Quantifying Cloud Adjustments and the Radiative Forcing due to Aerosol-Cloud Interactions in Satellite Observations of Warm Marine Clouds

Aerosol-cloud interactions and their resultant forcing remains one of the largest sources of uncertainty of future climate scenarios. The effective radiative forcing due to aerosol-cloud interactions (ERFaci) is a combination of two different effects, how aerosols modify cloud brightness (RFaci, intrinsic) and how cloud extent reacts to aerosol (cloud adjustments CA, extrinsic). Using satellite observations of warm clouds from the NASA A-Train constellation from 2007 to 2010 along with MERRA-2 reanalysis and aerosol from the SPRINTARS model, we evaluate the ERFaci in warm, marine clouds and its 5 components, the RFaciwarm and CAwarm , while accounting for the liquid water path and local environment. We estimate the ERFaciwarm to be -0.32 ±0.16 Wm−2. The RFaciwarm dominates the ERFaciwarm contributing 80% (-0.21 ±0.15 Wm−2), while the CAwarm enhances this cooling by 20% (-0.05 ±0.03 Wm−2). Both the RFaciwarm and CAwarm vary in magnitude and sign regionally, and can lead to opposite, negating effects under certain environmental conditions. Without considering the two terms separately, and without constraining cloud-environment interactions, weak regional ERFaciwarm signals may be 10 erroneously attributed to a damped susceptibility to aerosol.

The radiative forcing of the albedo effect, or the sudden microphysical response to aerosol loading (RFaci), is dependent on the activation and eventual microphysical initiation of aerosol as cloud droplets, which can be influenced by local dynamics, the stability of the boundary layer, and the initial cloud state (Su et al., 2010). "Model" conditions simulated by Twomey only 60 exist in the most pristine, stable southern oceans (Gryspeerdt et al., 2017;Hamilton et al., 2014). Depending on the region studied, aerosol can increase the cloud albedo as expected, or in certain cases, lead to a dimming effect, such as when aerosol loading reaches a critical point or the local meteorology regulates the sign and/or magnitude of ACI (Gryspeerdt et al., 2019b;Christensen et al., 2014). Studies conflict to what degree the RFaci dominates the ERFaci, in part because the cloud acts as a "buffered system" and mitigates the RFaci depending on the thermodynamic conditions, making the quantification of the 65 RFaci particularly challenging (Goren and Rosenfeld, 2014;Feingold et al., 2016;Stevens and Feingold, 2009).
Efforts to understand the other component of the ERFaci, cloud adjustments, have been similarly clouded in uncertainty.
Cloud lifetime and extent are highly susceptible to aerosol (Dagan et al., 2018). Models have shown that aerosol affects the distribution of liquid throughout the cloud and vertical motion within the cloud, greatly perturbing the cloud's lifetime, precipitation, and extent (Ramanathan et al., 2001;Dagan et al., 2016). Aerosol can act to increase the lifetime of clouds 70 through delayed collision coalescence, or decrease the lifetime through evaporation-entrainment and induced cloud feedbacks (Albrecht, 1989;Small et al., 2009). A satellite observation-based study of ship tracks showed clouds experience a expansion or shrinking of cloud extent depending on whether the clouds are at an open or closed state and the background state of the aerosol (Chen et al., 2015). The cloud adjustment response depends on the cloud state and a sequence of reactions dictated by the environment (Gryspeerdt et al., 2019b). As such, cloud adjustments remain the largest source of variability of ERFaci in 75 global climate models (Fiedler et al., 2019).
To account for influences and variation in the ERFaci warm , RFaci, and cloud adjustments, we constrain the liquid water path, relative humidity of the free atmosphere, and stability of the boundary layer and covariances between them before evaluating the susceptibility of the effect in the same fashion as DL19. These constraints are held fixed first on a global and then on a regional basis to diagnose regime specific then regionally specific responses. Finally, the decomposed ERFaci, or the sum of 80 the RFaci and cloud adjustments, is found, with constraints on the environment and cloud state, for precipitating and nonprecipitating scenes on a regional basis. Our methodology aims to reduce biases by accounting for the regionally specific aerosol and thermodynamic conditions (Feingold, 2003). The relationship between aerosol and cloud response has been proven to be sensitive to regional features like aerosol type or meteorology (Twohy et al., 2005;Chen et al., 2014)(DL19). Aerosolcloud interactions experience a non-linear relationship with liquid water path therefore it is important to separate this complex 85 relationship from ACI and the associated forcing in order to reduce the effects of this non-linear relationship on our results (Gryspeerdt et al., 2019b). GHz radar with a ∼ 1.7 km along track, 1.4 km cross track resolution, and 480 m vertical resolution (Stephens et al., 2018;Tanelli et al., 2008). A number of cloud properties can be inferred using the CPR backscatter including cloud top height, cloud type, and accompanying radiative effects.

