An Observational Analysis of a Persistent Extreme Precipitation Event in the Post-Flood Season over a Tropical Island in China

: Featuring unique tropical land–sea contrast and mesoscale terrain, Hainan Island in China is endowed with active mesoscale convections of special regional characteristics. Persistent extreme precipitation events (PEPs) during the post-ﬂood season, triggered by multi-scale interactions among mid-latitude and tropical weather systems, exhibit notable mesoscale features, long duration and high rainfall rates with low forecasting performance. This study is motivated by a failure to forecast a PEP in two stages with distinct characteristics and predictabilities, in the post-ﬂood season over Hainan Island on 16–18 October 2020. Based on multiple sources of remote sensing and high-resolution rain gauge records, detailed observational analyses were conducted using a ﬂow decomposition method. Water vapor divergence (WVD) and its three components were used to investigate the spatial distribution and temporal evolution of two stages with distinct characteristics and predictabilities during this PEP. Decomposed moisture components can be used to determine how and to what extent large- and sub-synoptic scale moisture convergence contributes to PEPs in the tropics, under similar synoptic backgrounds. Joint applications of multiple sources of remote sensing data and ﬂow decomposed WVD are proposed to further assist predicting PEPs in terms of rainfall location and evolution.


Introduction
The recent IPCC report has officially demonstrated that regional persistent extreme precipitation events (PEPs) are increasing in frequency and intensity in many regions and globally [1,2]. Increased persistent precipitations cause fatalities and economic losses, and threaten the ecology of the planet. Intense research has been continuously conducted on the large-scale circulations and moisture budgets of PEPs over East Asia [3], Europe [4], North America [5], and mainland China [6][7][8][9][10][11][12]. Climatological studies on the relationship between increasing global temperatures and precipitation variability [13][14][15] have further suggested that uneven extreme floods and droughts will tend to occur more in future. Besides this uncertainty on a climate scale, mechanisms for the initiation, moisture aggregation and weakening of each individual PEP are not clear from the perspectives of synoptic and sub-synoptic scales. Besides, few works have assessed tropical islands with abundant moisture supplies in the post-flood season against background circulations on planetary and synoptic scales. Unlike the mid-latitudes, the tropics have a relatively homogeneous air mass and fairly uniform distribution of surface temperature and pressure. Therefore, local planetary and synoptic scales. Unlike the mid-latitudes, the tropics have a relatively homogeneous air mass and fairly uniform distribution of surface temperature and pressure. Therefore, local and mesoscale effects are more dominant than synoptic influences. In recent years, rapid progress has been made in understanding the mechanisms of PEPs over Hainan Island (denoted by the red box in Figure 1a), a tropical island to the south of mainland China, including diurnal cycles in the pre-summer season [16,17] and synoptic characteristics during the post-flood season [18][19][20][21]. Characterized by multiscale features, PEPs in the post-flood season are known to be potentially disastrous, leading to dangers to public safety and property, agriculture, and damage prevention. It is thus reasonable to further explore different signals of large and sub-synoptic scale moisture convergence, to improve forecasting skills for such events.   Table 1. Moisture budgets are widely used as indicators for locations of and changes in anomalous precipitation [22,23]. Trends and variability of atmospheric water vapor have been studied globally [24,25] and in different regions, such as mainland China [26,27], North America [28], and the tropics [29]. Among the four moisture budget components, i.e., total precipitable water, evaporation, precipitation, and water vapor divergence (WVD), WVD has been identified as the dominant factor [30]. Moisture supply from the South China Sea has been found to play a leading role in PEPs over South China [31,32]. Equipped with abundant water vapor, the northeasterly low-level jet over the north South China Sea is known as the most prominent signal of PEPs over Hainan island [18]. Previous studies [19][20][21] have also demonstrated that as a result of multi-scale interactions between large-scale and mesoscale circulations, PEPs in the post-flood season involve tropical depression, cold surges, subtropical highs, and mesoscale convective systems (MCSs), etc. Although considerable progress has been made in the understanding of synoptic features, it remains unclear how the mesoscale systems are developed and organized. Due to limited understanding of the multi-scale interactions and model deficiencies, predicting the location and timing of heavy rainfall during these events remains a challenging task.
Flow decomposition approach is a powerful tool to facilitate studies of multi-scale interactions. From synoptic to climatic analysis, statistical tools to reveal averages over time or space are utilized to partition stationary and transient components [23,33]. Barnes filter [34] was adopted to extract synoptic or geostrophic components from the total flow in a study of diurnal precipitation in the Meiyu front [35,36]. For mesoscale to synoptic studies, flow decomposition firstly originated from the PV concept established by Hoskins [37] with solid physical foundations. However, mathematical difficulties in solving balanced models and choices of dynamic approximations for extreme events limit its availability and applicability in operational predictions. As a simple decomposition method, the Helmholtz theorem separates wind into rotational and divergent components [38]. The rotational component describes the large-scale movement and can be linked directly to geopotential, while the divergent component depicts ageostrophic or sub-synoptic motions. It has been widely used in atmospheric and oceanic circulations [39][40][41][42][43], as well as data assimilations [44][45][46][47].
Despite considerable research carried out into synoptic understandings [18][19][20][21], the ability to predict PEPs in the post-flood season over Hainan Island in terms of location and timing remains limited due to its association with mesoscale systems. The relationship between sub-synoptic scale processes and rainfall evolution was rarely addressed in the literature, such that more studies are still needed. During 16-18 October 2020, a disastrous PEP occurred over Hainan Island. This was typical in the post-flood season, involving multiscale interactions among systems from mid-latitudes and the tropics, with different forecast performance of NWP in different rainfall stages. The aim of this study is to use various remote sensing data along with other observational datasets to investigate the performance of the decomposed WVD components, where synoptic analysis and numerical prediction failed, in assessing the location and evolution of precipitation during a PEP over Hainan Island.
The remainder of this paper is organized as follows. Section 2 describe the datasets, the water vapor budget equations, and the WVD method adopted in this study. Section 3 presents traditional analyses of the synoptic background, convective organization, and the different performances of numerical forecasts during the two stages. The main results relating to the decomposed WVD in the two stages are provided in Section 4, demonstrating signals associated with the spatial and temporal evolution of rain pattern during this event. Lastly, this paper is summarized in Section 5, along with discussion. Rain gauge observations from an automatic weather station observation network were used to provide rainfall observations over land. There are 558 dense rain gauges from routine surface stations and automatic weather stations (DZZ4) across Hainan Island, with a time interval of 1 h and spatial resolution of 5-20 km. Thus, this dataset is adequate for the sub-synoptic investigations of spatial and temporal precipitation distributions over land.

