A method for estimating effective ice particle radius Re at the tops of tropical deep convective clouds (DCC) is developed on the basis of precomputed look-up tables (LUTs) of brightness temperature differences (BTDs) between the 3.7 and 11.0 μm bands. A combination of discrete ordinates radiative transfer and correlated k distribution programs, which account for the multiple scattering and monochromatic molecular absorption in the atmosphere, is utilized to compute the LUTs as functions of solar zenith angle, satellite zenith angle, relative azimuth angle, Re, cloud top temperature (CTT), and cloud visible optical thickness τ. The LUT-estimated DCC Re agrees well with the cloud retrievals of the Moderate Resolution Imaging Spectroradiometer (MODIS) for the NASA Clouds and Earth's Radiant Energy System with a correlation coefficient of 0.988 and differences of less than 10%. The LUTs are applied to 1 year of measurements taken from MODIS aboard Aqua in 2007 to estimate DCC Re and are compared to a similar quantity from CloudSat over the region bounded by 140°E, 180°E, 0°N, and 20°N in the Western Pacific Warm Pool. The estimated DCC Re values are mainly concentrated in the range of 25–45 μm and decrease with CTT. Matching the LUT-estimated Re with ice cloud Re retrieved by CloudSat, it is found that the ice cloud τ values from DCC top to the vertical location where LUT-estimated Re is located at the CloudSat-retrieved Re profile are mostly less than 2.5 with a mean value of about 1.3. Changes in the DCC τ can result in differences of less than 10% for Re estimated from LUTs. The LUTs of 0.65 μm bidirectional reflectance distribution function (BRDF) are built as functions of viewing geometry and column amount of ozone above upper troposphere. The 0.65 μm BRDF can eliminate some noncore portions of the DCCs detected using only 11 μm brightness temperature thresholds, which result in a mean difference of only 0.6 μm for DCC Re estimated from BTD LUTs.
- A new method for estimating effective radius of tropical deep convection
- Radius is mainly 25–45 micrometers and decreases with cloud top temperature
- Mean value of cloud top optical depth corresponding to estimated radius is about 1.3
 Knowledge of ice particle effective radius Re of tropical deep convective clouds (DCCs) is important for understanding the important roles of DCCs in the physical and chemical processes occurring in the tropical tropopause layer (TTL) and the stratosphere [Fueglistaler et al., 2009, and references therein]. For example, Re plays an important role in cloud radiative forcing, particularly shortwave radiative forcing of ice clouds including DCCs and thereby has been used as a key factor for the parameterization of ice cloud radiative properties implemented in climate models [Hong et al., 2009, and references therein]. Smaller ice particles are more likely to remain suspended in the air entering the stratosphere and therefore deposit moisture there [Sherwood, 2002; Iwasaki et al., 2010]. Jensen et al.  found that the potential for irreversible dehydration near the tropical tropopause caused by DCCs depends on DCC Re. Sherwood et al.  reported that climatological maxima in lightning activity are associated with small ice particles near DCC tops and suggested this relationship strengthens the importance of aerosols as well as dynamics in electrification. Effective ice particle size is also critical for better understanding of cirrus clouds since the ice microphysics of DCCs has a strong influence on the characteristics and development of cirrus clouds [Yuan and Li, 2010, and references therein].
 Fan et al.  suggested that more accurate retrievals or measurements of DCC Re can provide better understanding of the heterogeneous and homogeneous freezing parameterizations applied in the numerical cloud models, which are important for characterizing effect of aerosols on DCC Re [e.g., Fan et al., 2007; Jiang et al., 2011]. However, reliable characterization of DCC Re from observations remains a major challenge [Iwasaki et al., 2010; Chiriaco et al., 2007] owing to the sensitivities of sensors to different viewing geometry and spatial and diurnal coverage in retrieving Re [Comstock et al., 2007; Waliser et al., 2009]. It was emphasized by Minnis et al.  that cloud retrieval algorithms utilizing channels common to most meteorological satellite imagers have the advantage of producing long records of consistent cloud properties including Re, which is important for understanding climate variations and predictions [Waliser et al., 2009].
