We developed a cloud mask scheme that combines measurements from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellites. First, we developed a cloud mask scheme for CALIPSO using a threshold of the attenuated total backscattering coefficient and a spatial continuity test. We then developed a combined CloudSat-CALIPSO cloud mask. These cloud masks were applied to 3 months of data from September to November 2006, and the vertical distributions of zonal mean cloud fractions and cloud coverage were analyzed. We also examined the standard vertical feature mask (VFM) cloud scheme. The VFM occasionally made false detections because of its horizontal averaging procedure and seemed to misclassify noise or aerosols as clouds. In addition, the VFM appeared to significantly overestimate low-level clouds. Below 2 km, the cloud fraction differed by as much as 25% between the VFM and our combined scheme. We also compared the zonal mean cloud coverage for the topmost layer detected by the sensors using our CALIPSO scheme, the VFM, our combined CloudSat-CALIPSO scheme, and the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) results. For low-level clouds (>680 hPa), the MODIS result was larger than that of our CloudSat-CALIPSO scheme, and results from the VFM and our CALIPSO scheme differed by as much as 15%. The CALIPSO, CloudSat-CALIPSO, and MODIS results were similar for total cloud coverage, but the VFM result was different. Because of possible misclassification at low levels, the VFM showed the largest cloud coverage in middle and low latitudes.
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 Clouds profoundly regulate the energy budget of the Earth [Ramanathan et al., 1989; Rossow and Lacis, 1990; Wielicki et al., 1995]. They cool the Earth by reflecting sunlight back to space while concurrently warming the Earth by absorbing and reemitting thermal radiation emitted by the surface and atmosphere. Clouds also contribute to the three phases of the atmospheric hydrological cycle; condensing water vapor and forming precipitation with latent heat release [Stephens, 2005].
 To overcome this situation, the CloudSat satellite with millimeter-wavelength radar and the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite with two-wavelength backscattering lidar were launched on 28 April 2006. Both satellites were inserted into nearly identical orbits ∼1 min behind the Aqua satellite and are part of the A-train constellation of satellites [Stephens et al., 2002]. An observational strategy for synergistic use of the vertically resolved clouds and aerosol data obtained by these satellites over the whole globe should help us to constrain and improve climate models and better understand our climate system.
 Distinguishing clouds from other features such as noise and aerosols is the first step in studying clouds using CloudSat cloud radar and CALIPSO lidar data. The CloudSat project releases a “cloud mask” that identifies the locations of signal bins that are significantly different from noise and determines the probability of hydrometeors [Marchand et al., 2008]. On the other hand, the “vertical feature mask” (VFM) developed by the CALIPSO team identifies “features” by reference to any boundaries of enhanced signal by averaging the horizontal resolution; the features are then categorized as cloud, aerosol, or totally attenuated [Vaughan et al., 2005] (available at http://www-calipso.larc.nasa.gov/resources/project_documentation.php). However, the VFM has been found to occasionally make false detections through its horizontal averaging procedure and may also misclassify noise or aerosols as cloud (and vice versa), as noted by Marchand et al.  and Holz et al. .
 Cloud radar can penetrate optically thick clouds in which lidar cannot detect the cloud bottom. In contrast, compared to lidar, radar has less sensitivity to small particles such as subvisible cirrus (SVC) or shallow water droplets because the nature of Rayleigh scattering depends on the sixth power of the particle diameter. Therefore, the combined use of radar and lidar observations is effective for minimizing the respective cloud detection deficiencies of each technology. Recently, Mace et al.  analyzed global hydrometeor distribution by combining the CloudSat cloud mask and the CloudSat gridded VFM. However, several issues stemming from the VFM may have affected their results.
 In this study, we first developed a new cloud mask scheme for CALIPSO, using a threshold of the attenuated total backscattering coefficient and a spatial continuity test. The former criterion was originally developed for the ground-based lidar system described by Okamoto et al.  for the midlatitudes and was further tested in the tropical western Pacific by Okamoto et al. . Next, we developed a combined CloudSat-CALIPSO cloud mask. We applied these cloud mask schemes to 3 months of data from September to November 2006 and analyzed the resulting vertical distributions of zonal mean cloud fractions and cloud coverage. We also compared results from our cloud masks, the VFM, and the MODIS.
Section 2 describes the CloudSat and CALIPSO data and the cloud mask schemes. Section 3 presents examples of the results from our masking schemes and from the VFM. Section 4 analyzes the global zonal mean cloud fractions, vertical distribution of cloud coverage, and zonal mean cloud coverage, as well as comparing the results with those by VFM and MODIS. Finally, section 5 is the conclusion.
