10–30‐day moist static energy evolutions related to the persistent heavy rainfall event in different stages of flood season over South China

In this study, the flood season in South China (SC) was divided into three stages: two first rainy seasons (FRSs) around the South China Sea summer monsoon onset and one second rainy season when Typhoon prevails, denoted as FRS1, FRS2, and SRS, respectively, and then we diagnosed the moist static energy (MSE) budget associated with the 10–30‐day persistent heavy rainfall (PHR) over SC during these periods. The results indicate that there are great differences in the recharge of PHR‐related MSE in different stages of the flood season in SC: The FRS1 MSE associated with PHR moves southeastward from midlatitude; the large MSE is maintained in SC during the FRS2; during the SRS, the MSE perturbation propagates from the tropical western North Pacific to SC. From the perspective of the local MSE budget in SC, meridional and zonal advection play a key role in the maximum MSE change in the FRS1; the FRS2 and SRS MSE tendency is mainly determined by zonal advection and meridional advection, respectively. In contrast, the 10–30‐day propagating perturbation of MSE changes during both the FRS1 and FRS2 are mainly affected by the zonal advection, while the meridional circulation is dominant in the SRS. The cumulative contribution of external forcing (including radiation and surface heat fluxes) during the SRS to the propagation of PHR‐related MSE perturbation can reach more than 30%, and the closer to the land, the stronger the external forcing. During the FRS (including FRS1 and FRS2), however, the external forcing contributes little, even negatively.

PHR is also found in China and mainly reflected in the occurrence of frequency and intensity (Chen & Zhai, 2013), and especially, a significantly increased intraseasonal variability intensity of land monsoon precipitation was observed over Southeast China during the past four decades (Liu et al., 2022), which is mainly attributed to the negative phase of the Inter-decadal Pacific Oscillation and the warm phase of the Atlantic Multi-decadal Oscillation, augmented by increased greenhouse gas emission (Liu et al., 2022;Wang et al., 2013Wang et al., , 2018. The PHR in mainland China mainly occurs in southern China and is closely linked to intraseasonal oscillation (ISO) (Hui & Fang, 2016a, 2016bLi et al., 2015;Ren et al., 2013;Wang et al., 2017;Zheng & Huang, 2018). Therefore, Gao et al. (2016) introduced a regional ISO index to monitor the PHR in South China (SC). Generally, the ISOs include high frequency (HF) and low frequency (LF) oscillations with periods of 10-20 (or 10-30) and 30-60 days, respectively (Hui & Fang, 2016a, 2016bKrishnamurthy & Shukla, 2007;Li et al., 2015Li et al., , 2018Mao & Chan, 2005;. Over the lower reaches of the Yangtze River Basin, the HF-ISO mode has a comparable intensity to the LF-ISO mode (Yang et al., 2010), whereas, in SC, the intensity of the HF-ISO mode is much greater than that of the LF-ISO mode (Li et al., 2015;Zheng & Huang, 2018). Furthermore, the dominant structure of the HF-ISO mode associated with PHR over SC is a northwest-southeast-oriented wave train, with a low-level cyclonic anomaly and a high-level anticyclonic anomaly over the convection center, in which the HF-ISO disturbances move northwestward from the Philippine Sea (Li et al., 2015).
Regarding development of ISO convection, the moisture mode (or moisture dynamics) theory is widely accepted. In this theory, the positive moisture anomalies in the planetary boundary layer (PBL), mainly induced by the PBL convergence, have a leading phase to the ISO convection, which should destabilize the atmosphere to develop the ISO convection and associated PHR (Hsu & Li, 2012;Jiang et al., 2004;Zheng & Huang, 2018). Moreover, the PBL convergence is largely attributed to internal atmospheric dynamics including the mechanism of baroclinic vorticity advection in the monsoon season (Bellon & Sobel, 2008), barotropic vorticity advection in the pre-monsoon season , and the effect of vertical easterly wind shear (Drbohlav & Wang, 2005;Jiang et al., 2004;Li et al., 2021;Wang & Xie, 1997), and external forcing has a partial contribution (e.g., Kemball-Cook & Wang, 2001;Zheng et al., 2020).
