Understanding and predicting climate changes requires accurate measurements of Earth's radiation budget. Due to its large variability in space and time, the cloud radiative effect (CRE) poses arguably the greatest difficulty in estimating the radiation budget balance at both the top of the atmosphere (TOA) and surface. Complexities in cloud three-dimensional structures, in particular, are one of the primary sources of the uncertainty and difficulty, which affect satellite cloud observations as well as CRE calculations in global climate models (GCMs).

Cloud 3-D effects manifest themselves in multiple forms: cloud is visibly irregular and the internal mass structures are also inhomogeneous. The cloud vertical structures are difficult to resolve in passive satellite observations. Subsequently, they are significantly simplified in GCMs. Oversimplified or improper treatment of the cloud 3-D structure increases the uncertainties or generates additional biases of satellite cloud property retrievals (), GCM simulations of cloud fields and atmospheric constituent retrievals .

As one key vertical aspect of cloud 3-D structure, cloud slantwise tilt is inherently linked to cloud thermodynamics and gravity waves coupled with heating profiles. Systematic cloud tilt structures can have profound impacts on cloud remote sensing and radiation calculations. For example, they partially account for the anisotropy of the cloud radiative forcing and modulate the hydrological cycle . Neglecting or misrepresenting the cloud tilt induces additional biases in satellite retrieval of cloud properties (e.g., ) and increases uncertainty of model CRE estimation (e.g., ). In GCM, cloud slantwise tilt is tied to the “overlap” parameter, which is assumed to be “maximum-random” globally in most GCMs to achieve the desired cloud fraction or radiation balance. However, studies have shown that this parameter has large geographical and temporal variations around the globe , which implies that the prevailing assumption in GCMs needs to be improved and could be constrained by satellite observations.

Very few global surveys have been published on cloud tilt structures so far. It is difficult for passive sensors because of their coarse vertical/horizontal resolutions and variable penetration depths, yielding ambiguous information about cloud internal structures. Nevertheless, were able to derive cloud tilt statistics of the upper troposphere cloud in the zonal direction using radiance data from NASA's Aqua Atmospheric Infrared Sounder (AIRS) and NOAA's Microwave Humidity Sounder (MHS). Ground-based radar observations, plotted in the time series domain, often show tilt structures, which are however contaminated by rainfall signals from time to time .

In this study, we make a novel use of polar-orbiting CloudSat Cloud Profiling Radar (CPR) data to characterize global cloud tilt structures in the meridional direction. CloudSat provides unprecedented quality of high-resolution ice water content (IWC) measurements for investigating cloud internal structures in the upper troposphere (UT) . By integrating CloudSat IWC along different slant paths, we find that ice clouds at height greater than 11 km are systematically tilted poleward from active convection centers in the tropics [30∘ S, 30∘ N]. The observed cloud tilt structures resemble the divergent flow at the top of deep convection and convergence below in the tropical branch of the Hadley circulation.

Launched in April 2006 into a sun-synchronous orbit, CloudSat has the same equator crossing time (∼ 01:30/13:30 local time) on the ascending/descending as other A-Train constellation members. CloudSat CPR, a 94 GHz nadir-scan radar, returns the aggregation of 600 pulses every 0.16 s during which the platform travels 1.1 km

