We compare cirrus presence and heights (CTHs) using oblique stereo by the Multiangle Imaging SpectroRadiometer (MISR) with measurements from ground-based cloud radar and lidar sensors at the Tropical Western Pacific (TWP) sites operated by the U.S. Department of Energy Atmospheric Radiation Measurement Program. Precise point-wise comparisons, limited to only 195 coincident cases, showed that the total number of cirrus retrieved using oblique-stereo analysis improved to 70% from 39% using the standard-stereo technique. The stereo technique detects cloud with the highest contrast, which is often at lower altitude. The oblique-stereo technique's efficiency depends on the thickness and number of underlying cloud layers. A histogram approach allowed similar regions to be compared statistically with many more samples and showed three distinct peaks at ≈13 km, 15 km, and 19 km related to deep convective clouds, tropical tropopause layer (TTL) cirrus, and overshooting convective clouds, respectively. Most differences between the satellite and ground-based measurements resulted from a number of cases of invalid cloud comparisons (14%), blunders from edges and broken clouds (7%), low contrast stereo mismatches (4%), and under-estimation of CTHs (3%). Overall, the oblique-stereo analysis detected a cirrus-top layer in 65% of all the valid coincident cases, mostly <1 km in thickness. The oblique-stereo derived cirrus CTHs differed from the heights of cirrus-top layers from ground-based cloud radar and lidar by −0.5 ± 1.0 km, validating the MISR retrievals. This suggests global thin cirrus retrievals are possible with the oblique-stereo technique after the screening of occasional blunders.
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 Cirrus clouds are key regulators of the Earth's radiative balance [Ramanathan and Collins, 1991; Hansen et al., 1997] covering 20–40% of the Earth [Lynch, 1996; Wang et al., 1996] and up to 70% of the tropics at any given time [Wylie and Menzel, 1999]. These are cold clouds composed of asymmetric ice particles that scatter only a small amount of solar radiation and prevent a large quantity of infrared radiation from leaving the earth-atmosphere system. In the thermal infrared, ice is highly absorptive and reradiates about half of the absorbed energy back to the earth, thereby heating the column below it [Liou, 1986; Lynch, 1996]. An accurate understanding of cirrus distribution in terms of its varying optical depth, altitude, and coverage is vital in estimating the radiative effects of high clouds on the climate system.
 Traditionally, cirrus clouds have been defined on the basis of visual observations from the surface by observers [Lynch et al., 2002], but the perception of visibility in terms of color and contrast also depends on factors such as viewing geometry, target illumination, and the angular scattering properties of cloud particles [Sassen et al., 1989]. Cirrus with visible optical depths τ < 0.1 can easily be missed by both ground and satellite observations [Lynch, 1996]. Many experiments have been conducted over the last two decades using ground-based lidar to understand cirrus properties [Nee et al., 1998; Platt et al., 1998]. Several case studies over the tropics showed cirrus clouds occurred in 29%–44% of the observations [McFarquhar et al., 2000; Comstock et al., 2002]. These clouds were mostly thin (<2 km), high (7 km < CTH < 20 km), and radiatively significant (cloud forcing > 10 W m−2) when τ exceeded 0.06.
 Due to lack of spatial coverage, global cirrus climatology from ground-based lidar stations is limited. Ground-based lidar observations are also affected by the presence of dense lower clouds [Comstock et al., 2002; Sassen et al., 2008]. The deployment of space-borne lidar has helped in understanding cirrus cloud climatology to a greater extent. This includes the launch of CloudSat Cloud Profiling Radar and CALIPSO Cloud-Aerosol Lidar with Orthogonal Polarization payloads as part of the A-Train constellation of satellites [Stephens et al., 2002; Winker et al., 2007]. Studies using combined CloudSat and CALIPSO data suggest global cirrus occurrence of 17% with maximum zonal coverage of 60% to 70% in the tropical belt at relatively high altitudes [Sassen et al., 2008; Nazaryan et al., 2008; Haladay and Stephens, 2009].
 The space-borne lidar has increased global data coverage, with improved vertical resolution, but it so far lacks the temporal coverage that is necessary to understand the changes occurring in cloud properties over decadal time scales. CloudSat and CALIPSO only have data available from April 2006, but the Multiangle Imaging SpectroRadiometer (MISR) on board the Terra satellite has been active since 2000. Another advantage of MISR over CALIPSO is swath, where MISR covers a wider area in the across-track direction in comparison to CALIPSO. Additionally, MISR views the Earth simultaneously at nine widely spaced angles and provides radiometrically and geometrically calibrated images in four spectral bands at each of the angles. MISR instrument does not observe nighttime clouds, but it can detect clouds from changes in reflection at different viewing angles and can determine the height of such clouds using stereoscopic techniques.