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An along track warm cloud fraction is defined using cloud top height from 2B-CLDCLASS-LIDAR and freezing level from 2C-PRECIP-COLUMN. 2B-CLDCLASS-LIDAR combines CloudSat's CPR with CALIPSO lidar observations in order to discern even the thinnest clouds. At each pixel, the cloud fraction is defined by the amount of cloud uptrack and downtrack of that pixel at a 12 km scale, chosen to approximate the scale of marine boundary layer processes and accentuate small scale changes in extent compared to other large sizes (e.g. 1 • x 1 • ). Using a smaller scale such as 12 kms for cloud fraction will 105 allow even minute changes in the cloud extent to be detected by our methodology; using a larger size such as 96 km (∼1 • ) may diminish cloud breakup processes within large stratocumulus decks or minimize effects on trade cumuli. 2B-CLDCLASS-LIDAR includes collocated Cloud-Aerosol Lidar with Orthogonal Polarization (CALIPSO) satellite lidar backscatter measurements to identify thin, shallow clouds that may escape detection by the CPR (Sassen et al., 2008). Cloud top heights from 2B-CLDCLASS-LIDAR, defined using a combination of collocated lidar and CPR measurements, are required to be below 110 the freezing level . The freezing level of 2C-PRECIP-COLUMN is obtained from European Centre for Medium-Range Weather Forecasts (ECMWF) analyses and is used to separate warm from mixed and ice phase clouds. Focusing only on warm phase clouds helps reduce the uncertainty associated with retrievals of mixed and ice phase clouds.
Cloud fraction is combined with shortwave top of atmosphere forcings from the CloudSat 2B-FLXHR-LIDAR product to approximate the effect of aerosol on albedo. 2B-FLXHR-LIDAR uses a combination of CPR and CALIPSO measurements 115 along with MODIS cloud properties and atmospheric conditions from ECMWF as input to a radiative transfer model that computes top of atmosphere shortwave fluxes that have been shown to agree well with CERES observations (Henderson et al., 2013). The mean shortwave flux at the top of atmosphere is weighed by a mean incoming solar radiation at the top of atmosphere in our analysis to account for diurnal variation of incoming solar radiation not sampled by the sun-synchronous A-Train orbit. 120 We use aerosol index (AI) as a proxy for aerosol concentration from MODIS. The AI is the product of the Angstrom exponent, calculated using aerosol optical depth (AOD) at 550 and 870 nm, and the AOD at 550 nm. AI has been shown to have a higher correlation with CCN compared to AOD (Stier, 2016;Hasekamp et al., 2019). Cloudy scene AI is determined by interpolating between clear scenes along track. This interpolation may reduce the accuracy in completely overcast scenes, however for most scenes where cloud fraction is < 1, this interpolation should be sufficiently accurate. Aerosol swelling in high 125 humidity environments also leads to some uncertainty in AI but but should be limited to select high humidity environmental regimes. Pre-industrial aerosol information is provided by Spectral Radiation-Transport Model for Aerosol Species (SPRINT-ARS), an atmosphere-ocean general circulation model (Takemura et al., 2000). Pre-industrial aerosol errors lead to the majority of uncertainty in ACI due to uncertainties in transport, source, and concentration of pre-industrial aerosol conditions (Chen and Penner, 2005).

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The sign and regional variations in susceptibilities found using MODIS AI shown within this study were evaluated against susceptibilities found using MACC and SPRINTARS aerosol in order to qualitatively scrutinize any error due to aerosol retrieval (Douglas, 2017). MACC and SPRINTARS provide independent aerosol estimates not susceptible to swelling, instrument sensitivity or retrieval error.. The fact that our results were qualitatively similar using modeled aerosol provides confidence that the derived susceptibilities shown are not simply an artifact of using satellite-derived AI.

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The analysis is constrained to clouds with LWPs between 0.02 to 0.4 kgm −2 using the Advanced Microwave Scanning Radiometer for Earth Observing Satellite (AMSR-E), an instrument aboard Aqua that infers water vapor and precipitation amounts using six microwave frequencies over a ∼14 km area (comparable to the averaging scale of our cloud fraction) (Parkinson, 2003;Wentz and Meissner, 2007). While the footprints of CloudSat and AMSR-E do not perfectly overlap, the AMSR-E LWP is used to establish a scene based constraint on the clouds in order to better consolidate our observations into 140 regimes. AMSR-E's footprint is within ∼2.5 km of CloudSat's track, meaning both sensors are observing the same, liquid clouds (Lebsock and Su, 2014). Imposing these LWP limits in place removes only ∼1% of observations leaving over 1.8 million satellite observations for analyses, but avoids possible skewing by extremely thick, bright clouds or extremely thin, dim clouds.
Environmental information to define local meteorological regimes is provided by the Modern-Era Retrospective analysis 145 for Research and Applications, version 2 (MERRA-2) reanalysis (Gelaro et al., 2017). To broadly characterize large-scale environmental conditions, MERRA-2 temperature and humidity profiles are collocated by taking the environmental profile within 30 minutes of a CloudSat overpass and within ∼ 1 2 • latitude and longitude. Vertical profiles of humidity and temperature are used to calculate the estimated inversion strength (EIS) of the boundary layer and the relative humidity at 700 mb (RH 700 ) to represent the humidity of the free atmosphere (Wood and Bretherton, 2006). By simultaneously stratifying the observations 150 by LWP, RH, and EIS, the analysis directly accounts for covariability between LWP and the local environment by separately evaluating the susceptibility of each environmental regime within distinct LWP limits (Douglas and L'Ecuyer, 2019).
Clouds are separated into precipitating and non-precipitating regimes using CloudSat's 2C-PRECIP-COLUMN precipitation flag. Clouds with a 0 precipitation flag, no precipitation detected, are designated as non-precipitating. Precipitating clouds are separated using flag 3, where rain is certain ). Our precipitating clouds include a majority of the drizzling 155 cases, as CloudSat's 2C-PRECIP-COLUMN's threshold for drizzle is -15 dB, which should capture all but the lightest drizzling clouds (Stephens and Wood, 2007).

