Responses of Mean and Extreme Precipitation to Different Climate Forcing Under Radiative-Convective Equilibrium

Chenyu MA, Wei YUAN, and Ji NIE*Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 0087, China

2Aviation Meteorological Center, Civil Aviation Administration of China, Beijing 100122, China

ABSTRACT Understanding the responses of mean and extreme precipitation to climate change is of great importance. Previous studies have mainly focused on the responses to prescribed sea surface warming or warming due to increases of CO2. This study uses a cloud-resolving model under the idealization of radiative—convective equilibrium to examine the responses of mean and extreme precipitation to a variety of climate forcings, including changes in prescribed sea surface temperature,CO2, solar insolation, surface albedo, stratospheric volcanic aerosols, and several tropospheric aerosols. The different responses of mean precipitation are understood by examining the changes in the surface energy budget. It is found that the cancellation between shortwave scattering and longwave radiation leads to a small dependence of the mean precipitation response on forcings. The responses of extreme precipitation are decomposed into three components (thermodynamic,dynamic, and precipitation efficiency). The thermodynamic components for all climate forcings are similar. The dynamic components and the precipitation-efficiency components, which have large spreads among the cases, are negatively correlated, leading to a small dependence of the extreme precipitation response on the forcings.

Key words: climate forcing, mean precipitation, extreme precipitation

1. Introduction

The response of the hydrological cycle to global warming is one of the key topics in climate research. The mean precipitation sensitivity (MPS, i.e., the fractional change in mean precipitation with 1°C of surface warming) is constrained by the radiative energy budget. Results from global climate models (GCMs) indicate a rate of about 2—3% K-1for the MPS for warming caused by increases in greenhouse gases (GHGs; Allen and Ingram, 2002; Held and Soden, 2006; O'Gorman and Schneider, 2008). There is,however, no apparent constraint for extreme precipitation sensitivity (EPS, i.e., the fractional change in extreme precipitation with 1°C of surface warming). It has been argued that the increase in extreme precipitation may roughly follow the increase in atmospheric water vapor, which is ～7% K-1according to the Clausius—Clapeyron (CC) relation (Allen and Ingram, 2002; Trenberth et al., 2003; Kharin et al.,2007). GCM simulations show that the EPS has remarkable regional patterns, with over 30% K-1in some tropical regions and negative EPS in some subtropical regions,mainly due to the change in vertical ascent (Emori and Brown, 2005; Pfahl et al., 2017). Simple CC scaling is not enough to explain the EPS, and other factors need to be considered.

The majority of previous studies on the hydrological responses to climate changes have focused on GHGinduced warming, particularly for EPS studies. While anthropogenic CO2is the primary cause of current global warming, there is also a variety of climate forcings that may cause or contribute to climate change. For example, atmospheric aerosols, either from natural sources such as volcano eruptions or from anthropogenic emissions, can affect atmospheric radiation directly and indirectly by changing cloud properties (Albrecht, 1989; Robock, 2000; Myhre et al., 2013). Changes in surface type can alter the surface albedo (Myhre et al., 2013). Solar insolation has an 11-year cycle, and over the geological time scale it has increased by about 20% from the Archean Eon (～2.7 billion years ago)(Kasting, 2010). Changes in deep-ocean circulation, which operates on a time scale of several thousands of years or longer, can induce surface energy flux anomalies to the atmosphere, which may also be viewed as climate forcing.Because the above-mentioned climate forcings affect the climate system's energy budget in different ways, they may result in different hydrological responses.

There are several possible reasons why the hydrological response may depend on the nature of the climate forcing. Firstly, the vertical profiles of the radiative forcing of the climate forcing are different. The GHG forcing increases the longwave emissivity; changes in insolation and albedo modify the shortwave flux at the top and bottom of the atmosphere, respectively; and the radiative forcing of aerosols depends on the properties and vertical profiles of aerosol concentrations. Secondly, in addition to direct radiative effects, aerosol can also affect cloud microphysics,which may further modify convection and precipitation processes (Grabowski, 2000; Wu, 2002). Thirdly, unlike the well-mixed GHGs, some climate forcings (e.g., aerosol forcing) are regional and may lead to different large-scale circulation anomalies. GCM simulations indicate that the MPS is different for the warming due to GHGs (1—3% K-1), insolation (2.5—3.1% K-1), and aerosols (3.7—3.8% K-1) (Andrews et al., 2009; Ming et al., 2010; Shiogama et al., 2010; Frieler et al., 2011; Ming and Ramaswamy, 2011; Pendergrass and Hartmann, 2012; Boucher et al., 2013; Kvalev?g et al.,2013; Levy II et al., 2013). The dependence of EPS on climate forcing is inconclusive. Some studies have suggested that the EPS does not depend on the emissions scenario or driving force (Pendergrass et al., 2015; Sillmann et al.,2017), while others have indicated that the EPS due to aerosol forcing is significantly different from that caused by GHG forcing (Lin et al., 2016; Myhre et al., 2017). Furthermore, the EPSs for forcings other than GHGs and aerosols have not been explored.