2. Data and Mask Schemes
 We analyzed data from the CloudSat 2B-GEOPROF (release R04) and CALIPSO lidar level 1B (version 2.01) products with atmospheric profile data from the European Center for Medium-range Weather Forecasting (ECMWF) for September–November 2006. CloudSat carries a nadir-looking 94 GHz Cloud Profiling Radar (CPR). The backscattered signal is oversampled to generate a range bin every 240 m in the vertical. The CPR profiles are produced every 1.1 km along the orbit track [Stephens et al., 2008] and measure the power backscattered by hydrometeors as a function of distance from the radar. The minimum detectable radar reflectivity factor is approximately −30 dBZe. The primary CALIPSO instrument is the Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP), which has 0.532 and 1.064 μm channels [Winker et al., 2009]. Along with range-resolved observations of backscatter intensity at the two wavelengths, the CALIOP also measures the linear depolarization ratio at 0.532 μm. The fundamental vertical and horizontal resolutions are 30 m and 333 m, respectively. This fine resolution is only available for the region up to 8.2 km. The profiles from 8.2 km up to 20.2 km are averaged onboard the satellite to 60 m vertical and 1 km horizontal resolutions.
 The four CloudSat-CALIPSO cloud mask schemes are based on the cloud masks used in the shipborne observations in the western Pacific Ocean near Japan reported by Okamoto et al. . The schemes are CloudSat only, CALIPSO only, both CloudSat and CALIPSO, and either CloudSat or CALIPSO. The CloudSat only cloud mask scheme C1 utilizes the CPR level 2B-GEOPROF cloud mask. The CPR cloud mask algorithm considers the signal-to-noise ratio, spatial continuity, and horizontal averaging to identify significant signals from noise and to assign a confidence level (ranging between 0 and 40) for whether a CPR bin contains hydrometeors [Marchand et al., 2008]. In this analysis, if a CPR bin has a cloud mask value ≥20, it is recognized as a cloud bin and estimated to have a <5% incidence of false detection. This value is adopted so that small water clouds in the lower atmosphere are detected. The lowest CPR bins (∼1 km) are dominated by surface clutter; thus, these bins are excluded from our analysis. With 2B-GEOPROF release R04, the estimated surface clutter is subtracted from the signal in the four lowest bins above the surface. After this clutter rejection, detection is improved and hydrometeors are detectable as low as at ∼720 m (CloudSat 2B GEOPROF R04 Quality Statement, May 2007, available at http://www.cloudsat.cira.colostate.edu/dataICDlist.php?go=list&path=/2B-GEOPROF).
 The CALIPSO only scheme C2 is different from the standard cloud mask, i.e., the CALIPSO lidar level 2 VFM [Vaughan et al., 2005]. The C2 scheme is based on two criteria. The first criterion is that the attenuated total backscattering coefficient at 0.532 μm β′532(z) of CALIPSO exceeds a threshold value βth that depends on the altitude z and the range r from the satellite to the bin of interest. This criterion is calculated for the original resolutions of the CALIPSO level 1B data, i.e., 30 m vertical and 333 m horizontal at altitudes <8.2 km and 60 m vertical and 1 km horizontal at altitudes >8.2 km by
where Pm(z, r) = βm(z)/r2, βm(z) is the volume molecular backscattering coefficient derived from ECMWF data [Hostetler et al., 2006] (available at http://www-calipso.larc.nasa.gov/resources/project_documentation.php), and Pn and σn are the remaining noise signals after onboard subtraction of the background signal. The standard deviation of Pn is estimated using P(z, r) = β′532(z)/r2 averaged horizontally at a 19–20 km altitude for five profiles corresponding to 5 km along-track distances, respectively. We assumed that this altitude region is cloud free. Although polar stratospheric clouds (PSCs) are rarely found at a 19–20 km altitude [Sassen et al., 2008], when such clouds do exist in that region, our assumption may lead to failed detection. The possibility also exists that the assumption could affect the cloud fraction statistics in those regions. We additionally noticed that the 19–20 km altitude is not the optimal range for estimating the remaining noise. Since remaining noise can be estimated by a similar procedure at higher altitudes (e.g., at 39–40 km), extending our algorithm to different altitude ranges will be straightforward in future analyses. We plan to change the altitude range from the current 19–20 km to much higher altitudes to estimate the remaining noise, especially in daytime. In Figure 1, we present an example of β′532(z) and the βth profile acquired in a pass over the North Atlantic Ocean on 8 October 2006 (∼20°N latitude and ∼27°W longitude; see Figure 3). CALIPSO detected cirrus cloud with its maximum backscatter centered at 11.5 km and Saharan dust layers below 5 km. The threshold for aerosol βth,aerosol below 5 km effectively detected clouds and excluded dust signals. Although some noise spikes or dust signals exceeded βth, these will be eliminated by the second criterion, i.e., the spatial continuity test.