In contrast, the other thinking of the moisture mode theory emphasizes the column-integrated moist static energy (MSE) tendency. Generally, a buildup of column MSE occurs before ISO deep convection, and MSE is discharged during and after ISO convection (Hendon & Liebmann, 1990;Kemball-Cook & Weare, 2001;Maloney, 2009). This process is the so-called chargedischarge cycle. Many previous studies have used the column-integrated MSE tendency to understand the development and propagation of the ISO convection or PHR (Adames & Kim, 2016;Kim et al., 2014;Raymond & Fuchs, 2009;Sobel & Maloney, 2012Zheng et al., 2021), while the MSE tendency related to ISO convection is mainly attributed to horizontal MSE advection in lower-troposphere (Adames & Wallace, 2015;Jiang, 2017;Kim et al., 2014;Sobel et al., 2014;Wang & Li, 2020b). This understanding implies that a low-level MSE change mainly determines the column-integrated MSE tendency which is closely linked to the development and propagation of ISO convection.
Predicting PHR is very challenging. Previous studies have proposed some methods to improve the prediction of SC PHR and achieved some results (e.g., Huang et al., 2022;Porson et al., 2019;Wu et al., 2020). However, we still lack a clear and systematic understanding of the physical process of SC PHR. In current sub-seasonal to seasonal prediction models, the prediction skill of SC PHR is quite low, especially compared to South Asian, Australian, and South American monsoon regions, and the main reason is that the Madden-Julian oscillation (Madden & Julian, 1971, 1972) effect is mainly located over western North Pacific (WNP) rather than over SC land region (Liu et al., 2022). This study attempted to reveal the relationship between the SC PHR and the column MSE in different stages of the rainy season and understand the MSE budget and relative roles in the SC PHR processes related to 10-30-day ISO. Through this work, we expect to further understand the main dynamic processes of the occurrence of SC PHR and obtain the signals that can be used for PHR prediction in SC. The data sets and methods used in this study are described in the next section. The characteristics of the SC PHR associated with 10-30-day ISO and their relationship with MSE are presented in Section 3. Section 4 presents the vertically integrated MSE budget related to the PHR over SC in different stages of the rainy season, which is followed by a summary.
2 | DATA AND METHODS

| Data
In this study, the data used include daily precipitation from the China Meteorological Administration (CMA) surface stations in SC with 176 sites for the period January 1, 1961, through December 31, 2017, and daily three-dimensional winds, water vapor, geopotential height, and air temperature from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis (Kalnay et al., 1996) with 2.5 Â 2.5 grids for the same period. The other data sets include the daily surface fluxes (surface solar radiation, longwave radiation, latent, and sensible heat fluxes), precipitation, and the daily top-ofatmosphere net shortwave and longwave radiation from the NCEP-NCAR reanalysis with a T62 Gaussian grid. Note that the surface fluxes are positive upward. The climatological mean is from 1981 to 2010, and anomalies by removing the climatological mean were filtered by a 10to 30-day band-pass filter. For convenience, the NCEP-NCAR reanalysis was interpolated into 1 Â 1 spatial resolution.

| Methods
In this study, a band-pass filter is applied to the daily data, and the LF component (>30 days) is derived from the deviation from the synoptic-scale component (<10 days) and 10-30-day HF-ISO component. Furthermore, composite analysis and lead-lag correlation analysis are introduced to understand the processes of the PHR events over SC related to 10-30-day ISO. The day with 10-30-day filtering PHR precipitation maximum was chosen as the reference day (zero-day) for composite.