The goal of this study is to investigate the responses of the hydrological cycle, including the MPS and EPS, to a variety of climate forcings. This problem is examined using a cloud-resolving model (CRM) under the idealization of radiative—convective equilibrium (RCE). CRMs, which are more reliable than GCMs in resolving convective-scale dynamics,have been shown to be a useful compliment to GCMs in studies of the hydrological cycle (e.g., Held et al., 1993; Lau et al., 1993; Sui et al., 1994; Romps, 2011; Singh and O'Gorman, 2014; Nie et al., 2018). The idealization of RCE,which excludes the inhomogeneity in the surface conditions and the large-scale circulations, provides a clean testbed for our propose. Previous CRM studies have shown that the increase in extreme precipitation in response to surface warming is greater than that of the mean precipitation(Romps, 2011; Singh and O'Gorman, 2014). Muller et al.(2011) showed that the changes in vertical ascent contribute negatively to the EPS and cancel out the thermodynamic contributions from increases in atmospheric moisture. Muller (2013) further showed that the degree of convective organization may affect the EPS. However, most previous CRM studies have only considered GHG forcing or prescribed SST warming.

A variety of climate forcings are examined in this study, including changes in sea surface temperature (SST),CO2, solar insolation, surface albedo, stratospheric aerosols,and tropospheric aerosols. As will be shown later, both the MPS and EPS show certain, but not large, dependence on the forcings. For the MPS, we examine the radiative budget to understand the different pathways of how the forcing affects mean precipitation. We show that, due to the cancellation between downward shortwave and downward longwave radiation, the MPS only weakly depends on the forcings. For the EPS, we apply a scaling method (O'Gorman and Schneider, 2009) to decompose the EPS into three components: dynamic, thermodynamic, and precipitation-efficiency components. Due to the cancellation between the effects of vertical ascent and precipitation efficiency, the EPS also only weakly depends on the forcings. The exception is black carbon (BC) forcing, which has a much smaller MPS and EPS than the other forcings. Section 2 introduces the numerical model and experimental design. Results are presented in section 3. Section 4 provides some discussion and summarizes our conclusions.

2. Model and experimental design

The model used here is the System of Atmospheric Modeling (Khairoutdinov and Randall, 2003), version 6.8. All simulations are run in a three-dimensional domain of 128 km ×128 km in the horizontal direction, with a resolution of 1 km.The vertical grid has 64 levels, with the grid spacing gradually increasing from 37.5 m at the surface to 500 m above 7 km. There are six water species in the microphysics scheme: water vapor, cloud liquid, cloud ice, snow, rain,and graupel. The interactive radiation scheme is from the National Center for Atmospheric Research Community Climate Model (Kiehl et al., 1998). A slab ocean of 0.5 m is used as the surface condition. The surface fluxes are interactively computed using Monin—Obukhov similarity theory.

Eight kinds of climate forcing are investigated in this study (Table 1), each with a pair of control and perturbed runs. The control runs of these experiments share the same settings (except the SST case): the CO2concentration is 355 ppm, and the insolation is set as annual mean values at 0°,without seasonal or diurnal variation, with a solar constant of 1367 W m-2. All the aerosol species have zero concentration. With the above insolation condition, the equilibrium SST will be much higher than our desired reference climate state. Thus, similar to the treatment in Romps (2011), a downward heat flux of 95 W m-2is applied at the bottom of the slab ocean to cool the equilibrium SST to be 299.6 K. The imposed flux sink may be viewed as heat moving into the deeper ocean and then being transported to higher latitudes by ocean circulation. In the SST experiment, the control run has a prescribed SST of 299.6 K.