Methodology
In DL19, environmental and cloud state regimes were imposed on a regional basis in order to identify regime specific behavior of aerosol-cloud-radiation interactions. Within each regime, we regressed the cloud radiative effect (CRE) against AI in order 160 to find the susceptibility of warm cloud radiative properties to aerosol. We use these same susceptibilities within section 3.1 to quantify the total warm, marine ERFaci. DL19 found that the susceptibility varies regionally and by regime, however the ERFaci warm depends on the magnitude to which aerosol has increased since pre-industrial times. Further, the ERFaci warm does not diagnose what characteristics of the cloud are causing the effect, prompting us within this paper to decompose the ERFaci warm into the effects on the albedo and the effects on cloud extent.

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The mean shortwave flux at the top-of-atmosphere from CloudSat's 2B-FLXHR-LIDAR along with our definition of warm cloud fraction from 60 • S to 60 • N are used to define the RFaci warm and cloud adjustment terms of the ERFaci warm . We first calculate the ERFaci warm on a regional basis with regime constraints using estimates of the susceptibility of the warm CRE to aerosol from DL19 and pre-industrial and present-day AI from SPRINTARS. We then use a partial derivative decomposition to separate out the RFaci warm and cloud adjustment terms. These terms are evaluated globally as susceptibilities with constraints 170 on the local meteorology and cloud state following the methodology of DL19. The RFaci warm and cloud adjustments are evaluated regionally with constraints on cloud state and local meteorology. The decomposed ERFaci warm is evaluated for precipitating and non-precipitating scenes to account for the potential effects of precipitation on ACI. Finally, the sum of the RFaci warm and cloud adjustments, the decomposed ERFaci warm , is compared against the first estimate of the ERFaci warm .

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Following DL19, the ERFaci warm and components are evaluated within a constrained space on both a global and regional scale. LWP is held approximately constant using a set of twelve LWP limits on a global basis and five LWP limits on a regional basis. This is in line with the original work of Twomey, who surmised that only for a fixed LWP will the cloud albedo increase in more polluted conditions. The local meteorology is defined by the stability of the boundary layer and the relative humidity of the free atmosphere. Both the stability, characterized by the estimated inversion strength, and the relative humidity of the 180 free atmosphere, defined at the 700 mb level, have been shown to influence the sign and magnitude of the susceptibility of the CRE to aerosol (Wood and Bretherton, 2006;Ackerman et al., 2004;De Roode et al., 2014). The resulting regimes are used to minimize the effects of buffering, or reduced observed response, by the cloud state or surrounding environment to accurately isolate the susceptibility of the cloud to aerosol under controlled conditions. Buffering can entail the cloud being too thick and impervious to changes due to aerosol due to its high LWP, offsetting and opposite reactions of the cloud resulting in reduced 185 mean signal, or the environment acting to damp the cloud reaction, such as an unstable boundary layer reducing the impact of aerosol on cloud lifetime (Fan et al., 2016;Stevens, 2007). Using EIS and RH 700 does not guarantee to limit all covariability between the environment, aerosols, clouds, and their interactions. Some covariability may still exist, such as surface winds that may affect both clouds and aerosol (Nishant and Sherwood, 2017). These constraints only account for the major environmental controls on clouds and aerosol-cloud interactions, some more minor or less common environmental controls may still exert an 190 influence on our results. While binning our observations by environmental regime should control for some modulation the environment has on aerosol-cloud interactions, it does not fully capture aerosol-environment interactions. For example, in some regions such as off the coast of Africa, biomass burning results in smoke layers that absorb incoming radiation and warm the atmosphere (Cochrane et al., 2019). This could affect the humidity and temperature of the local environment. Environmental regime con-195 straints would capture how the altered environment may regulate aerosol-cloud interactions, but separation into such regimes does not address how the aerosol has impacted the environment.

Decomposing the ERFaci
A Newtonian-based method is employed to represent the ERFaci warm as a sum of its parts, the RFaci warm and cloud adjustments. A positive ERFaci warm , RFaci warm , or cloud adjustment denotes a damped cooling effect of the cloud while a negative 200 sign denotes an additional cooling due to aerosol-cloud interactions. If the shortwave cloud radiative effect is the product of the cloud fraction (CF) and the cloudy sky shortwave flux at the top-of-atmosphere (SW Cloudy ): then, taking the derivative of the CRE with respect to the log of aerosol index, we find the effective radiative forcing due to aerosol-cloud interactions (ERFaci) or the change in the CRE with respect to aerosol: where ∆ln(AI) is the change in ln(AI) from pre-industrial to present-day conditions derived from SPRINTARS. SPRINTARS is a 3-D aerosol model that includes emission, advection, diffusion, chemistry, wet deposition, and gravitational settling of multiple species of aerosol driven by a general circulation model developed by the University of Tokyo (Takemura et al., 2000(Takemura et al., , 2005.