 The threshold values for aerosol βth,aerosol and noise βth,noise are selected to exclude aerosol and noise, and the inflection point is fixed at 5 km. This threshold value for aerosol is vital to eliminate bins associated with aerosols because the CALIPSO signal in this wavelength is sensitive to small particles. For water clouds, the lidar ratio (extinction/backscatter) has a nearly constant value close to 19 sr [e.g., O'Connor et al., 2004]. By using the 19 sr lidar ratio, the corresponding extinction coefficient for clouds having βth,aerosol is estimated to be 1.07 × 10−4/m, and the resultant cloud optical depth τc for such clouds is 0.11 when the cloud has a geometrical thickness of 1 km. By introducing the threshold of βth,aerosol, the C2 mask does not detect cloud with τc < 0.11. However, in low-level cloud observations at the Department of Energy Atmospheric Radiation Measurement (ARM) program at the Southern Great Plains Central Facility, Ponca City, Oklahoma, from January 1997 to December 2002, the frequency of low-level clouds with τc < 5 was significantly low (∼1%) [Dong et al., 2005]. Therefore, C2 may not greatly underestimate low-level clouds, but detection of a low-level cloud might be affected by the existence of an upper cirrus layer when these two cloud layers overlap. The βth,aerosol has been tested for ship-based lidar data obtained in midlatitude and tropical cruises [Okamoto et al., 2007, 2008]. These results were also compared with another widely used method in which the gradient of the backscattering coefficients is used to discriminate aerosols and clouds. The comparisons showed excellent agreement in cloud detection between the two methods. Furthermore, the cloud cover estimated using the βth,aerosol over the tropical western Pacific Ocean, a region that is often influenced by Asian dust [e.g., Murayama et al., 1999], also agreed well with other results [Okamoto et al., 2008]. Dense dust aerosols near the source regions may have larger β′532(z) than βth,aerosol, and a lifted dust layer over the high altitude may be observed above 5 km. However, the height-resolved global distribution of dust observed by CALIPSO revealed that the height layer most influenced by dust is 1–3 km, and the attenuated backscattering coefficient at 1.064 μm β′1064 for Saharan dust rarely exceeds 0.4 × 10–5/m/sr [D. Liu et al., 2008]. Applying the backscatter color ratio for dust of ∼0.75 reported by Z. Liu et al.  to this β′1064 yields a β′532 of 5.33 × 10−6/m/sr, which is lower than the βth,aerosol. Therefore, we consider that βth,aerosol is valid and that our results are not significantly affected by fixing the inflection point.
 The second criterion is the spatial continuity test, introduced to eliminate pixels associated with aerosol and noise contaminations. Figure 2 presents a graphical representation of this test: We first created a “sliding data window,” including information from neighboring bins in both the horizontal and vertical dimensions. Consider a data window made up of two-dimensional 5 × 5 bins. Each bin is surrounded by 24 pixels. If half of these 25 pixels satisfy the first criterion (i.e., cloud fraction >0.5), the pixel of interest is considered to be cloud in the C2 mask scheme. The data window sizes are 5 × 5 bins at altitudes <5 km and are 9 × 9 bins at altitudes >5 km. We then applied this test to the original resolution of the CALIPSO data. As a result, the data window sizes are 150 m vertical and 1.67 km horizontal at altitudes <5 km, 270 m vertical and 3 km horizontal at altitudes 5–8.2 km, and 540 m vertical and 9 km horizontal at altitudes >8.2 km. This means that our method potentially does not detect cloud with a horizontal dimension <0.8 km. The reason for changing the window size is that larger noise and weaker signals occur due to thin cirrus above 5 km in daytime. In the vicinity of the transition point (5 km), the same results were assigned vertically to the five bins (150 m) above 5 km and three bins (90 m) below 5 km. We treated the transition at 8.2 km in the same way as at 5 km. These distances are smaller than or comparable to 240 m so that edge effects are mitigated in the process of averaging the results to the CloudSat grid (240 m vertical and 1.1 km horizontal resolutions). To avoid misclassification of the land surface as cloud, application of the C2 mask is restricted to bins in which altitude is greater than surface elevation plus 120 m.
 We determined the minimum detectable backscatter (MDB) at 0.532 μm for SVC at 15 km altitude with 240 m vertical by 1.1 km horizontal resolution during September–November 2006. The MDB for the C2 scheme was estimated for the bin with a cloud mask value of 1.0, which was used to avoid averaging effects. Similarly, the MDB for the averaged VFM was estimated for a cloud fraction of 1. The MDB values for C2 are 1.1 × 10−6/m/sr (nighttime) and 5.9 × 10−7/m/sr (daytime). The VFM values are much smaller than our values, i.e., 1.5 × 10−11/m/sr (nighttime) and 3.0 × 10−11/m/sr (daytime).
 Since the C1 and C2 results have differences in spatial resolution and pointing angle, an averaging procedure is necessary to interpolate the two data sets onto a common grid. For this procedure, we exclude data for which the along-track distance between the footprints of CloudSat and CALIPSO exceeds 0.55 km. The results from C1 are vertically averaged so that each profile has the same altitude registration with respect to the geoid data. These results include 83 vertical bins with a vertical resolution of 240 m. The horizontal resolution of 1.1 km is the same as the original CloudSat resolution. The minimum and maximum heights are 0 and 20 km, respectively. In addition, C2 results that lie within the CloudSat footprint are averaged so that the vertical and horizontal resolutions match those of the above C1 grid. The C1 and C2 mask values thus range from 0 to 1. The CloudSat and CALIPSO scheme C3 is then as follows. When both the C1 and C2 averaged mask values exceed 0.5, the corresponding bin in the averaged grid is considered cloud. The C3 scheme indicates the smallest occurrence of cloud among the four schemes and is used in the combined radar-lidar retrieval algorithm [e.g., Okamoto et al., 2003, 2010]. For the CloudSat or CALIPSO scheme C4, only one of the values for C1 and C2 must exceed 0.5 for the corresponding bin to be considered cloud. Although this scheme results in the largest cloud frequency among the four schemes, it should be noted that separating precipitation from clouds is generally not attempted in CloudSat signals. According to Haynes and Stephens , 18% of the clouds detected by CloudSat produce detectable precipitation over tropical oceans.