Table 1. The experimental designs in this study. The vertical profile of the volcanic aerosol added in the Aer_str experiment is shown in Fig. S1. The vertical profiles of the tropospheric aerosols added in the Aer_tro, Aer_sul, and Aer_bc experiments are shown in Fig. S2. In the Aer_tro experiment, the amplitude of the added aerosols is 20 times those in Fig. S2. In the Aer_sul experiment, the amplitude of the added sulfate aerosol is 30 times that in Fig. S2. In the Aer_bc experiment, the amplitude of the added black carbon aerosol is 200 times that in Fig. S2.

Next, we introduce the perturbed runs. In the SST experiment, the perturbed run has a prescribed SST of 302.6 K.Note that the prescribed SST experiment does not conserve energy for the surface. For the other experiments, the SST is calculated interactively with the slab ocean. In these experiments (except the SST case), the magnitude of forcing in the perturbed runs is chosen so that the changes of equilibrium SST are around 3 K. In the perturbed run of the CO2experiment, the CO2concentration is doubled, leading to a warming of SST by 2.7 K. In the perturbed run of the Ins experiment, the solar constant is increased to 1385 W m-2. In the perturbed run of the Alb experiment, the surface albedo is decreased to 0.025 (compared with 0.045 in the control run). There are nine aerosol species (eight tropospheric aerosols and one stratospheric aerosol) in System of Atmospheric Modeling (Table S1 in Electronic Supplementary Material, ESM). All the tropospheric aerosols only have shortwave radiative effects, and the stratospheric (volcano) aerosol (75% sulfuric acid and 25% water) has both shortwave and longwave effects. In the perturbed run of the Aer_str experiment, volcanic aerosol is added in the lower stratosphere (Fig. S1 in ESM) to mimic the effects of major volcano eruptions. The magnitude of the added volcanic aerosol is 1 × 105Tg, which is about 600 times that of a major volcanic eruption such as Samalas (Liu et al., 2016). The Aer_tro experiment is designed to examine the effects of tropospheric aerosols. The vertical distributions of the tropospheric aerosols are the global and annual-mean profiles from a GCM study (Fig. S2; Kipling et al., 2016). To reach a large SST difference of 3.1 K, the added aerosol concentrations are 20 times larger than the GCM results shown in Fig. S2. Additional experiments are performed to examine the individual effects of two representative tropospheric aerosols: sulfate aerosol (the Aer_sul experiment), which has a strong scattering effect on shortwave radiation; and BC (the Aer_bc experiment), which has a strong absorbing effect on shortwave radiation. Note that the magnitude of forcing in the two runs is also tuned accordingly, to have an SST change of about 3 K. All the runs are integrated for more than 1000 days, so that a statistical equilibrium is reached.As an example, several key domain-mean variables and cloud variables of the control and perturbed runs of the CO2case are shown in Fig. S3 and Fig. S4. The domain-mean variables are sampled every 5 min and the 3D snapshots are sampled every 6 h for the last 250 days (total of 72 000 samples of means and 1000 samples of 3D snapshots).

The responses of the hydrological cycle are calculated by taking the differences between the perturbed run and the control run in each pair of experiments. Extreme precipitation is defined as the surface precipitation rate at the 99.9th percentiles with all grid points considered (including grids with zero precipitation). For the five cases of SST, CO2, Ins,Alb, and Aer_bc (called group 1 hereafter), the perturbed runs have warmer SST than the control runs. For the other three cases of Aer_str, Aer_tro, and Aer_sul (called group 2), adding these aerosols cools the SST. For better comparison, all the results are normalized by the SST changes.Thus, the results of cases in group 2 should be interpreted as removing aerosols from a background state of zero (this is justified if the hydrological response is nearly linear for small perturbations).

