Deconvolution of boundary layer depth and aerosol constraints on cloud water path in subtropical stratocumulus decks

The liquid water path (LWP) adjustment due to aerosol–cloud interactions in marine stratocumulus remains a considerable source of uncertainty for climate sensitivity estimates. An unequivocal attribution of LWP adjustments to changes in aerosol concentration from climatology remains difficult due to the considerable covariance between meteorological conditions alongside changes in aerosol concentrations. We utilise the susceptibility framework to quantify the potential change in LWP adjustment with boundary layer (BL) depth in subtropical marine stratocumulus. We show that the LWP susceptibility, i.e. the relative change in LWP scaled by the relative change in cloud droplet number concentration, in marine BLs triples in magnitude from −0.1 to −0.31 as the BL deepens from 300 to 1200 m and deeper. We further find deep BLs to be underrepresented in pollution tracks, process modelling, and in situ studies of aerosol– cloud interactions in marine stratocumulus. Susceptibility estimates based on these approaches are skewed towards shallow BLs of moderate LWP susceptibility. Therefore, extrapolating LWP susceptibility estimates from shallow BLs to the entire cloud climatology may underestimate the true LWP adjustment within subtropical stratocumulus and thus overestimate the effective aerosol radiative forcing in this region. Meanwhile, LWP susceptibility estimates in deep BLs remain poorly constrained. While susceptibility estimates in shallow BLs are found to be consistent with process modelling studies, they overestimate pollution track estimates.

Abstract. The liquid water path (LWP) adjustment due to aerosol-cloud interactions in marine stratocumulus remains a considerable source of uncertainty for climate sensitivity estimates. An unequivocal attribution of LWP adjustments to changes in aerosol concentration from climatology remains difficult due to the considerable covariance between meteorological conditions alongside changes in aerosol concentrations. We utilise the susceptibility framework to quantify the potential change in LWP adjustment with boundary layer (BL) depth in subtropical marine stratocumulus. We show that the LWP susceptibility, i.e. the relative change in LWP scaled by the relative change in cloud droplet number concentration, in marine BLs triples in magnitude from − 0.1 to −0.31 as the BL deepens from 300 to 1200 m and deeper.
We further find deep BLs to be underrepresented in pollution tracks, process modelling, and in situ studies of aerosolcloud interactions in marine stratocumulus. Susceptibility estimates based on these approaches are skewed towards shallow BLs of moderate LWP susceptibility. Therefore, extrapolating LWP susceptibility estimates from shallow BLs to the entire cloud climatology may underestimate the true LWP adjustment within subtropical stratocumulus and thus overestimate the effective aerosol radiative forcing in this region.
Meanwhile, LWP susceptibility estimates in deep BLs remain poorly constrained. While susceptibility estimates in shallow BLs are found to be consistent with process modelling studies, they overestimate pollution track estimates.

Introduction
The aerosol radiative forcing due to changes in cloud reflectivity of low-level marine clouds remains one of the largest sources of physical uncertainty in climate sensitivity estimates. Estimates of total aerosol radiative forcing from the Fifth Assessment Report (AR5) issued by the Intergovernmental Panel on Climate Change (IPCC) range from −0.1 to −1.9 W m −2 Zelinka et al., 2014). Based on these estimates, increased cloud reflectivity due to anthropogenic aerosol may have posed a substantial offset to the greenhouse gas forcing.
However, this cooling term is likely to reduce in coming years as anthropogenic emissions of aerosols decline (Smith and Bond, 2014). Yet, the quantification of aerosol-induced changes in cloud scene albedo remains important for reducing the uncertainty in overall forcing. Subtropical marine stratocumulus are of particular relevance; the stratocumulus decks in the subtropics contribute strongly to the cooling of the planet by reflecting ∼ 40 % of incoming solar radiation on average, in a region of high solar intensity (Bender et al., 2011).
