Snow-induced buffering in aerosol–cloud interactions

Complex aerosol–cloud–precipitation interactions lead to large differences in estimates of aerosol impacts on climate among general circulation models (GCMs) and satellite retrievals. Typically, precipitating hydrometeors are treated diagnostically in most GCMs, and their radiative effects are ignored. Here, we quantify how the treatment of precipitation influences the simulated effective radiative forcing due to aerosol–cloud interactions (ERFaci) using a stateof-the-art GCM with a two-moment prognostic precipitation scheme that incorporates the radiative effect of precipitating particles, and we investigate how microphysical process representations are related to macroscopic climate effects. Prognostic precipitation substantially weakens the magnitude of ERFaci (by approximately 54 %) compared with the traditional diagnostic scheme, and this is the result of the increased longwave (warming) and weakened shortwave (cooling) components of ERFaci. The former is attributed to additional adjustment processes induced by falling snow, and the latter stems largely from riming of snow by collection of cloud droplets. The significant reduction in ERFaci does not occur without prognostic snow, which contributes mainly by buffering the cloud response to aerosol perturbations through depleting cloud water via collection. Prognostic precipitation also alters the regional pattern of ERFaci, particularly over northern midlatitudes where snow is abundant. The treatment of precipitation is thus a highly influential controlling factor of ERFaci, contributing more than other uncertain “tunable” processes related to aerosol–cloud–precipitation interactions. This change in ERFaci caused by the treatment of precipitation is large enough to explain the existing difference in ERFaci between GCMs and observations.


Introduction
Aerosols play significant roles in the climate system (Twomey, 1977;Albrecht, 1989) by modifying the radiation budget (aerosol-radiation interactions, ARIs) and the hydrological cycle through interactions with clouds (aerosolcloud interactions, ACIs). Quantitative estimates of anthropogenic aerosol forcing, however, are still largely uncertain  because of the complex interactions among aerosols, clouds, and climate across wide spatiotemporal scales (Mülmenstädt and Feingold, 2018). Reducing these uncertainties associated with the effect of aerosol forcing on climate is one of the most challenging issues in climate science (Seinfeld et al., 2016).
A key uncertainty arises from the complex response of clouds to aerosol perturbations (Wang et al., 2012). Clouds are considered to respond to perturbed aerosols in two opposing ways, i.e., the so-called "cloud lifetime" effect (Albrecht, 1989) and the "buffered system" effect (Stevens and Feingold, 2009), in a regime-dependent manner (Wood, 2012;Michibata et al., 2016). The cloud water susceptibility to aerosols depends strongly upon cloud type (Christensen et al., 2016), as well as ambient environmental conditions (Toll et al., 2019), which results in non-monotonic cloud responses  and therefore diverse impacts on climate (Chen et al., 2014).
These observational findings are also supported by process modeling studies using large-eddy simulations (Lebo and Feingold, 2014;Seifert et al., 2015). General circulation models (GCMs), however, show a large spread in cloud susceptibility to aerosols Zhang et al., 2016), and they tend to overestimate the magnitude of ACI compared with satellite retrievals (Malavelle et al., 2017). This means that current GCMs are not able to reproduce the buffering of cloud responses to aerosol perturbations (Jing et al., 2019). Aerosol-induced radiative forcing at the top of the atmosphere (TOA) that includes rapid adjustments caused by ACI, termed effective radiative forcing (ERF aci ), varies widely among GCMs (Shindell et al., 2013;Zelinka et al., 2014). This results in a "best estimate" of global annual mean ERF aci of −0.45 W m −2 with a 90 % confidence interval of −1.2 to 0.0 W m −2 , as reported in the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC AR5). This uncertainty range has remained large (e.g., Bellouin et al., 2020) since the early IPCC reports.