http://disc.sci.gsfc.nasa.gov/atdd/documentation/ATrainTracks.pdf

By differencing the CloudSat IWP in the upper troposphere (11–17 km) along the 77∘ viewing angles (S-view minus N-view), we found that UT ice cloud mass in the tropics tilted systematically poleward in both hemispheres, as shown in the left panel of Fig.  for the December–January–February (DJF) and right panel for the June–July–August (JJA) composites. The time separation roughly characterizes two broad tropical deep convective zones, namely South America, southern Africa and the western Pacific during DJF, and west of Central America, western Africa and the Asian Monsoon region including the Maritime Continent during JJA. The maps derived from ascending and descending orbits separately are highly similar to each other (not shown). Given the fact that CloudSat's orbit is not strictly perpendicular to the equator (82∘ angle at the equator), any signal from the zonal direction projected to the orbit track would be with the opposite sign between the ascending and descending orbits. Therefore, the highly consistent geographic patterns between the day (ascending) and night (descending) imply that the signals should mainly originate from the meridional direction rather than the zonal direction. The relative importance of the mass asymmetry due to the systematic tilt, as measured by ΔIWP/IWP, could easily reach up to 20 % near the two flanks of the aforementioned tropical deep convective zones (Fig. c and d). The sign of the difference is consistent among all four view-angle pairs (not shown), except that the magnitude increases with increasing view angle values, indicating that the UT ice cloud mass is tilted in a very shallow angle with respect to the horizon (≤ 90∘ - 77∘ = 13∘). However, these clouds are not completely flat, which should otherwise result in no difference of IWP between paired views. A similar analysis has also been carried out with DARDAR IWC profiles, and the patterns are highly consistent with those found from CloudSat except that the magnitude of the difference is slightly smaller while the relative importance remains the same order of magnitude (Fig. ). This is to be expected for IWP as CloudSat alone can detect the majority of cloud ice. The broad consistency between CloudSat and DARDAR analysis results show the robustness of our findings.

From Figs.  and , we see that the patterns are more zonal during JJA than those during DJF, mainly because the continental deep convective centers are located further south during DJF than the latitude migration of the Intertropical Convergence Zones (ITCZs). The “upward-diverging” feature is not only ubiquitous to the tropics, but also present at the north and south flanks of mid-latitude summer active convection regions such as the Southern Pacific Convergence Zone (SPCZ) during DJF, and central United States and southern Europe during JJA, where deep convective towers often penetrate upward beyond the 11 km level. Note that the smoothing window is narrower in the top panels of Fig.  to highlight these mid-latitude details. The major reason that no signals were found from the rest of mid-latitude area is due to a shallower tropopause height there (< 11 km). The same analyses were performed by truncating the mid-latitude troposphere into the 5–8 and 8–11 km sectors. Systematic poleward tilt is discovered in the 8–11 km layer cloud in the winter mid-latitudes along storm tracks (not shown). Therefore, we should not interpret too much about the relative importance of maps in the mid-latitudes as the sample size is very limited above 11 km.

Intuitively, the systematic cloud tilt should be somewhat related to the local or general circulation. In the meridional direction at the tropics, the Hadley Cell dominates the tropospheric circulation, which has the convergence flow at the lower level in the tropics, and divergence flow at the upper level in the subtropics. In reality, the Hadley Cell has a complicated longitudinal structure. The cloudy-sky meridional wind derived from Modern-Era Retrospective analysis for Research and Applications (MERRA) analysis data sets is overlaid as arrows in Fig. a and b to illustrate the divergent upper-level branch of the Hadley Cell circulation in most places over the tropics. Here, the cloudy-sky is defined as MERRA IWC larger than 10 mg m-3 anywhere between 11 and 17 km in altitude. The divergent flow is generally larger at the peripheries of the active tropical convective regions than that close to the centers, coinciding with the largest cloud asymmetry patterns. This suggests that the systematic UT cloud mass tilt does somewhat follow the general circulation in the meridional direction at the tropics. However, the meridional wind in the Asian Monsoon and Maritime Continents region during JJA is predominantly southward, while the UT cloud mass tends to tilt the same way as other regions in the tropics. The dominant southward flow in this area is associated with pan-continental-scale anti-cyclonic monsoon circulation, yet the cloud mass tilt is not controlled by this large-scale circulation but still follows the Hadley-cell type of divergence flow pattern. More interestingly, the results suggest that UT cloud mass tilt does not follow the shape of the tropopause that slopes down away from the equator. The implications will be discussed in the next section. The meridional wind over central USA and southern Europe during JJA is very small and non-divergent, again indicating that the UT cloud tilt does not always follow the general circulation.