In particular, cloud adjustments to changes in aerosol concentration remain highly uncertain . As defined in IPCC AR5 , adjustments quantify the net response of cloud-radiative properties to external forcing agents such as anthropogenic aerosols. Through microphysical or thermodynamic adjustments, such as decreased precipitation rates (Albrecht, 1989), increased mixing rates at cloud top (Ackerman et al., 2004), or the sedimentation-entrainment feedback (Bretherton et al., 2007), the thermodynamics of the cloud is impacted and the liquid water path (LWP) may be altered. Adjustments in cloud fraction (CF) by changes in aerosol concentration may also increase the overall albedo of the cloud scene (Gryspeerdt et al., 2016;Andersen et al., 2017;Possner et al., 2018). However, these effects cannot be addressed within the framework of this study due to the insufficient accuracy in CF retrievals under polluted conditions (e.g. Twohy et al., 2009). It is therefore mentioned here for completeness but will not be discussed further.
In order to constrain the uncertainty range reflected within the wide range of AR5 forcing estimates, numerous studies have since quantified the individual contributions of the Twomey effect (Twomey, 1991) and LWP adjustments in global-scale long-term satellite records (Sekiguchi et al., 2003;Quaas et al., 2008;Lebsock et al., 2008;Bellouin et al., 2013;Bender et al., 2016;Gryspeerdt et al., 2017Gryspeerdt et al., , 2019McCoy et al., 2017;Rosenfeld et al., 2019), pollution track data sets (Ackerman et al., 2000;Christensen and Stephens, 2011;Christensen et al., 2014;Chen et al., 2015;Malavelle et al., 2017;Toll et al., 2017Toll et al., , 2019Bender et al., 2019), and large-eddy simulations (LES) or cloud-resolving simulations in combination with field observations (see Fig. 1 for references). Satellite-based estimates of large data sets provide long-term near-global constraints for the Twomey effect and the LWP adjustment. However, they are prone to numerous sources of uncertainties. These include, but are not limited to, uncertainties in N d changes for a given change in aerosol metric, the distortion of the true sensitivity due to relatively coarse retrieval scales (McComiskey and Feingold, 2012), and the covariability between meteorological factors and aerosol indices. Average forcing estimates for the Twomey effect alone range between −0.2 and −1.0 W m −2 (Quaas et al., 2008;Lebsock et al., 2008;Bellouin et al., 2013;Mc-Coy et al., 2017). The LWP adjustment may induce a partially compensating positive forcing to the Twomey effect, due to a decrease in cloud field LWP . Meanwhile, the LWP adjustment inside the convective cores of low clouds may be positive (Rosenfeld et al., 2019), which would locally amplify the aerosol-cloud forcing due to the Twomey effect.
In the case of pollution tracks, the issue of covariability between confounding factors is avoided, and a clear detection and attribution of the cloud response to the aerosol perturbation itself, or at least to the corresponding change in N d , is possible. Each individual track is associated with a spatially confined cloud response due to aerosol perturbations by ship or volcano plumes for a given set of meteorological conditions. However, these tracks are rare. It is estimated that merely 0.002 % of all ocean-going ships generate a ship track (Campmany et al., 2009). Though a recent estimate suggests that this number might underestimate the true ship track frequency (Yuan et al., 2019). Furthermore, they are only found within a narrow window of meteorological condi-tions (Durkee et al., 2000). Therefore, while these estimates are prone to fewer uncertainties in detection and attribution of aerosol forcing, the representativeness of such estimates remains unclear.
