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<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1598866</article-id>
<article-id pub-id-type="doi">10.3389/feart.2025.1598866</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Comparison of preconvective environments between warm-sector and frontal heavy rainfall events in South China</article-title>
<alt-title alt-title-type="left-running-head">Wan et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/feart.2025.1598866">10.3389/feart.2025.1598866</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Wan</surname>
<given-names>Yijing</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2925433/overview"/>
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<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Dongyang</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Donghai</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>School of Atmospheric Sciences, Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies, Key Laboratory of Tropical Atmosphere-Ocean System, Ministry of Education, Sun Yat-Sen University</institution>, <addr-line>Zhuhai</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai)</institution>, <addr-line>Zhuhai</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Zhuhai Public Meteorological Service Center</institution>, <addr-line>Zhuhai</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>National Observation and Research Station of Coastal Ecological Environments in Macao, Macao Environmental Research Institute, Macau University of Science and Technology</institution>, <addr-line>Macao SAR</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/291079/overview">Yi-Leng Chen</ext-link>, University of Hawaii at Manoa, United States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2131635/overview">Mingxin Li</ext-link>, Chinese Academy of Meteorological Sciences, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3022356/overview">Kao-Shen Chung</ext-link>, National Central University, Taiwan</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Donghai Wang, <email>wangdh7@mail.sysu.edu.cn</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>23</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1598866</elocation-id>
<history>
<date date-type="received">
<day>24</day>
<month>03</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>04</day>
<month>09</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Wan, Wang and Wang.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Wan, Wang and Wang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>This study aims to identify the environmental differences between frontal heavy rainfall (FHR) and warm-sector heavy rainfall (WSHR), which frequently occur during early summer (April-June) over South China. Using 14 years of hourly rain-gauge data and high-resolution radiosonde observations, a total of 132 WSHR events and 84 FHR events are quantitatively investigated. FHR events occur most frequently in late May, while WSHR events demonstrate an increasing trend from April to June. WSHR events exhibit a pronounced diurnal variation, with a peak at 0800 LST (Local Standard Time, LST &#x3d; UTC &#x2b;8 h). In contrast, FHR events have a peak at 0400 LST. The WSHR and FHR events typically occur under favorable convective conditions characterized by abundant water vapor, moderate convective available potential energy (CAPE), and moderate to severe deep wind shear. Compared to FHR events, WSHR events are associated with more abundant water vapor at 500 hPa, greater warm cloud depth, a lower lifting condensation level, and stronger warm advection. FHR events are characterized by more water vapor in the lower troposphere, stronger instability, and stronger 0&#x2013;6 km wind shear. Additionally, WSHR events exhibit higher wind speed below 800 hPa than FHR events, while the wind speed in the upper troposphere for FHR events is 3&#x2013;4 m s<sup>-1</sup> larger than that in WSHR events. The thermodynamic characteristics associated with WSHR and FHR events, as revealed in this study, have significant implications for enhancing our understanding of heavy rainfall in South China.</p>
</abstract>
<kwd-group>
<kwd>warm-sector heavy rainfall</kwd>
<kwd>frontal heavy rainfall</kwd>
<kwd>sounding</kwd>
<kwd>preconvective environmental conditions</kwd>
<kwd>South China</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Atmospheric Science</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Heavy rainfall is one of the most destructive natural hazards in South China during the pre-summer rainy season (<xref ref-type="bibr" rid="B67">Wu et al., 2020a</xref>). However, its prediction remains unsatisfactory in operational weather forecasting and scientific research. Previous studies have shown that two types of heavy rainfall generally occur during the pre-summer rainy season (April-June), one is frontal heavy rainfall (FHR) and the other is warm sector heavy rainfall (WSHR). FHR typically occurs near the synoptic-scale frontal zone, where the northerly cold airflow converges with southerly warm airflow (<xref ref-type="bibr" rid="B13">Ding, 1994</xref>; <xref ref-type="bibr" rid="B81">Zhao et al., 2007</xref>). In contrast, WSHR often occurs more than 200 km ahead of a surface front in the warm sector or occurs in the confluence zones of southwesterly and southeasterly airflows, even in the southwesterly airflow without conspicuous convergence (<xref ref-type="bibr" rid="B33">Huang et al., 1986</xref>; <xref ref-type="bibr" rid="B47">Luo et al., 2017</xref>). Both WSHR and FHR events cause severe flooding, considerable economic loss and serious injury (<xref ref-type="bibr" rid="B66">Wu and Luo, 2016</xref>; <xref ref-type="bibr" rid="B42">Liu et al., 2019</xref>; <xref ref-type="bibr" rid="B73">Zeng and Wang, 2022</xref>).</p>
