The southward movement preference of large-scale persistent extreme precipitation events over the Yangtze River Valley during Mei-yu period

Among all rainfall events, heavy rainfall that affects large areas and persists for days can cause serious �ooding, severe casualties, and substantial economic losses. In this study, we identify the extreme precipitation events that affect a large area and have persistence of more than three days (LPEPEs) in China during 1961–2013. The LPEPEs incline to occur in summer and over southern China, coinciding well with the rainy season in China. The movement of LPEPEs is dominated by the tendency to extend southward, especially for the LPEPEs during the Mei-yu period (LPEPEs-M). The dynamical composite analyses on the southward-moving LPEPEs-M show that the southward extension is generated by the combined effect of the large-scale circulation con�guration and the diabatic heating caused by large-scale condensation. The latent heating results in a cyclonic anomaly from the middle to the lower levels. Therefore, westerly and easterly anomalies are produced to the south and north of the heating center, respectively. The two anomalies manipulate the vertical distribution of meridional winds which is dominated by the large-scale circulation to both sides of the rainband. This kind of anomaly con�guration, together with the quasi east-west zonal distribution of diabatic heating, creates a pattern with positive and negative PV tendency to the south and north of the heating center, leading to LPEPE system development to the south of the precipitation center. Therefore, the LPEPE rainband has a preference to move southward over the Yangtze River Valley during the Mei-yu period. We also test the dynamical mechanism with a numerical sensitivity experiment using the WRF model. In the experiment without latent heating feedback, the Mei-yu rainband moves northward and extends to central and North China. While in the experiment with the latent heating feedback, the rainband intensi�es and extends southward. The southward extension preferences of the LPEPE can provide an internal dynamical of the stagnation of East Asian summer evolution.

To further analyze the dynamical characteristics of LPEPEs, researchers classify LPEPEs rstly according to synoptical con gurations or locations of the LPEPEs. Tang et al. (2006) classi ed 193 persistent heavy rainfall events into westerly type, easterly type, and westerly and easterly encounter type according to the average circulation characteristics at 500hPa. Bao (2007) classi ed the persistent heavy rainfall events into Bohai Sea-western Liaoning Province type, the northern meridional type, the southern front type, and the tropical depression type in South China, with the southern front type as the most frequent one.
Dynamical analysis reveals that the LPEPEs depend on the large-scale circulation con guration (Bao, 2007;Chen and Zhai, 2013;Zou and Ren, 2015). Zhang and Zhi (2010) pointed out that there is an updraft anomaly over the Yangtze River when the Western Paci c subtropical high (WPSH) and the South Asian High (SAH) approach each other, favoring the heavy rainfall in the middle and lower reaches of the Yangtze River and south of the Yangtze River. Hu et al. (2019), using clustering analysis to classify extreme rainfall events in the middle reaches of the Yangtze River in early summer (June and July), showed that the eastward expansion of South Asia High and intensi ed westerly jets provide an additional forcing for local rising motion. The southwesterly jet to the south of the rainband provides su cient and continuous water vapor for LPEPEs (Wang et al., 2013). Therefore, both the intensity and location of LPEPEs are closely connected with the large-scale circulation con guration.
Thermodynamical analyses demonstrate that the diabatic heating can also in uence the intensity and the location of LPEPEs. The diabatic heating of the synoptical system intensi es the precipitation by the conditional instability of the second kind mechanism (CISK) (Chen et al., 2003;Cho and Chen, 1995). Tremendous diabatic heating results in a cyclonic anomaly to the north of the WPSH, obstructing the northward migration of WPSH (Liu, 1999;Wang et al., 2009Wang et al., , 2011, further con ning the movement of LPEPEs. The heavy rainfall in the middle and lower reaches of the Yangtze River is highly related to Mei-yu, the elongated rainband extending from the Yangtze River to Japan in mid-summer. The subtropical Mei-yu fronts usually move southward/southeastward or remain quasi-stationary (Chen, 1992;Chen and Chang, 1980;Chen and Chi, 1980). But some LPEPEs also show great northward migration (Chen et al., 2006;Wang et al., 2016). By case study, several studies pointed out that the horizontal advection process predominates the meridional movement of LPEPEs (Chen et al., 2006;Wang et al., 2016). Recently, some other case studies focused on the northward-moving Mei-yu fronts to the east of the Taiwan Island also emphasized the effects of diabatic heating in manipulating the meridional wind (Chen et al., 2006). Hu et al. (2021) derived a new frontogenesis function, and found that the diabatic heating is always frontogenetical in the pre-frontal and frontal zone throughout the entire lifecycle of Mei-yu fronts and is the dominant forcing during the front intensi cation stage. Wang et al. (2022) used this new frontogenesis function to analyze a heavy rainfall event in the 2020 extreme Mei-yu season, and revealed a symbiotic relationship between Mei-yu rainfall and the morphology of the Mei-yu front. Since the two northward jumps of the monsoon rain belt is the most remarkable feature of the East Asian summer monsoon region, researchers mainly focus on the northward moving heavy rainfall events, leaving the mechanism of southward moving LPEPEs-M unexplored.