The same holds true for estimates based on LES, cloudresolving model studies, and field observations. At this resolution, insights into the interplay between microphysical, radiative, and thermodynamic processes can be obtained. Yet, the estimates are representative of the conditions sampled and may not be valid generally or at larger spatial scales. The LES community recently started to address these limitations, e.g. through extensive LES ensembles (Glassmeier et al., 2019). Here we would like to draw attention to the fact that previous analyses of LES, cloud-resolving models, and field campaigns have predominantly focused on shallow boundary layers. Figure 1 shows that most field campaigns and high-resolution modelling studies quantifying aerosolcloud-radiation interactions have been conducted in BLs below 1 km in depth. Figure 1 shows the global distribution of stratocumulus regimes across BL depth, which was characterised by Muhlbauer et al. (2014) in terms of cloud-top height ( Fig. 10 in Muhlbauer et al., 2014). The probability density function (PDF) by Muhlbauer et al. (2014) is representative of all low clouds over the oceans (see original paper for further methodology). We find the global PDF to be comparable to the distribution of stratocumulus against BL depth in the subtropics alone ( Fig. S1 in the Supplement). The PDF for disorganised clouds in Fig. 10 of Muhlbauer et al. (2014) was omitted here. These scenes were governed by broken cloud decks of low CF (CF = 40 %), resembling shallow cumulus rather than stratocumulus.
The LWP adjustment within shallow cumulus seems to be governed by lateral entrainment effects and moisture gradients (e.g. Jiang et al., 2006;Seifert et al., 2015). This is in stark contrast to stratocumulus cloud decks (CF > 80 %) where the LWP adjustment is predominantly governed by vertical gradients in moisture, stability, and aerosol. Thus, the LWP adjustment in shallow cumulus may differ from adjustments in stratocumulus, which is the focus of this study. The distinction between detraining shallow cumulus under strong inversions and precipitating stratocumulus becomes semantic in the case of cloud scenes associated with high cloud fraction. For this reason, results of the Atlantic Trade Wind Experiment (ATEX) are included in Fig. 1.
In the subtropics merely 30 % of stratocumulus reside at the predominant depth range sampled in the field and studied within most high-resolution simulations. Results from merely three campaigns and few modelling studies are discussed within the literature that reside within a height range deeper than 1 km where over 70 % of marine stratocumulus are found. The campaigns containing measurements of deep stratocumulus cloud decks are ATEX, EPIC (East Pacific Investigation of Climate), and VOCALS-REx (VAMOS -Variability of the American Monsoons -Ocean-Cloud-Atmosphere-Land Study Regional Experiment). Merely 25 % ( Fig. 1) of all high-resolution modelling studies investigating the influence of aerosol concentrations on cloud properties in marine stratocumulus decks (i.e. Xue et al., 2008;Caldwell and Bretherton, 2009;Mechem et al., 2012;Berner et al., 2013;Possner et al., 2018) are based on deep BL field campaigns.
The lack of process studies in deep boundary layers, despite their prominence, motivates us to explore the dependence of cloud adjustments on BL depth. This is further supported by recent findings that show an explicit dependence of the LWP adjustment on BL depth in pollution tracks . Here, we focus on regions dominated by marine stratocumulus, and we explore these relationships within 10year records in the subtropics. The data set is described in Sect. 2. The change of mean cloud properties with BL depth is presented in Sect. 3, while the impact of BL-depth covariance with LWP, and N d on the LWP adjustment estimate, is presented in Sect. 4.

Data description
The relationship between LWP and N d at different BL depths is analysed in the semi-permanent stratocumulus regions of the subtropics (Fig. 2). The analysis is based on a 10-year climatology of daily in-cloud radiation retrievals between 2007 and 2016, at a spatial resolution of 1 • × 1 • . Daytime in-cloud retrievals for LWP, N d , and effective radius (R eff ) are obtained from the level 3 Moderate Resolution Imaging Spectroradiometer (MODIS) collection 6 product Platnick et al., 2017). As in previous collections, independent retrievals of cloud optical depth and R eff are obtained using the visible and near-infrared radiances at 2.1 and 0.86 µm .
The R eff retrieval is further used to distinguish between precipitating (R eff ≥ 15 µm) and non-precipitating (R eff < 15 µm) cloud scenes. For the year 2007, an independent retrieval of precipitation probability (Eastman et al., 2019) was available (Fig. S2). During this year, the R eff criterion splits the data set into regimes where the precipitation probability remains below 50 % (equivalent to non-precipitating clouds) and above 50 % (equivalent to precipitating clouds).
