Estimating the CMIP6 Anthropogenic Aerosol Radiative Effects with the Advantage of Prescribed Aerosol Forcing

: The prescribed anthropogenic aerosol forcing recommended by Coupled Model Intercomparison Project Phase 6 (CMIP6) was implemented in an atmospheric model. With the reduced complexity of anthropogenic aerosol forcing, each component of anthropogenic aerosol effective radiative forcing (ERF) can be estimated by one or more calculation methods, especially for instantaneous radiative forcing (RF) from aerosol–radiation interactions (RFari) and aerosol–cloud interactions (RFaci). Simulation results show that the choice of calculation method might impact the magnitude and reliability of RFari. The RFaci—calculated by double radiation calls—is the deﬁnition-based Twomey effect, which previously was impossible to diagnose using the default model with physically based aerosol–cloud interactions. The RFari and RFaci determined from present-day simulations are very robust and can be used as ofﬂine simulation results. The robust RFari, RFaci, and corresponding radiative forcing efﬁciencies (i.e., the impact of environmental properties) are very useful for analyzing anthropogenic aerosol radiative effects. For instance, from 1975 to 2000, both RFari and RFaci showed a clear response to the spatial change of anthropogenic aerosol. The global average RF (RFari + RFaci) has enhanced (more negative) by ~6%, even with a slight decrease in the global average anthropogenic aerosol, and this can be explained by the spatial pattern of radiative forcing efﬁciency. aF RAD and aFdA RAD are the clear-sky aF CcRAD and aF Cc dA RAD , respectively. Without the impact of natural aerosols, the global average values of aF CcRAD and aF RAD are − 0.33 and − 0.64 W m − 2 , respectively. The global mean aF Cc dA RAD and aFdA RAD is 0.12 and 0.19 W m − 2 , respectively, and these values are approximately one-third of the RFari strength without the inﬂuence of natural aerosols (i.e., aF CcRAD and aF RAD ). These results suggest that the natural aerosol radiative effect might have an obvious impact on estimating RFari. The model diversity in estimating RFari might stem from the difference in the host model natural aerosol.


Introduction
One of the guiding questions of the Coupled Model Intercomparison Project Phase 6 (CMIP6) is "how does the earth system respond to forcing?" [1]. Without reliable forcing estimates, it is very difficult to compare climate model responses to changes in forcing, especially the radiative forcing estimates for short-lived atmospheric aerosols [2,3]. Thus, idealized experiments have been designed to highlight and understand the differences in climate model responses to specified common anthropogenic aerosol forcing [4,5]. Given these concepts, a simple plume implementation of the second version of the Max Planck Institute Aerosol Climatology (MACv2-SP) was developed for climate models, which provides prescribed anthropogenic aerosol optical properties and normalized changes in cloud droplet number [6,7].
The anthropogenic aerosol effects on the planetary energy balance can be expressed as effective radiative forcing (ERF), which can be decomposed into the contributions of instantaneous radiative forcing (RF) and rapid adjustments (i.e., ERF − RF) [8][9][10][11]. As the complexity of anthropogenic aerosol forcing decreases (i.e., MACv2-SP), the RF from anthropogenic aerosol-cloud interactions (RFaci) and the RF from anthropogenic aerosol-radiation interactions (RFari) can be calculated by double radiation calls (i.e.,  [5]. Nine plumes (five industrial and four biomass) are used to capture the spatial distribution of the anthropogenic aerosol in the MACv2-SP. The spatial structure (horizontal structure and vertical structure) and annual cycle of each plume are parameterized as a basis function to represent the anthropogenic aerosol. Here, a brief introduction is provided to better understand the radiative forcing variables used in this study. To represent anthropogenic aerosol-radiation interactions, MACv2-SP provides anthropogenic aerosol optical properties (i.e., the aerosol optical depth (AOD), single-scattering albedo, and asymmetry factor). In the radiation scheme, total aerosol optical properties are calculated based on the anthropogenic aerosol optical properties from MACv2-SP and natural aerosol optical properties from the default mechanism of the host model. As only smaller, fine-mode aerosol contributes to MACv2-SP, only shortwave anthropogenic aerosol optical properties are provided. To represent the anthropogenic aerosol Twomey effect, MACv2-SP provides a normalized change in cloud droplet number (rNc). The rNc is the increasing ratio of cloud droplet number (Nc) as compared to the host model background Nc (i.e., only natural aerosols contribute). In the year 1850 (pre-industrial times, PI), there was no anthropogenic aerosol forcing in MACv2-SP, and so the rNc is taken as a constant, 1. After 1850, the rNc (>1) is used to tune the host model Nc and ensure that the proportional change in Nc caused by anthropogenic aerosol is insensitive to background Nc. Notably, only the warm cloud Twomey effect, which refers to cloud optical thickness under a fixed liquid water content increased by anthropogenic aerosol [18], is considered in the design of MACv2-SP. Based on this conception, the rNc is only used for calculating warm cloud optical properties in the radiation scheme. In the cloud microphysics scheme, the Nc is not affected by the rNc (i.e., no cloud-lifetime effect).
The GAMIL model is a Grid-point Atmospheric general circulation Model of IAP LASG with a finite difference dynamical core, developed by the Institute of Atmospheric Physics, Chinese Academy of Sciences [17,[19][20][21][22][23]. Details of the GAMIL model can be found in the study of Li et al. 2020 [17]. Radiative transfer is solved by delta-Eddington approximation with 19 solar spectral bands [24,25]. In the default GAMIL model, the natural aerosol direct radiative effect is represented by given natural aerosol optical properties. Here, anthropogenic aerosol optical properties from MACv2-SP were superimposed. In the default GAMIL model, the indirect aerosol effects are treated by a detailed two-moment cloud microphysics scheme [23]. In all experiments in this study, the Nc used in the cloud microphysics scheme was calculated based on a dataset of prescribed PI aerosols (i.e., natural aerosol), which includes sulfate, hydrophobic black carbon, hydrophilic black carbon, hydrophobic organic carbon, hydrophilic organic carbon, dust, and sea salt. For considering the anthropogenic aerosol Twomey effect provided by MACv2-SP (i.e., rNc), the warm cloud optical properties used in the radiation scheme were calculated by Nc × rNc, instead of Nc.