In this study, we focus on the mobility and the related dynamical and thermodynamical mechanisms of LPEPEs, with attention to the direction preference of LPEPEs. Section 2 introduces datasets and the de nition of LPEPEs. Section 3 shows the temporal and spatial distribution and the movement features of LPEPEs and con rms the southward extension preference of LPEPEs. In section 4, we conclude the background circulation con guration of southward-moving LPEPEs-M and discuss the related dynamical mechanism. In Section 5, the PV tendency equation is calculated to uncover the mechanism of diabatic heating in helping the LPEPEs-M southward movement. Latent heating sensitive experiments are run by the WRF model to verify the diabatic heating effect in Section 6. The discussion of the results and conclusion are provided in section 7.

Data
The daily and monthly precipitation grid data set (V2.0) is derived from China's high-density ground stations (2472 national meteorological observation stations) by the National Meteorological Information Center of China Meteorological Administration (CMA) (http://data.cma.cn). This grid dataset has a horizontal resolution of 0.5°×0.5° from 1961 to 2013, and the spatial interpolation is based on the TPS (thin-plate spline) method. It can accurately re ect the spatial and temporal variation characteristics of precipitation . This dataset has been widely used in precipitation-related studies (Zhang et al., 2017;Zhao et al., 2019).
In addition, the circulation parameters of wind, geopotential height, and temperature are adopted from the fth-generation ECMWF reanalysis (ERA5), which has a horizontal resolution of 0.25° ×0.25° and 37 vertical levels from 1000 hPa to 1 hPa. The ERA5 dataset is used to analyze the synoptic circulation characters, the atmospheric apparent heat source (Q 1 ), the apparent moisture sink (Q 2 ), and the potential vorticity tendency equation, and to initialize the numerical simulation experiment. The onset and retreat dates of the Mei-yu period in China are based on the "Indices of Mei-yu Monitoring" (Shao, 2016). According to this criteria, Mei-yu includes three types in China: Mei-yu (in the south of the Yangtze River), Mei-yu (in the middle and lower reaches of the Yangtze River), and Mei-yu (in the Yangtze-Huaihe River basin). In this study, the Mei-yu period includes all three types.

De nition of LPEPE
There is no uniform de nition of LPEPEs. Different de nitions of LPEPEs always contain three criteria, including precipitation intensity criteria, duration criteria, and coverage criteria (Bao, 2007;Wang et al., 2014). Several methods were used to de ne the large-scale persistent extreme precipitation events (Bao, 2007;Chen and Zhai, 2013;Ren et al., 2012). Since we focus on the mobility feature of LPEPEs, the objective identi cation technique for extreme regional events ("candied fruits" method) (Ren et al., 2012) is utilized in this study. The LPEPE is detected in the following steps and criteria (concept diagram illustrated in Fig. 1a). Firstly, the large-scale extreme precipitation patterns (LEPs) are identi ed as the sizeable continuous region (the grid number no less than 60 for the 0.5×0.5 latitude-longitude grid dataset, approximately 14×10 4 km 2 ) with the daily precipitation no less than 25 mm at each grid (Bao, 2007;Chen and Zhai, 2012;Ren et al., 2012). Secondly, a large-scale persistent extreme precipitation event (LPEPE) is de ned as an LEP persisting for at least three days. The LEPs of two consecutive days are considered the same event when the LEP coincidence degree is greater than 20% (Wang et al., 2014).
