The signature of the stratospheric Brewer‒Dobson circulation (BDC) in tropospheric cloudiness is investigated in CloudSat and CALIPSO data from June 2006 through April 2011. During the Northern Hemisphere winter, periods of enhanced stratospheric wave driving are associated with increased cloud incidence in the tropical tropopause transition layer (TTL) juxtaposed against decreased cloud incidence in the Arctic troposphere. The results are consistent with the physical linkages between (1) the BDC and near‒tropopause temperature and (2) near‒tropopause temperature and upper tropospheric cloud incidence. The key finding of the work is that changes in the stratospheric circulation not only influence cloud amounts in the troposphere but also that they do so in a coupled manner that links climate variability in the Arctic and upper tropical troposphere. The results provide a pathway through which stratospheric processes influence tropospheric climate that is in addition to stratosphere/troposphere dynamical coupling.
 The stratospheric Brewer‒Dobson circulation (BDC) is marked by large‒scale upwelling in the tropical stratosphere and downwelling in the extratropical stratosphere [e.g., Holton et al., 1995]. The circulation consists of a relatively shallow cell in the lowermost stratosphere that extends from the tropics to low‒middle latitudes, and a deeper cell that extends to polar latitudes [Plumb, 2002; Birner and Bon̈isch, 2011]. The shallow cell and its associated temperature anomalies are believed to be driven primarily by breaking equatorial planetary waves and synoptic‒scale waves [Held and Hoskins, 1985; Plumb and Eluszkiewicz, 1999; Boehm and Lee, 2003; Kerr‒Munslow and Norton, 2006; Norton, 2006; Randel et al., 2008; Ryu and Lee, 2010; Garny et al., 2011; Chen and Sun, 2011; Grise and Thompson, 2012; Zhou et al., 2012]; the deeper cell and its associated temperature anomalies are believed to be driven primarily by planetary‒scale wave breaking in the extratropical stratosphere [Haynes et al., 1991; Holton et al., 1995; Ueyama and Wallace, 2010; Zhou et al., 2012; Grise and Thompson, 2013].
 The BDC has important implications for global climate. It influences temperatures and concentrations of ozone and water vapor throughout much of the global stratosphere [Brewer, 1949; Dobson, 1956; Holton et al., 1995; Mote et al., 1996; Shepherd, 2007]. It transports sulfate aerosols due to explosive tropical volcanic eruptions to middle and high latitudes [Robock, 2000]. And notably, it is predicted to increase in strength in response to anthropogenic emissions of carbon dioxide in virtually all climate change simulations [e.g., Butchart and Scaife, 2001; Butchart et al., 2006; Li et al., 2008; Garcia and Randel, 2008; McLandress and Shepherd, 2009; Butchart et al., 2010]. The purpose of this study is to demonstrate that variability in the BDC also has a significant influence on clouds at tropospheric levels in two key regions of the atmosphere: the tropical tropopause transition layer (TTL) and the Arctic troposphere.
 Clouds play a central role in the climate of both the TTL and Arctic troposphere. The TTL extends from roughly the level of near‒zero clear‒sky radiative heating in the upper tropical troposphere (∼15 km) to the lower stratosphere (∼18.5 km) [e.g., Highwood and Hoskins, 1998; Fueglistaler et al., 2009]. Clouds in this region not only impact the radiative budget of the tropics [Liou, 1986; Prabhakara et al., 1988; Ramanathan and Collins, 1991; Jensen et al., 1996; Rosenfield et al., 1998; McFarquhar et al., 2000; Hartmann et al., 2001; Haladay and Stephens, 2009] but also regulate the water vapor content and chemical balance in the global stratosphere [Holton et al., 1995; Rosenfield et al., 1998; Jensen et al., 2001; Holton and Gettelman, 2001; Gettelman et al., 2002]. Clouds in the Arctic troposphere play a similarly important role in the polar radiative budget [e.g., Curry et al., 1996; Kay et al., 2011] and potentially contribute to long‒term changes in Arctic sea‒ice [Francis et al., 2005; Kay et al., 2011; Kay and Gettelman, 2009].
