Our modeling framework has been previously described by Westervelt et al. (2018), Westervelt et al. (2017), and Conley et al. (2018). Briefly, we employ three coupled atmosphere–ocean–land–sea ice climate models with fully interactive chemistry of aerosols and trace gases: (1) Geophysical Fluid Dynamics Laboratory Coupled Climate Model version 3 (GFDL CM3) (Donner et al., 2011), (2) Goddard Institute for Space Studies ModelE2 (GISS-E2-R) (Schmidt et al., 2014), and (3) Community Earth System Model version 1 (CESM1) (Neale et al., 2012). The model configuration for each is very similar to that used for CMIP5. For further model description and model evaluation, we refer readers to Westervelt et al. (2017) and Naik et al. (2013). Only CESM1 includes prognostic simulation of aerosol size distribution (Conley et al., 2018, and references therein). Of particular relevance for our results is the model treatment of black carbon. In GFDL CM3 black carbon is internally mixed with only sulfate in the radiation code, whereas in CESM1, black carbon is internally mixed with all aerosol constituents within a given aerosol mode. In GISS-E2, black carbon is externally mixed with other aerosol species (Schmidt et al., 2014).

We conduct for each model a long “present-day” control simulation of up to 400 years in length, forced by perpetual year 2000 (2005 for NCAR CESM1) conditions, including all emissions of aerosols and their precursors and greenhouse gas concentrations. We also conduct individual regional aerosol perturbation simulations of at least 160 years and as long as 240 years in each model, in which the anthropogenic aerosol or aerosol precursor emissions for a certain region are completely removed (100 %) or reduced by the amount shown in Table 1. Aerosol emissions removals are instantaneous and we do not consider the effect of a long time-evolving drawdown. The first 20 years of the perturbation simulations are discarded in the response calculation. We choose the magnitude of relative emissions reductions in order to have roughly equivalent emissions decreases for a particular species across regions and models. As an example, “ISO2” refers to a simulation with perpetual year 2000 conditions (2005 for NCAR CESM1), perturbed by setting all anthropogenic SO2 emissions over India to zero. Other than the regional aerosol emissions perturbation, all other model settings remain identical to the control. Long control and perturbation simulations allow us to establish statistical significance and separate forced responses from internal climate variability.

We also conduct a set of simulations for each perturbation and control in each model using modeled climatological fixed sea surface temperatures (SSTs) and sea ice cover (SIC) in order to calculate ERF. These simulations only use the atmosphere and land components of the climate models and are not coupled to the ocean and sea ice models but are otherwise identical to our longer coupled model integrations. ERF is determined by differencing the perturbation simulation minus the control simulation. Estimates of ERF performed in this manner include the instantaneous radiative forcing plus the rapid adjustments from the atmosphere and the land. For the aerosol perturbation simulations, the ERF is calculated based on 50 years of simulation data for CESM1, 80 years for GFDL CM3, and 160 years for GISS-E2 (to allow detection of a smaller forcing observed in that model). The ERF associated with a doubling of CO2 (2×CO2) is also calculated using the fixed-SST method from simulations similar to 4×CO2 fixed-SST simulations conducted for the CMIP5 experiments. For comparison, the present-day minus pre-industrial aerosol ERF in CESM1, GFDL CM3, and GISS-E2 is -1.52, -1.60, and -0.76 Wm-2, respectively (Allen et al., 2015). This version of the GISS-E2 model does not include the aerosol–cloud lifetime effect, resulting in a smaller ERF, as discussed below.

We estimate the change in surface temperature between the control and perturbation simulations as the cotemporal annual mean differences (perturbation minus control), and we perform a paired sample modified Student t test where the pairs are cotemporal samples of the perturbation and the control. The modified t test accounts for autocorrelation in the model surface temperature time series by calculating an effective standard error, which utilizes an effective sample size based on the lag-1 autocorrelation. A time series showing autocorrelation overestimates the number of independent samples when calculating statistical significance, but our approach, based on Conley et al. (2018) and Zwiers et al. (1995), corrects against this overestimation. We also use the false discovery rate procedure of Wilks (2016) on our t tests over our gridded atmospheric data, which limits the fraction of erroneously rejected null hypotheses in a field of mutually correlated t tests (at each grid point).