Finally, the LPEPE is screened to keep the extreme events that the maximum total precipitation is no less than 250 mm. During 1961-2013, 82 LPEPEs were identi ed, with the date and duration information listed in Table 1. Table 1 Detailed information on all LPEPEs. "Day 1" is the rst day of an LPEPE, and "Duration" is the time span (number of days) of an LPEPE. "WP1" is averaged latitude and longitude of all grids in the LEP weighted by the daily precipitation on the rst day of the LPEPE.  Lon max ( p ( lat ( i ) ) ) 6 "nlat" is the total number of grided latitudes in LEP, "nlon" is the total number of grided longitudes in LEP. "Lat max ( p ( lon ( i ) ) ) " is the latitude of maximum precipitation at the longitude of lon(i). " Lon max ( p ( lat ( i ) ) ) " is the longitude of maximum precipitation at the latitude of lat(i)".
The direction of an LPEPE is considered as the vector from the LEP location of the rst day to the last day. If the latitude difference of an LPEPE between the last day and the rst day is negative, the event is then classi ed as a southward extension LPEPE. Accordingly, three vectors can be de ned using MP, WP, and AP. An example is shown in Fig. 1b, which is the MP, WP, and AP of an LPEPE randomly chosen on Jun 21st, 1986. The LPEPE is mainly caused by the southwest vortex over the middle reaches of the Yangtze River; the maximum daily precipitation is 263 mm, breaking the historical records in the Huangshi City (Ge et al., 1989).

Apparent heat source and apparent moisture sink
The apparent heat source (Q 1 ) and (Q 2 ) are analyzed to investigate the thermal dynamical and moisture characters of LPEPEs. The function of Q 1 and Q 2 are described in Hsu and Li (2011). Here Q 1 represents the total diabatic heating (including radiation, latent heating, and surface heat ux). Q 2 represents the latent heating due to condensation or evaporation processes and subgrid-scale moisture ux convergences (Yanai et al., 1973). heating is the major contributor to the diabatic heating during an LPEPE in the Mei-yu season. Therefore, the combination analyses between Q 1 and Q 2 are adapted to epitomize the precipitation feedback to the circulation (Liu, 1999).

Potential vorticity (PV) tendency equation
To investigate the internal dynamical processes of the LPEPEs during the Mei-yu period, the Ertel potential vorticity (PV) equation is diagnosed. The PV in pressure coordinates is ,9 in which f is the Coriolis parameter, θ denotes the potential temperature, u and v represent zonal and meridional winds, respectively. PE is the Ertel PV.

Composite method
Considering the moving features of LPEPEs, both the traditional and dynamic composite methods are used. In the dynamic composite, the location of LEP (here WPs are used) is taken as the origin of coordinates, then to make a composite for every LPEPE in the same scope on each day in the moving coordinate system. Thus, the composite center is the origin of the coordinates, which moves along with the LPEPE, and the coordinates indicate the distances to the composite center . Since the majority of LPEPEs persist for three days (54 out 82 LPEPEs, 67%), we use the rst three days' dynamic composite analysis results. Three degrees departing from the composite center in meridional direction and zonal direction can well re ect the adjacent dynamic and thermal dynamic features. The dynamic composite analysis method also has been used in studies on southwest vortices and typhoons (Li et al., 2014;Li et al., 2004).

Model setup and design of sensitivity experiments
The non-hydrostatic version 4.2 of the Weather Research and Forecasting Model (WRF) (Skamarock et al., 2019) was adopted to simulate the LPEPE and analyze its characteristics and evolution. The model has 38 sigma levels in the vertical, and the model top is set at 50hPa. The main model schemes include (i) the Kain-Fritsch (new Eta) cumulus parameterization scheme (Kain, 2004), (ii) the Goddard scheme Tao et al., 2016) for microphysics, (iii) the YSU scheme (Fairall et al., 2003) for the boundary layer, (iv) the Noah Land Surface scheme (Alapaty et al., 2008) for the land surface layer, (v) the RRTM scheme for longwave (Mlawer et al., 1997), (vi) and the Dudhia's scheme (Dudhia, 1989) for shortwave radiation parameterization.
