The A-Train satellite constellation has dramatically increased the temporal and spatial coverage of atmospheric ice water content estimates. The new data are derived by retrieval algorithms designed to estimate atmospheric cloud ice water content from remotely sensed measurements. Such retrieval algorithms rely on simplifying assumptions regarding the characteristics of ice particles in the atmosphere. In this study, the sensitivities of CloudSat ice water content retrievals to frozen particle characteristics are tested by generating CloudSat-like retrievals from profiles of known ice water content. CloudSat actively measures vertical profiles of radar reflectivity in clouds with a 94-GHz cloud-profiling radar. Ice water content is retrieved in each cloudy profile at temperatures below 0°C. To assess the CloudSat radar-only ice water content retrieval algorithm (version 5.0 in Release 3 [R03] and version 5.1 in Release 4 [R04] of 2B-CWC-RO), we apply a 94-GHz reflectivity simulator to profiles of ice water content generated by a cloud-resolving numerical model and comprising various frozen particle species (ice, snow, and graupel). The CloudSat ice water content retrieval algorithm is applied to the profiles of simulated reflectivity, and the results are compared to the modeled profiles of known frozen water mass. The results from each version of the algorithm are shown to be sensitive to the characteristics of the frozen particle size distributions and particle densities. Tests of version 5.0 indicate that height varying information could improve retrievals. Despite the addition of a height varying component implemented in version 5.1, similar positive biases are indicated in the tests of each algorithm.
 The influences of upper-tropospheric ice clouds play an important role in affecting the global radiation budget and climate system [e.g., Starr and Cox, 1985; Liou, 1986; Ramanathan et al., 1989; Wielicki et al., 1995; Stephens, 2005]. Until the present decade, estimates of atmospheric ice water content (IWC) have been severely limited in both temporal and spatial coverage. As a result, atmospheric models vary widely in globally averaged representations of IWC in comparison to other quantities (e.g., precipitation, precipitable water) that have been more comprehensively observed on a global scale (e.g., D. E. Waliser et al., Cloud Ice: A climate model challenge with signs and expectations of progress, submitted to Journal of Geophysical Research, 2008).
 Derived estimates of atmospheric IWC have dramatically increased in recent years owing to passive and active retrieval techniques by the A-Train satellite constellation [Stephens et al., 2002] and are now provided by CloudSat [Stephens et al., 2002] and the Aura Microwave Limb Sounder (MLS) [Waters et al., 2006]. These new estimates permit in-depth study of global atmospheric ice mass and provide a long-needed foundation for model evaluation [e.g., Li et al., 2005, 2007; D. L. Wu et al., Aura MLS cloud ice measurements and comparisons with CloudSat and other correlative data, submitted to Journal of Geophysical Research, 2008].
 Important sampling and sensitivity issues must be considered when comparing IWC derived from the A-Train measurements to output of frozen water mass from global atmospheric models. These include model output sampling to match the A-Train satellite orbital tracks in time and space, and accounting for instrument/algorithm sensitivities [see Li et al., 2007]. Additionally, consideration must be given to which components of the frozen water mass are retrieved by an instrument and associated retrieval algorithm. This is important since many global models represent atmospheric frozen water mass differently (Waliser et al., submitted manuscript, 2008). Some models have a single suspended hydrometeor field (e.g., ECMWF [Tiedtke, 1993; Jakob, 2000]), while others (e.g., multiscale modeling framework (MMF) [Tao et al., 2006]) allow for the simultaneous presence of multiple frozen hydrometeor fields (e.g., cloud ice, snow and graupel particles).
 Although retrievals of global IWC have increased substantially in the last few years, significant difficulties remain in terms of ensuring the robustness of the observations, owing primarily to the complex nature of frozen particles in the atmosphere (e.g., particle densities, shapes, size distributions) and the difficulties of addressing mixed-phase clouds. These complicating factors make ice water estimates from space and associated retrieval algorithm development particularly difficult (see Comstock et al.  for a detailed discussion). This paper investigates the accuracy and sensitivity of the CloudSat radar-only IWC retrieval algorithm (versions 5.0 and 5.1 used to generate Release 03 and 04 respectively, and described by R. T. Austin et al. (Retrievals of ice cloud microphysical parameters using the CloudSat millimeter-wave radar and temperature, submitted to Journal of Geophysical Research, 2008)) by testing its performance with a large sample of vertical profiles generated by a cloud-resolving numerical model (CRM) that allows multiple frozen hydrometeors to coexist in the atmosphere. The retrieval algorithms are applied to simulated reflectivities created by assuming differing characteristic properties of the cloud ice, snow and graupel profiles generated by the CRM. The frozen particle properties varied in these tests include the cloud ice particle size distribution and density, as well as the snow particle mass versus dimension relationship for specific snow particle types. Since scenes viewed by CloudSat may consist of a single type of frozen particle or a mixture of differing types of frozen hydrometeors, these tests provide insights into how best to utilize retrieved IWC from CloudSat, as well as how the retrievals may be influenced by varying ice particle properties. In this paper, IWC is defined as any frozen water mass, independent of the particle type or size.
 In section 2, the methodology taken to test the CloudSat ice water retrieval algorithm is described and the importance of variable frozen water mass characteristics (e.g., densities, size distributions) in the atmosphere is discussed. In section 3, simulated CloudSat-like retrievals of IWC are assessed for a set of experiments with varying cloud ice and snow particle characteristics. Section 4 summarizes relevant conclusions and plans for future research.
