the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Global observations of aerosol indirect effects from marine liquid clouds
Trude Storelvmo
Anna Possner
Interactions between aerosols and liquid clouds are one of the largest sources of uncertainty in the historical radiative forcing of climate. One widely shared goal to reduce this uncertainty is to decompose radiative anomalies arising from aerosol–cloud interactions into components associated with changes in clouddroplet number concentration (Twomey effect), liquidwaterpath adjustments, and cloudfraction adjustments. However, there has not been a quantitative foundation for simultaneously estimating these components with global satellite observations. Here we present a method for assessing shortwave radiative flux anomalies from the Twomey effect and cloud adjustments over ocean between 55^{∘} S and 55^{∘} N. We find that larger aerosol concentrations are associated with widespread cloud brightening from the Twomey effect, a positive radiative adjustment from decreasing liquid water path in subtropical stratocumulus regions, and a negative radiative adjustment from increasing cloud fraction in the subtropics and midlatitudes. The Twomey effect and total cloud adjustment have contributed −0.77 ± 0.25 and −1.02 ± 0.43 W m^{−2}, respectively, to the effective radiative forcing since 1850 over the domain (95 % confidence). Our findings reduce uncertainty in these components of aerosol forcing and suggest that cloud adjustments make a larger contribution to the forcing than is commonly believed.
 Article
(5495 KB)  Fulltext XML

Supplement
(3313 KB)  BibTeX
 EndNote
Changes in aerosol concentrations over the industrial era have modified clouds and perturbed the global radiation balance at the top of the atmosphere (Raghuraman et al., 2021; Kramer et al., 2021). The radiative flux perturbation resulting from these cloud changes, known as the effective radiative forcing from aerosol–cloud interactions (ERF_{aci}), is estimated to be −0.84 ± 0.61 W m^{−2} between 1750 and 2019 (90 % confidence interval, CI, from Forster et al., 2021). ERF_{aci} is much more uncertain than the positive radiative forcing from carbon dioxide changes (+2.16 ± 0.26 W m^{−2}), meaning that ERF_{aci} offsets a potentially large but highly uncertain portion of historical greenhousegas forcing. Reducing this uncertainty would improve assessments of climate sensitivity and committed future warming (Matthews and Zickfeld, 2012; Mauritsen and Pincus, 2017; Sherwood et al., 2020; WatsonParris and Smith, 2022).
An extension of these forcing estimates is to characterize how changes in different cloud properties contribute to ERF_{aci}, thereby providing insight into the relative importance of different processes. For instance, as cloud condensation nuclei (CCN) become more abundant, liquid clouds typically form smaller but more numerous droplets. The change in cloud droplet effective radius (r_{e}) and number concentration (N_{d}) directly increases cloud optical thickness – a mechanism known as the Twomey effect (Twomey, 1977). The reduction of cloud droplet size can also enhance evaporation or reduce precipitation, causing adjustments in cloud thickness, lifetime, or morphology (Albrecht, 1989; Pincus and Baker, 1994; Rosenfeld et al., 2006; Bretherton et al., 2007). Separating the radiative impacts of the Twomey effect and cloud adjustments is thus an important step towards understanding the causes of ERF_{aci}.
Recent community assessments find that the components of ERF_{aci} all have considerable uncertainty. The Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) estimates that the Twomey effect is −0.7 ± 0.5 W m^{−2}, the adjustment of liquid water path (LWP) is +0.2 ± 0.2 W m^{−2}, and the adjustment of liquidcloud fraction is −0.5 ± 0.4 W m^{−2} (90 % CIs for forcing between 1750 and 2014) (Forster et al., 2021). Another assessment by the World Climate Research Programme reports even larger uncertainties (Bellouin et al., 2020). In particular, they find that the cloudfraction adjustment is especially uncertain: it could be negligibly small or large enough to offset most of the historical carbondioxide forcing.
Constraints from satellite observations offer a path toward reducing this uncertainty, but in practice it has been difficult to isolate relationships between aerosols and radiative anomalies caused by changes in individual cloud properties (Feingold et al., 2022). Furthermore, previous global observational studies that attempt to quantify these relationships used separate methods for estimating the Twomey effect, LWP adjustment, and cloudfraction adjustment, so their estimates may suffer from limitations that differ from one ERF_{aci} component to another (Forster et al., 2021). This complicates efforts to rigorously compare the Twomey effect and cloud adjustments. Here we address these challenges by adapting techniques from the cloudfeedback literature. We develop a cloud radiative kernel that separates the radiative anomalies caused by changes in r_{e}, LWP, and liquidcloud amount, and we relate each of these radiative anomalies to local aerosol concentrations and N_{d}. This facilitates an assessment of the Twomey effect and liquidcloud adjustments over the global ocean.
2.1 Satellite data, reanalysis, and climate model output
We analyze monthly gridded satellite observations from 2003 through 2020 obtained from the Moderate Imaging Spectroradiometer (MODIS) MCD06COSP dataset version 6.2.0 (Pincus et al., 2023). This dataset combines observations from MODIS instruments on the Aqua and Terra satellites. Our primary unit of analysis is a joint histogram of pixel counts for liquidtopped clouds partitioned by r_{e} and LWP. Histogram counts are normalized by the number of all valid pixels in the grid box and then multiplied by 100 to convert the units to cloud fraction (Fig. 1a). These histograms represent the fractional occurrence of liquidtopped clouds that are exposed to space; hence they do not include cases where liquid cloud is obscured by overlying ice. LWP is defined by the vertical integral of cloud liquid water mass per unit area, and r_{e} is defined by the ratio of the third and second moments of the clouddroplet radius distribution. These two variables are estimated with the MODIS 3.7 µm retrieval algorithm (Platnick et al., 2017).
We also use daily gridded N_{d} estimates from MODIS (Gryspeerdt et al., 2022a) and monthly gridded radiative flux retrievals from the Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled ed. 4.1 and FluxByCldTyp ed. 4.1 datasets (Loeb et al., 2018; Sun et al., 2022). The MODIS N_{d} estimates can be biased when r_{e} is sufficiently small, when the cloud visible optical thickness is sufficiently small, or when threedimensional radiative transfer effects contribute to the measured radiances (Grosvenor et al., 2018). To avoid these problematic cases, N_{d} is estimated for singlelayer liquid clouds that satisfy several conditions: (i) r_{e} is larger than 4 µm; (ii) cloud optical thickness is larger than 4; (iii) cloud fraction at 5 km resolution is larger than 0.9; (iv) the solar zenith angle is less than 65^{∘}; (v) the satellite viewing zenith angle is less than 55^{∘}; (vi) the subpixel heterogeneity index defined by Zhang and Platnick (2011) is less than 0.3; (vii) the MODIS estimate of r_{e} is largest from the 3.7 µm retrieval algorithm, followed by the 2.1 µm retrieval algorithm and then the 1.6 µm retrieval algorithm; and (viii) cloud optical thickness is in the top 10 % of values in 100 km × 100 km regions (“Z18 sampling” in Gryspeerdt et al., 2022a). The final condition preferentially selects the convective cores in cloudy scenes (Zhu et al., 2018). Most cloud droplets in shallow convective clouds form near the cloud base, so N_{d} in convective cores depends on the CCN concentration in air that enters the cloud from below (Rosenfeld et al., 2019). Thus, N_{d} in convective cores typically does not represent N_{d} in the entire cloud, but it serves as an indicator of CCN concentration near cloud base. We denote the estimated clouddroplet number concentration as ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ to distinguish it from the clouddroplet number concentration in the entire cloud. For consistency with the MODIS cloud histograms, we use ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ estimates from the MODIS 3.7 µm retrieval algorithm, and we combine data from the Terra and Aqua satellites. Daily values of $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ are averaged across the satellite platforms and over 1month intervals, weighted by the number of pixels with a valid ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ retrieval.
Monthly meteorological fields and the drymass concentration of sulfate aerosol at 910 hPa, s, are obtained from MERRA2 reanalysis (Gelaro et al., 2017; Randles et al., 2017). We consider sulfate aerosol because it dominates the anthropogenic influence on CCN (Charlson et al., 1992; Stevens, 2015), and we select data from 910 hPa rather than the surface because the 910 hPa level is a better indicator of aerosol concentration near cloud base (Painemal et al., 2017). The sulfate data are determined from biascorrected observations of total aerosol optical depth from cloudfree pixels and simulations from a global model that represents the sources, sinks, and chemistry of sulfate and its precursor gases. The data assimilation accounts for aerosol swelling in humid environments and filters out pixels near clouds that are affected by retrieval bias (Randles et al., 2017). The main limitation of the sulfate data is that the total aerosol optical depth is constrained by observations, but aerosol species distributions and vertical profiles are not. These data provide an additional indicator of cloudbase CCN concentration that is independent of the MODIS estimates of ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$.
Finally, we use output from historical simulations of 20 global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). The simulations are run from 1850 through 2014 with realistic emissions of greenhouse gases, aerosols, and aerosol precursor gases. Sulfate mass concentration from the model output is converted to pressure coordinates and linearly interpolated to 910 hPa. The models are listed in Table S1 in the Supplement.
2.2 Quantifying aerosol indirect effects
We first relate variability of aerosols to the radiative effects of liquid clouds – relationships we call “aerosol indirect effects.” Our analysis begins with the MODIS joint histograms of liquidcloud fraction, C, partitioned by r_{e} and LWP (Fig. 1a). For a given latitude, longitude, and time, the shortwave (SW) radiative flux anomaly at the top of the atmosphere that is induced by liquid clouds, R^{′}, is estimated according to
where r and l represent the r_{e} and LWP dimensions of the histogram, and primes denote monthly anomalies relative to the local climatological seasonal cycle. The cloud radiative kernel, $\partial R/\partial {C}_{rl}$, represents the SW flux anomaly that would occur if the cloud fraction C_{rl} were to increase by 1 % with all noncloud factors fixed (Fig. 1b). The kernel is computed with the RRTMG radiative transfer model (Clough et al., 2005) following a method similar to that of Zelinka et al. (2012). We then adapt a method of cloudfeedback analysis developed by Zelinka et al. (2013) to decompose R^{′} into contributions from different cloud properties:
where ${R}_{{r}_{\mathrm{e}}}^{\prime}$, ${R}_{\text{LWP}}^{\prime}$, and ${R}_{\text{CF}}^{\prime}$ are the SW flux anomalies caused by r_{e}, LWP, and cloudamount anomalies, respectively – each computed with the other properties held fixed. We note that ${R}_{{r}_{\mathrm{e}}}^{\prime}$ is the radiative anomaly that is caused by variations in r_{e} with fixed LWP, so it is equivalent to the radiative anomaly that is caused by variations in N_{d} with fixed liquidwater content. ${R}_{\text{res}}^{\prime}$ is the residual of the decomposition. The radiative kernel and MODIS joint histograms reproduce monthly observations of R^{′} across the global ocean with a bias of about +4.6 % (Appendix A). The methods for computing the kernel and decomposing R^{′} are described in Appendix A and B.