3. Examples of C2, C4, and CALIPSO VFM
 The CloudSat reflectivities and the CALIPSO lidar backscattering coefficients were averaged to have the same vertical and horizontal resolutions as the results from our cloud mask schemes. We then produced merged data sets containing CloudSat reflectivities, CALIPSO lidar backscattering coefficients, and cloud mask results. Figures 3 and 4 show examples of latitude-height cross sections of CloudSat reflectivity, CALIPSO lidar backscattering coefficient at 0.532 μm, depolarization ratio, and cloud mask results for C2. In Figure 3, the CALIPSO signal clearly detected cirrus clouds, as well as Saharan dust aerosols indicated by a high depolarization ratio (∼20%) with small attenuation (Figure 3c). Boundary layer clouds were not detected by CloudSat (Figure 3a). To compare C2 and VFM results, we first made a binary version of the VFM at the original CALIPSO resolution, where all bins with a VFM value equal to 2 (meaning cloud) were set to 1, and bins were set to 0 otherwise. This binary VFM was then averaged to match the resolution of our merged data sets. Figure 3e shows the averaged cloud mask results of the binary VFM. As mentioned in section 2, the VFM first finds “features,” which are any extended and contiguous areas of significant backscatter signal, by adopting a nested, multigrid averaging scheme to improve the signal-to-noise ratio for the very weakest signals [Vaughan et al., 2005]. It then attempts to classify a feature as a cloud or an aerosol using multidimensional probability density functions (PDFs) for the layer mean β′532(z) and the layer-integrated ratio between two channels (color ratio) at coarse spatial averaging resolutions [Liu et al., 2004]. When dense dust optical properties are close to those of cloud, their PDFs overlap and misclassifications can occur. Both C2 (Figure 3d) and the VFM (Figure 3e) successfully detected convective, cirrus, and boundary layer clouds. The VFM misclassified dust as cloud in the range from 21°N to 29°N below ∼4 km. Cloud edge detection was slightly greater by the VFM (e.g., ∼20°N at ∼11 km) because of its horizontal averaging procedure.
 In fact, regions of hygroscopic growth of aerosols can occur around clouds due to high relative humidity [Nishizawa et al., 2008]. As a result, at high concentrations distinguishing clouds from sulfate, carbonaceous aerosols, and sea salt is rather difficult. In general, dust and carbonaceous aerosols do not tend to grow with humidity and may not be difficult to discriminate from clouds. Figure 1 shows the case of dust illustrated by a high depolarization ratio (∼20%) with small attenuation.
Figure 4 shows another example that consisted of high clouds and water clouds with large CALIPSO backscattering (Figure 4b). Although CALIPSO detected SVC, CloudSat did not detect this type of cloud (Figure 4a) (e.g., ∼24.5°N at ∼15 km). Both C2 (Figure 4d) and the VFM (Figure 4e) identified high cirrus (e.g., ∼9°N at ∼13 km) and water cloud tops (e.g., ∼21°N at ∼3 km). The VFM seemed to misclassify the horizontally averaged weak signals located in attenuated areas as cloud (e.g., ∼10.5°N below ∼10 km). The C2 and VFM results also differed for areas below water cloud tops, where the CALIPSO signal was nearly fully attenuated. We believe that the VFM classified some of these fully attenuated areas as cloud whereas our C2 cloud mask detected only the topmost part of water clouds. It is worth noting that the transient recovery response of the CALIPSO 0.532 μm detector caused by a strong signal from the surface or a dense cloud is not ideal [McGill et al., 2007] and probably led to the misclassification in the VFM.
Figure 5 illustrates an example for broken clouds. Figures 5a, 5b, and 5c show the CALIPSO lidar backscattering coefficient at 0.532 μm, the cloud mask results for C2, and the averaged VFM results, respectively. CALIPSO seemed to detect broken clouds (with small clouds ∼1 km wide) and maritime aerosols as clouds below 2 km. Our C2 mask (Figure 5b) detected clouds with large backscattering. In contrast, the cloud areas detected by the VFM (Figure 5c) were considerably larger than those detected by C2, possibly due to the former's horizontal averaging procedure and misclassification of aerosols or noise as clouds.
 We also examined the cloud fraction that could be detected by C2 at 1/3 km horizontal resolution for the broken-cloud case (Figure 5). For this purpose, we relied on information for 1/3 km cloud detection flags in the VFM. First, we averaged the VFM flags in a similar way, i.e., each CloudSat grid had a dominant flag value corresponding to the original CALIPSO grid. The results showed that the C2 scheme detected 98% of bins in which the most dominant VFM flag was 1/3 km in the CloudSat grid. In addition, the VFM might have a tendency to give a false detection and/or misclassification at lower detection resolution, whereby our C2 scheme gives a reference solution.