 CloudSat uses a millimeter-wave (94 GHz) nadir-viewing cloud profiling radar (CPR) to penetrate and actively measure vertical profiles of radar reflectivity in clouds [Stephens et al., 2002]. CloudSat data allows for study of global cloud cover [e.g., Mace et al., 2007], cloud depth and echo intensity [e.g., Marchand et al., 2008]. These data can be used with auxiliary CloudSat products (e.g., MODIS radiance measurements, ECMWF temperatures), to classify cloud type [Sassen and Wang, 2008], retrieve estimates of visible optical depth, retrieve estimates of ice and liquid water contents [Austin and Stephens, 2001; Austin et al., submitted manuscript, 2008], and estimate precipitation [Haynes and Stephens, 2007; Matrosov, 2007].
Figure 1 shows the framework used to assess CloudSat radar-only IWC retrievals in this study. As a starting point, vertical profiles of ice and liquid water content are generated by a CRM. Specifically, version 3.7.4 of the Penn State University/National Center for Atmospheric Research (PSU/NCAR) MM5 model [Grell et al., 1994] was used to generate model profiles over the western Pacific for January 2005 (Figure 2). The domain setup consisted of an outer domain at 36 km resolution and two nested interior domains at 12, and 4 km resolution. Output was generated at 6-hourly intervals. The outer domain was initialized at 0600 UTC 1 January 2005, using the NCAR/NCEP Reanalysis data set updated every 12 h. The outer 36 km domain was used to supply the initial and boundary conditions for the interior domains. The simulation used the following parameterization options on each domain: Betts-Miller cumulus scheme [Betts and Miller, 1993], Eta planetary boundary layer [Janjic, 1994], the cloud radiation scheme [Dudhia, 1989], and the Reisner-Thompson microphysical scheme [Reisner et al., 1998; Thompson et al., 2004]. The Reisner-Thompson scheme is a 5-class bulk microphysics with prognostic variables for cloud ice number concentration and mass mixing ratios of cloud ice, snow, graupel, cloud liquid water and rain. Frozen hydrometeors in the microphysical scheme exchange mass through growth/destruction and other microphysical processes. Cloud ice mass is autoconverted to snow when the diameter of the ice particles exceeds 150 microns. Graupel mass is formed/increased when the riming rate of frozen particles exceeds, by a predetermined factor, the growth of frozen particles through deposition. Hereafter, the modeled values of IWC (being the sum of cloud ice, snow and graupel) are referred to as IWCtrue.
 The primary purpose of the CRM simulation was to generate vertical profiles of hydrometeor fields, not to forecast a specific atmospheric event. Thus, the precise location of clouds and precipitation within the model domains were not as important as the generation of a representative sample of each. Since the innermost (4 km) domain has 331 × 248 grid points, instantaneous model output during the simulation provides 82,088 vertical profiles of the five hydrometeor fields (three ice species and two liquid species) when present, as well as atmospheric state variables (e.g., temperature, winds, relative humidity). The results presented in subsequent sections are based on model profiles generated at hour 36 of the simulation (valid at 1800 UTC 02 January 2005). Assessment of other model validation times showed hour 36 to be a representative sample. To illustrate the utility of the process employed in this study to ultimately simulate CloudSat-like radar-only IWC retrievals, Figures 3 and 4 focus on one specific precipitation feature present within the 4 km domain. The precipitating cell had both large values of rain mixing ratio near the surface and ice mass in the upper levels (Figure 3). A vertical cross section through this cell reveals the presence of all 5 hydrometeor species within the precipitating cloud (Figures 4a and 4b). The vertical cross section in Figure 4a (along the A–B segment in Figure 3) comprises of 21 individual vertical hydrometeor profiles (this subset of 21 profiles is from the total 82,088 profiles in the 4-km domain at forecast hour 36).
 The vertical profiles of atmospheric ice and water species are used as inputs for a radar reflectivity simulator called QuickBeam [Haynes et al., 2007], indicated by box 2a in Figure 1. QuickBeam allows a user to select options (e.g., radar frequency, hydrometeor phase, size distribution shape, density, and mass-diameter relationship) to be used in the calculation of reflectivity at each vertical level of a given profile of hydrometeors. QuickBeam simulates attenuated and unattenuated reflectivity using full Mie calculations, with backscatter coefficients computed at each of 320 logarithmically spaced particle sizes (from 0.1 to 10 mm) of the particle size distribution (based on Mie scattering code, refer to QuickBeam documentation for details) using the refractive indices of liquid [Ray, 1972] and frozen particles [Warren, 1984]. QuickBeam was applied to the vertical profiles from the MM5 simulation to generate 94 GHz radar reflectivity for the 82,088 vertical profiles in the 4 km model domain (as if CloudSat had passed above each model grid point). QuickBeam options matching the CPR on CloudSat (i.e., radar frequency of 94 GHz computed in a top-down fashion) were specified. The model hydrometeor profiles are linearly interpolated to a vertical resolution of 0.25 km, thus the simulated reflectivity profiles have a vertical resolution of 0.25 km, consistent with CloudSat. Figure 4d illustrates sample QuickBeam output (with a minimum threshold set at −30 dBZ to mimic the minimum detection threshold of the CPR on CloudSat) along the example vertical cross section shown in Figures 4a and 4b. Since simulated reflectivity is highly dependent on the set of assumptions a user provides concerning the particle characteristics (e.g., densities, size distributions), a number of tests were performed to assess a variety of particle characteristics when simulating reflectivity for the set of vertical profiles. The assumptions of each test are based on what has been observed and/or measured in field studies, with the goal of assessing the sensitivity of the results after the CloudSat IWC retrieval algorithm has been applied to the profiles of simulated reflectivity. It should be noted that while attempts have been made to minimize errors associated with simulating 94 GHz reflectivity using QuickBeam (e.g., performing full Mie calculations), potential exists for error in the process of simulating reflectivity from model output and assumed particle properties. The potential uncertainties introduced by simulating reflectivity from modeled fields should not be discounted as a source of the comparative agreement or disagreement presented in our analyses in later sections.