 The shortwave infrared (SIR) band centered at 3.7 μm is primarily sensitive to cloud Re and has been extensively used to retrieve Re and other cloud properties with combinations of additional solar bands and/or infrared bands [Minnis et al., 2011, and references therein]. Owing to the large visible optical depths τ of DCCs, the daytime reflected SIR solar radiance is essentially independent of the DCC τ [e.g., Minnis et al., 1998]. On the basis of this feature, 3.7 μm reflectance has been used to estimate optically thick ice cloud Re by numerous researchers [e.g., Sherwood, 2002; Rosenfeld and Lensky, 1998; Lensky and Rosenfeld, 2006; Lindsey and Grasso, 2008]. Brightness temperature differences BTD between the 3.7 and the infrared (IR) 11.0 μm channels are sensitive to cloud τ and Re during daytime [Stone et al., 1990]. When τ becomes large, the IR radiance effectively becomes a constant value, so the BTD over DCCs are essentially sensitive only to Re. Dong et al.  suggested that the BTDs over optically thick ice clouds are less influenced by atmospheric absorption than the 3.7 μm band alone.
 The objective of this study is to develop offline look-up tables (LUTs) on the basis of simulated BTDs from a rigorous radiative transfer model for estimating tropical DCC Re, which remains a challenge. The motivation for developing the new LUT method is to quantify tropical radiative forcing over DCC more effectively than using currently available methodology and to specify more homogenous DCC calibration targets [Minnis et al., 2008a; Doelling et al., 2010]. Different from previous studies on estimating ice cloud Re using passive satellite imagers using the 3.7 μm band, solar reflectance and thermal emission at the 3.7 μm band are not separated and combined together to build the BTD LUTs in section 2. In section 3, the LUT-estimated DCC Re is first compared with the results of ice cloud Re retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) for the NASA Clouds and Earth's Radiant Energy System (CERES) Project (CERES-MODIS) [Minnis et al., 2011]. The LUTs are then applied to 1 year of measurements in 2007 taken from the MODIS aboard Aqua to estimate DCC Re. The results are compared to the values of a similar quantity from CloudSat over the region bounded by 140°E, 180°E, 0°N, and 20°N in the Western Pacific Warm Pool. Conclusions are given in section 4. The advantage of this approach is that it is simple and requires minimal auxiliary information to implement (i.e., only measurements of brightness temperatures at 3.7 and 11.0 μm bands), making it straightforward for estimating DCC Re.
2. Look-Up Table and Methodology
 The discrete ordinates radiative transfer model (DISORT) [Stamnes et al., 1988] is conjoined with correlated k distribution routines developed by Kratz  for the MODIS bands to compute radiances at 3.7 and 11.0 μm during daytime. Visible (VIS; 0.65 μm) channel bidirectional reflectance distribution functions (BRDFs) are built to assist detection of DCCs on the basis of 11 μm brightness temperatures (BT11) for an additional option.
 For optically thick clouds, surface reflectance and emission have little impact on BTD [Dong et al., 2008]. Particularly, because of the large τ of tropical DCCs, the surface albedo and emissivity variations can be neglected. Surface albedos of 0.05 and 0.02 are set for computing solar radiances at 0.65 and 3.7 μm, respectively. A surface emissivity of 0.98 is used for computing the SIR and IR radiances. Tropical DCCs have high vertical extensions approaching or penetrating the TTL. Thus, the atmospheric effects on the radiances are essentially from atmospheric water vapor above the upper troposphere. The precipitable water above 11 km altitude is less than 0.3% from the total atmospheric precipitable water [Badescu, 1988]. Furthermore, both 3.7 and 11.0 μm are located in atmospheric windows. So, the standard tropical atmospheric profile is used for computing atmospheric absorption at 3.7 and 11.0 μm. Only changes in column ozone above the upper troposphere are considered for the VIS BRDFs. The 11 ice cloud models from Minnis et al.  are used for all computations. The Re used in this study, which is defined as the ratio of total volume of cloud particles to the total projected area and multiplied by 0.75, can be derived from formula given by Minnis et al. . Six-dimensional BTD LUTs are built at 18 solar zenith and 18 satellite zenith angles, μ0 and μ, respectively, and covering the range, 0°–85°; 37 relative azimuth angles Δϕ between 0°–180°; 11 Re values from about 3 to 80 μm; 6 cloud top temperatures (CTT) from 190 to 215 K (cloud base height is set at 9 km and about −30°C); and 4 τ values from 25 to 100. Six-dimensional VIS BRDF LUTs are built for these same μ0, μ, Δϕ, Re, and τ and 7 stratospheric column ozone values of 100–400 DU. Owing to large values of DCC τ, the effect of variations in DCC cloud base heights on radiances over DCCs is neglectable [Hong et al., 2007; Garrett et al., 2009], particularly for BTDs and VIS BRDFs. The cloud base height is set at 9 km with a temperature of about −30°C for computing the LUTs.