N d is estimated based on the relationship established by Boers et al. (2006) and Bennartz (2007) for marine boundary layer clouds: where ρ w denotes the density of water, eff = f ad ad is the effective rate of increase in adiabatic liquid water content with increasing height, and R eff|top denotes the effective radius at cloud top. All assumptions regarding the degree of adiabaticity and the proportionality constant k between the true and effective N d are the same as in Eastman and Wood (2016). The retrievals are restricted to sensor viewing angles between 0 and 65 • (Grosvenor and Wood, 2014), which does not pose a strong constraint in the subtropics. The data are further limited to regions with high CFs exceeding 80 %. This restriction permits the best possible accuracy in N d retrievals, which assumes plane-parallel clouds and restricts the analysis to large-scale stratocumulus cloud decks only, which have the largest radiative impact. All cloud properties are in-cloud mean values only, which are not weighted by areal CF within each 1 • × 1 • grid box. The retrieval of BL height (H BL ) used in this study was first presented in Eastman and Wood (2016) and analysed in Eastman et al. (2017). The retrieval is based on a combination of MODIS and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) cloud retrievals (Vaughan et al., 2004). The Clouds and the Earth's Radiant Energy System (CERES) Single Scanner Footprint One Degree (SSF1deg) retrievals of all-sky (A toa ) and clearsky albedo (A clr ) based on the top-of-atmosphere shortwave fluxes (Kato et al., 2013) were used to estimate A cld from It should be noted that the above equation can only provide an estimate of the cloud albedo. This definition, due to the separation of clear and cloudy skies, is highly sensitive to the definition of CF. CF retrievals are afflicted with uncertainty, due to swelling of aerosols in the high-relative-humidity environment near cloud edges (Twohy et al., 2009); rather than a dichotomy, clear and cloudy skies represent a continuum of albedo values (Charlson et al., 2007). Yet, Eq. (2) has been shown to provide a useful estimate of cloud albedo in the subtropical stratocumulus regions we focus on here.
Further environmental factors considered in this study, such as the lower tropospheric stability (LTS) and the free troposphere (FT) relative humidity (RH FT ), are obtained from the Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2) reanalysis (Rienecker et al., 2011;Molod et al., 2015). The LTS is defined as the change in potential temperature between 700 hPa and the surface. Conditions are considered non-stable if the change in potential temperature between these two pressure levels remains below 15 K. RH FT is diagnosed as the mean RH between the inversion and 700 hPa. Environmental conditions are considered to be dry if RH FT falls below 50 % and moist otherwise.

Covariance between cloud properties and boundary layer depth
Here, we analyse the change in cloud properties of subtropical stratocumulus as a function of H BL . Each cloud property is binned into 100 m H BL intervals within which the 10-year mean and standard deviation are computed. The resulting relationships, which include data from all four predominant stratocumulus cloud decks, are shown in Fig. 3. All cloud properties change significantly (at the 95 % level) with H BL . The largest relative changes are observed for LWP (Fig. 3b) and N d (Fig. 3e), while merely moderate and small changes are observed in R eff (Fig. 3d) and A cld (Fig. 3a) Table 1 for details on fitting parameters). The climatology of precipitating clouds is shown in blue. For completeness, the climatology for non-precipitating clouds is shown in Fig. S3. against ln H BL to identify the exponent of the LWP-H BL relationship (Fig. 3b). Meanwhile, a simple linear regression is obtained for all other cloud climatologies (Fig. 3a, d, e). To understand the relative sensitivity amongst cloud properties to changes in H BL , the slopes obtained by linear regression in the physical, as opposed to logarithmic space, are scaled by the climatological mean (Table 1).
As expected, larger LWPs are associated with deeper BLs (Fig. 3b). In particular we find LWP to scale as LWP ∝ H 0.33 BL (Table 1). Therefore, LWP scales considerably weaker with H BL than H c . Combining these two relationships, it follows that in adiabatic clouds H c ∝ H 0.17 BL . That is, H c increases on average by merely 2 m for every 100 m increase in H BL . Thus, H c seems largely independent of H BL variations.