 Each generated profile of attenuated radar reflectivity is provided as input to the CloudSat IWC radar-only retrieval algorithm. The algorithm, with versions 5.0 and 5.1 described in detail by Austin et al. (submitted manuscript, 2008), uses an estimation theory approach described by Rodgers . A priori values of total ice particle number concentration and two size distribution defining parameters are used to build the state vector, with the measurement vector comprising measured radar reflectivity from the CPR (note that a complementary version of the IWC retrieval algorithm (not yet released and not considered here) uses daytime visible optical depth estimates to supplement the measurement vector). The state parameters in algorithm version 5.0 (used to generate Release 03 data), the number concentration and modified gamma distribution width parameter, are assumed to be constant with height. In version 5.1 (used to generate Release 04 data), a lognormal distribution for ice particles is assumed, and the state parameters (number concentration, geometric mean diameter and width parameter) are allowed to vary with height, with a priori values assigned according to empirically derived relationships versus temperature from in situ data (Austin et al., submitted manuscript, 2008). A forward model is used to relate the unknown cloud parameters that make up the state vector to the measurement vector of radar reflectivities. The retrieval algorithm is formulated to find the iterative solution which minimizes a cost function described by Austin et al. (submitted manuscript, 2008). The solution of two of the three distribution parameters are height invariant in v5.0, but all three can vary with height for v5.1. IWC is then derived in each version of the algorithm using the estimated distribution parameters and assumed ice particle density. Convergence tests are performed to test the viability of the derived solution. For the full mathematical representation and more complete description of the retrieval algorithm, see Austin et al. (submitted manuscript, 2008).
 The IWC radar-only retrieval algorithm assumes that measured reflectivity is due to Rayleigh scattering for ice particles (an assumption valid for scattering particles smaller than ∼100 μm at the CloudSat CPR frequency of 94 GHz), and applies a correction factor for Mie scattering effects to account for larger frozen particles [Stephens, 1994]. For large frozen particles, density variations with particle size have been found in numerous studies of naturally occurring frozen particles [e.g., Locatelli and Hobbs, 1974; Mitchell et al., 1990; Brown and Francis, 1995]. Despite these known variations in frozen particle density, they are not explicitly considered in either version of the CloudSat IWC retrieval algorithm. Instead, a constant density of 917 kg m−3 is assumed.
 The simulated retrieved values of IWC (hereafter referred to as IWCs_ret) obtained by applying each version of the retrieval algorithm to the profiles of simulated reflectivity are directly compared to the model values of IWC (i.e., IWCtrue) that were used to begin the simulated retrieval process. For example, IWCs_ret for the western most profile displayed in Figure 4d is plotted against IWCtrue for the same profile and is shown in Figure 4e. By comparing IWCs_ret and IWCtrue, interesting results concerning the performance of the IWC retrieval algorithm under different conditions (i.e., cloud ice only, snow only, mixtures of cloud ice and snow) are revealed. In section 3, results of multiple tests performed to examine the effects of various assumptions (e.g., size distributions, density) of cloud ice and snow particles and their influence on retrieved IWC are assessed.
2.2. Characteristics of Frozen Water Mass in the Atmosphere
 It is necessary to make assumptions regarding the characteristics of the frozen mass at each level of a given profile generated by the cloud-resolving model when applying QuickBeam to simulate 94 GHz reflectivity. The present investigation considers seven experiments performed for each version of the IWC retrieval algorithm. Experiments 1–4 allow for variations in the representation of cloud ice particles, while holding constant the assumptions about the density and size distributions of snow and graupel particles. Experiments 5–7 are used to investigate the effects of variable snow density on the accuracy of the retrievals by allowing the snow particle density to vary while holding constant the cloud ice particle properties. The details of the assumptions used for each experiment, with supporting references, can be found in Table 1 and are discussed in more detail in the appropriate subsections of section 3.
Table 1. Descriptions of Sensitivity Tests and the Assumptions Made for Each
 The results of the tests are presented next and represent a limited subsample of the full potential range of variation in particles shapes, densities, PSDs, etc. that may be present in nature. The tests presented serve as an initial effort to assess the CloudSat IWC radar-only retrieval algorithm and its sensitivities when multiple frozen hydrometeor species are present. Since minimal graupel existed in the set of profiles for which simulated retrieval solutions were found in the present study, a set of tests varying the assumptions of the graupel PSD and density were not performed.
3.1. Description of Simulated Profiles
 In this section, profiles of IWCtrue (from the CRM) and simulated IWCs_ret using the CloudSat ice-only (IO), radar-only (RO) retrieval algorithm (Austin et al., submitted manuscript, 2008) are compared. Each modeled profile is classified as ice-only, liquid-only, ice and liquid, or clear. A threshold of 1 mg m−3 is set for both IWCtrue and LWCtrue to classify the profiles. A profile with exclusively ice (liquid) exceeding 1 mg m−3 for at least one level in the profile is considered ice (liquid)-only. If both ice and liquid exceed 1 mg m−3 in the profile, it is considered an ice and liquid profile, while if neither exceeds the threshold, the profile is considered clear.