 BT11 thresholds have been extensively used to identify DCCs. The DCCs identified by BT11 thresholds alone can be contaminated by optically thick ice clouds outside the core area of the cloud [e.g., Tian et al., 2004; Hong et al., 2005; Liu et al., 2007]. Some high, thick ice clouds that are identified as DCCs by BT11 can be eliminated by setting a VIS reflectance threshold [Fu et al., 1990]. The VIS BRDF LUTs were developed to use together with BT11 thresholds to eliminate such contamination of high, thick ice clouds. In the present study, two methods are used to identify tropical DCCs, one uses BT11 thresholds alone and the other combines BT11 thresholds with VIS BRDF LUTs.
 An example of the computed BTD LUTs is shown in Figure 1 as a function of Re for DCCs having τ between 25 and 100 and CTT of 215 and 200 K at the specified viewing geometry (μ0 = 30°, μ = 45°, and Δϕ = 60°). For a given DCC with a specified CTT, BTD is essentially only sensitive to Re. This feature is particularly true for small Re owing to stronger SIR solar reflectance for smaller particles [e.g., Minnis et al., 1998, 2011; Han et al., 1994; Platnick and Twomey, 1994; Lindsey and Grasso, 2008]. Optical depth has negligible influence on the BTD, particularly for larger τ. Figure 1 also shows that an accurate CTT is important for using the LUTs to estimate Re. As a blackbody, the DCC CTT can be directly estimated using the satellite-observed BT11 [Smith and Platt, 1978] or an adjusted value, since BT11 was found to be slightly warmer than CTT [Minnis et al., 2008b]. The 6 CTTs are then converted to 6 BT11 values at nadir over DCCs on the basis of CTT and the simulated BT11 at nadir. Before using the LUTs, the initial observed BT11 at off nadir is adjusted to nadir using a correction factor that is built as functions of μ and BT11 at the μ using the simulated BT11. The adjustments of BT11 from off nadir to nadir have root-mean-square errors (RMSEs) below 0.3 K for all DCCs.
 Figure 2a shows the VIS BRDF as a function of Re at the specified viewing geometry for DCCs having τ between 25 and 100 and column ozone of 250 DU in the stratosphere. As expected, the VIS BRDF is primarily sensitive to τ and only slightly affected by Re. Essentially the VIS BRDF is small when τ is small and Re is large. So, the LUTs having τ = 25 with the specified viewing geometry and column ozone are re-constructed using the minimum BRDF among the computed BRDFs at all Re. In this way, the LUTs are downsized from six dimensions to four dimensions of μ0, μ, Δϕ, and column ozone. Figure 2b shows the remarkable angular dependence of the VIS BRDF from the four-dimensional LUTs. The patterns are shown at μ0 = 30° and μ0 = 60° with μ varying from 0° to 85° along the radius and Δϕ between 0° and 180° along the counterclockwise direction. The effect of changing the column ozone above the tropopause on the VIS BRDF is investigated by showing the BRDF differences resulting from increasing the above-cloud ozone loading from 200 DU to 300 DU. The ozone effects (Figure 2c) are distinct at large μ0 and μ and can be over 0.1 with a change of 100 DU.
 The process for retrieving the DCC Re is straightforward. First, BT11 measurements at μ are corrected to nadir using the regressions developed above. Then, a pixel is identified as a DCC if the corrected BT11 at nadir is less than the specified BT11 threshold (range of 190–215 K in the present study) for detecting DCCs. When measurements of the VIS reflectance are employed to constrain DCC detection, an additional criterion is that the reflectance measurement should exceed those from the four-dimensional VIS BRDFs in the LUTs. After DCCs are identified, Re can be estimated using the six-dimensional LUTs of BTD on the basis of known μ0, μ, Δϕ, above-cloud column ozone, BT11 at nadir, and a specified τ at 25, 50, 75, or 100.