4. Global Distributions During September–November 2006
4.1. Zonal Mean Cloud Fraction
 We examined the zonal mean cloud fractions obtained by each mask as well as the differences between results for September–November 2006 (Figure 6). The cloud fraction at a given altitude was defined as the number of cloud bins (mask values >0.5) divided by the total number of observations at that level. The vertical resolution was 240 m, and the horizontal resolution was 2.0° latitude. Note that the C1 and C4 results include hydrometeor fractions, i.e., clouds and drizzle. When the CALIPSO signal became attenuated, we assigned the totally attenuated bins to the cloud free category instead of the as missing category This treatment might have led to underestimation of cloud fractions by C2 (and also for the averaged VFM) at lower altitudes. Furthermore, the C2 and averaged VFM results contain PSCs at higher altitudes in the polar region, although the VFM algorithm attempts to exclude PSCs by specifying a threshold for allowable cloud base heights above the local tropopause.
 The C1 result in Figure 6a clearly shows a Hadley cell, illustrated by the deep convection column located near 7.5° and the nearly cloud free subtropical high. The midlatitude storm track regions in both hemispheres have substantial cloud fractions (∼55%). Cloud top height in the upper troposphere observed by CALIPSO is higher than that by CloudSat by 1–2 km depending on the latitude (Figure 6f). Figure 6f also shows improved detection by CALIPSO in areas below 720 m, where surface clutter hinders detection by CloudSat. The cloud fractions by C2 in middle and low altitudes (below 12 km for the equatorial region and 8 km at ±60° latitude) are lower than those by C1 because of CALIPSO signal attenuation. The C4 result (Figure 6d) highlights the complementary nature of CloudSat and CALIPSO observations. The improvement in detection can be seen in the cloud tops and at below ∼720 m (Figure 6d). The differences between C2 and averaged VFM (i.e., averaged VFM - C2) were calculated (Figure 6g) to be ∼25% below 2 km, 10% around the top of the deep convection column located near 7.5°, and 15% in the high latitudes. In the low altitudes, the differences arose for the reason discussed in section 3. On the other hand, in the high altitudes (especially in the tropics), the C2 scheme may miss some SVC, which have relatively weak signals and are often nearly indistinguishable from noise. The inflection point of the threshold values was fixed at 5 km in the C2 scheme, which may lead to underestimation in the high latitudes below that point.
 Note that the VFM makes a correction for attenuation whereas the C2 scheme does not. The C2 method may sometimes fail to detect clouds under cloud layers. We also examined the zonal mean cloud fraction difference between the original C2 and a modified version wherein the attenuated bins are excluded for September–November 2006. We considered only the bins detected by CloudSat below the cloud tops detected by CALIPSO as attenuated ones. The difference was as large as 2% over the whole area (not shown). CloudSat might not detect all of the clouds detected by CALIPSO. Thus, to explore this issue, we performed the following analyses. To investigate the cloud fraction missed by CloudSat, we compared the zonal mean cloud coverage of low clouds (cloud top pressure >680 hPa) by CloudSat and CALIPSO during September–November 2006, considering only the topmost layers (further details of this comparison are discussed in section 4.3). The results were 38% cloud coverage for C2 and 24% for C1 at ∼45° latitude (not shown). Thus we found that up to ∼34% [= 38 − (24/38)] of clouds are undetected by CloudSat. As noted above, we found a 2% difference between the original C2 scheme and the modified C2 scheme in which attenuated bins are excluded for September–November 2006. Dividing this value by 34% gives a result of 6%, which shows the effect of not correcting for attenuated bins in our scheme. We consider this a small value.
 The VFM and our technique typically produce different sorts of errors. The VFM is more prone to false positives, whereas our method will more likely generate false negatives. Because it does not utilize any horizontal averaging, our C2 scheme may miss some clouds that have relatively weak signals at high altitudes. In contrast, because the VFM uses sometimes substantial horizontal averaging, it will, by definition, report a higher rate of false positives than the C2 method, especially in tenuous but broken cloud fields. While the VFM will average up to 80 km horizontally, the C2 mask has a uniform final horizontal resolution of 1.1 km. However, although the C2 results are reported at a 1.1 km resolution, as a result of the spatial continuity test and the averaging over the CloudSat grid, the individual pixels are not wholly independent.
 The ideal spatial scale for any cloud mask depends on the requirements of the user. Currently, the global cloud resolving model with the finest spatial scale (Nonhydrostatic Icosahedral Atmospheric Model; NICAM) has a horizontal resolution of 3.5 km [Miura et al., 2007]. Thus when the VFM reports a cloud having a horizontal resolution of 80 km (as is often the case at high altitudes), researchers using the VFM are forced to estimate the distribution of the cloud fraction on some horizontal scale larger than 80 km. Because such large scales may be too coarse to be useful for the modeling community, we have chosen to report our results at a fixed horizontal scale of 1.1 km. By maintaining the horizontal resolution at a fixed value, we can apply a uniform detection threshold to identify clouds. Similarly, modelers can use the same approach when using the CALIPSO signal simulator. By using the same threshold values to identify “clouds,” researchers can much more fairly compare their model results with observed clouds.
