## Introduction

Unlike other climate change drivers, the temperature and cloud response—and in some cases, the precipitation response1—to absorbing aerosol is dominated by rapid adjustments.2 Recent modeling studies suggest that these adjustments, which include the aerosol–cloud semi-direct effect (SDE), lead to a negative radiative perturbation, thereby offsetting some of the positive direct forcing of absorbing aerosol, resulting in a relatively weak surface temperature response.2,3,4 Climate models from the Precipitation Driver Response Model Intercomparison Project (PDRMIP) show that a tenfold increase in BC leads to a robust increase in globally averaged low-level cloud, but a reduction in mid-level and in particular, high-level cloud.2 These responses are consistent with the simulated vertical co-location of absorbing aerosol and cloud, including relative humidity reductions and cloud burn-off when BC and cloud are co-located,5,6 but also enhanced low-level cloud due to increases in stability when BC is located above the cloud.7,8,9,10,11 Qualitatively similar cloud responses are obtained in several other recent studies.12,13,14 Consistent with these cloud changes, and in particular the large high-cloud reduction and enhanced longwave cooling, the annual global mean rapid adjustment in these simulations ranges from −0.39 to −1.44 W m−2 for a tenfold increase in BC;2,12 −2.8 W m−2 for 25 × BC;14 and −0.25 W m−2 for present-day BC emissions.13 Thus, model simulations indicate that rapid adjustments—primarily due to cloud responses—offset up to 60% of the direct radiative forcing associated with BC.2

The climate impact of absorbing aerosols, however, is associated with significant uncertainty.15,16 This is related to several factors, including underestimation of BC emission inventories and absorption aerosol optical depth, which implies too little aerosol solar absorption in the atmosphere and therefore, underestimation of BC direct radiative forcing.15,17,18,19,20,21 The vertical profile of absorbing aerosol is also important, as it impacts the direct radiative forcing, as well as the rapid adjustments and precipitation response.9,15,18,22,23,24,25 In the context of the aerosol–cloud SDE, different cloud responses are obtained depending on the vertical co-location of absorbing aerosol and cloud.9,15,26

Large inter-model diversity exists in simulated BC vertical profiles, with models likely overestimating the amount of BC aloft.15,18,27,28 This could be related to a variety of factors, including vertical resolution,29 convective processes,28,30 scavenging,31 or aging.32 Thus, given these uncertainties in aerosol simulations—particularly related to the vertical profile of absorbing aerosol—the corresponding aerosol–cloud SDE may not be properly constrained by the aforementioned studies.

Aerosol observations, including the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP)33 allow the the aerosol vertical profile to be constrained. Here, we estimate the aerosol–cloud SDE using three different climate models (Methods), including the Community Atmosphere Model version 4 (CAM4)34 and CAM5,35 as well as the Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model version 2.1 (AM2.1),36 forced with monthly observationally constrained fine-mode aerosols without dust and sea salt37 (Methods; STANDARD simulations). Unlike the anthropogenic fraction, the fine-mode fraction of aerosol amount—which is largely anthropogenic—can be constrained by observations. We also conduct analogous observationally constrained aerosol simulations, but with [a.] vertically uniform aerosol atmospheric heating (VERTUNIF simulations) and [b.] half the forcing (i.e., monthly surface reduction in solar radiation and atmospheric solar heating reduced by 50%; HALF simulations). These simulations are compared with PDRMIP 10xBC aerosol simulations (Methods). We do not attempt to quantify interannnual variability, instead focusing on the climatological mean signal. However, there is a considerable year-to-year variability in biomass burning, which implies similarly large internannual variability in the aerosol–cloud semi-direct effect.

## Results

### Observationally constrained fine-mode aerosols

Figure 1 shows the annual mean atmospheric solar absoprtion (FATM) and reduction in surface solar radiation (FSFC) for observationally constrained fine-mode aerosols, without dust and sea salt. The maximum atmospheric heating occurs over central Africa (due to biomass burning), India (due to biofuel burning and fossil fuel combustion), and China (due to fossil fuel combustion). The sunlight absorption by aerosols comes largely from BC, but brown carbon (or organic aerosols) also contributes to the absorption. Figure 1 also shows the vertical profile of the atmospheric solar heating rate response in CAM4 STANDARD (other models are similar). Most of the heating occurs near the surface, peaking at ~925 hPa, and then rapidly decaying to zero near ~500 hPa. Although aerosol simulations generally reproduce a similar spatial distribution of FSFC and FATM, their vertical aerosol heating profile is more uniform, with relatively large heating that extends through the upper troposphere.2 Based on PDRMIP 10xBC simulations, the atmospheric solar heating response remains relatively large up to 100 hPa, with most models exhibiting a secondary peak near 200 hPa (Fig. 1c). The percent of average shortwave heating above 500 hPa, relative to the column average, ranges from 70% in CAM5-PDRMIP to 110% in HadGEM2, with a multi-model PDRMIP mean of 86%. This is considerably larger than that based on the observationally constrained heating profile, at 2% (by design, VERTUNIF yields 100%). Moreover, the lower-tropospheric heating maximum is elevated relative to observationally constrained fine-mode aerosols (~850 vs. 925 hPa). These large differences in simulated versus observed vertical aerosol heating profile imply corresponding differences in the aerosol–cloud SDE (i.e., cloud adjustment).