Radar Observations
The regional radar mosaics of composite reflectivity operationally created by Hainan Meteorological observatory were used to examine the evolution of mesoscale systems. The composite reflectivity (CR) based on 6 S-band Doppler radars in the network of China new generation weather radar (located at the red pins in Figure 1a, including Haikou, Sanya, Dongfang, Xisha, Zhanjiang, and Yangjiang as listed in Table 1) was created every 6 min with a horizontal spatial resolution of about 2.15 km.

Satellite Precipitation Products
The satellite product used in this study is the Climate Prediction Center morphing technique (CMORPH). CMORPH with spatial resolution of 8 km and temporal resolution of 30 min was derived from geostationary satellite infrared imagery to obtain relatively high-quality precipitation estimates from passive low-orbit satellite microwave data. CMO-PRH covers rainfall over the ocean, and thus supplemented surface-based rain gauge observations over Hainan Island. The shape and intensity of the precipitation features were morphed during the interval between microwave sensor scans by performing a time weighted linear interpolation [48]. For consistency in temporal resolution, the CMORPH rainfall data and the ERA5 data used in the present study each have a temporal resolution of 1 h.

Reanalysis Data
ERA5 [49] is the fifth generation of the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis data, which has been significantly upgraded from ERA-Interim [50]. It provides improved spatial and temporal resolutions, with a horizontal grid spacing of 0.25 • × 0.25 • and a time interval of 1 h at surface and on 37 pressure levels, with variable uncertainties evaluated using ensemble reanalysis products. Historical observational data and satellite products are each used in advanced data assimilation and model systems to estimate atmospheric conditions more accurately. The technique has therefore been widely used to identify and analyze synoptic environmental systems as well as moisture supplies. Detailed variables from the reanalysis data and local observational datasets adopted in this study are listed in Table 1.

