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 Multi-sensor cloud height observations are investigated and compared in terms of vertical and latitudinal distributions of monthly mean cloud occurrence frequency (COF). Although this study emphasizes the standard Multiangle Imaging SpectroRadiometer (MISR) cloud top height (CTH) retrieval, the strengths and weakness among different passive and active remote sensing techniques with respect to cloud detection and height assessment are also discussed. The standard MISR CTH retrieval is less sensitive to high thin cirrus than the Atmospheric Infrared Sounder (AIRS) and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), but MISR provides more accurate CTH retrievals in the middle and lower troposphere compared with other passive sensors, especially for clouds in the planetary boundary layer.
 Cloud feedbacks are recognized as a primary source of uncertainty in climate models and predictions [Randall et al., 2007]. Characterizing vertical distributions of clouds is critical for understanding physical processes of the feedbacks associated with different types of clouds, but reliable global observations remain lacking, which motivated the recent missions for the CloudSat [Stephens et al., 2002] and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellites [Winker et al., 2003]. Passive satellite sensors in the past have not been able to resolve cloud vertical structures with the resolution needed; but their abilities continue to improve with new, advanced observing techniques, such as stereoscopic viewing (Multiangle Imaging SpectroRadiometer, or MISR) [Diner et al., 2005] and hyper-spectral infrared (IR) spectroscopy (Atmospheric Infrared Sounder, or AIRS) [Chahine et al., 2006]. Longer temporal record, wider swath/sampling and broader spectral range make passive observations irreplaceable and complementary to active measurements. As algorithms mature and the liquid cloud property retrieval is further quantified [e.g., L'Ecuyer et al. 2006], the value of vertically-resolved cloud distributions and inter-annual variations of global cloud amount, height and frequency increases.
 In this study, differences and relationships of vertical distributions of cloud occurrence frequency (COF) from various passive and active sensors are investigated, with the primary emphasis on the MISR stereo cloud top height (CTH) retrieval from the standard algorithm [Moroney et al. 2002; Muller et al., 2002]. The month of January 2008 is used for the intercomparative study. In addition to MISR and AIRS, two other passive sensors are also included: the Moderate Resolution Imaging Spectroradiometer (MODIS) (IR and visible bands) for cloud top pressure (CTP) and the Ozone Monitoring Instrument (OMI) (UV O2-O2) for effective cloud pressure. For active sensors, CTH and multi-layer clouds from CALIPSO and CloudSat are analyzed to evaluate the statistics obtained from the passive sensors.
 To characterize vertical distributions of COF, we define COF(z) at each height as cloud fraction or occurrence probability in a unit volume. For single layer clouds, the sum of the clear-sky probability and the vertically integrated COF(z), which only has a single value in the situation, will be unity. However, in the case of multi-layer clouds, COF(z) will have multiple values, so the sum of the clear sky and the integrated COF(z) will exceed unity. The COF(z) has unit of % per km, whereas the traditional column-integrated COF is in percent. It is challenging for passive techniques to measure volume COF accurately because they must determine both areal cloud fraction and cloud height correctly. This study aims to highlight and better understand differences of the COF(z) among several passive sensors.
2. MISR Stereo CTH
 MISR retrieves CTH with a stereophotogrammetric technique using its three near-nadir cameras (0°, ±26°) [Moroney et al., 2002], based on the geometric relation between CTH and the parallax in the consecutive stereoscopic views. This technique has two main advantages over those relying on thermal contrast for cloud detection and height retrieval. First, it does not require knowledge of atmospheric thermal structure. For example, at mid-to-high latitudes and in the boundary layer where temperature vertical lapse rates are frequently weak, isothermal conditions or temperature inversions are often present. In these circumstances the thermal-contrast-based techniques may have difficulty in detecting clouds from the background and may assign cloud heights incorrectly [Garay et al., 2008]. Second, MISR CTH retrievals are less sensitive to absolute radiometric calibration error, as in all passive visible sensors, since stereo matching technique deals with position of radiance patterns, not intensity [Muller et al., 2002]. Simply matching these patterns to determine their locations, which yields CTH and cloud motion, does not require very accurate radiometric calibration. This makes MISR observations more attractive for detecting cloud trends/variations than the techniques that apply cloud detection thresholds to absolute radiances. In those cases, the effects of solar activity (in visible wavelengths) and CO2 increase (in IR wavelengths) must be accurately accounted for [e.g., Kahn et al. 2008].