MSE is defined as m = c p T + gh + Lq, where T is the temperature, c p is the specific heat at constant pressure, g is the gravitational acceleration, h is the geopotential height, L is the latent heat of vaporization at 0 C, and q is the specific humidity. A mass-weighted vertical integral from 1000 to 300 hPa is applied to calculate the tropospheric total MSE. Following Neelin and Held (1987), the column-integrated MSE budget can be written as where the angle brackets represent a mass-weighted vertical integral from the surface (here, taken as 1000 hPa) to the top of the troposphere (here, taken as 300 hPa), p is the pressure, v is the horizontal wind vector, and ω is the vertical pressure velocity. The first term on the left in Equation (1) is the vertically-integrated MSE tendency, the second term denotes the change in MSE due to vertical advection, and the third term represents the horizontal advection of MSE. LH is the surface latent heat flux, SH is the surface sensible heat flux, LW represents the longwave radiation, and SW represents the shortwave radiation. In this study, LW h i and SW h i were estimated by SLW minus TLW and TSW minus SSW, respectively. Here, SLW is the surface net LW, TLW is the top-of-theatmosphere net LW, SSW represents the surface net SW, and TSW represents the top-of-the-atmosphere net SW.
Of interest is the HF-ISO time scale, so a band-pass filter was applied to Equation (1) to obtain where quantities with a subscript 10-30 represent a 10-30-day band-pass-filtered field.

| Definition of regional PHR
Following Lin et al. (2020), a PHR event in this study is defined when the regional precipitation meets the given conditions for 3 consecutive days or more. The given conditions include the ratio of the number of stations with precipitation larger than 50 mm to the total number of stations in the region greater than or equal to 4%, and regional average precipitation exceeding 1.5 times the standard deviation (std). In this study, the SC region is 107-120 E, 21-26 N (see the box in Figure 1), where 267 regional PHR events are obtained. The SC region was chosen based on the significant correlation coefficients between the precipitation anomalies at the point where the occurrence frequency maximum in the south of China is located and the precipitation anomalies (Lin et al., 2020;Zheng et al., 2022). Since we are interested in the intraseasonal persistent rainfall, so we chose PHR events related to 10-30-day ISO by using the criterion: the regional mean 10-30-day filtering precipitation is greater than 0.5 times the std and lasts for 4 days or more; at the same time, the PHR process defined by Lin et al. (2020) is at least 3 days in this period.

| Case selections
According to the characteristics of the background circulation, the flood season in SC is usually divided into two stages: the first rainy season (FRS; from April 1 to June 30) and the second rainy season (SRS; from July 1 to September 30). Since the basic state of the circulation is significantly different before and after the SC Sea summer monsoon (SCSSM) onset, in this study, we divided the SC flood season into three stages: the FRS before the SCSSM onset (FRS1, from April 1 to the onset date of the SCSSM; Zheng et al., 2011), the FRS after the onset of the SCSSM (FRS2; from the onset date of the SCSSM to June 30), and the SRS. As shown in Figure 1, FRS1 is featured by a strong WNP subtropic high and a strong upper-level westerly belt controlling SC, FRS2 a significant southwesterly monsoon in the low-level and a weak westerly impact relative to that in the FRS1, and SRS an evident tropical monsoon trough and an upper-level easterly. From the definitions above, a total of 208 10-30-day ISO-related PHR events during the flood season (April-September) in SC from 1961 to 2017 were obtained, including 44 events in FRS1, 67 events in FRS2, and 97 events in SRS. The following analysis is based on the 10-30-day ISO-related PHR events chosen at each stage of the flood season. Figure 2 shows the correlation between the PHR precipitation averaged over SC and precipitation anomalies at each stage of the flood season. Here, the NCEP-NCAR precipitation, consistent with the observed precipitation over SC on the 10-30-day time scale (figure not shown), is used for analysis because it has a larger spatial distribution (including the ocean). During the FRS1, precipitation anomaly mainly propagated from north to south, and when approaching SC, it also moved eastward ( Figure 2a); during the FRS2, PHR precipitation mainly reflected an eastward-propagating component, with a very small meridional component ( Figure 2b); during the SRS, precipitation propagates northwestward mainly from the tropical WNP ( Figure 2c). It can also be seen from the composite Hovmöller diagram (see Figure 3) that the PHR precipitation during the FRS1 exhibits the characteristics