To test robustness of the results, we make one set of R^{′} estimates in which only fully cloudcovered pixels are included in the histograms and a second set of estimates in which fully and partly cloudcovered pixels are both included. We refer to these cases as MODIS_{CLD} and MODIS_{CLD+PCL}, respectively. The filter of the MODIS_{CLD} case avoids retrieval biases that affect partly cloudy pixels, but it may introduce a sampling bias by excluding some cloud elements. The opposite is true for MODIS_{CLD+PCL}. Both cases are presented to explore tradeoffs between the accuracy and completeness of the satellite cloud data.
We relate R^{′} to sulfate and clouddroplet concentrations using cloudcontrolling factor analysis (Scott et al., 2020; Myers et al., 2021). Our analysis closely follows the method of Wall et al. (2022; hereafter W22) except that we generalize their results by applying cloudcontrolling factor analysis to R^{′} and each of its components. The cloudcontrolling factor method approximates R^{′} as a linear combination of seven local cloudcontrolling factors x_{i}:
The first six x_{i} terms include sea surface temperature, estimated inversion strength at the top of the planetary boundary layer (Wood and Bretherton, 2006), lowlevel advection across a surfacetemperature gradient, surface wind speed, relative humidity at 700 hPa, and vertical wind at 700 hPa. Collectively these terms represent all of the standard largescale meteorological controls on liquid clouds in the marine boundary layer that have been proposed in the literature (Scott et al., 2020). The final x_{i} term can be either ln s or $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$. All meteorological terms and ln s are calculated with MERRA2 data and linearly interpolated to the native 1^{∘} × 1^{∘} grid of MODIS. We then select oceancovered grid boxes, remove the climatological seasonal cycle and leastsquares linear trend from all variables in each grid box, and average the anomalies over a 5^{∘} × 5^{∘} grid that spans 55^{∘} S to 55^{∘} N. For each ocean grid box, R^{′} is regressed against anomalies of the seven cloudcontrolling factors using ordinary leastsquares multilinear regression. Separate regressions are performed with ln s and $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ as the final predictor. Thus, the regression coefficients $\partial R/\partial \mathrm{ln}s$ and $\partial R/\partial \mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ represent the relationship between R^{′} and local anomalies of ln s or $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ with all meteorological predictors held constant. The goodness of fit of the regression model is determined by computing the fraction of R^{′} variance that it explains in each grid box and then spatially averaging the results over the domain. On average, the regression method explains 46 % of the R^{′} variance when ln s is the final predictor and 49 % of the variance when $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ is the final predictor. We also apply the method to ${R}_{{r}_{\mathrm{e}}}^{\prime}$, ${R}_{\text{LWP}}^{\prime}$, and ${R}_{\text{CF}}^{\prime}$ to estimate the Twomey effect, LWP adjustment, and cloudfraction adjustment.
Our analysis differs from existing global estimates of aerosol indirect effects in several ways. First, estimates that control for fewer meteorological factors are susceptible to bias from correlations between meteorology and aerosols (Mauger and Norris, 2007; Gryspeerdt et al., 2016; Andersen et al., 2017). Our method minimizes this bias by controlling for all of the standard largescale meteorological drivers of liquid boundarylayer clouds that have been proposed in the literature. Second, estimates derived from daily or monthly gridbox averages of r_{e} and LWP suffer from aggregation bias because these properties are nonlinearly related to cloud albedo (Feingold et al., 2022; Goren et al., 2023). Our method avoids this bias by inferring cloud radiative effects from joint histograms of r_{e} and LWP rather than gridbox averages. Third, studies of ship tracks, industrial plumes, or volcanic eruptions offer some of the most captivating evidence of aerosol indirect effects, but the estimates they provide may not be representative of the global scale (Possner et al., 2018; Toll et al., 2019; Glassmeier et al., 2021). Our method avoids this potential sampling bias by estimating aerosol indirect effects across the global ocean. Fourth, no global observational study has simultaneously estimated the Twomey effect, LWP adjustment, and cloudfraction adjustment, so comparisons of these components have been complicated by the fact that each one is estimated using different data, methods, assumptions, and uncertainty quantification (Forster et al., 2021). Our method avoids this complication by estimating all components with a single, selfconsistent framework. Our estimates of aerosol indirect effects could still be affected by satellite retrieval biases, but they improve upon existing estimates in these four ways (Painemal and Zuidema, 2011; Ma et al., 2018).
We next present estimates of the Twomey effect and cloud adjustments across the global ocean. The Twomey effect can occur whenever the CCN concentration is small enough that it limits the number of droplets that form in cloud updrafts. This condition is usually satisfied over ocean, so the Twomey effect is expected to be ubiquitous in oceanic clouds (Rosenfeld et al., 2014). Indeed, we find that increasing sulfate concentration is associated with significant cloud brightening from ${R}_{{r}_{\mathrm{e}}}$ changes across most of the global ocean (Fig. 2a). Cloud brightening is also observed in response to increasing ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ (Fig. 2b), but we caution against overinterpreting statistical significance of this relationship because ${R}_{{r}_{\mathrm{e}}}$ and ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ are both inferred from the MODIS r_{e} retrievals (${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ is inferred using 10 % of the data). Nevertheless, these results show that most marine liquid clouds exhibit the Twomey effect.
In contrast, previous work has shown that cloud adjustments can differ from one cloud regime to another (Zhang et al., 2022). As cloud droplets become smaller, they sediment more slowly out of the cloudtop entrainment zone, and they evaporate more quickly when exposed to entrained air. This enhances evaporation and reduces LWP in nonprecipitating clouds (Bretherton et al., 2007; Small et al., 2009). Clouds with smaller droplets also form precipitation more slowly through collision and coalescence. This may cause other changes in cloud properties, including deeper cumulus clouds, longer cloud lifetimes, larger stratiform areas detrained from precipitating cloud elements, or changes in mesoscale cellular structure (Albrecht, 1989; Pincus and Baker, 1994; Rosenfeld et al., 2006; Seifert et al., 2015; Possner et al., 2018; Dagan et al., 2017; Goren et al., 2022). The cloud adjustments can, in turn, affect CCN concentration by changing precipitation scavenging or sulfate formation in cloud droplets (Wood et al., 2012; Kang et al., 2022; Andreae and Rosenfeld, 2008). Some of these mechanisms depend on the meteorological conditions, so they may vary regionally (Chen et al., 2014; Possner et al., 2020; Zhou et al., 2021; Zhang and Feingold, 2023).
The estimated cloud adjustments exhibit regional variations that are consistent with some of these proposed mechanisms. The radiative adjustment from LWP changes is positive in much of the subtropics, and it maximizes in areas of semipermanent stratocumulus clouds and directly downwind (Fig. 2c and d). This spatial pattern suggests that enhanced evaporation in nonprecipitating stratocumulus may contribute to the LWP adjustment (Bender et al., 2019). Weak or insignificant LWP adjustments are found across much of the midlatitude oceans, despite the fact that precipitating clouds occur less frequently in these regions as sulfate aerosols become more abundant (W22). This weak overall LWP adjustment might be partly explained by the fact that different cloud regimes in extratropical cyclones exhibit adjustments that may counteract one another (Naud et al., 2017; McCoy et al., 2018). Furthermore, the radiative adjustment from cloudfraction changes is negative in most of the subtropics and midlatitudes, suggesting that adjustments in these regions may involve changes in cloud lifetime, size, or morphology as well (Fig. 2e and f). Subtropical stratocumulus regions exhibit offsetting adjustments from LWP changes and cloudfraction changes. In these cases, as CCN become more abundant, the overall liquidcloud fraction increases, but the increase is disproportionately large in cloud elements with belowaverage LWP. This combination is consistent with larger stratiform areas detrained from precipitating clouds or a shift from open to closed mesoscale cellular convection (Possner et al., 2018; Rosenfeld et al., 2006). Thus, aerosoldriven changes in evaporation and precipitation may both contribute to cloud adjustments. The spatial patterns of the adjustments predicted with ln s resemble those predicted with $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$, suggesting that the estimated adjustments are robust.
We determine the relative importance of the Twomey effect and cloud adjustments at the global scale by averaging the regression coefficients over ocean. These averages can be interpreted as the cloud radiative anomalies that would occur if sulfate concentration and ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ were increased by a factor of 2.7 at every location. Uncertainty quantification for these estimates is described in Appendix C. For the regressions against ln s and $\mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$, we find that the Twomey effect and cloudfraction adjustment both significantly increase SW reflection to space (Fig. 3). The cloudfraction adjustment enhances SW reflection by between 43 % and 250 % compared to the Twomey effect alone (95 % CI), so it makes a substantial contribution to the overall aerosol indirect effect. The large relative magnitude of the cloudfraction adjustment is consistent with the observed cloud response during a volcanic eruption in Holuhraun, Iceland, and the uncertainty range for this adjustment overlaps with other observational estimates (Chen et al., 2022; Gryspeerdt et al., 2020). Furthermore, the LWP adjustment reduces SW reflection to space, offsetting between 6 % and 87 % of the Twomey effect. This uncertainty range is comparable to the range of estimates from Diamond et al. (2020) and Gryspeerdt et al. (2019). However, it differs from a shiptrack analysis by Manshausen et al. (2022), who find that the LWP adjustment increases SW reflection rather than reduces it. This apparent discrepancy may be a consequence of the fact that localized, shortterm aerosol perturbations such as shipping emissions can give rise to different cloud adjustments than sustained aerosol perturbations over larger spatial and temporal scales (Glassmeier et al. 2021). Although the LWP adjustment and cloudfraction adjustment counteract one another, the total cloud adjustment is still significantly negative, and it is comparable to the Twomey effect. Furthermore, the estimated Twomey effect and total cloud adjustment are similar for the MODIS_{CLD} and MODIS_{CLD+PCL} cases, indicating that they do not change substantially when partly cloudy pixels are filtered in different ways. The Twomey effect and total cloud adjustment are also qualitatively consistent when different N_{d} datasets are used, and they are an order of magnitude larger than $\partial {R}_{\text{res}}/\partial \mathrm{ln}s$ and $\partial {R}_{\text{res}}/\partial \mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ (Figs. S1 and S2 in the Supplement). These results robustly show that the Twomey effect and total cloud adjustment cause comparable changes in topofatmosphere SW flux.