Calculation Method and Updated Diagnostic Package
There is no perfect method to determine the ERF. One recommended way to calculate the ERF is by using the radiative flux perturbation method from the top-of-the-atmosphere (TOA) energy balance difference between two simulations with and without anthropogenic aerosol but the same sea surface temperature (SST) [8][9][10]. In this study, this fixed-SST method was used to calculate the ERF. The RF can be calculated by double radiation calls in the model diagnostic package, and the rapid adjustments can be diagnosed as ERF − RF [7,13].
Using GAMIL with MACv2-SP, the anthropogenic aerosol ERF from combined aerosolradiation and aerosol-cloud interactions (also named as ERFari + aci) can be decomposed into the anthropogenic aerosol RFari (i.e., instantaneous direct effect), the anthropogenic aerosol RFaci (i.e., instantaneous Twomey effect), and rapid adjustments (i.e., ERFari + aci − RFari − RFaci). Notably, these rapid adjustments cannot be decomposed into the rapid adjustments from aerosol-radiation interactions and the rapid adjustments from aerosol-cloud interactions because all adjustments interact with each other at each model time step. The ERF (short for anthropogenic aerosol ERF) from two simulations with and without anthropogenic aerosol-radiation interactions only (ERFari) can be decomposed into the RFari (short for anthropogenic aerosol RFari) and corresponding rapid adjustments from aerosol-radiation interactions. Among these rapid adjustments, the rapid adjustment induced by the changes in clouds is referred to as the semi-direct effect [8,9]. The ERF from aerosol-cloud interactions only (ERFaci) can be decomposed into the RFaci (short for anthropogenic aerosol RFaci) and corresponding rapid adjustments (no lifetime effect).
In order to use several possible calculation methods to diagnose RFari and RFaci, the radiation subroutine needs to be called many times to provide different net radiative fluxes at the TOA. All shortwave net radiative fluxes diagnosed from the radiation scheme are listed in Table 1. For the convenience of remembering, these variables are named according to a certain rule. The capital letter "F" denotes the benchmark of shortwave net radiative fluxes at the TOA, which excludes the radiative effects of clouds and aerosols (both anthropogenic aerosol and natural aerosol). The subscript letters ("A", "a", "C", or "Cc") indicate the radiative forcing factor considered in the radiation transfer calculation, as compared to the benchmark "F". The letters correspond to: natural aerosol optical properties ("A"); anthropogenic aerosol optical properties ("a"); background cloud optical properties ("C"); cloud optical properties with the Twomey effect ("Cc"). The "C" was calculated based on Nc, and the "Cc" based on Nc × rNc. Here, we introduce a few variables that are listed in Table 1. According to the naming rule, F AaCc considers all radiative forcing factors, which is the commonly called the shortwave net radiative flux. F Aa is clear-sky F AaCc . Compared to F AaCc , F AaC excludes the anthropogenic aerosol Twomey effect ("c"). Compared to F AaCc , F ACc excludes the anthropogenic aerosol direct radiative effect ("a"). Compared to F AaCc , F Cc excludes the total (natural and anthropogenic) aerosol direct radiative effect ("A" and "a").
Model diagnostic instantaneous radiative forcing variables were calculated as the difference between two net radiative fluxes listed in Table 1. Table 2 lists the variables analyzed in this study. These variables are also named according to a certain rule. Anthropogenic aerosol ("a") direct radiative forcing is named as aF XX . Total (natural and anthropogenic) aerosol ("A" and "a") direct radiative forcing is named as AaF XX . Cloud ("Cc", with the Twomey effect) forcing is named as CcF XX . Background cloud ("C", without the Twomey effect) forcing is named as CF XX . The instantaneous Twomey effect ("c") is named cF xx. Here, the subscript "XX" refers to background radiative forcing factors (i.e., "A", "a", "C", and "Cc") that are considered in the radiation transfer. For instance, both aF ACc (aF Acc = F AaCc − F ACc ) and aF Cc (aF Cc = F aCc − F Cc ) indicate anthropogenic aerosol ("a") radiative forcing. Compared to aF ACc , aF Cc excludes the impact of the natural aerosol direct radiative effect ("A"). Notably, all aF XX indicate RFari, and all cF XX indicate RFaci.

Experimental Design
In order to show each component of the ERF and the impact of the spatial shift in anthropogenic aerosol, five experiments-referred to as BASE, RAD, TMY, ALL, and PAT-were carried out in this study. The experimental setups are summarized in Table 3. The natural aerosol direct and indirect effects were considered in all the experiments. The BASE experiment did not consider anthropogenic aerosol forcing. In contrast to the BASE experiment, the PD (year 2000) anthropogenic aerosol radiative effect and Twomey effect provided by MACv2-SP were added in the ALL experiment, the RAD experiment only added the anthropogenic aerosol (year 2000) direct radiative effect, and the TMY experiment only added the Twomey effect (year 2000). The PAT experiment (PAT is short for spatial pattern) was similar to the ALL experiment, but the year 1975 was used for calculating the anthropogenic aerosol forcing. All experiments were atmosphere-only simulations with same prescribed climatological ocean surface conditions. Anthropogenic aerosol data calculated from MACv2-SP during a given year were used in the model simulations, which did not change from year to year. All simulations were run for 11 model years at a horizontal grid resolution of 80 × 180 and 26 vertical levels. It is noteworthy that the TOA (i.e., the second top interface level,~2.6 hPa) is different from the top of the model (i.e., the first top interface level, 0). The first year was considered as a spin-up period and not included in the analysis. The standard deviations, which were estimated from the averages of each year (i.e., 10 averages), were used for variability analysis.