Considering the in uence of latent condensation heat and internal thermodynamics, the effects of latent heating on the mobility of LPEPE were investigated via sensitivity experiments. The latent heat release associated with cloud microphysics and the cumulus parameterization scheme was turned off in the sensitivity run (SEST) so that the latent heat has no feedback on the circulation. In the control run (CTRL), however, the model was run with full physics, so the latent heat has forcing on the circulation. The model simulation was carried out for a randomly chosen LPEPE in 2003. The WRF model was run for 119 hours starting at 0000 UTC 7th July 2003, using the ERA5 dataset at intervals of six hours as the initialization. Figure 2 shows the domain used for all simulations, covering eastern China and the South China Sea, with a horizontal resolution of 5 km. All the experiments were launched with identical initial and boundary conditions.

The Spatial And Temporal Distribution
This study detected 82 LPEPEs (Table 1) (Zhang and Fan, 1995) and the disaster conditions and disaster reports published annually in the Journal "Disaster Reduction in China", there is a close relationship between the ooding disasters and the LPEPEs, with 69 out of 82 LPEPEs (more than 84%) associated with ooding disasters. For the rest 13 LPEPEs, ten of them occurred in the period from 1966 to 1976, when the disaster datasets were often lost.
The number of LPEPEs during the 1990s and 2000s is more than in other decades, with 22 LPEPEs occurring in the 1990s, 18 in the 2000s, while 9 in the 1970s, and 17 in the 1980s. Zou and Ren (2015) pointed out that China experienced more severe and extreme regional rainfall events in the 1990s. The years with more than two LPEPEs are 1973LPEPEs are , 1982LPEPEs are , 1995LPEPEs are , 1996LPEPEs are , 1998LPEPEs are , 1999LPEPEs are , 2002LPEPEs are , and 2007. Most LPEPEs occurred in the summer season, with 32 in June, 26 in July, and 10 in August (Fig. 3a). According to the dataset of landfall tropical cyclones by Ying et al. (2014), 15 LPEPEs are related to typhoons. As we mainly focus on the characteristics of LPEPEs in the Yangtze River Valley during Mei-yu, which is considered as the results of the mid-latitude front system, we exclude the typhoon-associated cases, leaving 67 LPEPEs. Among them, 46 LPEPEs occurred in the Mei-yu period (LPEPEs-M). The LPEPEs-M (asterisk) and typhoon-associated LPEPEs (bolded) are listed in Table 1.
Most LPEPEs prefer southern China and eastern China, with 94% and 98% occurring south of 35°N and east of 105°E, respectively (Fig. 3d). Using the distribution of MPs (Fig. 3e) and APs (Fig. 3f) got similar results. The temporal and spatial distribution of LPEPEs is similar to the previous studies (Bao, 2007;Chen and Zhai, 2012;Tang et al., 2006).
The LPEPE direction, de ned as the displacement vector difference of MPs (or WPs and APs) between the last day and the rst day of the LPEPE, has a preference to shift southward (Fig. 3b), especially for LPEPEs-M (Fig. 3c). Using WPs, 33 out of the 46 (72%) LPEPEs-M move southward. The ratio is similarly high if MPs or APs are used, which is 31 out of 46 (67%) for MPs, and 32 out of 46 (70%) for APs (Fig. 3c).

The Dynamical And Thermodynamical Features Of Southwardmoving Lpepes-m
The composite of the 33 southward-moving LPEPEs-M reveals the typical circulation con guration during the LPEPEs over the Yangtze River valley (Fig. 4), which usually include the following key components: 1. the stable and eastward extension of the high-level South Asian High (SAH), represented by the 1252dagpm contours at 200 hPa, 2. the fast eastward retreating Western Paci c Subtropical High (WPSH), represented by the 588-dagpm contours at 500 hPa, 3. the combination of low-level southwesterly (shadings in Fig. 4d-4f) and high-level westerly (shadings in Fig. 4a-4c), 4. a relative low-pressure system around Southwest China at the low level of 850 hPa (Fig. 4d-4f).
