplets grow rapidly is difficult to detect for clouds with strong rain but may be possible to detect clouds with weak rain because such process occurs in the onset of precipitation, that is clouds with weak rain.
Figure 3 shows the same data as Figure 2 but only for PRCs with rain rates smaller than 2 mm/h (solid line) and larger than 2 mm/h (dotted line). For clouds with stronger rain, τ remains almost constant, whereas for clouds with weaker rain, the tendency is similar to that for NPCs shown in Figure 2. For clouds with stronger rain, LWP increases with rain rate, which probably is associated with changes in thermodynamics conditions as mentioned above. For clouds with weaker rain, smaller change in LWP with re is expected for re > rc which is likely due to rapid growth of cloud droplets to by collision.
Figure 4 shows that variations of LWP with re for NPCs and PRCs with weak and strong rain. LWP increases overall with re. For strong rain, LWP increases linearly with re, which corresponds to almost constant τ for re > rc shown in Figure 3. The reduction of τ resulting from an increase in re is compensated by an increase in LWP for heavier rain. For clouds with weaker rain, the tendency to increase in LWP with re is similar to that for NPCs. For re < rc, LWP increases with re significantly, but increases slowly for re > rc. The tendency to increase slightly in LWP for re > rc corresponds to the tendency to decreases in τ with re shown in Figure 3 and supports the interpretation that the decreases in τ is likely due to rapid growth of cloud droplets as mentioned above.
 Space-borne radar and visible and infrared scanner were used to determine the degree to which precipitation might alter the relationship between τ and re. This relationship has been used to find evidence of the indirect effects of aerosols, but there is not yet consensus on whether they are positively or negatively correlated. No clear correlation has been reported on a global scale because τ is affected by many factors, among which the effect of precipitation is one of the most uncertain. To study the effect of precipitation, we assessed the relationship between τ and re in terms of the critical size of cloud droplets.
 We found that the relationship between τ and re changes sign at re = rc. On a global average, τ tends to increase with increasing re and is largest at rc. This tendency to increase is due to condensational growth. When droplets exceed the critical radius, τ tends to decrease with increasing re. This is due to collision-coalescence growth. These features were observed for NPCs and clouds with weak rain. For clouds with strong rain, different tendency was observed which is associated with significant changes in thermodynamics conditions, such as entrainment. Variations of LWP with re support above interpretation. This study reveals that precipitation has a considerable effect on the τ − re relationship and sheds new light on the correlation of τ and re.
 This study is partly supported by the Japan Aerospace Exploration Agency and by Grant-in Aids for Scientific Research 18540437, Japan Society for the Promotion of Science. The TRMM data were provided by the Japan Aerospace Exploration Agency.