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All susceptibilities are found using MODIS AI, while only the ∆ln(AI) term uses SPRINTARS modeled aerosol. The lowest 12% of aerosol indices are ignored when determining a susceptibility, as these have been shown to have little to no correlation with CCN compared to higher indices (Hasekamp et al., 2019). Error in MODIS AI estimates adds the greatest source of uncertainty in the observationally based portion of this study, however, signals derived are all robust enough to be observed even when random error is added to 10% of the AI estimates. The regressions within all regime constraints, from The susceptibility ( ∂CRE ∂ln(AI) ) can be obtained directly from satellite estimates of top-of-atmosphere clear-sky and all-sky fluxes and aerosol index or further decomposed into separate albedo and cloud fraction responses using Equation 1. Applying the chain rule to equation 2, combined with the definition of CRE from Equation 1, gives: where the overbars represent means.
The sum of the right hand terms represent the decomposition susceptibility: The first term of Equation 4 represents the cloud adjustment susceptibility to aerosol, which to first order is the effect of aerosol 225 on the cloud extent: The cloud adjustment forcing is the product of the cloud adjustment susceptibility λ CA and the change in AI from pre-industrial to current times ∆ln(AI): The cloud adjustment susceptibility (λ CA ) is described by its most notable effect, the enhancement and sustainment of clouds as a result of precipitation suppression. We define the cloud adjustments as the product of the change in cloud fraction with respect to aerosol index and the mean cloud shortwave forcing. By multiplying by the mean cloud shortwave forcing, a change in cloud extent is converted to a change in the reflected shortwave. While this term does not explicitly account for precipitation, we separate clouds by rain state and determine the difference in the RFaci warm and cloud adjustments between 235 precipitating/non-precipitating clouds; this difference is likely close to the overall effect of precipitation on aerosol-cloudradiation interactions.
This cloud adjustment term accounts for the main process, the change in extent of clouds by aerosol, however many other studies define the cloud adjustment term by the change in LWP by aerosol. We choose to instead focus on the expansion or shrinking of clouds by aerosol and constrain any LWP effects.
Research has yet to establish how and where LWP increases or 240 decreases due to aerosol-cloud interactions; focusing on the changes to cloud extent reduces the error in the adjustment term due to this uncertainty.
The second term on the right hand side of Equation 4 represents susceptibility of warm cloud radiative forcing due to aerosolcloud interactions (RFaci): where the associated forcing is the product of the RFaci warm susceptibility λ RF aci and the change in AI from pre-industrial to current times ∆ln(AI): Radiative Forcing due to aci = λ RF aci × ∆ln(AI) The RFaci warm susceptibility is the change in the shortwave effect owing to changes in cloud droplet radius, an immediate, fast response. The outgoing shortwave radiation for cloudy scenes depends on the cloud albedo; a brighter, whiter cloud will 250 reflect more incoming solar radiation, increasing SW Cloudy at the top of the atmosphere. SW Cloudy is weighted by the annual solar insolation cycle in order to normalize the term and reduce the impact of changes in the incoming solar flux. RFaci warm is weighted by mean cloud fraction since the net effect of brighter clouds depends on how extensive they are.
Finally, to account for the dependence of each susceptibility (RFaci, CA, and total) on the meteorology and cloud state, each susceptibility (λs from above) is evaluated in distinct EIS, RH, and LWP regimes regionally. The product of each susceptibility 255 and ∆ln(AI) is the resulting forcing of the aerosol-cloud-radiation interaction: where W i,j,k,l is the weighting factor, N is the number of limits imposed, and λ is the susceptibility being evaluated (ERFaci warm , RFaci warm , or CA) regionally (N Reg ) with constraints on LWP, EIS, and RH 700 . W i,j,k,l weights the ERFaci warm , RFaci warm , and cloud adjustments by the number of observations in each regime and also by the areal size of the region.