The composite analyses of southward-moving LPEPEs-M depict a westward-extending WPSH and an eastward extending SAH, compared with the climatologic WPSH (Fig. 4a-Fig. 4c, blue dash contours) and SAH (Fig. 4a-Fig. 4c, red dash contours) of the Mei-yu season. On the rst day of LPEPEs-M, the SAH extends 5 degrees eastward from the climatology, and the WPSH extends 7 degrees westward from the climatology. The overlap of WPSH and SAH creates a favorable circulation con guration for ascending anomaly and heavy rainfall over the middle and lower reaches of the Yangtze River (Zhang and Zhi, 2010). The Yangtze River region is located at the right entrance of the high-level westerly jet stream center. The presence of the high-level westerly jet and the eastward-extending SAH produces divergence over the middle to lower reaches of the Yangtze River (Fig. 4a-Fig. 4c, gray shades) (Hu et al., 2019). Meanwhile, the strong low-level southwesterly jet, with weak southerly to the north of the rainband (Fig. 5d-Fig. 5f), produces convergence over the middle to lower reaches of the Yangtze River (Fig. 4d-Fig. 4f, gray shades) (Chen and Zhai, 2016; Hu et al., 2019).
During the LPEPEs-M, the divergence at the high level and the convergence at the low level coincidently contribute to an intense updraft over the middle to lower reaches of the Yangtze River (Du et al., 2008).
The strong upward motion is veri ed above the Lat wp , associated with convergence at the lower levels and divergence at higher levels ( Fig. 5a-Fig. 5c).
There is a low-pressure system around Southwest China (Fig. 4d-Fig. 4f). Fifteen out of the 33 southward- During the rainfall process, the high-level jet gets weaker, which results in the southward-moving positive center of ∂v ∂y at the high levels in the condition that the SAH is quasi-stable. The positive center of ∂v ∂y is over the middle to the lower reaches of the Yangtze River on the rst day (Fig. 4a), while to the south of the Yangtze River on the third day (Fig. 4c). The southward-moving positive center of ∂v ∂y is the major contributor to the southward-moving divergence at the high levels, so that the variation of divergence center is consistent with the ∂v ∂y . The low-level jet and related convergence over South China get weaker and retreat southward. The convergence band is over the south of the Yangtze River on the rst day and to the south of the Yangtze River on the third day. The southward movement of divergence at the high level and convergence at the low-level contribute to the southward movement of upward motion (Fig. 5a  -Fig. 5c), and the LPEPEs-M (presented by Lat wp ).
From the rst day to the second day, the west edge of WPSH retreats eastward from 119°E to 123°E.
However, on the second day of LPEPEs-M, the low-level jet, which is closely associated with the WPSH, is still at almost the same position and intensity as on the rst day. Chen et al. (2006) attributed the lowlevel jet movement to the diabatic heat. During LPEPEs, latent condensation heating is the major contributor to diabatic heating (Fig. 4g -Fig. 4i). Q 1 shows similar characteristics as Q 2 , both moving southward from the lower reaches of the Yangtze River to South China (Fig. 4g -Fig. 4i), indicating that the atmospheric heating sources from the latent condensation heating of the intense precipitation.
Inconsistent with the WPSH retreated eastward, Q 1 and Q 2 move southward slightly on the second day, synchronizing with the rainband and the low-level jet. The vertical vorticity tendency equation shows a southerly anomaly below the diabatic heating center by the β effect (Lin et al., 2005;Liu, 1999;Zhao et al., 2021). The potential vorticity analysis also con rms the effect of diabatic heating in intensifying the southwesterly jet in Section 5.
Dynamically, the large-scale circulation bene ts the heavy rainfall over the middle to lower reaches of the Yangtze River. During the rainfall process, the updraft motion produced by the divergence at the high level and the convergence at the low level moves southward, consistent with the rainband, which indicates the domination of large-scale circulation in the southward extension process of LPEPEs-M. However, the rainband is not synchronous with the WPSH, implying other mechanisms for the southward extension preference of LPEPEs-M. The thermodynamical effects of diabatic heating on the southward extension preference are investigated using the PV tendency equation in Section 5.

The Pv Tendency Diagnosis
The dynamic composite analyses of the PV tendency equation are calculated to determine the mechanism of large-scale circulation and the diabatic heat in manipulating the meridional movement of LPEPEs-M. Cho and Chen (1995) proposed that the west of the Mei-yu front (east of China) is shallow.