 According to the criteria above, ice-only profiles accounted for approximately 18% of the total profiles in the 4 km model domain. About 10% of the profiles were liquid-only and 9% of the profiles had both ice and liquid in amounts exceeding 1 mg m−3. The remaining 63% of the profiles in the 4 km domain were classified as clear. IO-RO retrievals were obtained for all levels in a profile exceeding the −30 dBZ CloudSat CPR detection threshold. Application of a classification algorithm similar to the cloud classification product used for CloudSat (step 2b in Figure 1) showed a wide range of simulated cloud types present in the model domain. About 20% were classified as “high” clouds, while 10% were altocumulus with the following types accounting for less than 5% each: altostratus, stratocumulus, nimbostratus and “deep.” Direct comparison of model IWCtrue to the simulated retrievals, presented in subsequent sections, is restricted to those profiles with ice water present at or above 7 km (i.e., no cloud below 7 km), analogous to the “high ice” classification in the 2B-CLDCLASS CloudSat product [Sassen and Wang, 2008]. We limit our analyses to these specific situations to avoid added complexities associated with retrievals in profiles containing both liquid and ice hydrometeors. These specifications resulted in excess of 150,000 simulated retrievals for each test (at heights ranging from ∼7 km to ∼15 km), with a simulated retrieval being defined as each cloudy (>−30 dBZ) occurrence in a profile. Therefore, numerous individual simulated retrievals may exist at different levels for a given profile. The results of the simulated retrievals are presented in the following subsections.
3.2. Retrieval Sensitivities to Cloud Ice Particle Characteristics
 Tests 1–4 (see Table 1) were designed to test the sensitivity of the IO-RO retrieval algorithm to different representations of cloud ice particles used in the calculations of simulated reflectivity. Tests Ice_5M, Ice_5E and Ice_5G assume that the density of cloud ice particles is 500 kg m−3 (hence the ‘5’ in their name), while Ice_9G assumes that the density is that of pure ice, 917 kg m−3. The assumptions of the cloud ice particle size distribution are varied for these tests and are constrained in the reflectivity simulation by the model predicted value of mass and when necessary, the particle number concentration. For each of the four tests, snow and graupel present in the profile are assumed to be constant density spheres (having densities of 100 kg m−3 and 400 kg m−3 respectively) and conform to exponential distributions (as expressed by Thompson et al. ). Experiment Ice_5M assumes a monodisperse field for cloud ice particles (hence the ‘M’ in the naming convention used). This simplistic representation is used in some model microphysical parameterization schemes [e.g., Tao and Simpson, 1993; Schoenberg Ferrier, 1994; Reisner et al., 1998], and although it is likely not the most realistic choice for representing the cloud ice particles [e.g., McFarquhar and Heymsfield, 1996] the results of this test demonstrate the algorithm performance for a very crude cloud ice representation. With the goal of assessing IWCs_ret in situations with more realistic properties, cloud ice particles are assumed to follow an exponential distribution for test Ice_5E, with a temperature varying distribution slope parameter based on work by Ryan . Ice_5G and Ice_9G assume that cloud ice follows a modified gamma distribution. Since the only varying assumption between experiments Ice_5G and Ice_9G is cloud ice particle density, their results are also used to examine the effects of different cloud ice particle density assumptions.
 In the next subsections, the results from the four cloud ice tests are presented for versions 5.0 and 5.1 of the CloudSat IO-RO retrieval algorithm. A series of plots and statistics, described here, are used for each to demonstrate the retrieval performance for each of the tests. The statistics and data plotting methods used in this section are also used for the tests with varying snow particle properties presented in following sections.
 For each test, number density plots (gridded at 2 mg m−3 × 2 mg m−3) of the logarithm of the percentage frequency of occurrence between the IWCs_ret and the IWCtrue are shown and discussed. These plots were constructed by considering profiles having convergent retrieval solutions in each of the four cases (e.g., Ice_5M, Ice_5E, Ice_5G, Ice_9G), such that the same sample of profiles is considered in each panel of a given figure (e.g., Figures 5a−5d). In addition to the shaded frequency of occurrence, the average bias for each test is given in terms of the average difference between the simulated retrieval (IWCs_ret) and the model value (IWCtrue), and as both an average percent difference per retrieval (APDPR, given by equation (1)) and as a percentage difference of total mass bias for the collection of simulated retrievals (PDTOT, given by equation (2)).