As a consequence of the challenges described above, GCMs tend to show more negative ERF aci than that inferred from satellite retrievals (Quaas et al., 2009;Chen et al., 2014) even though retrieval errors (Ma et al., 2018) are considered (Michibata and Suzuki, 2020). This suggests that current GCMs may be missing a compensating warming effect caused by aerosols. The "missing warming" in GCMs may be solved by taking aerosol effects on (i) deep convective clouds (Wang et al., 2011) and (ii) mixed-phase clouds ) into consideration, as these effects can modify the ice microphysics due to aerosols and also lead to an adjustment in the longwave component (Lohmann, 2017). A recent multi-model analysis (Heyn et al., 2017) demonstrated that simpler GCMs that parameterize the aerosol effect on liquid-phase clouds alone have negligibly small longwave ERF, whereas more sophisticated GCMs that include microphysical adjustments of ice-and mixed-phase clouds as well as liquid-phase clouds produce larger-magnitude ERF values for both the terrestrial (ERF LW ) and solar (ERF SW ) components. The changes to ERF LW and ERF SW were found to nearly cancel each other out and result in a net ERF (ERF Net ) of a magnitude that is similar to that generated by the simpler GCMs. The robustness of this near cancelation, however, largely depends on how microphysical processes in ice-and mixed-phase clouds, which are typically much more complex than in liquid-phase clouds (Lohmann, 2017), are represented in GCMs.
Among these processes, precipitation processes involving falling hydrometeors (i.e., rain and snow) are particularly simplified in current GCMs, which is likely to lead to nonnegligible uncertainty in ERF aci . In general, precipitation is treated diagnostically in GCMs (hereinafter "DIAG"), with precipitation being immediately removed from the atmosphere within a single model time step. This over-weights autoconversion relative to accretion to produce precipitation (Posselt and Lohmann, 2008), which results in the pronounced sensitivity of cloud water to aerosols because autoconversion is the only process that directly depends on aerosols (Gettelman et al., 2013). Snow also has significant effects on collection processes among other hydrometeors (Sant et al., 2015), as well as on atmospheric circulation (Li et al., 2014). However, snow-induced impacts on ERF aci are much less understood (Waliser et al., 2011) be-cause extremely limited GCMs incorporate prognostic precipitation with the radiative effects of falling hydrometeors (see discussion in Michibata et al., 2019).
This study investigates this unexplored area of ACI, with a particular focus on precipitation (rain and snow) processes and their impacts on ERF aci and with the goal of advancing our understanding of the fundamental linkage of microphysical process representations to their macroscopic climate effects. For this purpose, we use a recently developed global aerosol-climate model, MIROC6-SPRINTARS (Tatebe et al., 2019), which is implemented with a two-moment prognostic precipitation scheme (hereinafter "PROG") that includes the radiative effects of precipitation . Through a comparison with the traditional DIAG scheme, we use the PROG-scheme model to identify the source of discrepancies in ERF aci between GCMs and satellite observations that are related to precipitation processes. A suite of sensitivity experiments is also performed with the model to isolate the relative contributions of different microphysical processes to ERF aci and to quantify how uncertainties inherent in these processes translate to ERF aci uncertainty. This single-model approach has the advantage of not being affected by varying physics representations, as in the case of multi-model analysis (see "Materials and methods").

MIROC6-SPRINTARS aerosol-climate model
We used version 6 of the global aerosol-climate model, MIROC6-SPRINTARS (Tatebe et al., 2019) in this work. The aerosol module, SPRINTARS , predicts the mass mixing ratios of the main aerosol species in the troposphere (black carbon, organic matter, sulfate, soil dust, and sea salt) and gas-phase precursors of sulfate (sulfur dioxide and dimethyl sulfide) and organic matter (terpene and isoprene). The cloud microphysics are based on the prognostic probability density function (PDF) scheme, which represents the subgrid-scale variability of temperature and total water content (Watanabe et al., 2009) and is coupled to an ice microphysics scheme (Wilson and Ballard, 1999). The model treats cloud water and ice using a two-moment representation, by prognosing both mass and number mixing ratios . Cloud droplet nucleation is represented by a Köhler-theory-based parameterization (Abdul-Razzak and Ghan, 2000). Note that although the standard version of MIROC6-SPRINTARS uses Berry's autoconversion parameterization (Berry, 1968), results presented in this paper apply an alternative formulation based on Khairoutdinov and Kogan (2000), which is used in the PROG version  for a robust comparison (described later). The default MIROC6-SPRINTARS model treats pre-cipitation diagnostically, and its radiative effect is not considered.