Water Vapor Budget Equations
The Eulerian atmospheric water budget equation for an atmospheric column of unit area [51,52] is adopted as follows: (1/g) ps 0 ∂ t q dp where q represents specific humidity, P and E indicate the precipitation and the evaporation from the underlying surface, respectively. Vertical integration is performed between the surface pressure, p s , and top. Due to the impenetrability of the atmosphere, ω vanishes at the surface and the top. Equation (1) becomes: (1/g) ps 0 ∂ t q dp + (1/g) ps 0 ∇ (qv) dp + E = P.
The first term in the left-hand-side of Equation (2), ∂ t q, represents the difference between q at two successive times. According to the literature on water vapor flux budget [52][53][54], the area is relatively small and is bounded within two meridians and latitude circles. The third term in the left-hand-side of Equation (2) can be calculated using the bulk aerodynamic formula [30,55]: where ρ a is the air density, C E is the turbulent exchange coefficient for moisture, U is the 10 m wind speed, q sat (SST) is the saturation specific humidity at the SST, and q a is the 10 m specific humidity. For the studies of cold season precipitation over a small domain with short duration, the influence of E on Equation (2) is less important than the vertically integrated WVD.

Hybrid-Integral Method for Decomposing WVD in a Limited Mesoscale Domain with Complex Flow Fields
According to the Helmholtz theorem, the horizontal velocity v can be partitioned into rotational and divergent components (denoted by v r and v d ) represented by streamfunction ψ and velocity potential χ, respectively, as follows: where k is the unit vector in the vertical direction and ∇ is the horizontal gradient operator. For a limited domain D, the following relationships hold: Here ζ and α are vorticity and divergence, respectively; ∂D denotes the boundary of domain D; v s and v n are the tangential and normal velocity along ∂D.
Considering the special characteristics of Hainan Island in terms of its mesoscale terrain, a newly developed accurate hybrid-integral scheme [56] was first used to solve ψ and χ. Secondly, Equations (5) and (6) were adopted to obtain v r and v d . Thirdly, the integrand in the second term in the left-hand-side of Equation (2) is calculated as the summation of three components as follows: The non-divergent property of v r is used in the above derivation. As seen in Equation (9), WVD (denoted by Q v all ) is thus partitioned into three components as: flow field divergence (denoted by Q v div ), moisture convection term by non-divergent or large-scale motions (denoted by Q v L ) and by divergent or sub-synoptic scale motions (denoted by Q v S ).

Overviews of Synoptic and Convective Environments
A persistent heavy rainfall occurred over Hainan Island during 16-18 October 2020, which presented a typical synoptic pattern in the post-flood season. Figure 1 shows the large-scale circulations during the event. Hainan Island is in a moist environment with precipitable water over 55 mm, to the southwest of the western Pacific subtropical high ( Figure 1a). In the boundary layer, a remnant of a tropical depression of high equivalent potential temperature (θ e ) moved northwestward towards the north coast of Vietnam, interacting with a cold surge characterized by low θ e from mid-latitudes (Figure 1b). Such a pattern gave rise to strong pressure gradients in the planetary boundary layer (PBL) and therefore a persistent notable boundary layer jet (BLJ) over the north of the South China Sea (SCS).
As shown in Figure 1c, a well-defined BLJ at 925 hPa with wind speed over 18 m·s −1 developed upstream of Hainan Island (around 18.5 • N, 110 • E) starting 0000 UTC 16 October 2020. The horizontal velocity of the BLJ exhibited notable variation and reached its maximum (about 24 m s −1 ) at around 0000 UTC 17, lasting about 36 h. This strong and persistent BLJ increased abundant horizontal moisture transports, resulting in specific humidity of greater than 16 g kg −1 and a deep moist layer of high relative humidity (85-100%) up to 500 hPa (not shown) over the north SCS. Given such a favorable ambient environment of a deep moist layer and continuous energy supply, a PEP occurred continuously over Hainan Island for a duration of 60 h (Figure 1d), resulting in a maximum accumulated rainfall of 600 mm, with 46 rain gauge stations exceeding 250 mm in the southeast area. Multiple rain gauge stations received hourly rainfall rates exceeding 30 mm·h −1 . This PEP affected more than 27,700 people, damaged farm crops over 6.7 thousand hectares and cost nearly 120 million RMB in direct economic losses.
Temporal and spatial precipitation variations in the southeast and the south of the island exhibited different patterns during this event. Heavy rainfall in the southeast was mainly produced in a 24 h period of time from 1200 UTC 16 to 1200 UTC 17 (hereafter referred to as the early stage), while in the south the major precipitation period lasted about 24 h from 1200 UTC 17 to 1200 UTC 18 (hereafter referred to as the later stage). A comparison of 24 h accumulated precipitation simulated by ECMWF with the observed precipitation is given in Figure 2, showing that the observed daily accumulated precipitation exhibited spatial differences with 24 h accumulated precipitation ending 1200 UTC 17 being southwest-northeast oriented, and the 24-h accumulated rainfall on the next day (ending 1200 UTC 18) moving southward and becoming north-south oriented. It is encouraging that the model well predicted the location of the heavy rainfall ( Figure 2a) although it under-predicted the maximum rainfall amount, which is common for a global model. However, on the next day when the rain belt moved southward, the NWP model failed to predict the spatial alternation (Figure 2b).

