Summer Extreme Precipitation in Southern China from the Perspective of Moisture Static Energy

: The extreme precipitation (EP) in the early and late rainy seasons in Southern China is investigated from the perspective of moist static energy (MSE). At the synoptic time scale, the EP is accompanied by the charge – discharge paradigm of the vertically integrated MSE ( h MSE i ); the positive h MSE i anomaly reaches the peak one day before EP and decreases quickly during the event. The charge – discharge paradigm of h MSE i is dominated by the horizontal and vertical advection, respectively. However, synoptic systems responsible for the h MSE i charge in the early and late rainy seasons are different due to the different horizontal distributions of climatological MSE in the lower troposphere caused by the northward migration of solar radiation and the monsoon system. At the interannual time scale, more EP in the early (late) rainy season is associated with the higher seasonal-mean h MSE i that can be caused by the anomalous anticyclone (cyclone) in the western North Paci ﬁ c induced by the SST anomalies in the tropical Indian Ocean and central North Paci ﬁ c (the tropical Paci ﬁ c). The multimodel ensemble mean of CMIP6 models reproduces well the observed h MSE i – EP relationship in both the historical and Shared Socioeconomic Pathway 5 – 8.5 (SSP5 – 8.5) runs. Moreover, the mean state of h MSE i increases in the SSP5 – 8.5 compared to historical runs along with more frequent occurrence of EP events. Hence, h MSE i can serve as a useful metric for studying EP in Southern China at various time scales.


Introduction
Southern China (SC) is the wettest region in China.It experiences frequent occurrences of extreme precipitation (EP) and thus suffers tremendous loss by the concomitant flooding.To improve our understanding, prediction, and mitigation of the EP in SC, several field campaigns have been conducted since the 1970s (e.g., Huang 1986;Chen and Zhao 2004;Zhang et al. 2011;Luo et al. 2017).It has been observed that in the early rainy season, when the quasi-stationary cold front of the East Asian summer monsoon is located in SC, the EP can occur near the front and/or in the warm sector 200-300 km to the south of the front (Huang 1986).The frontal EP is mainly induced by the confluence of cold and warm air and the subsequent strong baroclinic instability.The warm-sector EP is less influenced by the baroclinic instability since the meridional temperature gradient there is small.In contrast, presence of a low-level jet (LLJ) is believed to play an important role in initializing the warm-sector EP at its termini and supplying abundant moisture from the South China Sea (SCS) (e.g., Du and Chen 2019;Liu et al. 2020).In general, the warm-sector atmosphere is unstable and characterized by large convective available potential energy (CAPE), small convective inhibition, and high precipitable water, which are all conducive to development of mesoscale convective systems (Luo et al. 2017).A cold pool left over by former convection and the complex topography in SC are also important for triggering the warm-sector convection (Wang et al. 2014).In the late rainy season when the monsoonal front jumps stepwise northward to the Yangtze River valley and North China, the EP in SC is mainly caused by the tropical synoptic systems that propagate from the SCS and western North Pacific, such as the tropical depression, tropical cyclone, Rossby waves, and boreal summer intraseasonal oscillation (BSISO) (e.g., Ren et al. 2002;Hsu et al. 2016;Ren et al. 2018).
The low-frequency, large-scale drivers are crucial to the formation of EP in SC (e.g., Yuan et al. 2019).In the early rainy season, an anomalous anticyclone in the western North Pacific can increase the occurrence of EP by enhancing the warm moisture transport to SC via the anomalous southwesterlies along its northwestern flank.In stark contrast, in the late rainy season, more frequent EP is closely related to an anomalous cyclone in the western North Pacific with its center a little northward than the abovementioned anomalous anticyclone in the early rainy season.The anomalous northerly winds along the western flank of the anomalous cyclone reduces the warm and moist monsoonal airflow out of SC and thus favors the occurrence of EP in SC (Yuan et al. 2019).Both the anomalous anticyclone and cyclone are closely related to the sea surface temperature (SST) anomalies in the tropical oceans but in different basins (e.g., Xie et al. 2009;Wu et al. 2017;Yuan et al. 2019).In addition, the tropical SST anomalies, especially those related to El Niño-Southern Oscillation (ENSO), can also modify the occurring frequency, intensity, and propagation speed of BSISO (e.g., Lin 2019;Liu et al. 2016;Chen et al. 2020) and the genesis and track of tropical cyclones in the western North Pacific (e.g., Chan 1984;Wu and Wang 2004;Camargo et al. 2007) that often bring EP to SC in the late rainy season.