Results
Because only shortwave anthropogenic aerosol optical properties are provided by MACv2-SP, only shortwave radiative forcing variables are analyzed. When analyzing a radiative variable, it is necessary to know which experiment it comes from. To show the source of the variable, the experiment name is added in superscript. For example, the AaF Cc from the ALL experiment is denoted as AaF Cc ALL , and the difference in AaF Cc between the ALL and BASE experiments is denoted as AaF Cc ALL−BASE . Furthermore, for ease of expression, " " is used to denote the difference between two simulations (e.g., ∆AaF Cc ). For convenience of searching and comparison, the global annual mean radiative variables from all experiments are listed in Table A1. Based on Table A1, the different calculation methods for estimating anthropogenic aerosol radiative effects are summarized in the Appendix A. Figure 1 shows the all-sky and clear-sky RFari derived from two kinds of calculation methods. The RFari from the difference between two simulations (AaF Cc RAD−BASE ) and the RFari from one simulation (aF ACc RAD ) show the same global cooling at −0.21 W m −2 . It should be noted that all regions of RFari (aF ACc RAD ) are statistically significant, whereas RFari (AaF Cc RAD−BASE ) is not statistically significant over some regions. RFari is usually more negative under clear-sky conditions than under all-sky conditions [26,27]. As expected, both AaF RAD−BASE and aF A RAD (i.e., clear-sky RFari) show a stronger (more negative) global cooling at −0.45 W m −2 . Compared to all-sky RFari (AaF Cc RAD−BASE ), clear-sky RFari (AaF RAD−BASE ) has more statistically significant regions. This result can be attributed to the fact that the difference in cloud optical properties between the RAD and BASE experiments is excluded. Unlike aF A RAD , there are still some statistically nonsignificant regions of AaF RAD−BASE due to model internal year-to-year variability. The comparison between AaF Cc RAD−BASE (AaF RAD−BASE ) and aF ACc RAD (aF A RAD ) indicates that the RFari estimated by a model diagnostic radiative forcing variable from one simulation is more robust than that estimated by the difference between two simulations. The aF ACc RAD and aF A RAD are scarcely affected by model internal year-to-year variability and can be considered as offline simulation results. There are many other methods for calculating RFari (e.g., AaF Cc ALL−TMY , AaF Cc ALL−BASE , and aF ACc ALL ). It is necessary to point out that AaF Cc ALL−TMY and AaF Cc ALL−BASE are similar to AaF Cc RAD−BASE , and aF ACc ALL is almost the same as aF ACc RAD (not shown). Both all-sky RFari and clear-sky RFari show some regions with a warming effect ( Figure 1). Kinne (2019) explained this warming effect by dimming over snow and lower clouds [26]. Taking the snow-covered regions as an example, a relatively larger proportion of downward solar radiation is reflected by the surface (not shown), and thus, the role of anthropogenic aerosols in absorbing and scattering the reflected solar radiation (warming effect) becomes relatively important.

Annual Mean Results
We found that the GAMIL model shows a very strong all-sky and clear-sky natural aerosol RF (-5.74 and −8.58 W m -2 , AaF Cc BASE and AaF BASE in Table A1), which has an obvious impact on calculating the all-sky and clear-sky RFari (0.12 and 0.19 W m -2 , aF Cc dA and aFdA in Table A1). Therefore, it is necessary to analyze the RFaci without the impact of natural aerosol. Taking the results from the RAD experiment as an example to explain (Figure 2), aF Cc RAD excludes the natural aerosol impact as compared to aF ACc RAD . The aF Cc dA RAD (aF Cc dA RAD = aF ACc RAD − aF Cc RAD ) indicates the impact of natural aerosols on estimating RFari. The aF RAD and aFdA RAD are the clear-sky aF Cc RAD and aF Cc dA RAD , respectively. Without the impact of natural aerosols, the global average values of aF Cc RAD and aF RAD are −0.33 and −0.64 W m −2 , respectively. The global mean aF Cc dA RAD and aFdA RAD is 0.12 and 0.19 W m −2 , respectively, and these values are approximately onethird of the RFari strength without the influence of natural aerosols (i.e., aF Cc RAD and aF RAD ). These results suggest that the natural aerosol radiative effect might have an obvious impact on estimating RFari. The model diversity in estimating RFari might stem from the difference in the host model natural aerosol. We found that the GAMIL model shows a very strong all-sky and clear-sky natura aerosol RF (-5.74 and −8.58 W m -2 , AaFCc BASE and AaF BASE in Table A1), which has an obvi ous impact on calculating the all-sky and clear-sky RFari (0.12 and 0.19 W m -2 , aFCcdA and aFdA in Table A1). Therefore, it is necessary to analyze the RFaci without the impact o natural aerosol. Taking the results from the RAD experiment as an example to explain ( Figure 2), aFCc RAD excludes the natural aerosol impact as compared to aFACc RAD . The aFCcdA RAD (aFCcdA RAD = aFACc RAD − aFCc RAD ) indicates the impact of natural aerosols on esti mating RFari. The aF RAD and aFdA RAD are the clear-sky aFCc RAD and aFCcdA RAD , respec tively. Without the impact of natural aerosols, the global average values of aFCc RAD and aF RAD are −0.33 and −0.64 W m −2 , respectively. The global mean aFCcdA RAD and aFdA RAD i 0.12 and 0.19 W m −2 , respectively, and these values are approximately one-third of the RFari strength without the influence of natural aerosols (i.e., aFCc RAD and aF RAD ). These results suggest that the natural aerosol radiative effect might have an obvious impact on estimating RFari. The model diversity in estimating RFari might stem from the difference in the host model natural aerosol.

Figure 1. Annual mean maps for the present-day (year 2000) anthropogenic aerosol alland clear-sky (right) instantaneous radiative forcing from aerosol-radiation interaction
The results calculated as the differences between the RAD and BASE experiments are sho upper panels. The results provided by the RAD experiment only are shown in the lower pa global average is given in the upper-right corner. Hatching represents the nonsignificant a 90% confidence level of Student's t-test.