 Also, cloud boundaries detected from ground-based and space-borne lidar are based on backscatter profiles, which include the effects of molecular and particulate scattering. To accurately detect clouds using lidar measurements, algorithms have to distinguish signal changes due to random noise and signal increase from aerosols from those due to clouds [Wang and Sassen, 2001]. Several ground-based and space-borne lidar studies indicate a decrease in high cloudiness during the hours of solar noon and day-night differences in high cloud occurrence due to solar background signals in the lidar backscatter profiles [Comstock et al., 2002; Nazaryan et al., 2008; Dupont et al., 2010]. However, a significant advantage of MISR CTH stereo retrieval is that the technique is purely geometric and has little sensitivity to the sensor calibration [Muller et al., 2002]. In comparison to MODIS CTH retrievals, the stereo retrieval works independently without any knowledge of the atmospheric thermal structure, reducing height errors from temperature inversions [Garay et al., 2008; Harshvardhan et al., 2009].
 MISR provides a global distribution of CTH with 1.1 km sampling and retrieves heights of low-level clouds that agree with climatology from other satellites [Wu et al., 2009]. Several studies have been conducted exploring MISR's standard-stereo algorithms ability to retrieve CTH when compared to active ground-based sensors [Marchand et al., 2007; Naud et al., 2002, 2004, 2005a, 2005b], with some studies indicating MISR's inability to retrieve thin, high clouds due to failure of the standard-stereo algorithm to find suitable matches in the pattern, especially for cirrus with optical depths below 0.3 [Zhao and Di Girolamo, 2004; Marchand et al., 2007; Mueller et al., 2008]. Prasad and Davies  introduced an oblique-camera stereo retrieval technique to improve thin cirrus cloud detection with MISR. The CTH retrieved using the oblique-stereo technique involved similar stereo matching techniques as described by Muller et al.  and Moroney et al. . The only difference was that the oblique cameras further away from nadir were used as reference for stereo matching, whereas the MISR standard stereo uses a combination of near-nadir cameras. A similar technique has been used for stereo observations of polar stratospheric clouds. Here, low stratospheric clouds (<18 km) showed agreement in CTH by 1 ± 2 km when compared to a satellite-borne lidar [Mueller et al., 2008]. This technique used 1100 m sampled oblique near infrared images, whereas the oblique-stereo technique uses 275 m sampled red band images. The oblique-stereo analysis detected cirrus to an optical depth of 0.1, with improved height precision of 252 m, and enhanced detection of high clouds by 46%. Prasad and Davies  compared oblique-detected CTH with coincident CTH derived from MODIS, but no comparisons were made with coincident ground-based measurements.
 Therefore, the intent of this study is to compare the MISR oblique-derived cirrus heights with precision point measurements from the ground-based cloud radar and lidar (represented as CRL from hereon) at the Atmospheric Radiation Measurement's (ARM) Tropical Western Pacific (TWP) sites that include Nauru, Manus, and Darwin. We also include comparisons of MISR standard-derived cirrus heights with CRL. The limitations with oblique and standard derived cirrus are examined with detailed case studies including cases where both standard and oblique techniques fail. The effects of the geometrical thickness and the number of cloud-layers on the standard and oblique-stereo retrieval process are explored in each comparative scene. To include more cases of cirrus over the TWP sites, we also employed a statistical analysis approach with histogram comparisons characterizing the same region with increased samples. This new study outlines MISR's ability to retrieve cirrus with all its enhancements and limitations.
2 Description of Data
2.1 MISR Cloud-Top Height
 The Multiangle Imaging SpectroRadiometer (MISR) instrument was launched in December 1999 on the NASA EOS Terra satellite that flies in a near-circular, 705 km sun-synchronous orbit, providing a multi-angle coverage of the entire Earth in 9 days at the equator and 2 days near the poles. It has an equatorial crossing time at about 10:30 A.M. and an orbit repeat cycle of 16 days. It consists of nine pushbroom cameras that measure radiance in four spectral bands centered at 443, 555, 670, and 865 nm corresponding to blue, green, red, and near-infrared color bands, respectively. These cameras view a scene from nine different nominal angles relative to earth's surface, namely 70.5°, 60.0°, 45.6°, 26.1° forward, nadir, and 26.1°, 45.6°, 60.0°, and 70.5° aft (also denoted as Df, Cf, Bf, Af, An, Aa, Ba, Ca, and Da, respectively). The red-band radiance is available at a resolution of 275 m for all cameras over a swath width of 360 km.