To estimate extreme temperature responses to aerosol perturbations, we use the “FClimDex” Fortran package (http://etccdi.pacificclimate.org/software.shtml) developed by the Expert Team on Climate Change Detection and Indices (ETCCDI) to estimate 27 climate extreme indices. Daily minimum, maximum, and mean surface air temperature is input to the extremes package for each of our simulations for which daily data were available, including the control simulation. Cotemporal differences were then taken as for mean temperature, and we performed modified paired t tests (perturbation and control) to assess significance. Extreme temperature analysis was not performed on all of our simulations but rather a subset of simulations that demonstrated the highest mean temperature response. Further, we only perform extreme analysis on simulations conducted for at least 160 years of daily data, as shorter time periods are not sufficient to build up robust statistics. We discard the first 20 years of each perturbation simulation (as with the mean surface temperature analysis) and use the corresponding matching years in the control run when creating the differences. We focus our analysis on the TXx index, one of the most commonly analyzed extreme indices in the existing literature. TXx is defined as the maximum of the maximum daily temperature in a given time period (e.g., over a model-simulated year) (Sillmann et al., 2013). We explored results using other temperature indices and found the results to be qualitatively similar to the results for TXx, and thus we do not include these additional indices in the main text (see Supplement).

Figure 1 shows the ∼160–240-year annual mean surface temperature response in each of the three models for six regional aerosol perturbations. An analogous figure for all of the remaining simulations can be found in Fig. S1 in the Supplement. The change in temperature in Fig. 1 and all following figures is the “perturbation minus control”, representing the temperature response to a removal or reduction of emissions of anthropogenic aerosols and their precursors. Generally, the response is overwhelmingly positive (warming) with large regions of statistical significance in each of the three models for most simulations. We find a larger temperature response in GFDL CM3 and CESM1 (first and second columns of Fig. 1) compared to GISS-E2, consistent with the smaller magnitude of aerosol ERF in GISS-E2 (see Sect. 5) resulting from a lack of a cloud lifetime effect in that model (Westervelt et al., 2017, 2018). In all three models, the largest remote temperature responses are over the Arctic, owing to the well-established polar amplification phenomenon (Smith et al., 2019; Stjern et al., 2019). Surface temperature response is strongest in the US SO2 and Europe SO2 simulations in all three models, with annual mean local and remote temperature increases of up to 1 K or higher. Despite different regions of emissions perturbations, the salient features of the spatial distribution of surface temperature response are similar between the US SO2, China SO2, US ALL (SO2, BC, and organic carbon aerosol (OA) combined), Europe SO2, and EU ALL (Fig. S1 in the Supplement) perturbations in all models, suggesting that aerosol forcing in Northern Hemisphere midlatitudes (NHMLs) induces a qualitatively consistent spatial response pattern. This pattern features strong Arctic warming, differential heating of the Northern Hemisphere compared to the Southern Hemisphere, strong local responses, and far-reaching remote responses across continents (e.g., European warming in response to US SO2 emissions reductions). The response pattern is also similar to regional modifications of land surface albedo as reported in Seneviratne et al. (2018). Climate responses to aerosol perturbations can also project onto known modes of climate variability, such as El Niño–Southern Oscillation (ENSO), as described in Westervelt et al. (2018). The temperature response to US SO2 emissions removal in CESM1 (Fig. 1b) resembles an El Niño-like response, with cooling in the western tropical Pacific Ocean coupled with warming in the eastern tropical Pacific Ocean. In GFDL CM3, most simulations regardless of region or aerosol species result in cooling (sometimes statistically significant) south of 60∘ S along the Antarctic coast starting roughly at the 180∘ meridian coupled with surrounding statistically significant warming (e.g., EU SO2, Fig. 1d), suggesting interaction with the Amundsen Sea Low (ASL), which exerts significant influence on Antarctic climate (Raphael et al., 2016). However, this is also a region of strong climate variability in GFDL CM3.

Although the surface temperature response to Indian SO2 and BC emissions reductions is small in all models, despite the tropical location of the emissions perturbation, changes in temperature still occur at both poles in all models, with some statistical significance. Removal of black carbon emissions (Fig. 1p, q, and r) elicits a very different temperature response in each of the three models in spatial distribution, sign, and magnitude, indicating a strong dependence of the surface temperature response on different model assumptions for black carbon, including different mixing state assumptions. Additionally, as reported in Westervelt et al. (2018), aerosol ERF from India BC perturbations is small (ranging from -0.04 to 0.06 Wm-2 across the three models) and statistically insignificant, resulting in climate responses that may be influenced by internal variability. The weak forcing in the black carbon simulations may also reflect the role of rapid adjustments (Stjern et al., 2017; Smith et al., 2018), including the semi-direct effect of BC on clouds (Allen et al., 2019). The climate response to BC perturbations in other regions, such as US BC (Fig. S1g and h in the Supplement), is also marked by disparate temperature responses, further highlighting the sensitivity of climate response to model physics, and in some cases representing noise when forcing signals are small. The role of transport of BC from source regions remote to the Arctic may also be a contributor to the Arctic temperature response (Wang et al., 2014).