Thus, the dynamic composite analyses of the PV tendency equation  were calculated at 850hPa (Chen et al., 2003;Wang et al., 2022). Besides, southwest vortexes, mesoscale convective systems, and other low-pressure systems can also be detected at 850hPa.
The PV tendency (PET) is positive to the south of the rainband, and negative to the north of the rainband (Fig. 6). Thus, the low-pressure systems are more likely to move southward. The dipole pattern of PET is considered as the result from PE1 to PE6 by the PV tendency equation. The positive values of PE1 to PE6 increase the PE, helping enhance the cyclone or weaken the anticyclone, and therefore contribute to the precipitation of the rainband and the related condensation latent heat. Contrarily, the negative values weaken the cyclone and contribute to the decay of the rainfall system. The PV tendency caused by the horizontal PV ux divergence is positive in and to the north of the rainband, and negative to the south of the rainband (Fig. 7a to Fig. 7c), which is opposite to the dipole pattern of PET and can contribute to the persistence and northward movement of rainband. Although PE1 (Fig. 8a-8c) partially offsets PE2 (Fig. 8d-8f) over the rainband, PE2 is the major contributor to the horizontal PV ux divergence, which is mainly caused by the meridional wind gradient perpendicular to the rainband. The meridional distribution of meridional winds is greatly governed by the low-level southwesterly jet, which is in uenced by the WPSH and diabatic heating. The diabatic heating can produce a southerly anomaly below the heating center, therefore, strengthen the low-level jet (Chen et al., 2006;Liu, 1999). The vertical PV ux divergence (PE3) weakens the rainband (Fig. 8g-8i).
As for thermodynamical factors, the redistribution of PV, which arises from the horizontal uneven distribution of Q, is responsible for the meridional movement of the LPEPEs-M. Figure 7d to Fig. 7f show dipole patterns of PE4 + PE5, with positive in the south and negative in the north of the rainband. The PE4 is the dominator of PE4 + PE5 (Fig. 8j-8l).
As the Mei-yu rainband has a quasi-zonal orientation, this causes ∂Q ∂y >0 to the south of the rainband and ∂Q ∂y <0 to the north (Fig. 5d-Fig. 5f). The dipole pattern of PE4 is mainly associated with the vertical distribution of zonal wind. To the south of the rainband, there is a climatological easterly jet at the high level and a southwesterly jet at the low level during the Meiyu season (Zheng et al., 2007). The vertical center of the low-level jet to the south of the rainband is at 850hPa (Joseph and Sijikumar, 2004). Liu (1999) described a cyclone anomaly below the diabatic heat center around 500hPa by the complete vertical potential vorticity equation. Therefore, there is a westerly/easterly anomaly to the south/north of the rainband. With the diabatic heat effect, the westerly anomaly lifts the zonal wind center to above 600hPa (Fig. 5d -Fig. 5f) to the south of the rainband, therefore, leading to ∂u ∂p <0. Together with ∂Q ∂y >0, this results in the positive value of PE4 below 600hPa.
To the north of the rainband, there is a high-level westerly jet at 200hPa during the Meiyu season, leading to ∂u ∂p <0. With the diabatic heat, the easterly anomaly decelerates the westerly below the 600 hPa, while not strong enough to reverse the vertical distribution of zonal wind ( ∂u ∂p <0). Combined with ∂Q ∂y <0 to the north of the rainband, this causes a negative value of PE4 in this region. Accordingly, the PE4 shows a dipole pattern (Fig. 8j-8l), consistent with PET (Fig. 6). Coupling with the meridional distribution of Q, the vertical distribution of westerly is favorable for the southward extension of the rainband of LPEPEs-M or preventing the rainband from moving northward. The effect of PE4 highlights the synergism of the diabatic heating and the con guration of high-and low-level jets.
Compared with other terms, the uneven distribution of Q in the zonal direction (PE5) is the weakest (Fig. 8m-8o). The vertical gradient of Q (PE6) is positive over the rainband, which helps to strengthen the precipitation intensity of the rainband (Fig. 8p-8r). The PE6 re ects the effect of the vertical uneven distribution of diabatic heat. The diabatic heating intensi es the precipitation by strengthing the lowpressure system, similar to the CISK mechanism (Chen et al., 2003;Cho and Chen, 1995;Liu, 1999).