 MISR uses its viewing geometry of the nine cameras to simultaneously retrieve cloud-top motion and height. It retrieves the cloud-top motion on a 70.4 km grid and then uses these motion vectors to provide a correction to the apparent disparities in cloud feature locations that are then used to retrieve CTH [Horvath and Davies, 2001; Muller et al., 2002]. The operational stereo matching algorithm uses a stereo matching technique described in detail by Muller et al.  and Moroney et al. . Briefly described here, using a 70.4 km × 70.4 km search grid on the images, the height and velocity of the most distinctive cloud features are derived using three forward or aft viewing cameras. Running a second set of stereo matchers with the nadir and the near-nadir camera pairs yields the stereo height product [Moroney et al., 2002]. MISR red-band data with sampling of 275 m are used for stereo matching, but the stereo height product sampling is reduced to 1.1 km for faster processing. The image disparities are converted to height by first assuming no cloud motion (stereo height without wind) and then by accounting for winds deduced from the existing 70.4 km domain cloud motion vector (stereo height best wind) [Diner et al., 1999; Marchand et al., 2007].
 The standard MISR Level 2 Top-of-Atmosphere/Cloud Stereo-MIL2TCST (version F08_0017) product is processed with stereo matching of the nadir (An) and the near-nadir (Af, Aa) camera pairs. The near-nadir camera pairs maximize coverage and provide sharpest imagery and the needed contrast for the stereo-matchers. The near-nadir stereo matching works best for thicker, low-level clouds that provide enough contrast for the stereo-matchers to retrieve cloud heights, but the stereo matching fails in the case of thin, high cirrus clouds (τ < 0.3) when the contrast in the matching nadir and near-nadir camera is low. Prasad and Davies  showed that using oblique-camera pairs (Ca-Da) enhances the detection of cirrus cloud height to an optical depth of 0.1.
 In this study, we use the oblique analyzed stereo product with sampling of 1.1 km. A detailed description of the oblique-stereo technique is shown in the study of Prasad and Davies . Briefly described here, the oblique-stereo product is produced using the standard-stereo matching technique, but with the oblique cameras as reference. The heights retrieved are geo-registered with respect to the oblique camera. Moreover, the time difference between alternate cameras accounts for the movement of clouds due to winds. Mapping the oblique-stereo heights onto the nadir camera requires corrections for parallax and cloud motion due to winds. To correct for errors in height retrieved due to cloud motion between adjacent oblique cameras, the along-track component of the National Centers for Environmental Prediction (NCEP) wind is utilized depending on the location and height of the cloud. For consistency of winds with location, the NCEP winds were averaged over the whole MISR block. Next, the location of the cloud with respect to the nadir camera is calculated. This requires corrections for along-track parallax that adds to the cloud motion due to winds in the along-track direction. The across-track parallax was negligible, but cloud motion in the across-track direction was accounted for in calculating the location of clouds projected at nadir. The relevant NCEP wind vectors (block averaged) were chosen according to the height of clouds. All CTHs above 10 km were sensitive to oblique analysis and represented thin cirrus clouds missed by the standard-stereo technique.
2.2 Ground-Based Data Sets
 To assess the cirrus CTH retrieved using MISR's oblique analysis, we utilize the cloud boundaries determined from a combination of radar and lidar sensors at the United States (U.S.), Department of Energy, Atmospheric Radiation Measurement (ARM), Tropical Western Pacific (TWP) sites. The TWP site includes ground stations based at Nauru (0°31′15.6″S, 166°54′57.60″E), Manus (2°3′39.64″S, 147°25′31.43″E) and Darwin (12°25′28.56″ S, 130°53′29.75″E). The cloud boundaries data product is known as the active remote sensing of cloud layers (ARSCL) data set as outlined by Clothiaux et al. .
 The ARSCL data product contains cloud-top boundaries from micropulse lidar [Campbell et al., 2002] when it fully penetrates the clouds. Otherwise, it utilizes the millimeter cloud radar [Moran et al., 1998] to retrieve the cloud-top boundary [Clothiaux et al., 2000]. The radar occasionally misses thin high ice clouds that are not sufficiently reflective at millimeter wavelengths. Also, during periods of moderate to heavy rainfall, the radar signal gets severely attenuated. The optically thick clouds attenuate lidar signals introducing more uncertainty. However, the bias in radar and lidar CTH is <300 m when the lidar penetrates the clouds [Marchand et al., 2007].