To estimate robustness of the surface temperature responses to regional aerosol perturbations, we use the sign (warming or cooling) and the statistical significance as a point of comparison between the three models. Figure 2 shows the agreement between models in sign and statistical significance in each of the aerosol perturbation simulations that were conducted by all three models. We find widespread agreement in sign and significance in the US SO2 (Fig. 2a), Europe SO2 (Fig. 2b), China SO2 (Fig. 2c), and US ALL (SO2, BC, and OA combined, Fig. 2d) simulations. Using sign agreement in three models as a minimum for a qualification of robustness (light blue), the most robust responses are to Europe SO2 removal, where 81 % of the Earth's surface qualifies as robust (values in the upper right of Fig. 2 panels). On the other hand, the response to India BC is robust across only 39 % of the Earth's surface. We conclude that climate responses to black carbon over India exhibit large variability between models compared to climate responses from source regions such as the US and Europe, likely due to the small forcing exerted by the BC perturbation simulations.

The three models frequently agree in the sign and significance of Arctic warming, indicating that the Arctic surface temperature response is one of the most robust features of climate response to regional aerosol perturbations. Local responses are also robust; in particular the US SO2 and US ALL perturbations show high levels of robustness (green and dark blue in Fig. 2a and d) over North America. The models agree in sign and significance in the remote Arctic temperature response even in the case of the India BC and African biomass burning emissions perturbations, suggesting that the Arctic warming response is somewhat independent of emissions region or aerosol composition. Overall, all three models agree on sign and at least two report statistical significance over 32 % of the Earth's surface (66 % when not including significance) in response to removal of US SO2 emissions.

In Fig. 3, we present the global and regional mean surface temperature response to 14 different emissions perturbations in each of the three models. The emissions reductions forcing these temperature changes are roughly the same across models within a given perturbation scenario (Table 1). The global mean surface temperature response (Fig. 3a) indicates warming in 33 of the 34 simulations (US BC in GFDL CM3 being the only example of global cooling) and is significant at the 95 % confidence level in 30 of the 34 perturbation simulations. The Europe and US emissions perturbations (e.g., ESO2, EALL, USO2) cause the largest global mean temperature increases across all regions and aerosol compositions, resulting in a global mean warming of about 0.15 K. The SO2 perturbations tend to result in greater warming than OA or BC (which can also result in global cooling). CESM1 and GFDL CM3 tend to warm more than GISS-E2, although not for all simulations.

We break down the regional climate response into latitude bands, following the approach used by Shindell and Faluvegi (2009), by regionally averaging the temperature responses from 60 to 90∘ N (Arctic, Fig. 3b), 30 to 60∘ N (Northern Hemisphere midlatitudes, NHMLs, Fig. 3c), 30∘ S to 30∘ N (tropics, Fig. 3d), and 30 to 90∘ S (Southern Hemisphere, Fig. 3e). Surface temperature increases approach 1 K regionally averaged over the Arctic (60 to 90∘ N) in CESM1 and GFDL CM3, with GISS-E2 simulating smaller but still often statistically significant warming responses. The Arctic responds most strongly to European aerosol perturbations (e.g., ESO2, EALL), perhaps owing to the greater proximity of the European continent to the Arctic region. However, even remote regional aerosol perturbations, such as India SO2 (ISO2) or South American biomass burning (SABB), lead to Arctic warming in all of the models (Fig. 2), with some statistical significance. NHML temperature changes (Fig. 3c) are mostly dominated by these local perturbations. On the other hand, the temperature response to the emissions perturbations local to the tropics (red labels in Fig. 3d) is roughly the same in magnitude and significance as the response to some of the “remote” perturbations. Emissions perturbations local to the tropics exert a larger temperature response in the Arctic than they do either locally or in the closer NHML region. In the Southern Hemisphere (Fig. 3e), we find consistent, statistically significant warming in CESM1 but less warming in GFDL CM3 and GISS-E2, owing to the localized Antarctic cooling in the case of GFDL CM3. Overall, responses in the Southern Hemisphere are less statistically significant.