3. Results

3.1. Mean precipitation sensitivity

We first examine the changes in basic thermodynamic variables driven by different forcings (Fig. 1). The atmospheric temperature (T) increases with surface warming(Fig. 1a). The upper troposphere warms more than the lower troposphere does, because convection maintains the temperature profiles close to the moist adiabatic, which has a lapse rate decreasing with warming. For all the cases except that of Aer_bc, the δT values are close to each other, especially in the lower troposphere due to the strong constraint of moist convection. The outlier, the Aer_bc case, has significantly larger δT due to the strong shortwave absorbing in the lower troposphere. The changes in specific humidity (δq,Fig. 1b) are proportional with δT following the CC relationship. Throughout most of the troposphere, the cloud fraction decreases with warming (Fig. 1c). The cloud base moves downward slightly, and the cloud top moves upward in association with upper-tropospheric warming. This is consistent with previous studies (Bretherton, 2015; Vogel et al.,2016). Focusing on the tropopause layer, for the cases in group 1, the surface warming is associated with increases in tropopause height and cooling at the stratosphere (Fig. 1d),due to a rising of the effective emitting level (Vallis et al.,2015). For the cases in group 2 (Aer_str and Aer_tro, and Aer_sul), the aerosol perturbations induce radiative heating at the upper-troposphere—lower-stratosphere, leading to warm responses there. As a result, the tropopause height slightly decreases in these cases. The differences suggest that different radiative effects of perturbations may cause different adjustments of tropopause height.

With CO2doubling, the mean precipitation increases 3.9% K-1(Table 1), consistent with previous CRM studies(Muller et al., 2011; Romps, 2011). The MPS in CRM simulations is larger than the results of GCMs (2—3% K-1), presumably partly due to the lack of large-scale circulation in the CRM, and partly due to the relatively high control SST here. For the other cases, the MPS ranges from 4.2% K-1(the Aer_str case) to 5.8% K-1(the Aer_tro case), except the outlier of the Aer_bc case, which shows a decrease in precipitation by 1.2% K-1(Table 1). To better understand the causes of the MPS differences among the cases, we use the surface energy budget framework (Roderick et al., 2014):

where RSd/RSuis the surface downward/upward shortwave radiative flux, RLd/RLuis the surface downward/upward longwave flux, and H/E is sensible/latent heat flux. The variables in Eq. (1) are anomalies between the perturbed and the control runs. Since in the equilibrium state the precipitation is equal to the evaporation (i.e., the latent heat flux after unit conversion), Eq. (1) may be used to diagnose the MPS from the radiative energy perspective.

The results of the radiative energy budget are shown in Fig. 2a. The cases in group 1 show a decrease in downward shortwave flux (RSd), mainly due to the enhanced scattering effect associated with increased water vapor. In the Aer_bc case, the strong shortwave absorption by BC further heavily reduces RSd. The cases in group 2 have positive or zero RSd. Remember that the results of these cases should be thought of as removing aerosols from the control state (the last paragraph in section 2). Removal of the shortwave scattering aerosols (e.g., dust and sulfate) leads to increases in RSd.The changes in upward shortwave flux (RSu) are small overall, except for the Alb case in which the decreased albedo reduces the surface reflection of shortwave radiation. The changes in net shortwave flux (RS=RSd-RSu) have a range of-1.74 W m-2K-1to 1.47 W m-2K-1among the cases,except Aer_bc, which has an RSof -8.27 W m-2K-1.

The changes in upward longwave flux (RLu) have very similar values (～6 W m-2K-1) for all the cases. This is consistent with the theoretical estimation from the black-body radiation of 4σTs3(taking surface temperature Ts=300 K,this gives a value of 6.1 W m-2K-1). The changes in downward longwave flux (RLd) have larger differences among the cases, dominating the variations of RL. We have confirmed that the changes in net shortwave and longwave radiation are mainly due to the clear-sky radiation, while the contribution from the changes in cloud is small (Fig. 2b). The changes in sensible heat flux (H) are negligible, except for the Aer_bc case in which the increase in surface-layer air temperature reduces the temperature differences between the surface air and the surface, leading to a decrease in the sensible heat flux.

Fig. 1. The changes in (a) temperature, (b) specific humidity, (c) cloud fraction, and (d) temperature near the tropopause with unit surface warming. The black dashed line in (c) is the control run cloud fraction profile (divided by five to share the same x-axis as the anomalous profiles). In (d), the y-axis is the pressure above (positive) and below (negative) the tropopause of the control run.