3. Application and Discussions
3.1. Comparison With CERES-MODIS-Retrieved Re
 To simplify complex, highly variable mixtures of habits and distributions of ice crystal sizes, most passive satellite retrieval algorithms assume a vertically homogeneous ice cloud with a prescribed set of habits and size distributions to perform retrievals of ice cloud microphysical properties. Typically, each algorithm makes different assumptions about the particle habits used in the retrievals. Also, different retrieval algorithms can use different passive satellite imagers, so that the retrieved results may be dependent on the retrieval algorithms and sensors used [Chiriaco et al., 2007; Comstock et al., 2007; Lindsey and Grasso, 2008; Waliser et al., 2009]. On the basis of these facts and the danger of measuring DCC properties in situ, it is difficult to validate retrieved ice cloud microphysical properties. To avoid the differences caused by different ice cloud models used for retrieving the DCC Re, the LUT-estimated DCC Re is compared with the results from CERES-MODIS analyses [Minnis et al., 2011] that utilize consistent ice cloud models.
 Figure 3 shows the comparison results for an Aqua MODIS granule over the Western Pacific Warm Pool at 02:35 UTC on 1 February 2007. Only BT11 threshold of 215 K is used for DCC detection and the DCC fraction is about 12% in this granule. It is clear that the geographical distribution of LUT-estimated DCC Re is in good agreement with that for the CERES-MODIS-retrieved Re (Figures 3b and 3c). The 1-D and 2-D histogram distributions of the comparison of Re are shown in Figure 4. Statistically, the LUT-estimated DCC Re (33.05 ± 5.57 μm, mean value and standard deviation) values are essentially the same as those from CERES-MODIS (32.93 ± 6.21 μm). The estimated Re is highly correlated with a correlation coefficient of 0.988. The RMSE is about 1.13 μm. In 67.8% and 99.8% of the DCCs, the differences in Re are less than the RMSE and three times the RMSE (3.39 μm), respectively. From these results, it is concluded that the differences between LUT-estimated DCC Re and CERES-MODIS Re are less than 10%.
3.2. Comparison With CloudSat-Retrieved Re
 Ice cloud Re values are estimated on the basis of 3.7 μm band is near the cloud top [e.g., Sherwood, 2002] since the radiation at 3.7 μm at the top of atmosphere comes mostly from cloud top [Rosenfeld et al., 2004]. The vertical distribution of DCC Re can be estimated by radar measurements, thus, providing an opportunity to investigate the depth from cloud top to the location where the 3.7 μm estimated DCC Re is located.
 The constructed LUTs are applied to BTDs taken from the MODIS/Aqua Calibrated Radiances 1 km 5 Min 1B Narrow Swath Subset along CloudSat (MAC021S0) to estimate the DCC Re. The VIS reflectances used for assisting DCC detection (optionally) are also taken from MAC021S0. The MAC021S0 cross-track width of 10 km consists of 11 MODIS pixels, which results in a horizontal resolution of ∼1 km (http://mirador.gsfc.nasa.gov/collections/MAC021S0__002.shtml). The LUT-estimated Re is then compared to the radar-only ice Re from the CloudSat product, 2B-CWC-RO (version 008), that consists of one hundred twenty-five 240 m thick vertical bins with a horizontal resolution of about 1.3 km × 1.7 km [Austin et al., 2009]. The 2B-CWC-RO ice cloud products are generated from CloudSat reflectivity measurements using the retrieval algorithms described by Austin et al. . The MODIS/Aqua Geolocation Fields 1 km 5 min 1A Narrow Swath Subset along CloudSat V2 (MAC03S0, http://mirador.gsfc.nasa.gov/collections/MAC03S0__002.shtml) is used to collocate the MAC021S0 with 2B-CWC-RO using the nearest-neighbor method within a maximum distance of 0.5 km. This study uses all of the 2007 collocated data over the region bounded by 140°E, 180°E, 0°N, and 20°N in the Western Pacific Warm Pool. In 2007, the collocation of near 2600 MODIS granules and 1200 CloudSat cross tracks over this region. Half were taken during daytime and generate over one million matched MODIS and CloudSat measurements. Using a BT11 threshold of 215 K, the detected DCC fraction over the region is about 2.7% which is close to the result from Fu et al. . With additional VIS BRDF LUTs, the DCC fraction decreases to about 1.8% by removing some contaminated high, thick ice clouds associated with DCCs.