We found that the GAMIL model shows a very strong all-sky and clear-sky aerosol RF (-5.74 and −8.58 W m -2 , AaFCc BASE and AaF BASE in Table A1), which has ous impact on calculating the all-sky and clear-sky RFari (0.12 and 0.19 W m -2 , aFC aFdA in Table A1). Therefore, it is necessary to analyze the RFaci without the i natural aerosol. Taking the results from the RAD experiment as an example to ( Figure 2), aFCc RAD excludes the natural aerosol impact as compared to aFACc aFCcdA RAD (aFCcdA RAD = aFACc RAD − aFCc RAD ) indicates the impact of natural aerosol mating RFari. The aF RAD and aFdA RAD are the clear-sky aFCc RAD and aFCcdA RAD tively. Without the impact of natural aerosols, the global average values of aFC aF RAD are −0.33 and −0.64 W m −2 , respectively. The global mean aFCcdA RAD and aF 0.12 and 0.19 W m −2 , respectively, and these values are approximately one-thir RFari strength without the influence of natural aerosols (i.e., aFCc RAD and aF RAD results suggest that the natural aerosol radiative effect might have an obvious im estimating RFari. The model diversity in estimating RFari might stem from the d in the host model natural aerosol.  Figure 1 but for the all-sky (left) and clear-sky (right) instantaneous direct effect without the natural aerosol radiative effect (RFari, upper panels) and the impact of th aerosol radiative effect on calculating RFari (lower panels).  Table A1). It is noteworthy that the standard deviations listed in Table A1 indicate the year-to-year variability of the global average, and those shown in Figure 3 represent the year-to-year variability of every model grid. Thus, the global averages of the standard deviations shown  Table A1. For a local region, the semi-direct effect standard deviation is usually much larger than the 10-year average. This suggests that it is very difficult for a local region to yield a reliable multi-year average of the semi-direct effect, even with a long-term simulation (e.g.,100-year simulation). The standard deviation from CF A RAD-BASE is similar to that from CF A ALL-TMY , and this result indicates that the magnitude of the year-to-year variability (i.e., the standard deviation) of the semi-direct effect is relatively stable. There are many other methods for calculating the semi-direct effect (e.g., CcF A RAD-BASE , CcF RAD-BASE , CcF A ALL-TMY and CcF ALL-TMY ). It is necessary to point out that CcF A RAD-BASE and CcF RAD-BASE are similar to CF A RAD-BASE , and CcF A ALL-TMY and CcF ALL-TMY are similar to CF A ALL-TMY (not shown).
ence (0.13 W m −2 ) is less than their corresponding standard deviations, which mated from the global averages of each year (0.18 and 0.15 W m −2 , Table A1). It worthy that the standard deviations listed in Table A1 indicate the year-to-year va of the global average, and those shown in Figure 3 represent the year-to-year va of every model grid. Thus, the global averages of the standard deviations shown in (4.06 and 4.12 W m −2 ) are dozens of times larger than those listed in Table A1. Fo region, the semi-direct effect standard deviation is usually much larger than the average. This suggests that it is very difficult for a local region to yield a reliabl year average of the semi-direct effect, even with a long-term simulation (e.g.,100-y ulation). The standard deviation from CFA RAD-BASE is similar to that from CFA ALLthis result indicates that the magnitude of the year-to-year variability (i.e., the s deviation) of the semi-direct effect is relatively stable. There are many other met calculating the semi-direct effect (e.g., CcFA RAD-BASE , CcF RAD-BASE , CcFA ALL-TMY and TMY ). It is necessary to point out that CcFA RAD-BASE and CcF RAD-BASE are similar to CFA and CcFA ALL-TMY and CcF ALL-TMY are similar to CFA ALL-TMY (not shown). This paragraph analyzes anthropogenic aerosol indirect effects. Both ΔC ΔCcFA can be used to quantify aerosol indirect effects on warm clouds induced Twomey effect [9]. Here, in order to exclude semi-direct effect, "Δ" only denotes ference between two simulations with and without Twomey effect (i.e., TMY − BA ALL − RAD). CcF TMY−BASE is almost the same as CcFA TMY−BASE , and CcF ALL−RAD is alm same as CcFA ALL−RAD (not shown). This suggests that the impact of natural aerosol mating aerosol indirect effects is negligible. Here, only ΔCcFA (i.e., CcFA TMY− CcFA ALL−RAD ) are analyzed ( Figure 4). The ΔCcFA can be decomposed into ΔcFAC an [ΔCcFA = Δ(CcFA − CFA) + ΔCFA = ΔcFAC + ΔCFA]. Because both cFAC BASE and cFA zero, and both cFAC TMY and cFAC ALL denote the instantaneous Twomey effect (i.e. In other words, the anthropogenic aerosol indirect effects (i.e., CcFA TMY−B CcFA ALL−RAD ) can be decomposed into the instantaneous Twomey effect (i.e., cFAC cFAC ALL ) and subsequent changes in cloud forcing induced by the Twomey effect BASE and CFA ALL-RAD ). Figure 4 shows these variables. Both cFAC TMY and cFAC ALL give This paragraph analyzes anthropogenic aerosol indirect effects. Both ∆CcF and ∆CcF A can be used to quantify aerosol indirect effects on warm clouds induced by the Twomey effect [9]. Here, in order to exclude semi-direct effect, "∆" only denotes the difference between two simulations with and without Twomey effect (i.e., TMY − BASE and ALL − RAD). CcF TMY−BASE is almost the same as CcF A TMY−BASE , and CcF ALL−RAD is almost the same as CcF A ALL−RAD (not shown). This suggests that the impact of natural aerosol on estimating aerosol indirect effects is negligible. Here, only ∆CcF A (i.e., CcF A TMY−BASE and CcF A ALL−RAD ) are analyzed (Figure 4) and CF A ALL-RAD show that there are a few statistically significant regions, the comparison between CF A TMY-BASE and CF A ALL-RAD shows that these statistically significant regions are not fixed. In short, the rapid adjustment in cloud forcing (i.e., ∆CF A ) is obviously affected by model internal year-to-year variability. It is clear that the perturbation of the anthropogenic aerosol indirect effects (∆CcF A , upper panels of Figure 4) depends almost entirely on its rapid adjustment (∆CF A , lower panels of Figure 4). Similarly to the semidirect effect, it is very difficult for a local region to yield a reliable multi-year average of ∆CF A . Therefore, it is necessary to decompose anthropogenic aerosol indirect effects into a robust instantaneous Twomey effect (i.e., definition-based Twomey effect) and unstable subsequent changes in cloud forcing induced by the Twomey effect. With the benefit of this decomposition, the model intercomparison study can focus on the robust instantaneous Twomey effect.