The positive PE tendency produced by the PE6, related to the vertical distribution of the diabatic heating, is almost offset by the negative PE tendency produced by the PE3, related to the vertical motion. This re ects a balance between diabatic warming and adiabatic cooling due to ascent motion (Rodwell and Hoskins, 2001). However, the diabatic heating contributes to the vertical motion dramatically. Miao et al. (2017) pointed out that the effect of latent heat is as strong as 30%~50% of the wind circulation, maintaining the warm-sector heavy rainfall development. The total PE tendency produced by PE3 + PE6 is positive to the south of the rainband (Fig. 7g-7i), which favors the southward extension of LPEPEs-M.
In conclusion, the persistence of the rainfall systems is mainly maintained by the horizontal PV ux divergence in the meridional direction (PE2), and the vertically uneven distribution of Q (PE6). At the same time, the southward extension is mainly caused by the redistribution of PV (PE4), which arises from the uneven distribution of Q in the meridional direction and con guration of circulation, especially the zonal wind.

The Simulation Of 2003 Lpepe
To investigate the effect of latent heating on the mobility of LPEPEs, numerical experiments were carried out for a randomly chosen southward extension LPEPE from July 8 to July 10, 2003. The model description and experiment design are introduced in section 2.2.6. Sensitivity numerical experiments were also carried out for other cases, such as the LPEPEs starting on Jun 24, 1964, andJun 23, 1969, the similar results were obtained, con rming the effect of the diabatic heating in favoring the southward movement of the rainband (Figures not shown).
The rainband of this event slightly shifts southward over the north of the Yangtze River (Fig. 9a -Fig. 9c, shades), and the rainfall is mainly caused by two low vortexes along the shear line (Zhou and Li, 2010). Meanwhile, the west ridge of WPSH (represented with 150dagpm at 850hPa) extends around Taiwan Strait (Fig. 9a -Fig. 9c, contour) and shows eastward retreating.
The CTRL run simulates a similar stagnant rainband and a slightly southeastward retreating WPSH (150dagpm, 850hPa) (Fig. 9d -Fig. 9f). While in the sensitivity experiment, which turns off the latent heating effect, the persistence of the heavy rainband is not reproduced. The simulated weakening rainband migrates from the north of Yangtze River to Huang-Huai Plain (Fig. 9g -Fig. 9i). And the west ridge of WPSH extends more westward and norward in the sensitivity experiment than in the observation and CTRL run. Therefore, without the latent heat forcing, the rainband and WPSH migrate northward signi cantly. And the latent heating is the critical intrinsic forcing that leads to LPEPEs persistence over the Yangtze River Valley.
The geopotential height difference between the CTRL and SEST shows a cyclone anomaly over the Meiyu rainband (Fig. 10a -Fig. 10c), which can be explained by the mechanism that the condensation latent heating forces a cyclone anomaly below the heating center (about 400hPa-500hPa) by depressing the isobaric surface (Liu, 1999). The cyclone anomaly obstructs the WPSH's northward migration.
The zonal wind difference shows a westerly anomaly to the south of the rainband, and an easterly anomaly to the north of the rainband at the low levels ( Fig. 10a-10c). The condensation latent heat difference extends from the low level to the middle level, and the center is at the middle level (about 500hPa) (Fig. 10d-10f, Fig. 10g-10i), therefore, leading to ∂Q ∂y >0 and ∂u ∂p <0 below 600hPa to the south of the rainband. The forced easterly anomaly to north of the rainband is not strong enough to reverse the vertical distribution of the zonal wind, therefore maintaining ∂u ∂p <0 and ∂Q ∂y <0 to the north of the rainband. This causes positive PE4 and negative PE4 to the south and north of the rainband, respectively, leading to system development to the south. Hence, the latent condensation heat favors the rainband shifting southward, and obstructs the rainband from migrating northward. Analysis of the vertical cross-section along another longitude (e.g., 114°E) shows similar processes (Figures not shown).

