Linear depolarization ratio (δ) data from the summer/winter seasons over the first 2 years of Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite operations in the green (0.532 μm) laser channel are analyzed and interpreted in terms of ice cloud microphysical properties. That is, we use variations in δ as a proxy of cloud formation and environmental conditions that affect ice crystal shape and orientation. The cloud detection algorithm is tuned mainly to cirrus clouds, but also includes polar stratospheric clouds (PSC) and optically thin, low and midlevel ice clouds at high latitudes. As anticipated from ground-based polarization lidar studies, δ increase with increasing height/decreasing temperature, and the effects of horizontally oriented plate crystals in lowing δ are evident by comparing data obtained close to the nadir (0.3°) and off-nadir (3.0°) pointing directions. These differences in δ average 0.01–0.03, although this anisotropic scattering effect is particularly apparent at low altitudes in the mid and high latitudes. Unexpected findings include decreasing δ with increasing latitude, and δ in detected PSC that are usually similar to cirrus clouds. However, δ in PSC are lower in a belt in the lower stratosphere in the Southern Hemisphere and generally lower in the Northern Hemisphere, but higher in lower stratospheric nacreous clouds in both hemispheres. There are also significant differences in the ice cloud δ measured at night and day, but this is assumed to result from factors associated with day/night differences in CALIPSO data collection. Global average δ are 0.34–0.36 for day, and 0.23–0.26 for night.
 Every electromagnetic wave at any instant of time can be characterized by a state of polarization [Swindell, 1975]. This state of polarization involves an instantaneous plane of polarization that can be invariant with time (linearly polarized in some arbitrary direction), or undergoing rotation (circular polarization, or elliptical polarization in the general sense). A state of random polarization can be considered as a jumble of waves doing a near infinite number of their individual things.
 The capricious nature of polarized waves is readily apparent during the scattering of light by hydrometeors in the atmosphere, which tend to have dimensions much larger than the incident (visible) wavelengths. This is the realm of geometrical optics, where Mie theory offers a precise solution to scattering in all directions provided that the scatterer is spherically symmetrical, while approximate theories must be relied on for irregular particles [Liou et al., 2002]. Excluding the forward-scattering diffraction process, which does not depolarize the light in the shadows edge, scattering that involves internal skew rays (i.e., nonnormal to the surface) will alter the polarization state of the scattered light. Reducing the problem to pure backscattering at 180°, the case for lidar, we find that spheres only have raypaths that preserve the incident polarization properties, while according to ray tracing the backscattering from nonspherical particles create depolarization in the backscatter except in the case of normal, or specular, reflections [Liou and Lahore, 1974; Sassen, 1991]. This is important because some ice crystals such as plates display large flat faces that are effective in creating nondepolarizing reflections, which also tends to orient them uniformly in space as a result of aerodynamic drag forces, such that backscatter depolarization can depend significantly on the lidar pointing angle [e.g., Platt, 1978; Noel and Sassen, 2005].
 Ray-tracing findings show that when randomly arrayed, the basic ice crystal habits generate different amounts of backscatter depolarization [Takano and Liou, 1995]. The linear depolarization ratio δ is commonly used in the lidar field to quantify changes in the backscattered polarization state, and is defined as the ratio of returned laser energies in the perpendicular to parallel planes of polarization relative to that transmitted. (Note that these two lidar signals can contain contributions from air molecules, aerosols, and clouds, such that the term total linear depolarization ratio is appropriate.) In going from thin hexagonal plates to long column ice crystals, the predicted δ increase from 0.34 to 0.56, suggesting that lidar signals can be used to infer ice crystal shape.
 Since polarization lidars have been around [Schotland et al., 1971], cirrus clouds have been under their scrutiny. As a matter of fact, polarized photons and cirrus cloud particles are an ideal match [Sassen, 1991, 2005a], while the need to better understand high cloud properties for climate studies is well established [e.g., Liou, 1986; Stephens et al., 1990]. Up to recently, much of what we know about the properties of these high clouds has come from extended ground-based polarization lidar studies from various parts of the world. However, the results have not always been in good agreement, which could be attributed either to experimental uncertainties or to valid regional differences in ice crystal shapes caused by the cloud formation processes or local aerosol effects. For example, in the comparison of the temperature dependencies of δ given by Sassen and Benson , although similar trends from midlatitude sites in the Northern and Summer Hemispheres were found, tropical cirrus results differed by up to δ ≈ 0.2. All climatological lidar studies, however, reveal an increasing trend in δ with increasing height/decreasing temperature.