 Figure 5 shows an example of comparing LUT-estimated DCC Re from the MODIS data with Re derived from CloudSat. DCC systems are shown along the CloudSat track at about 02:36–02:39 UTC (167.35°E, 2.78°S to 165.40°E, 6.36°N) on 1 February 2007 by CloudSat 1B-CPR reflectivities (version 008). The 1B-CPR has the same vertical and horizontal resolutions as 2B-CWC-RO and a minimum detectable reflectivity of approximately −26 dBZ [Stephens et al., 2002]. Cloud tops from 2B-GEOPROF-LIDAR [Mace et al., 2007] are also shown in Figure 5a since the CALISPO lidar [Winker et al., 2007] is more sensitive to small ice particles and thin cloud layers with respect to the CloudSat radar [McGill et al., 2004]. Figure 5a shows that some of the DCC cloud tops penetrate into the TTL.
 The DCCs, identified using a BT11 threshold of 215 K, are shown as the light blue and black dots in Figure 5b. The black dots correspond to only those DCCs identified using both the BT11 threshold and the thresholds from the VIS BRDF LUTs. Using the VIS BRDF thresholds eliminates some DCCs identified by the BT11 threshold beyond the convective cores. This feature is clearly shown around 02:36:40 and 02:38:20 UTC in Figure 5b. The above-cloud column ozone amount used for the VIS BRDF LUTs was taken from ozone profiles in ECMWF-AUX product (version 008). The BTD LUTs for τ = 25 are then applied to the identified DCCs to obtain a value of Re. Vertical profiles of 2B-CWC-RO ice cloud Re are shown along the CloudSat track. The LUT-estimated Re values are compared with 2B-CWC-RO Re profiles to locate the altitude where the two values are the same. This altitude, shown by the red dots in Figure 5b, indicates that that LUT-estimated Re is quite consistent with the 2B-CWC-RO Re near the DCC radar tops, but well below the CALIPSO tops.
 Figure 6a shows probability density functions (PDFs) of the LUT-estimated Re using τ = 25 for DCCs identified using the BT11 thresholds of 215 and 200 K alone or combined with the VIS thresholds over the chosen region for all of 2007. The LUT-estimated DCC Re's are mainly concentrated in the range of 25–45 μm. The DCCs identified with the lower BT11 threshold have smaller Re values than those identified with the higher BT11 threshold. This feature is in good agreement with earlier findings that demonstrate a decrease in ice cloud particle sizes with diminishing cloud temperatures [Yuan and Li, 2010, and references therein]. Although inclusion of the VIS BRDF thresholds can eliminate some noncore areas of DCCs detected using BT11 thresholds alone, these additional constraints have negligible impact on the Re values retrieved using the BTD LUTs. This conclusion is clearly supported by the similarity of PDFs for DCCs with and without the VIS thresholds.
3.3. Effect of Variations in DCC τ on LUT-Estimated Re
 In order to investigate effects of variations in DCC τ on LUT-estimated Re, the BTD LUTs for τ = 25, 50, 75, and 100 are used to estimate the DCC Re separately. Figure 7 shows the mean values of Re for DCCs using BT11 thresholds of 190–215 K with and without using the VIS BRDF thresholds. It is clearly seen again that DCC Re values decrease with cloud temperature. The differences in DCC Re estimated with different τ LUTs are less than 3.3 μm (about <10%) for all BT11 thresholds and LUTs. The distinct differences are between LUTs with τ = 25 and τ = 50. This feature agrees with the impact of τ on the LUTs seen in Figure 1. The physics of this feature is that most of the contributions to the BTD are from the reflected SIR solar radiance, which reaches its saturated value when τ is above 32 [e.g., Minnis et al., 1998].
 Including the VIS BRDF thresholds for DCC detection essentially has no influence on Re. Differences less than 0.6 μm in Re are found between those without BRDF constraints and with BRDF constraints for DCC detection. Moreover, the differences decrease with BT11 thresholds and tend to be zero. This characteristic is as expected since DCCs detected using lower BT11 thresholds are more likely to be associated with convective cores than those using greater BT11 thresholds. Considering the negligible effects of including the VIS BRDF on the LUT-estimated DCC Re, it is concluded that Re can be efficiently estimated by BTD with a BT11 threshold, a method that provides the advantage of using only two bands.
 DCC Re plays important role in better understanding physical and chemical processes in the TTL and stratosphere. Accurate knowledge of DCC Re is a key factor of both ice cloud radiative and physical parameterizations implemented in numerical weather/climate models [Waliser et al., 2009, and references therein]. However, it is still a major challenge for observing reliable characterization of DCC Re [Iwasaki et al., 2010; Chiriaco et al., 2007].
