A-Train estimates of the sensitivity of warm rain likelihood and efﬁciency to cloud size, environmental moisture, and aerosols

. Precipitation efﬁciency has been found to play an important role in constraining the sensitivity of the climate through its role in controlling cloud cover, yet understanding of its controls are not fully understood. Here we use CloudSat observations to identify individual contiguous shallow cumulus cloud objects and compute the ratio of cloud water path to rain water path as a proxy for warm rain efﬁciency (WRE). Cloud objects are then conditionally sampled by cloud-top height, relative humidity, and aerosol optical depth (AOD) to analyze changes in WRE as a function of cloud size (extent). For a ﬁxed cloud-top height, 5 WRE increases with extent and environmental humidity following a double power-law distribution, as a function of extent. Similarly, WRE increases holding environmental moisture constant. There is surprisingly little relationship between WRE and AOD when conditioned by cloud-top height, suggesting that once rain drop formation begins, aerosols may not be as important for WRE as cloud size and depth. Consistent with prior studies, results show an increase in WRE with sea surface temperature. However, for a given depth and SST, WRE is also dependent on cloud size and becomes larger as cloud size increases. Given 10 that larger objects become more frequent with increasing SST, these results imply that increasing precipitation efﬁciencies with SST are due not only to deeper clouds with greater cloud water contents, but also the propensity for larger clouds which may have more protected updrafts.

2018). Nam et al. (2012) hypothesized that shallow cumulus are too reflective in climate models, possibly because model precipitation efficiencies are too weak. This results in excess cloud water which increases cloud optical depth and shallow 25 cumulus reflectance. Prior observational and modeling studies found the precipitation efficiency of shallow cumulus increases as sea-surface temperature (SST) increases in response to climate change (Lau and Wu, 2003;Bailey et al., 2015;Lutsko and Cronin, 2018). Factors including environmental moisture (e.g. Heus and Jonker, 2008;Schmeissner et al., 2015), entrainment (e.g. Korolev et al., 2016;Pinsky et al., 2016b, a), and aerosols (e.g. Koren et al., 2014;Dagan et al., 2016;Jung et al., 2016b, a) help regulate both thermodynamic and dynamical processes that promote favorable conditions important to not only warm rain 30 production, but also the efficiency of the conversion of cloud water to precipitation. To better constrain cloud parameterizations of these processes and subsequently climate sensitivity to low cloud cover, more observations-based studies analyzing physical processes influencing warm rain efficiencies are needed.
In an ideal shallow cumulus cloud, liquid water content increases adiabatically from cloud base to top. However, liquid water content is generally only 50% -80% of the adiabatic values due to entrainment (Gerber et al., 2008). Evaporation induced by 35 cloud-edge mixing not only impacts shallow cumulus updraft strength, but also the number and size of droplets within a cloud (Lu et al., 2012), with increased evaporation potentially reducing the number and size of available droplets. Using a large-eddy simulation (LES), Moser and Lasher-Trapp (2017) found the influence of entrainment decreases from cloud-edge to center of individual shallow cumulus as they grow larger. This results in liquid water content at cloud center being closer to adiabatic in larger clouds, because fewer droplets evaporate away at cloud-center. This implies that the collision-coalescence 40 process is more efficient at cloud center, because there is more cloud water available to be collected by large droplets. At cloud edge, there are not only fewer droplets but also smaller droplets, potentially reducing collision-coalescence efficiencies there. This is consistent with other LES results that found shallow cumulus updrafts are more insulated from entrainment as they increase in size (e.g. Heus and Jonker, 2008;Burnet and Brenguier, 2010;Tian and Kuang, 2016). LES and limited fieldcampaign observational studies have shown that cloud updrafts not only become more protected as cloud size increases, but 45 also as environmental moisture increases (Heus and Jonker, 2008;Schmeissner et al., 2015;Hernandez-Deckers and Sherwood, 2018). Romps (2014) used a cloud model to show that precipitation efficiency decreases as relative humidity decreases, because precipitation evaporates more readily in a drier environment. Considering environmental moisture scales with temperature, this is consistent with results found by Lau and Wu (2003) which show the efficiency of warm rain production increases as SSTs increase using Tropical Rainfall Measuring Mission (TRMM) satellite observations. Given LES results showing that shallow 50 cumulus updrafts are more protected as clouds grow in size and/or environmental moisture increases, we hypothesize larger droplets will be evident closer to the cloud base and increase WRE in larger cloud objects, because the cloud-core of larger cloud objects is more protected from entrainment.