 With the April 2006 launch of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite, however, the situation has changed dramatically, because Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) depolarization data in the green (0.532 um) laser channel are now available globally. The data commenced on 15 June 2006, including measurements collected in both the nadir and off-nadir viewing directions, at a vertical resolution of 60 m in the upper troposphere and with a ground footprint of 333 m [Winker et al., 2007; Hunt et al., 2009]. This unique data set is important because we assert that variations in laser depolarization contain information reflecting the basic cloud microphysical, environmental, and formation processes in ice clouds.
 We have begun the analysis of this extended data set by examining the nature of the surprisingly large δ variations in ice clouds as functions of geographic location, season, height, and day versus night overpass data. CALIPSO and other members of the A-train constellation of satellites fly in a Sun-synchronous 705 km orbit, with repeated 01:30 and 13:30 local mean times for crossing the equator [Stephens et al., 2002]. As of the time of this writing, CALIOP has emitted approximately 1.8 billion laser shots into the Earth's atmosphere.
2. Data Analysis
 The data analysis algorithm uses both CALIPSO Level 1 and 2 cloud data products to calculate suitably averaged, ranged-resolved δ. (Note that the Level 2 depolarization data product involves the vertical integration of the signals through each identified cloud layer [see Cho et al., 2008].) The Level 1 data used here include the attenuated parallel and perpendicular backscatter profiles for each recorded laser shot, and the corresponding temperature profile. To reduce the effects of signal noise on calculating δ, the backscatter data at each height are averaged over 15 consecutive shots. Depending on the height above mean sea level (MSL), this yields height resolutions ranging from 30 to 180 m in our realm of interest: the data resolution is 30 m from the surface to 8.3 km, 60 m from 8.3 to 20.2 km, and 180 m up to 30.1 km MSL. The temperature profiles are similarly averaged. Next, Level 2 data are examined to obtain all identified cloud top and base heights: note that this data product is based on the same 15-shot averages as we apply to Level 1 data. This yields a repeated 5 km long cloud column data product.
 We next decide which of the Level 2 layers are to be included in the analysis based on criteria developed earlier for visually identified cirrus clouds [Sassen, 2002a; Sassen et al., 2008], but also including in the current study polar stratospheric clouds (PSC) and likely some diffuse midlevel ice clouds. The criteria for identifying cirrus and other ice clouds are that they must be transparent to lidar probing (i.e., cloud optical depth <∼3.0–4.0), and have cloud top temperatures colder than −40°C according to Sassen and Campbell . This approximate optical depth limit is determined by searching for a lidar return, below the highest suitable cloud layer, either at the Earths' surface height, or the top of a lower cloud layer that attenuates the laser pulse (and thus is rejected from further analysis). In effect, this avoids the inclusion in our sample of dense ice, water, and mixed phase clouds, which may produce photon multiple scattering depolarization increases [Hu et al., 2006; Cho et al., 2008], and most aerosol layers. The δ are calculated using the integrated backscatter signals at each height within those cloud layers identified in Level 2 data and passing our criteria. The vertical δ profiles are saved along with temperatures and location. Each day of compiled data is gridded into 5.0° latitude by 5.0° longitude bins and then into monthly averaged data files.
 Currently, only selected time intervals have been analyzed using this algorithm. We have chosen the three month periods representing Northern and Southern Hemisphere summers and winters (i.e., JJA and DJF) for both the initial nadir and the subsequent off-nadir viewing periods. Separate analyses are made for day and night CALIPSO observations. The results are presented in terms of global latitude versus longitude plots to show geographical differences, and latitude versus height plots to reveal the effects of cloud height/temperature on laser depolarization, for the first time, on a global scale.