Convective Organization
An examination of radar composite reflectivity (Figure 3a,d) indicates that two linear MCSs were responsible for this PEP. These two northwest-southeast oriented belts of high CR values (with the central value above 50 dBZ) were organized nearly parallel to each other, resulting in heavy rainfall in the southeast and south of Hainan Island respectively. A comparison of rain gauge observation (Figure 2a,b) and radar reflectivity (Figure 3a,d) reveals two rainfall stages in the event. During the early stage, the high CR belt of MCS1 moved across the southeast coast (denoted by the blue rectangle in Figure 1a), producing precipitation with a maximum rainfall rate of 64.7 mm·h −1 . In the later stage after MSC1 dissipated, a new convective line (MCS2) was generated at the south coast (denoted by the green rectangle in Figure 1a). It moved in the same direction as MCS1 towards the south of the island, and was responsible for the heavy rainfall in the south of the island.

Convective Organization
An examination of radar composite reflectivity (Figure 3a,d) indicates that two linear MCSs were responsible for this PEP. These two northwest-southeast oriented belts of high CR values (with the central value above 50 dBZ) were organized nearly parallel to each other, resulting in heavy rainfall in the southeast and south of Hainan Island respectively. A comparison of rain gauge observation (Figures 2a,b) and radar reflectivity (Figure 3a,d) reveals two rainfall stages in the event. During the early stage, the high CR belt of MCS1 moved across the southeast coast (denoted by the blue rectangle in Figure 1a), producing precipitation with a maximum rainfall rate of 64.7 mm·h −1 . In the later stage after MSC1 dissipated, a new convective line (MCS2) was generated at the south coast (denoted by the green rectangle in Figure 1a). It moved in the same direction as MCS1 towards the south of the island, and was responsible for the heavy rainfall in the south of the island.