Adiabaticity is known to change with cloud depth in marine stratocumulus (Merk et al., 2016;Braun et al., 2018). Furthermore, we find that clouds in deep BLs are more likely to precipitate than clouds in shallow BLs (Fig. 3c). Consequently, one might expect cloud adiabaticity to change as a function of H BL due to the change in likelihood of precipitation (F prec ). However, we find that the LWP-H BL relationship is hardly impacted by precipitation (Table 1: columns 6  and 7). It also seems unlikely that the functional relationship between adiabaticity and H c would be sufficient to reduce the quadratic exponent of the LWP-H c relationship to that of the sub-linear exponent in the LWP-H BL relationship. It therefore follows that LWP scales very differently and seemingly independently with H BL and H c in marine subtropical stratocumulus.
Thermodynamic adjustments in LWP and H c occur rapidly (hourly timescale), while adjustments in BL depth and thus LWP occur on longer timescales (multi-day timescale). H c is predominantly constrained by the vertical displacement of H b , as has been quantified by LWP budgets (Wood, 2007;van der Dussen et al., 2014;Ghonima et al., 2015;Hoffmann et al., 2020). H b in turn is governed by the Clausius-Clapeyron relation in response to variability in BL humidity and temperature. Meanwhile, the multi-day evolution of H BL and thus LWP characterises their evolution as a function of external drivers such as gradients in sea surface temperature (SST), FT conditions, and large-scale advection. This is consistent with the weak relationship between H c and H BL inferred here from climatology.
LWP increases more rapidly with H BL under dry FT and non-stable lower tropospheric conditions (Table 1 columns 2-4). This behaviour is consistent with cloud-scale observations (Eastman and Wood, 2018), simulations , and mixed-layer theory (Dal Gesso et al., 2014). Under low-RH FT conditions, cloud-top cooling and cloud-top-generated mixing are more effective. Therefore, a deeper and moister mixed layer associated with larger LWP can be maintained. Thus, the reinforcement of the cloud through stronger radiative cooling has a larger impact on LWP, than the increased drying through entrainment under low-RH FT conditions. Similarly, the weaker buoyancy jump across the inversion under non-stable lower troposphere conditions likely induces less warming in the sub-cloud layer as the BL deepens, which corresponds to a weaker upward shift of the cloud base.
Meanwhile, deeper BLs are characterised by lower N d (Fig. 3e). As the BL deepens, F prec (Fig. 3c), and thus the N d sink through collision-coalescence processes, increases. Yet, N d primarily decreases with H BL in non-precipitating BLs (Fig. S3). This suggests that precipitation scavenging is not the only constraint on N d . In the absence of precipitation, we attribute the negative correlation between N d and H BL to (i) the climatological deepening of the BL away from the cold upwelling zones near the coasts (Fig. 2a) and (ii) the increasing distance to continental sources of anthropogenic pollution, which manifest in a pronounced negative gradient in N d (Fig. 2b). This is also explicitly illustrated in Fig. S4.
The negative correlation vanishes in a deregionalised and deseasonalised version of this data set (Fig. S5). Following Bender et al. (2016), we remove geographical and seasonal trends. In doing so, the significant negative correlation between N d and H BL in non-precipitating clouds disappears. This further confirms that the observed negative correlation between N d and H BL in non-precipitating clouds is intrinsic to the data, but it is not a manifestation of a given physical process.
The observed negative correlation disappears in the presence of precipitation ( Fig. 3e and Table 1). Our two process hypotheses governing the negative correlation between N d and H BL are not impacted directly by precipitation. Yet the negative correlation vanishes. This also holds true for the deseasonalised and deregionalised N d climatology (Fig. S5). It follows that precipitation is the predominant constraint on climatological N d in subtropical marine stratocumulus at this scale. In addition F prec changes with H BL . Thus, a significant negative slope manifests within the whole N d climatology (c N d = −0.3), as the fraction of precipitating to nonprecipitating clouds changes. Therefore, the N d climatology of all subtropical stratocumulus is constrained to a first-order approximation by precipitation and to a second-order approximation by the proximity to sources of cloud condensation nuclei.