 The MISR CTH used in this study is the “StereoHeight_WithoutWinds” product from the latest version (F08-0017) of the standard Level 2 (swath) TC_STEREO file, which is derived from the red (672 nm) band assuming no winds. The algorithm searches and matches patterns at the 275-m pixel level that have sufficient radiance contrasts, and reports heights of these features, or CTH, at 1.1 km resolution [Moroney et al., 2002: Muller et al., 2002]. Designed to process all the red-band data obtained globally, the pattern matching is computationally efficient with integer pixel quantization in pattern position, which is equivalent to ∼560 m in height precision. Clouds are reported if the pattern height is greater than the terrain height + one standard deviation of the local terrain height + 560 m. The standard deviation of MISR 1.1-km terrain height is computed from higher-resolution terrain data, which can vary from sub-meter over water to ∼400 m in choppy mountainous areas. Lower clouds may be detected, but their height makes them indistinguishable from the surface based on the accuracy limits of the retrieval.
 The effective MISR swath is ∼380 km from the 705 km Terra orbit. Because sun-glint effects over water can cause noisier CTH retrievals on the east side of the swath due to the 10:30 am sun-synchronous orbit, only ∼200 km of the west side of the swath is used.
 We did not use the “StereoHeight_BestWinds” product in the Level 2 file, which is derived from a simultaneous cloud height and wind retrieval [Horváth and Davies, 2001; Davies et al., 2007], because the sampling of the joint retrievals is poor and quite selective with preference to certain types of clouds. Instead, we chose to correct the “StereoHeight_WithoutWinds” using the daily 00Z GEOS-5.1 (Goddard Earth Observing System Model, Version 5.1) analysis winds at a 0.67° × 0.5° longitude-latitude resolution. Only the wind in the along-track direction was required because this wind component affects the parallax calculation and the subsequent CTH retrieval. In the MISR retrieval, a 1 m/s along-track wind corresponds to a 94 m difference in height. Projecting the analysis winds onto the MISR track, the wind-induced height shift is corrected for each CTH retrieval.
Figure 1 shows the COF(z) statistics of MISR CTH with and without the wind correction. The wind correction in MISR COF(z) is evident, especially at mid and high latitudes where the along-track wind speeds are strong and the corrected vertical distributions are shifted to a lower altitude in the upper troposphere (UT). There is a slight decrease in these tropical UT peaks with the wind correction. The wind-corrected COF(z) in the planetary boundary layer (PBL) peaks at about the same altitude across all latitudes but shows a higher probability after the wind correction. The PBL clouds in the Southern Hemisphere (SH) exhibit a higher COF(z) than those in the Northern Hemisphere (NH), consistent with spaceborne lidar observations [Berthier et al., 2008]. For January and August 2008, the altitudes (PBL top, ∼5 km and ∼13 km) of the tropical trimodal peaks [Johnson et al., 1999] are impacted little by the wind correction.
3. Other Data Sets
 The AIRS data used are obtained from the Version 5 (V5) AIRS L2 operational retrieval, which employs a two-cloud-layer model that fits 58 channels in the 655–812 cm−11 (12.3–15.3 μm) region for each footprint individually. The retrieval quantities are effective cloud fraction (fA), which is the multiplication of spatial cloud fraction and cloud emissivity [Susskind et al., 2006; Kahn et al., 2007], CTP and cloud top temperature, both reported at the AMSU (Advanced Microwave Sounding Unit) resolution that varies from ∼40 km at nadir to ∼100 km at the edge of swath. The AIRS swath (∼1400 km) is wide enough to cover most of the globe twice daily. For the COF(z) calculation, the effective cloud fraction fA, as defined by Kahn et al. , is averaged into 1-km height bins using the retrieved CTP that is converted to CTH. Both daytime and nighttime observations are used in computing monthly cloud statistics.