 The current evidence for linkages between stratospheric dynamics and clouds in the TTL derives from two primary observations. First, field experiment data reveal linkages between the incidence of tropical stratospheric waves and changes in cirrus near the tropical tropopause [e.g., Boehm and Verlinde, 2000]. Second, the seasonal cycle of cirrus in the uppermost tropical troposphere is more closely tied to the seasonal cycle of temperatures in the lowermost stratosphere than it is to the tropospheric processes [Zhang, 1993; Virts and Wallace, 2010]. That said, the seasonal cycle of tropical tropopause temperatures is influenced by both tropospheric and stratospheric processes [Holton et al., 1995; Ueyama and Wallace, 2010; Grise and Thompson, 2013]. Thus, the coherence between the seasonal cycles of TTL cirrus and tropical tropopause temperatures is not necessarily indicative of a stratospheric influence on upper tropical tropospheric clouds. We are unaware of any study that has explicitly linked wave‒driven variability in the BDC to the incidence of clouds in the polar troposphere.
 Here we provide evidence for robust linkages between the stratospheric BDC and cloud incidence in both the TTL and polar troposphere on month‒to‒month timescales. The analyses exploit 5 years of remotely sensed cloud incidence data derived from the merged CALIPSO/CloudSat data set. The data are described in section 2; the results are presented in section 3; conclusions are provided in section 4.
2 Data and Analysis Details
 The cloud data used in the study are from the CloudSat and CALIPSO satellites [Stephens et al., 2002]. The cloud fraction data are obtained from the Level 2B Geometrical Profiling‒LIDAR product (2B‒GEOPROF‒LIDAR; version P2R04), which combines information from the CloudSat Cloud Profiling Radar (CPR) and CALIPSO lidar. The merged CALIPSO/CloudSat data provide a more reliable estimate of TTL cirrus than the CALIPSO data alone since the radar is capable of sensing optically opaque cirrus near convection that may be missed by the lidar pulse [Mace et al., 2009; Haladay and Stephens, 2009]. The analyses here are based on roughly 5 years of CloudSat observations from June 2006 through April 2011.
 The results are presented in terms of “cloud incidence,” which provides a quantitative estimate of the likelihood of a cloud within a given volume sensed by the satellite. The CloudSat and CALIPSO satellites orbit the Earth roughly 14.5 times per day. The CloudSat footprint is roughly 1400 m cross track and 2500 m along track, and the vertical sampling is at roughly 240 m. Cloud incidence is calculated within all 1400 × 2500 × 240 m 3volumes sampled by the satellite and is then binned into monthly mean, zonal‒mean data with spatial resolution 1.5° (latitude) × 240 m (vertical). Cloud incidence ranges from 0 to 100%: cloud incidence of, say, 50% at 20°N and 5 km altitude indicates that a cloud was observed 50% of the time within the 1.5° × 240 m region centered on 20°N and 5 km. See Verlinden et al.  for a more detailed description of the calculation of cloud incidence and the reason of using cloud incidence rather than ice/liquid water content.
 Instantaneous relationships between cloud incidence and temperature are assessed using the CloudSat European Centre for Medium‒Range Weather Forecasts Auxiliary (ECMWF‒AUX) product. The ECMWF‒AUX product is created by interpolating the ECMWF variables to the same spatial and temporal resolution as the CloudSat CPR bins [Partain, 2004; Benedetti, 2005]. Relationships between cloud incidence and the meteorology on annual and interannual timescales are assessed using the European Centre for Medium Range Weather Forecasts (ECMWF) Interim Reanalysis (ERA‒Interim) [Simmons et al., 2007]. The ERA‒Interim reanalysis is available at six‒hourly increments on a 1.5° × 1.5° horizontal mesh and at 37 discrete pressure levels.
 Tropopause height is defined following the World Meteorological Organization (WMO) lapse rate definition [WMO, 1957]. That is, the tropopause is defined as the lowest level z at which (1) the lapse rate is less than 2 K km −1, and (2) the average lapse rate between z and all higher levels within 2 km does not exceed 2 K km −1. Static stability is defined as , where g is 9.81 m s −2and θ is the potential temperature. Anomalies are computed by subtracting the long‒term mean annual cycle from the data.