### Cloud responses

Figure 2a shows global annual mean vertical profiles of the cloud response to observationally constrained fine-mode aerosol forcing without dust and sea salt (STANDARD). Weak increases occur near the surface (especially in CAM4), which then give way to much larger decreases that span the entire troposphere, extending from ~950 to 250 hPa. Consistently, all models show global annual mean cloud reductions for low-, mid-, and high-level clouds (Methods), with the largest decreases in low- and mid-level clouds (Table 1). The annual mean low cloud response varies between −0.43% in GFDL to −0.14% in CAM4. The annual mean mid-level (high) cloud response varies from −0.26% in CAM4 to −0.21% in GFDL (−0.04% in GFDL to −0.12 % in CAM5). Figure 2b shows that these cloud responses are consistent with the corresponding change in relative humidity (RH). All three models show weak increases in RH near the surface, which then transitions into larger decreases in RH throughout most of the troposphere.

Across the three models, similar spatial cloud responses exist in several regions. Figure 3 shows low clouds generally increases over areas with large atmospheric heating, including Africa and parts of southeast Asia (Supplementary Fig. 1 shows model agreement). Low-cloud reductions occur over Indonesia, the Indian Ocean, and parts of the Northern Hemisphere mid- and high latitudes. Generally, similar signed cloud responses occur over both land and ocean, except for high-level cloud, which increases over land, but decreases over ocean in all models. The bulk of this high cloud increase occurs over central Africa, and is associated with an increase in vertical motion and convective mass flux, particularly in the upper troposphere (Supplementary Fig. 2). Although convective mass flux is generally reduced in response to the stabilizing effects of aerosol atmospheric heating—particularly in the lower troposphere—the large amount of atmospheric heating over Africa (Fig. 1) acts to destabilize the mid- and upper troposphere, resulting in rising air and an increase in high cloud. To a lesser extent, this is also the case over parts of southeast Asia.

### Mechanisms for cloud changes

All three models yield an increase in lower-tropospheric stability (S), primarily due to warming at 700 hPa (Supplementary Table 1; Supplementary Fig. 2). This increase in stability traps moisture near the surface, leading to a corresponding increase in near-surface RH and cloud, including significant increases in cloud and relative humidity at the model’s bottom level. CAM4 yields the largest increase in cloud at the model’s bottom level (Table 1), which is consistent with its S-based marine stratocumulus parameterization (Methods). However, above the near-surface, decreases in lower-tropospheric RH are consistent with an overall decrease in low cloud. For example, RH925–700 decreases between −0.19 to −0.37% in GFDL and CAM4, respectively (Supplementary Table 1). Similarly, decreases in mid- and upper-tropospheric RH are consistent with decreases in mid and high cloud. RH600–500 decreases between −0.09 to −0.25% in GFDL and CAM4; RH300–250 decreases between −0.01 and −0.22% in GFDL and CAM5, respectively. A more detailed regression analysis (Supplementary Discussion; Supplementary Table 2) shows that RH is generally the best predictor, with S (vertical motion) also important for the low cloud (mid and high cloud) response (Supplementary Fig. 3). Thus, observationally constrained aerosol forcing yields overall cloud reductions, most of which is driven by decreases in RH and subsequent cloud burnoff.

The vertical profile of simulated climatological clouds differs in our models (Supplementary Fig. 4). For example, CAM5 shows the largest amount of cloud throughout the atmospheric column; GFDL shows the least amount of low-level cloud; and CAM4 shows the least amount of mid-level cloud. However, there does not seem to be a clear connection between the cloud response, and the amount of climatological cloud, implying parameterization differences (Methods) likely drive the bulk of any contrasting cloud responses in these models.

