Tropical anvil clouds play important roles in redistributing energy, water in the troposphere. Interacting with dynamics at a wide range of spatial and temporal scales, they can become organized internally and form structured cells, transporting momentum vertically and laterally. To quantify small-scale structures inside cirrus and anvils, we study view-dependence of the cloud-induced radiance from Atmospheric Infrared Sounder (AIRS) using channels near CO2 absorption line. The analysis of tropical eight-year (30°S–30°N, 2003–2010) data suggests that AIRS east-views observe 10% more anvil clouds than west-views during day (13:30 LST), whereas east-views and west-views observe equally amount of clouds at midnight (1:30 LST). For entire tropical averages, AIRS oblique views observe more anvils than the nadir views, while the opposite is true for deep convective clouds. The dominance of cloudiness in the east-view cannot be explained by AIRS sampling and cloud microphysical differences. Tilted and banded anvil structures from convective scale to mesoscale are likely the cause of the observed view-dependent cloudiness, and gravity wave-cloud interaction is a plausible explanation for the observed structures. Effects of the tilted and banded cloud features need to be further evaluated and taken into account potentially in large-scale model parameterizations because of the vertical momentum transport through cloud wave breaking.
 As prevalent features throughout the tropics, anvil clouds in the upper troposphere exsert a net radiative forcing to the surface [Houze, 1982; Stephens et al., 1990; Kubar et al., 2007], and their impacts on the Earth's climate system are significant [e.g., Hartmann et al., 2001; Soden, 2004]. Global Circulation Models (GCMs) simulations are sensitive to cloud microphysics when we calculate heating profiles due to clouds [Clement and Soden, 2005]. These clouds comprise a significant portion of stratiform precipitation [Cheng and Houze, 1979] and water vapor transport from the lower atmosphere to upper atmosphere [Tian et al., 2004], which are also closely associated with properties of cloud particles inside anvils (e.g., microphysical composition, organization, etc.). Tropical anvil clouds have been widely studied from the radiative and hydrological perspectives during the last two decades with satellite observations and high-resolution GCM simulations [e.g., Houze, 1982; Johnson and Young, 1983; Yuan et al., 2011], but cloud dynamics, a more difficult problem, has received relatively less attention.
 Anvil clouds from cumulus convection are often associated with fine structures that carry heat and momentum fluxes. Momentum transport from cumulus convections has been recognized for modifying regional or global-scale circulations [e.g., Zhang and Wu, 2003; Kang et al., 2010], but the parameterization is oversimplified [e.g., Lane and Moncrieff, 2010]. The vertical momentum transport by anvil clouds, however, was seldomly explored. A better understanding of the organization and orientation of anvil cloud internal structures will improve not only heat and moisture calculations, but also improve our knowledge of momentum budget in the atmospheric circulations.
 In this study, we examine the view-angle dependent cloudiness from Atmospheric Infrared Sounder (AIRS) for tropical anvils. The view-angle dependence in cloudiness was previously reported with other satellite measurements using microwave and near-infrared bands, but most of the observed view-angle dependence was induced by artifacts related to sun-glint [Campbell, 2004], particle scattering [Varnai and Marshak, 2007], polarization misalignment [Weng et al., 2003] and radio frequency interference [Buehler et al., 2005]. As a thermal infrared (IR) technique, AIRS does not have many of these problems, and there is little evidence of significant scan-dependent calibration error associated with the instrument [Tobin et al., 2006]. AIRS sampling within a given swath differs by about 2 hrs in local time near the equator, of which the diurnal variation of cloud properties can only account for a small fraction of the view-dependent differences reported in this study. Thus, tilted and banded structures within anvils are suggested as the likely underlying cause of the view-dependent asymmetry in AIRS cloudiness observations, of which gravity waves might be one of the possible explanations.
2. AIRS Measurement and Data Analysis
 AIRS is a high spectral resolution spectrometer and sounder that measures Earth atmosphere thermal emissions in three infrared wavebands (3.75–4.61 μm, 6.20–8.22 μm and 8.80–15.40 μm). Its scan contains 90 footprints cross track with angles ranging between ±49.5° from the nadir, producing a swath width of ∼1600 km and a nadir footprint with a diameter of ∼13 km. Onboard on polar orbiting Aqua satellite since May 2002, AIRS provides observations at fixed local solar times (1:30 and 13:30 LST) at the equator, and its scans are approximately in the east-west direction in the tropics (AIRS scan line intercepts the equator with an angle of 8°). AIRS channels have relatively poor vertical resolution for the cloud detection, compared to the lidar and radar measurements on the A-train, but its image produces complementary “global coverage and longest time span” [Kahn et al., 2007].