2.2 Brewer‒Dobson Circulation Index
 As noted in section 1, the deep, equator‒pole branch of the stratospheric Brewer‒Dobson circulation is driven primarily by planetary‒scale wave breaking in the extratropics [Haynes et al., 1991; Holton et al., 1995; Ueyama and Wallace, 2010; Zhou et al., 2012; Grise and Thompson, 2013]. The net planetary wave driving in the extratropical stratosphere is proportional to the vertical flux of wave activity in the lowermost stratosphere. The vertical flux of wave activity in the lower stratosphere is, in turn, proportional to the zonal‒mean meridional eddy flux of heat at 100 hPa: v∗T∗100 hPa, where the brackets denote the zonal mean and asterisks denote the deviation from zonal mean. Similar indices of stratospheric wave driving have been exploited by Waugh et al. , Newman et al. , Randel et al. [2002a], Polvani and Waugh , and Ueyama and Wallace .
 The planetary wave drag due to topography‒excited stationary waves is much larger in the Northern Hemisphere (NH) than it is in the Southern Hemisphere (SH), and it is very weak during summer when the lower stratospheric zonal flow is easterly [Charney and Drazin, 1961]. As such, the planetary‒scale wave‒driven BDC has largest amplitude in the NH and during boreal winter [e.g., Yulaeva et al., 1994; Rosenlof, 1995]. For this reason, we focus on the wave fluxes averaged poleward of 30°N (v∗T∗100 hPa, 30−90°N), and regressions on the wave fluxes are centered on the months October–March. The fluxes are calculated from six‒hourly instantaneous v and T and then averaged to form monthly means.
 The results hinge on the links between stratospheric wave driving and near‒tropopause vertical motion and thus temperatures. On month‒to‒month timescales, stratospheric wave driving is correlated with temperatures during both the current and subsequent month, i.e., the radiative relaxation timescales in the lower stratosphere are roughly 1 month [e.g., Newman and Rosenfield, 1997; Randel et al., 2002b]. For this reason, following Ueyama and Wallace , we define our index of the BDC as weighted average of v∗T∗100 hPa, 30−90°N formed from the previous and current months values. The corresponding weights are determined via an empirical fit of the v∗T∗100 hPa, 30−90°Ntime series to lower stratospheric temperature anomalies averaged between 30°S–30°N and 70–100 hPa. As noted in Ueyama and Wallace , the weights applied to the previous and current months values of v∗T∗100 hPa, 30−90°N are roughly two and one, respectively. That is, the BDC index value for month i is defined as follows:
where (i) is the current month and (i−1) is the previous month. The results are not sensitive to the specific weights chosen in the regression for defining the BDC index, e.g., analyses based on weights ranging from 1:1 to 3:1 yield similar results. The resulting BDC index time series is then standardized so that it is dimensionless. The standardized BDC index is hereafter referred to as BDCNH. The results are not sensitive to the specific reanalysis product used to create the BDC index (the correlation coefficient between BDCNHindices generated from the ERA‒Interim and National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Reanalyses data sets is r=0.99).
 Variability in the large‒scale BDC during NH winter influences tropopause temperatures and thus near‒tropopause static stability in both the tropics [e.g., Yulaeva et al., 1994; Highwood and Hoskins, 1998; Gettelman and Forster, 2002; Birner, 2010] and Arctic [e.g., Birner, 2010; Grise et al., 2010]. In this section, we will first establish the robustness of the linkages between cloud incidence and tropopause temperatures in both these regions. We will then draw on the inferred linkages to motivate and support the analyses between cloud incidence and stratospheric wave driving.
3.1 Cloud Incidence as a Function of Sea Surface Temperature (SST) and Tropopause Temperature
 The left and middle panels in Figure 1examine the vertical distribution of cloud incidence over the tropical ocean as a function of sea surface temperature (SST; Figure 1a) and over the tropical ocean and land as a function of tropopause temperature (Figure 1b). The tropics are defined as regions equatorward of 30° within which SSTs exceed 300 K (Figure 1a), and tropopause temperatures are less than 198 K (Figure 1b). The right panel examines the vertical distribution of cloud incidence as a function of tropopause temperatures over the Arctic poleward of 60°N (Figure 1c). The results in Figure 1are based on contemporaneous relationships between (a) cloud incidence from CloudSat/CALIPSO product and (b) sea surface and tropopause temperatures from the ECMWF‒AUX product. The seasonal cycle has not been removed from the data, and the results were calculated on a volume‒by‒volume basis for all satellite swaths from June 2006 through April 2011. They reflect information gleaned from more than 2 × 10 8individual profile measurements over the tropics and more than 9 × 10 7individual profile measurements over the Arctic. The results are not sensitive to the specific thresholds chosen to define the tropics and the Arctic.