### Semi-direct cloud responses and rapid adjustments

Figure 4a–c shows the aerosol–cloud SDE (Methods) for all three STANDARD simulations. All models yield a positive global annual mean SDE. The largest SDE occurs in GFDL at 0.52 W m−2, followed by CAM5 and CAM4 at 0.30 and 0.29 W m−2, respectively (Table 1). Similar (but smaller in magnitude) results exist for HALF (simulations with 50% less aerosol forcing). For example, GFDL yields an SDE of 0.30 W m−2, followed by CAM5 and CAM4 at 0.17 and 0.14 W m−2, respectively (Table 1). Thus, HALF simulations generally yield an SDE about 50% as large as in STANDARD. Several regions of SDE model agreement exist, including the Indian Ocean, most of south America, and parts of the NH mid-latitudes (Fig. 5a). Moreover, the SDE is dominated by shortwave effects, which drive the positive SDE; longwave effects act to mute the positive SDE. These changes are consistent with the corresponding changes in clouds. Low clouds tend to have a net cooling effect on the planet, due to high albedo; high clouds tend to have a net warming effect, due to their greenhouse effect. Mid-level clouds are a combination of both, but we find they tend to affect the SDE similarly to low-level clouds. Thus, the decrease in low- and mid-level cloud drives the positive SDE (in the shortwave), and the decrease in high-level clouds weakens this through enhanced longwave cooling. We also note that the rapid adjustments are positive in all models (Table 1), and dominated by the aerosol–cloud SDE. Although non-cloud adjustments (e.g., changes in temperature and moisture) also contribute to the rapid adjustments, this contribution is smaller (−0.09 to 0.03 W m−2 in STANDARD) than that due to cloud adjustments.

In contrast, several recent studies have shown the rapid adjustments (RAPADJ) to absorbing aerosol are negative.2,4 PDRMIP 10xBC aerosol simulations yield a multi-model mean rapid adjustment of −0.94 W m−2, ranging from −0.55 to −1.48 W m−2, similar to previously published values.2 Additional analyses reveals that the rapid adjustment is dominated by the longwave component, with a multi-model mean of −1.05 W m−2, ranging from −0.45 to −2.24 W m−2 (Supplementary Table 3). The corresponding multi-model mean shortwave component is 0.12 (−0.22 to 0.76) W m−2. The importance of longwave radiation to the rapid adjustment is consistent with the corresponding cloud changes (Fig. 2c). PDRMIP models yield increases in low cloud (0.07; 0.03 to 0.11%), decreases in mid-level cloud (−0.17; −0.50 to 0.02%), and most importantly, relatively large decreases in high cloud (−0.37; −0.79 to −0.09%), which is consistent with the negative RAPADJ–LW. Furthermore, PDRMIP cloud responses are consistent with the corresponding RH change (Fig. 2d). Although PDRMIP models show smaller decreases in high cloud over land (including increases over Africa and parts of India/southeast Asia), as compared with ocean, high cloud decreases over both ocean and land.

Unfortunately, most PDRMIP models did not archive the relevant diagnostics to quantify the importance of the aerosol–cloud SDE to the rapid adjustment. Calculation of the shortwave cloud forcing due to absorbing aerosol using standard techniques leads to a positive bias (in the shortwave), by increasing the radiative warming when the absorbing aerosol lies above clouds.38 Thus, it is necessary to use either the clean sky cloud radiative forcing or the clear-sky instantaneous radiative forcing (IRF), and only four models archived these diagnostics (Methods). These four PDRMIP 10xBC simulations yield an aerosol–cloud SDE ranging from −0.41 to −1.26 W m−2, with a multi-model mean of −0.97 W m−2 (Table 1). Moreover, the SDE is dominated by longwave radiation, with SDELW ranging from −0.35 to −1.57 W m−2, with a multi-model mean of −0.82 W m−2. Thus, the aerosol–cloud SDE is a relatively large negative number in PDRMIP 10xBC simulations, dominated by longwave radiation. This agrees with the aforementioned cloud changes, and in particular, the large decrease in high cloud (Supplementary Table 3). Although this conclusion is consistent with a recent PDRMIP 10xBC study using alternative methodologies,4 some discrepancies related to the magnitude of the cloud (and non-cloud) adjustment exist (Methods).