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Constraints on LWP reduces the secondary effects of aerosol on LWP or LWP on susceptibility, as aerosol can result in thicker clouds and thicker clouds may have a damped reaction to aerosol. Constraining the meteorology separates signals forced by aerosol and the environment (Stevens and Feingold, 2009). On a global scale the approach outlined in DL19 identifies regime specific behavior; when applied on regional scales, the regimes allow a process level understanding of the mean regional behavior (Mülmenstädt and Feingold, 2018). This approach is optimal for our satellite based observations where larger scale 265 parameters like AOD, AI, and cloud extent are less impacted by retrieval errors than specific properties of the aerosol.
The RFaci warm and cloud adjustment susceptibilities are first understood with limits on the environment and cloud states on a global scale. Their individual forcings are then found with constraints on the environment and cloud state regionally and contrasted against initial estimates of the ERFaci warm evaluated under the same constraints. The susceptibility estimates are not forcings. Forcings are the product of the susceptibilities (λ RFaci or λ CA ) and the change in the aerosol index from pre-270 industrial times to current estimates (∆ ln(AI)). It is possible that even these estimates of forcing are slightly different than the definition of forcing from the IPCC or model based studies which difference top-of-atmosphere forcings in polluted vs.
non-polluted GCM runs (Penner et al., 2011). The sum of these forcings, which we will term the decomposed ERFaci warm , is contrasted against the simple expression for ERFaci warm evaluated directly using Equation 2. By separating out the individual components of the ERFaci warm , the physical processes of aerosol-cloud-radiation interactions can be better understood. The 275 difference between the ERFaci warm and the decomposed ERFaci warm represents uncertainty in the linear decomposition owing to covariability, non-linearity, and other effects not quantified by our approach. In reality, there should be a covariability term at the end of Equation 4 to relate how a change in RFaci warm may affect cloud adjustment processes or vice-versa, however a limitation of satellite observations are that they cannot temporally relate events meaning covariance between the two terms cannot be accurately quantified (Seinfeld et al., 2016). We focus on the main cloud adjustment, the effect of aerosol on the 280 cloud extent/lifetime, however other cloud adjustment effects exist that our simple calculation of a decomposed ERFaci warm misses, such as how precipitation suppression directly leads to changes in cloud extent or how suppression could lead to a later invigorated state of the cloud and faster dissipation.
Precipitation is indicated by the 2C-RAIN-PROFILE rain rate along the entire 12 km track segment (L'Ecuyer and Stephens, 2002). The decomposition susceptibility is found for precipitating and non-precipitating scenes globally using equation 9. Only 285 the decomposition terms are found separately for precipitating and non-precipitating pixels. The CERES footprint is larger than the CloudSat's, meaning while CloudSat could see an entire 12 km along track segment with no rain, the CERES footprint could still contain rain and influence the regression.
Uncertainty in each effect is found first by assuming the uncertainty in the observations lies in the AI, then by assuming a majority of the overall uncertainty in the ERFaci warm from error in the pre-industrial aerosol concentration estimates (Hamilton 290 et al., 2014). Error is added randomly to AI to find how aerosol swelling or inaccurate retrievals of aerosol near cloud could alter susceptibility estimates. Aerosols swell in the vicinity of clouds, which increases their size and affects the MODIS retrieved AI (Christensen et al., 2017). To assess how significantly this may affect results we have randomly added errors of 10% to our AI estimates and re-derived all signals with all regime constraints. Even with extreme amounts of error in AI, the signals within our environmental and LWP regimes are robust. Uncertainty in the observations is most likely to come from the AI as 295 CloudSat 2B-FLXHR-LIDAR fluxes have been shown to have at most ∼10 Wm −2 error in shortwave top-of-atmosphere fluxes (Henderson et al., 2013). The error from AI is then combined with randomly adding error to the pre-industrial AI estimates from SPRINTARS to quantify how error in the pre-industrial aerosol may lead to uncertainty in the ERFaci warm , RFaci warm , and cloud adjustments. Overall, the majority of uncertainty in any ERFaci estimate lies in the pre-industrial aerosol estimate (Chen and Penner, 2005;Carslaw et al., 2013;Stevens, 2013).

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3 Results and Discussion

Estimate of the ERFaci
The warm cloud ERFaci, or the effective radiative forcing due to aerosol cloud interactions is -0.32 Wm −2 when found with constraints on the liquid water path, stability, and free atmospheric relative humidity applied regionally. As stated before, a negative ERFaci/RFaci/Cloud Adjustment denotes additional cooling due to aerosol-cloud interactions. Figure 1 shows each 305 component of Equation 9 and the resulting regional distribution of the ERFaci warm . The ERFaci warm is found applying Equation 2 regionally with regime constraints following DL19. This is within the range reported by the fifth IPCC report (-0.05Wm −2 to -0.95Wm −2 ) but suggests the net cooling effect is toward the lower end of the expected range. Note, however, that this estimate neglects contributions from cold or mixed phased clouds and land regions (Boucher et al., 2013). This first estimate of the ERFaci warm represents the sum of all effects of aerosol on the warm cloud radiative effect with no distinction 310 between the RFaci warm and CA warm and is representative of how aerosol-cloud interactions may be altering the current radiative budget (Carslaw et al., 2013).
As expected, marine stratocumulus decks in the Southeast Pacific and South Atlantic exhibit the largest ERFaci warm , exceeding -3.0 Wm −2 off the coast of Chile. The peak cooling is observed in the southern hemisphere, where the marine stratocumulus cloud decks subsist due to the strong inversions and cool sea surfaces (Wood, 2012). The storm tracks region in Interestingly, ACI is responsible for a net warming of as much as 0.6 Wm −2 in the tropical Atlantic and Indian oceans.
Diagnosing the cause of this warming cannot be done through the ERFaci warm , as it is impossible to accurately attribute it to 320 a reduced albedo or cloud adjustment process. This signature, in particular, motivates decomposing the ERFaci warm into the RFaci warm and cloud adjustment components to allow the instantaneous albedo response to be separated from slower cloud processes. The physical processes resulting in a warming differ between the two components as the cloud adjustments are on a macrophysical scale while the RFaci warm is due to microphysical interactions between aerosol and CCN. The decomposition in Equation 3 allows the specific underlying physical processes responsible for this positive (warming) forcing to be assessed 325 regionally.
The change in aerosol index is most notable off the coast of Asia and along the European coasts. Emissions from large coastal cities lead to large increases in AI, particularly changes in sulfuric aerosol (McCoy et al., 2017). The AI may have decreased off the coast of Australia due to the overall aerosol size increasing, which would decrease the Angstrom exponent and therefore AI (Carslaw et al., 2017). The northern hemisphere has had much larger changes in AI since pre-industrial times 330 compared to the southern hemisphere due to the differences in anthropogenic activity between the two hemispheres. While the southern hemisphere has not experienced the same extreme changes in AI as the coast of Asia, the strong susceptibility of these warm clouds to aerosol combined with the local expansive clouds leads to a large cooling signal throughout the southern oceans.