of southeastward propagation, during the FRS2, it mainly propagates eastward, and during SRS it is featured by northwestward propagation (the propagation characteristics are clearer when the local part is zoomed in. Figure not shown). Figures 2 and 3 show a consistent result at each stage of the flood season in SC. Furthermore, the verticallyintegrated MSE tendencies shown in Figure 3 are very similar to the characteristics of precipitation, with the maximum preceding the precipitation by a few days. Moreover, over the SC region, the column-integrated MSE and the precipitation anomalies have a similar pattern ( Figure 4). Although previous work (e.g., Liu et al., 2020) also found that the propagation of intraseasonal divergent related to the PHR during different stages of the flood season over East China, which was determined by the location of the upper-level westerly jet and strength of monsoon trough, we can see from Figure 4 that a buildup of column-integrated MSE occurs before PHR, and column MSE is discharged during and after precipitation maximum over SC. It implies that the recharge-discharge cycle of MSE (Hendon & Liebmann, 1990;Kemball-Cook & Weare, 2001;Maloney, 2009) plays an important role in regulating the PHR over SC. Thus, this allows us to understand SC PHR development and propagation in terms of MSE changes (e.g., Zheng et al., 2021), since the occurrence and development of PHR over SC can be explained by the column MSE and the MSE tendency, respectively. Figures 5-7 show the detailed 10-30-day evolution of the column-integrated MSE change and precipitation during the FRS1, the FRS2, and the SRS, respectively, from which, we can see their relationship more clearly. During FRS1, there is a significant positive column MSE tendency at the midlatitudes 7 days ahead of the precipitation maximum, and then gradually develops to the southeast ( Figure 5). On À5 days, a positive precipitation anomaly appeared in the northern part of SC and mainly moved southward. This southward propagating ISO, or named the front, is usually a trigger for the SCSSM onset (Chang & Chen, 1995). It can be seen that the movement of the precipitation center does not match the movement of the MSE tendency center, implying that the MSE change is not suitable for diagnosing the PHR of FRS1 in SC, especially the processes of propagating precipitation on the 10-30-day time scale. F I G U R E 2 Correlation coefficients of PHR precipitation averaged over SC and precipitation anomalies at (a) FRS1, (b) FRS2, and (c) SRS of flood season. Shading indicates more than 99% confidence level, À6 to 0 days indicates that the precipitation is 6 days ahead of the maximum PHR precipitation in the same period.

| PHR CHARACTERISTICS AND THEIR RELATIONSHIP WITH MSE
The PHR during the FRS2 shows a positive column MSE change in western SC on À7 days and then moved eastward, while a significant precipitation anomaly appears in SC on À5 days and gradually shifts eastward (Figure 6), which can also be seen in Figure 3. Although the eastward shift of the MSE change and precipitation is obvious during the FRS2, the main center is still limited to SC (Figures 3 and 6). Therefore, for the PHR of FRS2, the local MSE change may play a major role, since Figure 4b indicates a close relationship between them. Figure 7 shows that the PHR during the SRS has a positive change in MSE over the southeast of the Philippine Sea on À10 days, and gradually moves northwestward. The significantly positive precipitation anomaly in the tropical WNP appears on À8 days, also moving northwestward with the MSE tendency, implying that the SC PHR F I G U R E 4 Composite 2.5 times precipitation (bar, mm day À1 ), columnintegrated MSE (red line, 106 J m À2 ) and its tendency (blue line, 106 J m À2 day À1 ) over SC during (a) FRS1, (b) FRS2, and (c) SRS. Positive and negative values in the time coordinate represent after and before the reference day (maximum PHR precipitation), respectively.
F I G U R E 5 PHR precipitation (shaded, mm day À1 ) and column MSE tendency (contours, W m À2 ) composites during the FRS1 based on the maximum PHR precipitation (0 days). Only composite values exceeding the 90% confidence level are shown in the figure. The red box indicates the calculation area and time of the cumulative MSE budget.
in SRS is closely linked to the propagation of 10-30-day intraseasonal precipitation, which is reported by previous studies (e.g., Li et al., 2015;Zheng & Huang, 2018). In addition, the propagation characteristics of the anomalous precipitation and MSE perturbation are similar, and the MSE change is a few days ahead of the precipitation (Figures 3 and 7). This suggests that the PHR of SRS is not only related to SC local MSE changes but also has a close relationship with the recharge of MSE and the propagation of MSE perturbation. F I G U R E 6 As in Figure 5, but for FRS2.