A limitation of these results is that the MODIS_{CLD} and MODIS_{CLD+PCL} cases have offsetting differences in the estimated LWP and cloudfraction adjustments (Fig. 3). This means that the estimates of the individual LWP and cloudfraction adjustments depend on filtering of partly cloudy pixels, but the estimate of the total cloud adjustment does not. One implication is that aerosol variations must be associated with changes in the relative amounts of partly and fully cloudcovered pixels. Partly and fully cloudy pixels reside on cloud edges and interiors, respectively, so a change in the relative amounts of these pixels implies a change in the cloud perimetertoarea ratio (W22). This suggests that the global cloud adjustment may involve changes in the horizontal size or morphology of the clouds. A case study demonstrating this concept is presented in Appendix D. A second implication is that whenever aerosol perturbations change the cloud size or morphology, the conventional practice of estimating the individual LWP and cloudfraction adjustments will inevitably lead to results that depend on the classification and filtering of partly cloudy pixels. Thus, instrument sensitivity, horizontal resolution, and subjective pixelclassification thresholds can all affect the results. In contrast, we find that more robust results can be obtained by estimating the total cloud adjustment. Our analysis provides the first direct assessment of this quantity from observations, reanalysis, and radiative transfer modeling.
We next combine estimates of aerosol indirect effects and historical sulfate changes to infer ERF_{aci}. The forcing estimates use sulfate rather than ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ because sulfate concentration is a widely available output variable from GCMs but ${\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ is not. Assuming that sulfate dominates the anthropogenic influence on CCN (Charlson et al., 1992; Stevens, 2015), we estimate SW ERF_{aci} from liquidtopped clouds according to
where Δln s is the change in sulfate concentration between preindustrial (1850–1859) and presentday (2005–2014) conditions simulated by GCMs that participated in CMIP6. This method of estimating ERF_{aci} has been validated with volcanic eruptions and other known variations of regional sulfurdioxide emissions (W22).
We note that this method differs from that of a similar study by W22 in three ways. First, we estimate ERF_{aci} from all liquidtopped clouds, while W22 estimate ERF_{aci} from lowlevel clouds, defined as clouds with tops between the surface and 680 hPa. We applied their method to estimate SW ERF_{aci} from all liquidtopped clouds, and we found that the result is about 26 % larger in magnitude than the estimate of SW ERF_{aci} from lowlevel clouds. Second, we estimate SW ERF_{aci}, while W22 estimate net ERF_{aci}. Thus, their estimate includes an additional ERF_{aci} component from changes in longwave radiation, which offsets about 14 % of the SW component (Appendix B). Third, we estimate ERF_{aci} with MODIS observations and radiative kernels, while W22 estimate ERF_{aci} with CERES observations for their main result. Our kernelbased estimates of R^{′} are about 4.6 % larger in magnitude than the corresponding CERES observations (Appendix A). These three factors cause our ERF_{aci} estimates to have a larger magnitude than those reported by W22.
Our method for estimating ERF_{aci} can be applied to each component of the aerosol indirect effect to quantify the associated historical effective radiative forcing. The Twomey effect contributes a negative instantaneous radiative forcing (IRF_{aci}) that peaks in subtropical stratocumulus regions and the midlatitude oceans of the Northern Hemisphere (Fig. 4a). Forcing is relatively large in stratocumulus regions because these clouds exhibit a strong radiative response to CCN perturbations (Fig. 2), and forcing is relatively large in the Northern Hemisphere midlatitudes because these regions are close to anthropogenic aerosol sources. The geographic pattern and magnitude of the IRF_{aci} generally agree with the estimates of McCoy et al. (2017), Kinne (2019), and Jia et al. (2021). Furthermore, the IRF_{aci} is comparable to the effective radiative forcing from the combined effect of LWP adjustments (A_{LWP}) and cloudfraction adjustments (A_{CF}) (Fig. 4b). Thus, the magnitude of the overall ERF_{aci} peaks in the subtropical stratocumulus regions and the Northern Hemisphere midlatitudes as well (Fig. 4c).
We average the forcing components over ocean between 55^{∘} S and 55^{∘} N to quantify their largescale climate impacts. Confidence intervals are computed accounting for regressionslope uncertainty and intermodel spread in the estimates of Δln s (Appendix C). To frame our results in the context of the existing literature, we compare our estimates with forcing calculations from an assessment of the World Climate Research Programme (WCRP) (Bellouin et al., 2020) and forcing estimates from 14 GCMs that participated in the Coupled Model Intercomparison Project Phase 5 (CMIP5) and AeroCom experiments computed by Gryspeerdt et al. (2020) (Table S1). We repeat the original WCRP analysis except that we restrict the calculation to SW forcing over ocean between 55^{∘} S and 55^{∘} N, as described in the Supplement. The GCM forcing estimates are averaged over ocean between 55^{∘} S and 55^{∘} N as well. Although all forcing estimates are computed over the same spatial domain, their time periods differ slightly from one another: The presentday reference years are 2005–2014 for our estimates, 2005–2015 for the WCRP estimates, and 2000 for the CMIP5 and AeroCom estimates, and the preindustrial reference years are 1850–1859 for our estimates, 1850 for the WCRP and CMIP5 estimates, and 1860 for the AeroCom estimates (Bellouin et al., 2020; Zelinka et al., 2014; Ghan et al., 2016). These differences in the reference periods could cause differences in ERF_{aci} of 0.1 W m^{−2} or less (IPCC, 2021).
Averages of IRF_{aci}, cloud adjustments, and the overall ERF_{aci} are compared in Fig. 5. We find that A_{CF} is significantly negative, and A_{LWP} is more likely than not to be positive, but the magnitudes of these estimates depend on filtering choices for partly cloudy pixels. The three remaining components are insensitive to partly cloudy pixel filtering: the IRF_{aci} is −0.77 ± 0.25 W m^{−2}, the total cloud adjustment is −1.02 ± 0.43 W m^{−2}, and the overall ERF_{aci} is −1.86 ± 0.62 W m^{−2} (95 % CIs from MODIS_{CLD}). These results lie inside the ranges of the corresponding WCRP and GCM estimates, and the median IRF_{aci} agrees very well with the WCRP and GCM values. However, our results reduce uncertainty of each component by at least 62 % relative to the confidence intervals of the WCRP and at least 23 % relative to the range of GCMs. Furthermore, the WCRP and GCM estimates do not rule out the possibility that the total cloud adjustment is positive or an order of magnitude smaller than the IRF_{aci}. According to our analysis, however, such a small or positive adjustment is implausible. Thus, our analysis reduces uncertainty in the historical IRF_{aci} and total cloud adjustment, and it clarifies the relative importance of these components.
The oceanaverage SW ERF_{aci} can be scaled to establish an upper bound for the globalaverage net ERF_{aci}. Let ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{net},\mathrm{g}}$ be the globalaverage net ERF_{aci}, and let ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{net},\mathrm{d}}$ be the domainaverage net ERF_{aci}, where the domain includes ocean areas between 55^{∘} S and 55^{∘} N. Assuming that the average net ERF_{aci} is negative outside the domain (Diamond et al., 2020), it follows that
where f=0.56 is the fraction of global surface area covered by the domain. ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{net},\mathrm{d}}$ can be expressed as
where ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{sw},\mathrm{d}}$ is the domainaverage SW ERF_{aci}, and β is the fraction of SW ERF_{aci} that is offset by longwave ERF_{aci}. Our radiative kernel cannot accurately assess longwave cloud radiative effects, so β is estimated by applying cloudcontrolling factor analysis to CERES satellite data instead (Appendix B). The resulting uncertainty range is β = 0.14 ± 0.06 (90 % CI). We evaluate Eq. (2) with the bounds of the 90 % CIs of β and ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{sw},\mathrm{d}}$ from the MODIS_{CLD} and MODIS_{CLD+PCL} cases and then select the leastnegative value of ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{net},\mathrm{d}}$ to evaluate Eq. (1). The result constitutes an upper bound for ${\mathrm{ERF}}_{\mathrm{aci},\mathrm{net},\mathrm{g}}$.
The above reasoning implies a 95 % probability that the global net ERF_{aci} from liquid clouds is more negative than −0.56 W m^{−2} (relative to 1850–1859). Equivalent upper bounds from the published literature include −0.07 W m^{−2} from the WCRP assessment and −0.3 W m^{−2} from the observationbased estimate of the IPCC Sixth Assessment Report (relative to 1850 and 1750, respectively) (Bellouin et al., 2020; Forster et al., 2021). Our analysis thus supports a more stringent upper bound on global ERF_{aci}. This constraint is similar to another estimate from cloudcontrolling factor analysis presented by W22, but our estimate invokes weaker assumptions because it does not extrapolate forcing to areas outside the domain. Our upperbound estimate also complements evidence from global energybalance arguments, which constrains the lower bound of ERF_{aci} (Stevens, 2015; Smith et al., 2021).
We analyze MODIS satellite data and adapt techniques from the cloudfeedback literature to quantify aerosol indirect effects from liquidtopped clouds. Our method avoids aggregation and sampling biases that may affect some previous studies, and it controls for all of the standard largescale meteorological drivers of liquid boundarylayer clouds that have been proposed in the literature, thereby minimizing biases from confounding meteorological factors (Possner et al., 2018; Glassmeier et al., 2021; Feingold et al., 2022). Furthermore, the Twomey effect, LWP adjustment, and cloudfraction adjustment are simultaneously quantified with a single, selfconsistent framework. This guarantees that all of the components, and their uncertainties, are quantified in a consistent way. Although it is important to continue characterizing satellite retrieval biases, to include new meteorological cloudcontrolling factors as they are discovered, to investigate nonlinear and nonlocal relationships between clouds and their controlling factors (Lewis et al., 2023), and to quantify additional ERF_{aci} components from icecontaining clouds, our method overcomes several limitations that affect previous observational estimates of aerosol indirect effects.
