All observations are from instruments aboard NASA A-Train satellites from 2007 to 2010 and from 60∘ S to 60∘ N. The aerosol index (AI) from MODIS serves as our aerosol concentration proxy, while the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) provides the mean cloud liquid water path of the scene. CloudSat's Cloud Profiling Radar (CPR) is used to define cloud extent, and we employ WALRUS to infer changes in latent heating and vertical motion within cloud profile. CloudSat is limited by its temporal resolution, seeing the entire globe once every ∼16 d compared to other Earth-observing instruments like MODIS aboard Aqua which has a daily resolution. By using multiple years of data from CloudSat, we can in some ways bypass the reduced temporal resolution; however, it is possible that some rare phenomena will be missed by CloudSat or will not be well represented by our dataset.

The aerosol index is the product of the Ångström exponent and the aerosol optical depth measured at 550 nm and is better correlated with cloud droplet concentrations than AOD . MODIS AI is available in clear-sky scenes over the ocean, meaning cloudy AI must be interpolated from nearby cloud-free scenes . We remove AI within 2 km of the clouds in order to reduce the influence of aerosol swelling in high-humidity scenes . We define pristine conditions as those with an AI less than 0.042 and polluted as those with an AI higher than 0.09. These roughly correspond to the lower and upper 20 percentiles of our dataset. Avoiding intermediate AIs reduces the possibility our analysis captures possible transition states as clouds move out of the aerosol-limited regime .

Clouds are limited to LWPs between 150 and 200 g m-2 using AMSR-E . AMSR-E LWP is utilized as a rough constraint on cloud liquid water content, with the spatial extent and depth of the cloud constrained by the CloudSat CPR. Although we constrain LWP to homogenize the clouds observed, using LWP as a constraint introduces an uncertainty due to the effects of aerosol on LWP. There remains large uncertainties on how aerosol may increase (or decrease) LWP due to environmental confounders; these ignored effects may have led to changes in the eventual, precipitating cloud state . Therefore, some uncertainty remains within our results as we do not control for this lifetime effect on invigoration. Cloud extents are defined using CloudSat's 2B-CLDCLASS-LIDAR product by sorting clouds by the number of contiguous cloudy pixels and limiting the analysis to clouds with at most 15 contiguous, cloudy pixels, approximately the size of AMSR-E footprints . This cloud-based partitioning is analogous to the cloud-object-based partitioning used by , except that while focused on deep convective systems, our clouds are constrained to shallow convective types. We focus on cumulus warm clouds, rather than stratus or stratocumulus, in order isolate the effects of aerosol on shallow convection.

Environmental information is provided by the MERRA-2 reanalysis. We define the stability of the atmosphere using the estimated inversion strength (EIS) . 1EIS=LTS-Γm850×z700+ΓmLCL×LCL, where Γm is the moist-adiabatic potential temperature gradient, and LTS is the lower tropospheric stability.

Stability of the boundary layer controls the depth of the cloud, making it imperative that this relationship is constrained in order to separate aerosol effects from environmental forcings . Unstable environments are defined as having an EIS below 1 K, while stable environments are defined as having an EIS above 3 K. This partitions environments into two main regimes: trade cumuli (unstable) and cumuli from stratocumulus-to-cumulus transitions (stable). A dry free atmosphere alters the distribution of liquid throughout the cloud layer, thereby directly impacting precipitation formation processes as well. In order to control for these interactions, clouds are further subset into a dry regime whereby the RH700 is below 30 % to analyze how dry air entrainment may impact invigoration processes.

The Wisconsin Algorithm for Latent heating and Rainfall Using Satellites (WALRUS) provides information on the latent heating and vertical motion profiles in the atmosphere. The algorithm combines CloudSat's CPR observations with a database of warm rain states derived from the Regional Atmospheric Modeling System (RAMS) simulations to emulate realistic latent heating rates and related vertical motion . WALRUS limits our analysis to maritime clouds with heights less than the freezing level and only those that exhibit reflectivity greater than 0 dBZ somewhere in the column, consistent with the rain certain flag in CloudSat's 2C-PRECIP-COLUMN product . Our results do not include the effects of drizzle on possible invigoration processes. This should also focus our results on only the growing and mature stages of shallow convection. Signals of invigoration are derived based on changes in the latent heating within the cloud, defined by WALRUS as the difference between the condensation and evaporation rates. Precipitation formation rates correspond to the latent heat release within the cloud, while evaporation due to entrainment at the cloud top or virga (below cloud evaporation of drizzle) is indicated by cooling from WALRUS. We refer to the evaporation at cloud top as due to entrainment; however, WALRUS does not simulate entrainment rates; therefore, we are inferring from the evaporation at the top of the cloud profiles that this cooling is due to entrainment. Enhanced turbulence, or the change in vertical velocity, is determined by the difference in vertical velocity between polluted and pristine environments.

