This paper introduces a technique for cloud phase discrimination based on linear polarization measurements made by space-based lidar. Using CALIPSO Level 2 data products, a 3-dimensional histogram of the depolarization ratio, δ, and the effective lidar ratio, Sc,eff, is derived for all optically thick clouds measured during July 2006. A second histogram is derived using data from early November, 2006. By analysis of the relationship between δ and Sc,eff, and an examination of their spatial correlations, water clouds, ice clouds with randomly oriented particles and ice clouds with horizontally oriented particles are clearly differentiated. For clouds having the same depolarization ratios, the effective lidar ratios of water clouds are significantly smaller than the effective lidar ratios of ice clouds comprised of randomly oriented particles. The variance of the depolarization ratios within water clouds is significantly larger than it is in ice clouds containing horizontally oriented particles. Depolarization ratios and effective lidar ratios are negatively correlated for water clouds, and positively correlated for ice clouds with horizontally-oriented particles. For the optically thick ice clouds observed by CALIPSO, approximately half contain some fraction (up to 100%) of horizontally oriented particles.
 Ground-based and aircraft-based lidars can readily determine cloud phase using depolarization ratios [Sassen, 1991]. The spherical particles in water clouds do not depolarize the lidar backscatter signal, whereas the randomly oriented crystals in ice clouds introduce significant depolarization. However, for space lidars such as CALIPSO [Winker et al., 2003], which has a footprint size of 90 meters at the Earth's surface, water clouds can exhibit a strong depolarization signal due to the presence of multiple scattering [Hu et al., 2001]. Multiple scattering can thus introduce a substantial amount of error in cloud phase discrimination derived from space-based measurements.
 Previous Monte Carlo simulation studies of lidar backscatter and depolarization [Hu et al., 2001, 2003] have demonstrated that for the spherical particles in water clouds and many types of aerosols, the layer integrated depolarization, δ, and the layer effective multiple scattering factor, η, are related via the following equation [Hu et al., 2006a, 2006b]:
 Another simple and accurate form of this equation is
 As seen in Figure 1, these two expressions yield essentially identical results for all water clouds for which CALIPSO would measure, with a depolarization ratio of less than 0.45.
 It is not always possible to estimate the cloud lidar ratio (extinction-to-backscatter ratio) directly from CALIPSO data. We can, however, estimate an effective lidar ratio, Sc,eff. Sc,eff is the product of the single-scattering lidar ratio, Sc, and the layer-effective multiple scattering factor, η, and is computed using [Platt et al., 1999]
 Here γ′ is the layer integrated attenuated backscatter and T2 is the measured two-way transmittance. For the measurements made at 532 nm, both quantities are reported in CALIPSO level 2 cloud data product. For opaque layers, the two-way transmittance is zero. For transmissive layers, T2 is estimated using the backscatter from clear air beneath the cloud. For water clouds, Sc has a near constant value very close to 19 sr [Pinnick et al., 1983; O'Connor et al., 2004; Hu et al., 2006a, 2006b].
 From equations (2) and (3), we expect that δ and Sc,eff are negatively correlated for water clouds; that is
 Due to multiple scattering, the effective lidar ratios derived from CALIPSO measurements of water clouds are generally small. For a water cloud to have an integrated depolarization ratio greater than 0.2, large amounts of multiple scattering must occur (e.g., η < 0.45), and thus the effective lidar ratio will be significantly smaller (Sc,eff < 9 sr) than the corresponding single scattering lidar ratio (Sc = 19 sr).
 When compared to water clouds, ice clouds composed of randomly oriented particles will have larger values of Sc,eff (around 17 sr) and larger depolarization ratios (around 0.4). However, for those ice clouds that contain some fraction of horizontally oriented particles, especially plates, the values of both δ and Sc,eff are anywhere from slightly to very substantially lower. Because the backscatter from horizontally oriented plates is specular reflection, the incident polarization state is preserved, and the return signal is not depolarized. Similarly, the lidar ratio for these same plates approaches 1, as essentially all of the extinction is backscatter. Due to this combination of highly polarized backscatter and small lidar ratio, only a small fraction of horizontally oriented plates is required to reduce both the depolarization ratio and the effective lidar ratio of ice clouds. For this reason, distinguishing between water clouds and ice clouds with horizontally oriented particles requires more information than just the δ − Sc,eff relation. This extra information includes the variance of depolarization within each cloud profile and the δ − Sc,eff correlation for adjacent cloud measurements. The next section compares the theoretical analysis with global cloud statistics from CALIPSO data.
2. Cloud Phase Signature in CALIPSO Data
 In its standard data acquisition mode, the CALIPSO lidar points along track at an angle of 0.3° from true nadir. However, during the time period from November 6–15, 2006, the satellite was reconfigured to point the lidar at a much larger angle of 3° off-nadir. This special 3°-tilt angle was chosen specifically to avoid the specular reflections arising from horizontally oriented particles embedded in cirrus clouds. Figure 2 presents the statistics of the depolarization – effective lidar ratio relation for all opaque clouds, both ice and water, measured during this period. The color in the figure indicates the number of occurrences. A clear separation is evident between water clouds (lower left group clustered around the dashed line) and ice clouds (upper right group centered at a depolarization ratio of 0.4 and an effective lidar ratio of ∼17.5 sr). For most ice clouds, the depolarization ratios are larger than 0.3 and the effective lidar ratios are greater than 14. The layer integrated depolarization of water clouds sometime can be as high as 0.4. For water clouds with depolarization ratios greater than 0.1, the effective lidar ratios are generally less than 11 sr. As δ approaches 0.3, Sc,eff reduces to less than 7 sr.