The above surface energy budget analysis suggests a strong negative correlation between RSdand RLdthrough the linkage of atmospheric temperature changes (δT). A larger δT is associated with a greater δq, and thus a stronger scattering of shortwave radiation and a more negative RSd(Fig. 3a).On the other hand, a warmer atmosphere sends more longwave radiation back to the surface, resulting in a more positive RLd(Fig. 3b). The δT used in Fig. 3 is sampled at the 630-hPa level, because the above argument applies in the lower troposphere where water vapor is abundant and longwave backward radiation is strong. Results with other lower tropospheric levels also show high correlation. As the δT level increases, their correlation decreases, but it is still significant. The cancellation between RSand RLleads to a relatively weak dependence of the MPS on the forcings examined here. The exception is the BC forcing, in which the absorption by BC is superimposed on the scattering of water vapor, leading to a very strong reduction in downward shortwave radiation reaching the surface and a decrease in precipitation.

3.2. Extreme precipitation sensitivity

The EPS is greater than the MPS for all kinds of forcing (Table 1). The EPS ranges from 4.7% K-1to 6.7% K-1among all the cases except the outlier of the Aer_bc case,which has an EPS of 1.8% K-1. Due to the small temporal and spatial scale, precipitation extremes are not constrained by any long-term energy budget. Instead, dynamic and cloud microphysics can play important roles in determining the EPS (Muller et al., 2011; Singh and O'Gorman, 2014).

We use a scaling of precipitation extremes (O'Gorman and Schneider, 2009; Muller et al., 2011) to understand the dependence of the EPS on forcing. This scaling approximates precipitation extremes (Pe) with

Fig. 2. (a) Perturbation analyses of the surface energy budget based on Eq. (1). (b) Separation of RS and RL into clear-sky and cloudy components.

In Eq. (3), δ denotes differences between the perturbed and control runs of each experiment. The right-hand-side terms of Eq. (3) represent three components of EPS, which are the thermodynamic component (the increases in saturation water vapor), the dynamic component (the changes in vertical velocity), and the component due to the changes in precipitation efficiency. Note that the δε/ε term is neglected in the previous study by Muller et al. (2011) because it is small for GHG forcing. However, our numerical simulations show that, for other climate forcings, the δε/ε term is not negligible. Note that the δε/ε term is diagnosed here. It includes both the contribution of cloud and precipitation microphysics to the EPS and higher-order cross terms between the components in Eq. (2).

The decomposition of EPS based on Eq. (3) is shown in Fig. 4. The thermodynamic components for all cases are similar, with values around 10% K-1. Under RCE, the changes of temperature profiles are closely tied to SST changes following moist adiabatic profiles (Fig. 1a). Thus, δT and the thermodynamic componentsof these cases are very close to eachother. The Aer_bc case has alarger δT,corresponding to a larger thermodynamic component. Overall, the differences among the thermodynamic components are relatively small and do not explain the spread of EPSs.

Fig. 3. Correlations between (a) δT at 630 hPa and RSd, and (b) δT at 630 hPa and RLd, of all the cases.

The dynamic component is negative for all the cases(Fig. 4), with a sizeable spread. The key to understanding the dynamic component is the changes in vertical ascent during extreme precipitation. The changes in ωe(Fig. 5a) show that the amplitude of ωein the middle troposphere decreases, and the level of the ωepeak shifts upward.Although these cases share common features with a previous study (Muller et al., 2011) of GHG forcing, the amplitude of the ωechanges is different, leading to different dynamic components. The weakening of vertical ascent largely explains the dynamic component, as shown by the high correlation between the dynamic components and the changes in 500-hPa ωe(Fig. 5b). The above analysis with δωe, although able to explain the dynamic component diagnostically, has a fundamental limitation insofar as it requires information (ωe) on the extreme-precipitation grids. For lower-resolution models, such as GCMs, the convective-scale processes are not explicitly resolved, meaning these convective-scale variables are unavailable. Here, we move one step further to link the dynamic component to the larger-scale (i.e., CRM domain-mean) variables. It is found that there is a strong negative correlation between the dynamic components of the EPS and the changes in tropopause pressure (Fig. 5c), suggesting the effect of ωechange is related to the change in tropopause height. This is consistent with a qualitative argument based on the convective plume perspective that, as the tropopause level rises, the convective available potential energy increases, tending to enhance convective ascent (Singh et al., 2014, 2017). For the cases in group 2, the tropopause levels slightly decrease(Fig. 1d), corresponding to large negative dynamic components of EPS (Fig. 4).