WALRUS is limited only to warm cloud precipitation, reducing our ability to understand mixed-phase convection. It is possible some of the rain events observed are the remnants of mixed-phase precipitation events that were unsuitable to infer latent heating profiles by WALRUS. Our conclusions drawn within are only for warm-phase rain events. The latent heating profiles from WALRUS are based on a limited range of simulations from RAMS, meaning it is possible that some environmental states were not represented by the RAMS runs/WALRUS inference and could lead to some amount of error in our analysis. We limit our observations to only rain certain scenes, discarding drizzling and higher rain rate observations that may attenuate the CloudSat signal. This reduces some of the uncertainty due to a model-derived, observationally based product. As have also commented, the results herein could instead be reframed as how the RAMS microphysics scheme would map onto real observations of global precipitation.

WALRUS employs a Bayesian Monte Carlo method in order to derive a probabilistic latent heating profile. While precipitation amounts alone can be used to infer total latent heating in the column, vertically resolved reflectivity profiles allow the inference of the distribution of latent heating throughout the profile, below, within, and above the cloud. The Bayesian Monte Carlo method relies on an a priori distribution of possible characteristics to connect to the CloudSat observations. The a priori database is created using the RAMS model with simulations based on the Atlantic Trade Wind Experiment field campaign. The model is run at a 250 m horizontal and 100 m vertical resolution for a set of sea surface temperatures (293, 298, and 303 K). QuickBeam produces radar reflectivity profiles and attenuation signals from the RAMS simulation, which are sampled every 40 min for the database. Overall, WALRUS had 1.4 million possible a priori warm rain structures against which observed CloudSat reflectivities are compared to retrieve the most physically realistic latent heating and associated vertical motion rates. For more information please refer to .

Cloud profiles are partitioned according to the individual cloud base and cloud top heights determined for each profile using CloudSat's 2B-CLDCLASS-LIDAR CloudLayerBase and CloudLayerTop products. These heights are used to distinguish the in-cloud region from the environment below or above it. The maximum above-cloud cooling due to evaporation is found by taking the maximum of all evaporative cooling rates starting at the cloud top to the top of the profile. The cloud top is obvious in the latent heating profiles (Fig. ); the abrupt shift from heating to cooling indicates the entrainment zone of the cloud near the cloud top. The mean below-cloud cooling rate is similarly found using the cloud base height from 2B-CLDCLASS-LIDAR and taking the sum of all evaporative cooling rates at the cloud base to the bottom of the profiles (approximately ground level). The geometrical center of the cloud is the midpoint of the cloud (e.g., for a 7 km cloud as seen in Fig. , the midpoint is 3.5 km); therefore, the profiles on either side are used to determine the behavior of the geometrical center of the cloud.

Theoretical arguments for warm rain invigoration predict that in a more polluted environment the rate of collision–coalescence and therefore precipitation production increases. Our analysis suggests that, on average, clouds in polluted environments do not show increased rates of precipitation formation relative to those in pristine environments (black solid line, Fig. ). The difference between polluted (solid) and pristine (dashed) conditions is minimal when clouds in environments are considered together. However, when separated according to the environmental stability, it is evident that the reason for this is not that the warm rate intensity is unaffected by aerosol loading; it is that clouds react differently under stable and unstable conditions. In unstable environments, polluted conditions lead to a marked increase in precipitation rate relative to unstable, pristine conditions (blue, dotted line) for all rain systems smaller than ∼6 km. Conversely, stable, polluted conditions (red, solid line) lead to a decrease in precipitation rate relative to stable, pristine conditions (red, solid line). The opposite reactions in stable vs. unstable conditions offset each other, giving the impression that warm rain is unaffected by aerosol loading when in actuality its sensitivity is environmentally dependent. Invigoration is only identifiable when stability is accounted for, and this suggests that aerosol-induced invigoration of shallow convection may exhibit marked spatial patterns globally. While our analysis does account for some amount of covariation between meteorology and aerosol–cloud interactions, there is some added uncertainty due to the inherent relationships between aerosol and meteorology, as certain meteorological conditions may lead to high or low aerosol loading.

