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.

1 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 (Boucher et al., 2013; 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 (Bellouin et al., 2019). As defined in IPCC AR5 (Boucher et al., 2013), 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., 2017, 2019; McCoy 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., 2017, 2019; Bender 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; McCoy 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 (Gryspeerdt et al., 2019). 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 conditions (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.

Figure 1 Probability density function (PDF) for closed, open-cell, and disorganised stratocumulus layers against cloud-top height. This figure is adapted from Fig. 10 in Muhlbauer et al. (2014). Coloured bars denote the range of cloud-top heights sampled during each campaign listed in the legend. LES and cloud-resolving studies investigating aerosol–cloud–radiation interactions are colour-coded by the campaigns they are based on (with the exception of model study 8, which is based on an idealised profile). Grey shading denotes narrow BL-depth interval within which 75 % of all modelling studies reside. Future analyses of past campaigns summarised in Zuidema et al. (2016) will likely increase the data points sampled in deeper BLs. References: Jiang et al. (2002), Johnson et al. (2004), Lu and Seinfeld (2005), Bretherton et al. (2007), Sandu et al. (2008), Hill et al. (2008), Hill and Dobbie (2008), Yi et al. (2008), Xue et al. (2008), Caldwell and Bretherton (2009), Ackerman et al. (2009), Sandu et al. (2009), Hill and Feingold (2009), Mechem et al. (2012), Jenkins et al. (2013), Petters et al. (2013), Berner et al. (2013), Tonttila et al. (2017), Zhou et al. (2017), Possner et al. (2018), Augstein et al. (1973), Lenschow et al. (1988), Albrecht et al. (1988, 1995), Stevens et al. (2003), Bretherton et al. (2004), Lu et al. (2007, 2009), and Wood et al. (2011).

The same holds true for estimates based on LES, cloud-resolving 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 aerosol–cloud–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 ($\stackrel{\mathrm{‾}}{\mathrm{CF}}=\mathrm{40}$ %), 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 (Toll et al., 2019). Here, we focus on regions dominated by marine stratocumulus, and we explore these relationships within 10-year 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.

2 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 $\mathrm{1}{}^{\circ }\times \mathrm{1}$^∘. 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 (King et al., 2003; 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 (Platnick et al., 2003).

Figure 2 (a) Boundary layer height (H_BL), (b) cloud droplet number concentration (N_d), (c) liquid water path (LWP), and (d) low-cloud precipitation probability (F_prec) are shown. Regions of subtropical stratocumulus decks are marked in red and were defined in Eastman and Wood (2016) based on surface observations of Hahn and Warren (2007).

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:

$$\begin{array}{}\text{(1)}& N_{\mathrm{d}}=\sqrt{\mathrm{2}}{\displaystyle \frac{\mathrm{3}}{\mathrm{4}k\mathit{\pi }{\mathit{\rho }}_{\mathrm{w}}}}{\mathrm{\Gamma }}_{\mathrm{eff}}^{\frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \frac{{\mathrm{LWP}}^{\frac{\mathrm{1}}{\mathrm{2}}}}{R_{\mathrm{eff}|\mathrm{top}}^{\mathrm{3}}}},\end{array}$$

where ρ_w denotes the density of water, Γ_eff=f_adΓ_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 $\mathrm{1}{}^{\circ }\times \mathrm{1}$^∘ 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 clear-sky albedo (A_clr) based on the top-of-atmosphere shortwave fluxes (Kato et al., 2013) were used to estimate A_cld from

$$\begin{array}{}\text{(2)}& A_{\mathrm{toa}}=\mathrm{CF}\cdot A_{\mathrm{cld}}+(\mathrm{1}-\mathrm{CF})\cdot A_{\mathrm{clr}}.\end{array}$$

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.

3 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), respectively.

Figure 3 Scaling of (a) A_cld, (b) LWP, (c) F_prec, (d) R_eff, and (e) N_d against H_BL. Mean and standard deviation of the 10-year subtropical stratocumulus climatology (see Fig. 2) are shown in red within each height bin (100 m intervals). Fits across the climatology are superimposed in black (see 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.