3. Nadir Results
 In Figures 1–6 are presented results for the months of JJA 2006 and 2007, and DJF 2006–2007 when the CALIPSO viewing angle of 0.3° was very close to the nadir direction. (Note that a brief period of off-nadir data collected after 21 August 2007 is excluded from this analysis.) In other words, if horizontally oriented planar ice crystals represented a significant fraction of the total crystals present at any location, δ could be considerably lowered in comparison to those collected a few degrees or more off the nadir (see next section), sometimes even approaching zero [Sassen and Benson, 2001]. Day and night three monthly seasonal averages are given in Figures 1 and 2 (for JJA in both 2006 and 2007) and 4–5 (for DJF in 2006–2007), and the corresponding monthly averaged results for the zonal height distributions in Figures 3 and 6. It is important to note that for the months selected, the data for high latitudes correspond to summer/winter seasonal effects on cloud formation, as is particularly apparent in the varying presence of PSC extending up to 27 km MSL.
 In general, it is clear that the δ derived from CALIOP nadir data are on average significantly higher in tropospheric ice clouds a) during the day compared to night, and b) in the tropics and midlatitudes compared to higher (>∼50°) latitude locales. (The possible effects of errors from signal noise caused by scattered sunlight and other causes will be discussed below.) Moreover, as expected from extended ground-based polarization lidar studies of cirrus clouds, δ tend to increase with increasing height, i.e., with decreasing temperature (Figures 2 and 5). The trend in the night data is similar, but some δ decreases are indicated as the tropical tropopause is approached.
 As for the basic effects of geography on the average δ, which are more readily apparent in the night plots in Figures 1 and 4, it appears that the highest δ (>∼0.25 at night) are generally confined to those areas in the tropics and subtropics that have the highest global frequencies of cirrus clouds in the corresponding months [see Sassen et al., 2008, Figure 3], and which are indicated to generally be associated with deep convective clouds [Sassen et al., 2009]. These areas include for DJF the Amazon Basin, southern Africa, the Malaysian region, and the central Pacific Ocean, and for JJA central America, the Indian Ocean Monsoon region, and the western Pacific Ocean. The strong depolarization generated in JJA over southern South America and its eastern coast, on the other hand, does not correspond to an area of significant cirrus cloud production. (It does correspond, however, to the location of the South Atlantic Anomaly, which produces a major increase in the green channel dark noise that may affect δ values [Hunt et al., 2009]).
 The availability of results from two consecutive JJA seasons allows for the evaluation of interannual variations of ice cloud formation processes that are reflected by changes in lidar depolarization. In many respects the findings from the two seasons are surprisingly consistent. In Figure 1 (top), although the uniform drop in δ at a latitude of ∼+60° seems unrealistic, many details of the day and night δ variations are quite similar for the two years, such as the midlatitude regions showing lower depolarization and high latitude regions showing higher depolarization. The patterns in the latitude versus height displays in Figures 2 and 3 are also very similar, indicating a degree of year-to-year repeatability in both tropospheric and PSC ice cloud conditions. Apart from a few departures, like the July 2006 apparent aerosol peak at +60–65° latitude extending above the tropospheric cirrus, note the persistence of the two δ maxima in the upper troposphere at about +10° and −40° latitudes, and the similar PSC properties.
 In comparison, the plots for the 2007–2008 DJF nadir data reveal only some subtle seasonal differences in the geographic pattern of the average δ for tropospheric ice clouds (Figure 4). The latitude versus height displays in Figures 5 and 6 show stronger depolarization extending to higher latitudes in the winter hemisphere, and a tongue of low δ values in December extending into southern midlatitudes in the cloud top region (night only). PSC are nearly absent at this time in the Northern Hemisphere, but not entirely (see section 4).