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Cloud LWP plays an integral role in modulating the strength of aerosol-cloud interactions. When first theorized by Twomey in 1977, the LWP of the cloud was considered to be constant as the first effect takes place. With this in mind, we first hold the LWP approximately constant and evaluate the decomposition susceptibility, Equation 4, within distinct LWP regimes. While both the RFaci warm and cloud adjustments are dependent on LWP, they appear to have inverse relationships (Figure 2). λ Sum is found to increase with increasing LWP, reaching a peak susceptibility between 0.06 and 0.15 kgm −2 before asymptotically leveling off in the thickest LWP regime between 0.2 to 0.4 kgm −2 . For the lowest LWPs, the cloud adjustment susceptibility dominates.
Thicker clouds are less susceptible to precipitation suppression, the key process to initiating many of the cloud adjustments (Sorooshian et al., 2009;Michibata et al., 2016;Fan et al., 2016). This is reflected in the very muted cloud adjustment suscepti-345 bility for higher LWPs past ∼0.1 kgm −2 . This inflection point is also where precipitation is more likely to occur in warm clouds and could be a sign of precipitation modulating the effects of aerosol on the cloud fraction (Lebsock et al., 2008;L'Ecuyer et al., 2009;Stevens and Feingold, 2009). An alternative explanation is that thicker clouds with larger LWPs are more likely to precipitate, scavenging aerosol and weakening the susceptibility. Aerosol-cloud-precipitation interactions complicate cloud adjustment processes in higher LWP clouds; the true susceptibility may be masked by covariance between aerosol and precipi-350 tation in these clouds (McCoy et al.). Precipitation would have an instantaneous effect on many cloud adjustment processes as major sink of liquid water within the cloud and therefore dampening process to other possible adjustments. Our framework for the cloud adjustment effect only considers processes which impact, either directly or indirectly, the cloud fraction. At higher LWPs, there are precipitation and other adjustment processes we do not account for that may later on change the radiative properties of the clouds, such as invigoration increasing the cloud depth and therefore both the longwave and shortwave cloud 355 radiative effect (Rosenfeld et al., 2008;Koren et al., 2014). While regime constraints on LWP do reduce the covariability between aerosol-cloud interactions and the role LWP plays 365 in regulating these interactions, it does not remove all sources of covariability between LWP, aerosol, the environment, and cloud properties. Aerosol has been shown to negatively correlate with LWP (Gryspeerdt et al., 2019a). It is possible that this relationship, and the inherent relationship between the environment and LWP, could affect results shown.

Constrained by local meteorology
When further separated by meteorological regimes defined by stability and RH 700 of the free atmosphere, the influence of the 370 environment becomes clearer as strong variations in both the sign and magnitude of RFaci warm and CA warm with environmental regime are evident (Figure 3). Both the RFaci warm and cloud adjustment susceptibilities show warming responses in the most unstable, driest regimes. This is likely due to both the albedo and cloud extent being heavily influenced by entrainment-evaporation feedbacks (Small et al., 2009;Christensen et al., 2014). λ CA shows a warming in the highest humidity, most stable regimes which may reflect cloud breakup processes like the stratocumulus to cumulus transition.

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The total decomposed ERFaci warm susceptibility, given by the sum of both the RFaci warm and cloud adjustments within each individual stability and humidity regime, exhibits strong regime specific susceptibilities demonstrating the importance of understanding the total warm cloud radiative response to aerosol with consideration of the environment. Constraints on meteorology allow us consider how meteorology influences the cloud response to aerosol. Without these constraints, any derived susceptibilities could be attributed environmental responses. While cloud darkening occurs in only the most unstable 380 regime ( < -1.8 K), λ CA continues to show a warming response in moderately neutral environments (∼2K). This suggests that the instantaneous response (RFaci) is more sensitive to local meteorology than the slower cloud adjustments.
The dominant cooling of λ RFaci and λ CA in stable regimes illustrates the potential of a stable inversion to strengthen ACI.
The peak cooling of λ CA occurs in a relatively dry atmosphere ∼27% RH 700 . In this environment, the cloud extent rapidly increases as a response to aerosol, however the cloud is topped by a strong, stable inversion that prohibits much of an deepening 385 of the cloud perhaps instigating the effect to push horizontally rather than vertically (Christensen and Stephens, 2011). λ RFaci peaks in stable, but comparatively more moist environments where entrainment of moist air from the free atmosphere promotes activation of all available aerosol to CCN, rapidly increasing the albedo. This response may be similar to other regions where trade cumuli form and the FA is relatively moist (Koren et al., 2014).
Finally, while λ RFaci shows less variation in sign, it exhibits more variation in magnitude between meteorological regimes 390 indicating the importance of accounting for meteorological influences in order to capture this specific environmental regime dependence. It is possible with additional constraints, understanding how other components of the meteorology is affecting these terms would become more clear. It is also possible λ RFaci is impacted by some semi-direct effects by smoke aerosol which would lead to a cloud dimming and positive susceptibility. Semi-direct effects are not accounted for by our methodology, however aerosol within the cloud layer could lead to cloud breakup processes, a dimmer albedo, and changes to the local 395 environment by the absorbing aerosol.