We use ∼80-year fixed-SST and SIC atmosphere-only simulations in each of the three models to diagnose ERF due to each aerosol emissions perturbation. The global mean ERF from the 34 simulations ranges from about -0.1 to 0.3 Wm-2, though all but six simulations (several of the BC emissions perturbations) have ERF greater than zero. In Fig. 7, we plot global mean surface temperature response from the ∼200-year coupled model simulations against global mean ERF for every perturbation simulation. We find a strong positive correlation among all models (r=0.64 for CESM1, r=0.79 for GFDL CM3, and r=0.76 for GISS-E2), consistent with previous studies (Liu et al., 2018; Marvel et al., 2016). There is substantial overlap and a similar slope for all three models (∼0.4K (Wm-2)-1), indicating that, on a global mean basis, the models are each similarly sensitive to regional aerosol forcing. We further analyze the climate sensitivity to aerosol forcing in the following section.

For a selection of simulations in which the aerosol ERF was statistically significant, we calculate in Fig. 8 the climate sensitivity parameter (K (Wm-2)-1) to the regional aerosol perturbations as the quotient between the equilibrium global surface temperature response from the coupled model simulations and global ERF using the fixed-SST approach, similar to the equilibrium climate sensitivity (ECS) approach used for CO2. We also present the equilibrium climate sensitivity to a doubling of CO2 (2×CO2) in each of the three models using the same fixed-SST methodology for comparison to the aerosol climate sensitivity. We find that the climate sensitivity parameter for aerosol perturbations varies by model and by forcing, but mostly ranges from about 0.5 to 1.0 K (Wm-2)-1 in each of the three models, which is comparable to the values for CO2 sensitivity of approximately 1.0 K (Wm-2)-1 in GFDL CM3 and CESM1 and 0.5 K (Wm-2)-1 in GISS-E2. Surface temperature appears to be most sensitive to European SO2 emissions in GFDL CM3, US SO2 emissions in CESM1, and US ALL (SO2, BC, and OA combined) emissions in GISS-E2. The 2×CO2 climate sensitivity and the aerosol climate sensitivity for European SO2, European ALL, and US SO2 are approximately equivalent at about 1.0 K (Wm-2)-1 for GFDL CM3 and CESM1. The aerosol climate sensitivity is also in good agreement (overlapping error bars in Fig. 8) for the US SO2 emissions perturbation between the three models. However, the aerosol climate sensitivity is often substantially greater than 2×CO2 climate sensitivity in GISS-E2, consistent with results from Marvel et al. (2016), discussed further below. Differences between aerosol climate sensitivity and 2×CO2 climate sensitivity can be explained by the differences in both the temperature response and the associated ERF for each perturbation. In particular, ERF may be quite different between heterogeneous forcing agents relatively smaller in magnitude such as regional aerosols and large, more globally homogeneous forcing agents such as CO2. Using 11 models including GISS-E2, Smith et al. (2018) found that rapid adjustments reduce the ERF for BC aerosol but increase the ERF for CO2 forcing, consistent with the hypothesis that differences in ERF can explain differences in the temperature sensitivities shown in Fig. 8.

Previous work by Marvel et al. (2016) and Hansen et al. (2005) using only the GISS-E2 climate model found that the forcing efficacy of global aerosol reductions is greater than that of CO2. We extend this finding for GISS-E2 to regional aerosol emissions reductions, as the climate sensitivity parameter in all but one of our regional aerosol perturbation simulations in GISS-E2 is larger than the 2×CO2 perturbation. In contrast, the aerosol climate sensitivity parameter in both GFDL CM3 and CESM1 is smaller than or about equal to that of 2×CO2. We can conclude at minimum that aerosol forcing efficacy is model dependent, especially for regional aerosol perturbations, and this further highlights the importance of using multiple models to estimate or constrain estimates of ECS that include forcing from a diverse set of agents. The CMIP6 experiments may be used to shed further light on the relative efficacy of aerosol and greenhouse gas forcing, though not for regional perturbations.