 On the basis of rigorous radiative transfer modeling, six-dimensional BTD LUTs for estimating DCC Re are established as functions of μ0, μ, Δϕ, Re, CTT, and τ. Four-dimensional LUTs of VIS BRDF are also built as function of μ0, μ, Δϕ, and column amount of ozone above upper troposphere to use optionally together with BT11 thresholds for removing contamination by non-DCC, optically thick ice clouds that cannot be distinguished from DCCs identified by BT11 thresholds alone. After identifying DCCs on the basis of BT11 or with the additional, optional criterion of VIS BRDF, DCC Re are estimated straightforwardly and efficiently using offline BTD LUTs by interpolating on the basis of the observed viewing geometry, BT11, and τ that can be supposed to be a value between 25 and 100.
 Using the same ice cloud models as the CERES-MODIS cloud retrievals [Minnis et al., 2011], the LUT-estimated DCC Re for an Aqua MODIS granule over the Western Pacific Warm Pool at 02:35 UTC on 1 February 2007 was compared to results from CERES-MODIS. The estimated DCC Re values agree well with a correlation coefficient of 0.988 and an RMSE of about 1.13 μm. The differences between LUT-estimated DCC Re and CERES-MODIS Re are less than 10%.
 MAC021S0 data for all of 2007 over the chosen region (140°E–180°E, 0°N–20°N) in Western Pacific Warm Pool were analyzed with the BTD LUTs to estimate DCC Re. The LUT-estimated DCC Re values are mainly concentrated in the range of 25–45 μm and they decrease with CTTs. The LUT-estimated Re were then compared to the radar-only ice Re from collocated 2B-CWC-RO. The LUT-estimated Re are in agreement good with 2B-CWC-RO Re near DCC tops. It is found that ice cloud τ values from the DCC top to the vertical location of 2B-CWC-RO Re corresponding to the LUT-estimated Re values are mostly less than 2.5 with a mean value of about 1.3 after accounting for the highest layer of thin cirrus (mean of τ is about 0.1) missed by CloudSat [Haladay and Stephens, 2009]. Applying the BTD LUTs requires a DCC τ in the range of 25–100. The different choices of DCC τ can result in differences of less than 3.3 μm (<10%) for the LUT-estimated DCC Re from LUTs for DCCs identified by BT11 thresholds alone or with additional VIS BRDF thresholds. Although the use of additional VIS LUTs eliminates some thick non-DCC ice clouds detected by BT11 thresholds used alone, the estimated DCC Re distributions are essentially the same with or without the extra constraints. Therefore, the BTD LUTs constructed here can be used by themselves with BT11 to estimate DCC Re.
 Owing to our limited knowledge of the natural variability of ice cloud microphysical properties including ice particle size distributions, habits and their typical mixing percentages, the practical approach is to use some typical and homogenous values for computing radiative properties of general ice clouds. Different ice cloud models have been used extensively [Baran, 2009] and they can induce uncertainties in the retrieved ice cloud microphysical properties [e.g., Chiriaco et al., 2007; Yang et al., 2007, 2008a, 2008b]. Because vertical photon transport in ice clouds is affected by both vertical distributions of cloud optical thickness and particle size [Platnick, 2000; Kokhanovsky, 2004], solar reflectance and thermal emission can be affected by the vertical inhomogeneity of Re [Wang et al., 2009; Zhang et al., 2010]. Using the homogeneous assumption for ice cloud microphysical properties, commonly used for ice cloud retrieval algorithms, the vertical inhomogeneity of ice cloud Re can cause potential errors in the present LUT-estimated Re, but no more than any of the other techniques employing the 3.7 μm channel for retrieving Re. Investigating the impact is a challenge owing to variable vertical inhomogeneity in ice cloud Re values. At this point, our statistical investigation of the ice cloud τ at DCC top above the vertical location of the CloudSat-retrieved Re corresponding to the LUT-estimated Re provides a step in assessment of this issue.
 We thank the NASA CloudSat project for providing the 2B-CWC-RO, 1B-CPR, ECMWF-AUX, and 2B-GEOPROF-LIDAR data used in this study, which are taken from the CloudSat Data Processing Center at Colorado State University. The MODIS data are archived at NASA's Goddard Earth Sciences Data and Information Services Center. This research was supported by NASA through the CERES, CALIPSO, and CloudSat programs.
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