3 Analysis Approach
 MISR views the TWP sites twice within a 16 day cycle throughout the year. Table 1 lists the number of MISR overpasses available for the comparative study over the TWP sites. The MISR overpass specifies a patch size of 3.3 km × 3.3 km over Nauru, Manus, and Darwin. To get coincident MISR and ARSCL data, the time of the MISR overpass was matched with the time (nearest to 10 s) of the ARSCL data derived from the TWP ARM sites. The patch size also accounts for mismatch due to time (±10 s) and geo-registration errors resulting from cloud motion. The coincident MISR and ARSCL data were screened for cirrus cases present in the ARSCL data. CTHs above 10 km were screened to match MISR's oblique-stereo cirrus retrieval threshold [Prasad and Davies, 2012]. All CTHs with base heights above 10 km from the ARSCL data were representative of typical cirrus clouds detected with TWP CRL. Therefore, the 3.3 km × 3.3 km patch over the TWP ARM site is filtered for the maximum height in order to account for cirrus clouds within the patch. This follows from CRL's sensitivity to thin clouds that detects clouds as high as 19 km. A median filter was not utilized because cirrus clouds are horizontally extensive [Uthe and Russell, 1976], and the oblique-stereo technique missed homogeneous cirrus [Prasad and Davies, 2012], hence a maximum filter should closely capture the top-most cirrus layer height over the TWP site, especially when cloud fraction within the 3.3 km × 3.3 km is low. The MISR overpass is during the daytime; hence, all the coincident MISR and ARSCL cases studied were representative of daytime cirrus clouds over the tropics.
Table 1. Summary of MISR Overpasses Over TWP Sites
Lidar/Radar Cirrus Cases
 All the cases studied over the TWP ARM site were classified into three categories, namely oblique-agreement, standard-agreement, and MISR-difference. Oblique-agreement cases were representative of enhanced cirrus detection after oblique analysis and were not retrieved using standard-stereo analysis. Similarly, standard-agreement cases were representative of situations when the MISR standard algorithm retrieved cirrus heights while the oblique analysis either failed due to pattern mismatch or produced the same height as the standard algorithm. Apart from the MISR agreement cases, there were cases where neither the standard nor the oblique analysis retrieved any cirrus height, but the TWP CRL retrieved CTH above 10 km. These cases with no MISR agreement were classified as MISR difference cases.
4 Case Studies
 This section examines examples of stereo height retrieved from oblique analysis technique in order to demonstrate in more detail the limitations of the MISR standard approach compared to the oblique analysis. These cases were selected for only two categories (oblique-agreement and MISR-difference). The standard-agreement cases have been left out because several other publications [Marchand et al., 2001, 2007; Naud et al., 2004, 2005a, 2005b] have compared MISR standard-stereo retrieved heights with active ground-based sensors. Most of the results show a relative bias of 0.1–2.0 km between MISR stereo retrieved cirrus height and the ground-based active sensors. MISR oblique-stereo technique works best for cirrus retrievals over tropical ocean, especially with optical depths >0.1 [Prasad and Davies, 2012]. Therefore, the case studies were chosen over Nauru, a small island in the tropics with a land area of only ≈21 km2.
4.1 Cirrus Clouds With Oblique-Agreement
 Figure 1 illustrates MISR's oblique-stereo retrieval of cloud height for thin cirrus clouds over Nauru (outlined by a 3.3 km × 3.3 km grid box in red). The top, middle, and bottom of Figure 1 show the MISR nadir image, the standard-stereo, and the oblique-stereo CTH retrievals, respectively. Similarly, Figure 2 shows the vertical profile of clouds retrieved by CRL and MISR for the above cases. The results shown below apply to the grid box over Nauru only. CRL classified Case I (18 January 2004) as a multi-layer cloud (three layers). It is apparent from Figure 2 that the oblique-stereo technique detects the thicker (≈0.1 km) lower layer missing the relatively thinner (≈45 m) upper layers. However, the oblique-stereo analysis retrieved CTH ≈9 km below the cirrus top-layer. This was an improvement in comparison to the standard-stereo retrieval, but the oblique-stereo technique missed the closest CRL layer by ≈8 km. It is evident from the spatial distribution of the oblique-stereo retrieved CTH that this was due to a blunder caused by the edge of the clouds that has been earlier reported by Naud et al.  and Marchand et al. .
 Case II (15 March 2007) was also classified as a multi-layer cloud (three layers). Here, the standard-stereo technique missed all the layers (mostly thin) completely due to low contrast in the nadir images. However, the oblique-stereo technique performed better, detecting the top-layer to be within 0.1 km of the CRL. Case III (21 June 2002) included clouds that were of higher contrast. The oblique-stereo, standard-stereo, and CRL CTHs were 14.4 km, 13.1 km, and 12.8 km, respectively. The top-layer detected by lidar was thin (≈90 m), but the total geometrical thickness of layers below it was ≈9 km, and this likely attenuates the lidar signal, underestimating the height. The cloud radar also had signal attenuation due to rain indicated from the precipitation flags. The standard-stereo technique retrieved similar height when compared to CRL, but the oblique-stereo technique detected thinner cirrus above the thicker cloud that the standard-stereo missed due to low contrast, and this was under-estimated by CRL due to signal attenuation.
 Generally, MISR oblique-stereo performs best with non-homogeneous clouds with higher contrast in the images from oblique views that favor the stereo-matching algorithm. The contrast in the images also depends on the geometrical thickness and number of underlying layers. Thicker single-layer clouds are detected from MISR oblique-stereo, but multi-layered thick clouds underneath thin high cirrus attenuate CRL signals during rainy conditions.