The EP, by nature, is caused by strong convection that converts other forms of energy such as latent heat and internal energy into kinetic energy.The CAPE is often calculated when conducting case studies of EP (e.g., Luo et al. 2017).It estimates the total amount of energy that an air parcel can convert during an undiluted ascent by vertically integrating the virtual temperature difference between the air parcel and the environment from the level of free convection to the level of neutral buoyancy.As such, the bigger the difference between the source level where the air parcel originates and the atmosphere aloft, the larger the CAPE and the stronger the convection.EP events in SC are typically associated with high CAPE, particularly in the presence of strong LLJs (Du et al. 2022).However, in East Asia, EP events can occur when the atmosphere is close to moist neutral stratification, characterized by a nearly uniform, equivalent potential temperature and high relative humidity in the vertical from the lower to middle troposphere, resulting in a medium or even small CAPE (#500 J kg 21 ) (e.g., Ninomiya 2004;Li et al. 2012;Chen et al. 2014).This phenomenon also holds true for some EP events in SC during nighttime.Although the humid middle troposphere can lower the CAPE, it is conducive to development of strong convection by reducing the entrainment of dry air into the updrafts and the modification of the boundary layer by the dry downdrafts (e.g., Gray 1998;Montgomery et al. 2006).In addition, the EP in East Asia is closely related to the atmospheric convergence from the lower troposphere to around 400 hPa (Li et al. 2012).The humid middle troposphere can thus help fuel the convection.Hence, when considering the EP in East Asia, the moisture potential energy (MSE) can be a good alternative to CAPE to describe the EP-related convective instability.The MSE is the sum of internal energy, potential energy, and latent heat, and its vertical integration, hMSEi, represents the gross moist stability of the whole air column.Neelin and Held (1987) showed that the minimum hMSEi collocates with the intertropical convergence zone, indicating the export of hMSEi by strong convection.The export of hMSEi is also found during the deep convection related to the Madden-Julian oscillation (MJO), whereas a buildup of hMSEi occurs prior to the deep convection (e.g., Hendon and Liebmann 1994;Bladé and Hartmann 1993).This chargedischarge paradigm of hMSEi related to the MJO is mainly regulated by the horizontal and vertical advection of moisture, respectively (e.g., Maloney 2009;Sobel et al. 2014).Besides, an increase (decrease) in hMSEi is observed east (west) of the deep convection of MJO.Such a zonal asymmetry in the hMSEi tendency facilitates the eastward propagation of MJO (e.g., Jiang 2017;Wang et al. 2017).For the coupled models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012), successful simulation of the zonal asymmetry in the hMSEi tendency is believed to determine their realistic reproducibility of the eastward propagation of MJO (e.g., Jiang 2017;Wang et al. 2017).A recent study by Feng et al. (2020) found the chargedischarge paradigm of hMSEi during the convective rainfall of tropical-depression-type waves.Hence, the hMSEi, together with its budget equation, is an effective tool to diagnose convection and to attribute the relative contribution of different processes as described in the following data and methods section.
So far, there has been little research on diagnosing the hMSEi during the EP in SC.Inspired by the studies mentioned above, we devote this study to investigating the hMSEi-EP relationship in SC.This not only provides a new perspective to analyze the EP but also helps reveal the relative contribution of different atmospheric processes and anomalous heating on the EP formation.The rest of the study is organized as follows.Section 2 introduces the data and methods.The observed hMSEi-EP relationship at the synoptic and interannual time scales are presented in sections 3 and 4, respectively.Section 5 assesses the reproducibility of the observed hMSEi-EP relationship in the historical experiments and future projections by the state-of-the-art coupled models participating in CMIP6.Conclusions and discussion are given in section 6.

Data and methods
The gridded daily precipitation based on more than 2400 observation stations in China with a horizontal resolution of 0.5 3 0.5 from 1979 to 2016 is provided by the Chinese Meteorological Administration (CN05.1;Wu and Gao 2013).The daily and monthly NCEP-DOE AMIP-II reanalysis (Kanamitsu et al. 2002) and monthly NOAA Extended Reconstructed Sea Surface Temperature, Version 5 (ERSST.v5;Huang et al. 2017) for the same period are adopted.The daily outputs of historical runs  and future projection (2064-99) under Shared Socioeconomic Pathway 5-8.5 (SSP5-8.5)scenario by 15 CMIP6 models downloaded from the Earth System Grid Federation (ESGF) centers (https://esgf-node.llnl.gov/search/cmip6/) are also used.(Table 1).When focusing on the synoptic and interannual time scales, the 11-yr highpass Fourier harmonic filter is applied to remove the lowfrequency variations in all datasets prior to further analyses.The anomaly here is calculated as the deviation from the climatological seasonal cycle.Composite and linear regression are the major analysis methods.The statistical significance is examined by the two-tailed t test.
The MSE is the sum of internal energy, potential energy, and latent heat, where C p is the specific heat at the constant pressure, T is the temperature, g is the gravitational acceleration, z is height, L is the latent heat of evaporation at 08C, and q is the specific humidity.The hMSEi represents the gross moist stability of the air column, and its budget can be calculated as follows: Here, the angle brackets denote the vertical integral from the surface to the top of the atmosphere (100 hPa in this study), p is pressure, v is the vertical velocity, V is the horizontal velocity, LH and SH are the surface latent and sensible heat fluxes, and LW and SW are the longwave and shortwave radiation.The tendency of hMSEi on the right-hand side is thus determined by the vertical advection, horizontal advection, surface latent and sensible heat fluxes, and the vertically integrated shortwave and longwave radiation.
In the early and late rainy seasons, the EP formation is quite different, as mentioned in the introduction section, and thus the hMSEi-EP relationship is investigated in each season separately.Here, the early and late rainy seasons refer to May-June (MJ) and July-August (JA), following Wang et al. (2009) and Yuan et al. (2019).We note that April-June is also commonly used as the early rainy season in SC.However, the results obtained in this study do not change much regardless of April-June or May-June being used.The EP at each grid in each season is defined as the daily precipitation larger than the threshold value that is the 95% percentile of all daily precipitation in that season.If greater than 15% of grids in SC (208-288N, 1068-1208E) have the EP on the same day, SC, as a region, is regarded to experience the EP on that day, and the regional mean precipitation is regarded as the amount of EP.Here, 15% is selected roughly in accordance with the observed spatial scale of the synoptic EP event in SC (e.g., Luo et al. 2017).We note that if there are several continuous days when greater than 15% of grids have the daily precipitation above the threshold values, they are considered as one EP event and the day with the largest precipitation is the occurrence day of this event.Figures 1a and 1b show the observed threshold values of EP in MJ and JA.It is clear that the EPs in MJ are generally larger than those in JA, due to the larger MJ precipitation related to the monsoonal rain belt (Fig. 1c).In addition, the JA threshold values are larger along the coastal than inland regions mainly because the JA EP is closely associated with the tropical systems, such as tropical cyclones (Cai et al. 2018).By the EP definition, 134 (118) EP events are selected in MJ (JA) during 1979-2016; about three events occur per season with the mean duration of 1.4 (1.7) days.Since the number of EP events per season is small, the 95th percentile of precipitation (R95p) referred to the accumulated amount of EP in each season is adopted to reflect the interannual variations of EP.The observed R95p in MJ and JA is not closely related with the correlation coefficient of 20.17 during the period of interest (Fig. 1d), ensuring the necessity to separately analyze their characteristics.