 The dashed yellow line in Figure 2 is the theoretical curve for water clouds, computed using equation 4. The theoretical curve agrees well with CALIPSO observations, and confirms that the clouds in the lower left group are indeed water clouds. The small difference between theory and observation is attributed to a combination of measurement noise and a non-ideal detector transient response that can occur for strong signals (D. M. Winker et al., Initial performance assessment of CALIOP, submitted to Geophysical Research Letters, 2007).
 When examining CALIPSO data acquired outside the 3° tilt mode period, the impact of horizontally oriented particles on cloud phase discrimination is obvious. Figure 3 shows the same quantities as Figure 2 for all data acquired during July 2006, when the lidar was pointing at its standard 0.3°-off-nadir angle, and was thus exposed to the specular reflection (glint) of horizontally oriented particles embedded in ice clouds. As in Figure 2, only opaque clouds were used to compile the statistics. Figure 3 shows that close to half of all non-water clouds are located in the high-depolarization, high extinction-to-backscatter ratio region (upper right) that is characteristic of ice clouds comprised of randomly oriented particles. The remaining ice clouds are those which contain some horizontally oriented particles, where the lidar ratio can be as low as 1 and depolarization ratio approaches zero for horizontally oriented plates. The data points for these clouds are found clustered around the dashed yellow line of Figure 3, which was computed using the following empirically-derived relation:
 For a given depolarization ratio, δr, of those ice particles other than the horizontally oriented particles, the contribution to the CALIPSO lidar backscatter made by the these particles, f, can be estimated from the measured depolarization, δ, using
 Ice clouds containing horizontally oriented particles can be separated from water clouds when the variance of the depolarization within the cloud layer is considered. For water clouds, the depolarization ratios measured at the near-range boundary of the cloud (i.e., at cloud top for a down-looking lidar such as CALIPSO) are quite low, often approaching zero. The range-resolved depolarization ratios rise steadily with increasing penetration into the cloud, due to multiple scattering effects, and can eventually reach as high as 1. Conversely, the particulate depolarization ratios for ice clouds containing horizontal particles change very little as a function of penetration into a layer, because multiple scattering by these particles rarely contributes any additional depolarization to the backscattered signal.
 For ice clouds containing horizontally oriented particles, the variance-to-mean ratio, defined as the variance of the depolarization ratios within each cloud lidar profile divided by the layer mean depolarization ratio, is normally less than 1.6. The variance of the depolarization ratios within a water cloud profile is much larger than the mean depolarization ratio of the profile, and the ratio of the variance to the mean is normally greater than 2. Figure 4 shows a scatter plot of this variance-to-mean ratio for both water clouds and those ice clouds containing horizontally oriented particles, using the same July 2006 data that was used to construct Figure 3.
 A variance-to-mean ratio of 1.8 was selected as the threshold value for separating water clouds from horizontally oriented particles. This variance-to-mean depolarization threshold is applied to the data originally shown in Figure 3, with the results being shown in Figure 5. As can be seen by comparing these two figures, ice clouds with horizontally oriented particles are successfully removed from the water cloud distribution when this threshold technique is employed. It should be noted too that slope of the vertically resolved depolarization ratios with respect to range contains similar discriminatory information. However, this slope is not reported in the standard CALIPSO Level 2 products, and its derivation would require the use of CALIPSO Level 1 data.
 The along-track spatial correlation of depolarization ratio and effective lidar ratio is also useful information for differentiating water clouds from horizontally oriented particles. The correlation coefficient, ξ, is computed from the closest 15 lidar shots for which a similar cloud top height has been detected:
 As shown in Figure 3, ξ is positive for horizontally oriented particles and negative for water clouds. The distribution of ξ for the July 2006 data is shown in Figure 6. This spatial correlation of depolarization ratio and effective lidar ratio is especially important when attempting to assess cloud phase for transparent clouds with relatively small optical depths.
3. Summary and Discussion
 Because of the significant multiple scattering contribution to the lidar backscatter measurements made by CALIPSO, the near zero depolarization assumption for water cloud backscatter is no longer valid. Based on Monte Carlo simulations and CALIPSO data analysis, this study demonstrates that, when the depolarization ratio – effective lidar ratio relation is considered, reliable cloud phase discrimination is possible when using space based lidar measurements. The effective lidar ratio can be estimated directly from layer integrated attenuated backscatter and the two-way transmittance of the layer. Both of these quantities are available in the standard CALIPSO level 2 data product.
 As is the case for ground based lidar systems, CALIPSO's layer integrated depolarization ratio alone does not necessarily provide enough information to separate super-cooled water clouds from horizontally oriented particles. The horizontally oriented particles contribute at least partially to the lidar backscatter in close to half of all opaque ice clouds observed. Tilting the CALIPSO laser by 3° effectively removes the backscatter contribution of the specular reflection, and thus helps achieve more accurate cloud phase discrimination. For cloud phase discrimination using lidar data obtained during near-nadir pointing laser operations, which has been CALIPSO's routine data acquisition mode, a depolarization variance method is introduced. This new method is shown to effectively differentiate between water clouds and ice clouds containing horizontally oriented particles. In addition, the spatial correlation documented between depolarization ratio and effective lidar ratio further improves our ability to discriminate super-cooled water clouds from ice clouds with horizontally oriented particles. Ice clouds containing only randomly oriented particles are clearly separated from water clouds in the CALIPSO measurements when the depolarization ratios and the effective lidar ratios are considered together. For thinner clouds having lower signal-to-noise ratios, cloud phase discrimination can also benefit from cloud temperature and height information.
 This research has been supported by the MIDAS project of NASA Radiation Science Program under Hal Maring, and CALIPSO project. The study benefited a lot from discussions with Mark Vaughan.