3.2.1. Version 5.0 (Release 03) Results
 The results from the cloud ice tests for algorithm version 5.0 show a positive overall bias for each of the four tests (Figure 5). The largest positive bias occurred in the test that represented cloud ice particles least realistically (Figure 5a) as a monodisperse field (i.e., all particles are the same size and mass). For more realistic assumptions of cloud ice PSD (i.e., exponential and modified gamma distribution) the positive bias was smaller (Figures 5b−5d). The number density plots (Figures 5b−5d) for tests Ice_5E, Ice_5G, and Ice_9G reveal what appears to be a lobe-like feature corresponding to IWCtrue values between 0–40 mg m−3 and smaller IWCs_ret values between 0 and 30 mg m−3. Figure 6 shows that this feature corresponds to situations in which most of the modeled frozen ice water mass consisted of cloud ice particles in the absence of snow and graupel particles. Further investigation into potential causes for this behavior has revealed that the use of height-invariant particle parameters in v5.0 can contribute to underestimates of IWC in ice clouds and overestimates of IWC in snow. This effect is most pronounced in profiles consisting of large values of cloud ice above a region of snow particles. In these situations, the height-invariant terms (number concentration and distribution width parameter) must each take a single constant value throughout the column that will allow for a convergent solution (Austin et al., submitted manuscript, 2008). For profiles having a large range of reflectivity values, the ice particle number concentration (a height-invariant parameter in v5.0) must be large to fit the large reflectivity values in the profile. As a result, ice particle diameter values in the part of the cloud containing only cloud ice must be overly reduced for the small reflectivity values, since the height-invariant number concentration is so large. As a result, IWC is underestimated in the region having only cloud ice particles and overestimated in the snow particle region. Similar effects have been found in v5.0 retrieval tests of liquid profiles having both drizzle and cloud water, with the end result being an overestimate of LWC in the part of the profile containing the drizzle and an underestimate of LWC in the part of the profile that contained only cloud-sized particles. It should be noted that tests on the data presented in this section suggest that profiles consisting of only cloud ice (i.e., no snow beneath cloud) do not exhibit the same underestimates in retrieved IWC. In fact, the algorithm performs quite well for profiles with very little snow present (<10% mass from snow at all levels of a profile), which represents situations with exclusively thin ice clouds. The values of IWCs_ret and IWCtrue for this subset of profiles shows considerable agreement and suggests that retrieval biases in thin ice clouds are reduced in comparison to the overall large bias indicated by the entire set of retrieved profiles. Data from a similar profile subset is presented in the next section for v5.1 results.
 Even with the height-invariant parameter constraints in v5.0, Figures 5b−5d suggest that IWCs_ret values for these tests are typically within a factor of 2 of IWCtrue when IWCtrue is primarily cloud ice particles (Figures 6b−6d). It also illustrates that retrievals made when the frozen ice mass primarily comprises constant density spherical snow particles (recall that for this sample of profiles little graupel was present) are typically in excess of the corresponding value of IWCtrue. It is apparent that the simulated retrievals for Ice_9G, when cloud ice is dominant (Figure 6d), matches IWCtrue relatively well. This agrees with the cloud ice characteristics assumed for this test, as they closely match those assumed by the v5.0 retrieval algorithm (i.e., modified gamma distribution and density of pure ice). Strong positive biases still exist for the Ice_9G experiment when IWCtrue primarily comprises constant density spherical particles (e.g., snow).
 These tests suggest that the CloudSat IO-RO version 5.0 retrieval algorithm may underestimate IWC when predominantly cloud ice particles are present and overestimate total IWC when snow particles (assumed to be constant density spheres) comprise most of the frozen water mass. Links between increasing temperature and ice crystal growth and/or aggregation are well documented [e.g., Houze et al., 1979; Lo and Passarelli, 1982; Gordon and Marwitz, 1986; Mitchell, 1988; Field and Heymsfield, 2003]. The systematic behavior displayed by the gridded scatterplot in Figure 7a showing the average retrievals height for experiment ICE_5G (plotted on the same 2 mg m−3 × 2 mg m−3 grid as presented in Figures 5 and 6) suggests that the height-invariant constraint of the version 5.0 algorithm may play a role in limiting the overall retrieval performance. As previously illustrated and discussed, the lobe-like feature corresponding to a high ratio of cloud ice to total IWCtrue corresponds to the highest-altitude retrievals (12.5–14.5 km). For simulated retrievals at lower altitudes (below 12.5 km) cloud ice is less abundant (Figure 6c) and the simulated retrieval IWCs_ret values show a strong positive bias.
 A simple ad hoc test shows that using information about the height of the retrieval with the retrieval itself could incorporate some information about the vertical variation of ice water properties for version 5.0 IWC retrievals. A simple adjustment lookup-table, based on Figure 7a, is tested and applied as follows:
The two-dimensional lookup table used to estimate the IWC adjustment (ΔIWC) was constructed by computing the difference between IWCs_ret and IWCtrue and using this value with the height at which each simulated retrieval occurred. The lookup-table is generated on the basis of Figure 7a (Ice_5G) and applied to a dependent set of profiles (i.e., the same Ice_5G profiles used to generate the lookup-table values), reducing the total biases (PDTOT) from +44% to +13% (Figures 7b and 7c). The same lookup-table is also applied to an independent set of simulated retrievals from a July 2006 simulation over the same 4 km domain. Figures 7d and 7e show a bias decrease between the original and adjusted simulated retrievals for the July data after applying a correction generated from the January 2006 data.
 This adjustment example is used here to demonstrate the importance of carrying vertically varying IWC property information in the CloudSat retrieval algorithm. The results demonstrate that more accurate IWC retrievals would potentially be possible if height varying properties of the IWC were considered during the retrieval process, which would then allow for potential errors in the retrieval system to be tracked and quantified. Version 5.1 of the IWC retrieval algorithm attempts to better estimate profiles of IWC from CloudSat reflectivity measurements by allowing for height-varying components of the ice particle size distribution parameters (Austin et al., submitted manuscript, 2008). This algorithm version is applied to the four ice tests and the results are presented in the next subsection.
3.2.2. Version 5.1 (Release 04) Results
 Tests 1–4 were performed using the CloudSat IWC algorithm version 5.1. Figure 8 shows the results of these tests, with corresponding bias statistics in the same manner as the results from using the v5.0 algorithm. The shaded frequency of occurrence patterns and biases are very similar for the v5.1 algorithm tests in comparison to v5.0 results (see Figure 5). While both algorithm versions appear to result in substantial positive biases for the population of profiles and ice particle properties considered in these four tests, some interesting differences were also found.