The EP events from the historical experiment in each model are selected by exactly the same approaches as in the observations except that the threshold value of EP is determined by the model's own climatology.For the far-future projection, the threshold value of EP in each model is kept the same as its historical experiment, which facilitates the exploration of possible change in the EP frequency under global warming.As a result, 141 (127) EP events after the multimodel

The observed hMSEi-EP relationship at the synoptic time scale
Temporal evolution of the anomalies in precipitation and hMSEi averaged over SC 7 days before and after the occurrence of EP in MJ is shown in Fig. 2a.It is interesting to see that the occurrence of EP is accompanied by the charge and discharge of hMSEi; the hMSEi increases gradually, reaches the peak 1 day before the EP, and declines thereafter.The charge-discharge process is dominantly controlled by the latent heat and internal energy anomalies (Fig. 2c).During the charge, the horizontal advection plays the major role through the horizontal wind anomaly acting on the climatological hMSEi gradient, particularly in the lower troposphere (Figs.3a,c and  4a,c).The maximum horizontal advection occurs at 850 hPa 1 day before the EP, due to the large zonal gradient of climatological MSE and the large zonal wind anomaly (Fig. 4c).During the discharge, the hMSEi anomalies are mainly caused by the vertical advection related to the strong vertical motion of EP (Figs. 3a,e).In contrast to the dynamical processes, contribution of the heat fluxes is negligible to the buildup and export of hMSEi, due to the compensating impacts of the surface sensible and latent heat fluxes and the column-integrated long-and shortwave radiation (Fig. 3g).
To further illustrate the role of horizontal wind anomalies on the hMSEi budget, the evolution of large-scale atmospheric circulation at 850 hPa, where the maximum contribution of horizontal advection to the hMSEi charge occurs, is prepared in Fig. 5.It is clear that an anomalous anticyclone exists south of SC in the SCS and western North Pacific 3 days before the occurrence of MJ EP, while an anomalous cyclone appears in northwestern China (Fig. 5a).The anomalous cyclone moves southeastward along the edge of Tibetan Plateau, approaching SC and leading to the enhanced southwesterly anomalies between the anomalous cyclone and anticyclone (Figs.5c,e).Since the climatological MSE at 850 hPa west and south of SC in the lower troposphere is higher than that in SC, mainly due to more humid and warmer atmosphere (Fig. 6a and Figs.1a,c,e,g in the online supplemental material), the southwesterly anomalies can advect the higher climatological MSE to SC and results in the increased hMSEi (Figs.3a,c and 4a,c).The anomalous cyclone and anticyclone become narrower on the day of EP, and then fade away thereafter (Figs.5g,i,k).In contrast to the horizontal advection, the vertical advection induced by the strong convection during the EP discharges the hMSEi, with the maximum discharge occurring on the EP day (Figs.3a,e).To illustrate the causality, vertical distributions of the climatological MSE and anomalous vertical velocity on the EP day are prepared in Fig. 7a.It is clear that the climatological MSE over SC is higher in the lower and upper troposphere and has the minimum value near 600 hPa (Fig. 7a, blue line).This is because the decreasing contribution of moisture and temperature to the MSE with height is first surpassed by the increasing contribution of geopotential height at around 600 hPa.Hence, the vertical gradient of climatological MSE with height is negative below but positive above 600 hPa (Fig. 7a, green line).As a result, the strong upward motion related to the EP convection within almost the whole air column (Fig. 7a, red line) leads to the net discharge of hMSEi (Figs.3a,e).
The increased precipitation in SC 1-2 days before and after the EP day can change the atmospheric thermal condition and lead to significant anomalies in the surface heat flux and the vertically integrated radiation (Figs.2a and 3g).We know that the air column with the increased moisture and cloud cover related to the increased precipitation generally absorbs more longwave and shortwave radiation (Fig. 3g).On the other hand, the increased cloud cover can reduce the shortwave radiation reaching the ground surface, which may result in the decreased surface temperature and upward surface sensible heat flux.Also, the nearly saturated atmospheric boundary layer due to the increased precipitation can reduce the upward latent heat fluxes from the surface to the overlying atmosphere.As the increased longwave and shortwave radiation is well offset by the decreased surface sensible and latent heat, the thermal processes together contribute little to the hMSEi charge before the MJ EP (Figs. 3a,g).It is worth mentioning that the southwesterly anomalies between the pair of anomalous cyclone and anticyclone 1-2 days before the MJ EP enhance the occurrences of LLJ at 850 hPa; more than half of the MJ EP events are accompanied by the preceding LLJ (Fig. 8a).Here the LLJ is detected by the same method as used by Du and Chen (2019); the wind speed is greater than 10 m s 21 .As a result, abundant warmer and moister airflow is transported to SC, which charges the hMSEi and fuels the precipitation at the LLJ terminus 1-2 days before the EP, although the precipitation amount is much less than that on the EP day (Figs.2a and 9a,c).The LLJ can also modify the surface heat flux; the warmer airflow helps reduce the upward sensible heat flux, but the high wind speed boosts the upward latent heat flux, especially over southwestern SC (Figs. 8a,c,e).