We also used another version of the model that employs a prognostic precipitation framework . This version prognoses mass and number mixing ratios for both rain and snow, as well as cloud liquid and ice condensates (full two-moment scheme). Microphysical processes are calculated iteratively by using sub-time steps (60 s), except for the sedimentation of precipitation, which can be shorter subject to the vertical Courant-Friedrichs-Lewy (CFL) criteria. The PROG scheme considers the radiative effect of precipitating hydrometeors. The particle shapes of solid hydrometeors are prescribed by assuming hexagonal columns for cloud ice and dendrite crystals for snow bulk categories, which correspond to elements of a radiation table (Yang et al., 2013). For more details, please refer to the model description for the latest version of MIROC6 (Tatebe et al., 2019;Michibata et al., 2019).

Experimental setup
We performed sets of simulations with different aerosol emissions for the years 2000 (present day, PD) and 1850 (pre-industrial, PI). All simulations used prescribed climatological sea surface temperature and sea ice. Simulations were integrated for 6 years, with the last 5 years being used in the subsequent analysis. The model resolution was T85L40 (ca. 1.4 • resolution in longitude and latitude with 40 vertical levels), and the standard model time step was 12 min. The modeled cloud cover and its horizontal distribution ( Fig. S1) are in good agreement with CALIPSO-GOCCP satellite data (Chepfer et al., 2010) in PROG but underestimated in DIAG, which were evaluated using the COSP2 satellite simulator package (Swales et al., 2018) using an additional full 1-year run under the PD conditions.
Additional sensitivity experiments were performed, by replacing the precipitation framework, changing the liquid autoconversion scheme, and masking ice microphysics and aerosol freezing processes (discussed later in Sect. 4). To quantify how the treatment of precipitation influences the simulated ERF aci , two experiments, i.e., one that incorporates a prognostic treatment of rain but not snow (PRDS) and another that applies the full prognostic version (PROG), were compared with the default simulation with diagnostic precipitation (DIAG). To evaluate the snow radiative effect, a pair of simulations with and without snow radiation were also carried out using the PROG framework. For liquid microphysics, four commonly used autoconversion schemes -BE68 (Berry, 1968), BE94 (Beheng, 1994), LD04 (Liu and Daum, 2004), and SB06 (Seifert and Beheng, 2006) -were compared with the default PROG simulation using the KK00 scheme (Khairoutdinov and Kogan, 2000). Results from the sensitivity experiments which were adjusted by a factor of 0.1 for the Wegener-Bergeron-Findeisen (WBF) process (Wegener, 1911;Bergeron, 1935;Findeisen, 1938), aggre-gation, riming efficiency, and freezing ratios of homo-and heterogeneous nucleation were subtracted from the default PROG result to quantify the impact of the targeted process. In this study, ERF aci is defined as the change in net cloud radiative forcing at the TOA under clean sky (Ghan, 2013) with fixed ocean conditions but allows atmospheric processes including rapid adjustments in the response to aerosol changes, from PI to PD .
If needed, these experiments were retuned so that the imbalance of the radiative flux at the TOA remained within 1.0 W m −2 . Model tuning was conducted by modifying the scale factor for accretion rate but not autoconversion for the warm rain process because the latter can influence the magnitude of ACI due to the direct relation to droplet number (Michibata and Takemura, 2015;Jing et al., 2019) and thus the precipitation initiation . This is effective for modifying SW radiation, but if needed, cloud ice and snow processes were also tuned for modifying LW radiation by changing scale factors for the fall speed of hydrometeors, which may be uninfluential on ERF aci because they are not involved directly in the hydrometeor number densities.