Discussion And Conclusions
We de ned the LPEPE as a large continuous region (the grid number no less than 60 for the 0.5×0.5 latitude-longitude grid dataset) with the daily precipitation no less than 25mm that can persist for at least three days, and the total maximum daily precipitation is more than 250mm. 82 LPEPEs were detected from 1961 to 2013, among which 15 LPEPEs were related to typhoons. After excluding the typhoonrelated LPEPEs and LPEPEs in other periods, we got 46 LPEPEs in the Meiyu season.
We found that the LPEPEs have the tendency to move southward, especially during the Mei-yu period, with 72% of the LPEPEs-M shifting southward. The southward-moving LPEPEs-M are associated with large-scale circulation systems, including the weakening high-level jet, stable SAH, eastward retreating WPSH, and southward retreating low-level jet. The PV tendency analyses demonstrate that the intensity of the rainfall systems is partially maintained by the PV ux convergence, which is associated with the low-level meridional wind convergence, and is also contributed by the latent condensation heat of the LPEPEs-M.
The tremendous diabatic heating is essential for the southward shifting of LPEPEs-M. During an LPEPEs-M, a large amount of latent condensation heat is released at the middle levels, generating a cyclone anomaly from the middle to lower levels above the rainband. The westerly/easterly anomaly is located to the south/north of the rainband, produced by the cyclone anomaly. The westerly anomaly lifts the center of low-level zonal wind, usually at 850hPa, to 600hPa, resulting in ∂u ∂p >0 to the south of the rainband below 600hPa. While the easterly anomaly does not reverse the ∂u ∂p <0 to the north of the rainband. Coupled with the meridional diabatic heating distribution, the zonal wind con guration generates PV to the south of the rainband and diminish PV to the north of the rainband, creating a condition that favors the southward movement of the rainband. This also has the effect of hindering the northward mitigation of the rainfall system. The sensitivity experiment for a randomly chosen LPEPE from 8th to 10th July It's well known that the East Asian summer monsoon is characterized by alternative stagnation and rapid northward movement, usually with three stationary periods and two abrupt northward jumps. Especially during the Mei-yu period, the rain belt stagnates over the Yangzte River Valley for about one month. This remarkable stepwise and standing feature has been explained from the viewpoint of seasonal changes in the general circulation in East Asia (Ding and Chan, 2005;Ye et al., 1958), climatological intraseasonal oscillation (Qian et al., 2002), the continuous southward intrusion of cold air and accompanying frontal systems (Wu and Wang, 2001), warm advection in the mid-troposphere from the Tibetan Plateau (Sampe and Xie, 2010). In this study, we illustrated that the large-scale rainfall could release abundant latent heat.
By forcing secondary circulation, the diabatic heating can reinforce the large-scale rainfall, and shift the rainfall system southward. This process has the effect of hindering the northward migration of the primary rain belt, therefore, can be the intrinsic reason for the rain belt stagnation.
This study mainly focuses on LPEPEs during the Mei-yu season. The interaction between latent heat and large-scale circulation needs to be further studied for the whole summer season. Meanwhile, whether the size and orientation of rainfall patterns have different feedback on the synoptic system is also an important question that needs further investigation.   The terrain height of the simulation area. The grid resolution is 5km, and the grid number is 652×565. The dashed box is the concerned area of LPEPE.     The dynamic composite analysis of vertical cross-section along the Lon wp from the rst day to the third day. (a-c) the convergence (shadings, units: ×10 -6 ·s -1 ) and vertical velocity (dash lines, units: ×10 -2 ·pa·s -1 ). (d-f) the Q 1 (shadings, units: ×10 -6 ·K·s -1 ), ∂Q 1 / ∂y (green contours, units: ×10 -9 K·s -1 m -1 ) and zonal wind (black contours, units: m·s -1 ). The black, blue, and red dots are the dynamic composite Lat wp on the rst, second and third day of LPEPEs.

Figure 6
The dynamic composite analysis of PET (shadings, units: PVU, 1PVU=×10 -12 m 2 ·s -2 ·K·Kg -1 ) at 850hPa and the dynamic composite rainband (black contours, units: mm) from the rst to the third day. The Xaxis and Y-axis are the longitude and latitude departure (units: degree) from the WPs (0,0), respectively.