We apply our method to constrain aerosol indirect effects across the global ocean. We find that increasing CCN concentration is associated with widespread cloud brightening from the Twomey effect, a positive radiative adjustment from decreasing LWP in subtropical stratocumulus regions, and a negative radiative adjustment from increasing cloud fraction in the subtropics and midlatitudes. The estimated aerosol indirect effects are combined with historical sulfate changes simulated by CMIP6 models to quantify the associated SW ERF_{aci}. The Twomey effect and total cloud adjustment are estimated to contribute −0.77 ± 0.25 and −1.02 ± 0.43 W m^{−2}, respectively, to the SW ERF_{aci} averaged over ocean between 55^{∘} S and 55^{∘} N (95 % CIs). Our findings reduce uncertainty in these components of aerosol forcing and suggest that liquidcloud adjustments make a larger contribution to the forcing than is commonly believed.
We compute a SW cloud radiative kernel for the MODIS r_{e}–LWP joint histogram to quantify the effect of liquidcloud anomalies on the topofatmosphere SW flux. The radiative kernel is similar to that of Zelinka et al. (2012) with two exceptions. First, our kernel represents liquidtopped clouds, while their kernel represents clouds of all phases. Second, our kernel is partitioned by r_{e} and LWP, while their kernel is partitioned by cloudtop pressure and cloud optical thickness. Besides these exceptions, we calculate the kernel by closely following the method of Zelinka et al. (2012).
The first step of the kernel calculation is to quantify the clearsky upward SW flux at the top of the atmosphere for various combinations of surface albedo, latitude, and calendar month. Calculations are performed with the RRTMG radiative transfer model (Clough et al., 2005) using inputs that include the climatological seasonal cycle of humidity from MERRA2, a standard ozone profile, and a solar constant of 1361 W m^{−2}. For a given latitude and month, we chose a day in the middle of the month and calculate the average of the cosine of the solar zenith angle μ_{i} for each 1 h interval throughout the day. We then scale μ_{i} by ${\mathrm{SW}}_{\downarrow ,\mathrm{CERES}}/{\mathrm{SW}}_{\downarrow ,\mathrm{day}}$, where ${\mathrm{SW}}_{\downarrow ,\mathrm{day}}$ is the dailymean insolation for the day in the middle of the month, and ${\mathrm{SW}}_{\downarrow ,\mathrm{CERES}}$ is the monthlymean insolation from CERES satellite data (Loeb et al., 2018). This step ensures that the monthlymean insolation for the radiative kernel is equal to that of CERES. We compute the clearsky SW flux for each of the 24 μ_{i} terms and then average the results. The calculations are performed using surface albedo of 0, 0.5, and 1. The final result is a matrix of clearsky upward SW flux at the top of the atmosphere as a function of surface albedo, latitude, and calendar month.
The next step is similar to the clearsky calculations except that an overcast and horizontally uniform liquid cloud is introduced in the radiation code. The r_{e} and LWP of the cloud are varied, and cloudtop pressure is set to 850 hPa to match the modal value retrieved by MODIS. For r_{e}, we use the standard MODIS retrieval algorithm, r_{e,std}, and the 3.7 µm retrieval algorithm, r_{e,3.7}. Monthly gridded values of r_{e,std} and r_{e,3.7} have a correlation coefficient of 0.92 over ocean, but they are generally different because r_{e,3.7} represents conditions closer to the cloud top (Platnick, 2000). We therefore prescribe r_{e} inside the cloud as
where τ_{c} is the visible optical depth below cloud top, and ${\stackrel{\mathrm{\u0303}}{r}}_{\mathrm{e},\text{std}}\equiv m{r}_{\mathrm{e},\mathrm{3.7}}+b$, where m=1.14 and $b=\mathrm{0.35}$ µm. The coefficients m and b are determined by regressing r_{e,std} against r_{e,3.7} using all monthly 1^{∘} × 1^{∘} ocean grid boxes, and the τ_{c}=3 threshold is chosen from weighting functions estimated by Platnick (2000). Using these relationships, we calculate the topofatmosphere SW flux with different combinations of r_{e,3.7} and LWP that correspond to the bins of the MODIS r_{e}–LWP joint histogram. Separate calculations are performed for synthetic clouds at the four edges of each bin, and the results are averaged to get one value of upward SW flux at the top of the atmosphere for each bin. We then subtract the resulting value from the clearsky upward SW flux to determine the SW cloud radiative effect (CRE). These calculations produce a matrix of SW CRE above an overcast liquid cloud as a function of latitude, surface albedo, calendar month, r_{e}, and LWP.
The final step of the calculation is to convert the overcastsky SW CRE to a cloud radiative kernel, K. Let C_{rl} be the liquidcloud fraction in effective radius bin r and LWP bin l. The K matrix represents how anomalies of C_{rl} affect R with all noncloud factors fixed:
K_{rl} is computed by dividing the overcastsky SW CRE by 100 %. We apply linear interpolation to transform K_{rl} from latitude–surfacealbedo space to latitude–longitude space using the climatological seasonal cycle of clearsky surface albedo from CERES. The final radiative kernel has units of $\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{\%}}^{\mathrm{1}}$ (watts per square meter per percentage of cloud fraction), and it is a function of latitude, longitude, calendar month, r_{e}, and LWP (Fig. 1b).
We validate the radiative kernel by comparing R^{′} observations from the CERES FluxByCldTyp dataset (Sun et al., 2022) with R^{′} estimates computed from the kernel and MODIS r_{e}–LWP joint histograms. The kernel estimates are regressed against the CERES observations using data from all monthly 1^{∘} × 1^{∘} ocean grid boxes between 55^{∘} S and 55^{∘} N from 2003 through 2020. The regression slope is 1.046 ± 0.005 (95 % CI) (Fig. A1). Thus, biases of our radiative kernel and differences between the MODIS and CERES cloudphase retrieval algorithms cause the kernelbased values of R^{′} to overestimate the magnitude of their CERES counterpart by +4.6 ± 0.5 %.
For a given latitude, longitude, and time, the total liquidcloudinduced SW flux anomaly at the top of the atmosphere, R^{′}, is
We decompose the term on the right side of Eq. (B1) to estimate how much cloudamount anomalies, r_{e} anomalies, and LWP anomalies contribute to R^{′}. The decomposition closely follows the method described in Appendix B of Zelinka et al. (2013) except that our radiative kernel and histogram have different dimensions.
First, let C_{tot} be the total liquidcloud fraction summed over all histogram bins. We express ${C}_{rl}^{\prime}$ as
where overbars denote values from the local climatological seasonal cycle. The first term on the right side of Eq. (B2) represents the anomalies of C_{rl} that would occur if ${C}_{\text{tot}}^{\prime}$ were distributed among the r_{e}–LWP bins such that the normalized distribution in the histogram remains the same as the climatology. In other words, this term accounts for a change in total liquidcloud fraction, holding the proportion of clouds in each histogram bin fixed. The second term on the right side of Eq. (B2) accounts for anomalies of C_{rl} that remain after removing $({\stackrel{\mathrm{\u203e}}{C}}_{rl}/{\stackrel{\mathrm{\u203e}}{C}}_{\text{tot}}){C}_{\text{tot}}^{\prime}$. This term represents shifts in the distribution of r_{e} and LWP with the total liquidcloud fraction fixed. By construction, ${C}_{rl}^{\ast}$ vanishes when it is summed over all histogram bins.
Next, we decompose the radiative kernel into two terms:
Here, K_{0} is the average of K_{rl} weighted by the climatological cloud fraction,
and ${\widehat{K}}_{rl}\equiv {K}_{rl}{K}_{\mathrm{0}}$. With the relationships in Eqs. (B1)–(B4), R^{′} can be expressed as
We next decompose ${\widehat{K}}_{rl}$ into three components:
where
and
R^{′} can then be expressed as
The first term on the right side of Eq. (B5) is the SW flux anomaly that would occur if the anomaly of total liquidcloud fraction were distributed among the r_{e}–LWP bins such that the proportion of cloud fraction in each bin is the same as the climatology. This term represents the contribution of cloudamount anomalies to R^{′}. The second term on the right side results from multiplying an effective kernel that accounts for systematic variations in r_{e} by the change in cloud fraction at each r_{e} bin. This term represents the contribution of r_{e} anomalies to R^{′} with LWP and total liquidcloud fraction held fixed. The third term on the right side is similar to the second term except that it represents the contribution of LWP anomalies to R^{′} with r_{e} and total liquidcloud fraction held fixed. The final term on the right is the residual of the decomposition. The cloud amount, r_{e}, LWP, and residual components of R^{′} are denoted by ${R}_{\text{CF}}^{\prime}$, ${R}_{{r}_{\mathrm{e}}}^{\prime}$, ${R}_{\text{LWP}}^{\prime}$, and ${R}_{\text{res}}^{\prime}$, respectively. In the Supplement, we validate the R^{′} decomposition using syntheticdata test cases in which ${R}_{{r}_{\mathrm{e}}}^{\prime}$ and ${R}_{\text{LWP}}^{\prime}$ can be estimated theoretically with the twostream radiative transfer approximation (Fig. S3). We also verify that ${R}_{{r}_{\mathrm{e}}}^{\prime}$ and ${R}_{\text{LWP}}^{\prime}$ are similar when different common assumptions are made about cloud vertical structure, including a vertically uniform cloud model, an adiabatic cloud model, and the twolayer cloud model from the kernel calculation.
The final step of the decomposition is to adjust ${R}_{\text{CF}}^{\prime}$ to account for obscuration effects from nonliquid clouds. Because MODIS is a passive instrument, changes in nonliquid clouds can artificially change the retrieved liquidcloud fraction if they obscure liquid clouds from the satellite view. We control for these obscuration effects by replacing ${C}_{\text{tot}}^{\prime}$ in Eq. (B5) by $[{C}_{\text{tot}}/(\mathrm{100}\phantom{\rule{0.125em}{0ex}}\mathit{\%}{I}_{\text{tot}}\left){]}^{\prime}\right(\mathrm{100}\phantom{\rule{0.125em}{0ex}}\mathit{\%}{\stackrel{\mathrm{\u203e}}{I}}_{\text{tot}}$), where I_{tot} is the retrieved fraction of nonliquid clouds. This change of variables is adapted from the procedure recommended by Scott et al. (2020).