 To detect clouds at different view angles, we analyze the L1B radiance data with a method similar to the technique used by European Centre for Medium-Range Weather Forecasts (ECMWF) in data assimilations [McNally et al., 2006]. Ten channels near 15 μm CO2 band are used, and they are aggregated with respect to the peak pressure of their weighting functions (WFs) to produce the radiances at 200, 400 and 800 hPa (see Table 1 in Text S1 of the auxiliary material). The 15 μm CO2 band is a conventional choice for cloud height retrievals [Menzel et al., 1983]. We chose not to use AIRS L2 products in the study because they are on a coarser (50 km × 50 km) resolution and only use the nadir 3 × 3 footprints [Susskind et al., 2003].
 Detecting clouds from clear-sky variability has been challenging for all remote sensing techniques. For AIRS radiances in the tropics, we first obtain a probability density function (PDF) from the all-sky radiances at each pressure level. The PDF is computed independently at each view angle from a month worth of data in the tropics (30°S–30°N) to make the sample size large enough while eliminate the impact from the increase of CO2 on drifting of the PDF peaks. The PDF peaks are defined as the “clear-sky reference” (TB0), similar to McNally et al. . The brightness temperatures (TB) lower than TB0 − 3δ are considered as cloud presence (TBc), where δ is the standard deviation of the clear-sky portion of each PDF, characterizing clear-sky variabilities (e.g., from temperature, water vapor and ozone). An example is given in Figure 1a with bold blue (black) line corresponding to TB0 (TB0 − 3δ). The parabola shape of TB0 is a path length effect of the CO2 channels from the temperature lapse rate in the tropical troposphere (i.e., WF peaks at side-views are about 1–1.5 km higher than that at the nadir view by assuming a lapse rate of −6.5 K/km). The increasing path length allows slant views to be more sensitive to high thin clouds.
 We define ΔTB as the difference of TB − TB0, which can be grouped into three categories in the case of ∣ΔTB∣ > 3δ: “warm”, “medium” and “cold”. The larger the ΔTB magnitude is, the thicker and higher clouds are. Quantitatively, we define the three types of clouds as TB0 − 3δ > TBc > TB0 − 6δ, TB0 − 6δ > TBc > TB0 − 15δ, and TBc < TB0 − 15δ, respectively, representing optically “thin”, “medium thick” and “very thick” clouds, by assuming cloud particle shape and size distributions are the same among all groups. Physically, the three groups roughly correspond to cirrus, anvil (the blue region in Figure 1a), and cumulonimbus clouds. To characterize cloud fine structures, we use a 3-pt running mean to remove the cloud background and capture the view-to-view TB fluctuations in terms of 3-pt variance (σ2). Depending on the mean TBc, the derived variance is tagged (colored in Figure 1b) to reflect the cloud strength (ΔTB) under which σ is computed. The definitions to separate three types of clouds are very rough, because the cirrus bin still has clear-sky contaminations, and some warm-cloud scenes in 400 hPa and 800 hPa channels are apparently classified wrongly into clear-sky scenes. Since the cirrus is upper bounded by TB0 − 3δ, about 0.3% of clear-sky measurements might have contaminated the cirrus cloud detection. We try to minimize possible effects of this contamination by differencing the AIRS 3-pt variances obtained from the symmetric view angles with respect to nadir and infer cloud structure from the variance difference.
 CloudSat cloud water content (liquid + ice) data set is also used in this study to interpret the observed AIRS TBc. Operating on the same “A-train” orbit, CloudSat measurements are approximately one minute away from AIRS, producing the similar temporal sampling. Over a period of month, it is reasonable to assume that both instruments had the same ensemble of clouds [Kahn et al., 2008]. ECMWF ERA-interim monthly mean zonal wind is used for vertical wind shear calculation.
 The relative difference from the mean at 200 hPa channel, as shown in Figure 1c in terms of percentage difference, characterizes the view-angle dependent difference in cloud occurrence as a function of the 90 AIRS views during daytime. The other two levels (400 and 800 hPa) look essentially the same to that at 200 hPa, except that ΔTB has larger dynamical range and deeper penetration into the lower troposphere (not shown). Only ocean part for the western Pacific warm pool (WP, [15°S–15°N, 105°E–150°W]) and land in central Africa (CA, [15°S–0°N, 15°E–45°E]) are presented in Figure 1c. To obtain Figure 1c, the cloud counts are first normalized by the total count number at each view angle to obtain cloud occurrence frequency as a function of TBc at this view angle. The mean cloud occurrence frequency is then derived at each ΔTB bin by averaging values from all the view angles, and finally we compute the deviation from the mean (%). We compile monthly cloud statistics separately for ascending and descending orbits for AIRS data since September 2002, and Figure 1c is the average of ascending data from eight Januaries (2003–2010).