average RFaci of −0.10 W m −2 . All regions of cFAC TMY and cFAC ALL are statistically significa and cFAC TMY is almost the same as cFAC ALL . This result indicates that the simulated RF (i.e., instantaneous Twomey effect) is very robust. The rapid adjustment in cloud forci estimated by CFA TMY−BASE shows global cooling at −0.07 W m −2 , whereas CFA ALL−RAD show global warming at 0.06 W m −2 . It should be noted that their difference (0.13 W m −2 ) is le than their standard deviations of the global average (0.16 and 0.17 W m −2 , Table A1). Fu thermore, although both CFA TMY-BASE and CFA ALL-RAD show that there are a few statistica significant regions, the comparison between CFA TMY-BASE and CFA ALL-RAD shows that the statistically significant regions are not fixed. In short, the rapid adjustment in cloud fo ing (i.e., ΔCFA) is obviously affected by model internal year-to-year variability. It is cle that the perturbation of the anthropogenic aerosol indirect effects (ΔCcFA, upper pan of Figure 4) depends almost entirely on its rapid adjustment (ΔCFA, lower panels of Figu  4). Similarly to the semi-direct effect, it is very difficult for a local region to yield a reliab multi-year average of ΔCFA. Therefore, it is necessary to decompose anthropogenic aer sol indirect effects into a robust instantaneous Twomey effect (i.e., definition-bas Twomey effect) and unstable subsequent changes in cloud forcing induced by t Twomey effect. With the benefit of this decomposition, the model intercomparison stu can focus on the robust instantaneous Twomey effect.   Figure 5 compares the seasonal variations in anthropogenic AOD, RFari, and corresponding radiative forcing efficiency (RFari/AOD). The radiative forcing efficiency (hereafter "efficiency") is used to indicate the impact of environmental properties (such as surface albedo, solar insolation and even clouds) on the RFari [26]. Anthropogenic AOD is highest in the Northern Hemisphere summer (0.037) and lowest in winter (0.027). Both aF ACc RAD (with the impact of natural aerosol) and aF Cc RAD (without the impact of natural aerosol) show the strongest RFari in summer (−0.25 and −0.40 W m −2 ) and the weakest (less negative) RFari in winter (−0.15 and −0.26 W m −2 ). The efficiency also shows notable seasonal variations. In the Northern Hemisphere, there is more snow cover and less sunshine during the winter season. As expected, the global average efficiency is weakest in winter. This is also a reason for the weakest RFari during the winter season. In the Southeast Asia region, the efficiency in summer is weaker than that in other seasons. This might be caused by there being relatively more clouds during the summer season. Under this influence, the global mean efficiency is strongest in autumn, not in summer. The global average efficiency without the influence of natural aerosol is approximately −10 W m −2 per unit anthropogenic AOD, and this value is close to the estimate (−12 W m −2 per unit AOD) from an offline radiative transfer model with MACv2 [26].

Seasonal Variability
Atmosphere 2021, 12, x FOR PEER REVIEW 10 of 19 Figure 5 compares the seasonal variations in anthropogenic AOD, RFari, and corresponding radiative forcing efficiency (RFari/AOD). The radiative forcing efficiency (hereafter "efficiency") is used to indicate the impact of environmental properties (such as surface albedo, solar insolation and even clouds) on the RFari [26]. Anthropogenic AOD is highest in the Northern Hemisphere summer (0.037) and lowest in winter (0.027). Both aFACc RAD (with the impact of natural aerosol) and aFCc RAD (without the impact of natural aerosol) show the strongest RFari in summer (−0.25 and −0.40 W m −2 ) and the weakest (less negative) RFari in winter (−0.15 and −0.26 W m −2 ). The efficiency also shows notable seasonal variations. In the Northern Hemisphere, there is more snow cover and less sunshine during the winter season. As expected, the global average efficiency is weakest in winter. This is also a reason for the weakest RFari during the winter season. In the Southeast Asia region, the efficiency in summer is weaker than that in other seasons. This might be caused by there being relatively more clouds during the summer season. Under this influence, the global mean efficiency is strongest in autumn, not in summer. The global average efficiency without the influence of natural aerosol is approximately −10 W m −2 per unit anthropogenic AOD, and this value is close to the estimate (−12 W m −2 per unit AOD) from an offline radiative transfer model with MACv2 [26].  average RFaci (cF AC TMY ) in winter, spring, summer, and autumn are −0.06, −0.10, −0.15, and −0.09 W m −2 , respectively. The seasonal variability of RFaci is stronger than that of RFari. Similar to the efficiency for RFari, the efficiency for the Twomey effect was calculated by RFaci / (rNc −1). The RFaci efficiency also shows notable seasonal variations. In every season, the RFaci efficiency over the ocean is usually larger than that over the land-a result that is in agreement with the spatial distribution of shortwave cloud forcing (not shown). In other words, the RFaci efficiency usually enhances (more negative) with increasing cloud forcing. In the East Asia region (i.e., an area with a high anthropogenic aerosol burden), shortwave cloud forcing is strongest in summer (not shown). As a result, the RFaci efficiency is also strongest in summer. It should be noted that, in the East Asia region, the RFari efficiency is weakest in summer, owing to stronger cloud forcing ( Figure 5). This is the reason why the seasonal variability of RFaci is stronger than that of RFari. The seasonal variability of the anthropogenic aerosol Twomey effect is presented in Figure 6. Consistent with anthropogenic AOD (Figure 5, top row), the droplet number increasing factor (rNc) is largest in the Northern Hemisphere in summer (1.077) and smallest in winter (1.071). Regionally, rNc peaks over East Asia in every season. The global average RFaci (cFAC TMY ) in winter, spring, summer, and autumn are −0.06, −0.10, −0.15, and −0.09 W m −2 , respectively. The seasonal variability of RFaci is stronger than that of RFari. Similar to the efficiency for RFari, the efficiency for the Twomey effect was calculated by RFaci / (rNc −1). The RFaci efficiency also shows notable seasonal variations. In every season, the RFaci efficiency over the ocean is usually larger than that over the land-a result that is in agreement with the spatial distribution of shortwave cloud forcing (not shown). In other words, the RFaci efficiency usually enhances (more negative) with increasing cloud forcing. In the East Asia region (i.e., an area with a high anthropogenic aerosol burden), shortwave cloud forcing is strongest in summer (not shown). As a result, the RFaci efficiency is also strongest in summer. It should be noted that, in the East Asia region, the RFari efficiency is weakest in summer, owing to stronger cloud forcing ( Figure 5). This is the reason why the seasonal variability of RFaci is stronger than that of RFari.  