3 Weakening of ERF aci with prognostic precipitation Figure 1 compares geographical distributions of ERF aci simulated by the DIAG and PROG models. In DIAG, a strong negative ERF aci is observed over East Asia, Europe, and North America where anthropogenic pollution dominates. This is attributed to the cloud lifetime effect caused by anthropogenic aerosols, which increases low warm clouds and hence shortwave reflectance. The global annual mean ERF aci reaches −1.7 W m −2 , which is outside the bound of the uncertainty range (−1.2 W m −2 ) in IPCC AR5. The geographical pattern is consistent with other GCMs (Shindell et al., 2013;Zelinka et al., 2014).
In PROG, however, the majority of the strong negative forcing over anthropogenic regions is reduced significantly, resulting in a reduction of around 54 % in global-mean ERF aci . Although the geographical pattern is somewhat different from previous reports using other GCMs (discussed in the next section), the global mean ERF aci (−0.8 W m −2 ) is much closer to satellite-based estimates (Chen et al., 2014;Christensen et al., 2016Christensen et al., , 2017Douglas and L'Ecuyer, 2020). The total aerosol ERF associated with ARI and ACI (ERF ari+aci ) in PROG (−1.1 W m −2 ) is only half that generated by DIAG (−2.1 W m −2 ). This significant reduction in ERF aci in PROG results from a substantial weakening of ERF SW aci , particularly over midlatitudes of the Northern Hemisphere, and enhanced warming of ERF LW aci over low latitudes in both hemispheres (Fig. 1c). The zonal distribution shows that stronger (weaker) ERF LW aci accompanies stronger (weaker) ERF SW aci , which is in line with Heyn et al. (2017). To understand the impact of precipitation treatment on ERF aci , decompositions of global mean ERF aci   (Chen et al., 2014;Christensen et al., 2016Christensen et al., , 2017Douglas and L'Ecuyer, 2020) and their probable range (box-whisker) calculated by correcting the effect of retrieval limitations (Michibata and Suzuki, 2020) based on Ma et al. (2018) are also shown. Error bars and plots in MIROC6 represent the minimum-maximum and median of the interannual variability, respectively. Shaded in light-green is the uncertainty range of ERF aci estimated from IPCC AR5 . The prognostic rain with a diagnostic snow scheme is denoted as "PRDS". The sensitivity experiment without snow radiative effects is denoted as "OFF / SnwRad". into its SW and LW components are shown for alternate configurations of precipitation in MIROC6 (Fig. 2). Figure 2 confirms that the significant reduction of ERF aci in PROG is contributed to by both increased ERF LW aci and weakened ERF SW aci , in stark contrast to previous CMIP5 model results (Heyn et al., 2017) in which cloud-ice-induced changes to ERF SW and ERF LW cancel each other out to result in few net ERF changes within the DIAG framework. This difference in the present study from previous results is attributed to the snow-induced modulation of ACI newly incorporated into our model.
The impact of snow on ACI can be understood in more detail using the results shown in Fig. 2, which includes two intermediate versions of PROG, i.e., one that incorporates prognostic rain but diagnostic snow (PRDS) to isolate the relative impacts of rain vs. snow on ERF aci and one that represents prognostic rain and snow but without the radiative effects of snow (OFF / SnwRad). Regarding the LW component, the global mean ERF LW aci of PROG (+0.7 W m −2 ) is more than twice as large as those of DIAG (+0.2 W m −2 ) and PRDS (+0.3 W m −2 ). The OFF / SnwRad simulation also shows weaker ERF LW aci relative to the standard PROG simulation (Fig. 2). These results suggest that the warming LW effect comes mainly from adjustments induced by snow together with its radiative effects, in addition to cloudice effects included in CMIP5 models as well as our model. The ERF LW aci is significant over the Indian Ocean and Southeast Asia (not shown), which is also similar to the other model, CAM5-MARC-ARG (Grandey et al., 2018). This is attributable to the increased ice nuclei (IN) due to biomass burning for example, partly supporting the convective invigoration  although GCMs do not have the capability to resolve the convective cloud systems. The increased IN results in a faster glaciation and thus enhances snowfall due to the WBF process (i.e., glaciation indirect effect). These mixed-and ice-phase microphysical processes are more elaborated in the PROG scheme, and the associated LW change induced by snow is incorporated only in PROG, which contributes to the higher ERF LW aci across the globe. The