F I G U R E 7 As in Figure 5, but for SRS.

| Advection
The maximum precipitation occurs a few days (3-4 days) after the maximum MSE tendency when the MSE budget is calculated based on Equation (2) as shown in Figure 8. We can see that the horizontal advection term is the most important for the local MSE tendency during the PHR event at each stage of the flood season in SC. During the FRS1, the zonal advection and meridional advection of MSE are both important (Figure 8a). During FRS2, zonal advection has the greatest contribution to the MSE tendency (Figure 8b), while meridional advection plays a major role during the SRS (Figure 8c). However, a significant MSE budget residual is noted in the PHR of each stage (Figure 8), which was mainly attributed to the analysis increment in the reanalysis data (Jiang, 2017;Kiranmayi & Maloney, 2011;Mapes & Bacmeister, 2012). Even if a higher spatial-temporal resolution data set is used, a substantial MSE budget residual may exist (e.g., Jiang, 2017;Kiranmayi & Maloney, 2011). Thus, an entirely comprehensive understanding of the MSE recharge-discharge cycle related to the PHR events over SC may not be possible from the local MSE budget.
In addition, Wang and Li (2020a) argued that for a propagating large-scale system, the quantitative budget calculation over a fixed domain at a fixed phase may cause discrepancies regarding the relative importance of the specific processes. As mentioned above, the vertically integrated MSE in the PHR process has a propagating characteristic (Figures 2 and 3), with a close relationship with the large-scale circulation (Figure 1). Therefore, we introduce the cumulative contribution to describe the relative role of each item in the MSE tendency, that is, during the PHR of FRS1, the terms in Equation (2) were projected on the positive phase of the MSE change, and the values were accumulated over the significant process and domain (e.g., À6 to 0 days, 105-140 E, 15-40 N, as shown in Figure 5). Although the fixed domain is shown in Figures 5 and 6, the domain used for accumulating varies with the propagation of MSE perturbation due to the projection of the positive phase of the MSE change. Thus, the accumulative MSE budget can reflect key processes along the propagation path.
From Figure 9, we can see that the key role in the southeastward-propagating perturbation of MSE tendency on the 10-30-day time scale is zonal advection during the FRS1. Compared with the local contribution in SC (Figure 8a), the meridional advection is significantly reduced and even becomes a negative contribution (Figure 9a). Figure 8b and Figure 9b show a similar result, implying the development of PHR during FRS2 is mainly due to the local zonal advection of MSE. It can be seen from Figure 9c that the largest contribution to the 10-30-day northwestward-propagating perturbation of MSE tendency during the SRS is still meridional advection, while the contribution of zonal advection is almost negligible. It is worth noting that the residual term for calculating the cumulative MSE budget is much smaller than calculating the local one, which is probably due to the smoothing effect of the cumulative calculation and lends confidence to our findings.
To calculate the effects of different time scales, following , the anomalous fields were separated into the LF (≥30 days), HF-ISO (10-30 days), and synoptic-scale (<10 days) components, that is where A is the anomalous field, the star represents the LF component, the prime represents the HF-ISO component, and the double prime denotes the synoptic-scale field. As can be seen from Figure 10a, the main contribution to the 10-30-day component of the zonal advection of MSE during the FRS1 is the interaction between the LF field and the 10-30-day component, namely the advection of 10-30-day MSE by the background LF zonal wind, and the cumulative contribution rate can reach more than 80%. In addition, the advection of LF MSE by the 10-30-day zonal wind and the interaction of synoptic-scale components play a moderate role. During the FRS2, both the advection of 10-30-day MSE by the background LF zonal winds and the advection of background MSE by the 10-30-day zonal winds have a significant effect on the MSE tendency, with a similar positive contribution (Figure 10b). During the SRS, the main contributing terms are the same as those in FRS2, but for the meridional advection (Figure 10c).