Ice cloud tilt in the middle troposphere (5–11 km) still has some ambiguities due to large uncertainties embedded in IWC retrievals below 9 km for heavily precipitating cases. The simplified assumption of IWC/liquid water content (LWC) partitioning of this data set in mixed-phase conditions contributes another big source of uncertainty. Even if we could exclude those cases, IWC itself cannot reveal the entire cloud mass/shape structure in the lower level as liquid and mixed-phase clouds dominate there (e.g., the rounded bottom of deep convective clouds of Fig. a between 9 and 10∘ N). Preliminary results from CloudSat suggest that 5–11 km ice cloud mass at the tropics tilt the opposite way to that in the UT (i.e., equatorward, part of which will be shown in Fig. b), although the cloudy-sky wind at that altitude range is still weakly divergent in the broad picture as suggested by MERRA analysis and Multi-angle Imaging SpectroRadiometer (MISR) mid-level wind data sets (not shown). Meanwhile, mass tilt in this altitude range is barely statistically significant at a 95 % confidence level as noted in DARDAR (not shown). Given the fact that the ice mass tilt in the middle troposphere is largely debatable, we will show using the WRF simulations that CloudSat results might be more reasonable.

As seen in Fig. d, the UT cloud tilt is relatively more important along the ITCZ cloud bands to the west of Central America and central Africa, while the situation is more complicated and less important in the Asian Monsoon region. Therefore, west of Central America (WCA), with a relatively simple surface condition, is an ideal region to conduct a numerical experiment to investigate the underlying causes of the observed tilt.

In the WRF experiments, we randomly selected three days within 1 month to initialize the simulation (1, 15, 30 August 2009). Each simulation lasted for 2 days. The National Center for Environmental Prediction (NCEP) Global Forecast System (GFS) Final analyses (FNL) served as the boundary and initial conditions. In a nested configuration, the model has a primary domain (D01) with a 30 km horizontal resolution, a secondary domain (D02) with a 10 km horizontal resolution and the innermost domain (D03) with a 3.3 km horizontal resolution. Each nested domain is driven along the lateral boundary conditions supplied by the parent domain with coarse resolution. The domain map is shown in Fig. . The vertical resolution is roughly 500 m from the surface up to 50 hPa (the model top). The inner domain boundary is [118, 77∘ W; 2.5∘ S, 22.5∘ N]. No damping of vertical motion or gravity wave is specified. As part of the provided microphysical scheme in WRF, the Morrison double moment scheme with forecast for six hydrometers in every time step was employed for all runs . Since the cumulus parameterization has been turned off in D03, this configuration can reasonably capture the cloud vertical structure, despite the fact that clouds smaller than 24 km horizontally and 4 km vertically (∼ 8 × grid size) would be significantly under-resolved. Results from D02 with cumulus parameterization served as the sensitivity experiment to test whether realistic convection without subgrid-scale parameterization is the key to reproduce the observed cloud slantwise tilt. The hourly output from D02 and D03 was first interpolated to 250 m vertical and 1.1 km horizontal resolution and then analyzed and averaged together to represent the climatological mean condition.

Overall, D03 simulations show impressive agreement with CloudSat observation in terms of the geographical distributions of the mean IWP and the systematic ice cloud mass tilt in both the middle and upper troposphere. Given the fact that we are comparing 6-day simulations (with a hourly outputs; Fig. c and d) with 12 months of CloudSat overpass samples in the same region (Fig. a and b), the D03 simulations are good enough to qualitatively represent the climatological spatial patterns of middle-level converging and upper-level-diverging cloud mass tilt. The cloud structural inclination again fits the conceptual picture of flow convergence in the lower level and divergence in the upper level within the rising branch of the Hadley Cell. As the simulated mean IWP shows two centers of enhancement in the upper troposphere, the systematic “upward-diverging” cloud tilt structures occur at the north and south flanks of both centers separately (Fig. c). This feature again demonstrates that systematic cloud tilts in the UT always occur at the meridional peripheries of deep convective centers but not within the center.