The temporal evolution of precipitation and hMSEi anomalies related to the EP in JA are highly analogous to that in MJ; the hMSEi charges before the occurrence of EP, reaches the peak one day earlier than the EP and discharges rapidly thereafter (Fig. 2b).Similarly, the buildup and export of hMSEi are mainly controlled by the latent heat and internal energy (Fig. 2d).Also, the charge of hMSEi can be largely attributed to the horizontal advection through the anomalous wind acting on the climatological MSE gradient, while the discharge is dominated by the vertical advection (Figs.3b,d,f).However, compared to MJ, the maximum horizontal advection in JA in the lower troposphere is at 925 hPa and smaller (Figs.4a,b).The synoptic systems that cause the JA EP are also different (Fig. 5).About five days before the JA EP, a pair of anomalous cyclone and anticyclone first appear in the western North Pacific in the lower troposphere and then propagate northwestward toward SC (Figs. 5b,d,f).We note that with the northward advance of solar radiation and monsoonal circulation, the maximum center of climatological MSE in the lower troposphere west of SC moves northward in JA compared to MJ (Fig. 6).Meanwhile, a local maximum center appears near the northern boundary of SC at around 248-298N owing to the increased air temperature and moisture (supplemental Figs.1b,d,f,h).The northwestward propagation of the anomalous cyclone and the related northerly and westerly anomalies along its western flank advect the higher climatological MSE to SC (Figs. 4b,d and 6b), resulting in the increased MSE.We note that the maximum horizontal advection occurring at 925 hPa in JA is mainly due to the fact that both the maximum zonal and meridional gradients of the climatological MSE appear at 925 hPa.On the other hand, the smaller maximum horizontal advection in JA than MJ in the lower troposphere is due to the compensating impacts of meridional advection along the western and eastern flanks of the anomalous cyclone (Fig. 4).The anomalous cyclone at 925 hPa in JA is quite narrow in the zonal direction, and thus the positive contribution to the MSE charge by the anomalous northerlies along the western flank can be largely offset by the negative contribution by the anomalous southerlies along the eastern flank as indicated by the small negative meridional velocity averaged over SC at 925 hPa (Fig. 4d).However, above 925 hPa, the meridional advection by the anomalous northerlies is important to the hMSEi charge in JA (Fig. 4d).In the upper troposphere, the horizontal advection at 150 hPa in both MJ and JA is positive due to the prevailing of the anomalous northwesterlies over SC before and during the occurrence of EP (Figs. 4  and 6c,d).They can advect the higher climatological MSE northwest of SC that is mainly resulted from the higher air temperature due to the lower vertical height above the ground level.The integral horizontal advection from the lower to upper troposphere leads to the broadly increased hMSEi over SC one day before the EP (supplemental Fig. 2).
The different heat flux anomalies 1-2 days before and after the EP in JA are all significant and caused by the increased precipitation as in MJ except that the surface latent heat flux anomalies 1-2 days before the EP are positive, right opposite to those in MJ (Figs. 2a,b, 3g,h and 8c,d).This is mainly because the southwesterly anomalies between the northwestward-propagating pair of anomalous cyclone and anticyclone largely increase the frequency of LLJ over the coastal ocean near SC (Fig. 8b).The LLJ significantly increases the precipitation over the coastal SC 1-2 days before the PE, although the precipitation amount is much smaller than that in the EP day (Figs.9b,d).The high wind speed related to the LLJ also boosts the latent heat release from the coastal ocean, resulting in the positive surface latent heat flux (Fig. 8d).Even so, the net contribution of heat flux to the hMSEi charge is still much smaller than that of the horizontal advection (Fig. 3b).
Although the anomalous cyclones appear over SC during the occurrence of EP in both MJ and JA, they approach SC from different directions (Fig. 5).This is probably because of the opposite meridional gradient of lower-tropospheric climatological MSE; the negative (positive) meridional gradient requires the anomalous southerlies (northerlies) to charge the MSE (Figs. 4c,d).Hence, the EP formation in the early rainy season needs the synoptic disturbance from the mid-high latitudes, while that in the late rainy season is accompanied by the northwestward propagation of tropical systems such as the Rossby waves.However, regardless of the different synoptic systems, the atmosphere in SC is anomalously charged before the occurrence of EP, but discharged during and after the EP in both the early and late rainy seasons (Fig. 3).