 The lobe-like pattern in the IWCtrue versus IWCs_ret occurrence density plots that resulted from the height-invariant constraint of the v5.0 algorithm is greatly reduced for the v5.1 tests as a result of the new algorithm's capability to allow for height-varying ice particle parameters in the algorithm formulation. This development should begin to address the issues raised in the previous section which demonstrated the importance of considering vertically varying components of the ice mass field. The reduction in the lobe feature in the v5.1 tests does, however, increase the overall positive bias since almost all IWCs_ret for v5.1 are greater than IWCtrue. It should also be noted that since v5.1 assumes ice particles follow a lognormal particle size distribution, the differences between this form and a modified gamma form could also contribute to the increased positive bias for the v5.1 Ice_5G and Ice_9G tests.
 It is of interest to understand not only how the IWC retrieval algorithm performs overall on a large sample of profiles, but also how it performs for specific sets of like profiles. The previous subsection alluded to the fact that the v5.0 retrieval algorithm seemed to have reduced biases for profiles of predominantly cloud ice particles in the absence of significant snow (i.e., thin ice clouds). Tests of this subset of profiles for v5.1 also show that the algorithm is quite accurate for these types of situations (Figure 9) with IWCs_ret and IWCtrue within about 25% for most simulated retrievals.
 While both v5.0 and v5.1 exhibit positive biases for the cloud ice tests, it is apparent that large contributions to these biases are a result of snow particles at large values of IWCtrue. The following sections consider the effects of variable snow particle density by testing both algorithm versions with snow particles assumed to have densities consistent with snow habit dependant empirically derived mass-diameter relationships instead of constant density spheres.
3.3. Retrieval Sensitivities to Snow Particle Characteristics
 Results in section 3.2 demonstrate that the CloudSat radar-only IWC retrieval algorithm is sensitive to the characteristics of cloud ice particles (e.g., particle size distribution shape and particle density). It was noted that significant differences between the IWCtrue and the IWCs_ret arise when the total frozen mass is comprised primarily of snow particles. It is not surprising that large differences may exist for retrievals consisting of large frozen particles. Density variations with particle size are known to occur naturally, yet these variations are not specifically accounted for in the IWC retrieval algorithm, nor is Mie scattering by large particles explicitly considered. Vertical variations of the size distribution of snow particles have also been shown to exist in naturally occurring clouds [e.g., Houze et al., 1979; Field et al., 2005; Woods et al., 2008]; while these effects are not accounted for in v5.0 of the retrieval scheme, v5.1 does allow for height-varying size distribution state parameters.
 To assess the sensitivity of the simulated retrievals to different snow particle densities, tests 4–7 (Ice_9G, Snow_CT, Snow_DN, Snow_NE; see Table 1) hold constant the properties of cloud ice and graupel particles while allowing snow particle properties to vary. Snow particles are treated as constant density (100 kg m−3) spheres in Ice_9G, as was the case for each of the tests of cloud ice characteristics. Tests (5–7) allow snow particle density to vary with size according to mass versus dimension relationships for three different naturally occurring snow habits. Experiment Snow_CT (see Table 1) assumes that snow particles follow the mass-dimension (M-D) relationship of single particles and aggregates of unrimed radiating assemblages of plates, sideplanes, bullets, and columns as measured by Locatelli and Hobbs . Since these particles typically form at temperatures colder than −18°C, they are often referred to as “cold-type” crystals [e.g., Woods et al., 2008]. For the Snow_DN experiment, a M-D relationship of dendrites is assumed [Woods et al., 2007]. Dendrite particles form and grow at temperatures near −15°C [Magono and Lee, 1966]. For experiment Snow_NE, snow mass is assumed to follow the M-D relationship of needle-shaped particles [Cunningham, 1978]. These particles typically grow between temperatures of −8°C and −3°C [Magono and Lee, 1966]. The three snow particle types chosen for investigation (cold-type, dendrite and needle) encompass particles that may be encountered over the depth of the atmosphere and also represent a wide range in terms of particle densities [e.g., Woods et al., 2007].
 While studies have demonstrated a variety of methods to represent snow particle PSDs to account for their evolution resulting from microphysical processes and particle growth (e.g., Field et al.  derived a universal functional form for PSDs as a combined exponential and gamma function), the snow size distribution is assumed to be exponential with a temperature-dependent intercept parameter in the tests presented here. The temperature dependency is designed to account for particle aggregation as temperatures increase [Houze et al., 1979] and is commonly used in mesoscale model microphysical parameterization schemes [e.g., Reisner et al., 1998; Thompson et al., 2004; Woods et al., 2007]. This assumption, combined with variable snow particle density, affects the number concentration at each snow particle size for a given mass mixing ratio. As a result, simulated reflectivities differ between experiments Snow_CT, Snow_DN and Snow_NE, leading to a range of IWCs_ret values for a given value of IWCtrue.