4.2 Cirrus Clouds With MISR-Difference
 The top, middle, and bottom of Figure 3 show the MISR nadir image, the standard-stereo and the oblique-stereo CTH retrievals, respectively. These cases did not retrieve any CTH above 10 km from either the standard-stereo or the oblique-stereo analysis over Nauru (3.3 km × 3.3 km grid box). Similarly, Figure 4 shows the vertical profile of clouds retrieved by CRL and MISR for the above cases. Case I (29 November 2000) was classified as a multi-layer cloud (six layers) with the top cirrus layer at an altitude of 17 km and a thickness of 45 m. The oblique-stereo failed due to featureless clouds, whereas the standard-stereo missed the lowest layer by ≈8 km as illustrated in Figure 4.
 CRL detected a single-layer cirrus cloud in Case II (21 October 2003) with an altitude (thickness) of ≈13 (0.5) km. The standard-stereo technique failed to retrieve it due to sunglint, whereas the oblique-stereo had low contrast in the target image due to the presence of homogenous single-layer cirrus. The effect of sunglint introduced noisy retrievals, CTH above 20 km (rounded to 20 km) evident around the Nauru site. Case III (21 August 2001) also represented a single-layer cirrus detected over Nauru by the CRL with an altitude of ≈19 km, but neither the standard nor the oblique-stereo technique detected it due to low thickness (≈45 m) and contrast over clear ocean. The regions outside Nauru show broken clouds at a sub-pixel resolution that are also missed by the standard-stereo technique [Marchand et al., 2007].
5 Comparison of MISR Stereo-Height With ARSCL Data
 Here, the overpass coverage of MISR over TWP sites is used in order to make precise point-wise comparisons of all the coincident cases. A one to one comparison between ground and both standard and oblique-MISR product is conducted in section 5.1. Additionally, section 5.2 explores how the differences between MISR (both products) and ground observations depend on the cloud geometrical thickness, and then section 5.3 explores how these differences depend on the number of cloud layers in the atmospheric column.
5.1 Height Difference Statistics
 The MISR clouds represented here are the standard-stereo derived (H) and the MISR oblique-stereo derived (h) CTH with no cloud motion (without-winds component represented as ww) and after accounting for cloud motion using NCEP reanalysis winds (best winds components represented as bw). The MISR best winds height product was not used because of poor sampling and sensitivity to selective clouds [Prasad and Davies, 2012].
 The height difference statistics, including the number of cases, mean, and the standard deviation of the differences between TWP and MISR retrievals for oblique-agreement (OA), standard-agreement (SA), and MISR-difference (MD) cases are given in Table 2. In 195 of the coincident cases investigated, 31% had oblique-agreement, 39% had standard-agreement, and the rest of the cases (30%) showed MISR differences. Figure 5 shows a comparison of MISR oblique-agreement best winds CTH and TWP CRL retrieved CTH for TWP ARM sites. The difference in TWP and MISR heights shows a positive mean bias of ≈2 km exists for Nauru, whereas Manus and Darwin show negative mean biases of ≈2 km, and ≈3 km, respectively, for cases where the oblique analysis detected cirrus. Similarly, Figure 6 shows the standard-agreement cases with the wind corrections applied to the retrieved stereoscopic heights. Each TWP site gave a negative mean bias of ≈1–2 km. Also, ≈25% of the MISR-difference cases showed that both (oblique and standard) MISR stereo techniques failed to retrieve any heights. This is most likely due to low contrast in the reference camera used for stereo matching [Prasad and Davies, 2012]. The rest of the cases (≈75%) showed low MISR heights, whereas the CRL data detected high cirrus. These cases include cirrus clouds over thick, low clouds that appear with higher contrast in MISR images.
Table 2. Summary of Height Difference Statistics
Standard Deviation (km)
 The relative mean biases shown in all the cases above include errors resulting from the MISR standard (oblique) stereo-height algorithm that can offset the height by as much as 560 (252) m [Moroney et al., 2002; Prasad and Davies, 2012]. Another source of error in the height retrievals comes from the NCEP wind corrections. Figure 7 shows the difference in MISR heights retrieved with best winds and without winds corrections for the TWP ARM sites. The effect of NCEP winds on MISR height was within ±600 m for all the TWP sites. Errors also result from fixed MISR data grid where the retrieved height has an offset of 280 m from the true surface height at any point on the globe [Marchand et al., 2007].