Convective Organization
An examination of radar composite reflectivity (Figure 3a,d) indicates that two linear MCSs were responsible for this PEP. These two northwest-southeast oriented belts of high CR values (with the central value above 50 dBZ) were organized nearly parallel to each other, resulting in heavy rainfall in the southeast and south of Hainan Island respectively. A comparison of rain gauge observation (Figures 2a,b) and radar reflectivity (Figure 3a,d) reveals two rainfall stages in the event. During the early stage, the high CR belt of MCS1 moved across the southeast coast (denoted by the blue rectangle in Figure 1a), producing precipitation with a maximum rainfall rate of 64.7 mm·h −1 . In the later stage after MSC1 dissipated, a new convective line (MCS2) was generated at the south coast (denoted by the green rectangle in Figure 1a). It moved in the same direction as MCS1 towards the south of the island, and was responsible for the heavy rainfall in the south of the island. Convective precipitation from ERA5 indicates that the data model well depicts the convective activities of the event. While hourly rainfall rates of large-scale precipitation remained below 2 mm·h −1 at both stages (Figure 3b,e), convective precipitation with hourly rainfall rates exceeding 2 mm·h −1 (Figure 3c,f) exhibited a fairly good agreement with the location of high CR belts (Figure 3a,d). An examination of the evolution of hourly convective precipitation further suggests increased rainfall rates at the later stage than at  Convective precipitation from ERA5 indicates that the data model well depicts the convective activities of the event. While hourly rainfall rates of large-scale precipitation remained below 2 mm·h −1 at both stages (Figure 3b,e), convective precipitation with hourly rainfall rates exceeding 2 mm·h −1 (Figure 3c,f) exhibited a fairly good agreement with the location of high CR belts (Figure 3a,d). An examination of the evolution of hourly convective precipitation further suggests increased rainfall rates at the later stage than at the early stage. Considering that the convective precipitation is generated by the convection scheme and the cloud scheme in the IFS (ECMWF Integrated Forecasting System), the activities of MCSs at these two stages tend to be related to different extents to the subsynoptic processes.

Decomposed WVD at Early Stage
As mentioned in Section 3.1, this event was caused by a strong BLJ over the north SCS upstream from Hainan Island. Figure 4 shows the pressure-time profile of horizontal wind vectors at Wanning. At the early stage, heavy rainfall started right after the establishment of a northeasterly BLJ at about 0000 UTC 16 October, and the hourly rainfall rate decreased rapidly below 5 mm·h −1 before 0000 UTC 17. To analyze the moisture convergence at the early stage, we investigated the domain averaged decomposed WVD components in Equation (9) over the southeast coast (the green rectangle in Figure 1a).  As shown in Figure 5a,b, Qv all converged below 700 hPa as southwesterly low level jet dominated this area before 15 October. After the easterly flow prevailed at around 1200 UTC 15, Qv all persistently converged below 900 hPa and diverged above up to 600 hPa nearly throughout the early stage. In spite of notable variation of hourly rainfall observed in this area, both Qv all and Qv div show strong convergence in the lower troposphere, indicating persistent flow convergence during this stage. Furthermore, Qv L exhibited clear deep-layer convergence (the green rectangle in Figure 5c) prior to the increase of hourly rainfall rate, indicating enhanced large-scale water vapor convergence as a result of the change of low level wind direction below 500 hPa (Figure 4). Triggered by favorable largescale moisture convergence, a high CR belt of MCS1 developed and moved towards the southeast coast (Figure 3), producing persistent precipitation with a maximum rainfall rate of 31.3 mm·h −1 in Waning and 64.7 mm·h −1 over the southeastern island. During the As shown in Figure 5a,b, Q v all converged below 700 hPa as southwesterly low level jet dominated this area before 15 October. After the easterly flow prevailed at around 1200 UTC 15, Q v all persistently converged below 900 hPa and diverged above up to 600 hPa nearly throughout the early stage. In spite of notable variation of hourly rainfall observed in this area, both Q v all and Q v div show strong convergence in the lower troposphere, indicating persistent flow convergence during this stage. Furthermore, Q v L exhibited clear deep-layer convergence (the green rectangle in Figure 5c) prior to the increase of hourly rainfall rate, indicating enhanced large-scale water vapor convergence as a result of the change of low Atmosphere 2022, 13, 679 9 of 16 level wind direction below 500 hPa (Figure 4). Triggered by favorable large-scale moisture convergence, a high CR belt of MCS1 developed and moved towards the southeast coast (Figure 3), producing persistent precipitation with a maximum rainfall rate of 31.3 mm·h −1 in Waning and 64.7 mm·h −1 over the southeastern island. During the heavy rainfall, Q v L below 700 hPa gradually weakened and is eventually dominated by areas with positive value. By 0000 UTC 17, Q v L exhibits strong signals of large-scale moisture divergence (the pink rectangle in Figure 5c) with Q v S diverging significantly below 800 hPa (Figure 5d). As a result, MCS1 weakened and finally dissipated. Rain gauge observations also show that the rainfall rate at Wanning decreased from 31.3 mm·h −1 to below 5 mm·h −1 .  Figure 1d) superimposed with hourly precipitation (units: mm·h −1 ), for Wanning (green triangle in Figure 1d).
To conclude briefly, the rainfall in the southeast coast at the early stage was triggered by large-scale moisture convergence. The high predictability of precipitation by the NWP model in this period is possibly related to the large-scale ambient flow and the clear synoptic signal. The decomposed Qv div indicates persistent flow convergence during this stage, while Qv L and Qv S correspond well to the initiation and cessation of the heavy precipitation.