PROG scheme also reduces the SW component (ERF SW aci ) relative to DIAG, particularly over anthropogenic regions (Fig. 1b) in the Northern Hemisphere midlatitudes. A well-known mechanism for the reduction in ERF SW aci is the enhancement of accretion with a smaller contribution from autoconversion, as in PROG (not shown), with only the latter process depending upon the cloud droplet number concentration (N c ) (Posselt and Lohmann, 2008). The smaller contribution of autoconversion in PROG mitigates the excessive cloud water susceptibility to aerosols that occurs in DIAG models Michibata et al., 2019). However, Fig. 2 shows that the replacement in liquid-phase pre-cipitation alone from DIAG to PRDS cannot explain the significant reduction of ERF SW aci from DIAG to PROG, suggesting that ice-phase processes involving falling snow influence the magnitude of ERF SW aci , as discussed in the next section. This reduction of ERF SW aci in PROG relative to DIAG is also impossible to explain by the response of cloud ice alone, because cloud ice should increase ERF SW aci towards more negative values because of aerosol-induced increases in cloud optical thickness. This is indeed what is happening with the DIAG framework in the CMIP5 multi-model results (Heyn et al., 2017), in which models with aerosol effects on cloud ice (not snow) show much stronger ERF SW aci , which is large enough to cancel the enhancement of ERF LW aci . In contrast, our PROG model reduces ERF SW aci . We hypothesize that the prognostic treatment of snow plays an important role in weakening ERF SW aci through microphysical processes involving cloud water and snow, as discussed below.

Relationship of microphysics and ERF aci
Next, we discuss the role of prognostic precipitation in determining ERF aci by addressing the following two questions raised in the previous section: 1. Why does the geographical pattern of ERF aci in PROG differ from that of DIAG?
2. Why does the prognostic treatment of snow effectively weaken ERF SW aci ?
To this end, we first explore how precipitating hydrometeors can modulate the cloud water susceptibility to perturbed aerosols. Figure 3 shows how the change in the cloud liquid water path (CLWP) relates to changes in precipitating hydrometeor paths, i.e., the rainwater path (RWP) and the snow water path (SWP), through pre-industrial (PI) to present-day (PD) changes in aerosols. The PD-minus-PI change (susceptibility) in RWP is highly correlated (r = 0.59) with that in CLWP (Fig. 3a). We interpret this strong correlation to be the result of the close co-variance of cloud and rainwater through aerosol perturbations, with the cloud water being a direct source of the rainwater. The PD-minus-PI change in SWP is also positively correlated, though weaker (r = 0.39), than that in CLWP (Fig. 3b), suggesting that precipitating snow also co-varies with cloud water through aerosol perturbations. Given that SWP is significantly larger than RWP in our model ( Fig. S2; see also Michibata et al., 2019), and that snowflakes, with residence times longer than those of rain, are more likely to interact with clouds, the increased CLWP caused by anthropogenic aerosols can act as an efficient source of snow via interactions among cloud droplets and snowflakes (e.g., riming), likely resulting in the evident robust positive relationship.
These positive correlations between precipitating hydrometeors and cloud water suggest that aerosol-induced increases in cloud mass are caused, in part, by increases in rain and snow in PROG, in contrast to those caused by increases in cloud water and ice alone in DIAG. Given that raindrops and snowflakes are optically much thinner in the SW spectrum than cloud droplets and ice crystals, respectively, increases in precipitating hydrometeors can explain both the stronger ERF LW aci and weaker ERF SW aci in PROG compared with DIAG ( Figs. 1 and 2). Furthermore, falling snow is more likely to deplete underlying cloud droplets in PROG, with its explicit representation of the riming process, which can lead to a reduction of cloud water susceptibility to aerosols. This proposed mechanism can also explain the systematic change in the geographical distribution of ERF aci between DIAG and PROG (Fig. 1). Indeed, regions with a significant reduction in ERF aci (i.e., over East Asia, Europe, and North America) correspond well to those with large values of SWP (Fig. S3), where the PD − PI increase in CLWP is also reduced significantly (Fig. S4). These results lend further credence to the hypothesis of snow-induced buffering of ACI in our model.
