Currently approaching its sixth year in space, the CALIPSO satellite collects lidar linear depolarization ratios δ from 0.532 μm laser backscatter, an indicator of particle phase, shape, and orientation. We examine one-yearδaverages for day and night periods when the lidar was pointing close to the nadir (0.3°) and off-nadir (3.0°), in terms of geographic location and zonal height averages. For the first time, also given is the dependency ofδon temperature versus latitude for ice clouds. The analysis involves all ice clouds with a cloud top temperature of <−40°C, which include mainly cirrus and altostratus, as well as some polar stratospheric clouds identified by CALIPSO. We find significant differences from ∼−10° to −30°C between the nadir and off-nadir data, consistent with the effects of horizontally oriented plate crystals: overall the off-nadirδ are increased by ∼0.05 globally. Strong dependencies of δ also occur with latitude and height. Day minus night δ differ by 0.02–0.03. The global average day plus night δfor nadir and off-nadir data are 0.318 and 0.365, respectively. As expected from ground-based studies,δ increase steadily with decreasing temperature, which is particularly apparent in the nadir data because of oriented plate effects. These findings have implications for the modeling of radiative transfer through ice clouds.
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 Polarization diversity lidar is a basic tool for the probing of clouds and aerosols that dates back to the beginnings of laser atmospheric research [Schotland et al., 1971]. Although a variety of more sophisticated techniques have evolved [Weitkamp, 2005], measuring laser backscatter depolarization is an important application that is seeing increasing use by virtue of its ability to infer particle phase, type, and shape. This includes the inclusion of dual-polarization channels on the CALIOP lidar system aboard the CALIPSO satellite [Winker et al., 2007] at the 0.532 μm wavelength, which is a constituent of the A-train formation of meteorological satellites [Stephens et al., 2002]. The availability of CALIPSO lidar depolarization data is proving to be an important supplement for microphysical analyses [e.g., Hu et al., 2007; Cho et al., 2008; Sassen and Zhu, 2009; Noel and Chepfer, 2010; Okamoto et al., 2010].
 A major justification for the April 2006 launch of CALIPSO was the ability of its polarization lidar to classify the global distribution of clouds, especially the clouds of the middle and upper troposphere that present difficulties for probing using the cloud radar (CloudSat) and passive methods also available from the A-train. According to theoretical ray-tracing simulations of laser backscatter depolarization [e.g.,Takano and Liou, 1989], ice crystal shape has a fundamental influence on the lidar linear depolarization ratio (δ, the ratio of the returned laser powers in the planes of polarization orthogonal and parallel to that of the linearly-polarized source). The effects of uniformly oriented crystal populations such as horizontally-oriented ice plates, however, also have a major impact: they produce near-zeroδ when probed in the zenith (or nadir) direction [Platt et al., 1978; Sassen and Benson, 2001; Noel and Sassen, 2005] because aerodynamic drag forces align the large mirror-like faces of the plates in the horizontal plane. This effect, however, rapidly diminishes as the incident lidar angle falls off the vertical direction.
 In an earlier study [Sassen and Zhu, 2009], curious patterns in the global character of ice cloud δwere found, including significant differences with height, latitude, and in day versus night and nadir versus off-nadir measurements. While oriented plate crystal effects could explain many of these findings, we reexamine here the day/night differences and directly correlate the data with cloud temperature using one-year averages of CALIPSO polarized signals prior to and following the 28 November 2007 lidar viewing angle change from 0.3 to 3.0°.
2. CALIPSO Data Analysis
 Our data analysis algorithm processes CALIPSO Level 1 and 2 standard data products, using the Version 2 dataset. Level 1B data provide attenuated total (parallel plus perpendicular) and perpendicular polarized backscatter profiles at a horizontal resolution of 333 m and a vertical resolution varying from 30–240 m depending on altitude. From CALIPSO Level 2 data products, we employ the 5-km cloud layer product to initially obtain cloud height boundaries. Various horizontal (5-km, 20-km, and 80-km) signal averaging schemes are used to obtain sufficient signal-to-noise ratios to detect even tenuous cloud and aerosol layers in the atmosphere, but by using the 5-km cloud detection product we have selected relatively strongly-scattering clouds for analysis. This minimizes the inclusion of aerosol layers in our cloud sample, and also diminishes the impact of molecular scattering on lowering laser depolarization in weakly-scattering ice clouds. This differs from that used inSassen and Zhu , which included all cloud layers detected at any of the three horizontal signal averages. The parallel (total minus perpendicular) and perpendicular backscatter profiles, along with their interpolated temperatures (derived from global models), are then extracted from the Level 1 file.