Lastly, the precipitation efficiency component of EPS also has large variations. This component is negatively correlated with the dynamic component (Fig. 5d), so that the total EPS has relatively small variations. This negative correlation may be understood as follows: Given the time scale for the conversion of cloud-water condensation to precipitation is nearly unchanged with warming, the faster the convective updrafts ascend, the less time it takes for cloud updrafts to reach the cloud top, and the smaller the portion of cloud liquid water that can be converted into rainfall. Due to this cancellation effect, the EPS is not very sensitive to different climate forcings under RCE in our CRM simulations.

Fig. 4. The decomposition of EPS based on Eq. (3).

Fig. 5. (a) δωe (the changes in pressure velocity conditioned on extreme precipitation to unit surface warming). The black dashed line in (a) is the ωe of the control runs (rescaled by dividing it by 10 for better visualization). (b) Scatterplot of δωe at 500 hPa and the dynamic components of EPS. (c) Scatterplot of changes in tropopause pressure and the dynamic components of EPS. (d) Scatterplot of the precipitation-efficiency components and the dynamic components of EPS.

4. Discussion and conclusions

This paper has examined the responses of mean and extreme precipitation to warming due to a variety of climate forcings in a CRM under RCE. When the concentration of CO2is doubled, the increase in mean precipitation is 3.9% K-1, which roughly agrees with previous CRM studies (Muller et al., 2011; Romps, 2011). Other climate forcings, including prescribed SST, solar insolation, surface albedo, stratospheric volcanic aerosols, and tropospheric aerosols, lead to increases ranging from 4.2% K-1to 5.8% K-1,except the case of BC forcing, which has a slight decrease in mean precipitation. The different responses of mean precipitation are understood by examining the changes in the surface energy budget. The surface warming is associated with a warmer and moister atmosphere. The surface downward shortwave flux decreases due to the stronger scattering effect associated with more abundant water vapor, while the surface downward longwave flux increases because of the warmer atmosphere. The negative correlation between shortwave and longwave radiation flux at the surface narrows the mean precipitation differences among the cases. In the BC forcing case, the strong absorption of shortwave radiation by BC causes a large reduction in surface downward shortwave flux that exceeds the increases in backward longwave radiation, leading to a decrease in mean precipitation by 1.2% K-1. The EPS is greater than the MPS for all forcings.The change in extreme precipitation is decomposed into three components: the thermodynamic, dynamic, and precipitation-efficiency components. The thermodynamic components are similar among all the cases, since they are strongly constrained by the SST changes. The dynamic components are negative for all cases, with large variation. The changes in vertical velocity profiles show weakening in the middle troposphere and upward shifts of peaks. The dynamic components are correlated with the shifts in tropopause levels among the cases. The precipitation-efficiency component is negatively correlated with the dynamic component, presumably due to the constraint of the time scale of the conversion of cloud water to precipitation. The cancellation between the dynamic and precipitation-efficiency components leads to a small dependence of extreme precipitation on forcings.

The idealization of RCE removes the impacts of largescale circulation changes on the MPS and EPS. An additional pair of experiments with imposed large-scale ascent(section S1) implies that the large-scale ascent drives the MPS approaching the CC scaling. The large-scale ascent also amplifies the EPS. However, further study is required to better survey the effects of large-scale motion on mean and extreme precipitation responses (Lau et al., 1993; Sui et al., 1994; Wu and Moncrieff, 1999). Besides, this study only considers the direct radiative effects of aerosol forcing and neglects the impacts of aerosols on cloud microphysics.The main conclusion suggests that changing the radiative flux in different ways is not likely to generate large differences in the MPS and EPS, due to the cancellation mechanism discussed above. The exception is absorption of shortwave radiation in the atmosphere (i.e., the BC forcing),since the other forcing considered here may be thought of as the surface warming leading to atmospheric warming, while the Aer_bc case warms the surface by warming the atmosphere. The results of this study also suggest that the discrepancies in the dependence of the EPS on climate forcing in GCM studies (e.g., Pendergrass et al., 2015; Lin et al.,2016; Myhre et al., 2017; Sillmann et al., 2017) are more likely due to the different treatments of cloud microphysics.Further efforts on reducing the uncertainties of the impact of aerosol on cloud microphysics will benefit our understanding of how mean and extreme precipitation respond to climate change.

Acknowledgements.The authors thank the two anonymous reviewers and the editor for their valuable reviews, as well as Qiang FU and Qian CHEN for discussion. This research was supported by the National Natural Science Foundation of China (Grant No. 41875050).

Electronic supplementary material:Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-020-9236-1.