The weakly positive scaling in R eff against H BL is consistent with the relationships between LWP, N d , and H BL . The decrease in N d with H BL is insufficient to offset the increase in LWP. The combined increase in LWP and R eff with BL deepening results in a significant but inconsequential increase in A cld with H BL (Table 1). Stratocumulus with cloud tops above 1 km are associated with larger LWP, lower N d , larger R eff , and an elevated A cld of 0.01 as compared to stratocumulus with cloud tops below 1 km.

Liquid water path adjustment
The climatological fields of LWP and N d display a significant correlation and anticorrelation with H BL . The largest climatological values of LWP are found in deep BLs with low N d (Fig. 4a). The increase in LWP with H BL is consistent with Fig. 3b. The displayed sensitivity of LWP to N d is potentially attributable to a multitude of competing factors, and not all are representative of cloud adjustments. The decrease in LWP with increased levels of pollution has been noted multiple times in observations, and various process hypotheses have been put forward.
Less polluted clouds could potentially be associated with weaker entrainment drying through the entrainmentsedimentation feedback (Bretherton et al., 2007). Alternatively, increased rates of precipitation in cleaner environments could stabilise the cloud (Wood, 2012), which results in weaker overall cloud-top entrainment of dry subsaturated air (Ackerman et al., 2004). Furthermore, recent results show that the strengthening of convective overturning in the subcloud layer through precipitation can also have a net positive impact on LWP (Goren et al., 2018). All these are ex-  Gryspeerdt et al. (2019). A minimum number of 100 points within each ln N d -ln H BL bin was required to be included in the climatology shown in opaque contours (a-e). The bivariate (simple linear) regression across the two-dimensional (one-dimensional) climatology is shown in transparent contours (as black line) in panels (a)-(d). White and grey lines in (a) denote the region of the phase space containing 80 % and 90 % of all data, respectively. The slopes of all fits are summarised in Table 1. amples of adjustments to the initial cloud microphysical response caused by an increase in droplet number. However, other factors not representative of cloud adjustments, such as the climatological covariance between H BL and N d noted in Sect. 3, may impact s lwp estimates. Table 1. This table summarises the regime dependence of each slope. The relationship between cloud properties and H BL is determined logarithmically (ln ∼ c ln ×ln H BL for = LWP) or as normalised linear slopes (c = c / where ∼ c ×H BL for ∈ {R eff , N d , A cld } and denotes the average). Slopes were determined by linear regression if and only if (i) a significant fit was obtained at the 95 % confidence level and (ii) the fit explained at least 80 % of the variance of the climatological relationship shown in Fig. 3. If no such fit is obtained, "×" is given. The regime dependence of s lwp , which is defined and discussed in Sect. 4, is summarised in the last two rows. Estimates for s lwp were either obtained by simple linear regression or by a bivariate fit taking the covariability between LWP, N d , and H BL into account. All slopes are given to the significant digit, which is determined based on the error of the respective fit. Error statistics and sample sizes for each category are provided in Table S1  Here, we estimate s lwp by either fitting ln LWP against ln N d as in Gryspeerdt et al. (2019) or by fitting the twodimensional surface of ln LWP against ln H BL and ln N d . Both fits are simple linear, single-, or bivariate regressions across the phase space containing 80 % of all data (Fig. 4a). Both fitting approaches yield similar negative s lwp estimates. Taking the covariance with H BL into account merely reduces the magnitude of s lwp from −0.33, which is consistent with previous global estimates of marine low-level clouds , to −0.28 (Table 1). Therefore, the bivariate fit of the entire climatology is likely subject to the same confounding factors impacting LWP adjustments as in Gryspeerdt et al. (2019). Furthermore, the two predictor variables, H BL and N d , of the bivariate fit are not independent (Fig. 3e), which may bias the s lwp estimate.