The buffering process, via interactions among hydrometeors described above, depends strongly on the fundamental uncertainty in model representations of various microphysical processes. We therefore now further explore how ERF aci and its buffering by precipitation processes are sensitive to microphysical process representations as summarized in Fig. 4 (see also Sect. 2.2 for details of experiments). The processes examined here are the autoconversion of liquid droplets; the Wegener-Bergeron-Findeisen (WBF) process; the aggregation of ice crystals, riming, and ice nucleation by freezing aerosols, which are all important sources of uncertainty in GCMs (Lawson and Gettelman, 2014;Sant et al., 2015). As expected, the simulated ERF aci is highly sensitive to the autoconversion scheme used, mainly because of its varying dependence on N c among the various schemes (Jing et al., 2019). A different liquid autoconversion scheme with PROG can change ERF aci by 39 %, from −18 % to +21 % (blue bars in Fig. 4). The impacts of the autoconversion scheme on ERF aci , however, are smaller than those of the treatment of rain and snow (ca. 54 % change).
The mixed-and ice-phase processes (WBF, aggregation, and riming), represented more explicitly with a larger degree of freedom in PROG than in DIAG, can change ERF aci by 15 %, from −13 % to +2 % (cyan bars in Fig. 4). Among the mixed-and ice-phase microphysics processes, the process found to most influence ERF aci is the riming of cloud droplets on snow, supporting the hypothesized mechanism of snow-induced buffering of ACI discussed above. The magnitude of ERF aci is sensitive to ice nucleation processes as well (green bars in Fig. 4), because the change in ice number concentration directly controls the size of the crystals and thus the conversion timescale from ice to snow in our model. Although the ERF aci variations with changing liquid and ice microphysical processes do not reach the difference of ERF aci between the DIAG and PROG (i.e., 54 %), both wet scavenging of aerosols and coalescence scavenging of cloud droplets Figure 3. Relationship between the change in annual mean CLWP and that in annual mean (a) RWP and (b) SWP, from the change in aerosols from PI to PD conditions, simulated using the PROG scheme. Box-whisker plots represent the 10th, 25th, 50th (black "+"), 75th, and 90th percentiles of the data within each bin based on the annual mean. Plots in red show the mean. The correlation coefficient (r) is given in the figure. also contribute to the ACI reduction (McCoy et al., 2020) due to the accretion-driven buffering mechanisms (Michibata and Suzuki, 2020), which should explain the remaining part of the ERF aci difference.
In summary, we found that the treatment of precipitation (PROG vs. DIAG) is the most influential factor controlling ERF aci (red bars in Fig. 4) among all of the "tunable knobs" associated with the various microphysical processes in our model. It should also be emphasized that the ERF aci change caused by the precipitation treatment (ca. 54 % in magnitude), absent from previous climate modeling studies, has the potential to resolve some of the differences between satellite estimates of ERF aci (Bellouin et al., 2013;Chen et al., 2014;Christensen et al., 2017) and GCMs (Shindell et al., 2013;Zelinka et al., 2014;Heyn et al., 2017). These findings need to be tested further using other GCMs as they incorporate prognostic precipitation in future studies.

Summary and future work
In this study, the sensitivities of ERF aci to various treatments of precipitation and microphysical process representations in a GCM have been systematically examined. As few GCMs incorporate explicit representations of two-moment prognostic precipitation with the radiative effects of precipitating hydrometeors -e.g., CAM6 MG2/MG3 , E3SM (Rasch et al., 2019), GISS-E3, and MIROC6 CHIMERRA ) -we used a single model framework to evaluate the sensitivities. This also allowed us to avoid uncertainties from inter-model differences in parameterizations other than the targeted processes.