Constraints on cloud state and local meteorology
As seen in Figures 2 and 3, the susceptibility of each component of the ERFaci warm varies with both cloud state and environmental regime. Therefore, when calculating each component of the ERFaci warm , both the meteorology and LWP must be accounted for. To accomplish this, the RFaci warm and CA warm susceptibilities are found with constraints on both the LWP 400 and environment (Figure 4). The shaded region of Figure 4 delineates the 10 to 90% range within each of the 11 cloud states of the susceptibility when further separated by the 100 environmental regimes used in Figure 3. Unlike Figures 2 and 3, λ is weighted by frequency of occurrence within each environmental state. This illustrates how the magnitude and sign of each susceptibility can vary by environmental regime even when LWP is held approximately constant. The weighted and summed susceptibility is -5.45 Wm −2 ln(AI) −1 with constraints on LWP, stability, and RH 700 globally. This is slightly smaller than the 405 susceptibility found in DL19, however that susceptibility took into account all changes in warm cloud CRE to aerosol while our decomposition only accounts for the two largest effects, the albedo and cloud extent susceptibilities to aerosol. The lowest LWP clouds (≤ 0.1 kgm −2 ) contribute most to the net susceptibility due to their abundance but also exhibit the widest range in susceptibilities across different meteorological states.
The two components exhibit different behavior in terms of susceptibility to cloud state (defined here by LWP). The cloud 410 adjustment susceptibility is largest for the lowest LWPs, while the RFaci warm susceptibility peaks around 0.06 kgm −2 and gradually declines. This may represent a "sweet spot" of cloud albedo susceptibility. Up to 0.1 kgm −2 , aerosol are easily activated and there are few processes beyond entrainment and activation to reduce the concentration within the cloud layer.
Beyond 0.1 kgm −2 , where the RFaci warm begins to decrease, the cloud may be influenced by precipitation formation, reducing the λ RFaci within each environmental regime.

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λ CA decreases in magnitude with LWP. Higher LWP clouds, independent of the environment, may be less susceptible to lifetime effects, as was seen in Figure 2. Precipitation suppression, the main driver of cloud adjustments, becomes less likely as LWP increases (Fan et al., 2016;Sorooshian et al., 2009). The thinnest and smallest clouds may have the the largest potential to experience a enhancement effect.

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Precipitation formation within the cloud and the environment surrounding modulate the susceptibility. When weighted by the relative frequency of occurrence, rather than overall frequency of occurrence, the susceptibility of precipitating clouds is shown to be much higher in some environments than non-precipitating clouds ( Figure 5). Precipitating clouds in humid environments especially, defined as having a RH 700 > 44%, have a much greater susceptibility than any other regime of clouds.
Unstable clouds show a reduced susceptibility in all cases, with precipitating clouds showing a warming effect in these envi-425 ronments while non-precipitating clouds experience an extremely damped cooling effect. Unsurprisingly, in dry environments and stable environments, precipitation does less to magnify the susceptibility and the difference between precipitating and non-precipitating susceptibilities is reduced.
Precipitating clouds reduce the amount of aerosol available to interact with warm clouds through wet scavenging, yet still may induce several other processes within the cloud that stimulate a response Gryspeerdt et al.. These include stabilizing the 430 boundary layer through virga, increasing the EIS and therefore susceptibility ( Figure 3). Precipitation formation within the cloud induces vertical motion and mixing of the cloud layer, increasing turbulence and mixing of the layer which may increase activation of aerosol and therefore the response of the cloud. Further work must be done to resolve how and to what magnitude precipitation alters the warm cloud radiative susceptibility to aerosol.

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With these considerations in mind, the sum of the RFaci warm and CA, or the decomposed ERFaci warm as we will refer to it, is -0.26 ±.15 Wm −2 found using Equation 9 (Figure 7). The components of the ERFaci warm , the RFaci warm and cloud adjustments, are found using Equations 5 and 7 and shown in Figure 6. The ERFaci warm from Figure 1 is slightly larger in magnitude than the decomposed ERFaci warm . Overall, their regional variations and magnitudes are extremely similar, suggesting the linear decomposition captures a majority of the ERFaci warm . The southern ocean dominates the decomposed 440 ERFaci warm , as is expected based on the susceptibilities. The difference in overall magnitude stems from a stronger dimming effect evaluated in the decomposed ERFaci warm (Figure 6). In the decomposed ERFaci warm , more regions experience a decrease in CRE with increasing AI compared to the ERFaci warm . This may be due to the definition of the decomposed ERFaci warm that allows either the RFaci warm or CA warm to reduce cooling.
A reduced albedo, or positive RFaci, has been noted by other observation based studies before (Chen et al., 2012). A positive RFaci warm can be caused by multiple processes. A semi-direct effect, where non-activated aerosol acts to decrease the total albedo of the cloud in the case of smoke, reducing the CRE of the cloud and therefore the RFaci warm (Johnson et al., 2004).
A decrease in the RFaci warm may also be due to any changes to the distribution of liquid water throughout the cloud layer. In certain environmental conditions, an increase in aerosol may lead to sedimentation within the cloud throughout the entrainment zone, which could decrease the cloud albedo and therefore CRE (Ackerman et al., 2004). If these two effects combined under 450 the "perfect storm" of aerosol and environmental conditions, the RFaci warm would have a large, positive effect.
The cloud adjustment term likewise undergoes a positive, or damped cooling, response in certain regions. A reduced cloud fraction due to aerosol-cloud interactions has been noted before by others (Small et al. (2009), Gryspeerdt et al. (2016). Chen et al. (2014) noted a decrease in LWP due to an increase in AI in their observationally based study, while other studies have indicated the LWP response and therefore cloud fraction response can be either positive or negative (Gryspeerdt et al., 2019a).