 Several interesting cloud properties emerge from the view-angle dependent statistics of AIRS observed cloudiness in the upper troposphere. First, oblique views observe at least 20% more “shallow” and “medium” clouds (i.e., cirrus and anvils) than the nadir view, whereas the near-nadir views detect more deep convective clouds. The former can be largely explained by the elevated WF crests at side view angles, since anvils and cirrus are always above the cumulonimbus clouds, as mentioned in section 2. For deep convective clouds with narrow individual towers, the oblique views tend to miss the longest cloud water path and reduce the TBc magnitude as would be detected from a nadir view. This effect may explain why the near-nadir views observe more deep convective cases than the oblique views.
 Secondly, an apparent asymmetry exists between east and west view angles for “shallow” and “medium thick” clouds. For all three cases in Figure 1c, up to 40% more medium thick clouds are found in the east than west view, and these clouds are slightly cooler at the east view angles as well. The largest difference occurs between the outmost two view angles for shallow clouds, and the view angles observing the most and least clouds moves toward the nadir as the cloud becomes thicker/colder (significant asymmetric regions are hatched in white lines, which is defined in the auxiliary material). The observed asymmetry is larger over the central Africa (land only) compared with warm pool (ocean only). This asymmetry dominates throughout the tropics, leading to an integrated east-view preference over the entire tropics (last column of Figure 1c). However, the asymmetry almost disappears in the descending orbit data except over the Central Africa (not shown), although the general pattern of view-dependent difference is similar.
 The asymmetry for the medium thick cloud (“anvil asymmetry factor”, equation (1)) can be quantitatively defined as the percentage deviation between averaged cloud counts over the two black boxes as specified in Figure 1c, in which the largest asymmetry comes from (view-angles between 25° and 49.5°, and ΔTB bins for the “medium thick” cloud group). We here define
The calculated AAF at 1:30 pm (1:30 am) LST is 6% ± 1.6% (−0.2% ± 0.5%) for January, which is the average over the entire tropics. The AAF is 3% over ocean and 15% over land at local noon time. The AAF increases with height, which is reasonable in that upper-level channels should see more anvils. AIRS scan width is ∼1600 km, covering two time zones at each scan. The time-zone difference of upper-level cloud can only account for 2% (0.6%) asymmetry over land (ocean) at local noon, and 1.5% (∼0%) at local midnight according to Tian et al. , which is too small to fully explain the asymmetry observed in this study during daytime.
 The observed view-angle asymmetry in AIRS cloudiness can be explained by embedded cloud structures on a small-scale or meso-scale (on the order of 10–100 km). As an infrared sounder, AIRS beams can see through very thin clouds, partly penetrating medium thick clouds, but would be completely blocked by thick clouds. Hence, AIRS results are expected to reveal internal structures of the thin and medium thick clouds, as well as the top layers of thick clouds. If multi-layer clouds present, AIRS always tend to only capture the upper-level cloud. The cloud brightness temperature TBc is a function of cloud top height, cloud thickness, cloud microphysics, and satellite view angle. The view-dependent asymmetry of AIRS cloud radiances would not exist if cloud layers had a straight column-like or blanket-like structure. The underlying cause of the asymmetry is more likely associated with structured convective clouds because tilted and banded updrafts and downdrafts inside cumulonimbus can generate very different cloud scattering effects depending on whether the view smears the cloud field or not. Such structures have already been well documented in the literatures [e.g., Lane and Moncrieff, 2010], and they can be easily found in anvils as well but have received little attention so far (e.g., CloudSat snapshot in Figure 2 of Text S1 of the auxiliary material).
Figure 2a is a schematic diagram illustrates how AIRS measures the cloud scattering under a structured deep convection scene, where view-angle dependent AIRS radiance observations can be found. For the monthly cloud statistics, if sampling is assumed to be randomly applied to the same ensemble, the symmetric AIRS view angles should have the same condition for cloud observations. If these clouds have no preferred internal structures, the amount of cloudiness seen from the symmetric pair of views should be same. However, clouds are associated with tilted periodical structures, the AIRS cigar-like WF will detect different cloud amounts depending on viewing geometry. The AIRS WF responds to the wavy structure inside the anvil differently purely depending on view angle. In this case AIRS should observe more anvil clouds from the east view than the west view, as the perturbed structures are largely smeared out by AIRS elongated WF along the viewing beam. Moreover, it is much more difficult to see through the high reflectivity region from the east view than the west view due to the elongation and the shape of the internal wavy structures. Hence, the view angle parallel to the major axis of the internal cells would observe anvils more frequently and with colder TBc.
 If this interpretation is correct, cloud internal organized structures would have preferentially westward tilting during day (i.e., ascending orbits), and less organized/tilted structures during night (descending orbits). Tilted and banded cloud structures should be reflected in small-scale cloud inhomogeneity as well. As a good proxy for cloud inhomogeneity, the 3-pt cloud variance is also used to evaluate the cloud structure asymmetry. The variance asymmetry factor (Δσ2) is defined as the variance differences between the two black boxes in Figure 1c (equation (2)).