The observed hMSEi-EP relationship at the interannual time scale
At the synoptic time scale, the hMSEi increases before the occurrence of EP as just illustrated in section 3, showing that the atmosphere needs additional energy to support the strong convection.This suggests that for the rainy season, when the atmosphere has the anomalously high seasonal-mean hMSEi, it could be conducive to more EP.Indeed, when the atmosphere in SC has the higher seasonal-mean hMSEi in MJ, SC experiences higher R95p (Fig. 10a); when the seasonal-mean hMSEi in MJ is higher than one standard deviation, the averaged EP frequency (R95p) increases by 18.13% (18.14%).The higher seasonal-mean hMSEi can be caused by the enhanced moisture transport from the southern oceans to SC via the anomalous southwesterlies along the northwestern flank of the anomalous anticyclone in the western North Pacific (Fig. 10c).As well studied in literature (e.g., Wang et al. 2000;Xie et al. 2009Xie et al. , 2016;;Wu et al. 2014;Yuan et al. 2019), the anomalous anticyclone is closely related to the local negative SST anomalies under its southeastern flank via the local air-sea interaction and the remote positive SST anomalies in the tropical Indian Ocean via the eastward-propagating, warm Kelvin waves.Hence, when the tropical Indian Ocean is warmer and the central North Pacific is cooler than normal, the seasonal-mean hMSEi in SC becomes anomalously high.This means that the background state of the atmosphere in SC contains more energy.Under such a condition, it may be easier for a passing-by synoptic system such as the midlatitude cyclone to trigger the EP.To further reveal the impacts of the SST anomalies on the MJ EP, Index1 is defined as the difference in the region mean SST anomalies between the tropical Indian Ocean (108S-208N, 508-1008E) and the central North Pacific (98-218N, 1608E-1608W).The correlation coefficient between Index1 and MJ R95p is 0.54, significant at the 99.9% confidence level (Fig. 11a).The atmosphere in SC charges less of hMSEi before the occurrence of MJ EP when Index1 exceeds one standard deviation, whereas it charges more of hMSEi when Index1 is less than minus one standard deviation (Fig. 11c).
Here, the charge of hMSEi is estimated as the difference in hMSEi between 1 and 3 days before the occurrence of EP.
As with the case of early rainy season, in the late rainy season, when the atmosphere in SC has the higher seasonalmean hMSEi, SC experiences more EP (Fig. 10b); when the seasonal-mean hMSEi is higher than one standard deviation, the averaged EP frequency (R95p) in JA increases by 34.4% (31.5%).The higher seasonal-mean hMSEi in JA can be caused by the northerly and westerly anomalies along the western flank of the anomalous cyclone centered in the western North Pacific.
As shown in Figs.4d and 6b, the climatological MSE in the lower troposphere in JA has the higher value west of SC and another local maximum center near the northern boundary of SC.The northerly and westerly anomalies advect the higher climatological MSE to SC (Fig. 6b), resulting in the  (Matsuno 1966;Gill 1980;Yuan et al. 2019).If we define Index2 as the difference of the region mean SST anomalies between the western (108S-108N, 908-1408E) and eastern (108S-108N, 1708E-1408W) poles, the linear correlation coefficient between Index2 and R95p in JA is 0.49, significant at the 99% confidence level (Fig. 11b).Hence, at the interannual time scale, when there are positive (negative) SST anomalies in the central (western) tropical Pacific, the seasonal-mean hMSEi in the late rainy season in SC is higher than normal.The atmosphere has more energy, charges less before the EP, and thus tends to have more EP (Fig. 11d).

The hMSEi-EP relationship in the CMIP6 models
So far, we have shown the close relationship between the hMSEi and EP in SC based on the observations.At the synoptic time scale, the EP occurrence is accompanied by the charge-discharge processes of hMSEi.At the interannual time scale, the higher seasonal-mean hMSEi in SC is conducive to more EP.Hence, it is interesting to examine whether the observed hMSEi-EP relationship can be simulated in the CMIP6 models.As shown in Figs.12a and 12b, the chargedischarge paradigm of hMSEi at the synoptic time scale in both the early and late rainy seasons is well reproduced by the multimodel ensemble mean of CMIP6 models in the historical runs; the hMSEi anomaly increases gradually, reaches the peak 1 day before the occurrence of EP, and decays thereafter.It is interesting to see that although the atmosphere in the CMIP6 models charges a similar value of hMSEi anomaly as in the observed, it produces weaker precipitation (Figs. 2a,b and 12a,b).This is probably because the CMIP6 coupled models generally simulate less precipitation in SC than the observed, likely due to the model biases in the convection scheme and/or representation of local topography (supplemental Fig. 3).
The buildup and export processes of hMSEi during the EP events remain almost the same in the far-future projections under the SSP5-8.5 scenario as in the historical runs (Fig. 12).This indicates that the model atmosphere in SC also needs the additional energy to support the EP occurrence regardless of possible change in the mean state under global warming.Compared to the historical runs, the atmosphere in the SSP5-8.5 runs charges more MSE before the EP and produces a larger amount of precipitation.This is probably because under global warming, the mean-state MSE and its horizontal gradient at the lower troposphere are increased (supplemental Fig. 4).If impacted by a similar EP-inducing synoptic system with similar strength of horizontal circulation, the atmosphere in the SSP5-8.5 run tends to charge more MSE, due to the higher horizontal gradient of the mean-state MSE.Meanwhile, the atmosphere in the SSP5-8.5 runs contains more moisture due to the higher air temperature under global warming, which may help produce more precipitation once the convection occurs (e.g., Berg et al. 2013;Fischer and Knutti 2016).However, the increasing ratio of the hMSEi anomaly is larger than that of the precipitation anomaly.The maximum hMSEi anomaly increases by 44% (32%) in MJ (JA) in the SSP5-8.5 compared to historical runs, but the precipitation anomaly of EP is only increased by 7% (13%) (Fig. 12).Held and Soden (2006) showed that if the global-mean surface air temperature (around 148C at present) increases by 18, about 7.1%, the column-integrated water vapor will increase at a rate of 7.5%, but the precipitation will increase only at a rate of 2.2%, due to the decreased vertical mass flux.Since the hMSEi anomaly is mainly contributed by the air temperature and humidity anomalies (Figs.2c,d), it is understandable that the increasing ratio of the hMSEi anomaly under global warming is larger than that of precipitation anomaly.However, it should be kept in mind that the discussion of Held and Soden (2006) is at the global scale, which may not fit the regional EP in SC.Further analyses are still needed in the future to investigate possible causality of the different increasing ratios of hMSEi and precipitation anomalies in SC under global warming.