In the middle troposphere, most ice clouds are convective cumulus. Some of previous case studies suggested that the tilt of convective core within a convective system could experience a life cycle of leaning downshear, upright and upshear with respect to the low-level wind shear . The climatological characteristic of the vertical orientation of deep convective cumulus has not been well studied nor understood at all. Both Fig. d observed by CloudSat and Fig. e simulated by WRF D03 experiment show generally opposite patterns to the UT ice clouds, so we can reach the conclusion that the mid-level ice cloud mass tends to exhibit a “converging” signature on a climatological mean. However, the discrepancy between DARDAR and CloudSat observations in the mid-level is still not explained. Also, the magnitude of ΔIWP is 5–10 times smaller in D03 simulation than that observed by CloudSat. The smaller ΔIWP in D03 may probably be attributed to the coarse model resolutions (3.3 km) that could not explicitly resolve enough details of the cloud structures. On the contrary, simulation results from D02 do not reproduce the observed mean IWP distribution and the mass asymmetries (Fig. e and f). Hence, we can conclude that the shutdown of cumulus parameterization (thereby, allowing the model to resolve clouds) is the key to successful generation of the systematic cloud mass tilts. In other words, realistic representation of convective processes is fundamental in capturing the cloud inhomogeneity.

UT systematic cloud tilt could introduce a non-trivial error to limb/sub-limb satellite retrievals of ice cloud mass. In this paragraph, we aim to check whether same issue could be present for ground instruments as well. To accomplish this, slantwise integration paths are now set to start from the ground (technically 3 km to avoid topography) upward and end at an altitude of 19 km, and the cloud location is now registered at the starting point of integration. This is illustrated in Fig. . Note that the southward view still means looking southward, but opposite to the satellite-based view. This ground-based concept should be differentiated from the previous “satellite-based view” shown in Fig. c. Here, the focus is to study the impact from the systematic ice cloud tilt on ground instrument measurements, rather than the physics of cloud vertical orientation. With this consideration, 19 km rather than 17 km was chosen as the ending point of mass integration since ice clouds rarely penetrate up beyond 19 km. Figure  gives the IWP difference of ground-based view from four pairs of view-angle versus the nadir view (Fig. a) and ΔIWP between paired views computed from CloudSat data (Fig. b). Surprisingly, slantwise IWP is only slightly smaller than the nadir IWP; the largest discrepancy, observed at the most oblique views (equivalent to 76∘) is only 4 % of the mean IWP across all latitudes. This is mainly originated from a slightly larger cloud occurring frequency at oblique view angles. Through the total column integration, the south–north difference induced by the systematic cloud tilt is also trivial compared to nadir mean (Fig. b). However, if we integrate from 11 km upward to 19 km using the ground-base viewing geometry, the results look almost identical to Fig.  (not shown). This is somewhat expected since it is not fundamentally different from the satellite view shown in Fig. c, and parallax effect should only be important to the boundaries of each grid box. As was explained and shown by Fig. b and d before, mid-troposphere ice cloud tilt presents the opposite direction of its counterpart in the UT region. This ground-based view study reveals that their effects can be largely canceled out through the total column integration, and, therefore, we can conclude that systematic ice cloud tilt may not induce potential uncertainty to ground cloud measurements. Consequently, it is not a concern either for satellite nadir or near-nadir measurements that penetrate through the total column of atmosphere.