3.3.1. Version 5.0 (Release 03) Results
Figures 10a−10d show frequency density plots for tests 4–7 of IWCtrue and IWCs_ret. As in the cloud ice sensitivity tests, these plots were generated by considering profiles having convergent retrieval solutions in all four cases (e.g., Ice_9G, Snow_CT, Snow_DN, Snow_NE), such that the same sample of profiles is considered in each of Figures 10a−10d. The lobe-like feature associated with those retrievals consisting of primarily cloud ice particles, discussed previously, remains evident in the experiment with snow treated as constant density spheres (Ice_9G), and is discernible for the experiment with snow assumed to be cold-type crystals (Snow_CT). Although not shown here, systematic differences between IWCs_ret and IWCtrue were found to vary with height similar to the v5.0 cloud ice test results seen in Figure 7a, suggesting that v5.0 retrievals would likely benefit from height-varying parameters in the retrieval process. The lobe feature is not obviously apparent for experiments Snow_DN and Snow_NE in which snow is assumed to be dendrites or needles respectively, as many of the retrievals at IWCtrue values between 0 and 40 mg m−3 are underestimates. At larger values, IWCs_ret is less than its corresponding value of IWCtrue in the Snow_DN and Snow_NE cases. The differences found between the Snow_CT simulated retrievals and those for Snow_DN and Snow_NE result from the reduced backscatter efficiency (Figure 11) of dendrites and needles, which act to reduce radar reflectivity. Essentially, the CloudSat IO_RO IWC algorithm retrieves IWC from a weaker reflectivity signal for these tests. The reduced reflectivity signal can lead to reductions in the amount of IWC retrieved and limit the impacts of height-invariant parameters in the retrieval process by reducing the range of dBZ in a profile.
 When IWCtrue is large (i.e., greater than ∼60 mg m−3), the CloudSat radar-only retrieval algorithm appears to perform best if the frozen mass is made up of particles similar in density to cold-type particles. At smaller values of IWCtrue, the algorithm performs better for particles having densities closer to dendrites and needles. Overall, it was found that while the simulated retrievals for the Snow_CT experiment were best at capturing retrievals with large IWCtrue values, it still possessed an average overall positive bias of +38% since the majority of IWC retrievals were for IWCtrue < 20 mg m−3. The tests with snow particles treated as dendrites and needles (Snow_DN and Snow_NE) also had positive total biases of 24% and 16% respectively, despite significantly lower values of IWCs_ret when IWCtrue was large. The overall positive bias for tests Snow_DN and Snow_NE is due to the high frequency of simulated retrievals having IWCtrue values for which positive biases existed.
3.3.2. Version 5.1 (Release 04) Results
 The snow particle variation tests were performed using v5.1 of the CloudSat radar-only IWC retrieval algorithm as well. Figure 12 shows the occurrence frequency density and bias statistics for each of the tests. As in the v5.0 tests, the overall bias in each of the tests was positive with the biases for the cold-type snow particle properties test being larger than the biases for dendrite or needle types. The biases are larger for the v5.1 tests as a result of larger values of IWCs_ret for values of IWCtrue. This can be seen by comparing the envelope of values in Figures 12 from v5.1 to the much narrower envelope of values from the v5.0 tests (Figure 10). For each algorithm version, the lower bound of the envelope in the frequency density plots is very similar, however the range of IWCs_ret for a given IWCtrue extends over larger IWCs_ret values for the v5.1 tests compared to the v5.0 tests. As a result, the positive biases have increased between v5.0 and v5.1 with values of PDtot increasing from 38% to 50% in Snow_CT, 24% to 35% for Snow_DN and 16% to 27% for Snow_NE. The increases in IWCs_ret are an improvement at values of IWCtrue larger than ∼20 mg m−3 in tests Snow_DN and Snow_NE, as IWCs_ret values were dramatically smaller than IWCtrue in the v5.0 tests.
 To further compare the snow sensitivity tests and the biases resulting from both versions of the retrieval algorithm, Figure 13 displays the average ratio of IWCs_ret to IWCtrue over the range of IWCtrue. At small IWCtrue (<10 mg m−3) large positive biases (i.e., ratios much larger than 1) exist when the entire collection of profiles are considered. Again, as described earlier in section 3.2.2, subsamples of only thin ice profiles would possess ratios much closer to 1. Figure 13 suggests that for IWCtrue values larger than 10 mg m−3 both algorithm versions most closely match IWCs_ret when the snow mass is composed of cold-type particles. Also, the version 5.1 test results indicate IWC retrievals when snow comprises either cold-type or dendrite particles are within ±25% of IWCtrue.
 In addition to understanding the performance of the CloudSat IWC retrieval algorithm for these various tests on individual retrievals, it is also of interest to understand the sensitivity of another important and often used (for comparison to GCMs, etc.) estimate from CloudSat, ice water path (IWP). Values of IWCtrue and IWCs_ret were integrated vertically for each of the tests discussed in this section (for both v5.0 and v5.1) to estimate IWP. The IWP for each set of profiles was averaged and a ratio of IWPs_ret/IWPtrue computed. The results are shown in Table 2 and indicate similar biases as for the individual retrievals. In each test, and for both algorithm versions, the simulated retrieved IWP for tests with realistic snow particle properties (i.e., cold-type, dendrite and needle) is within 50% of the average model value of IWP. It should also be noted that v5.1 IWP values are larger than v5.0, in agreement with our results of individual retrieval bias presented previously.
Table 2. Ratio of the Average Simulated Retrieved IWP to the Average Model IWP for the Ice_9G Test and the Three Snow Type Tests for the CloudSat IWC Retrieval Algorithm Versions 5.0 and 5.1a
IWPs_ret/IWPtrue (version 5.0)
IWPs_ret/IWPtrue (version 5.1)
Average simulated retrieved IWP, IWPs_ret; average model IWP, IWPtrue.