 There are interesting δ variations with height and geographical location at high latitudes in connection with PSC, which are particularly evident in the one month averaged latitude-height displays (Figures 3 and 6). It is likely that Type II PSC, which have cirrus-like properties [Palm et al., 2005], will be mainly detected, as indicated by the similar maximum lidar-derived PSC heights of ∼27 km MSL given by Campbell and Sassen . Over Antarctica, a region of δ ≈ 0.1 is generally present in the lower stratosphere before δ increase in the higher-altitude PSC, indicating a change in stratospheric particle shape, size or orientation with height. Moreover, there is evidence for relatively high δ of 0.45–0.55 associated with what we interpret as lower stratospheric nacreous clouds in both hemispheres. These regions are found in the night (i.e., winter) height-latitude displays between ∼±65–75° latitude and 12–14 km height, particularly in the months of June (Figure 3a, top right) and January (Figure 6, right middle). What suggests that they are mountain-wave induced nacreous clouds is their association with mountainous regions such as the Antarctic Peninsula and Victoria Land, and Scandinavia and Greenland. Relatively strong depolarization is suggested in the vertically averaged δ within these areas in Figures 1 and 4, but similar plots giving data only for >12 km MSL (not shown) more clearly indicate their associations with elevated terrain. Interestingly, a similar occurrence of DJF-season ‘cirrus' clouds is present in the Sassen et al.  climatological study, but it is now apparent they these clouds generate unusually high δ at heights not far above the tropopause. The night height-latitude display in Figure 6 for December also shows the presence of a thin Northern Hemisphere PSC at a height of 19.5 km MSL.
4. Off-Nadir Results
 Operations after 28 November 2007 (and to date) have been conducted with the CALIOP system pointed 3.0° off the nadir direction in order to study the effects of horizontally oriented ice crystals on depolarization and any errors associated with the determination of cloud optical depth from the reflection-enhanced signal strengths. A viewing angle of 3.0° off the vertical direction is sufficient to greatly reduce the effects of specular reflections on lidar δ, except perhaps in the case of the larger flutter angles experienced by dendritic ice crystals at relatively warm temperatures [Noel and Sassen, 2005]. Thus, presented in Figures 7–12 are the results of the analyses analogous to Figures 1–6.
 A general comparison of the previous nadir to these off-nadir results shows that in every case the latter δ values are somewhat higher. The off-nadir latitude versus longitude displays of vertically averaged δ do not appear to be conspicuously higher, but the height-latitude displays show more dramatic differences. For both day and night data, areas with δ lower than ∼0.15 are now nearly absent. These areas occurred previously mostly along the base of the ice clouds (i.e., at the warmest temperatures), and the off-nadir cloud ‘bases' as a result are somewhat higher. In other words, these midlevel to low-level tropospheric ice clouds composed of oriented planar crystals appear to be optically thin, with an enhanced probability of detection when nadir data is collected. Given by Sassen [2002b, 2005b] are examples of the sensing by polarization lidar of similar thin ice clouds at relatively low altitudes (for cirrus) at both mid and high latitudes, which are often if not typically composed of oriented plate crystals. Ice crystal nucleation in many cases may involve the deposition mode rather than the homogeneous freezing of haze particles typical of higher cirrus clouds.
 Other regions where oriented plate crystal returns are now absent or greatly reduced are at high altitudes in the southern midlatitudes (Figure 6, top right, versus Figure 9), which appear to extend into the lower stratosphere only at night, and at high latitudes in general. Even for the off-nadir data, however, it is clear that cirrus cloud δ are lower at high latitudes in both hemispheres, winter and summer. This is a consistent trend that shows that lidar depolarization in ice clouds tends to not only increase with height, but also to decrease with latitude. On the other hand, δ in the upper tropical atmosphere are similarly high in the nadir and off-nadir plots (compare Figures 2 and 8 and Figures 5 and 11), indicating that oriented plate crystals are not as common at these temperatures and locales.
 Also note that a measure of interannual variability in the presence of PSC is already indicated by the data. Comparing Figures 3 and 9 and Figures 6 and 12 reveals that although PSC are similarly abundant in the 2006, 2007, and 2008 Southern Hemisphere winters, it is only the 2007–2008 winter that shows evidence for significant Northern Hemisphere PSC. This strong Northern Hemispheric PSC occurrence is surprising, perhaps reflecting the dearth of lidar remote sensing sites in the vast Arctic region. PSC depolarization appears in Figure 8 to be somewhat higher in comparison to the nadir data, but interannual variations could be responsible for this. Note, however, that the band of relatively low δ from ∼12–17 km MSL just above the tropopause does not appear to be due to oriented plates, but to different crystal shapes, perhaps as a result of evaporation effects on particle shape during sedimentation [Nelson, 1998], or to different particle compositions in these lower PSC.