CloudSat, DARDAR observations and WRF “cloud-resolving” simulations all suggest that systematic UT cloud mass tilts tend to occur at the northern and southern peripheries of tropical deep convective regions. The corresponding cloudy-sky meridional wind climatology indicates that the observed/simulated systematic cloud tilt is likely associated with local large-scale divergent wind, which is a part of the Hadley Cell circulation. However, this explanation does not hold in the Asian Monsoon region, in the summer central United States or southern Europe, the latitudes of which beyond the reach of the rising branch of the Hadley Cell. More importantly, the largest systematic asymmetries do not occur near the most active convective centers where wind divergence is the largest. Besides, the upward sloping of UT cloud cannot be attributed to the meridional wind only. At 5–11 km, Hadley circulation computed from the reanalysis wind is weakly divergent. Therefore, the possible 5–11 km ice cloud equatorward tilt cannot attributed to the general circulation, either. Our results suggest that the structural characteristics of UT clouds, including anvil and cirrus clouds, are not simply controlled by the large-scale general circulation. The local in-cloud circulation must be critical.

We propose the climatological adding and canceling effect as the major cause of the observed cloud tilt pattern. As depicted by the conceptual diagram in Fig. , each individual convective cloud or cloud system could form such an upward-diverging cloud structure at the upper-level due to mass and momentum continuity. Within the active convection centers such as the ITCZ belt, a myriad of individual convection/convective systems would lead to a large cancellation of the tilt effect, and only at the northernmost and southernmost flanks can we identify such a net adding effect of systematic cloud inclination. It is remarkable that the adding effect dominates over the canceling effect across such a wide latitude range (5–10∘). This hypothesis may also explain the features occurring in the mid-latitude convective centers during summer seasons. The mid-level converging tilt, if real, may be also attributed to this adding and canceling effect assuming that the slantwise orientation of the convective core is determined by lower level wind below 5 km. Further analysis of wind-cloud tilt relationship is required to confirm this hypothesis. Unfortunately, due to the lack and difficulty of in-cloud wind measurements, we cannot test this hypothesis in this paper. It is also of great interest to study details of the “in-cloud wind versus tilt angle” relationship that is possibly affected by other factors (e.g., CAPE, vertical velocity, different stage of cloud development, etc.).

Clearly, neglecting systematic cloud tilt in satellite retrieval can result in additional biases especially for limb sensors (e.g., Microwave Limb Sounder), nadir sensors at slantwise view-angles (e.g., AIRS, MODIS) and conical sensors (e.g., Clouds and the Earth's Radiant Energy System). For example, acknowledged the impact on AIRS cloudiness in the zonal direction, where they concluded that up to 50 % of AIRS view-angle asymmetry could be attributed to the systematic westward-tilted cloud structures in the UT. Aura Microwave Limb Sounder (MLS) day (night) forward-looking view is analogous to CloudSat northward (southward) looking view with a shallower viewing angle (∼ 86∘). Therefore, the cloud ΔTB between MLS descending and ascending orbits contain mixed information from the cloud structures and cloud diurnal variation. This is a common issue for other cross-track sensors as well. Strikingly, the night and day radiance difference (ΔTB) from MLS forward scan at 640 GHz (peaking at ∼12 km) has a high degree of agreement with the IWP difference derived from CloudSat observation in terms of geographic locations and magnitudes, as shown in Fig. . The highly consistent pattern strongly suggests that systematic cloud tilt contributes to a significant part of MLS ΔTB signal. Based on our current study, the slantwise ice cloud mass orientation would result in errors of 5–20 % in IWP or IWC retrievals using an off-nadir scan angle. The errors would be systematic at the north and south flanks of the tropical deep convective centers with a latitude width of 5–20∘. The same order of magnitude of uncertainty would also be present inside the active convective centers when performing individual cloud profile retrieval, despite that the climatological impact is probably trivial due to the cancellation effect from large sampling. Hence, one should always be cautious of interpreting the ascending–descending difference purely as cloud diurnal variations or “over-correcting” all angle-dependent cloud asymmetries as observational biases/artifacts.