The maximum MSE transport by background flow in the FRS1 and FRS2 occurs at 700 hPa, that by the From Figure 11a,b, we can see that the background flow in both the FRS1 and FRS2 is a strong westerly, which results in a large zonal advection of MSE. In addition, Figure 12a shows the local meridional advection of background MSE by anomalous flow has a positive contribution (as shown in Figure 8a), which is offset in the cumulative MSE budget (Figure 9a) by the negative contribution of meridional advection by background flow at midlatitudes (30-40 N, Figure 11a), implying a less effect of meridional advection on the MSE tendency during the FRS1. Figure 12b shows that a much larger background MSE zonal gradient appears over SC than the meridional gradient. Since the development of PHR in the FRS2 and the associated MSE tendency are mainly of local processes, the main cumulative contribution of zonal advection on the MSE tendency includes the advection of background MSE and background flow (Figure 10b). During the SRS, the more evident background meridional flow and background MSE meridional gradient; thus, the meridional advection of background MSE and background flow plays a key role in the MSE tendency associated with the PHR in the SRS over SC.
Obviously, the background winds play a key role in determining the dominant process of the zonal advection of the anomalous MSE during the FRS, whereas the meridional advection during the SRS over SC (Figure 11), since the MSE anomaly and the ISO convection center are in phase. In contrast, we can see from Figure 13 that the anomalous winds transporting the mean MSE are mainly induced by ISO. These findings imply that the key recharge processes related to the PHR over SC are the advection of MSE, which is determined by the interactions between the ISO-induced perturbations and the background fields. F I G U R E 1 1 Composite anomalous precipitation (Shaded, mm day À1 ) and MSE (contours, J m À2 ) associated with the PHR over SC based on the precipitation maximum and background horizontal winds (m s À1 ) during (a) the FRS1, (b) the FRS2, and (c) the SRS. Only composite values exceeding the 90% confidence level and background wind speed greater than 3 m s À1 are shown in the figure. The vectors in (a) and (b) are 700-hPa horizontal winds, and those in (c) are 925-hPa horizontal winds. À4 days to À1 day represents 4 days to 1 day before the maximum PHR precipitation.
F I G U R E 1 2 As in Figure 11, but for composite 925-hPa anomalous winds (m s À1 ) and background MSE (contours, J m À2 ).

| External forcing
The external forcing here refers to the surface heat flux and longwave and shortwave radiation. Figure 8a shows that the longwave radiation contributes a little to the local maximum MSE tendency associated with the PHR during the FRS1, but the external forcing is generally negative. In contrast, the local contribution of external forcing during the FRS2 and SRS is around 10% (Figure 8b,c). It can be seen from Figure 9a that the cumulative contribution of external forcing to the 10-30-day southeastward-propagating perturbation of MSE tendency during the FRS1 is still negative, especially the negative contributions of longwave radiation and latent heat increase significantly.
The cumulative contribution of external forcing during the FRS2 is about 2% (Figure 9b), which is much smaller than the local contribution at the maximum MSE tendency (Figure 8b). This is because the calculation of the cumulative contribution is not only in the stage of maximum MSE tendency but also in the MSE development since the calculation area is limited to SC. In addition, the cumulative contribution of external forcing to the 10-30-day northwestward propagating perturbation of MSE tendency during the SRS exceeds 30% (Figure 9c), which is much larger than the regional average result (Figure 8c).
We calculated the contribution of the external forcing to the MSE change during the SRS day by day from À9 days to À1 day, as shown in Figure 14. Before À5 days, the contribution of external forcing is generally negative, which is mainly attributed to the surface latent heat flux anomaly. As can be seen from Figure 7, the large positive changes in MSE at this time are located in the tropical NWP, that is to say, the ocean evaporation is weakened at this stage. This is consistent with Kemball-Cook and Wang (2001). After À5 days, the external forcing has become more and more important, especially after the large positive change in MSE reached SC. This suggests that external forcing plays a key role in the ISO convection propagating to land, which is consistent with the conclusion of Zheng et al. (2020).