 The MODIS CTP product used is derived from the Collection 5 Level 2 MOD06 cloud property retrieval [Platnick et al., 2003] in which cloud-top pressure and temperature are reported at 5-km horizontal resolution. MODIS has a 0.25–1.0 km pixel resolution at nadir depending on the channel, and a 2330 km swath. For cloud detection, the MODIS uses IR and visible channel thresholds for cloud fraction retrieval [Ackerman et al., 1998; Frey et al., 2008] and IR channels for CTP retrieval [Menzel et al., 2008]. In this analysis the Aqua MODIS data are used and the zonal mean includes both daytime and nighttime measurements.
 The OMI data used here are from the version 3 OMCLDO2 product, which includes cloud pressure and effective cloud fraction, retrieved from the daytime O2-O2 absorption band at 477 nm [Acarreta et al., 2004; Stammes et al., 2008]. The cloud pressures from the O2-O2 absorption (OMCLDO2) and rotational Raman scattering (OMCLDZRR) overall exhibit similar morphology with the OMCLDZRR pressure being slightly lower (i.e., higher in cloud height). Both products are known to be systematically lower than the physical CTH as observed by lidar and thermal IR sensors [Sneep et al., 2008; Vasilkov et al., 2008]. The OMI nadir resolution is 13 × 24 km2 with a swath of ∼2600 km and daily global coverage.
 The CALIPSO data used are the version 2.01 05kmCLay product (M. A. Vaughan et al., Fully automated detection of cloud and aerosol layers in the CALIPSO lidar measurements, submitted to Journal of Atmospheric and Oceanic Technology, 2009) that reports up to 10 cloud layers (characterized by pairs of top and base heights) with 5 km horizontal resolution and 60 m vertical resolution. Statistics of cloud top and multi-layer occurrences are analyzed separately, in which layer thickness is factored into the volume COF calculation for the multi-layer statistics. Vertically overlapped portions of the version 2.01 cloud layers are counted only once to avoid double accounting; and only daytime CALIPSO data are used because of significant different nighttime detection thresholds.
 The CloudSat COF is computed from the R04 Level 1b data. A threshold of −26 dBZ is applied for cloud detection in a single reflectivity profile (at 1.4 × 1.8 km2 resolution), which is ∼3σ of the measurement precision as estimated by Tanelli et al.  and Wu et al. . As for CALIPSO, CloudSat cloud tops and multi-layers are analyzed separately to yield the statistics comparable to the CTH or CTP observed by passive sensors. Both day and night data are used in this study. To avoid surface contamination on cloud detection, only the radar reflectivities at heights 750 m above the terrain altitude are considered.
4. Results and Discussions
Figure 2 shows monthly zonal mean COF(z) as observed by MISR, AIRS, MODIS, OMI, CALIPSO, and CloudSat in January 2008. All COFs are reported as % per km. The most significant differences in the observed COF(z) are found primarily in four regions: tropical upper troposphere (TUT), tropical mid-troposphere (TMT), the PBL, and high latitudes.
 In the TUT, the COF(z) of MISR CTH peaks at 12–13 km, which is similar to MODIS but lower than COF(z) from AIRS, CALIPSO and CloudSat cloud top statistics. It is known that the MISR three-camera stereo technique tends to penetrate cirrus decks (especially in vast, homogenous layer cases) to match cloud patterns with better contrast clouds, or other underneath features with optical depth >0.1 [Marchand et al., 2007]. Thus, in the tropics the MISR CTH retrieval is likely to neglect most of high cirrus clouds. Among the sensors studied here, the CALIPSO lidar is most sensitive to cirrus layers and has the best vertical resolution, which could explain its highest COF(z) near the tropopause relative to all the other observations. In addition, the daytime COF(z) is found to be higher than the nighttime in the upper troposphere [Liu et al., 2008], which will make this daytime-only COF(z) statistic higher than those averaged over day and night. The CloudSat cloud top statistics, consistent with AIRS, exhibit a peak at ∼13–14 km. This is still slightly lower than CALIPSO and shows that CTH derived from thermal IR radiances frequently represent the middle or lower portions of cirrus layers [Weisz et al., 2007; Holz et al., 2008]. However, the CloudSat multi-layer statistics reveal cloud layers frequently occurring below cloud tops, which are obscured in IR and visible techniques. The OMI UV technique appears to have weak sensitivity to high ice clouds, showing no upper-tropospheric peak in COF(z). The OMI cloud retrieval tends to see through clouds with low optical UV/VIS optical depth and pick thicker clouds underneath. The overall OMI COF(z) distribution resembles the statistics of the obscured regions where the CALIPSO signals are completely attenuated (not shown).