Decomposed WVD at Later Stage
As the remnant of the tropical depression moved towards the coast of Vietnam during the later stage, the pressure gradient between the depression and the cold surge becomes stronger. The pressure-time profile of horizontal wind vector and hourly precipitation at Wanning is depicted in Figure 6, showing that the low-level ambient flow changed slightly, as the northeasterly jet over the south coast at early stage turned clockwise into the easterly jet ( Figure 6). Heavy rainfall in the south coast started at about 1200 UTC 17, nearly 36 h after the establishment of northeasterly BLJ at about 0000 UTC 16.  Figure 1d) superimposed with hourly precipitation (units: mm·h −1 ), for Wanning (green triangle in Figure 1d).
To conclude briefly, the rainfall in the southeast coast at the early stage was triggered by large-scale moisture convergence. The high predictability of precipitation by the NWP model in this period is possibly related to the large-scale ambient flow and the clear synoptic signal. The decomposed Q v div indicates persistent flow convergence during this stage, while Q v L and Q v S correspond well to the initiation and cessation of the heavy precipitation.

Decomposed WVD at Later Stage
As the remnant of the tropical depression moved towards the coast of Vietnam during the later stage, the pressure gradient between the depression and the cold surge becomes stronger. The pressure-time profile of horizontal wind vector and hourly precipitation at Wanning is depicted in Figure 6, showing that the low-level ambient flow changed slightly, as the northeasterly jet over the south coast at early stage turned clockwise into the easterly jet ( Figure 6). Heavy rainfall in the south coast started at about 1200 UTC 17, nearly 36 h after the establishment of northeasterly BLJ at about 0000 UTC 16.  Figure 1d).
An examination of the time series of hourly rainfall rates and domain averaged moisture convergence over the south coast (Figure 7) reveals that increased rainfall rate corresdonds with the strengthening of Qv all below 850 hPa. A comparison between Figure  7a,b reveals that Qv all is mostly determined by Qv div . In the boundary layer also, Qv div shows strong negative signals indicating low level flow convergence in this period. Below 500 hPa, Qv L exhibits notable convergence as a result of the change of low level wind direction (green rectangle in Figure 7c), with the negative signals stronger than those at the southeast coast (Figure 5c) continuing approximately throughout the later stage. In spite of clear signals of large-scale moisture convergence, the heavy rainfall over the south coast did not occur immediately. It is possible that stronger pressure gradients over the south coast at later stage indicate stronger sub-synoptic moisture convergence. An examination of Qv S reveals strong sub-synoptic moisture divergence (the green rectangle in Figure 7d) in this area. The near-surface divergence lasted nearly 36 h, until positive values of Qv S prevailed at 950 hPa (the pink rectangle in Figure 7d) after 1200 UTC 17. Due to favorable sub-synoptic moisture divergence, MCS2 became better organized and moved towards the south coast (Figure 3d), producing persistent heavy rainfall during the later stage with a maximum rainfall rate of 39.3 mm·h −1 in Sanya and 44.6 mm·h −1 over the south of the island. Qv S is observed to weaken after 1200 UTC 17, as the rainfall rate in the south coast decreased rapidly.  Figure 1d).
An examination of the time series of hourly rainfall rates and domain averaged moisture convergence over the south coast (Figure 7) reveals that increased rainfall rate corresdonds with the strengthening of Q v all below 850 hPa. A comparison between Figure 7a,b reveals that Q v all is mostly determined by Q v div . In the boundary layer also, Q v div shows strong negative signals indicating low level flow convergence in this period. Below 500 hPa, Q v L exhibits notable convergence as a result of the change of low level wind direction (green rectangle in Figure 7c), with the negative signals stronger than those at the southeast coast (Figure 5c) continuing approximately throughout the later stage. In spite of clear signals of large-scale moisture convergence, the heavy rainfall over the south coast did not occur immediately. It is possible that stronger pressure gradients over the south coast at later stage indicate stronger sub-synoptic moisture convergence. An examination of Q v S reveals strong sub-synoptic moisture divergence (the green rectangle in Figure 7d) in this area. The near-surface divergence lasted nearly 36 h, until positive values of Q v S prevailed at 950 hPa (the pink rectangle in Figure 7d) after 1200 UTC 17. Due to favorable sub-synoptic moisture divergence, MCS2 became better organized and moved towards the south coast (Figure 3d), producing persistent heavy rainfall during the later stage with a maximum rainfall rate of 39.3 mm·h −1 in Sanya and 44.6 mm·h −1 over the south of the island. Q v S is observed to weaken after 1200 UTC 17, as the rainfall rate in the south coast decreased rapidly.
A comparison of decomposed components in these two areas (Figures 5 and 7) also suggests different features of moisture convergence during the later stage. At the southeast coast, where no heavy rainfall was predicted, both Q v L and Q v S diverged in the PBL (Figure 5c,d) despite convergence of Q v all and Q v div (Figure 5a,b). On the contrary, Q v div and Q v S converge (Figure 7b,d) at the south coast where the heavy rainfall finally occurred.