| CONCLUSIONS AND DISCUSSIONS
In this study, the flood season in SC is divided into three stages (the FRS before and after the SCSSM onset and the SRS, denoted as FRS1, FRS2, and SRS, respectively), and the NCEP-NCAR reanalysis data were used to diagnose the MSE budget associated with the 10-30-day PHR over SC during these periods. The following results were obtained: F I G U R E 1 3 Regressed 925-hPa horizontal winds on the 10-30-day precipitation anomaly averaged over SC. The cross mark denotes the maximum precipitation on À2 days.
F I G U R E 1 4 Contribution of external forcing to the MSE tendency from À9 days to À1 day relative to the maximum PHR precipitation during the SRS.
• There are great differences in the recharge of PHRrelated MSE in different stages of the flood season in SC. During the FRS1, the MSE associated with PHR moves from midlatitude to southeast; the large MSE remains in SC during the FRS2, although it develops somewhat eastward; during the SRS, the MSE perturbation propagates from the tropical WNP to SC. It is worth noting that during the FRS1, the MSE center did not coincide with the convection center, which indicates that the MSE budget may not be suitable for diagnosing the development of PHR over SC during this period, especially the impact of the midlatitude system. • Locally in SC, the MSE change of the PHR developing stage during the FRS1 is mainly affected by horizontal advection, including meridional and zonal advection; the MSE tendency during the FRS2 is mainly determined by zonal advection; meridional advection is dominant during SRS. External forcing (including radiation and surface heat fluxes) contributes approximately 10% to the maximum MSE tendency associated with the PHR over SC during the FRS2 and SRS. • Regarding the propagation process of MSE perturbation, the MSE changes during the FRS1 and FRS2 are mainly affected by the zonal advection, while the meridional circulation is responsible for those in the SRS. The cumulative contribution of external forcing during the SRS on the PHR-related MSE propagation can reach more than 30%, mainly from the contribution of surface latent heat and radiation during and after the developing stage of PHR, and the closer to the land, the stronger the external forcing.
The 10-30-day PHR over SC during the FRS1 is closely related to the midlatitude system and that during the SRS is mainly affected by the tropical systems, while during the FRS2, the PHR over SC is influenced by both the tropical monsoon system and the midlatitude system (e.g., the westerlies), and its occurrence and development are almost always confined to SC, which is called "dragon boat water." Additionally, why does external forcing make little contribution to the propagation process of MSE perturbation associated with the 10-30-day PHR in the FRS, but it has a much larger contribution in the SRS? This is a question worth exploring in depth.
In the FRS1 and FRS2, the main process of the change in MSE related to the PHR occurs over the mainland, while the process in the SRS is mainly on the WNP, with the northwestward propagation to SC. As mentioned above, the propagation of MSE perturbation in the mainland can ignore the effect of external forcing, for example, in the FRS1 and the FRS2. In contrast, the external forcing, especially the land forcing, plays an important role in the propagation of PHR-related MSE perturbation from the WNP to SC, which is consistent with Zheng et al. (2020). That is why in the SRS, the closer to the land, the stronger the external forcing.
In this study, the flood season in SC was divided into three stages, and we found that the key process in the recharge of MSE is different during the FRS and the SRS. Whereas, when we focus on the whole period of the rainy season, the meridional advection of low-level moisture is highlighted, and the low-level synoptic-scale interactions also modulate the intraseasonal variability related to the PHR over SC (Zheng et al., 2022) via upscale feedback (e.g., Zhou & Li, 2010) of the WNP synoptic-scale wave trains (e.g., Lau & Lau, 1990), which is consistent with the result of Figure 10c. The zonal advection, however, contributes little to the PHR over SC considering the whole rainy season (Zheng et al., 2022). In contrast, the zonal advection plays a key role in the PHR over SC during the FRS. This implies that it is necessary to divide the flood season over SC according to the background circulation.