Polluted clouds exhibit first an increasing and then a decreasing relationship between the size of the rain system and the maximum latent heating within the cloud, while pristine clouds show a steady, linear increase in the rain formation rate as the size of the rain system increases (Fig. ). Rain formation in polluted clouds appears to increase with rain size up to 5 km and then either decrease (unstable, dry) or remain constant with size. This inflection point, whereby the behavior changes from increasing with rain size to decreasing, depends on both the stability of the boundary layer and the humidity of the free atmosphere. Pristine conditions do not show this same pattern, as for all meteorological conditions, an increase in rain size results in an increase in maximum heating.

The core of a warm convective system should theoretically exhibit the greatest invigoration of precipitation. Our results indicate this conceptual model is correct, as invigoration of the warm rain formation rate due to aerosol is most pronounced in the geometrical center of the rain system (Fig. ). Mean precipitation rates increase in the center of unstable, polluted clouds relative to both cleaner and more stable conditions. This effect is exacerbated in dry conditions (Fig. , bottom) until the rain system seems to hit a size inflection point around 7 km. While instability in polluted clouds leads to greater formation rates in the center, clouds in stable but equally polluted environments show a decrease in rain production relative to pristine conditions. This suppressive behavior is observed regardless of the overlying free atmosphere, as clouds in dry environments (Fig.  bottom) show the same behavior as all clouds (Fig. a).

That is not to say that the free atmosphere does not play a role in altering the thermodynamics or possibly invigorating the state of warm rain systems. Evaporative processes link entrainment, below-cloud evaporation, precipitation formation, and the energy budget of a cloud. When focusing on how aerosol may affect entrainment, the moisture content of the free atmosphere becomes a controlling factor. A drier atmosphere fosters greater evaporation rates above the cloud in more polluted environments (Fig. ). Cumuli generally have large rates of lateral entrainment that would not be captured by WALRUS; however, lateral entrainment would also affect the invigoration of any rain formation in the cloud layer. While increased mixing with the free atmosphere may lead to cloud deepening, when the boundary layer unstable, it may also lead to an early onset of cloud breakup processes through evaporation–entrainment . In some cases, increased entrainment and evaporation at the cloud top could lead to reduced cloud top heights, which is the opposite of an invigoration effect . Whether the growth of a particular cloud is enhanced or inhibited may depend on the distribution of liquid water near the cloud top and the ability of the cloud to penetrate the free atmosphere.

A drier atmosphere enhances cloud top evaporation in only unstable conditions; clouds in stable conditions are unaffected by a drier free atmosphere. This is likely due to the stronger capping inversion in stable conditions which limits mixing with the dry free atmosphere, limiting its effects on the cloud layer and, by extension, the invigoration process . While clouds in stable environments have similar responses in precipitation formation rates, inversion strength acts to limit evaporation at the cloud top. In theory, by limiting the amount of mixing with the free atmosphere, the inversion damps the ability of stable, polluted clouds to deepen compared to unstable, polluted clouds. While these clouds do not show signs of invigoration, stable, polluted conditions may prolong cloud lifetime by lessening cloud thinning processes .

That the cores of dry, polluted, unstable systems experience significantly greater rain formation rates than all other environments may suggest these clouds undergo some aggregation process focusing the majority of precipitation formation within the core of the cloud. This result agrees with a theoretical model posed by , where entrainment of dry air leads to a narrowing effect on the cumuli and enhancement of the core. Aerosol may act to invigorate this specific response by increasing the entrainment–evaporation at the cloud top, promoting turbulence within the cloud layer.

Below-cloud evaporation and its associated cooling destabilizes the boundary layer, which could then further invigorate the cloud layer through amplified turbulence . The effects of below-cloud evaporation on the stability are sensitive to the location of the cooling and drop size of the cloud; it is possible in some circumstances that cooling can act to stabilize the boundary layer. Figure  demonstrates that larger warm rain systems exhibit considerably more below-cloud evaporation than smaller systems. Evaporation, even when weighted by the size of the rain system, scales with the total amount of rain forming, as more rain means more possible below-cloud evaporation. Polluted clouds exhibit less below-cloud evaporation regardless of the stability and size of the rain system. This may imply that pristine conditions stabilize the boundary through below-cloud cooling and increasing the boundary layer temperature inversion.

There are two possible mechanisms that may lead to polluted environments having a relatively lower rate of evaporation below cloud compared to their pristine counterparts. The first mechanism relies on the change in droplet size due to the differences in where rain is being produced in the cloud under pristine and polluted conditions. In polluted conditions, rain may form higher within the cloud; as precipitation forms and drops fall, the drop grows larger as its path increases, decreasing the amount of evaporation below cloud base . So although aerosol loading decreases the mean cloud drop size, rain droplet size experiences an inverse effect, the magnitude of which is determined by the height within the cloud where precipitation forms.