We also wish to compare the SW and longwave (LW) components of cloud radiative effects. However, our radiative kernel assumes a constant cloudtop pressure, so it cannot accurately assess the LW component (Appendix A). Instead, we analyze observations of the SW and LW radiative effects of liquidtopped clouds from the CERES FluxByCldTyp dataset. We perform cloudcontrolling factor analysis with the CERES data to attain estimates of ERF_{aci} in addition to those presented in the main paper. The CERESbased estimate of ERF_{aci} averaged over ocean between 55^{∘} S and 55^{∘} N is −1.52 ± 0.51 W m^{−2} for SW radiation and +0.21 ± 0.13 W m^{−2} for LW radiation. The LW component offsets 14 ± 7 % of the SW component (95 % CIs). These values determine β in the upperbound estimate of global net ERF_{aci} (Eq. 2).
Uncertainty in our oceanaverage ERF_{aci} estimates arises from uncertainty in the regression coefficients representing $\partial R/\partial \mathrm{ln}s$ and uncertainty in the model estimates of Δln s. We first quantify the component that is attributable to regressioncoefficient uncertainty. For a particular latitude–longitude grid box i, let ϵ_{i} represent the halfwidth of the 95 % confidence interval of the gridbox mean ERF_{aci}. We estimate ϵ_{i} as
where σ_{i} is the standard error of the regression coefficient, N_{nom,i} is the nominal number of temporal degrees of freedom (the number of months in the record), N_{eff,i} is the effective number of temporal degrees of freedom, square brackets indicate the central estimate of a parameter, and t_{i} is the critical value of Student's t distribution at the $(\mathrm{1}\mathit{\alpha}/\mathrm{2})\mathrm{100}\phantom{\rule{0.125em}{0ex}}\mathit{\%}$ significance level using ${N}_{\text{eff},i}\mathrm{8}$ degrees of freedom and α=0.05. The ratio ${N}_{\text{nom},i}/{N}_{\text{eff},i}$ is estimated as $(\mathrm{1}+a)/(\mathrm{1}a)$, where a is the temporal lag1 autocorrelation of ${R}_{i}^{\prime}$. The ϵ_{i} terms are then combined to account for spatial averaging over the domain. Uncertainty of the domainaverage forcing, δ_{obs}, is
where ${N}_{\text{nom}}^{\ast}$ is the nominal number of spatial degrees of freedom (the number of latitude–longitude grid boxes in the domain), ${N}_{\text{eff}}^{\ast}$ is the effective number of spatial degrees of freedom, and w_{i} is the ocean area in grid box i. The ratio ${N}_{\text{nom}}^{\ast}/{N}_{\text{eff}}^{\ast}$ is estimated by applying Eq. (5) of Bretherton et al. (1999) to the gridded R^{′} data. The resulting value of δ_{obs} represents the halfwidth of the 95 % confidence interval of ERF_{aci} that is attributable to regressioncoefficient uncertainty. Confidence intervals for the spatial averages of $\partial R/\partial \mathrm{ln}s$ and $\partial R/\partial \mathrm{ln}{\stackrel{\mathrm{\u0303}}{N}}_{\mathrm{d}}$ are calculated similarly.
The second source of uncertainty of ERF_{aci} arises from intermodel spread in the estimates of Δln s. Because we have estimates from 20 climate models, we construct a 95 % confidence interval for ERF_{aci} that excludes 1 model and encompasses the range of the other 19. We first calculate 20 estimates of ERF_{aci} by multiplying Δln s from each model by $[\partial R/\partial \mathrm{ln}s]$. The halfwidth of the confidence interval, δ_{ln s}, is estimated as the minimum of $\mathrm{}{c}_{\mathrm{1}}{c}_{\mathrm{19}}\mathrm{}/\mathrm{2}$ and $\mathrm{}{c}_{\mathrm{2}}{c}_{\mathrm{20}}\mathrm{}/\mathrm{2}$, where c_{1}, c_{2}, c_{19}, and c_{20} are the smallest, second smallest, second largest, and largest values of the 20 ERF_{aci} estimates, respectively. This uncertainty analysis accounts for intermodel differences in aerosol processing, but it does not account for uncertainty in anthropogenic sulfurdioxide emissions because the climate model simulations apply the same emission values. However, sulfurdioxide emissions depend primarily on the sulfur content of fuel rather than the conditions of combustion, so global emission inventories have a relatively small uncertainty of about ± 11 % (90 % CI from Smith et al., 2011). This is expected to cause an equivalent fractional uncertainty in the global burden of anthropogenic sulfate aerosol (Charlson et al., 1992; Stevens, 2015). In contrast, intermodel differences in aerosol processing lead to an uncertainty of ± 43 % in the change in s since 1850 averaged over ocean (90 % CI estimated by computing the interval that includes 18 of the 20 CMIP6 models). The quadrature sum of these two components determines their combined uncertainty, so uncertainty in aerosol processing dominates the overall uncertainty in globalmean Δln s. Approximating δ_{ln s} from intermodel differences is therefore justified. Finally, we note that ERF_{aci} strongly depends on the preindustrial aerosol state, so our estimates are approximately valid as long as the intermodel spread in preindustrial aerosol concentrations encompasses the true values (Carslaw et al., 2013; Kinne, 2019). The possibility that CMIP6 models have systematic biases that violate this condition cannot be ruled out at this time.
The estimated δ_{obs} and δ_{ln s} represent independent sources of uncertainty, so they are combined in quadrature. The overall 95 % confidence interval is given by ERF_{aci} ± $\sqrt{{\mathit{\delta}}_{\text{obs}}^{\mathrm{2}}+{\mathit{\delta}}_{\mathrm{ln}s}^{\mathrm{2}}}$. Confidence intervals for IRF_{aci}, A_{LWP}, A_{CF}, and the total cloud adjustment are calculated similarly.
Different filtering methods for partly cloudy pixels in the MODIS_{CLD} and MODIS_{CLD+PCL} cases lead to offsetting differences in the estimated LWP and cloudfraction adjustments (Fig. 3). One possible explanation for this discrepancy is that CCN anomalies cause changes in the morphology or horizontal size of liquid clouds, thereby changing the relative amounts of partly and fully cloudy pixels (Possner et al., 2018; Rosenfeld et al., 2006). Here we examine a case study to demonstrate this concept.
We analyze instantaneous pixel data from the MODIS MOD06_L2 dataset collection 6.1 (Platnick et al., 2015) obtained during a single overpass of the Terra satellite on 27 September 2019. On this day, MODIS measured stratocumulus clouds in the southeast Pacific Ocean with different forms of mesoscale cellular convection. The clouds in Box C in Fig. D1a mostly exhibit closed cells, and the clouds in Box O mostly exhibit open cells. We select data from these boxes and bin the liquidcloud pixels into histograms of cloud fraction partitioned by LWP. Let C_{l} represent cloud fraction in LWP bin l. In one case, C_{l} and C_{tot} are computed by counting only the fully cloudy pixels (CLD), and in a second case, C_{l} and C_{tot} are computed by counting both fully and partly cloudy pixels (CLD + PCL). Box C contains mostly fully cloudy pixels, so the two cases have similar values of C_{l} and C_{tot} (Fig. D1b). In contrast, Box O contains broken clouds that have a smaller horizontal scale, a larger perimetertoarea ratio, and a larger proportion of partly cloudy pixels. The partly cloudy pixels cover about 13 % of the area of Box O, and their retrieved LWP is usually smaller than that of the fully cloudy pixels in the box. This causes a difference in C_{tot} and the C_{l} distribution between the CLD and CLD + PCL cases (Fig. D1c). Filtering of partly cloudy pixels therefore affects the gridboxlevel statistics of cloud fraction and LWP in this example.
We next examine differences between the cloudfraction histograms of the two boxes to demonstrate the implications for estimating R^{′}. For the purpose of this demonstration, let the baseline cloud population be defined by the clouds in Box O, and let the cloudfraction anomalies be defined by the cloud fraction in Box C minus the cloud fraction in Box O. The baseline and anomalies are indicated by overbars and primes, respectively. ${C}_{l}^{\prime}$ can be decomposed according to
where ${C}_{l}^{\ast}\equiv {C}_{l}^{\prime}\frac{{\stackrel{\mathrm{\u203e}}{C}}_{l}}{{\stackrel{\mathrm{\u203e}}{C}}_{\text{tot}}}{C}_{\text{tot}}^{\prime}$. This decomposition is equivalent to Eq. (B2) except that it is performed on a onedimensional LWP histogram rather than a twodimensional LWP–r_{e} joint histogram. The first term on the right side of the equation determines ${R}_{\text{CF}}^{\prime}$, and the second term determines ${R}_{\text{LWP}}^{\prime}$. Compared with the CLD case, the CLD + PCL case has a smaller value of ${C}_{\text{tot}}^{\prime}$ (Fig. D1d), which reduces the magnitude of ${R}_{\text{CF}}^{\prime}$. Furthermore, because the partly cloudy pixels in Box O occupy the smallest LWP bins, including these pixels in the histogram causes a less extreme shift in the ${C}_{l}^{\prime}$ distribution towards small LWP values between Box O and Box C. This reduces the magnitude of ${R}_{\text{LWP}}^{\prime}$ in the CLD + PCL case relative to that of the CLD case. Thus, including partly cloudy pixels in the histograms leads to offsetting changes in ${R}_{\text{CF}}^{\prime}$ and ${R}_{\text{LWP}}^{\prime}$ that reduce the magnitude of both terms. Our estimates of global cloud adjustments depend on filtering of partly cloudy pixels in a similar way, suggesting that the adjustments may involve changes in cloud size or morphology as well.
MATLAB code used to analyze data can be obtained by contacting the corresponding author. The RRTMG radiative transfer model is publicly available at https://github.com/AERRC/RRTMG_SW (Atmospheric and Environmental Research, 2020).