The entire phase space can be further characterised by F prec (Fig. 4e): 14 % (Table S1) of the climatological phase space is characterised by precipitating cloud scenes (Fig. 4b), 37 % by intermittently precipitating cloud scenes (Fig. 4c), and 48 % by non-precipitating clouds (Fig. 4d). The analysis shows that ln LWP increases with ln N d in the precipitating fraction of the cloud climatology (s lwp = 0.14) and decreases in the intermittently (s lwp = −0.23) and non-precipitating climatologies (s lwp = −0.28). Thus s lwp inferred from the entire climatology is dominated by the LWP-N d relationship in non-precipitating clouds.
The opposing response in precipitating and nonprecipitating regions is consistent with numerous previous studies (Albrecht, 1989;Ackerman et al., 2004;Bretherton et al., 2007;Wood, 2007;Wang et al., 2012;Suzuki et al., 2013;Gryspeerdt et al., 2019). While the largest fraction of H BL -N d phase space is characterised by non-precipitating clouds (Table S2), only a narrow band in close proximity to the coast lines of the Americas and the African con-tinent is characterised by little-to-no precipitation (F prec < 0.1, Fig. 2d). Most regions are characterised by intermittent rain occurrence (0.2 < F prec < 0.8) and are associated with more moderate susceptibilities of −0.23 or less (Fig. 5). Thus the results of Fig. 4c are representative of most stratocumulus regions in the subtropics. Overall, few stratocumulus regions are associated with an average positive susceptibility.
Non-precipitating and intermittently precipitating cloud climatologies are not sensitive to the fitting technique applied (Table 1). Yet, s lwp halved when the covariance of LWP with H BL is taken into account in consistently precipitating clouds. In order to gain further insight into the potential variance of s lwp with H BL , we calculated s lwp within constrained BL-depth ranges for the three precipitation regimes characterised in Fig. 4.
Analyses of ship tracks (Christensen and Stephens, 2011) and Lagrangian studies of cloud evolution (Eastman et al., 2017) have shown that H BL may increase under more polluted conditions. This, however, is not manifested within the H BL -N d climatology (Fig. 3e). Therefore, by constraining s lwp estimates in this manner, we attempt to remove some of the covariance between LWP, N d , and H BL , which may impact the estimated strength of the LWP adjustment.
S lwp in precipitating subtropical stratocumulus is considerably larger in BLs below 1.5 km in depth than in deeper BLs (Fig. 6b). While s lwp may be as large as 0.48, which constitutes a tremendous cloud adjustment in shallow BLs, it does not exceed 0.08 in deep BL clouds. It should be noted that the large, negative adjustment of s lwp = −1.0 within the first height bin in Fig. 6b is statistically significant but characterises a very small subsample of the total climatology.
Meanwhile, s lwp increases in magnitude from −0.1 in BLs below 500 m in altitude to −0.31 in BLs exceeding 1 km in depth (Fig. 6d). A weaker height dependence is observed  for intermittently precipitating cloud scenes (Fig. 6c). Both results of Fig. 6c and d are consistent with the increase in LWP susceptibility noted within pollution tracks around the globe . Moreover, the change in s lwp with H BL shown in Fig. 6c, which characterises the behaviour in most stratocumulus regions, is within a 1σ uncertainty range of s lwp estimates based on pollution tracks. Within pollution tracks, s lwp increased in magnitude from less than −0.01±0.13 in shallow BL clouds to −0.1±0.13 for a cloudtop height of 2 km .

Discussion and conclusions
Isolating the LWP adjustment due to changes in N d from potentially co-varying meteorological factors has remained a significant hindrance to quantifying the radiative forcing of aerosol-cloud interactions. It also is a likely cause of diverging estimates from low-cloud climatology, process-scale models, and pollution track estimates.