At the interannual time scale, more R95p in both early and late rainy seasons in the historical runs is closely related to the higher seasonal-mean hMSEi in SC (Figs. 13a,b).This is consistent with the observations, and confirms that if the seasonalmean hMSEi is higher than normal, the atmosphere in SC more easily fuels the EP event and thus tends to experience more EP.This interannual hMSEi-EP relationship can also be seen in the far-future projections (Figs.14a,b).
Although the interannual hMSEi-EP relationship in the ensemble mean of CMIP6 models is robust and consistent with the observations, the underlying mechanisms responsible for the higher seasonal-mean hMSEi in SC can be different from the observations.In MJ, the higher seasonal-mean hMSEi in both the historical runs and far-future projections can be largely attributed to the horizontal transport by the moister and warmer airflow along the northwestern flank of the anomalous anticyclone in the western North Pacific that can be induced by the positive SST anomalies in the tropical Indian Ocean and negative ones in the central North Pacific, as in the observations (Figs.10c, 13c and 14c).However, a discrepancy exists between the observations and model simulations: Significant positive SST anomalies appear in the tropical Pacific in the models but not in the observations.This is because both the positive SST anomalies in the tropical Indian Ocean and the negative ones in the central North Pacific are closely related to the preceding winter El Niño (supplemental Fig. 5a).However, the modeled El Niño in the CMIP6 models decays slower than the observed and sustains in the tropical Pacific in the early summer of the decaying year (Ye et al. 2023;supplemental Fig. 5b).These positive SST anomalies in the tropical Pacific do not contribute to the anomalous anticyclone in the western North Pacific since they generally cause anomalous cyclonic circulation in the lower troposphere in the western North Pacific as the direct Matsuno-Gill response.Furthermore, the SST anomalies are larger in the SSP5-8.5 than historical runs (Figs.13c and 14c), which does not necessarily reflect a closer relationship between the SSTs and MJ EP under global warming.In this study, the SST anomalies are obtained by the linear regression upon the MJ R95p.Hence, they are decided not only by the linear relationship with the MJ R95p but also by their own interannual variabilities.The multimodel ensemble-mean correlation coefficients between Index1 and the MJ R95p in the historical and SSP5-8.5 runs are 0.43 and 0.45, respectively.They are very close to each other, both explaining about 20% of interannual variations in the MJ R95p.Hence, the linear relationship between the SSTs and the MJ EP remains almost unchanged under global warming.The higher SST anomalies in the SSP5-8.5 run are due to their increased interannual variabilities under global warming.The multimodel ensemble-mean standard deviations of Index1 in the historical and SSP5-8.5 runs are 0.448 and 0.568C, respectively, an increase of 27.3% under global warming.
In JA, the multimodel ensemble mean shows that the higher seasonal-mean R95p and hMSEi in SC in both the historical and SSP5-8.5 runs are driven by the anomalous cyclone in SC, the anomalous anticyclone in SCS, and the resultant southwesterlies in between (Figs. 13d and 14d).This is in stark contrast to the observed anomalous cyclone in the western North Pacific (Fig. 10d).To discover possible causality of the discrepancy between the observations and model simulations, performance of each model in the historical run is assessed by calculating the spatial correlation coefficient between the observed and simulated streamfunction at 925 hPa over 178-348N, 1008-1258E, where the atmospheric circulation anomalies are crucial for the horizontal advection of MSE, as illustrated in sections 3 and 4. The resultant correlation coefficients range from 0.71 to 20.75.We then group the models with the top seven highest correlation coefficients as the highskill models among which the lowest correlation coefficient is 0. of the 925-hPa climatological MSE averaged over SC is 0.80 3 10 23 J m 21 kg 21 based on the multimodel mean of the high-skill models.Hence, in these models, the higher-thannormal hMSEi and R95p in JA are closely related to the westerly and northerly anomalies in SC along the anomalous cyclone in the western North Pacific (Figs. 16a,c), as in the observations (Figs.10b,d).On the other hand, the low-skill models fail to reproduce the positive meridional gradient of the climatological MSE in the lower troposphere due to the southward displacement of air temperature and humidity, probably raised by the model biases in the East Asian summer monsoon (Figs.6b and 15).The meridional gradient of the 925-hPa climatological MSE averaged over SC is 22.28 3 10 23 J m 21 kg 21 , based on the multimodel mean of the low-skill models.As a result, the higher-than-normal hMSEi and R95p in JA in the low-skill models are closely related to the southwesterly anomalies along the anomalous anticyclone in the western North Pacific (Figs. 16b,d).Combination of the two groups leads to the anomalous cyclone in SC and anticyclone in SCS as seen in Fig. 13d.However, differing from the observations, the simulated anomalous cyclone or anticyclone in the western North Pacific is closely related to the SST anomalies in the central North Pacific rather than the tropical Pacific (Figs. 10d and  16c,d).Similar results can be obtained in the SSP5-8.5 as in the historical runs (supplemental Figs. 6 and 7).Nevertheless, it seems that proper simulation of the horizontal distribution of climatological MSE plays a key role in the realistic reproduction of the large-scale atmospheric circulation anomalies responsible for the interannual variations in seasonal-mean hMSEi and EP in JA in SC.