In addition to the global temperature response and global ERF, we also estimate the regional temperature sensitivities. We use the approach of Shindell (2012), who introduced regional temperature potential (RTP) coefficients. These coefficients account for the spatial heterogeneity of aerosol forcing and temperature response and can be derived for any pair of response regions and forcing regions. Following the methods of Shindell (2012) and Lewinschal et al. (2019), we calculate, within each latitude band, the temperature response to regional aerosol perturbations as a function of the latitude band averaged ERF containing each aerosol perturbation region. We then normalize this quantity by the global mean equilibrium temperature response to global mean forcing, resulting in a dimensionless coefficient giving the equilibrium temperature response in latitude band x to forcing in region y. The response latitude band x can be any of the bands defined in Fig. 2, whereas forcing regions y are the latitude bands containing each of our 14 regional aerosol perturbation locations, either 30–60∘ N (NHMLs) or 30∘ S–30∘ N (tropics). As defined in Shindell (2012), RTP for a given pair of regions is 1RTP=dTxdFydTglobaldFglobal, where dT is change in temperature and dF is change in ERF. Because of the normalization by global mean temperature and global mean ERF, the RTP coefficients are unitless.

RTP coefficients in each latitude band for a given aerosol perturbation region are reported in Table 2 for GFDL CM3, Table 3 for GISS-E2, and Table 4 for CESM1. We present only RTP values for which the corresponding ERF and temperature response were statistically significant or for which data were available. The India, South America, and Africa entries in Tables 2–4 are based on a forcing average from the tropics since that region contains almost all of the statistically significant signal. All other values are based on the NHML latitude band forcing average. Higher values of RTP indicate higher sensitivity of the particular response region to the aerosol forcing regions. RTP values from individual models provide a range of possible estimates. Figure 9 shows the multi-model mean RTP coefficients for a selection of regional aerosol perturbation simulations, along with the mean of the NHMLs and tropics perturbations grouped together (“NHML tot.”, “tropics tot.”). Figure 9 indicates that the response to NHML forcing is consistent in all response regions regardless of where the aerosol forcing is longitudinally located within the NHMLs, as indicated by the similar RTP magnitudes in the first four clusters of bars (CSO2, ESO2, USO2, and UALL). Consistent with our earlier findings in Fig. 2, the Arctic always emerges as the most sensitive region to nonlocal aerosol forcing. After the Arctic, regional sensitivities are greatest for the NHMLs, tropics, and Southern Hemisphere (SH) for perturbations in the NHMLs (e.g., CSO2, ESO2, USO2, UALL). For tropical perturbations such as ISO2, SABB, and AFBB, either the SH or the tropics are most sensitive, after the Arctic. Across each of the aerosol perturbations, the RTP coefficients are similar in magnitude when grouped by similar latitudinal forcing locations.

Our findings are similar to those of Shindell (2012), but we find a higher sensitivity in the Arctic to NHML forcing (1.49, Fig. 9 “NHML tot.” versus RTP of 0.43 in Shindell, 2012). Shindell (2012) finds the Arctic is most sensitive to local forcing but we lack a perturbation simulation to diagnose that response here. Shindell (2012) reported an Arctic RTP for tropical forcing of 0.36, close to that of NHML forcing, indicating that aerosol perturbations in the tropics are also important for Arctic climate response, which qualitatively agrees with our findings in Fig. 9. Averaging the RTP values corresponding to statistically significant ERF and temperature response within a single latitude band (for example, average RTP of USO2, ESO2, and CSO2) yields a close match with Shindell (2012) RTP values, especially in the NHMLs and tropics. Shindell (2012) reports an RTP of 0.49 for NHML response to NHML forcing, very close to the average of our NHML forcings in Fig. 9, which is 0.46 (orange bar in Fig. 9 for “NHML tot.”). The other response regions (tropics and Southern Hemisphere) compare moderately well with Shindell (2012) for NHML forcing (0.25 versus 0.15 for the tropics and 0.1 versus 0.05 for the Southern Hemisphere). Shindell (2012) used an older model and an idealized forcing through an entire latitude band as opposed to our more realistic localized forcing, which may account for some of the differences in each region.

The uncertainty range in the final two clusters of bars in Fig. 9 gives the range of RTP values for the total NHML forcing using the model individual values to construct a high and low estimate. For the NHML forcing cases, which include USO2, CSO2, and ESO2, the responses are robust across our models and there is little intermodel variation, as indicated by the small uncertainty range in each of the four response regions under “NHML tot.”. For the tropical forcing cases, the models diverge (uncertainty bars under “Tropics tot.” in Fig. 9), especially in the regions remote to the tropics. These results imply that the use of RTP coefficients or similar simple climate response metrics for remote responses to forcing in NHML regions are more robust and reliable than those for remote responses to forcing in tropical regions.