 Moreover, notable differences in occurrence were observed for the TWP ARM sites, especially with Nauru and Manus. Manus cirrus clouds are geometrically thicker, warmer, and more frequent compared to Nauru, possibly due to the effects of deep convection [Massie et al., 2002]. Mace et al.  observed 47% (Manus) and 16% (Nauru) of cirrus that could be traced back to a deep convective activity within a 12 h period. Deng and Mace  showed that cirrus clouds are higher at Nauru than those above Manus using 6 years of millimeter cloud radar observations. Mather and McFarlane  found the frequency of occurrence of high cloud layers was 10% at Manus and 6% at Nauru. Nauru and Manus sites are closer to the ocean compared to Darwin that is more inland and can be affected by late afternoon-evening maximum in land convection [Liu and Zipser, 2008].
 Generally, cirrus detection with the oblique-stereo technique is within 1–2 km in comparison to CRL CTH from the TWP sites. There were distinct cases of large biases due to total mismatch of clouds, blunders from edges and broken clouds, low contrast stereo mismatches, and attenuation of CRL signals. These are discussed in more detail in section 6.
5.2 Geometrical Thickness
 The TWP CRL vertical profiles were also used to determine the geometrical thickness of cirrus. Figure 8 shows the variation of height difference between TWP and MISR retrievals with cirrus thickness using TWP CRL data. The height differences between the MISR and TWP CRL retrievals are greatly influenced by the geometrical thickness of cirrus clouds, especially for MISR height retrievals that are based on contrast. Thicker cirrus tends to have higher contrast in MISR imagery when compared to thinner cirrus.
 The MISR agreement cases including oblique-agreement and standard-agreement showed a distinct relationship with thickness for cases of positive and negative height difference. The cases where the TWP CRL detected higher clouds than MISR were geometrically thin. These were cases of multilayer cirrus clouds where MISR saw through thin cirrus clouds, but detected the lower cloud due to improved contrast in the images. However, there were cases where MISR detected higher clouds than the TWP CRL. These clouds were either geometrically thick single-layer clouds or thin clouds present under thick clouds. These could be attenuated by the lidar and missed by the cloud radar due to insufficient reflectivity, especially under rainy conditions [Clothiaux et al., 2000]. On the other hand, MISR-difference cases included geometrically thinner clouds than the MISR-agreement cases, implying that MISR was unable to see these thin clouds with any of its cameras due to low contrast. These clouds would typically be below the optical depth threshold of 0.1 for the oblique-stereo technique.
5.3 Number of Layers
 The TWP CRL vertical profile is used to determine the number of cloud layers detected for each case investigated. It can classify a maximum of 10 layers according to the backscatter profile of each scene. Figure 9 shows the normalized frequency of cases for oblique-agreement, standard-agreement, and MISR-difference, binned with respect to the total number of cloud layers. Single-layer cirrus clouds were ≈28% of all the cases investigated. This included 6% of cases with oblique-agreement, 9% of cases with standard-agreement, and 13% of cases with MISR-difference. Cirrus over lower layer (two-layers) also included ≈28% of all the cases investigated, which included 11% with oblique-agreement, 9% with standard-agreement, and 8% with MISR-difference. A notable difference observed is that the efficiency of oblique-agreement almost doubles in the presence of two layers. This is mainly due to the effect of parallax with oblique analysis, especially for multiple layers. The effect of parallax allows varying heights to appear at different locations on the oblique image as compared to the nadir image, thus helping the oblique-stereo matching algorithm to find more matches.
 Also, Figure 9 shows that the single layers dominate the MISR-difference cases. Here, ≈90% of the MISR-difference cases were single-layer clouds less than 1 km thick. The oblique and the standard-stereo techniques do not find sufficient contrast to retrieve the height of these clouds because they are too thin (<90 m).
6 Statistical Analysis
 To increase coincident data for comparison of TWP ARM and MISR-retrieved cirrus CTH, an hour of TWP CRL data before the MISR overpass was collocated onto MISR camera images after accounting for the drift in clouds due to winds. An example is illustrated in Figure 10. At the time of MISR overpass t0, clouds C0 and C1 appear at MISR image locations (xo,yo) and (x1,y1), respectively. Cloud C1 in the MISR image was also detected by CRL at the ground station at an earlier time t1. Thus, clouds detected by CRL can be collocated on the MISR image by calculating the drift due to winds. The time delay between the CRL and MISR overpass and the NCEP winds were used to calculate the drift of clouds on MISR camera images. Also, CTHs from both standard and oblique-stereo techniques were retrieved at these collocated coordinates. Furthermore, to filter cirrus clouds, the maximum CTH with base heights detected above 10 km was matched with the TWP CRL data using a 3.3 km × 3.3 km patch on MISR camera. A 3.3 km × 3.3 km patch minimizes errors in winds used for mapping oblique-camera images onto nadir. It also accounts for errors associated with the collocation of CRL and MISR data. Any perturbation in winds of 10 ms−1 and time of 10 s introduces 100 m of error in locating the cloud on the MISR's nadir camera. If all top-layer cirrus clouds seen by CRL are collocated on the MISR images, the overall distribution of cirrus CTH obtained from CRL and MISR (after applying maximum filter) should in principle be tightly correlated.