The “against-tropopause shape” and “against-mean meridional wind” cloud mass tilt has strong implications on the dynamical impact of cloud associated momentum and energy transport. We found from this study that structural characteristics of anvil and cirrus clouds tended to be determined by in-cloud circulation rather than the prevailing general mean flow. Moreover, the UT ice cloud mass tilt seems not to be controlled by the low-level wind shear because it remains the same between CloudSat ascending and descending orbits when the mid-latitude summer convections are at different stages . Are cloud induced momentum and energy fluxes at the tropopause level particularly strong over the regions where the systematic cloud mass tilt is the most apparent? Cloud-resolving-scale modeling studies (beyond what has initially been done here) are required to answer such kind of questions.

This study also has some implications for CRE evaluation. Studies have shown that CRE in the UT region also affected the cross-tropopause mass transport of atmospheric constituents . Cloud inhomogeneity within satellite footprint has been treated with sophisticated schemes by some satellite observational teams (e.g., CERES) in the calculation of shortwave (SW) CRE, but the longwave (LW) CRE calculation has not taken the cloud vertical asymmetry into consideration so far . Although thick clouds are opaque at IR band, thin clouds like cirrus are not. The IWP difference from observing a slantwise tilted cirrus at off-nadir views is expected to be positively correlated with TB difference at IR channels, causing an angle-dependent LW CRE estimation. claimed that LW CRE was different by 8–16 % between realistic vertical overlapping (i.e., vertical geometry) and the “maximum-random” assumption using a month-long cloud resolving simulation, which was on the same order of SW CRE uncertainty and in the same range as our estimation. Discrepancies among active and passive satellite sensors on the derived LW CRE may be partly attributed to the tilted cloud structures as well . Cloud tilts also affect the precipitation/rain pattern. For example, found that the estimates of surface rainfall were greatly improved when they switched the cloud-overlapping scheme from a standard option to a physical-based one.

By integrating and differencing CloudSat/DARDAR ice water content (IWC) along a pair of symmetric slant views, we find that tropical upper troposphere (UT, 11–17 km) ice cloud mass is ubiquitously tilted. The most prominent tilts occur in the north and south flanks of tropical deep convective centers such as the Asian Monsoon region and the ITCZs. The UT clouds in the tropics generally produce poleward-tilted ice columns, rendering significant view-angle dependent cloud ice differences. The slant-view IWPs can differ by 5–20 % from opposite scan angles, depending on what view angle is used. Cloud-resolving-scale WRF model simulations over the western Central American ITCZ showed good agreement with the CloudSat-observed cloud tilt structures at 11–17 km. Moreover, both CloudSat and WRF simulations suggest a mid-level (5–11 km) cloud mass converging tilt as well, while the total column integration of the opposite-tilted structures largely cancel out the effects of each other. The mid-level tilt is still debatable due to large uncertainties associated with the limitation of W-band radar in precipitating scenes and mixed-phase scenes, and the coarse resolution of WRF simulations.

These cloud tilt characteristics are consistent with the convective outflow from tropical deep convection as a result of mass conservation. The constructively adding and canceling effect of a large ensemble of tilted cloud ice mass, driven by in-cloud circulation, can explain the geographic distribution of systematic cloud mass tilt. However, due to lack of accurate in-cloud wind measurements, the proposed hypothesis has not been verified and remains to be tested in the future study.

This study for the first time presents a global characterization of cloud tilt structures in the middle and upper troposphere. The observed IWP differences in the paired slant views have important implications for remote sensing and modeling of global cloud systems, including satellite retrieval of cloud properties, atmospheric momentum and energy budget, CRE calculation and modulation of the hydrological cycle. The study raises more questions than answers, notably the wind-tilt angle relationship, and potential impacts on energy, momentum and hydrological cycles. More importantly, as GCMs continue to improve their resolution (e.g., NICAM; ), vertically tilted cloud structures will become explicitly resolved. The modeled cloud 3-D inhomogeneity is subject to verification against the observations as shown in this study.