Δσ2 is plotted as the black bold line in Figure 2b for July, 2006–2009 when CloudSat is operating. Since 800 hPa channel has the largest dynamic range, a factor of 16 (4) is multiplied to Δσ2 at 200 (400) hPa to facilitate the comparisons. Meanwhile, the cloud count difference is kept the same throughout different levels assuming the difference comes from the same clouds. The longitudinal variation of variance and cloud count difference match each other very well (Figure 2b), reaching a correlation coefficient of 0.63 at 200 hPa, and decreasing to 0.51 and 0.24 at 400 and 800 hPa, respectively, all of which pass the 95% statistical significance test. This agreement suggests that the observed asymmetries from “medium thick” cloud counts is very likely a result of tilted internal banded structures inside anvils, which are highly inhomogeneous. Moreover, the variations are largely coherent among different levels, especially for those large-amplitude ones. CloudSat cloud water content climatology exhibits three levels of clouds - low level boundary clouds centered around 850 hPa, middle level congestus clouds (700–500 hPa), and deep convective clouds that have centers around 400 hPa and extend their anvils to 200 hPa and above. However, it is evident that large-amplitude Δσ2 coincides with three deep convection-active regions (central Africa, Amazon rainforest and western Pacific marinetime Continent) but not with other level clouds. Results from the three levels are strikingly alike one another, reinforces our earlier assertion that those “relatively warm” clouds (i.e., “medium thick” clouds) derived from these AIRS channels are indeed mostly the anvils associated with deep convection instead of low level clouds. Δσ2 is merely significant for descending orbits almost anywhere (not shown), suggesting lack of preferential structured “medium thick” clouds at night, which is consistent with the low diurnal variation in cloud amount differences.
4. Summary and Conclusions
 Clouds detected from different AIRS FOVs show significant view-angle dependence. The observed asymmetry is consistent throughout the tropics for thin and medium thick upper-level clouds, showing more cloudiness in the east than west view. Moreover, this asymmetry is much larger over the land than over the ocean, and larger over the convection-active regions, namely, the central Africa, the western Pacific marinetime continent, and the Amazon rainforest. Observations from day and night reveal quite different results with larger asymmetry occurring more in day than at night. Besides, the AIRS slant view angles observe more thin and medium thick clouds.
 Since AIRS does not have any significant scan-dependent calibration error, the underlying cause of the observed view-dependence is attributed to cloud internal banded structures. We only focus on medium thick clouds in the current work where the largest asymmetry comes. These clouds are mainly anvils closely associated with the deep convection. These small-scale to mesoscale tilted and banded structures inside anvils are quantitatively evaluated from 3-pt cloud variances along each AIRS scan. We find that they are most prominent and preferably tilted westward in day when convection initiates over land, and tend to disappear at night, when convection begins to decay. Besides the diurnal variation, they coincide with the seasonal convective activities at the tropics, and the variance difference is anti-correlated with the wind shears (not shown).
 Convection is one of the most important sources for gravity waves that can in turn modulate the cloud formation [Fritts and Alexander, 2003]. Due to the critical-level filtering effect, the gravity waves that propagate through convective layers into the stratosphere tend to have opposite signs against the background wind, i.e., upgradient of the wind shear. Most of these propagating gravity waves are generated at the top of deep convection and interact with clouds, producing self-organized structures that become tilted and banded with respect to the background flow. Sensitive to strong vertical motions, banded structures can form inside anvils even when a convection is not strong. At night, when convection reaches its maximum strength, the entire troposphere is inherently unstable and gravity waves cannot propagate and grow in an unstable atmosphere. Therefore, gravity wave is a process provides a likely mechanism to account for the banded structures inside anvils as revealed by angle-dependent cloud variances, as well as in the view-dependent cloudiness. The detailed relationship between propagating gravity waves and the anvil structure will be further discussed in a separate paper.
 To conclude, we found from this study that the momentum transport from deep convection is unlikely evenly distributed in all directions in the upper troposphere. The inferred anvil structures, tilted and banded against the background mean flow, would exert an anisotropical forcing over deep convective regions due to the momentum deposition from these structured cloud systems. Further modeling investigations with the observed cloud asymmetry can quantify their impacts on global circulations in the upper troposphere and lower stratosphere.
 This work is performed at Jet Propulsion Laboratory. Helpful discussions with AIRS group, Kaoru Sato and Hye-Yeong Chun are highly appreciated. We would also like to thank the two reviewers for insightful suggestions and comments.
 The Editor thanks the two anonymous reviewers.