 A more detailed discussion of the vertical structure of cloud incidence as a function of SST and tropopause temperature is provided in the companion paper [Li et al. 2013, On the linkages between cloud vertical structure and large‒scale climate, to be submitted to Journal of Geophysical Research]. The key results in Figure 1for the purpose of this study are the strong linkages between tropopause temperatures and upper tropospheric clouds at both tropical and NH polar latitudes.
 In the tropics, cloud incidence increases by ∼10% K −1with increasing SST between 300 K to ∼303 K, and then decreases with increasing SST beyond that value (Figure 1a). The results in Figure 1a are reminiscent of those based on 1 year of CloudSat data shown in 2008]. The increases in upper tropospheric cloud incidence with increasing SST are consistent with the relationships between SST and deep convection for SST above ∼300 K [e.g., Lindzen and Nigam, 1987; Ramanathan and Collins, 1991; Waliser et al., 1993; Lau et al., 1997; Bony et al., 1997; Behrangi et al., 2012]. The decreases in high level clouds beyond ∼303 K could result from increased solar radiation in the regions of subsidence that lie adjacent to the convection maximum [Waliser and Graham, 1993; Waliser, 1996; Lau et al., 1997; Bony et al., 1997; Johnson and Xie, 2010; Kubar et al., 2010].
 Upper tropospheric cloud incidence is also strongly linked to tropical tropopause temperatures. Cloud incidence between ∼12 and 17 km decreases by ∼4% K −1with increasing tropopause temperature between 189 K and 198 K. The linkages between tropopause temperatures and cloud incidences are consistent with those derived from in situ observations of tropical stratospheric waves [Boehm and Verlinde, 2000], the seasonal cycle of TTL cirrus derived from CALIPSO observations [Virts and Wallace, 2010] and the deep convective TTL temperature signal based on collocated CloudSat and COSMIC data [Paulik and Birner, 2012].
 The linkages between tropopause temperatures and upper tropical tropospheric clouds (Figure 1b) are in part due to the coherence between tropopause temperatures and SSTs: regions of anomalously high SSTs are associated with enhanced deep convection which can force large‒scale equatorial waves. Deep convection and the equatorial waves are linked to both TTL temperatures and cirrus [e.g., Boehm and Lee, 2003; Norton, 2006; Virts et al., 2010]. To test the independent relationship between tropical tropopause temperatures and cloud incidence, we show in Figure 2the incidences of clouds between 15–18 km (top) and 10–15 km (bottom) as a function of sea surface (abscissa) and tropopause (ordinate) temperature. The 15 km level corresponds roughly to the base of TTL [e.g., Shepherd, 2007; Fueglistaler et al., 2009]. The results are focused on regions equatorward of 30° within which SSTs are higher than 300 K and tropopause temperatures are lower than 198 K.
 Cloud incidence between 15 and 18 km (Figure 2, top) is clearly a much stronger function of tropopause temperature than of SST. Regions with fixed SST are marked by increasing cloud incidence with decreasing tropopause temperature, whereas regions with fixed tropopause temperature exhibit very little dependence on SST. In contrast, tropical cloud incidence between 10 and 15 km (Figure 2, bottom) is a function of both tropopause and sea surface temperature. Cloud incidence increases with decreasing tropopause temperature but also exhibits a distinct peak near ∼302–303 K. The relationship between tropopause temperature and cloud incidence in the TTL (top panel) is not sensitive to the specific regions chosen to define the tropics, nor the specific altitudes chosen to define the TTL. For example, analyses based on other latitude bands (e.g., 5°S–5°N, 20°S–20°N) and other height levels (e.g., 16–17 km) yield similar results. The results in Figure 2(top) strongly suggest that tropopause temperature plays a central role in determining cloud incidence in the upper tropical troposphere.
 Similar linkages between tropopause temperatures and upper tropospheric clouds are found in the Arctic. Higher tropopause temperatures correspond to depression of the tropopause and thus increased static stability (and presumably anomalous downward motion) in the upper troposphere/lower stratosphere. Such conditions are marked by a reduction in cloud incidence above ∼5 km. Upper tropospheric cloud incidence increases by ∼2% K −1as tropopause temperatures decrease from ∼215 K to ∼200 K. The increases in low‒level clouds for tropopause temperatures greater than ∼230 K derive from the summer season (seasonal results not shown) and are consistent with the formation of low stratiform clouds over open water in regions of large‒scale subsidence.