### Sensitivity simulations

To test the hypothesis that the cause of the SDE sign difference using observationally constrained aerosols, relative to PDRMIP and other aerosol simulations, is related to the vertical aerosol heating profile (Fig. 1), we perform sensitivity simulations with observationally constrained aerosol forcing, but we apply it uniformly in the vertical (VERTUNIF simulations). Figure 2 shows that VERTUNIF yields very different results relative to STANDARD, and moreover, VERTUNIF yields cloud changes very similar to PDRMIP. Relatively large increases in cloud and RH occur near the surface, extending up to ~800 hPa. Above ~800 hPa, decreases in both cloud and RH exist, with relatively large reductions above ~300 hPa. Consistently, VERTUNIF yields increases in low cloud, decreases in mid-level cloud, and large decreases in high cloud (Table 1; Supplementary Fig. 6). Several regions of cloud response model agreement exist, particularly for high cloud (Supplementary Fig. 1). These changes are again consistent with ΔRH (Supplementary Discussion). Relative to STANDARD, VERTUNIF RH925–700 now increases and RH300–250 yields larger and more consistent decreases (Supplementary Table 1). In turn, the effective radiative forcing (ERF) swaps sign from positive to negative, as does the rapid adjustment and the aerosol cloud SDE (which still dominates the rapid adjustment). GFDL VERTUNIF yields an aerosol–cloud SDE of −0.41 m−2, which increases to −0.67 m−2 in CAM4 (Fig. 4d–f). SDE model agreement (Fig. 5b) also not only shows the dominance of a negative SDE, most notably over India and Southeast Asia, but also parts of Africa, Canada, and the North Atlantic. Moreover, the SDE is now dominated by longwave effects (cooling), consistent with the large decrease in high-level cloud. These results are also qualitatively consistent with other studies13,25 that found weaker decreases in high cloud and a less negative SDE when BC above 200 and 500 hPa was restricted.

## Discussion

Using observationally constrained fine-mode aerosol forcing, we find a robust positive aerosol–cloud SDE, that acts to warm the climate system. This response is consistent with the corresponding cloud changes, including relatively large decreases in low- and mid-level cloud. Aerosol simulations, however, yield the opposite response—a negative SDE, primarily due to large decreases in high cloud and enhanced longwave cooling. These differences are related to the vertical profile of aerosol atmospheric heating, with aerosol simulations yielding a relatively vertically uniform profile, with strong heating that extends up to 100 hPa. The negative SDE and the corresponding cloud changes are qualitatively reproduced with a simple idealized simulation forced with observationally constrained aerosols, but with vertically uniform atmospheric heating.

We note that our approach has uncertainties of its own (Methods), including lack of consistency between the aerosol forcing and simulated meteorology, as well as the simulated cloud fields. The fine-mode aerosol radiative forcing is also subject to observational errors, including aerosol optical depth and aerosol optical properties, such as the single-scatter albedo.39,40 Sensitivity tests were performed to quantify this uncertainty in observationally constrained fine-mode aerosol forcing,37 resulting in an atmospheric heating uncertainty range of ±0.25 W m−2. Uncertainty in CALIOP’s aerosol vertical profile also exists, including attenuation of the lidar signal. For example, optically thick aerosol layers above African biomass burning can completely attenuate the signal, leading to no retrievals below these levels.41 Our use of CALIOP’s total aerosol vertical distribution, regardless of aerosol type, also leads to additional uncertainty in the absorbing aerosol vertical profile.

Our simulations show a large cloud response over southern Africa and southeast Atlantic (Fig. 3). Some studies have argued that over these regions (and other regions where absorbing aerosols are present), there are potential meteorological influences that confound aerosol–cloud interactions, such as the SDE.42,43,44,45,46 For example, the presence of mid-tropospheric moisture and the southern Africa easterly jet correlate with the increase in the absorbing aerosols, and these meteorological changes appear to impact the cloud development over the southeast Atlantic, independent of the aerosol effect.45,46 Although we have not attempted to formally separate dynamical versus thermodynamical impacts, we do show that cloud changes are generally consistent with the traditionally defined SDE and changes in relative humidity and stability (e.g., Fig. 2; Supplementary Table 2). Nonetheless, a better understanding of how aerosol-induced changes in meteorology affect cloud responses is warranted.

Our focus has been to quantify the aerosol–cloud semi-direct effect based on anthropogenic aerosols, which is why the emphasis is on fine-mode aerosols without dust and sea salt. Although sea salt is a non-absorbing aerosol, dust is a weakly absorbing aerosol and thus has the potential to affect clouds via the semi-direct effect.10,26,47 Moreover, some dust is anthropogenic in nature due to agricultural activities and land-use change.48 Furthermore, climate change itself has likely perturbed dust emissions,49,50 which also implies an anthropogenic contribution to dust. Our analysis does not account for possible dust-related SDE effects.

Although our observationally constrained aerosol forcing contains more atmospheric warming than model estimates, we find similar conclusions—including a positive SDE—with smaller atmospheric heating (HALF simulations). This is consistent with the importance of the vertical aerosol atmospheric heating profile, as opposed to its magnitude. Furthermore, global models may not be able to simulate sub-grid- scale features (e.g., cloud-layer thickness, cloud-top entrainment) that may influence the SDE. However, they should adequately simulate the large-scale features important for the SDE, including changes in stability and relative humidity, and modification of the large-scale atmospheric circulation. Thus, despite the caveats of our approach, we conclude that aerosol simulations lead to a negatively biased SDE. We also suggest that this bias may translate into other aspects of the climate response, including surface temperature and precipitation.