The second possibility is that in environments with drier free atmospheres, clouds in unstable environments (both pristine and polluted) have much greater rates of evaporation below the cloud (Fig. a). The increased evaporation below cloud may be driven by vertical motion forced by increased evaporation in the entraining layer of the cloud (Fig. ), leading to more mixing throughout the cloud layer. This in turn leads to more activation of available cloud condensation nuclei, decreasing the mean drop size and increasing the rate of evaporation below the cloud in both polluted and pristine cases. It is possible that in polluted, unstable environments smaller droplets evaporate efficiently, quickly increasing the humidity of the lower boundary layer, resulting in an overall decrease in the rate of evaporation (relative to pristine conditions) as the cloud continues to precipitate . Or it may be that stable, polluted boundary layers show the lowest rates of below-cloud evaporation because they also have lower rates of precipitation formation. Establishing the specific processes responsible for the observed invigoration signatures is not possible from current satellite observations.

The implied effects on cloud lifetime in unstable, polluted conditions agree with Albrecht's original hypothesis, whereby aerosol works to increase cloud lifetime. The overall effect of aerosol loading on not just the thermodynamics but lifetime of the cloud depends heavily on the environment surrounding the cloud . In specific highly polluted conditions, whereby the boundary layer is unstable, it could be possible that below-cloud evaporation cools the lower boundary layer, while latent heating due to rain formation warms the cloudy portion of the boundary layer, which would act to stabilize an unstable boundary layer. This stabilizing effect would decrease in time, however, as the magnitudes of both the cooling below cloud and warming in cloud depend on the instability . The same stabilizing effect may be seen in pristine scenes as well, as clean clouds in unstable conditions also showed greater rates of below-cloud cooling due to evaporation. So while aerosol may work to help prolong lifetime through this stabilizing mechanism, the environment through a stabilizing feedback works to lengthen the cloud lifetime regardless of the aerosol conditions.

Results are consistent with the hypothesis that invigoration will increase vertical motion, which may lead to an increase in turbulence, as indicated by changes in vertical motion, within the cloud layer due to greater amounts of latent heat release . Figure  shows that clouds in polluted environments display higher updraft speeds within the cloud layer than those in pristine environments. This reaffirms an ongoing hypothesis that cloud deepening is driven by enhanced updrafts . Aerosol may act to redistribute water throughout the cloud, resulting in changes to the distribution of latent heating . Modifying where latent heat is released, especially increasing the difference between the center where rain formation is occurring and edge evaporation due to cloud edge entrainment, alters vertical motion and flow within the cloud layer. As seen in Fig. , edge and core behavior and latent heating signatures are markedly different. While it remains unclear how aerosol may affect the absolute amount of water within a cloud, it is clear that aerosol affects how water is distributed within the cloud .

When separated into stable and unstable environments (Fig. ) it becomes obvious how strongly stable environments damp invigoration. While unstable environments intensify the vertical motion within the cloud layer, stable environments show only a faint increase in vertical motion in the center of the cloud. This may explain why stable, polluted environments also manifest the smallest rates of evaporation due to cloud top entrainment, as these clouds have less overturning motion near the cloud tops. Though stable, polluted environments display a reduced core precipitation formation rate compared to their pristine counterparts, the reduced size of the polluted droplets may allow greater mobility and therefore vertical motion . Unstable, large rain systems (∼6 km) may have downdrafts within the cloud due to enhanced evaporation entrainment, leading to more in-cloud turbulence, overturning motion, and mixing.

It should be noted that increased rates of rain formation in unstable conditions could induce a positive feedback: latent heating increases from faster rain formation, which leads to more vertical motion and turbulence, greater updraft speeds, more entrainment, and therefore buoyancy fluctuations within the cloud, which in turn leads to more collision–coalescence and latent heating. This could explain both the greatly enhanced rain formation rates in the center (Fig. ) and intensified turbulence (Fig. ). However, this feedback may be particularly sensitive to the size of the rain system, as larger systems may decrease the chance of the feedback occurring. The scattered increases in turbulence seen in rain systems of size 6 km and the sloping off of rain formation rates at the same size imply a sensitivity to the size and organization of the system . It is possible this point may also represent how different clouds experience different optimal conditions for invigoration, as these larger clouds within the same environment may have a higher AI that would be needed to experience the same invigoration as their small, environmental counterparts . Additionally, any possible invigoration feedback may be moderated by a stabilizing effect induced in unstable conditions, whereby increased cooling due to evaporation below cloud and warming due to rain formation within the cloudy layer stabilize the boundary layer.