Signals Associated with the Spatial Evolution of Rain Pattern
It is proven by the above analysis and by observational facts that the two precipitating stages were triggered and maintained by different scales of moisture convergence. Rainfall at the early stage was triggered by large-scale moisture convergence over the southeast coast, while at the later stage it was triggered by sub-synoptic scale moisture convergence and flow convergence under favorable large-scale moisture supply conditions. As men-tioned in Section 3, the rainfall at the later stage was under-predicted. In this section, we investigate the performance of decomposed water vapor flux components to obtain further information about the alternation of rain pattern.  (Figure 5a,b). On the contrary and Qv S converge (Figure 7b,d) at the south coast where the heavy rainfall finally occ

Signals Associated with the Spatial Evolution of Rain Pattern
It is proven by the above analysis and by observational facts that the two pre ing stages were triggered and maintained by different scales of moisture conver Rainfall at the early stage was triggered by large-scale moisture convergence ov southeast coast, while at the later stage it was triggered by sub-synoptic scale m convergence and flow convergence under favorable large-scale moisture supply tions. As mentioned in Section 3, the rainfall at the later stage was under-predicted. section, we investigate the performance of decomposed water vapor flux compon obtain further information about the alternation of rain pattern. Figures 8 indicates 24 h averaged moisture convergence at 925 hPa at the later showing weak Qv L convergence ( Figure 8c) and notable different patterns of Qv S be the two areas concerned (Figure 8d). Despite the similar distribution of moisture c gence for Qv all and Qv div in both areas (Figure 8a,b), Qv S suggests moisture diverge the southeast coast and moisture convergence at the south coast (Figure 8d). It is noting that the moisture convergent belt of Qv S in Figure 8d agrees well with the h belt and hourly convective precipitation shown in Figure 3d,f. Therefore, it is reas   (Figure 8c) and notable different patterns of Q v S between the two areas concerned (Figure 8d). Despite the similar distribution of moisture convergence for Q v all and Q v div in both areas (Figure 8a,b), Q v S suggests moisture divergence at the southeast coast and moisture convergence at the south coast (Figure 8d). It is worth noting that the moisture convergent belt of Q v S in Figure 8d agrees well with the high CR belt and hourly convective precipitation shown in Figure 3d,f. Therefore, it is reasonable to assume that besides flow convergence denoted by Q v div , the decomposed Q v S must be critical to the alternation of the rain pattern.
To demonstrate this point, we further investigated the distribution of the hourly amount of precipitation during the later stage, using CMORPH and Q v S . As shown in Figure 9, at 0000 UTC 17 before the later stage (Figure 9a,d), Q v S diverged to the south of the island at about 17-18 • N. Note that the area of significant moisture convergence at 16-17 • N (Figure 9d) corresponds well to the location of hourly rainfall exceeding 20 mm in Figure 9a. The rain belt moved northward as the Q v S convergent zone moved northward (Figure 9b,e). At 1000 UTC 17, 2-h before the later stage, a western-eastern oriented subsynoptic convergent zone characterized by negative value Q v S can be seen to dominate the area from the south of the island to the southern sea ( Figure 9f). Correspondingly, the intensified rain belt with maximum hourly rainfall exceeding 50 mm developed in this area (Figure 9c). to assume that besides flow convergence denoted by Qv div , the decomposed Qv S must be critical to the alternation of the rain pattern. To demonstrate this point, we further investigated the distribution of the hourly amount of precipitation during the later stage, using CMORPH and Qv S . As shown in Figure 9, at 0000 UTC 17 before the later stage (Figure 9a,d), Qv S diverged to the south of the island at about 17-18°N. Note that the area of significant moisture convergence at 16-17°N (Figure 9d) corresponds well to the location of hourly rainfall exceeding 20 mm in Figure  9a. The rain belt moved northward as the Qv S convergent zone moved northward ( Figure  9b,e). At 1000 UTC 17, 2-h before the later stage, a western-eastern oriented sub-synoptic convergent zone characterized by negative value Qv S can be seen to dominate the area from the south of the island to the southern sea ( Figure 9f). Correspondingly, the intensified rain belt with maximum hourly rainfall exceeding 50 mm developed in this area (Figure 9c). In brief conclusion, the torrential rainfall in the later stage over the south coast, whic the model failed to predict, was triggered by the sub-synoptic moisture convergence an flow convergence under the background of ambient large-scale moisture supply. Qv S give clear signals of the alternation of rain pattern. In brief conclusion, the torrential rainfall in the later stage over the south coast, which the model failed to predict, was triggered by the sub-synoptic moisture convergence and flow convergence under the background of ambient large-scale moisture supply. Q v S gives clear signals of the alternation of rain pattern.