While perhaps not as important as organization (Minor et al., 2011) or cloud size (Jiang and Feingold, 2006), it is widely understood that aerosol concentrations act to suppress warm rain production (Twomey, 1974;Albrecht, 1989) by increasing 55 the cloud droplet concentration and reducing cloud droplet sizes (Squires, 1958). Albrecht (1989) found that increasing precipitation efficiency within a model is equivalent to decreasing the amount of cloud concentration nuclei (CCN), which reduces the amount of cloud water. Similarly, Saleeby et al. (2015) used a cloud model to recently find both cloud water and rain drop concentration decreases as cloud concentration nuclei increases. Lebsock et al. (2011) used CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) observations to show that as drop size decreases, the ratio of rain water to cloud 60 water also decreases. Together, these studies suggest the number of large droplets able to fall at sufficient terminal velocities to initiate collision-coalescence and continue growing to large enough sizes to fall out as rain decreases with increasing aerosol concentrations, which would reduce warm rain efficiency (WRE).
Observationally, prior studies have used satellite observations to infer the relationship between precipitation efficiency and both sea-surface temperature (Lau and Wu, 2003) and drop size (Lebsock et al., 2011). However, the relationship between 65 cloud water and precipitation as shallow cumulus grow larger, environmental moisture increases, and/or aerosol loading has only been investigated using cloud models (e.g. Moser and Lasher-Trapp, 2017) and limited field-campaign observations (e.g. Gerber et al., 2008). While these case and model studies provide insight into the physical processes, it is unclear how well they represent the shallow cumulus clouds observed globally. Satellites can observe a large enough sample size of shallow cumulus over different regions and during different stages of their lifecycle to gain a more holistic view of this relationship. Prior studies 70 have used TRMM and Global Precipitation Measurement Mission (GPM) observations to analyze warm rain production and efficiency (e.g. Lau and Wu, 2003). Unfortunately, TRMM and GPM are precipitation radars operating at the Ku-and Kabands not capable of observing the non-raining portions of clouds or light precipitation. Building off work in Smalley and Rapp (2020) that analyzed the relationship between rain likelihood and cloud size, this study uses the higher sensitivity radar of CloudSat in addition to MODIS observations to test the hypothesis that WRE is higher in larger shallow cumulus and is 75 modulated by environmental moisture and aerosol loading.

Data and Methods
To determine if larger shallow cumulus clouds are more efficient at producing warm rainfall, this study uses the CloudSat Cloud Profiling Radar (CPR; Tanelli et al., 2008) to identify individual contiguous shallow cumulus cloud objects. The CPR is a near-nadir pointing 94-GHz radar that can observe raining and non-raining cloud drops. It allows us to analyze the horizontal 80 distribution of cloud within a horizontal footprint of 1.4 x 1.8 km, and the vertical distributions of clouds within a 240 m bin within each cloudsat pixel.
Contiguous cloudy regions are initially identified using the 2B-GEOPROF  cloud mask confidence values ≥ 20, which removes orbit elements that may be influenced by ground clutter . Before identifying cloud objects, 2C-RAIN-PROFILE (Lebsock and L'Ecuyer, 2011) modeled reflectivity is mapped onto the two-dimensional 85 cloud mask field. As outlined by prior literature (e.g. L' Ecuyer and Stephens, 2002;Mitrescu et al., 2010;Lebsock and L'Ecuyer, 2011), modeled reflectivity adjusts the raw reflectivity for multi-scattering and attenuation when it is raining. As described by Smalley and Rapp (2020), we use a lower-tropospheric stability threshold of 18.55 K to separate cloud objects occurring in environments favoring stratocumulus development from those occurring in environments favoring shallow cumulus development. Shallow cumulus cloud objects are then identified using the methodology described by Smalley and Rapp 90 (2020) using the combined two-dimensional reflectivity field, with only single-layer cloud objects included. This study uses 2C-RAIN-PROFILE integrated precipitation water path path (W P ) > 0 to identify raining cloud objects and does not consider non-raining objects. We then store the median cloud-top height and maximum along-track extent (hereby extent) of each cloud object for later analysis.
Although CloudSat 2B-CWC-RVOD (Austin et al., 2009) does provide a cloud water path (W C ) product, the rain drop 95 size distribution used in 2B-CWC-RVOD is not the same as that used in 2C-RAIN-PROFILE. Additionally, Christensen et al. (2013) found that the 2B-CWC-RVOD algorithm struggles to filter out precipitation sized droplets in the presence of light precipitation and drizzle, which results in an overestimation of cloud water. This, coupled with differences in assumed drop size distributions by 2B-CWC-RVOD and 2C-RAIN-PROFILE, makes 2B-CWC-RVOD W C not ideal for this study, so we instead use MODIS W C . While there are biases in MODIS shallow cumulus W C , prior studies have found them to be small in 100 comparison to other satellite retrievals (e.g. Lebsock and Su, 2014). W C is then calculated for each CloudSat pixel by averaging the nearest nine MOD-06-1KM (Platnick et al., 2003) pixels, which have been previously matched to the CloudSat track in the MOD-06-1KM product (?). We then store and analyze the median W C associated with each cloud object.