Conclusions and discussion
In this study, we have investigated the summer EP events in SC from the perspective of MSE.The observations show that at the synoptic time scale, the EP occurrence is accompanied by the charge-discharge paradigm of hMSEi in both the early and late rainy seasons.The positive hMSEi anomaly increases and reaches the peak 1 day before the EP, but decreases rapidly during and after the EP.The buildup of hMSEi is mainly caused by the horizontal advection, while the export is due to the convection-related vertical advection.However, the synoptic systems responsible for the horizontal advection of hMSEi are different between the early and late rainy seasons.In the early rainy season, 3 days before the occurrence of EP, there is an anomalous anticyclone southeast of SC in the western North Pacific and an anomalous cyclone in northwestern China in the lower troposphere.The anomalous cyclone gradually approaches SC along the edge of the Tibetan Plateau.The anomalous southwesterlies between the anomalous cyclone and anticyclone advect the higher climatological MSE south and west of SC to SC, contributing predominantly to the buildup of hMSEi.Compared to the early rainy season, before the occurrence of EP in the late rainy season, a northwestsoutheast-oriented anomalous cyclone and anticyclone pair propagate northwestward from the western North Pacific to SC.When the anomalous cyclone reaches SC, the northerly and westerly anomalies along its western flank advect the higher climatological MSE in the lower troposphere to SC and charge the atmosphere.
The charge of hMSEi before the occurrence of EP at the synoptic time scale suggests that the atmosphere in SC needs additional energy to support the strong convection.This indicates that the higher seasonal-mean hMSEi is conducive to more occurrence of EP.Indeed, at the interannual time scale, when the atmosphere over SC has the higher seasonal-mean hMSEi in the early or late rainy season, more EP events occur.The higher seasonal-mean hMSEi in the early rainy season is closely related to the warmer SSTs in the tropical Indian Ocean and cooler SSTs in the central North Pacific that can induce the anomalous anticyclone in the western The observed hMSEi-EP relationship in SC can be seen in the historical runs and far-future projections under the SSP5-8.5 scenario by the CMIP6 models.The multimodel ensemble mean reproduces well the observed charge-discharge paradigm of the hMSEi during the EP at the synoptic time scale.It also reproduces well the close relationship between the seasonal-mean hMSEi and EP at the interannual time scale: the higher the seasonal-mean hMSEi, the more EP events.We note that the multimodel ensemble mean can also simulate the observed teleconnection between the seasonalmean hMSEi and SSTs in the tropical Indian Ocean and the central North Pacific in the early rainy season.However, it fails to simulate the observed teleconnection between the seasonal-mean hMSEi and the SSTs in the tropical Pacific in the late rainy season both in the historical and SSP5-8.5 runs.This is probably because only half of the CMIP6 models adopted here can reproduce the observed positive meridional gradient of the climatological MSE in SC at the lower troposphere in the late rainy season and thus the anomalous cyclone in the western North Pacific responsible for the increased R95p and seasonal-mean hMSEi.The other half simulate the opposite gradient and thus the anomalous anticyclone in the western North Pacific.However, no matter the anomalous cyclone or anticyclone, it is closely related to the SST anomalies in the central North Pacific rather than the tropical Pacific.Further studies are still required to explore possible origin of the model biases in the SC EP-SST teleconnection.
Besides the synoptic and interannual time scales, the hMSEi may also be used to project the possible change in EP under global warming.The number of EP events in SC in the early (late) rainy season is 141 (127) in the historical experiments, and 169 (160) in the far-future projections (Figs.17a,c), consistent with the increased EP frequency under global warming in literature (e.g., Pfahl et al. 2017).Meanwhile, the climatology of hMSEi in SC in the early (late) rainy season is 3.11 3 10 7 (3.15 3 10 7 ) J day 21 in the historical experiments, and increases to 3.18 3 10 7 (3.23 3 10 7 ) J m 22 in the far-future projections, owing to the increase in the latent heat from 0.59 3 10 7 (0.60 3 10 7 ) J m 22 to 0.61 3 10 7 (0.63 3 10 7 ) J m 22 and internal energy from 2.39 3 10 7 (2.43 3 10 7 ) J m 22 to 2.43 3 10 7 (2.47 3 10 7 ) J m 22 in MJ (JA) (Figs. 17b,d).This indicates that the increased mean-state hMSEi may foster the EP occurrence under global warming.Hence, it seems that the hMSEi can be used as a metric to investigate the EP in SC at various time scales; the higher the hMSEi, the more likely the occurrence of EP.This is, to some extent, analogous to the genesis potential index (GPI) of the tropical cyclone (e.g., Emanuel and Nolan 2004).However, we cannot find a specific threshold value above which the EP definitely occurs in SC.Even so, this study, for the first time to our knowledge, has successfully shown the close hMSEi-EP relationship at various time scales in both the observations and model simulations.This certainly enhances our understanding of EP in SC from the perspective of the atmospheric energy.It may also serve as a new metric to assess the model capacity on simulating the EP in SC.Here, only the performance of multimodel ensemble mean of CMIP6 is examined, and further studies are also needed to understand model spread on simulating the hMSEi-EP relationship and the origin of model biases.
ensemble mean occur in MJ (JA) in the historical experiments, and 169 (160) EP events in the far-future projections.It seems that the CMIP6 models, on average, simulate more frequent EPs than the observed.However, large model spread exists; the Fifth Generation Canadian Earth System Model (CanESM5) has the largest number of EP events of 205 (227) in MJ (JA), while the Institute for Numerical Mathematics Coupled Model, version 4.8 (INM-CM4.8),has the lowest number of 112 (54) in their historical runs.Hence, the observed EP number 134 (118) is right within the scope of model spread.