 The data sample is intended to include all types of ice clouds, even those that cause the complete attenuation of the laser pulses. Based on the climatological midlatitude cirrus-cloud dataset inSassen and Campbell , a maximum cirrus cloud top temperature of −40°C (i.e., the homogeneous freezing point of pure water) is first applied, which reduces the possibility of including clouds containing supercooled water [Pruppacher and Klett, 1997; Sassen, 2002]. A minimum temperature of −10°C is also applied for this reason. Thus, our findings are mainly derived from cirrus and altostratus clouds, although water-ice dominated polar stratospheric clouds (PSC) clouds likely to be detected by the 5-km CALIPSO detection algorithm [Sassen and Zhu, 2009] are also included in the sample.
Total (molecular plus aerosol plus cloud backscattering) δ profiles for the clouds selected by our criteria (corresponding to the sum of 15 consecutive laser shots at each height) are derived from the total parallel ‖ and perpendicular ⊥ backscatter coefficients (β) extracted from Level 1 data. That is,
where the subscripts refer to scattering from molecules, aerosols, and clouds.
 Such data are included in data files for all orbits for each day in 5° latitude by 5° longitude grid boxes globally. Yearly datasets are derived after summing all the parallel and perpendicular signals at each cloud height and temperature: average δ are not calculated by averaging individual δ calculated at lesser temporal scales.
3. Global Depolarization Findings
 Given in Figures 1 and 2are global views of 1-yr average ice cloudδfor nadir (top row) and off-nadir data in terms of day (left of each pair) and night displays of vertically-integrated (Figure 1) and height-resolved zonal (Figure 2) averages. Given in Table 1are the differences in the global vertically-integratedδfor day, night, day plus night, and day minus night for both nadir and off-nadir CALIPSO data. As described above, theseδare based on the signals summed in the two channels interpolated to the maximum 30-m vertical resolution interval.
Table 1. Yearly-Averaged Global CALIPSO Ice Cloudδfor Nadir (December 2006–November 2007) and Off-Nadir (December 2007–November 2008) Data for Day, Night, Day Plus Night, and Day Minus Night Measurements
Off-Nadir − Nadir
Day + Night
Day − Night
 It is obvious that significant variations occur in connection with geography, latitude, and height, and in nadir versus off-nadir and day versus night. In keeping with the effects of probing horizontally oriented planar crystals at nadir, the nadirδare considerably lower at low altitudes. Nadir versus off-nadir differences inδ at heights above ∼12 km MSL are not very noticeable in Figure 2, although the data attributable to PSC at high latitudes are more variable due perhaps to the smaller sample size. The specular reflections from plates generate strong backscattered signals, and their effects are more dramatically portrayed in the vertically-integratedδ at middle and high latitudes in Figure 1. Geographically, certain (mostly continental) regions like southern South America, the U. S. Great Basin, the southern Himalayas, central Africa, and Malaysia, tend to display higher δ probably as a result of the local cirrus cloud generating mechanisms. Table 1shows that the global nadir versus off-nadirδ differences are ∼0.05, while the day minus night differences are ∼0.025.
 Differences in day versus night vertically-integratedδare evident by the lower night-timeδ at high latitudes, and the higher δ in the tropics/midlatitudes during day (Figure 1). From Figure 2, diurnal differences are apparent at heights >∼12 km in cirrus, where they are lower at night particularly in the tropics. On the other hand, δdifferences in PSC are ambiguous, and probably correspond to cloud detection threshold effects. The causes of these day/night differences could be attributable to CALIPSO signal noise and thermally-induced signal drift issues, but also likely reflect cloud microphysical variations due to diurnal ice cloud formation, aging, and radiative effects. Diurnal differences in ice cloud formation based on CALIPSO and CloudSat data are discussed inSassen et al. [2008, 2009].
4. Global Temperature Variations
 The above depolarization findings may find a basic explanation in terms of cloud level temperature. Theoretical ray-tracing simulations [Takano and Liou, 1989] have established that the basic ice crystal habits generate differing δ according to the major internal ray paths, essentially increasing with increasing hexagonal particle axis ratio (i.e., length over width). When randomly oriented in space, thin plate crystals generate δ ∼ 0.3, whereas long solid column crystals yield δ ∼ 0.6 by virtue of their internal ray paths from multiple refractions and reflections off their large basal faces. (Hollow crystals and more complicated spatial particles are more difficult to treat, but these shapes appear to make a difference.) It is also known that ice crystal habit depends in a fundamental way on temperature [Pruppacher and Klett, 1997], with planar crystals like plates dominating between about −10° to −20°C, and columns and spatial crystal types at colder temperatures. Of course, ice crystal orientation also has a strong influence, particularly for horizontally oriented plates, which as mentioned produces an anisotropic lidar scattering medium involving zero depolarization at normal incidence.
 The CALIPSO data considered here are presented in terms of their temperature (in 5°C bins) and latitude dependence in Figure 3for both the nadir (left) and off-nadir measurements. These displays show the averaged day plus nightδ, indicating a steady increasing trend with decreasing temperature within the troposphere. It is again clear that δhave anomalously low values at the warmest temperatures treated here when probed in the nadir. It appears that the effects of widely-fluttering dendrites [Noel and Sassen, 2005], randomly-oriented plates, or both, are manifested at the warmest temperatures even in the off-nadir data.