 The probability distributions of cirrus derived using MISR oblique analysis and the TWP CRL within an hour before the overpass are shown in Figure 11. The distribution of CTH obtained after collocating cirrus clouds seen by CRL on MISR after oblique-stereo analysis are highly correlated (≈0.75) with each other. Interestingly, the peaks in both the CTH distributions are consistent with each other. Three distinct peaks appear at ≈ 13km, 15 km, and 19 km in the CRL distribution. Figure 12 shows the probability distribution of top-layer cirrus thickness detected from TWP CRL with distinct thickness at these peaks. CTHs at ≈13 km are thicker than clouds peaking at ≈15 km and 19 km. These anvil cirrus clouds (≈13 km) may largely result from deep convection in the TWP [Jiang et al., 2004; Dessler et al., 2006; Sassen et al., 2009]. The peak at ≈15 km corresponds to the tropical tropopause layer (TTL) [Fueglistaler et al., 2009]. It consists of cirrus clouds within the TTL layer that are thinner than deep convective clouds and are better captured by the CRL than MISR. Several publications identify these clouds as TTL cirrus coexisting in areas of deep convection [Liu, 2007; Fujiwara et al., 2009; Schwartz and Mace, 2010; Thorsen et al., 2011]. A smaller peak at an altitude of ≈19 km may result from overshooting convection [Sherwood and Dessler, 2000; Alcala and Dessler, 2002; Liu and Zipser, 2005]. These clouds do not appear to the CRL as one deep column all the way down from the ground because they mostly are remnants of convective activity. Similarly, a lower fraction of overshooting towers of cloud-tops as high as 19.8 km was detected with CALIPSO lidar [Fu et al., 2007], and overshooting convection over 17 km was also frequently observed from MISR over the TWP [Chae and Sherwood, 2010].
 In addition, the difference in oblique-stereo heights observed is significant when compared with the MISR's standard retrieval technique. The mean bias in height (TWP-MISR) improves to −0.5 km, and the root mean square (rms) error after oblique analysis is ≈3 km. The mean cirrus thickness was 0.8 km and 67% of all cirrus clouds detected were thin (<1 km). Furthermore, the effect of winds in retrieving heights was within (±600 m) over all the TWP sites. The expected rms error including the effects of wind (±600 m), pixel mismatch (standard (±560 m), oblique (±252 m)), fixed grid (±280 m), drift calculation (±100 m), and CRL retrieval (±300 m) is within 1 km.
 To distinguish the errors from valid comparisons of cirrus clouds using CRL and MISR, the bias in height (TWP-MISR) was sorted into 1 km bins and compared to corresponding cirrus top-layer thickness (sorted in 0.25 km bins). Table 3 presents a summary of key categories derived using the binned data set described above. Valid comparison cases with a bias within 3 km constituted 72% of all the cases. Fourteen percent of all cases showed an absolute bias between 3 km and 5 km resulting from comparisons of different clouds. Furthermore, 4% of cases with positive bias >5 km existed for thin (<1 km) clouds missed by the oblique-stereo technique due to low contrast in the images. On the other hand, 10% of cases had a bias <−5 km with MISR detecting much higher CTH than CRL. Three percent of the cases include errors due to under-estimation of CTH from CRL due to thicker clouds (>1 km) under rainy conditions and the rest (7%) include blunders resulting from stereo mismatch. After oblique analysis, ≈65% of all valid cases were centered at the mean difference within the acceptable uncertainty range (±1 km) with ≈49% of these cases being thin (<1 km).
Table 3. Comparison of CRL and MISR Oblique-Agreement CTH Distributions
Thickness <1 km
Thickness >1 km
Bias > 5 km
3 km < Bias ≤ 5 km
−3 km < Bias ≤ 3 km
−5 km < Bias ≤ −3 km
Bias ≤ −5 km
7 Discussion and Summary
 This study used ground-based radar and lidar measurements of CTH at the TWP ARM sites to assess the MISR CTH retrievals after oblique-stereo analysis for the duration of the MISR mission. Precise point-wise comparisons were limited, with only 195 coincident cases resulting from <17% of total MISR overpasses over TWP ARM sites. These cases showed that using oblique-stereo analysis, the number of cirrus retrievals improved to 70% from 39% using the standard-stereo technique. The CRL compared with oblique (standard)-stereo CTH showed mean difference of ≈−1.0 (3.0) km for all the TWP sites. However, there were a few distinctive outliers that may have affected these biases due to blunders from the edge of clouds. This was more common with standard-stereo technique [Naud et al., 2004; Marchand et al., 2007]. Earlier comparisons with ground-based active sensors and standard-stereo showed similar differences in height statistics. The difference between lidar and MISR CTH for high clouds was between 0.1 and 3.1 km [Naudet al., 2004] and MISR CTH agreed within −0.6 ± 0.6 km with radar CTH [Naud et al., 2005b]. More recently, Marchand et al.,  compared 4 years of MISR CTH with ground-based radar, lidar, and microwave radiometers over ARM sites showing MISR detected thin clouds with a height difference of −0.1 ± 1.3 km over Nauru.