Figure 5 but for the present-day (year 2000) droplet number increasing factor (rNc, upper panels), the instantaneous radiative forcing from aerosol-cloud interactions (RFaci, middle panels), and the efficiency for aerosolcloud interactions (lower panels). The area with a low anthropogenic aerosol burden (rNc < 1.07) is masked. Figure 7 shows the anthropogenic aerosol forcing data used in this study. The global average anthropogenic AOD in 2000 and 1975 are almost the same (0.032). Their difference (2000−1975) is −0.0007. This difference indicates that the global average AOD in the year 2000 is slightly less than that in 1975. Notably, there have been a few studies that estimated anthropogenic aerosol forcing based on MACv2-SP (e.g., [13,26]), and the year 2005 was chosen as the PD in these studies. However, in our study, the year 2000 was chosen as the PD rather than 2005, because the global average AOD in 2005 was 0.034 (not shown), which is obviously greater than that in 1975. In this study, the conclusion about the spatial pattern can be better explained if the global average AOD from the PD year is slightly decreased as compared to 1975. In other words, the comparison between 1975 and 2000 can better explain the conclusion of this paper. The global average rNc in 2000 (1.075) is also slightly less than that in 1975 (1.076). For the period from 1975 to 2000, the spatial pattern of anthropogenic AOD and rNc is noticably different. Anthropogenic aerosol pollution decreases over Europe and North America but increases over East and South Asia.  Figure 5 but for the present-day (year 2000) droplet number increasing factor (rNc, upper panels), the instantaneous radiative forcing from aerosol-cloud interactions (RFaci, middle panels), and the efficiency for aerosol-cloud interactions (lower panels). The area with a low anthropogenic aerosol burden (rNc < 1.07) is masked.   Figure 7). Furthermore, the global average cFAC increases (more negative) by −0.008 W m −2 from 1975 to 2000, which is also inconsistent with the trend of the global average rNc that slightly decreased from 1975 to 2000 (Figure 7). These results suggest that under the same global mean anthropogenic AOD and rNc values, changing anthropogenic aerosol spatial patterns have a clear impact on the global average RFari and RFaci. From 1975 to 2000, with major anthropogenic aerosol emissions occurring in East and South Asia instead of in Europe and North America, the global average anthropogenic aerosol RF (RFari + RFaci) enhanced (more negative) by ~6%. Each of FAC ALL-BASE , FAC PAT-BASE and FA-C ALL-PAT show that rapid adjustments are obviously affected by model internal year-to-year variability. Therefore, it is difficult to detect the change in the global average anthropogenic aerosol ERF (i.e., RF + rapid adjustments) caused by the spatial shift in anthropogenic aerosol. This is the reason why the EOF was decomposed into robust RF and unstable rapid adjustments in this section. ∆F AaCc = ∆(F AaCc − F ACc ) + ∆(F ACc − F AC ) + ∆F AC = ∆aF ACc + ∆cF AC + ∆F AC . In other words, the anthropogenic aerosol ERF (∆F AaCc ) can be decomposed into the RFari (aF ACc ), RFaci (cF AC ), and rapid adjustment (∆F AC ). Figure 8 shows comparisons of RFari (aF ACc and aF Cc ), RFaci (cF AC ), and rapid adjustment (∆F AC ) between the ALL (2000) and PAT (1975) experiments. From 1975 to 2000, both RFari and RFaci decrease (less negative) in Europe and North America but increase (more negative) in East and South Asia. This result is in agreement with the spatial changes in anthropogenic AOD and rNc (Figure 7). In terms of the global average, both aF ACc and aF Cc grew stronger (more negative) by −0.015 W m −2 from 1975 to 2000. These changes are very robust because the estimated aF ACc and aF Cc are scarcely affected by model internal year-to-year variability. Notably, this result is inconsistent with the fact that the global average AOD slightly decreased from 1975 to 2000 (Figure 7). Furthermore, the global average cF AC increases (more negative) by −0.008 W m −2 from 1975 to 2000, which is also inconsistent with the trend of the global average rNc that slightly decreased from 1975 to 2000 (Figure 7). These results suggest that under the same global mean anthropogenic AOD and rNc values, changing anthropogenic aerosol spatial patterns have a clear impact on the global average RFari and RFaci. From 1975 to 2000, with major anthropogenic aerosol emissions occurring in East and South Asia instead of in Europe and North America, the global average anthropogenic aerosol RF (RFari + RFaci) enhanced (more negative) by~6%. Each of F AC ALL-BASE , F AC PAT-BASE and F AC ALL-PAT show that rapid adjustments are obviously affected by model internal year-to-year variability. Therefore, it is difficult to detect the change in the global average anthropogenic aerosol ERF (i.e., RF + rapid adjustments) caused by the spatial shift in anthropogenic aerosol. This is the reason why the EOF was decomposed into robust RF and unstable rapid adjustments in this section.

Impact of Spatial Distributions
In order to determine why the global average anthropogenic aerosol RF is enhanced (more negative) even with a slight decrease in anthropogenic aerosol, the corresponding efficiencies are shown in Figure 9. The efficiencies from the ALL (2000) experiment are generally similar to those from the PAT (1975) experiment. Compared to the efficiencies in 2000, some high-efficiency areas over the Pacific Ocean in 1975 were masked, owing to a low anthropogenic aerosol burden (AOD < 0.005 or rNc < 1.07). Regionally, the radiative efficiencies for aF ACc , aF Cc , and cF AC over East and South Asia and their adjacent oceans are generally more negative than those over Europe and North America. This is the reason why, for the period from 1975 to 2000, the global average RF (RFari + RFaci) is enhanced (more negative) by~6%, even with a slight decrease in anthropogenic aerosols. In order to determine why the global average anthropogenic aerosol RF is enhanced (more negative) even with a slight decrease in anthropogenic aerosol, the corresponding efficiencies are shown in Figure 9. The efficiencies from the ALL (2000) experiment are generally similar to those from the PAT (1975) experiment. Compared to the efficiencies in 2000, some high-efficiency areas over the Pacific Ocean in 1975 were masked, owing to a low anthropogenic aerosol burden (AOD < 0.005 or rNc < 1.07). Regionally, the radiative efficiencies for aFACc, aFCc, and cFAC over East and South Asia and their adjacent oceans are generally more negative than those over Europe and North America. This is the reason why, for the period from 1975 to 2000, the global average RF (RFari + RFaci) is enhanced (more negative) by ~6%, even with a slight decrease in anthropogenic aerosols.