 To quantify the regional and global differences in ice cloud depolarization described above, Tables 1 and 2 give the zonal and global averaged δ for the day, night, nadir, and off-nadir data sets, for both the JJA and DJF seasons, respectively. In terms of the global δ averages, it is apparent that day minus night differences are close to 0.11 regardless of season or CALIOP pointing direction. Global averages range from 0.34 to 0.36 for day, and 0.23 to 0.26 for night data. As discussed below, these day/night differences significantly exceed expectations based on ground-based polarization lidar studies. Differences between off-nadir and nadir δ range from 0.01 to 0.03, which is generally consistent with the results given by Sassen and Benson , indicating that on average only a small amount of oriented plates are mixed in with randomly arrayed ice crystals. (Recall, however, that oriented plate crystals noticeably affect δ and cloud boundaries at low altitudes and high latitudes.) As far as latitudinal differences are concerned, off-nadir minus nadir δ are only ∼0.01–0.02 in the tropics, but increase to 0.04–0.05 at higher latitudes, suggesting that plate crystals are less common in the tropics, perhaps due to the effects of deep convection or the colder temperatures on ice crystal shape, size, and orientation.
Table 1. Vertically and Zonally Averaged δ Within the Indicated Latitude Belts for Various CALIPSO Polarization Lidar Operations for the Months of June–July–Augusta
Nadir data were collected in 2006 (2007), and off-nadir data were collected in 2008.
∼−85 to −60°
−60 to −30°
−30 to −15°
−15 to +15°
+15 to +30°
+30 to + 60°
+60 to ∼+85°
Table 2. Vertically and Zonally Averaged δ Within the Indicated Latitude Belts for Various CALIPSO Polarization Lidar Operations for the Months of December–January–Februarya
Nadir in 2007 and off-nadir in 2008.
∼−85 to −60°
−60 to −30°
−30 to −15°
−15 to +15°
+15 to +30°
+30 to +60°
+60 to ∼+85°
 Now more than two years into the CALIPSO mission, sufficient data has accumulated to begin tackling some climatological aspects of this unique global data set, long awaited by polarization lidar researchers. The goal of this initial study has been to explore the ice cloud microphysical properties of the global CALIOP depolarization data set. We summarize our main findings below:
 1. Depolarization in tropospheric ice clouds tends to increase with increasing height/decreasing temperature, as expected from various ground-based lidar studies.
 2. Depolarization in tropospheric ice clouds tends to decrease with increasing latitude, an unexpected finding.
 3. Depolarization in the PSC detected in the Southern Hemisphere is similar to tropospheric ice clouds, except it is lower in a band in the lower stratosphere. PSC occur less extensively in the Northern Hemisphere, and also seem to generate lower δ.
 4. The depolarization decreases caused by sampling horizontally oriented ice plates during nadir observations are less in the high tropical atmosphere compared to mid and high latitudes at low altitudes. Global averages show only a 0.01–0.03 increase in δ in the off-nadir data.
 5. Relatively strong depolarization seems to be associated with occasional lower stratospheric (nacreous) PSC in both hemispheres in regions where orographic effects are to be expected.
 6. There are significant (δ ≈ 0.11) average differences between day and night data, which are inconsistent with earlier ground-based data. Average global δ values are 0.34–0.36 for day, and 0.23–0.26 for night.