## Methods

### Global climate models

This study uses the National Center for Atmospheric Research (NCAR) Community Atmosphere Model version 4 (CAM4)34 and CAM5.35 Both models have a horizontal resolution of 1.9° × 2.5°; CAM4 has 25 vertical layers and CAM5 has 30. Their main shared physical parameterization is the Zhang-McFarlane deep convection scheme (bulk mass flux with CAPE closure).51 CAM4 uses a shallow convection scheme that involves three-level adjustment of moist static energy52 and a prognostic single-moment microphysics scheme, including diagnostic cloud fraction.53 Cloud fraction depends on several factors, including RH, S, water vapor, and convective mass fluxes. Three types of cloud are diagnosed: low-level marine stratus, convective cloud, and layered cloud. Layered clouds form when RH exceeds a pressure-dependent threshold. Marine stratocumulus clouds are diagnosed using an empirical relationship based on S. Convective cloud fraction is related to updraft mass flux in the deep- and shallow-cumulus schemes. The remaining cloud types are diagnosed on the basis of relative humidity.34

CAM5 uses a mass flux scheme with convective inhibition closure for shallow convection54 and a prognostic double-moment microphysics scheme55 with ice supersaturation56 and a diagnostic cloud fraction scheme for cloud microphysics and macrophysics. Although deep-cumulus cloud fraction is diagnosed as in CAM4, shallow cumulus fraction in CAM5 is directly computed using the definition of convective updraft mass flux from the new shallow convection scheme. Liquid stratus fraction is derived from the assumed triangular distribution of the total relative humidity. The sensitivity of liquid stratus fraction to the changes of grid-mean RH differs between the two models. Ice stratus fraction is also diagnosed, using a modified version of Slingo’s formula.

The rapid radiative transfer model (RRTMG) provides the radiative transfer calculations in CAM5, which is an accelerated and modified version of the correlated k-distribution model, RRTM.57,58,59 RRTMG divides the solar spectrum into 14 shortwave bands that span 0.2 μm to 12.2 μm. A two-stream δ-Eddington approximation is used and assumes homogeneously mixed layers while accounting for absorption and scattering in the calculation of reflectance and transmittance. Distinction is made between the direct solar beam and scattered radiation. The calculation of shortwave radiation in CAM4 is based on a δ-Eddington approximation.60,61,62 The solar spectrum is divided into 19 intervals, and the δ-Eddington solution for the reflectivity and transmissivity for each atmospheric layer under clear and cloud skies is calculated. The layers are then combined together, accounting for multiple scattering between layers, allowing upward and downward spectral fluxes to be estimated.

We also use the Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model version 2.1 (AM2.1),36 with a horizontal resolution of 2° × 2.5° and 24 vertical layers. Moist convection is represented by the Relaxed Arakawa–Schubert formulation.63 In this parameterization, convection is represented by a spectrum of entraining plumes which produce precipitation. Closure is determined by relaxing the cloud work function for each cloud in the spectrum back to a critical value over a fixed time scale. Large-scale clouds are parameterized with separate prognostic variables for specific humidity of cloud liquid and ice, with an updated treatment of mixed-phase clouds.64,65 Stratocumulus cloud cover is based on large-scale subsidence, diabatic cooling by radiation, and turbulent entrainment of warm and dry air from above the inversion.66 Shortwave radiation is based on an exponential sum fit with 18 spectral bands.67 The δ-Eddington method is used to solve for the layer reflection and transmission, while the thick-averaging method is used to combine layers.

Low-, mid-, and high-level clouds are directly calculated by each model. CAM4/5 assumes a maximum-random overlap, with low clouds based on pressure levels from the surface pressure to 700 hPa; mid-level clouds are based on 700–400 hPa; and high-level clouds are based on 400 hPa to the model top. For GFDL AM2.1, clouds are assumed to randomly overlap. Low clouds are calculated over 1000–680 hPa; mid-level clouds from 680 to440 hPa and high clouds from 440 to 10 hPa. For PDRMIP models, these cloud diagnostics were not available for all models. Thus, low-, mid-, and high-level clouds are approximated as simple vertical averages of the cloud fractions over given pressure levels.2 Low clouds are based on 1000–680 hPa; mid-level clouds are based on 680–440 hPa; and high clouds are based on 440–50 hPa. These are the same pressure levels used by ISCCP to define low-, mid-, and high-level clouds.