We found that the treatment of precipitation in GCMs (PROG vs. DIAG) has a significant impact on the magnitude of ERF aci (Figs. 1 and 2), which we interpret to be driven mainly by collection processes among precipitating snow and cloud droplets (i.e., riming). As the SWP is more than twice as large as the RWP in our PROG model, and is in good agreement with satellite retrievals , falling snowflakes efficiently accrete and deplete the underlying cloud water, thus partly canceling the CLWP response to aerosols. Changes in RWP and SWP through PI to PD aerosol perturbations were also positively correlated with those in CLWP (Fig. 3), suggesting that snow can co-exist with cloud water to a degree sufficient to buffer the cloud water response to aerosol perturbations (Fig. 4). The signatures of the snow-induced buffering are also found geographically over regions with significant reductions in ERF aci (e.g., East Asia, Europe, and North America) that correspond closely to regions with particularly large SWP (Figs. 1 and S3). Sets of sensitivity experiments, performed both with and without snow radiative effects, did not reveal a significant difference in ERF aci as a result of the near cancellation of SW and LW changes caused by snow. This means that the prognostic treatment of precipitation itself is critical for the buffering of ACI. Accordingly, the impact of a prognostic treatment of precipitation on the magnitude of ERF aci was greater than changes to any of the other tunable knobs inherent to the various microphysical processes (e.g., autoconversion, ice microphysics, and ice nucleation). Notably, precipitation-driven buffering effects (ca. 54 % change in ERF aci ) can broadly explain the current model-observation discrepancy in estimated ERF aci Lohmann, 2017).
However, the results presented here are based on a single GCM framework and need to be replicated using other GCMs as they incorporate prognostic precipitation frameworks in the future (Li et al., 2020). This is particularly true because little is known about aerosol influences on mixedand ice-phase clouds as well as deep convective clouds Fan et al., 2018) and cirrus clouds (Penner et al., 2018) at a fundamental process level, and the degree of microphysical complexity differs widely among GCMs (Heyn et al., 2017). Although the responses of clouds and precipitation to aerosol perturbations are therefore likely to be model dependent, the sign of the response of ERF aci to the precipitation framework and microphysical processes is consistent with a previous assessment using CAM5/MG2 , suggesting that the major findings of this study will apply across the models. Thus, it is left for important future studies to quantify the inter-model spread of ERF aci sensitivity to microphysical processes and their interplay with precipitation processes as more GCMs begin to include prognostic precipitation. Furthermore, a theoretical approach (Glassmeier and Lohmann, 2016) and idealized process modeling (Glassmeier et al., 2019) are also urgently required to solidify the process-level understanding of the snow-induced buffering hypothesis, which constitutes our important future work beyond the present study.
This study primarily focused on ERF aci sensitivities to the CLWP adjustment rather than cloud fraction adjustment, be-cause aerosol effects are directly linked to the CLWP change through the modification of the mass conversion rate from cloud water to rainwater that itself relates to the treatment of precipitation (i.e., DIAG vs. PROG). However, it is important in future studies to separate the ACI into the Twomey forcing and rapid adjustments of CLWP and cloud fraction (e.g., Goren and Rosenfeld, 2014;Mülmenstädt et al., 2019) for better understanding of how the treatment of precipitation influences micro-and macroscopic cloud properties (Michibata and Suzuki, 2020), which relates to the fundamental inter-model spread in ERF aci (Gryspeerdt et al., 2020;Bellouin et al., 2020).
Data availability. The results of the MIROC-SPRINTARS simulations used to produce the figures can be obtained from the corresponding author upon reasonable request.
Author contributions. TM developed the model, designed the research, carried out the simulations, performed the analysis, and wrote the manuscript. KS guided the model development and data analysis and helped with editing the paper. TT provided technical support in setting up the model in the supercomputer system and helped with model analysis. All authors read and approved the final paper.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. The authors would like to thank the developers of both SPRINTARS and MIROC. The new microphysics and radiation schemes were optimized by Koji Ogochi. Simulations by MIROC-SPRINTARS were executed on the SX-ACE supercomputer system of the National Institute for Environmental Studies, Japan. The authors thank the editor, Corinna Hoose, for editing the manuscript and Johannes Mülmenstädt (Pacific Northwest National Laboratory) and the one anonymous reviewer for providing constructive suggestions and comments, which helped to improve the manuscript. Review statement. This paper was edited by Corinna Hoose and reviewed by Johannes Mülmenstädt and one anonymous referee.