4.2. Cloud Coverage
 We then examined the cloud coverage for the topmost layer detected by sensors, as categorized by the cloud top height (low, >680 hPa; middle, 440–680 hPa; high, 0–440 hPa) for C1, C2, and averaged VFM, respectively, during September–November 2006. Cloud coverage was calculated for the low and middle levels as well as for the topmost layer. This analysis revealed the ability of active sensors to penetrate and detect low- and mid-level clouds. The cloud coverage in a grid box was defined as the number of cloud profiles (mask values >0.5) divided by the total number of profiles collected in a given grid box. The resolution was 2.0° latitude by 2.0° longitude grid boxes. Note that the results from C1 show hydrometeor coverage. In addition, the cloud coverage by C2 and averaged VFM at lower altitudes was underestimated because we assigned attenuated bins as being cloud free instead of as missing. The C2 and VFM results also contain PSCs at higher altitudes in the polar region, as mentioned above.
 We also analyzed MODIS cloud coverage for comparison. The MODIS cloud coverage in a latitude grid was calculated as the sum of cloud fractions divided by the total number of observations collected in a given grid. Comparisons between MODIS and CALIPSO and CloudSat-CALIPSO were carried out for collocated data. We used the collection 5 L2 Aqua MODIS cloud top pressure (CTP) and fraction subset collocated to the CloudSat field-of-view track under both daytime and nighttime conditions at 5 km resolution [Menzel et al., 2008]. Menzel et al.  examined the sensor resolution effects on CTP determination using a 1 km research product. They found that MODIS 5 km CTP tended to overestimate low cloud categories (<700 hPa) compared with the 1 km CTP, which might have resulted in overestimation of cloud coverage by MODIS. Comparisons with CALIPSO at 5 km resolution reveled that MODIS underestimates cloud top heights by 2.6 km [Holz et al., 2008]. In the MODIS cloud fraction scheme, the number of cloudy single 1 km resolution pixels within a 5 × 5 km area is used, which is estimated using the MODIS cloud mask product [Ackerman et al., 2008]. Global comparisons of the MODIS cloud mask results with CALIPSO results at 1 km resolution showed agreement of ∼87% for cloudy conditions in both day and night [Holz et al., 2008].
 Analysis of ground based radar and lidar observations has suggested that CloudSat could miss thin cirrus clouds having optical thickness of 0.1–0.3 [Stephens et al., 2002]. CALIPSO can detect clouds with an optical thickness as low as 0.01 [McGill et al., 2007]. Furthermore, Ackerman et al.  recently demonstrated that MODIS is insensitive to clouds with optical thickness smaller than 0.4 by comparing MODIS and ground based lidar measurements.
 For the topmost layer in the low level (Figure 7), C2 cloud cover is larger than that of C1 by ∼10%. Both C1 and C2 coverage results are relatively smaller over land than over ocean. This may indicate a high frequency of cloud overlap over land. The C2 results show very large cloud coverage (∼95%) over the western coasts of continents (e.g., California, Peru, and Guinea), which are regions known to be covered by low-level clouds (Figure 7b). In contrast, CloudSat shows modest cloud cover in these areas (Figure 7a). The difference between C2 and the VFM is large (up to ∼35%) in low and middle latitudes. Notable differences are seen between C2 and MODIS results. The MODIS cloud coverage over the western coasts of continents is somewhat smaller than that by C2. Except for these regions, the MODIS cloud cover is larger than that of C2 by ∼15% globally. The reason for the smaller MODIS values at western continental coasts is as follows: Low-level clouds frequently occur in these regions near the bottom of a temperature inversion and, in the presence of inversions, MODIS overestimates CTP [Holz et al., 2008]. The reason for larger MODIS results in other areas might be that our analysis overestimates CTP at the low level because it uses a 5 km resolution CTP by MODIS [Menzel et al., 2008].
 Note that there is a remarkable difference between the C1 and C2 results for all layers in the low level in Figure 8 and in the high level in Figure 11. As mentioned earlier, this is because CALIPSO can identify SVC, cloud tops, and low-level clouds that may not be detected by CloudSat. In the low level, extremely large cloud coverage by C2 (>90%) is shown at the northern and southern midlatitude storm track regions and subtropical latitudes over the western coasts of continents (e.g., California, Peru, and Guinea) that are known to be covered by low-level clouds (Figure 8b), whereas CloudSat shows modest cloud cover in these areas (Figure 8a). Significant differences were noted in cloud coverage over land and ocean between C2 and C1. The C2 cloud cover is larger over ocean and smaller over land compared with C1, especially over the western coasts of continents. This result can be explained as follows: CALIPSO detected more small particles than CloudSat. Thus, CALIPSO was superior in detecting low-level clouds when no mid- or high-level clouds were present above those clouds. Over land, deep convection often occurred, and CALIPSO could not detect the low-level clouds due to complete attenuation of signals above those low-level clouds; in this case, however, CloudSat could penetrate the convections and detect low-level clouds.
 We found very large differences between C2 and averaged VFM for low-level clouds. The VFM showed the largest cloud cover in most areas (Figure 8c). The averaged VFM results suggest that low-level clouds occur everywhere over the ocean; furthermore, contrast between land and ocean was rarely observed (Figure 8c). The difference between C2 and the averaged VFM found in this study corresponds to the difference between C4 and the combined CloudSat-CALIPSO results analyzed by Mace et al. .