 In the TMT, a COF(z) peak is evident at ∼5 km in MISR, OMI, CALIPSO, and CloudSat cloud top observations. This peak is associated with a narrow COF(z) enhancement at 2–5 km altitudes near ∼5°N, the latitude of ITCZ (inter-tropical convergence zone) in January [Johnson et al., 1999]. The AIRS data reveal a hint of this mid-tropospheric feature but lack sufficient vertical resolution to distinguish it from other low clouds. There is no indication of such a peak in the MODIS COF(z).
 For the PBL clouds, MISR and CALIPSO observations show a similar distribution with a peak at ∼1 km in altitude and higher COF(z) in the Southern Hemisphere. AIRS and MODIS have difficulties assigning an accurate pressure to the PBL clouds, in part because inversion layers in the PBL confuse the thermal IR techniques [e.g., Naud et al., 2005; Garay et al., 2008; Holz et al., 2008]. CloudSat observes the tops of PBL clouds but these liquid clouds produce weaker echoes than ice clouds, and have strong attenuation to the radar signal. With interference from surface echoes, it is challenging for CloudSat to resolve PBL clouds. OMI places most of its detected clouds in the lower troposphere except in the Tropics, as expected for its sensitivity to middle cloud pressure and for its retrieval of effective cloud fraction on a relatively-larger footprint. Further investigation is required to understand whether they are truly PBL clouds and the sensitivity of OMI to ice/liquid clouds.
 Finally, at high latitudes the COF(z) from passive sensors largely disagree with each other, particularly for low clouds, and all are different from the active observations (as the “truth” in this case). Both cloud detection and height assignment are problematic for the passive techniques. Lack of contrast over snow and icy surfaces poses great challenges for cloud detection; and furthermore, atmospheric thermal structures create additional difficulty for retrieving CTP. With the stereo technique, MISR can mitigate the second problem but further investigation is required to understand how many CTH retrievals are abandoned and why.
5. Summary and Conclusions
 Vertical and latitudinal distributions of monthly COF(z), which is a vertically distributed volume cloud occurrence frequency, were studied and compared among MISR, AIRS, MODIS, OMI, CALIPSO, and CloudSat observations in January 2008. Although this study emphasizes MISR stereo CTH retrievals, the strengths and weakness of different passive techniques were also discussed. We found that the MISR three-camera retrieval is less sensitive to high thin cirrus than AIRS and CALIPSO, but provides more accurate CTH in the middle and lower troposphere than other passive sensors, which is consistent with the finding in a MISR-MODIS study over the subtropical Pacific [Garay et al., 2008]. Especially in the PBL, the MISR stereo retrievals for CTH have comparable quality to CALIPSO observations, making it unique compared to other passive techniques in detecting PBL clouds from a 10:30 am equator-crossing orbit. Compared to CALIPSO, MISR's wider swath and longer observing history (since March 2000) provide better statistics for studying PBL clouds and associated processes and spatial/temporal variations of these phenomena. For future MISR algorithm improvements, better precision and accuracy of the CTH retrievals may be achieved with sub-pixel pattern matching (determining location of cloud patterns at a fraction of pixel resolution) or the use of additional off-nadir cameras. The latter will also enhance sensitivity of the MISR CTH retrieval to cirrus.
 This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). We would like to thank J. H. Jiang for providing CALIPSO reading code, and J. Blaisdell, Y. Hu, J. Joiner, R. Kahn, C. Trepte, and D. M. Winker for helpful discussions on AIRS, CALIPSO, MISR, and OMI data. GMAO efforts to provide the GEOS-5.1 analysis and the data processing by the NASA Langley Research Center Atmospheric Sciences Data Center are gratefully acknowledged.