The adiabatic LWP (LWP_ad) scales with cloud depth (H_c) as LWP${}_{\mathrm{ad}}\propto H_{\mathrm{c}}^{\mathrm{2}}$, where $H_{\mathrm{c}}=H_{\mathrm{BL}}-H_{\mathrm{b}}$ and H_b denotes cloud base. Based on this relationship, we regress ln LWP 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 $\mathrm{LWP}\propto H_{\mathrm{BL}}^{\mathrm{0.33}}$ (Table 1). Therefore, LWP scales considerably weaker with H_BL than H_c. Combining these two relationships, it follows that in adiabatic clouds $H_{\mathrm{c}}\propto H_{\mathrm{BL}}^{\mathrm{0.17}}$. 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 (Bretherton et al., 2013), 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 ($\stackrel{\mathrm{‾}}{c_{N_{\mathrm{d}}}}=-\mathrm{0.3}$), as the fraction of precipitating to non-precipitating 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.

Table 1 This table summarises the regime dependence of each slope. The relationship between cloud properties and H_BL is determined logarithmically ($\ln \mathrm{\Psi }\sim c_{\ln \mathrm{\Psi }}\times \ln H_{\mathrm{BL}}$ for Ψ=LWP) or as normalised linear slopes ($\stackrel{\mathrm{‾}}{c_{\mathrm{\Psi }}}=c_{\mathrm{\Psi }}/\stackrel{\mathrm{‾}}{\mathrm{\Psi }}$ where $\mathrm{\Psi }\sim c_{\mathrm{\Psi }}\times H_{\mathrm{BL}}$ for $\mathrm{\Psi }\in \mathit{\{}{R}_{\mathrm{eff}},N_{\mathrm{d}},A_{\mathrm{cld}}\mathit{\}}$ and $\stackrel{\mathrm{‾}}{\mathrm{\Psi }}$ 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 in the Supplement.

4 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 entrainment-sedimentation 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 sub-cloud layer through precipitation can also have a net positive impact on LWP (Goren et al., 2018). All these are examples 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.

Figure 4 Climatology of ln LWP against ln N_d and ln H_BL for (a) all subtropical stratocumulus (see Fig. 2), (b) fully precipitating stratocumulus, (c) intermittently precipitating stratocumulus, and (d) non-precipitating stratocumulus. Points are classified as fully precipitating (non-precipitating) if the fraction of precipitating cloud scenes shown in (e) exceeds 0.98 (remains below 0.02). All other cloud scenes are classified as intermittently precipitating. At the top of panels (a)–(d), ln LWP binned in ln N_d is shown as in 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.

Here, we estimate s_lwp by either fitting ln LWP against ln N_d as in Gryspeerdt et al. (2019) or by fitting the two-dimensional 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 (Gryspeerdt et al., 2019), 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 ($s_{\mathrm{lwp}}=-\mathrm{0.23}$) and non-precipitating climatologies ($s_{\mathrm{lwp}}=-\mathrm{0.28}$). 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 non-precipitating 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 continent is characterised by little-to-no precipitation (F_prec<0.1, Fig. 2d). Most regions are characterised by intermittent rain occurrence ($\mathrm{0.2}<F_{\mathrm{prec}}<\mathrm{0.8}$) 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.

Figure 5 Map of s_lwp which was obtained from bivariate linear regression of daily ln LWP, ln N_d, and ln H_BL retrievals at a spatial scale of 1^∘ × 1^∘. Regions where s_lwp is not statistically significant are masked in black.

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.

Figure 6 (a) s_lwp determined within 100 m height intervals for subtropical stratocumulus, (b) precipitating clouds only, (c) intermittently precipitating clouds, and (d) non-precipitating clouds. S_lwp was obtained from bivariate linear regression of the ln LWP surfaces shown in Fig. 4a–d within each height interval, respectively. Only statistically significant results at the 95 % confidence level are shown. The probability density function (PDF) of the subtropical cloud climatology across the height bins is superimposed.

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 $s_{\mathrm{lwp}}=-\mathrm{1.0}$ 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 (Toll et al., 2019). 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 $-\mathrm{0.01}\pm \mathrm{0.13}$ in shallow BL clouds to $-\mathrm{0.1}\pm \mathrm{0.13}$ for a cloud-top height of 2 km (Toll et al., 2019).

5 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 precipitating 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 cloud-radiative 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 ($s_{\mathrm{lwp}}=-\mathrm{0.33}$) 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 ($s_{\mathrm{lwp}}=-\mathrm{0.23}$). 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 estimates 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 (Toll et al., 2019). 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 $-\mathrm{0.22}<s_{\mathrm{lwp}}<-\mathrm{0.1}$ (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, and Gryspeerdt 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 non-precipitating, 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.