WRE of each shallow cumulus cloud object is calculated as WP WC . Note, this is a proxy for true WRE, because mass flux of water in and out of a cloud cannot be determined without a model, however this ratio has been used by prior observational 105 studies to analyze the amount of cloud water converted to rain water (e.g. Lebsock et al., 2011).
Considering reflectivity is a function of the drop size distribution to the sixth power, it is expected that the maximum reflectivity in non-raining cloud objects will occur near cloud-top, then shift downward as a cloud transitions from non-raining to raining. Wang et al. (2017) used the vertical reflectivity gradient (VGZ) to investigate warm rain onset. They found VGZ (positive down) reverses sign (positive to negative) when clouds transition from non-raining to raining. Given previous studies 110 and results shown in Smalley and Rapp (2020) finding rain is more likely as clouds grow larger in extent, it is hypothesized that the negative VGZ within individual raining cloud objects will increase in magnitude as cloud objects increase in extent. The methodology developed by Wang et al. (2017) is applied to find the VGZ for each pixel within every shallow cumulus cloud object. VGZ at cloud object center pixel (VGZ CP ) will then be compared to VGZ at cloud object edge pixel (VGZ EP ) to infer the impact of mixing on cloud object cores as a function of cloud size and environmental moisture.

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The influence of aerosols on the relationship between WRE and cloud object efficiency are determined using Aqua MODIS level-3 daily 550 nm aerosol optical depth (AOD) (Ruiz-Arias et al., 2013). Each cloud object is matched to the nearest 1 • x1 • gridbox AOD value. Note, this study does not consider the type of aerosol present in each environment, however this may also factor into the WRE.
Similar to Smalley and Rapp (2020), analysis is constrained to only marine shallow cumulus between between 60 N and 60 S.

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Measurements are constricted to June 2006 and December 2010 because CloudSat stopped taking night time measurements after 2010 due to a battery anomaly (Witkowski et al., 2012). Environmental moisture is classified using 6-hourly ECMWF-AUX (Cronk and Partain, 2017) average relative humidity below 3 km matched to each cloud object. Cloud-top height, environmental moisture, VGZ, and AOD are used to control and analyze the relationship between WRE and cloud object extent. Similar to Smalley and Rapp (2020), The spatial distribution of W P , W C , WRE, AOD, and extent of raining shallow cumulus cloud objects is analyzed by binning them to a 2.5 • x 2.5 • global grid. Figure 1a shows the spatial distribution of W P over the global ocean basins, with W P increasing equatorward. This is consistent with prior literature that found raining shallow cumulus are most frequent within the tropics (e.g. Smalley and Rapp, 2020). W P is largest near the Inter-Tropical Convergence Zone (ITCZ), South Pacific Convergence Zone (SPCZ), and tropical 130 warm pool, with values exceeding 45 g m −2 . Deep convection is more frequent here (e.g. Waliser and Gautier, 1993), so some objects may be transitioning from raining shallow cumulus to deeper convection. The results likely include a mix of frequently occurring tropical raining shallow cumulus and the early stages of developing deep convection possibly resulting in large W P over the tropics.
Spatial patterns in W C (Figure 1b) within the tropics generally follow W P , with values ranging between 110 g m −2 and 150 g m −2 in the tropics. Considering the tropics are more humid than the mid-latitude and polar regions, this is consistent with modeling studies that found less cloud water evaporates away in wetter environments (e.g. Hernandez-Deckers and Sherwood, 2018). Considering boundary layer depth scales with SST (e.g. Wood and Bretherton, 2004b), the boundary layer is generally deeper over the tropical oceans than the sub-tropical oceans. This supports deeper clouds (e.g. Short and Nakamura, 2000;Rauber et al., 2007;Smalley and Rapp, 2020) and could also help explain why W C and WP are largest in the tropics.
140 Figure 1c shows the spatial patterns in WRE follow spatial patterns in W P , with values increasing equatorward. Shallow cumulus cloud object WRE is largest within the ITCZ, SPCZ, and tropical warm pool, with values > 0.35. This is consistent with Lau and Wu (2003), who found precipitation efficiency is positively correlated with SST (e.g. Lau and Wu, 2003), and implies that WRE is higher in wetter environments.