Conclusions and Discussions
Climatological studies on persistent extreme precipitation events (PEPs) reveal that as the planet warms, PEPs are increasing in frequency and variability, threatening human lives, infrastructures, and ecosystems. Intense and thorough research has been carried out into summertime PEPs over mainland China and other mid-latitude regions around the world, while research on PEPs in the post-flood season over tropical islands has been lacking.
In this study, decomposed water vapor divergence (Q v all ) was applied to the analysis of a failure in forecasting two distinct stages of a PEP over Hainan Island, an important and fast-developing tropical region. Remote sensing data from multiple sources were used as evidence, together with local observation data. At the early stage when large-scale moisture convergence played a prevalent role in triggering the intense rainfall, the ECMWF model well depicted the large-scale circulation and also the precipitation locations. The high predictability at this stage is held to be related to the strong signal in the synoptic pattern. However, at the later stage when the rainfall was triggered by sub-synoptic moisture convergence and flow convergence, the model failed to predict the spatial evolution of the rain pattern.
The adoption of decomposed water vapor flux improves our understanding of this tropical PEP in the following aspects: (1) synoptic and sub-synoptic moisture convergence play different roles in triggering precipitation and influencing the evolution of rain bands during PEPs, (2) decomposed sub-synoptic component Q v S gives more clues to the missed rainfall by well depicting the evolution of sub-synoptic scale moisture convergence and rain belt, (3) variations of large-and sub-synoptic scale moisture convergence in the PBL are important in the forecast of tropical PEPs.
The method of decomposed water vapor divergence was earlier used in torrential rainfall events over the Yangtze River [6], tropical storms [57], and an extreme blizzard event in central Asia [58], revealing that the decomposed components give signals of snowfall and rainfall. Considering the limited understanding of the multi-scale interactions and model deficiencies during PEPs in the post-flood season over Hainan Island, this method may aid our understanding of different scales of moisture aggregation, provide local forecasters in the tropics with different signals of large-and sub-synoptic scale moisture convergence especially in the boundary layer, and can be introduced in operational forecasting by post-processing with numerical products. The improvement of forecasting skills for such disastrous and high-impact events is beneficial to public safety, property, agriculture, and prevention of damage.
With rapid developments in remote sensing and numerical modeling technologies, the new diagnostic method developed in this study will have further applications for practical tropical PEP forecasting.