3.2 The Signature of Brewer‒Dobson Circulation in TTL Cirrus and Arctic Tropospheric Clouds
 In this section, we will build on the relationships between tropopause temperature and cloud incidence established in Figures 1–2to demonstrate a robust link between the stratospheric Brewer‒Dobson circulation and clouds in both the TTL and Arctic troposphere. The BDC index (BDCNH) is based on the vertical flux of wave activity into the NH extratropical stratosphere during winter and is described in section 2.2.
 Before we examine the linkages between the BDC and tropospheric clouds on month‒to‒month timescales, we will first confirm the coherence between the annual cycles of NH stratospheric wave driving and cloud incidence in the TTL. The red line in Figure 3indicates cloud incidence averaged between 30°S–30°N and 15–18 km; the blue line shows the dimensionless BDCNH index. The two time series are clearly coherent: cloud incidence in the TTL and NH extratropical wave driving both peak during the boreal winter season. Virts and Wallace  demonstrated similar coherence between TTL cirrus and tropopause temperatures in 3 years of CALIPSO data. Tropical tropopause temperatures are influenced by both equatorial planetary and extratropical waves [Boehm and Lee, 2003; Kerr‒Munslow and Norton, 2006; Norton, 2006; Dima and Wallace, 2007; Virts et al., 2010; Grise and Thompson, 2013]. The coherence between cloud incidence in the TTL and extratropical planetary wave driving supports their conclusion that the large‒scale BDC plays a central role in the seasonal cycle of TTL cirrus.
 Figures 4–5examine the linkages between the BDC, atmospheric temperatures, and tropospheric clouds on month‒to‒month timescales during the NH winter months October–March. The analyses are based on anomalous data, i.e., the annual cycle has been removed from the BDCNHindex, atmospheric temperature, and cloud incidence. The temperature data is derived from ERA‒Interim.
 Figure 4a shows monthly mean, zonal‒mean temperature anomalies regressed on standardized wintertime values of the anomalous BDCNHindex. The solid black line indicates the climatological‒mean (October–March) tropopause height. As noted in numerous previous studies [e.g., Yulaeva et al., 1994; Rosenlof, 1995; Ueyama and Wallace, 2010; Zhou et al., 2012; Grise and Thompson, 2013], periods of enhanced wave driving in the extratropical stratosphere are associated with anomalously low temperatures in the tropical lower stratosphere and anomalously high temperatures in the polar stratosphere. The negative temperature anomalies in the tropical stratosphere extend down to the tropopause level, although the amplitude of the temperature anomalies decreases below 70 hPa, consistent with the diminishing signal of extratropical planetary wave breaking in the lowermost tropical stratosphere [Grise and Thompson, 2013; Ueyama et al., 2013]. The Arctic temperature anomalies extend down to at least 400 hPa, and the static stability anomalies are statistically significant at 600 hPa. These features are consistent with the penetration of the stratospheric residual circulation to the middle troposphere in the Arctic [see also Figure 9c in Thompson and Birner, 2012]. The penetration of the residual circulation to the Arctic troposphere suggests that stratospheric processes may influence cloud incidence far below the polar tropopause.
 Figure 4b shows the corresponding changes in atmospheric static stability. Here the red and blue lines indicate the climatological‒mean tropopause height plus (red) and minus (blue) the regression of tropopause height onto wintertime values of the BDCNH index. Periods of enhanced stratospheric wave driving lead to (1) anomalously high tropopause heights and anomalously low static stability at ∼100 hPa in the tropics juxtaposed against (2) anomalously low tropopause heights and anomalously high static stability in the upper troposphere/lower stratosphere in the Arctic. The linkages between stratospheric wave driving and static stability near the Arctic tropopause were also shown in Grise et al.  using GPS occultation data.
 Figure 4c shows the corresponding changes in cloud incidence. Month‒to‒month variability in stratospheric wave driving is associated with a distinct pattern of near‒tropopause cloudiness. Periods of enhanced stratospheric wave driving are marked by anomalously high cloud incidence near the tropical tropopause and anomalously low cloud incidence near the Arctic tropopause. The anomalies in tropical cloud incidence are limited to the tropopause region, whereas the anomalies in Arctic cloud incidence extend to the middle‒upper troposphere, consistent with the penetration of the residual circulation to middle tropospheric levels there.