 We also found significant coverage differences for the topmost layer (Figure 7) and for all layers (Figure 8), which correspond to the frequency of cloud overlap. For C1, regions in storm tracks and the Intertropical Convergence Zone (ITCZ) show large difference. Striking differences also appeared in storm tracks for the C2 and VFM results.
Figure 9 illustrates the mid-level coverage of the topmost layer for each mask. The difference among C1, C2, and VFM was small, and contrast between land and ocean was rarely observed. In each result, little coverage exists except in storm tracks, which suggests the rarity of clouds with tops located in the middle level. We found somewhat large cloud coverage by MODIS over the western coasts of continents, especially over Peru (∼57%) (Figure 9d). This may correspond to the MODIS overestimation of CTP in the low level, as described above.
 For C1 (Figure 10a) and C2 (Figure 10b) regarding all layers in the middle level, contrast between land and ocean was rarely observed, and the longitudinal variation of the cloud free subtropical high became clear. We can also see from the comparisons between Figure 9 (for the topmost layer) and Figure 10 (for all layers) that cloud overlap occurs frequently, as in the low level.
 In the high level (Figure 11), C2 showed significant cloud coverage (e.g., 70% in the ITCZ, central Africa, and central South America), with the largest feature of cloud cover extending from the Asian monsoon region to the western Pacific warm pool (Figure 11b). C2 indicated the set of subtropical jet streams with large cloud coverage. These high-level cloud distributions found by C2 are consistent with findings of previous studies [e.g., Jin et al., 1996; Wylie et al., 2005]. The cloud distributions by MODIS (Figure 11d) are similar to those by C1, C2, and VFM. The MODIS coverage is the same as that of C1 in the tropics but smaller in other regions.
Figure 12 presents the total cloud coverage for C1, C2, averaged VFM, C4, and MODIS during September–November 2006. The C1 result (Figure 12a) represents the longitudinal variation of the subtropical high in the ITCZ centered near 7.5°. As previously noted by Mace et al. , CloudSat clearly showed the South Pacific Convergence Zone (SPCZ) west of the International Date Line and significant cloud coverage in the northern and southern midlatitude storm track regions. In Figure 12b, remarkable cloud coverage of ∼90% is present over the whole area except for part of the subtropical high region, Greenland, and Antarctica. The cloud coverage by C2 was larger than that by C1 over the whole region because CALIPSO could detect SVC, the upper part of thin clouds, and low-level clouds that may not be detected by CloudSat. In the subtropical high region, the VFM result (Figure 12c) shows 30% more cloud than the coverage given by C2, largely stemming from the low-level difference between VFM and C2. Schemes C2 and C4 produced similar results (Figures 12b and 12d), suggesting a small contribution of C1 to the latter. MODIS, C2, and C4 produced similar results for total coverage except in the polar regions.
4.3. Zonal Mean Cloud Coverage
 We compared the zonal mean cloud coverage for the topmost layer detected by sensors among the C2, C4, averaged VFM, and MODIS schemes (Figure 13). In the low and middle levels, coverage was calculated for all layers as well as for the topmost layer detected by the sensors. The resolution was 2.0° latitude.
 For the topmost layer in the low level (Figure 13a), the C2 results are comparable to the C4 results, suggesting that C1 makes little contribution to C4. The averaged VFM coverage is larger than those of C2 and C4 by ∼15% in low- and middle-latitude regions, possibly due to the former's misclassification of dense aerosol and noise as clouds. The MODIS results are larger than those of C2 and C4 by ∼15% in all latitudes, but similar to the C2 and C4 results at ∼19°S latitude, where MODIS results may be underestimated due to overestimation of the CTP as mentioned above. We can also see a somewhat strange result in part of the polar region, in which the C2 result is larger than that of C4. This may have arisen from the C2 underestimation of occasional ice clouds in those regions extending below 5 km, ice clouds that are detected by C1.
 In the middle level (Figure 13b), C2, C4, VFM, and MODIS have similar very low cloud coverage for the topmost layer except for storm tracks. In contrast to the low level, MODIS shows somewhat large values near ∼19° latitude, which might correspond to overestimation of CTP in the low level. In the high level (Figure 13c), the C2 results are larger than MODIS results by ∼20% because MODIS has difficulty detecting optically thin ice clouds. Also, because the MODIS analysis assumes that all scenes have a single cloud layer, the MODIS scheme may not recognize thin, high-level clouds overlying thick, low-level clouds. The C2 and C4 values are similar because of the limited sensitivity of the CloudSat to the relatively small ice particles in the high level. Note that for the whole latitude range, averaged VFM values are larger than C2 values by ∼5%. As shown in Figure 13d, no significant differences appeared between total cloud coverage results by C2, C4, and MODIS except for the high-latitude regions, where MODIS apparently underestimated clouds. Passive sensors such as MODIS have difficulty detecting clouds over snow- or ice-covered surfaces because visible and thermal contrasts are reduced [Mahesh et al., 2004; Ackerman et al., 2008]. This result is consistent with findings from comparisons of MODIS and the Geoscience Laser Altimeter System (GLAS) [Spinhirne et al., 2005] and of MODIS and CALIPSO [Mahesh et al., 2004; Holz et al., 2008]. The averaged VFM findings are large in the middle and low latitudes and might be greatly affected by the misclassification in the low level.