5. Comparison With Previous Results
 Several extended ground-based polarization lidar studies, mostly from midlatitude stations, have demonstrated that cirrus cloudδ tend to increase with increasing height/decreasing temperature [Sassen and Benson, 2001]. As a matter of fact, most single time-height images of deep cirrus cloud systems display this effect. Differences in previous temperature trends are also evident between zenith and off-zenith datasets due to the effects of oriented planar crystals in the expected −10° to −20°C temperature interval. Nonetheless, differences in the magnitude of the basic depolarization trend are readily apparent in the results from different geographical locations/latitudes, such that the question of basic cirrus cloud depolarization, versus lidar systematic errors, remained until recently uncertain.
 CALIPSO depolarization data now provide the opportunity to examine the global distribution of ice cloud δ using a single lidar system. In our earlier study [Sassen and Zhu, 2009], we examined a broader sample of ice clouds that included optically thin clouds detected after CALIPSO signal averaging of up to 80 km. The consequences on the results are that the day versus night differences in cloud detection/frequencies are exaggerated at night with respect to the current approach, and importantly, depolarization is biased toward lower values at night because of the contributions of molecular backscattering to the total air plus cloud signal (see equation (1)). Since the pure molecular atmosphere produces δ ≈ 0.02, this Rayleigh scattering lowers the depolarization in clouds with weak backscattering.
 Nonetheless, it is apparent that the main depolarization feature noted here, a steady δincrease with increasing height/decreasing temperature, is consistent with earlier ground-based and CALIPSO polarization lidar analyses. The current ∼0.05 off-nadir minus nadir average difference is about twice as large as that reported previously inSassen and Zhu .
 Unlike the model treatment of the radiative effects of water clouds containing spherical cloud droplets, ice crystal clouds like cirrus present many uncertainties. The major added complexity is related to the diverse shapes of the crystals present, although obviously additional factors such as the vertical distribution of the size distribution and ice water content come into play. The polarization properties of laser backscattering can be considered as an analog of natural light scattering in the atmosphere, because δ are sensitive to the exact particle shape and orientation.
 The data presented here deal mainly with what would be identified by surface weather observers as cirrus and altostratus clouds, although PSC are included because according to depolarization, they often appear to have similar contents as other ice clouds [Sassen and Zhu, 2009], and modeled tropopause heights over the polar regions may not be reliable. It is clear that the effects of oriented plate crystals on ice cloud CALIPSO laser depolarization is significant within the expected crystal growth regime of ∼−10° to −30°C (Figure 3). Plate effects also tend to be more important in high latitude ice clouds (Figures 1 and 2).
 In terms of the relative number of oriented plates versus those poorly or randomly oriented, an estimate can be derived from the following equation suggested by Sassen and Benson  based on laboratory experiments:
where δis the measured off-nadir depolarization ratio,δi the nadir value, and N and β the number concentration and backscatter coefficient of horizontally (h) and randomly (r) oriented plates. Using the day plus night average δfor off-nadir (0.318) and nadir (0.365) measurements inTable 1, a ratio of non- to oriented- plates of roughly 2,500/1.0 is found fromequation (2)adding all temperatures. This is not a large relative number of oriented plates, but it must be kept in mind that their impact on radiation transfer is highly anisotropic and largely concentrated in certain latitudes and height/temperature ranges. Although the two CALIPSO viewing angles may not be ideal to assess orientated plate effects, the 0.3 and 3.0° nadir angles should yield results representative of the binary lidar outcome according to ground-based scanning lidar research [Noel and Sassen, 2005].
 The fundamental result of the observed δ-temperature dependence suggests that improved cirrus cloud radiative transfer models could follow by creating a simplified vertical gradient in ice crystal shape based on theδ trend. The use of a vertically homogeneous ice crystal shape model seems especially inappropriate. Although the tendency for the horizontal orientation of a portion of the plates at relatively warm temperatures is an anisotropic complication, even a model of a gradual change from plates to columns with height should be an improvement.
 The geographical/latitudinal differences in δ (Figures 1 and 2) are also quite interesting. These data imply that higher latitudes have lower δ and relatively more oriented plates, while certain continental areas have higher δ, especially in the tropics/subtropics. These differences must reflect the different ice particle shapes that depend on the cirrus cloud formation mechanism (e.g., convective-anvil, orographic, synoptic, etc.), or more specifically on the basic cloud-particle forming aerosol available for crystal formation and the microphysical effects of typical cloud updraft velocities (Sassen, 2002). CALIPSO lidar depolarization data will continue to provide a rich source of information on cloud and aerosol microphysics.
 This research has been support by NSF grant ATM-0645644, NASA grant NNX0A056G, and JPL contract NAS-7-1407.
 The Editor thanks two anonymous reviewers for assistance evaluating this paper.