All satellite data, reanalysis, and GCM output used in this study are publicly available. MODIS cloud histograms are available from the National Aeronautics and Space Administration (NASA) Level1 and Atmosphere Archive and Distribution System (https://doi.org/10.5067/MODIS/MCD06COSP_M3_MODIS.062, NASA, 2023b), MODIS N_{d} data are available from the Centre for Environmental Data Analysis (https://doi.org/10.5285/864a46cc65054008857ee5bb772a2a2b, Gryspeerdt et al., 2022b), CERES data are available from the CERES online ordering tool (https://cerestool.larc.nasa.gov/ordtool/jsp/EBAF42Selection.jsp, CERES, 2023a; https://cerestool.larc.nasa.gov/ordtool/jsp/FluxByCldTypSelection.jsp, CERES, 2023b), MERRA2 data are available from the NASA Goddard Earth Sciences Data and Information Services Center (https://doi.org/10.5067/LTVB4GPCOTK2, NASA, 2023a), and CMIP6 output is available from the CMIP6 online archive (https://esgfnode.llnl.gov/projects/cmip6/, WCRP, 2022). The SW cloud radiative kernel is available from GitHub (2023, https://github.com/caseywall7926/MODIS_ReLWP_kernel, Wall, 2023a; https://doi.org/10.5281/zenodo.8427293, Wall, 2023b). Estimates of the components of aerosol indirect effects and ERF_{aci} averaged over ocean are listed in Table S3.
The supplement related to this article is available online at: https://doi.org/10.5194/acp23131252023supplement.
CJW designed research, performed research, analyzed data, and wrote the original paper draft. TS and AP contributed ideas that shaped the study. All authors helped revise the original paper draft.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank Daniel McCoy, Ed Gryspeerdt, Robert Pincus, and Velle Toll for helpful discussions; Paul Hubanks, Robert Pincus, and Steven Platnick for supporting the design and implementation of the MODIS joint histograms; and Ying Chen and Jianhao Zhang for providing constructive reviews that improved the manuscript.
This project has received funding from the European Union’s Horizon 2020 Research and Innovation program under the Marie SkłodowskaCurie Action (grant agreement no. 101019911).
This paper was edited by Matthew Lebsock and reviewed by Ying Chen and Jianhao Zhang.
Albrecht, B. A.: Aerosols, cloud microphysics, and fractional cloudiness, Science, 245, 1227–1230, https://doi.org/10.1126/science.245.4923.1227, 1989.
Andersen, H., Cermak, J., Fuchs, J., Knutti, R., and Lohmann, U.: Understanding the drivers of marine liquidwater cloud occurrence and properties with global observations using neural networks, Atmos. Chem. Phys., 17, 9535–9546, https://doi.org/10.5194/acp1795352017, 2017.
Andreae, M. O. and Rosenfeld, D.: AerosolCloudPrecipitation Interactions Part 1: The Nature and Sources of CloudActive Aerosols, EarthSci. Rev., 89, 13–41, https://doi.org/10.1016/j.earscirev.2008.03.001, 2008.
Atmospheric and Environmental Research: RRTMGSW, GitHub [code], https://github.com/AERRC/RRTMG_SW (last access: 11 March 2021), 2020.
Bellouin, N., Quaas, J., Gryspeerdt, E., Kinne, S., Stier, P., WatsonParris, D., Boucher, O., Carslaw, K. S., Christensen, M., Daniau, A.L., Dufresne, J.L., Feingold, G., Fiedler, S., Forster, P., Gettelman, A., Haywood, J. M., Lohmann, U., Malavelle, F., Mauritsen, T., McCoy, D. T., Myhre, G., Mülmenstädt, J., Neubauer, D., Possner, A., Rugenstein, M., Sato, Y., Schulz, M., Schwartz, S. E., Sourdeval, O., Storelvmo, T., Toll, V., Winker, D., and Stevens, B.: Bounding Global Aerosol Radiative Forcing of Climate Change, Rev. Geophys., 58, e2019RG000660, https://doi.org/10.1029/2019rg000660, 2020.
Bender, F. A. M., Frey, L., McCoy, D. T., Grosvenor, D. P., and Mohrmann, J. K.: Assessment of aerosol–cloud–radiation correlations in satellite observations, climate models and reanalysis, Clim. Dynam., 52, 4371–4392, https://doi.org/10.1007/s003820184384z, 2019.
Bretherton, C. S., Widmann, M., Dymnikov, V. P., Wallace, J. M., and Bladé, I.: Effective Number of Degrees of Freedom of a Spatial Field, J. Climate, 12, 1990–2009 https://doi.org/10.1175/15200442(1999)012<1990:TENOSD>2.0.CO;2, 1999.
Bretherton, C. S., Blossey, P. N., and Uchida, J.: Cloud Droplet Sedimentation, Entrainment Efficiency, and Subtropical Stratocumulus Albedo, Geophys. Res. Lett., 34, 1–5, https://doi.org/10.1029/2006GL027648, 2007.
Carslaw, K. S., Lee, L. A., Reddington, C. L., Pringle, K. J., Rap, A., Forster, P. M., Mann, G. W., Spracklen, D. V., Woodhouse, M. T., Regayre, L. A., and Pierce, J. R.: Large contribution of natural aerosols to uncertainty in indirect forcing, Nature, 503, 67–71, https://doi.org/10.1038/nature12674, 2013.
Charlson, R. J., Schwartz, S. E., Hales, J. M., Cess, R. D., Coakley, J. A., Hansen, J. E., and Hofmann, D. J.: Climate Forcing by Anthropogenic Aerosols, Science, 255, 423–430, https://doi.org/10.1126/science.255.5043.423, 1992.
CERES: EBAF_Ed4.1, NASA [data set], https://cerestool.larc.nasa.gov/ordtool/jsp/EBAF42Selection.jsp (last access: 1 January 2023), 2023a.
CERES: FluxByCldTyp_Ed4.1, NASA [data set], https://cerestool.larc.nasa.gov/ordtool/jsp/FluxByCldTypSelection.jsp (last access: 1 January 2023), 2023b.
Chen, Y., Haywood, J., Wang, Y., Malavelle, F., Jordan, G., Partridge, D., Fieldsend, J., De Leeuw, J., Schmidt, A., Cho, N., Oreopoulos, L., Platnick, S., Grosvenor, D., Field, P., and Lohmann, U.: Machine Learning Reveals Climate Forcing from Aerosols is Dominated by Increased Cloud Cover, Nat. Geosci., 15, 609–614, https://doi.org/10.1038/s41561022009916, 2022.
Chen, Y. C., Christensen, M. W., Stephens, G. L., and Seinfeld, J. H.: SatelliteBased Estimate of Global AerosolCloud Radiative Forcing by Marine Warm Clouds, Nat. Geosci., 7, 643–646, https://doi.org/10.1038/ngeo2214, 2014.
Clough, S. A., Shephard, M. W., Mlawer, E. J., Delamere, J. S., Iacono, M. J., CadyPereira, K., Boukabara, S., and Brown, P. D.: Atmospheric Radiative Transfer Modeling: A Summary of the AER Codes, J. Quant. Spectrosc. Ra., 91, 233–244, https://doi.org/10.1016/j.jqsrt.2004.05.058, 2005.
Dagan, G., Koren, I., Altaratz, O., and Heiblum, R. H.: Timedependent, nonmonotonic response of warm convective cloud fields to changes in aerosol loading, Atmos. Chem. Phys., 17, 7435–7444, https://doi.org/10.5194/acp1774352017, 2017.
Diamond, M. S., Director, H. M., Eastman, R., Possner, A., and Wood, R.: Substantial Cloud Brightening From Shipping in Subtropical Low Clouds, AGU Adv., 1, 1–28, https://doi.org/10.1029/2019av000111, 2020.
Feingold, G., Goren, T., and Yamaguchi, T.: Quantifying albedo susceptibility biases in shallow clouds, Atmos. Chem. Phys., 22, 3303–3319, https://doi.org/10.5194/acp2233032022, 2022.
Forster, P., Storelvmo, T., Armour, K., Collins, W., Dufresne, J.L., Frame, D., Lunt, D. J., Mauritsen, T., Palmer, M. D., Watanabe, M., Wild, M., and Zhang, H.: The Earth's Energy Budget, Climate Feedbacks, and Climate Sensitivity, in: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: MassonDelmotte, V., Zhai, P., Pirani, A., Connors, S. L., Péan, C., Berger, S., Caud, N., Chen, Y., Goldfarb, L., Gomis, M. I., Huang, M., Leitzell, K., Lonnoy, E., Matthews, J. B. R., Maycock, T. K., Waterfield, T., Yelekçi, O., Yu, R., and Zhou, B., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, https://doi.org/10.1017/9781009157896.009, pp. 923–1054, 2021.
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L. Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G. K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., and Zhao, B.: The ModernEra Retrospective Analysis for Research and Applications, version 2 (MERRA2), J. Climate, 30, 5419–5454, https://doi.org/10.1175/JCLID160758.1, 2017.
Ghan, S., Wang, M., Zhang, S., Ferrachat, S., Gettelman, A., Griesfeller, J., Kipling, Z., Lohmann, U., Morrison, H., Neubauer, D., Partridge, D. G., Stier, P., Takemura, T., Wang, H., and Zhang, K.: Challenges in Constraining Anthropogenic Aerosol Effects on Cloud Radiative Forcing using PresentDay Spatiotemporal Variability, P. Natl. Acad. Sci. USA, 113, 5804–5811, https://doi.org/10.1073/pnas.1514036113, 2016.
Glassmeier, F., Hoffmann, F., Johnson, J. S., Yamaguchi, T., Carslaw, K. S., and Feingold, G.: AerosolCloudClimate Cooling Overestimated by ShipTrack Data, Science, 371, 485–489, https://doi.org/10.1126/science.abd3980, 2021.
Goren, T., Feingold, G., Gryspeerdt, E., Kazil, J., Kretzschmar, J., Jia, H., and Quaas, J.: Projecting Stratocumulus Transitions on the Albedo – Cloud Fraction Relationship Reveals Linearity of Albedo to Droplet Concentrations, Geophys. Res. Lett., 49, e2022GL101169, https://doi.org/10.1029/2022GL101169, 2022.
Goren, T., Sourdeval, O., Kretzschmar, J., and Quaas, J.: Spatial Aggregation of Satellite Observations Leads to an Overestimation of the Radiative Forcing Due To AerosolCloud Interactions, Geophy. Res. Lett., 50, e2023GL105282, https://doi.org/10.1029/2023GL105282, 2023.