### PDRMIP simulations

Ten global climate models simulated a control experiment using year 2000 greenhouse gas and aerosol concentrations or emissions, and an experiment in which anthropogenic BC concentration or emissions were increased by a factor of ten (10xBC).2 Five models fixed their control BC concentrations to the monthly multi-model mean present-day concentration of AeroCom Phase II; the 10xBC experiment used a tenfold increase of this anthropogenic BC concentration. In the remaining five models, the control simulation was performed using present-day BC emissions, and the 10xBC experiment used a tenfold increase in the anthropogenic BC emissions. CESM-CAM4, GISS-E2-R, IPSL-CM5A, and NorESM1 are concentration driven; CanAM4, CESM-CAM5, HadGEM2-ES, and MIROC-SPRINTARS are emissions driven. Generally, present-day emissions refer to the year 2000; however, in the case of HadGEM2-ES, the year 1860 was used (the 10xBC experiment used a tenfold increase in anthropogenic BC emissions from the year 2000). All PDRMIP simulations analyzed here are based on an atmosphere-only setup, where sea surface temperatures are prescribed. Most simulations were performed for 15 years. The fast response of a tenfold increase in BC is obtained by taking the difference between the 10xBC experiment and the corresponding control simulation.

CESM1-CAM5 10xBC responses shown here are based on new simulations, analogous to PDRMIP. These new integrations include the double-radiation calls to estimate the instantaneous radiative forcing (which were missing from the original CESM1-CAM5-PDRMIP 10xBC simulation). The HadGEM2-ES instantaneous radiative forcing of 3.55 W m−2 also comes from a second ensemble member of the PDRMIP 10xBC experiment, and is somewhat different than that previously published (3.29 W m−2).2 This difference is due to internal variability and associated meteorological differences and aerosol transport between the two HadGEM2-ES ensemble members.

### Experimental design

We conduct experiments with fixed sea surface temperature (fSST), which uses a repeating cycle of monthly climatological SSTs. The fSST setup prohibits significant global mean temperature change while keeping fast atmospheric responses, like the SDE. Experiments are run for 20 years, and the last 15 years are used in this study. Monthly observationally constrained fine-mode aerosol radiative effects (atmospheric heating rate and surface solar radiation reduction) are interpolated to each model’s horizontal resolution and incorporated into their radiation modules. The atmospheric heating rate is vertically interpolated to each model’s hybrid pressure levels. Although aerosol forcing is almost independent of solar zenith angle (θ) when the angle is small, aerosol forcing approaches zero as θ approaches 90°. Thus, the added aerosol radiative effect is multiplied by a scaling factor that depends on zenith angle.8,68 The climate response is estimated as the difference between the simulation with observationally constrained fine-mode aerosol (without dust and sea salt), and a corresponding control runs without observationally constrained fine-mode aerosol (STANDARD signal). The idealized vertically uniform heating simulations are analogous, but the monthly mean aerosol atmospheric heating is vertically averaged at each grid box, and this vertically averaged value is prescribed to all pressure levels >100 hPa. The climate response of vertically uniform heating (VERTUNIF signal) is obtained by taking a difference with the same control simulation. We also perform simulations analogous to STANDARD, but with half the aerosol forcing (HALF). At each grid box, the (monthly) reduction in surface solar radiation and atmospheric solar heating are reduced by 50%. Significance of all climate responses is based on a Student’s t test for the difference of means, using the pooled variance.

In the case of the CAM4 and GFDL models, which only include aerosol-direct effects, the radiative effects of the default aerosols are neglected (in both observationally constrained aerosol and control simulations) by removing them from the list of radiatively active species. With CAM5, which includes both direct and indirect aerosol effects, the radiative effects of the default aerosols cannot be simply neglected. Thus, CAM5 simulations (observationally constrained and control) use prescribed (as opposed to prognostic) modal aerosols. Although this represents a double counting of aerosol effects in the observationally constrained CAM5 simulation, the response (observationally constrained minus control) will remove the bulk of the radiative effects due to the default prescribed aerosols (which will be similar in observationally constrained and control simulations).