 The linkages between the BDC and cloud incidence revealed in Figure 4c are physically consistent with the relationships between (1) tropopause temperatures and cloud incidence (Figures 1and 2), (2) the BDC and tropopause temperatures and near‒tropopause static stability (Figures 4a and 4b), and (3) static stability and vertical motion. Regions of enhanced static stability near the tropopause level are associated with reduced cloud incidence, and vice versa, presumably through the inferred changes in vertical motion. The linkages between the BDC and cloud incidence revealed in Figure 4c are also highly significant. As shown in Figure 5, variability in the BDC accounts for more than 30% of the month‒to‒month variability in cloudiness in both the TTL and Arctic troposphere. The correlations are even higher (r=0.59) for TTL clouds limited to the latitude band 20°S–20°N and height levels 16–17 km (not shown). The associated correlation coefficients are significant at the 99% confidence level based on a one‒tailed test of the t‒statistic with an effective sampling size of 24 (using the criterion given in Bretherton et al. ).
 The results presented here are based on the covariability between cloudiness and stratospheric wave driving across five boreal winter seasons. We assessed the strength of analogous relationships in association with stratospheric wave driving in the SH during the 2006–2011 period. The analysis was performed for SH spring months when the planetary wave forcing in the SH is strongest (September–December). Eguchi and Kodera  provide anecdotal evidence of linkages between TTL cirrus and the BDC in association with the SH sudden warming of 2002. But we were unable to find a similar relationship between SH wave driving and TTL clouds during the CloudSat era, presumably because the amplitude of the wave driving in the SH is weak relative to that in the NH during the CloudSat era.
4 Concluding Remarks
 The planetary‒scale stratospheric Brewer‒Dobson circulation influences temperatures and static stability in the vicinity of the tropopause in both the tropics and Arctic. Periods of enhanced wave driving in the NH extratropical stratosphere are marked by lifting and cooling of the tropical tropopause juxtaposed against sinking and warming of the Arctic tropopause and vice versa. Here we exploited ∼5 years of data from the CloudSat and CALIPSO instruments to reveal that the influence of the BDC during NH winter extends to clouds in both the TTL and Arctic troposphere. The BDC accounts not only for the seasonal cycle in TTL cirrus (Figure 3) [Virts and Wallace, 2010] but also for ∼30% of the month‒to‒month variability in cloud incidence in both the TTL and Arctic troposphere during NH winter (Figures 4c and 5). The results reveal a novel pathway through which stratospheric processes can influence tropospheric climate.
 The linkages between the BDC and clouds in the TTL and Arctic troposphere are physically plausible and statistically robust. Upper tropospheric cloud incidence is linked to tropopause temperatures in both the tropics and over the Arctic (Figures 1and 2). Tropopause temperatures and static stability in both regions are, in turn, linked to variability in the BDC (Figures 4a and 4b). The subsequent linkages between variability in the BDC and clouds in the TTL and Arctic troposphere are significant at the 99% level (Figure 5).
 The linkages between the BDC and clouds in the TTL and Arctic troposphere have potential implications for both climate change and the ability of models to simulate such change. Climate change simulations reveal robust increases in the strength of the BDC in response to future increases in greenhouse gases [e.g., Butchart and Scaife, 2001; Butchart et al., 2006; Li et al., 2008; Garcia and Randel, 2008; McLandress and Shepherd, 2009; Butchart et al., 2010], and at least some observations suggest that such changes have already occurred [Thompson and Solomon, 2009; Hu and Fu, 2009; Lin et al., 2009; Young et al., 2012]. The changes in cloudiness associated with a strengthening of the BDC may have notable radiative effects on both the TTL and Arctic troposphere. The radiative effects of the linkages documented here and the ability of climate models to simulate such linkages remain to be determined.
 Thanks to William J. Randel and two anonymous reviewers for their helpful comments. Thanks to Graeme L. Stephens for funding support and insightful comments. YL was funded by CloudSAT via NASA JPL and the NSF Climate Dynamics program. DWJT is funded by the NSF Climate Dynamics program.