Grosvenor, D. P., Sourdeval, O., Zuidema, P., Ackerman, A., Alexandrov, M. D., Bennartz, R., Boers, R., Cairns, B., Chiu, J. C., Christensen, M., Deneke, H., Diamond, M., Feingold, G., Fridlind, A., Hünerbein, A., Knist, C., Kollias, P., Marshak, A., McCoy, D. T, Merk, D., Painemal, D., Rausch, J., Rosenfeld, D., Russchenberg, H., Seifert, P., Sinclair, K., Stier, P., van Diedenhoven, B., Wendisch, M., Werner, F., Wood, R., Zhang, Z., and Quaas, J.: Remote Sensing of Droplet Number Concentration in Warm Clouds: A Review of the Current State of Knowledge and Perspectives, Rev. Geophys., 56, 409–453, https://doi.org/10.1029/2017RG000593, 2018.
Gryspeerdt, E., Quaas, J., and Bellouin, N.: Constraining the Aerosol Influence on Cloud Fraction, J. Geophys. Res.Atmos., 121, 3566–3583, https://doi.org/10.1002/2015JD023744, 2016.
Gryspeerdt, E., Goren, T., Sourdeval, O., Quaas, J., Mülmenstädt, J., Dipu, S., Unglaub, C., Gettelman, A., and Christensen, M.: Constraining the aerosol influence on cloud liquid water path, Atmos. Chem. Phys., 19, 5331–5347, https://doi.org/10.5194/acp1953312019, 2019.
Gryspeerdt, E., Mülmenstädt, J., Gettelman, A., Malavelle, F. F., Morrison, H., Neubauer, D., Partridge, D. G., Stier, P., Takemura, T., Wang, H., Wang, M., and Zhang, K.: Surprising similarities in model and observational aerosol radiative forcing estimates, Atmos. Chem. Phys., 20, 613–623, https://doi.org/10.5194/acp206132020, 2020.
Gryspeerdt, E., McCoy, D. T., Crosbie, E., Moore, R. H., Nott, G. J., Painemal, D., SmallGriswold, J., Sorooshian, A., and Ziemba, L.: The impact of sampling strategy on the cloud droplet number concentration estimated from satellite data, Atmos. Meas. Tech., 15, 3875–3892, https://doi.org/10.5194/amt1538752022, 2022a.
Gryspeerdt, E., McCoy, D., Crosbie, E., Moore, R. H., Nott, G. J., Painemal, D., SmallGriswold, J., Sorooshian, A., and Ziemba, L.: Cloud droplet number concentration, calculated from the MODIS cloud optical properties retrieval and gridded using different sampling strategies, NERC EDS Centre for Environmental Data Analysis [data set], https://doi.org/10.5285/864a46cc65054008857ee5bb772a2a2b, 2022b.
IPCC: Annex III: Tables of historical and projected wellmixed greenhouse gas mixing ratios and effective radiative forcing of all climate forcers, edited by: Dentener F. J., Hall, B., and Smith, C., in: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, MassonDelmotte, V., Zhai, P., Pirani, A., Connors, S. L., Péan, C., Berger, S., Caud, N., Chen, Y., Goldfarb, L., Gomis, M. I., Huang, M., Leitzell, K., Lonnoy, E., Matthews, J. B. R., Maycock, T. K., Waterfield, T., Yelekçi, O., Yu, R., and Zhou , B., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, https://doi.org/10.1017/9781009157896.017, pp. 2139–2152, 2021.
Jia, H., Ma, X., Yu, F., and Quaas, J.: Significant Underestimation of Radiative Forcing by Aerosol–Cloud Interactions Derived from SatelliteBased Methods, Nat. Commun., 12, 1–11, https://doi.org/10.1038/s41467021238881, 2021.
Kang, L., Marchand, R. T., Wood, R., and McCoy, I. L.: Coalescence Scavenging Drives Droplet Number Concentration in Southern Ocean Low Clouds, Geophys. Res. Lett., 49, 1–10, https://doi.org/10.1029/2022GL097819, 2022.
Kinne, S.: Aerosol radiative effects with MACv2, Atmos. Chem. Phys., 19, 10919–10959, https://doi.org/10.5194/acp19109192019, 2019.
Kramer, R. J., He, H., Soden, B. J., Oreopoulos, L., Myhre, G., Forster, P. M., and Smith, C. J.: Observational Evidence of Increasing Global Radiative Forcing, Geophys. Res. Lett., 48, 1–11, https://doi.org/10.1029/2020GL091585, 2021.
Lewis, H., Bellon, G., and Dinh, T.: Upstream LargeScale Control of Subtropical LowCloud Climatology, J. Climate, 36, 3289–3303, https://doi.org/10.1175/JCLID220676.1, 2023.
Loeb, N. G., Doelling, D. R., Wang, H., Su, W., Nguyen, C., Corbett, J. G., Liang, L., Mitrescu, C., Rose, F. G., and Kato, S.: Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) TopofAtmosphere (TOA) Edition4.0 Data Product, J. Climate, 31, 895–918, https://doi.org/10.1175/JCLID170208.1, 2018.
Ma, P., Rasch, P. J., Chepfer, H., Winker, D. M., and Ghan, S. J.: Observational Constraint on Cloud Susceptibility Weakened by Aerosol Retrieval Limitations, Nat. Commun., 9, 1–10, https://doi.org/10.1038/s41467018050284, 2018.
Manshausen, P., WatsonParris, D., Christensen, M. W., Jalkanen, J. P., and Stier, P.: Invisible ship tracks show large cloud sensitivity to aerosol, Nature, 610, 101–106, https://doi.org/10.1038/s41586022051220, 2022.
Matthews, H. D. and Zickfeld, K.: Climate Response to Zeroed Emissions of Greenhouse Gases and Aerosols, Nat. Clim. Change, 2, 338–341, https://doi.org/10.1038/nclimate1424, 2012.
Mauger, G. S. and Norris, J. R.: Meteorological Bias in Satellite Estimates of AerosolCloud Relationships, Geophys. Res. Lett., 34, 1–5, https://doi.org/10.1029/2007GL029952, 2007.
Mauritsen, T. and Pincus, R.: Committed Warming Inferred from Observations, Nat. Clim. Change, 7, 652–655, https://doi.org/10.1038/nclimate3357, 2017.
McCoy, D. T., Bender, F. A. M., Mohrmann, J. K. C., Hartmann, D. L., Wood, R., and Grosvenor, D. P.: The global aerosolcloud first indirect effect estimated using MODIS, MERRA, and AeroCom. J. Geophys. Res. Atmos., 122, 1779–1796, https://doi.org/10.1002/2016JD026141, 2017.
McCoy, D. T., Field, P. R., Schmidt, A., Grosvenor, D. P., Bender, F. A.M., Shipway, B. J., Hill, A. A., Wilkinson, J. M., and Elsaesser, G. S.: Aerosol midlatitude cyclone indirect effects in observations and highresolution simulations, Atmos. Chem. Phys., 18, 5821–5846, https://doi.org/10.5194/acp1858212018, 2018.
Myers, T. A., Scott, R. C., Zelinka, M. D., Klein, S. A., Norris, J. R., and Caldwell, P. M.: Observational Constraints on Low Cloud Feedback Reduce Uncertainty of Climate Sensitivity, Nat. Clim. Change, 11, 501–507, https://doi.org/10.1038/s41558021010390, 2021.
NASA: MERRA2, Goddard Earth Sciences Data and Information Services Center [data set], https://doi.org/10.5067/LTVB4GPCOTK2, 2023a.
NASA: MCD06COSP_M3_MODIS – MODIS (Aqua/Terra) Cloud Properties Level 3 monthly, 1x1 degree grid, Distributed Active Archive Center [data set], https://doi.org/10.5067/MODIS/MCD06COSP_M3_MODIS.062, 2023b.
Naud, C. M., Posselt, D. J., and van den Heever, S. C.: Observed Covariations of Aerosol Optical Depth and Cloud Cover in Extratropical Cyclones, J. Geophys. Res.Atmos., 122, 10338–10356, https://doi.org/10.1002/2017JD027240, 2017.
Painemal, D., Chiu, J.Y. C., Minnis, P., Yost, C., Zhou, X., Cadeddu, M., Eloranta, E., Lewis, E. R., Ferrare, R., and Kollias, P.: Aerosol and Cloud Microphysics Covariability in the Northeast Pacific Boundary Layer Estimated with ShipBased and Satellite Remote Sensing Observations, J. Geophys. Res.Atmos., 122, 2403–2418, https://doi.org/10.1002/2016JD025771, 2017.
Painemal, D. and Zuidema, P.: Assessment of MODIS Cloud Effective Radius and Optical Thickness Retrievals over the Southeast Pacific with VOCALSREx In Situ Measurements, J. Geophys. Res.Atmos., 116, 1–16, https://doi.org/10.1029/2011JD016155, 2011.
Pincus, R. and Baker, M. B.: Effect of Precipitation on the Albedo Susceptibility of Clouds in the Marine Boundary Layer, Nature, 372, 250–252, https://doi.org/10.1038/372250a0, 1994.
Pincus, R., Hubanks, P. A., Platnick, S., Meyer, K., Holz, R. E., Botambekov, D., and Wall, C. J.: Updated observations of clouds by MODIS for global model assessment, Earth Syst. Sci. Data, 15, 2483–2497, https://doi.org/10.5194/essd1524832023, 2023.
Platnick, S.: Vertical Photon Transport in Cloud Remote Sensing Problems, J. Geophys. Res.Atmos., 105, 22919–22935, https://doi.org/10.1029/2000JD900333, 2000.
Platnick, S., Ackerman, S., and King, M.: MODIS Atmosphere L2 Cloud Product (06_L2). NASA MODIS Adaptive Processing System, Goddard Space Flight Center, USA, https://doi.org/10.5067/MODIS/MOD06_L2.061, 2015.
Platnick, S., Meyer, K. G., King, M. D., Wind, G., Amarasinghe, N., Marchant, B., Arnold, G. T., Zhang, Z., Hubanks, P. A., Holz, R. E., Yang, P., Ridgway, W. L., and Reidi, J.: The MODIS Cloud Optical and Microphysical Products: Collection 6 Updates and Examples from Terra and Aqua, IEEE T. Geosci. Remote, 3, 163–186, https://doi.org/10.1109/TGRS.2016.2610522, 2017.
Possner, A., Wang, H., Wood, R., Caldeira, K., and Ackerman, T. P.: The efficacy of aerosol–cloud radiative perturbations from nearsurface emissions in deep opencell stratocumuli, Atmos. Chem. Phys., 18, 17475–17488, https://doi.org/10.5194/acp18174752018, 2018.