 As shown in Figure 14a, the averaged VFM coverage for all layers in the low level is larger than that of C2 by up to 36% in all latitude regions, possibly due to VFM misclassification of dense aerosol and noise as clouds. The C4 results show large cloud coverage compared to the C2 results, especially in the ITCZ and storm tracks, because of the radar's ability to penetrate optically thick clouds and the inclusion of rain or drizzle in its cloud cover estimation. As expected, this tendency can also be observed in the middle level (Figure 14b). Somewhat unexpectedly, the C4 mid-level results are comparable to the averaged VFM results. This finding may be related to an overestimation of cloud cover by the VFM.
 Map comparisons for low and middle levels (Figures 7–10, respectively) revealed a striking difference between the topmost layer (Figure 13) and the all layer results (Figure 14), suggesting that cloud overlap frequently occurs, as also found in the ship-based radar and lidar measurements of Okamoto et al. , and may affect the statistics for all layers.
 We developed four cloud mask schemes for CloudSat cloud radar and CALIPSO lidar based on the ground observations reported by Okamoto et al. . These schemes were applied to 3 months of data to create merged data sets with matching vertical and horizontal resolutions. From these data sets, we examined the global vertical distributions of cloud fractions and coverage during September–November 2006. We also compared our results to CALIPSO VFM and MODIS data.
 Our analyses revealed four differences between C2 and the VFM: First, the VFM seemed to misclassify dust aerosol in the boundary layer as cloud; second, because of its horizontal averaging scheme, the VFM detected a slightly larger area of cloud edge; third, the VFM also seemed to misclassify horizontally averaged tenuous signals located in attenuated areas as cloud; and fourth, the VFM identified water cloud tops, including nearly fully attenuated areas below them, as cloud, whereas the C2 mask detected the water cloud tops only. A significant difference was found between the zonal mean cloud fraction by C2 and the averaged VFM result. In low altitudes (below 2 km), the averaged VFM cloud fraction was 25% larger than that of C2, possibly due to misclassification by the VFM. On the other hand, below 5 km in the high-altitude tropics and polar region, averaged C2 cloud covers were ∼10%–15% lower than averaged VFM results. This could be explained by overestimation of high clouds by the VFM, created by the large horizontal average in the VFM. Comparison of C1, C2, and C4 indicated that the complementary nature of CloudSat-CALIPSO measurements produced large improvements in cloud detection for cloud tops and cloud below ∼720 m. The comparison of cloud coverage also showed that the VFM possibly overestimated low-level clouds over ocean and rarely observed the contrast between land and ocean. In contrast, our C2 scheme showed the land-ocean contrast. No significant difference was found between C2 and C4 cloud cover, suggesting that C1 made only a small contribution to the total C4 result.
 For low-level cloud cover at the topmost layer detected by sensors, MODIS results were ∼15% larger than C2 results globally because MODIS CTP may have been overestimated. In low and middle latitudes, averaged VFM coverage was ∼35% larger than that of C2, possibly due to the former's misclassification of dense aerosol and noise as clouds. For mid-level clouds at the topmost layer, the C1, C2, VFM, and MODIS schemes produced similar results. Comparison of the results for the topmost layer and for all layers revealed that cloud overlap was a frequent occurrence in the low and middle levels. C2 and C4, reflecting the better sensitivity of lidar to thin clouds, showed greater high-level cloud cover than shown by MODIS. The VFM high cloud categories were larger than ours, possibly due to its horizontal averaging procedure. MODIS, C2, and C4 produced similar results for total cloud coverage; this finding supports the agreement previously found between MODIS cloud detection and GLAS or CALIPSO results, except in high latitudes [Mahesh et al., 2004; Holz et al., 2008]. These differences correspond to the difference between the C4 and combined CloudSat-CALIPSO results examined by Mace et al. .
 Several further research steps are needed to more accurately identify cloud distributions from CloudSat and CALIPSO data. To retrieve the cloud liquid water content, bins likely to contain drizzle or precipitation should be eliminated in the C1 scheme. Although several studies have identified drizzle or precipitation profiles in CloudSat observations [Sassen and Wang, 2008; Haynes et al., 2009], height resolution of drizzle and precipitation occurrences is needed. The joint European and Japanese satellite mission EarthCARE is scheduled to launch in 2013 and will carry a Doppler cloud radar, a high-spectral resolution lidar, a multispectral imager, and a broadband radiometer. The Doppler radar is expected to be a useful tool for discriminating precipitation and cloud particles [e.g., Illingworth et al., 2007].
 We are indebted to the CloudSat and CALIPSO science teams and engineers whose efforts and dedication made this study possible. This work was partly supported by the Ministry of Education, Culture, Sports, Science, and Technology, Japan, through Grants-in-Aid for Scientific Research B (19340132 and 22340133) and also by Special Coordination Funds for Promoting Science and Technology for Japanese Cloud Seeding Experiments for Precipitation Augmentation (JCSEPA).