Conclusions and Discussion
In this study, the prescribed anthropogenic aerosol forcing recommended by CMIP6 was implemented in the GAMIL model. Although the anthropogenic aerosol radiative effects were estimated, we have not paid attention to the similarities and differences between our estimates and those reported in other studies. This study focuses on how to

Conclusions and Discussion
In this study, the prescribed anthropogenic aerosol forcing recommended by CMIP6 was implemented in the GAMIL model. Although the anthropogenic aerosol radiative effects were estimated, we have not paid attention to the similarities and differences between our estimates and those reported in other studies. This study focuses on how to take full advantage of the prescribed anthropogenic aerosol forcing.
With reduced complexity of anthropogenic aerosol forcing, each component of the anthropogenic aerosol ERF can be estimated, and the RFari and RFaci can be estimated by all possible calculation methods. Simulation results show that both RFaci and RFari from a present-day simulation (i.e., double radiation calls) are very robust. These RFaci (e.g., cF AC ALL ) and RFari (e.g., aF ACc ALL ) are scarcely affected by model internal year-to-year variability and can be used as offline simulation results. However, the anthropogenic aerosol RFari determined by the difference in total aerosol RFari between preindustrial and present-day simulations (e.g., AaF Cc ALL−BASE , a commonly used method) is obviously affected by model internal year-to-year variability. This suggests that, if possible (e.g., using prescribed anthropogenic aerosol forcing), it is preferable to diagnose the RFari at each model time step. Simulation results also show that the impact of natural aerosols on calculating RFari is notable. Because the preindustrial aerosol (i.e., natural aerosol) level used for climate models is full of uncertainty [28], the impact of natural aerosols on calculating RFari might differ widely among climate models. If possible, it is also necessary to compare the RFari without the influence of natural aerosols. The RFaci-calculated by double radiation calls-is the definition-based Twomey effect (i.e., instantaneous Twomey effect), which was previously impossible to diagnose using the default model with physically based aerosol-cloud interactions. More importantly, the perturbation of the ERF depends almost entirely on its rapid adjustment (i.e., ERF − RF). If possible, it is better to decompose the ERF into stable components (i.e., RFari and RFaci) and unstable components (i.e., rapid adjustments).
In terms of the robust RFari and RFaci, the anthropogenic aerosol radiative effects can be estimated from various other perspectives. For instance, the seasonal variability of RFari and RFaci can be analyzed. The seasonal variability of the global average RFaci is much stronger than that of RFari. This can be explained by the corresponding radiative forcing efficiency, which indicates the impact of environmental properties (such as surface albedo, solar insolation and even clouds). Another example is the impact of the spatial shift in anthropogenic aerosol. For the period from 1975 to 2000, anthropogenic aerosol pollution decreased over Europe and North America but increased over East and South Asia. Excluding the unstable components of the ERF (i.e., rapid adjustments), its stable components (i.e., RFari and RFaci) show a clear response to the spatial shift in anthropogenic aerosols. The radiative forcing efficiencies for RFari and RFaci over East and South Asia and its adjacent oceans are generally stronger than those over Europe and North America, especially for RFaci. As a result, from 1975 to 2000, the global average RF (RFari + RFaci) was enhanced (more negative) by~6%, even with a slight decrease in the global average anthropogenic aerosols. In short, the robust RFari, RFaci, and corresponding efficiencies are very useful for analyzing anthropogenic aerosol radiative effects.
One should keep in mind that the conclusion, which comes from prescribed anthropogenic aerosol forcing, omits the coupling between synoptic systems and anthropogenic aerosol. For instance, rainier days are cloudier, but also have lower aerosol levels. If considering the rainy effect, over Southeast Asia, the RFaci and its efficiency might not be so strong in summer, which is also the rainy season ( Figure 6). On the other hand, it is difficult for climate models with physically based anthropogenic aerosol processes to directly calculate the robust components of the ERF (i.e., RFari and RFaci). Furthermore, it is clear that the efficiency is dependent on the modeled cloud properties. Because the differences in cloud properties among climate models are notable, the spatial pattern and seasonal variability of efficiency from the GAMIL model might be different from other models. The differences in estimating CMIP6 anthropogenic aerosol radiative effects among climate models can be explained by the differences in efficiency. Table A1 lists the global annual mean radiative variables from all experiments. As a supplement to the main text, this section introduces all possible calculation methods for estimating anthropogenic aerosol radiative effects based on the simulation results listed in Table A1. Meanwhile, the differences among these calculation methods are discussed.    There is an excess of methods for calculating RFari, and these methods can be classified into two categories. Firstly, the RFari can be diagnosed as the difference in all-sky total aerosol forcing between two simulations with and without anthropogenic aerosols (∆AaF Cc , AaF Cc = F AaCc − F Cc ). This method is the commonly used method introduced by Ghan (2013), and can be employed in climate models with physically based anthropogenic aerosol processes (i.e., anthropogenic aerosol mixed with natural aerosol) [9]. Using this method, the RFari can be quantified by AaF Cc RAD−BASE , AaF Cc ALL−TMY , and AaF Cc ALL−BASE . The differences between these three variables are small and not significant. The clear-sky RFari (i.e., ∆AaF) can be quantified by AaF RAD−BASE , AaF ALL−TMY , and AaF ALL−BASE . The differences between these three variables are also small and not significant. Secondly, the RFari can be obtained from a simulation with prescribed anthropogenic aerosol optical properties (e.g., the ALL or RAD experiment). Based on the ALL or RAD experimental results, both aF ACc (aF ACc = F AaCc − F ACc ), aF Cc (aF Cc = F aCc − F Cc ), and aF AC (aF AC = F AaC − F AC ) can represent the all-sky RFari. The aF Cc is obviously more negative than the aF ACc because the impact of natural aerosols on calculating the all-sky RFari is removed. The difference between aF ACc and aF AC shows the impact of the Twomey effect on calculating RFari, which is negligible. Both aF A (aF A = F Aa −F A ) and aF (aF = F a − F) can represent the clear-sky RFari. The obvious difference between aF A and aF (i.e., aFdA = aF A − aF) indicates the impact of natural aerosols on calculating the clear-sky RFari. It is noteworthy that all these anthrophonic aerosol direct radiative forcing variables (i.e., aFxx, where the subscript "XX" refers to background radiative forcing factor) from the RAD experiment are almost the same as those from the ALL experiment. This also suggests that the impact of the anthropogenic aerosol Twomey effect (i.e., the difference between the RAD and ALL experiments) on estimating RFari is negligible.