Here, we address whether LWP adjustments vary with BL depth and whether climatological susceptibility estimates are impacted by the covariance of cloud properties with H BL . Like previous studies, we find evidence for a positive relationship between LWP and N d climatologies in precip-itating marine stratocumulus (Albrecht, 1989;Christensen and Stephens, 2011;Wang et al., 2012;Suzuki et al., 2013;Rosenfeld et al., 2019), which is consistent with the suppression of precipitation. Particularly in shallow precipitating BLs (H BL < 1 km), the estimated susceptibility can become very large (s lwp > 0.4, Fig. 6). Such adjustments would correspond to a considerable enhancement of the negative cloudradiative forcing. However, these shallow, precipitating BLs are rare (10 %-25 % of all cloud scenes analysed within the 10-year climatology). Therefore, such cloud scenes are unlikely to govern the radiative forcing of aerosol-cloud interactions.
The LWP adjustment inferred from the entire climatology of marine subtropical stratocumulus (s lwp = −0.33) is driven by non-precipitating cloud climatologies which govern the climatological statistics, but are only representative of a small subset of stratocumulus regions in the subtropics. Susceptibility estimates restricted to the phase space of intermittently precipitating climatologies (Fig. 2d), which represent most stratocumulus regions in the subtropics, are lower (s lwp = −0.23). Performing a bivariate fit of the ln LWP phase space, which removes any potential impact of the LWP-H BL covariance on estimates of s lwp , does not provide substantially different results (Table 1) to previous global es-timates of s lwp in marine low clouds (Michibata et al., 2016;Gryspeerdt et al., 2019).
A further division of the entire phase space into BL-depth regimes showed that, overall, cloud adjustments seem less effective in shallow BLs. The potential increase in LWP adjustment with BL depth has very recently been noted in pollution tracks . Here, we show that this behaviour may generalise to the whole climatology. The simulated change in s lwp with H BL within clouds of intermittent precipitation is consistent with the lower end of s lwp estimates within the 1σ range inferred from pollution tracks. Stratifying the ln LWP-ln N d surface by BL depth further closes the gap between s lwp estimates inferred from climatology and cloud-scale modelling. Shallow BLs, such as the ones sampled during ASTEX and DYCOMS-II (Fig. 1), are associated with the range −0.22 < s lwp < −0.1 (Fig. 6c-d). This is consistent with estimates of s lwp obtained in LES experiments of these campaigns (Ackerman et al., 2004;Bretherton et al., 2007).
Different remote-sensing-based estimates for s lwp have been proposed. Their spatial distributions not only differ in magnitude but also in sign among one another (e.g. Michibata et al., 2016, andGryspeerdt et al., 2019), as well as compared to Fig. 5 of this study. This is likely a result of different methodologies of categorising and processing different retrievals. Different methodologies to distinguish between precipitating and non-precipitating clouds, as well as different methods to retrieve and process N d , may impact s lwp estimates. In particular, N d remains a highly uncertain retrieval from space-borne observations. For this study, we chose to limit the uncertainty of the physical retrieval of N d while capturing as much of the variability in the subtropics as possible. Stricter filtering approaches may yield less retrieval uncertainty, but they may imply a loss of some of the variability characteristic to the system. Either approach could influence s lwp estimates. Thus our results, like previous studies, are subject to this uncertainty and remain to be verified by independent data sets.
In summary, our results show that aerosol-cloud interactions may manifest differently in deep precipitating, and nonprecipitating, marine BLs as compared to shallow BLs. Furthermore, this work highlights the importance of understanding aerosol-cloud interactions in deep marine stratocumulus, which are underrepresented in currently analysed field data, numerical process models, and pollution tracks.
Author contributions. AP conceived this study and wrote the article. RE compiled the remote-sensing retrievals for the study. AP and RE performed the analyses with input from FB and FG. All authors contributed to the discussion of the results and editing of the article.
Competing interests. The authors declare that they have no conflict of interest.