Patterns in spatial extent shown in Figure 1d are similar to those found by Smalley and Rapp (2020), who used combined 145 CloudSat/CALIPSO to define extent, with extent decreasing from the stratocumulus regions east into the trade cumulus regions and north into the ITCZ. Interestingly, Figure 1c shows WRE also peaks in the southeast Pacific stratocumulus region, implying that WRE is high in regions with relatively low SST. However, Figure 1e shows that fewer than 40 shallow cumulus objects are observed in a given gridbox over this region in a four-year period, reducing confidence in WRE here. Together, Figures 1c and 1d indicate that the relationship between WRE and extent is complicated and potentially depends on cloud depth (which 150 increases in the tropics) and on environmental conditions including environmental moisture and aerosol loading.
To determine how WRE depends on cloud size, Figure 2 shows WRE as a function of cloud object extent. WRE follows a double power-law relationship, with WRE < 0.25 for cloud objects < 8.3 km and approaching 0.3 for cloud objects > 8.3 km.
Similar to these results, earlier studies have shown a double power-law distribution in shallow cumulus size (e.g. Benner and Curry, 1998;Trivej and Stevens, 2010), which will be discussed in further detail later.

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To address the impact of environmental moisture and cloud depth on WRE, Figure 3 shows the relationship between WRE and cloud object extent conditioned using cloud-top height and < 3 km relative humidity. Holding environmental moisture constant, WRE depends strongly on cloud-top height with WRE nearly doubling for each 0.5km increase in cloud top height for a given extent. For a given RH and top height, there is also an increase in WRE with extent. Holding top height constant, there is also an increase in WRE with increasing environmental moisture; however, increases in WRE are dominated by changing cloud size (depth and extent).
To support the hypothesis that larger shallow cumulus are able to sustain a larger droplet field within their cores to increase the precipitation efficiency, the variation in the VGZ across individual cloud objects is examined. We expect that VGZ will be a larger negative value near cloud center than cloud edge especially as cloud size increases. As an example, Figure 4a shows the change in median VGZ CP to VGZ EP for cloud objects with an extent of 10.2 km. VGZ decreases from 10 dBZ km −1 at 165 cloud object edge to approximately -20 dBZ km −1 at cloud object center. This demonstrates that larger droplets are present near cloud base near cloud object center compared to the edge. This implies, at least for extents of 10.5 km, drops grow larger near cloud object centers and may be more protected from mixing. Figure 4b shows the relationship between VGZ CP and VGZ EP as a function of extent and top height. For a constant cloud-top height, VGZ CP again follows a double power-law distribution. Specifically, the magnitude of the VGZ CP rapidly increases from 170 approximately 10 dBZ km −1 to 20 dBZ km −1 as extent approaches 8.3 km, while it plateaus around 20 dBZ km −1 for extents > 8.3 km. Conversely, VGZ EP decreases in magnitude, approaching 0 dBZ km −1 for the largest cloud object extents. However, it does not decrease as fast as VGZ CP , implying that the change in vertical reflectivity gradient in the center of cloud is driving changes in differences from center to edge. Figure 4b also shows that the change in VGZ CP depends on cloud-top height, with larger magnitudes for the tallest clouds. This is consistent with previous modeling studies that found larger shallow cumulus To determine how VGZ CP influences the relationship between WRE and extent, Figure 4c shows WRE as a function of extent conditioned by top height and VGZ CP , with WRE increasing as the magnitude of VGZ CP increases. This, coupled with 180 Figure 4b, illustrates that as shallow cumulus grow deeper and wider, drops at the center of the cloud can grow larger and scavenge more available cloud water. This is consistent with larger shallow cumulus being more efficient at producing rainfall, perhaps in part because they are less influenced by environmental mixing.
Until this point, this paper has focused on how cloud size and environmental moisture impacts WRE. However, it is also understood that aerosol concentrations influence both the number and size of droplets within a cloud, with larger aerosol con-185 centrations resulting in a greater number of smaller droplets (e.g. Twomey, 1974;Albrecht, 1989). As a result, we hypothesize increasing aerosol concentrations, which vary regionally (Figure 1f), increase the ratio of cloud droplets to rain drops, thus reducing WRE. Indeed, Figure 5c further supports this assertion. When conditioned by top height, WRE shows little dependence on AOD, and suggests that the conversion from W C to W P is more sensitive to cloud depth than aerosols. While these results seem counterintuitive, this analysis examines clouds in which precipitation has been detected. Examination of the likelihood of precipitation shows the expected decrease with increasing AOD (not shown). These results imply that once the condensation-200 coalescence is initiated, aerosol loading has a smaller impact on the conversion of cloud water to rain than other cloud or environmental characteristics.