Possner, A., Eastman, R., Bender, F., and Glassmeier, F.: Deconvolution of boundary layer depth and aerosol constraints on cloud water path in subtropical stratocumulus decks, Atmos. Chem. Phys., 20, 3609–3621, https://doi.org/10.5194/acp2036092020, 2020.
Raghuraman, S. P., Paynter, D., and Ramaswamy, V.: Anthropogenic forcing and response yield observed positive trend in Earth's energy imbalance, Nat. Commun., 12, 1–10, https://doi.org/10.1038/s41467021245444, 2021.
Randles, C. A., da Silva, A. M., Buchard, V., Colarco, P. R., Darmenov, A., Govindaraju, R., Smirnov, A., Holben, B., Ferrare, R., Hair, J., Shinozuka, Y., and Flynn, C. J.: The MERRA2 Aerosol Reanalysis, 1980 Onward. Part I: System Description and Data Assimilation Evaluation, J. Climate, 30, 6823–6850, https://doi.org/10.1175/JCLID160609.1, 2017.
Rosenfeld, D., Kaufman, Y. J., and Koren, I.: Switching cloud cover and dynamical regimes from open to closed Benard cells in response to the suppression of precipitation by aerosols, Atmos. Chem. Phys., 6, 2503–2511, https://doi.org/10.5194/acp625032006, 2006.
Rosenfeld, D., Andreae, M. O., Asmi, A., Chin, M., Leeuw, G., Donovan, D. P., Kahn, R., Kinne, S., Kivekäs, N., Kulmala, M., Lau, W., Schmidt, S. K., Suni, T., Wagner, T., Wild, M., and Quaas, J.: Global Observations of AerosolCloudPrecipitationClimate Interactions. Rev. Geophys., 52, 750–808, https://doi.org/10.1002/2013RG000441, 2014.
Rosenfeld, D., Zhu, Y., Wang, M., Zheng, Y., Goren, T., and Yu, S.: AerosolDriven Droplet Concentrations Dominate Coverage and Water of Oceanic LowLevel Clouds, Science, 363, eaav0566, https://doi.org/10.1126/science.aav0566, 2019.
Scott, R. C., Myers, T. A., Norris, J. R., Zelinka, M. D., Klein, S. A., Sun, M., and Doelling, D. R.: Observed Sensitivity of LowCloud Radiative Effects to Meteorological Perturbations over the Global Oceans, J. Climate, 33, 7717–7734, https://doi.org/10.1175/JCLID191028.1, 2020.
Seifert, A., Heus, T., Pincus, R., and Stevens, B.: LargeEddy Simulation of the Transient and NearEquilibrium Behavior of Precipitating Shallow Convection, J. Adv. Model. Earth Sy., 6, 513–526, https://doi.org/10.1002/2015MS000470, 2015.
Sherwood, S. C., Webb, M. J., Annan, J. D., Armour, K. C., Forster, P. M., Hargreaves, J. C., Hegerl, G., Klein, S. A., Marvel, K. D., Rohling, E. J., Watanabe, M., Andrews, T., Braconnot, P., Bretherton, C. S., Foster, G. L., Hausfather, Z., von der Heydt, A. S., Knutti, R., Mauritsen, T., Norris, J. R., Proistosescu, C., Rugenstein, M., Schmidt, G. A., Tokarska, K. B., and Zelinka, M. D.: An Assessment of Earth's Climate Sensitivity Using Multiple Lines of Evidence. Rev. Geophys., 58, 1–92, https://doi.org/10.1029/2019RG000678, 2020.
Small, J. D., Chuang, P. Y., Feingold, G., and Jiang, H.: Can Aerosol Decrease Cloud Lifetime? Geophys. Res. Lett., 36, 1–5, https://doi.org/10.1029/2009GL038888, 2009.
Smith, C. J., Harris, G. R., Palmer, M. D., Bellouin, N., Collins, W., Myhre, G., Schulz, M., Golaz, J. C., Ringer, M., Storelvmo, T., and Forster, P. M.: Energy Budget Constraints on the Time History of Aerosol Forcing and Climate Sensitivity, J. Geophys. Res.Atmos., 126, 1–20, https://doi.org/10.1029/2020JD033622, 2021.
Smith, S. J., van Aardenne, J., Klimont, Z., Andres, R. J., Volke, A., and Delgado Arias, S.: Anthropogenic sulfur dioxide emissions: 1850–2005, Atmos. Chem. Phys., 11, 1101–1116, https://doi.org/10.5194/acp1111012011, 2011.
Stevens, B.: Rethinking the Lower Bound on Aerosol Radiative Forcing, J. Climate, 28, 4794–4819, https://doi.org/10.1175/JCLID1400656.1, 2015.
Sun, M., Doelling, D. R., Loeb, N. G., Scott, R. C., Wilkins, J., Nguyen, L. T., and Mlynczak, P.: Clouds and the Earth's Radiant Energy System (CERES) FluxByCldTyp Edition 4 Data Product, J. Atmos. Ocean. Tech., 39, 303–318, https://doi.org/10.1175/jtechd210029.1, 2022.
Toll, V., Christensen, M., Quaas, J., and Bellouin, N.: Weak average liquidcloudwater response to anthropogenic aerosols, Nature, 572, 51–55, https://doi.org/10.1038/s4158601914239, 2019.
Twomey, S.: Influence of Pollution on Shortwave Albedo of Clouds, J. Atmos. Sci., 34, 1149–1152, https://doi.org/10.1175/15200469(1977)034<1149:TIOPOT>2.0.CO;2, 1977.
Wall, C. J.: MODIS ReLWP cloud radiative kernel, GitHub [data set], https://github.com/caseywall7926/MODIS_ReLWP_kernel (last access: 10 October 2023), 2023a.
Wall, C. J.: caseywall7926/MODIS_ReLWP_kernel: MODIS ReLWP cloud radiative kernel (v1.0), Zenodo, https://doi.org/10.5281/zenodo.8427293, 2023b.
Wall, C. J., Norris, J. R., Possner, A., McCoy, D. T., McCoy, I. L., and Lutsko, N. J.: Assessing Effective Radiative Forcing from Aerosol–Cloud Interactions over the Global Ocean, P. Natl. Acad. Sci. USA, 119, https://doi.org/10.1073/pnas.2210481119, 2022.
WatsonParris, D. and Smith, C. J.: Large uncertainty in future warming due to aerosol forcing, Nat. Clim. Change, 12, 1111–1113, https://doi.org/10.1038/s41558022015160, 2022.
WCRP: CMIP6 historical simulations, CMIP6 online archive [data set], https://esgfnode.llnl.gov/projects/cmip6/ (last access: 1 May 2022), 2022.
Wilks, D. S.: “The Stippling Shows Statistically Significant Grid Points.” How Research Results are Routinely Overstated and Overinterpreted, and What to Do about It, B. Am. Meteorol. Soc., 97, 2263–2274, https://doi.org/10.1175/BAMSD1500267.1, 2016.
Wood, R. and Bretherton, C. S.: On the Relationship Between Stratiform Low Cloud Cover and LowerTropospheric Stability, J. Climate, 19, 6425–6432, https://doi.org/10.1175/JCLI3988.1, 2006.
Wood, R., Leon, D., Lebsock, M., Snider, J., and Clarke, A. D.: Precipitation Driving of Droplet Concentration Variability in Marine Low Clouds, J. Geophys. Res.Atmos., 117, 1–11, https://doi.org/10.1029/2012JD018305, 2012.
Zelinka, M. D., Klein, S. A., and Hartmann, D. L.: Computing and Partitioning Cloud Feedbacks Using Cloud Property Histograms. Part I: Cloud Radiative Kernels, J. Climate, 25, 3715–3735, https://doi.org/10.1175/JCLID1100248.1, 2012.
Zelinka, M. D., Klein, S. A., Taylor, K. E., Andrews, T., Webb, M. J., Gregory, J. M., and Forster, P. M.: Contributions of Different Cloud Types to Feedbacks and Rapid Adjustments in CMIP5, J. Climate, 26, 5007–5027, https://doi.org/10.1175/JCLID1200555.1, 2013.
Zelinka, M. D., Andrews, T., Forster, P. M., and Taylor, K. E.: Quantifying Components of AerosolCloudRadiation Interactions in Climate Models, J. Geophys. Res.Atmos., 119, 7599–7615, https://doi.org/10.1002/2014JD021710, 2014.
Zhang, J. and Feingold, G.: Distinct regional meteorological influences on lowcloud albedo susceptibility over global marine stratocumulus regions, Atmos. Chem. Phys., 23, 1073–1090, https://doi.org/10.5194/acp2310732023, 2023.
Zhang, J., Zhou, X., Goren, T., and Feingold, G.: Albedo susceptibility of northeastern Pacific stratocumulus: the role of covarying meteorological conditions, Atmos. Chem. Phys., 22, 861–880, https://doi.org/10.5194/acp228612022, 2022.
Zhang, Z. and Platnick, S.: An Assessment of Differences Between Cloud Effective Particle Radius Retrievals for Marine Water Clouds from three MODIS Spectral Bands, J. Geophys. Res.Atmos., 116, 1–19, https://doi.org/10.1029/2011JD016216, 2011.
Zhou, X., Zhang, J., and Feingold, G.: On the Importance of Sea Surface Temperature for AerosolInduced Brightening of Marine Clouds and Implications for Cloud Feedback in a Future Warmer Climate, Geophys. Res. Lett., 48, https://doi.org/10.1029/2021GL095896, 2021.
Zhu, Y., Rosenfeld, D., and Li, Z.: Under What Conditions Can We Trust Retrieved Cloud Drop Concentrations in Broken Marine Stratocumulus? J. Geophys. Res. Atmos., 123, 8754–8767, https://doi.org/10.1029/2017JD028083, 2018.
 Abstract
 Introduction
 Data and methods
 Global analysis of aerosol indirect effects
 Implications for historical aerosol forcing
 Conclusion
 Appendix A: Cloud radiative kernel
 Appendix B: Decomposing cloud radiative effects
 Appendix C: Uncertainty
 Appendix D: Filtering of partly cloudy pixels
 Code availability
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References
 Supplement
 Abstract
 Introduction
 Data and methods
 Global analysis of aerosol indirect effects
 Implications for historical aerosol forcing
 Conclusion
 Appendix A: Cloud radiative kernel
 Appendix B: Decomposing cloud radiative effects
 Appendix C: Uncertainty
 Appendix D: Filtering of partly cloudy pixels
 Code availability
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References
 Supplement