 Also, there were notable differences observed in cirrus retrievals over the TWP sites. Manus cirrus-tops were more frequent, thicker, and lower compared to Nauru, possibly due to deep convective activity around Manus that is located in the core of the tropical warm pool [Massie et al., 2002; McFarlane et al., 2007]. Several other studies showed similar differences in cirrus distribution over Nauru and Manus [Mace et al., 2006; Deng and Mace, 2008; Mather and McFarlane, 2009], but were based on shorter timescale of observations. Top-layer cirrus over Darwin occurred more frequently in comparison to Manus and Darwin due to late afternoon-evening land convection [Liu and Zipser, 2008]. Sassen et al.  have also shown similar differences in cirrus distribution of thin cirrus over land and ocean.
 However, statistically significant CTH comparisons of coincident cases with CRL and MISR were possible with the inclusion of cirrus detected after accounting for the drift due to winds within an hour before the MISR overpass. The histogram comparison of CRL and MISR oblique-derived CTH over all TWP sites reduces errors due to wind-drift of clouds because the CTH distributions are independent of individual cloud locations. Overall, the mean bias improves to −0.5 km after applying the oblique-stereo technique. Consistent peaks and improved correlations of ≈0.75 exist between the CRL and MISR oblique-stereo histogram. Both CTH distributions showed distinct peaks at ≈13 km (deep convective clouds), ≈15 km (TTL cirrus), and ≈19 km (overshooting convective clouds). The deep convective clouds are thicker in comparison to TTL cirrus resulting from anvils detraining from deep convective towers that penetrate the TTL [Danielsen, 1982]. TTL cirrus is thinner and often subvisual [Wang et al., 1996]. It is better detected by the CRL than by MISR, as is evident from the size of peaks in the relative distributions. Both instruments equally detect lower frequencies of thin cirrus formed from overshooting convection, but MISR's oblique-stereo analysis showed this peak at ≈300 m higher than the CRL. This is likely to be associated with errors in height calculated by MISR due to the rapid overshooting. About 65% of all valid cases were centered at the mean within an expected uncertainty of ±1 km resulting from wind correction, pixel mismatch, fixed grid, drift calculation, and CRL retrieval. These cases were representative of valid comparisons with the highest confidence for validation of CTH. The rest of the cases were mostly invalid and highly likely to have resulted from different cloud comparisons.
 The oblique-stereo technique is robust, with many added advantages over the standard-stereo technique. Prasad and Davies  previously showed that MISR's oblique analysis retrieves thin cirrus heights (optical depths above 0.1) with an improved precision of 252 m and reduces the effect of wind errors on the height retrieval by 40%. The performance of MISR's stereo-matching algorithm depends on scene contrast. The type of cloud and its scattering properties dominate the contrast in the scene. The oblique view increases the sensitivity of contrast and reduces the problem of sunglint. A thin cirrus cloud layer over a thicker layer of cloud is easily detected with the oblique-stereo technique. This is missed by the standard-stereo technique due to higher contrast from the thicker layer. However, the oblique-stereo technique detects both layers, as they appear at different locations in the oblique view because of the parallax effect. The attenuation of the lidar signal by thick clouds underestimates the height of the cirrus layer and the cloud radar becomes unreliable during precipitation. Comstock et al.  also showed low clouds block high clouds approximately 11% of the time at Nauru during 1999.
 The oblique-stereo technique fails to retrieve heights with featureless clouds. This includes thin homogeneous, sub-pixel and broken clouds. Occasionally, blunders from the edge of clouds introduce errors in the retrievals. Running filters that are sensitive to spatially incoherent and unphysical heights (CTH > 20 km) could be used to screen out these blunders, but the retrieval of featureless clouds depends on the contrast threshold used in the standard algorithm. Lowering the contrast threshold for stereo matching would improve detection. Also, making use of other oblique camera pairs is likely to improve the quality of the results. Setting up a quality threshold based on successful CTH retrievals from both forward and aft oblique camera pairs within an acceptable range would be desirable, but limitations with computational processing power and time have to be considered. Implementation of these enhancements would provide a new data product of thin cirrus clouds from MISR with a global coverage and sampling of 1.1 km.
 The authors would like to thank Catherine Moroney for providing the oblique analyzed data product and Roger Marchand for his critical reviews. This work was supported by a research scholarship funded by Subcontract 1281858 between the California Institute of Technology/Jet Propulsion Laboratory and Auckland UniServices Limited.