Summary and Discussion
This study uses the methodology described by Smalley and Rapp (2020) to classify a large global shallow cumulus cloud object dataset from CloudSat and determine the relationship between WRE, cloud extent, environmental moisture, and aerosol 205 loading. We find that WRE increases as a function of cloud size (top height and extent) and environmental moisture. Benner and Curry (1998) found a double-power law distribution in shallow cumulus thickness as a function of cloud diameter, and Trivej and Stevens (2010) hypothesized that the shift from one power-law distribution to another results from small shallow cumulus that can rapidly grow in size until reaching the trade inversion. We find a similar relationship between WRE and extent, showing that one distribution exists with WRE increasing faster for extents < 8.3 km then slowly increasing above 210 this breakpoint. Trivej and Stevens (2010) also found that environmental factors, particularly environmental moisture, become important once cloud-top height reaches the trade inversion. Our results show that WRE is most sensitive to environmental moisture above an extent of 8.3 km, which we assume represents the average extent where cloud objects reach the trade inversion.
Unexpectedly, we find that for a fixed cloud depth, WRE is fairly insensitive to AOD. One explanation may be that, although 215 high AOD values do occur over the global ocean basins, the majority of cloud objects being sampled still form in relatively clean air, so the minority of cloud objects occurring over polluted regions have a small impact on the overall statistics. Another explanation may be that this analysis only includes precipitating clouds, so once collision-coalescence is initiated, the amount of cloud water converted to rain water is less influenced by aerosol concentrations.
Past studies conclude that precipitation efficiency increases as SST increases (Lau and Wu, 2003;Bailey et al., 2015;Lutsko 220 and Cronin, 2018). Considering warmer SSTs tend to result in deeper clouds (e.g. Wood and Bretherton, 2004a) and more humid environments (e.g. Chen and Liu, 2016), it is reasonable to expect that WRE would increase in response (e.g. Lau and Wu, 2003). Our results show that WRE is highest near the equator where SSTs are warmest. However, the general relationship between cloud size (depth and extent), environmental moisture, and WRE suggests that WRE is more sensitive to cloud size than environmental moisture. To directly address the SST dependence, Figure 6 shows the frequency distribution of extents 225 and the median WRE, both as a function of cloud-top height and SST. For a given cloud-top height, WRE does increase as a function of SST. However, for a fixed SST, WRE also increases as extent increases. Additionally, Figure 6 shows that the frequency distribution of cloud object sizes shifts toward more frequent larger extents with increasing SST. Together, these suggest that increasing WRE with SST shown in past studies not only results from the deepening clouds but also the shift towards more frequent larger clouds.

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Prior literature has shown that modeled shallow cumulus cores become more adiabatic as they grow larger (Moser and Lasher-Trapp, 2017), potentially resulting in larger drops. Figure 6 and our analysis of the relationship between VGZCP, extent, and WRE suggest drop growth is being enhanced near the base at the center of larger cloud objects, potentially resulting in more cloud water being scavenged by larger droplets and more efficient autoconversion and accretion processes. Most climate models parameterize autoconversion and accretion as functions of cloud and precipitation properties (e.g. Lohmann 235 and Roeckner, 1996;Liu and Daum, 2004;Morrison et al., 2005;Lim and Hong, 2010;Lee and Baik, 2017), but recently enhancement factors that depend on variations and covariations in WC and WP have been introduced to correct for biases due to subgrid-scale Wc and Wp inhomogeneity (e.g. Lebsock et al., 2013;Boutle et al., 2014;Witte et al., 2019). Presumably, the dependence of these enhancement factors on Wc variability would capture the increase in WRE with cloud depth shown here, however it is unclear if these enhancement factors based on the variance in Wc and Wp capture the effects of cloud extent on 240 WC and WP, and subsequently WRE. Our dataset provides an opportunity for a future analysis that could focus on investigating the relationship between subgrid-scale variability in WC, WP, WRE, and extent, which could help improve our understanding and simulation of precipitating shallow cloud processes in climate models.
Aerosol Optical Depth    Figure 6. The two-dimensional distribution of extent as a function of sea-surface temperature, conditioned by cloud-top height, is shown in panels A), C), and E) respectively. The median warm rain efficiency (Wp W −1 c ) as a function of Extent and sea-surface temperature are shown in panels B), D), and F) respectively.