### Observationally constrained aerosol forcing

Aerosol optical depth (AOD) is a popular measure of aerosol amount, and known to be the most reliable global-scale aerosol product. However, the ground-based AErosol RObotic NETwork (AERONET) locations are heterogeneously distributed over the planet, while less reliable satellite AODs have nearly global coverage. Satellite AOD from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging SpectroRadiometer (MISR) is therefore nudged toward AERONET AOD to obtain a globally reliable AOD from 2001 to 2010.69,70 The AOD Angstrom exponent is also derived by adjusting the satellite data toward AERONET data. Fine-mode aerosol optical depth (fAOD) at 500 nm is obtained by using AERONET fAOD and the total AOD to derive the fine-mode fraction (FMF). The AOD Angstrom exponent data are converted into the FMF data, which are then nudged toward AERONET FMF data to derive reliable FMF and fAOD over the globe. Observational data gaps—which are primarily confined to polar regions—are filled by the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model. GOCART accurately simulates most of the prominent AOD features in the satellite observations, within a factor of two for aerosol source and outflow areas.71 However, several GOCART biases have been identified, including an underestimation of aerosol extinction over India, overestimation of aerosol extinction in dust source regions, and overestimation of aerosol aloft over mid-latitude transport regions.72 Aerosol optical properties, such as the single-scatter albedo (SSA) and asymmetry parameter (ASY), are obtained by nudging GOCART SSA and ASY toward AERONET data.

Aerosol vertical profiles are obtained from the space-borne Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP).33 CALIOP is able to distinguish between dust and other type of aerosols, which generally do not depolarize light, resulting in six aerosol categories, including dust, marine, smoke, polluted dust, polluted continental, and clean continental.73 However, these aerosol categories were not used—the total aerosol vertical distribution was applied regardless of aerosol type. Daytime CALIPSO Level 2.0 data from June 2006 to October 2011 were processed to obtain a clear-sky aerosol extinction coefficient at 532 nm at the T42 spatial resolution and 500-m vertical resolution of the Monte Carlo Aerosol Cloud Radiation (MACR) model.74,75 The data gaps are filled using available neighboring data through linear interpolation. A climatological seasonal cycle for the entire data period is then constructed. The aerosol vertical profile from CALIPSO is scaled to match the AOD observations obtained by integrating AERONET, MODIS, and MISR data.37 To adjust the magnitude of AOD over cloud by CALIPSO data, 5° × 2° June 2006 to January 2012 globally gridded monthly mean daytime CALIPSO lidar Level 3.0 data76 is used, specifically, the ratio of clear-sky AOD to above-cloud AOD. This is used to modify the aerosol amount over cloud at each grid cell in the MACR model. For coarse-mode aerosols (which are not used here), the same vertical profiles are used. Because coarse-mode aerosols are not very absorbing, the effect on the vertical profile is very small.75

The direct aerosol effect is obtained by incorporating the integrated global aerosol data into an updated version of the MACR model.37 MACR is based on the Monte Carlo Independent Column Approximation (McICA) and uses satellite observations to describe multilayer cloud, surface albedo, and stratospheric column ozone, as well as ERA-Interim Reanalyzes for precipitable water. The 2001–2010 surface albedo and stratosphere column ozone come from the Clouds and the Earth’s Radiant Energy System (CERES) Synoptic Radiative Fluxes and Clouds (SYN) monthly product. Clouds come from the 2001–2010 averages of the merged daytime monthly mean CERES ISCCP-D2-like product, which is based on combined geostationary cloud retrievals and cloud retrievals from Terra/Aqua MODIS.75 Clouds were combined into four types: low, mid, high, and convective clouds. Between the four types, a random overlap scheme was applied. The key element of this updated version is the Monte Carlo radiative transfer solver combined with the Monte Carlo integration in the multi-dimensional parameter space, including solar zenith angles, aerosol–cloud configurations, and spectral bands. Despite monthly resolution of the three-dimensional model inputs, MACR was run for all 365 days of the year to address variations in the solar zenith angle, declination, and eccentricity of Earth’s orbit. For each day, 40,000 photons were deployed, and monthly inputs were interpolated in time and the model output was averaged over each month. The benefits of the Monte Carlo approach for radiative transfer is that it provides more accurate flux values relative to two stream approximations for both clear and cloudy skies.77

The global average atmospheric heating (FATM) and reduction in surface solar radiation (FSFC) for fine-mode aerosols without dust and sea salt, which include both natural and anthropogenic aerosols, is +3.64 W m−2 and −3.75 W m−2, respectively (−0.11 W m−2 TOA forcing). These estimates are several times larger than anthropogenic forcings estimated from models,78 which are 0.75 W m−2 for FATM and −1.02 W m−2 for FSFC. This large difference is consistent with model underestimation of absorbing aerosol, including black carbon optical properties and emissions, as well as omission of absorbing brown carbon.15,17,18,19,20,21 Furthermore, the observationally constrained FATM and FSFC are larger over land than oceans. FATM is 2.67 (5.82) W m−2 over ocean (land) and FSFC is −2.99 (−5.47) over ocean (land). Despite the relatively large aerosol forcing in STANDARD, we obtain similar conclusions—including cloud responses and a positive SDE—in our reduced aerosol-forcing simulation (HALF). This is consistent with the importance of the vertical aerosol atmospheric heating profile, as opposed to its magnitude.