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Any process that alters the cloud's liquid water path, such as evaporation-entrainment, may lead to a decrease in cloud fraction given certain environmental conditions.
The discrepancy between the two estimates of ERFaci warm (0.065 Wm −2 ) may be cloud adjustment effects or covariance between RFaci warm and CA warm not captured by the simple regression employed here. The error between the two lies well within the bounds of error of both estimates (±.16 and ±.15). While cloud extent changes are the dominant cloud adjustment 460 effect, changes in liquid water path due to precipitation suppression will have an impact on the radiative forcing as well.
Future work on understanding and evaluating the ERFaci warm must include other cloud adjustments and explicitly account for covariance between the RFaci warm and cloud adjustments. Although they occur on different time scales, the RFaci warm could be thought of as reactive to cloud adjustments. So while the cloud adjustment process may take hours, an albedo adjustment occurs simultaneously. 465 3.7 Regional variation due to precipitation individually). However, on average only ∼30% of warm clouds observed by CloudSat are precipitating, leading to a smaller net contribution to the total ERFaci warm shown in Figure 8. If in future climates, warm clouds rain more frequently, it is possible that the decomposed ERFaci warm could increase due to precipitating clouds higher susceptibilities, given the environmental conditions (EIS and RH) remain constant.
In regions where trade cumulus are more prevalent and the marine boundary layer is more unstable, precipitation clouds have the capacity to greatly decrease the cooling due to ERFaci warm (Figures 5, 8). However, this positive ERFaci warm is balanced by their expansive cooling throughout the southern ocean. More regions experience a cooling due to ACI when clouds are precipitating than not precipitating. Further, due to wet scavenging of aerosol, it is possible that precipitating clouds could 480 reduce semi-direct or direct effects and remove aerosol that could otherwise warm the atmosphere. The possible feedbacks or consequences of changes in precipitation require further research, especially since precipitation is heavily controlled by aerosol type as well as concentration.

Conclusions
The global distribution of the warm, marine cloud ERFaci and its components, the RFaci warm and cloud adjustments, are found 485 with constraints on cloud state and local meteorology following the methodology of DL19. The total effective radiative forcing due to aerosol-cloud interactions is -0.32 ±0.16 Wm −2 . The radiative forcing due to aerosol-cloud interactions is -0.21 ±0.12 Wm −2 . The forcing due to cloud adjustments from aerosol-cloud interactions is -0.05 ±0. Regionally, the ERFaci warm derived from the linear decomposition into RFaci warm and cloud adjustments agrees moder-495 ately well with that derived directly from the SW CRE, proving our method of decomposing the ERFaci warm to the first order components does capture the main effects adequately. Globally, the ERFaci warm is dominated by the RFaci warm , however the cloud adjustment term is found to contribute ∼ 1 5 of the total forcing. The cloud adjustments vary regionally in sign and magnitude, meaning in some regions the two effects are additive, while in others they may cancel each other out. In the south Atlantic, both effects lead to a warming, or positive, forcing as clouds both shrink and dim in this region, most likely due to the 500 prevalence of a drier free atmosphere and unstable boundary layer in this region. In the tropical Pacific, clouds dim while the cloud extent swells, leading to an overall muted cooling effect. Regions like this where the two signals have opposing signals are prime examples of why a decomposition of the ERFaci warm into its components is necessary. The muted signal in the tropical Pacific would most likely be attributed to offsetting reactions in the RFaci warm and CA warm , as this region shows a damped signal of ERFaci warm , if not for the knowledge that the RFaci warm and CA warm have opposing responses in this 505 region.
It is possible our simple methodology to evaluate cloud adjustments underestimates the possible forcing due to other adjustment processes or the possible covariance with the RFaci warm . If the difference between the ERFaci warm and the sum of the RFaci warm and cloud adjustments is assumed to arise from the missing forcing from other adjustments, the total contribution of the CA warm to the ERFaci warm would increase to -0.11 Wm −2 , or nearly a third, of the -0.32 Wm −2 . This would be consis-510 tent with a recent estimate by Rosenfeld et al. which found the relationship between Nd and cloud fraction, when constrained by LWP, still had a significant signal. Cloud adjustments are found to dominate over the RFaci warm at the lowest liquid water paths. Thus in regions or climate conditions that support enhanced prevalence of thin clouds, the cloud adjustment term would increase at the expense of the RFaci warm .
The southern hemisphere dominates the global ERFaci warm due ubiquitous marine stratocumulus in the South Pacific and 515 South Atlantic. The northern hemisphere storm tracks region in the North Atlantic and marine stratocumulus off California exert ∼ 1 5 the magnitude of forcing observed from the southern hemispheres pristine warm clouds. Warm clouds in the southern hemisphere are predisposed for aerosol-cloud-radiation interactions.
Cloud adjustments and RFaci warm varying regionally in sign and magnitudes implies that there are regions and conditions where the two components could effectively cancel each other out, thwarting short term, observation-based attempts at dis-520 cerning a noticeable change in cloud radiative effects due to aerosol. Moreover, the character of the clouds does not remain constant. Aerosol interactions that result in brighter clouds covering a smaller area, or dimmer clouds covering a larger area, represent important physical responses that may be masked by direct assessment of ERFaci warm from CRE alone. In these regions especially, care should be given to discerning which effect is dominating and to what magnitude.