The anthropogenic aerosol indirect effects on warm clouds are often estimated by their impact on shortwave cloud forcing, which is the difference in CcF Aa (CcF Aa = F AaCc − F Aa ), CcF A (CcF A = F ACc − F A ) or CcF (CcF = F Cc − F) between two simulations with and without anthrophonic aerosol. Ghan (2013) pointed out that ∆CcF Aa is positively biased due to the impact of the anthrophonic aerosol direct radiative effect [9]. This is the reason why CcF Aa ALL−BASE is obviously larger than CcF A ALL−BASE and CcF ALL−BASE . Because the TMY experiment does not consider the anthrophonic aerosol direct radiative effect, CcF Aa TMY−BASE is the same as CcF A TMY−BASE , and they are close to CcF TMY−BASE . In terms of definition, the Twomey effect is the instantaneous radiative forcing (i.e., RFaci). The aerosol indirect effects estimated by ∆CcF and ∆CcF A are not the exact Twomey effect because of the subsequent changes in cloud forcing from rapid adjustments. Both CcF A TMY−BASE and CcF A ALL−RAD include the rapid adjustments in cloud forcing induced by the Twomey effect. Compared to CcF A TMY−BASE , CcF A ALL−BASE also includes rapid adjustments in cloud forcing induced by the anthrophonic aerosol direct radiative effect (i.e., semi-direct effect). With MACv2-SP, the RFaci can be calculated by double radiation calls at each radiation time step. Based on the ALL or TMY experimental results, both cF AaC (cF AaC = CcF Aa −CF Aa = F AaCc − F AaC ) and cF AC (cF AC = CcF A − CF A = F ACc − F AC ) can represent RFaci (i.e., the definition-based Twomey effect). The comparison between cF AaC and cF AC indicates that the impact of the anthropogenic aerosol direct radiative effect on estimating RFaci is negligible. The difference between the anthropogenic aerosol indirect effects (i.e., the Twomey effect and corresponding rapid adjustments) estimated by ∆CcF A (e.g., CcF A TMY−BASE ) and the Twomey effect estimated by cF AC (e.g., cF AC TMY ) is the rapid adjustments in cloud forcing induced by the Twomey effect, which cannot be ignored. In other words, even if the lifetime effect is excluded, the definition-based Twomey effect cannot be approximated by the difference in cloud forcing between two simulations with and without the Twomey effect. Finally, it is necessary to point out that the modeled RFaci (i.e., cF AaC or cF AC ) from the TMY experiment is the same as that from the ALL experiment. This also suggests that the impact of the anthropogenic aerosol direct radiative effect (i.e., the difference between the TMY and ALL experiments) on estimating RFaci is negligible. The impact of the anthropogenic aerosol direct radiative effect on estimating the aerosol indirect effects on warm clouds (e.g., CcF Aa ALL−BASE − CcF A ALL−BASE ) is obvious, owing to the semi-direct effect. Attention should be paid to this difference.
This paragraph introduces the calculation methods for estimating the anthropogenic aerosol ERF, RF and rapid adjustments (ERF − RF). Unlike RF, the ERF and rapid adjustments must be estimated by the difference between two simulations with and without anthropogenic aerosol forcing. The anthropogenic aerosol ERF is calculated as ∆F AaCc . With the benefit of MACv2-SP, ∆F AaCc can be decomposed into ∆(F AaCc − F AC ) and ∆F AC .
It should be noted that the F AaCc − F AC from the simulation without anthropogenic aerosol is zero and the F AaCc − F AC from the simulation with anthropogenic aerosol represents RF (i.e., RFari + aci). Thus, ∆F AC indicates the rapid adjustments. The ERFari + aci is quantified by F AaCc ALL−BASE . The corresponding rapid adjustment is quantified by F AC ALL−BASE . Both RFari (aF ACc = F AaCc − F ACc , aF Cc = F aCc − F Cc , or aF AC = F AaC − F AC ) and RFaci (cF AaC = F AaCc − F AaC or cF AC = F ACc − F AC ) can be calculated based on the ALL experiment. It should be noted that RFari + RFaci may not be equal to RFari + aci (F AaCc ALL − F AC ALL ), except for aF AC ALL (RFari) + cF AaC ALL (RFaci) = aF ACc ALL (RFari) + cF AC ALL (RFaci) = (F AaCc − F AC ) ALL (RFari + aci). Because the rapid adjustments from aerosol-radiation interactions and the rapid adjustments from aerosol-cloud interactions will be mixed at each time step in the simulation, it is impossible to separate them in the ALL experiment. Another simulation, which switches off the Twomey effect or direct radiative effect is needed for estimating the rapid adjustments from the direct radiative effect or Twomey effect. Both F AC RAD−BASE and F AC ALL−TMY can represent the rapid adjustment from aerosol-radiation interactions. The ∆F AC can be decomposed into ∆CF A (CF A = F AC − F A ) and ∆F A . The ∆CF A (CF A RAD−BASE or CF A ALL−TMY ) indicates the anthropogenic aerosol semi-direct effect. The absolute value of the global average ∆F A (F A RAD−BASE or F A ALL−TMY ) is usually very small, and therefore, neglectable. As such, the anthropogenic aerosol rapid adjustments from aerosol-radiation interactions are often approximated by the semi-direct effect [8]. Both F AC TMY−BASE and F AC ALL−RAD can represent the rapid adjustment from aerosol-cloud interactions. It is noteworthy that the year-to-year variability (standard deviation in brackets) of rapid adjustments (i.e., ∆F AC ) is obviously larger than the annual mean. This is the reason why more attention has been paid to the stable RFari and RFaci in this study. The 10-year simulation is sufficient for calculating the stable RFari and RFaci.