FIG. 1 .
FIG. 1. Threshold values of extreme precipitation (mm day 21 ) in SC in (a) MJ and (b) JA during the period of 1979-2016.(c) Monthly climatology (bars; mm month 21 ) and standard deviation (line; mm month 21 ) of SC precipitation.(d) Normalized R95p in MJ (orange line) and JA (blue line).
FIG. 2. Composite anomalies in (a),(b) precipitation (red line; mm day 21 ) and hMSEi (blue line; 10 6 J m 22 ) and (c),(d) the hMSEi components (10 6 J m 22 ), including internal energy (purple line), potential energy (orange line), and latent heat (green line) 7 days before and after the occurrence of EP in SC in (a),(c) MJ and (b),(d) JA.Solid circles indicate the anomalies significant at the 95% confidence level.
FIG. 3. (a),(b) Composite tendency of hMSEi (dark line; W m 22 ) 7 days before and after the EP and the contributions from the vertically integrated horizontal advection (red line), the vertical advection (blue line), the net heat flux (green line), and the residual (gray line) in (a) MJ and (b) JA. (c),(d) Decomposition of the vertically integrated horizontal advection (solid red line; W m 22 ) to the anomalous (dashed orange line)/climatological (dashed yellow line) zonal wind acting on the climatological/anomalous MSE zonal gradient and the sum (solid yellow line), and the anomalous (dashed light blue line)/climatological (dashed dark blue line) meridional wind acting on the climatological/ anomalous MSE meridional gradient and the sum (solid gray line) in (c) MJ and (d) JA. (e),(f) Decomposition of the vertical advection (blue line; W m 22 ) to the anomalous (yellow line)/climatological (gray line) vertical velocity acting on the climatological/anomalous MSE vertical gradient in (e) MJ and (f) JA. (g),(h) Decomposition of the anomalous heat flux (green line; W m 22 ) to the column-integrated shortwave (red line) and longwave (blue line) radiation, and the surface latent (orange line) and sensible (yellow line) heat flux in (g) MJ and (h) JA.Solid circles indicate the anomalies significance at the 95% confidence level.

FIG. 6 .
FIG. 6. Horizontal distributions of climatological MSE (10 4 J kg 21 ) at (a) 850 and (c) 150 hPa in MJ and at (b) 925 and (d) 150 hPa in JA.The interpolated green vectors denote the composite anomalies in the horizontal wind (m s 21 ) 2 days before the occurrence of EP at the corresponding vertical level.

FIG. 7 .
FIG. 7. Vertical distributions of climatological MSE (blue line; 10 5 J kg 21 ), its vertical gradient (green line; 10 22 J kg 21 Pa 21 ), and the composite anomalies of vertical velocity (red line; 10 22 Pa s 21 ) averaged in SC at the day of EP in (a) MJ and (b) JA.The solid circles indicate the anomalies significant at the 95% confidence level.

FIG. 11 .
FIG. 11.Normalized time series of (a) R95p (red line) and Index1 (blue line) in MJ and (b) R95p (red line) and Index2 (blue line) in JA.The correlation coefficient between the two time series is shown in the upper-right corner.(c),(d) Composite anomalies in hMSEi (10 6 J m 22 ) 7 days before and after the EP for all EP cases (dark lines) and those when (c) the Index1 and (d) Index2 are larger than one standard deviation (red line) or less than minus one standard deviation (blue line).Index1 is defined as the difference of region-mean SST anomalies between the tropical Indian Ocean (108S-208N, 508-1008E) and the central North Pacific (98-218N, 1608E-1608W).Index2 is defined as the difference of the region-mean SST anomalies between the western (108S-108N, 908-1408E) and eastern (108S-108N, 1708E-1408W) tropical Pacific.The solid circles indicate the anomalies significant at the 95% confidence level.
FIG. 12. Composite anomalies in precipitation (red line; mm day 21 ) and hMSEi (blue line; 10 6 J m 22 ) 7 days before and after the occurrence of EP in SC in (a),(c) MJ and (b),(d) JA, based on the multimodel ensemble mean of CMIP6 models in (a),(b) historical experiments and (c),(d) far-future projection under the SSP5-8.5 scenario.Solid circles indicate the anomalies significant at the 99% confidence level.
FIG. 14.As in Fig. 10, but based on the multimodel ensemble mean of far-future projections under the SSP5-8.5 scenario by the CMIP6 models.
FIG. 16.As in Figs.10b and 10d, but based on the multimodel ensemble mean of historical experiments by the (a),(c) high-and (b),(d) low-skill CMIP6 models.

FIG. 17 .
FIG. 17.The multimodel ensemble mean of (a),(c) EP number and (b),(d) mean-state hMSEi (10 7 J m 22 ) in (a),(b) MJ and (c),(d) JA, based on the outputs of historical experiments (gray and blue bars) and far-future projections under SSP5-8.5 scenario (red and green bars) by the CMIP6 models.The vertical line at the top of each bar indicates the model spread.

TABLE 1 .
Brief description of 15 CMIP6 models.Most acronym expansions are available at http://www.ametsoc.org/PubsAcronymList.Other expansions include Australian Research Council Centre of Excellence for Climate System Science (ARCCSS), Chinese Academy of Sciences (CAS), Indian Institute of Tropical Meteorology Earth System Model (IITM-ESM), Centre for Climate Change Research (CCCR), and Norwegian Climate Centre (NCC).