We note that although this approach uses observations to constrain the fine-mode aerosol radiative effect, the results are subject to observation errors. AERONET SSA, in particular, is subject to uncertainties due to various assumptions used in the retrieval algorithms. Climatological AERONET SSA differs from in situ measured SSA by up to 0.02, with underestimation in low Ångström exponent areas and overestimation in high Ångström exponent areas.40 The maximum error of AERONET AOD is between 0.01 and 0.015 for Level 2.0 data.39 A direct validation of AERONET absorption AOD (AAOD) with unmanned aerial vehicle observations shows that AERONET AAOD errors are less than 20%.79

Sensitivity tests were performed to quantify the uncertainty (primarily due to AOD and SSA) in the observationally constrained fine-mode aerosol forcing used here.37 Fine-mode aerosols yield atmospheric absorption of 3.88 W m−2. This varies from 3.63 W m−2 (least absorbing case) to 4.08 W m−2 (most absorbing case), yielding an uncertainty range of about ±0.25 W m−2. These uncertainty estimates are based on modifying BC AOD and BC/organic aerosol (OA) SSA. Three different sets of simulated SSA are used:

$$\begin{array}{c}{\mathrm{SSA1}} = \left( {0.19{\mathrm{xBC}}\,{\mathrm{AOD}} + 0.85{\mathrm{xOA}}\,{\mathrm{AOD}} + {\mathrm{sulfate}}\,{\mathrm{AOD}}} \right.\\ \left. { +\; {\mathrm{sea - salt}}\,{\mathrm{AOD}} + {\mathrm{0}}{\mathrm{.96xdust}}\,{\mathrm{AOD}}} \right){\mathrm{/total}}\,{\mathrm{AOD}};\end{array}$$
(1)
$$\begin{array}{c}{\mathrm{SSA2}} = \left( {0.14{\mathrm{xBC}}\,{\mathrm{AOD}} + {\mathrm{0}}{\mathrm{.80xOA}}\,{\mathrm{AOD}} + {\mathrm{sulfate}}\,{\mathrm{AOD}}} \right.\\ \left. { +\; {\mathrm{sea - salt}}\,{\mathrm{AOD}} + {\mathrm{0}}{\mathrm{.96xdust}}\,{\mathrm{AOD}}} \right){\mathrm{/total}}\,{\mathrm{AOD;and}}\end{array}$$
(2)
$$\begin{array}{c}{\mathrm{SSA3}} = \left( {{\mathrm{0}}{\mathrm{.19xBC}}\,{\mathrm{AOD}} + {\mathrm{0}}{\mathrm{.98xOA}}\,{\mathrm{AOD}} + {\mathrm{sulfate}}\,{\mathrm{AOD}}} \right.\\ \left. { +\; {\mathrm{sea - salt}}\,{\mathrm{AOD}} + {\mathrm{0}}{\mathrm{.96xdust}}\,{\mathrm{AOD}}} \right){\mathrm{/total}}\,{\mathrm{AOD}}{\mathrm{.}}\end{array}$$
(3)

BC AOD above refers to the GOCART BC AOD at 550 nm. Parameters (e.g., 0.19 for BC SSA) in the above equations come from observational studies.80,81 In addition, in SSA2 (more absorbing case), the magnitude of BC AOD was doubled, given that simulated BC may be significantly underestimated.15 These are then nudged toward the AERONET SSA, giving three sets of semi-observational SSA.37 In terms of fine-mode dust and sea salt, with a baseline atmospheric heating estimate is 0.23 W m−2, sensitivity tests yield a corresponding uncertainty range from 0.16 to 0.26 W m−2. These sensitivity tests are based on using GOCART versus GISS ModelE2 fine-mode dust and sea salt.37

Uncertainty in the absorbing aerosol profile as derived from CALIPSO also exists, including attenuation of the lidar signal. For example, optically thick aerosol layers above African biomass burning can completely attenuate the signal, leading to no retrievals below these levels.41 Although our observationally constrained aerosol vertical profile is not based on individual CALIPSO aerosol categories, such attenuation can also lead to misclassification of aerosol type by the classification algorithm.82,83 However, our use of CALIPSO’s total aerosol vertical distribution, regardless of aerosol type, also leads to additional uncertainty in the absorbing aerosol vertical profile. This uncertainty is much smaller than the overall differences between the CALIPSO profile and simulated BC profiles.