4. Summary and Conclusions
 This study focused on assessing the sensitivity of the CloudSat radar-only IWC algorithm to various frozen particle properties. Two versions (v5.0 and v5.1) of the retrieval algorithm were evaluated and compared by a series of tests which varied cloud ice or snow particle properties. The evaluation was based on simulated retrievals of IWC from reflectivity profiles generated by applying a 94 GHz, top-down radar simulator (QuickBeam) to cloud-resolving model output. Direct comparison of the simulated retrievals (IWCs_ret) against the model ice water content values (IWCtrue) revealed sensitivities of the retrieval algorithm to assumptions of particle densities, mass versus diameter relationships and PSDs. A similar approach of using output from an explicit cloud resolving model to assess IWC radar algorithms for ice in cirrus at temperatures between −50°C and −70°C was used by Sassen et al. . They found that of several algorithms tested, several performed reasonably well under conditions similar to the empirical data sets from which the algorithms were developed. A similar conclusion can be made from the first set of sensitivity tests in this study designed to consider varying cloud ice particle properties. The IWCs_ret values were closest to the IWCtrue values for assumed properties nearest to those made in the retrieval algorithm (i.e., same ice particle density and distribution) when cloud ice is the primary component of the frozen water mass. When a mixture (cloud ice and snow) of frozen hydrometeors was present in a profile, both versions of the retrieval algorithm showed a strong positive bias (with snow assumed to be constant density spheres in calculations of simulated reflectivity, as in tests 1–4).
 A second set of sensitivity tests demonstrated the important influences that variable snow density may have on CloudSat radar-only IWC retrievals. These tests demonstrated that the retrieval algorithm was unable to account for the large variations caused by a wide range of particle types and their properties. As a result, the simulated IWCs_ret for both algorithm versions more closely matched IWCtrue values at large values of IWC (>10 mg m−3) for snow densities close to that of cold-type crystals, but are in better agreement at low values of IWCtrue (<10 mg m−3) for less dense particle types such as dendrites and needles. The average biases for all of the tests was positive despite individual simulated retrievals that were less than their corresponding true value (particularly for the experiments assuming dendrite and needle snow particles).
 The tests in this study also showed that for the western Pacific domain used to generate the CRM output, cloud ice particles were most abundant at the highest levels (12.5–14.5 km) with decreasing ratios of cloud ice particle mass to the total IWC below approximately 12.5 km. The results from tests using v5.0 suggested that significant reduction in retrieval bias may be obtained by accounting for vertically varying ice particle characteristics properties that are constrained to be constant with height in the v5.0 retrieval algorithm. Algorithm version 5.1 is designed to allow height-varying ice particle size distribution parameters. This advance in sophistication did seem to minimize the underestimation lobe present in v5.0 tests for profiles consisting of cloud ice particles suspended above regions of snow particles, but overall retrieval biases continued to be largely positive for v5.1 for the tests presented here.
 In situ and laboratory studies have shown a systematic behavior between snow particle habit formation, growth and the ambient temperature [e.g., Magono and Lee, 1966; Bailey and Hallett, 2002, 2004]. When possible, this information should be utilized in attempts to retrieve IWC throughout the depth of an atmospheric profile. This fact is particularly evident from our tests demonstrating the sensitivity of CloudSat IWC retrievals to snow particle properties. One principal difficulty lies in identifying frozen particle types in the atmosphere; information that could be invaluable in terms of accurate IWC retrievals. McFarlane et al.  presented a means of identifying both cloud phase and frozen particle habit near the tops of clouds using MISR and MODIS radiances. Alternatively, it may be possible to identify regions of particle formation and growth from attenuation based precipitation rate estimates [e.g., Matrosov, 2007]. Combining precipitation growth rates with temperature measurements over a range of levels of a vertical profile could enable inferences of particle types in a given ice profile based on likely snow particle morphology [e.g., Magono and Lee, 1966; Bailey and Hallett, 2002, 2004]. In the future, QuickBeam will likely have the ability to simulate 94 GHz reflectivity for a variety of particle habits using discrete dipole approximation [Haynes et al., 2007]. This new capability will allow reflectivity simulation for profiles of a variety of particle habits, such as those produced by a cloud-resolving model output capable of predicting frozen particle habits [Woods et al., 2007]. This should allow for a more detailed assessment of the role of particle type on IWC retrievals.
 The influences of different types of frozen particles on CloudSat IWC retrievals are apparent in the results of the tests performed in this study. As a result, analyses of the CloudSat IWC product should consider the potential impacts that both precipitating and nonprecipitating ice can have on such retrieved values. Thus, care should be taken when performing comparisons of ice water content estimates from CloudSat and other sensors/instruments (e.g., Aura Microwave Limb Sounder) in terms of what components of the frozen water mass in the atmosphere are derived or retrieved. Similar considerations should be made in efforts to validate global model representations of IWC as well (Waliser et al., submitted manuscript, 2008).
 The framework presented in this paper will allow future study of the CloudSat IWC retrieval algorithm and its sensitivity to naturally occurring characteristics of frozen particles. In addition, IWC retrievals in mixed-phase situations, which often employ simplistic assumptions to generate retrieved solutions (e.g., blending of ice and liquid solutions based on a temperature-dependent linear combination) will be investigated. The radar-only retrieval algorithm for liquid-only solutions can also be assessed, although considerable complications arise for liquid phase retrievals due to the potential for radar attenuation and the effects of multiple scattering by liquid drops.
 The authors wish to thank John Haynes for providing the QuickBeam reflectivity simulator software and documentation. The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.