 Unfortunately, the last finding indicates the presence of artifacts in the data set related to the effects of background signals from scattered sunlight in the green laser channel. Because of the vastly different background signal noise levels between day and night, it was recognized in the design of CALIPSO that on-board signal processing was needed to adjust the lidar receivers accordingly, as well as to reduce the backscatter data download rate [Hunt et al., 2009]. In addition to the day and night receiver channel sensitivity selections, the mean background signal during daytime is monitored using signals measured from the upper atmosphere, where backscattered signals should be negligible, and subtracted electronically. Low and high gain digitizers are used for each channel, and tests performed to determine if signals are saturated at full scale. The abrupt δ changes often apparent at ∼+60° latitude are considered to be an artifact of day versus night noise and gain selection effects (W. H. Hunt, personal communication, 2009). Interestingly, depolarization seems elevated near the location of the South Atlantic Anomaly, which produces a significant increase in the green channel dark noise.
 The evidence from extended ground-based polarization lidar research clearly contradicts the strength of the diurnal depolarization differences noted here. The mean δ from ruby (0.694 μm) lidar research at Salt Lake City, Utah (40° 49′ 00″ N, 111° 49′ 38″ W) was 0.33 for zenith measurements [Sassen and Benson, 2001]. Thus, the daytime CALIPSO data seem in compliance or slightly elevated, while those from the night are too low by about 0.10 (see Tables 1 and 2). More importantly, an examination of the mean diurnal δ variations from the same lidar data set [Sassen et al., 2003] found only a 0.05 maximum difference between day and night values, with the minimum corresponding to a +45° solar elevation angle (i.e., opposite in solar phase to that noted here). The total day versus night difference in δ averaged only 0.02.
 On the other hand, because CALIPSO measures the total linear depolarization ratio at a 0.532 μm wavelength, molecular scattering effects on depolarization can be expected to lower nighttime δ to some degree. This is because optically thin ice clouds with weak lidar signals will be detected preferentially during night, and it is these clouds that will display lower δ due to the near-zero δ generated by the molecular backscattering component. Although Sassen et al.  found only a 3.1% difference in the global average frequency of occurrence of cirrus clouds in day and night CALIPSO data, we find that in our sample the mean ice cloud base heights (not shown) are 0.5–1.0 km lower at night, especially at midlatitudes. Thus, those cloud regions that tend to show the lowest δ (see, e.g., Figures 3 and 12) are excluded from the daytime data set. Interestingly, mean cloud top heights are much more similar for day and night, differing by a few hundred meters in the tropics and subtropics. These findings reflect the fact that typical cirrus clouds display relatively strong signals at cloud top, where they are generated, but the signals generally fade away as cloud base is approached and molecular backscattering is enhanced [Sassen, 2002a]. We conclude that further research is needed to better understand the diurnal differences in the CALIPSO δ values.
 Despite these initial uncertainties, the global trends in δ must primarily reflect real cloud microphysical processes that affect ice crystal shape and orientation [Sassen, 1991]. For example, the depolarization decrease noted with increasing latitude may indicate ice cloud microphysical changes related to the warmer tropospheric temperatures generally experienced at high latitudes, and since these clouds are nearer to the Earth's surface, differences in the nucleation mechanisms of the ice particles. That is, the aerosol particles derived from the surface of the Earth that serve as ice nuclei will likely change with height [Sassen, 2005b], while the effects of deep convection, more prevalent in the tropics, could similarly have basic impacts on ice crystal shape and orientation. The fact that some of the highest depolarization found here is associated with apparent lower stratospheric polar nacreous clouds could reflect the effects of relatively strong orographic updrafts, which would modulate ice crystal concentration, size, and shape. It is also surprising that the boreal winter of 2007–2008 hosted a relatively large amount of PSC, a finding that may be due to a lack of Arctic lidar observing sites. These results suggest that additional CALIPSO depolarization studies will shed light on other basic ice cloud processes such as the impact of orographically induced cirrus, and the direct (contrail) and indirect effects of aircraft emissions on cirrus cloud content.
 In conclusion, this global lidar depolarization data set is an exciting development that will hopefully stimulate increased cloud microphysical/lidar research and further the likelihood of new, more advanced lidar satellite development.
 This research has been supported by NASA grant NNX08A056G (CALIPSO) and by NSF grant ATM-0630506. The authors thank the members of the CALIPSO science team, and especially W. H. Hunt and D. M. Winker for helpful discussions.