<p>Previous studies have shown the difference in statistical characteristics of WSHR and FHR events (<xref ref-type="bibr" rid="B67">Wu et al., 2020a</xref>; <xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>; <xref ref-type="bibr" rid="B21">Fu et al., 2023</xref>). WSHR events often occur in coastal areas, while FHR events mainly occur over inland regions. WSHR events tend to occur more frequently from April to June, which is closely related to the onset of summer monsoon, whereas the FHR events have an unobvious monthly variation (<xref ref-type="bibr" rid="B67">Wu et al., 2020a</xref>). Additionally, WSHR events have a peak in the early morning, which is mainly caused by the convergence between nocturnal low-level jets (LLJs) and land breezes, whereas FHR events have an afternoon peak. In contrast to FHR events that are driven by strong synoptic forcing, the trigger mechanisms for WSHR events are quite complicated, including topographic lifting (e.g., <xref ref-type="bibr" rid="B7">Chen et al., 2016</xref>; <xref ref-type="bibr" rid="B2">Bai et al., 2021</xref>; <xref ref-type="bibr" rid="B78">Zhang et al., 2022</xref>), local convergence initiated from low-level jets (e.g., <xref ref-type="bibr" rid="B16">Du and Chen, 2018</xref>; <xref ref-type="bibr" rid="B17">Du and Chen, 2019a</xref>; <xref ref-type="bibr" rid="B75">Zhang and Meng, 2019</xref>), and land-sea breeze (e.g., <xref ref-type="bibr" rid="B7">Chen et al., 2016</xref>; <xref ref-type="bibr" rid="B22">Gao et al., 2022</xref>), as well as their interactions (<xref ref-type="bibr" rid="B19">Du et al., 2020</xref>; <xref ref-type="bibr" rid="B80">Zhang S. et al., 2022</xref>; <xref ref-type="bibr" rid="B59">Su et al., 2023</xref>). Due to complex initiation and formation mechanisms, predicting whether WSHR events will occur in South China remains a great challenge (<xref ref-type="bibr" rid="B32">Huang and Luo, 2017</xref>; <xref ref-type="bibr" rid="B34">Huang et al., 2018</xref>; <xref ref-type="bibr" rid="B68">Wu et al., 2020b</xref>).</p>
<p>Environments for WSHR events are shown in many previous studies (<xref ref-type="bibr" rid="B61">Wang et al., 2014</xref>; <xref ref-type="bibr" rid="B66">Wu and Luo, 2016</xref>; <xref ref-type="bibr" rid="B41">Liu et al., 2018</xref>; <xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>; <xref ref-type="bibr" rid="B73">Zeng and Wang, 2022</xref>; <xref ref-type="bibr" rid="B74">Zeng et al., 2023</xref>). A warm, moist, and conditionally unstable low-level environment is conducive to the occurrence of WSHR events (<xref ref-type="bibr" rid="B5">Chen and Zhang, 2021</xref>; <xref ref-type="bibr" rid="B76">Zhang et al., 2022a</xref>). Proximity soundings of WSHR events often exhibit moderate-to-high convective available potential energy (CAPE), high precipitable water condition, weak vertical wind shear below 400 hPa, and a low-level jet near 925 hPa with weak warm advection (e.g., <xref ref-type="bibr" rid="B61">Wang et al., 2014</xref>; <xref ref-type="bibr" rid="B66">Wu and Luo, 2016</xref>; <xref ref-type="bibr" rid="B5">Chen and Zhang, 2021</xref>; <xref ref-type="bibr" rid="B74">Zeng et al., 2023</xref>). In contrast, FHR events are closely associated with a synoptic-system-related low-level jet with maximum wind speed at 850&#x2013;700 hPa (<xref ref-type="bibr" rid="B16">Du and Chen, 2018</xref>; <xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>). The preconvective conditions for FHR events are characterized by moderate-to-high CAPE, and high precipitable water condition (<xref ref-type="bibr" rid="B46">Luo et al., 2014</xref>; <xref ref-type="bibr" rid="B26">Han et al., 2021</xref>).</p>
<p>Over the years, many studies have investigated the environment and mechanisms of WSHR and FHR events in South China. Although the spatial and temporal differences of these two types of heavy rainfall have been noticed, there is less focus on the differences of preconvective conditions between WSHR and FHR events. WSHR events usually occur far away from the fronts, while FHR events are closely related to the fronts. Analysis of preconvective environments of WSHR and FHR events helps in understanding the reason for the occurrence of the two types of heavy rainfall. Therefore, a climate analysis is called for differentiating the preconvective environments between WSHR and FHR events.</p>
<p>Our motivation for this study is to identify skillful parameters for forecasting WSHR and FHR events in South China and to elucidate different formation mechanisms for WSHR and FHR events. The remainder of this paper is organized as follows. Section 2 describes the data and methods used in this article. Section 3 presents the statistical characteristics of WSHR and FHR events in South China during 2008&#x2013;2021. The discrepancies in environments between the WSHR and FHR events are shown in Section 4. Finally, the conclusions and discussion are given in Section 5.</p>
</sec>
<sec id="s2">
<title>2 Data and methods</title>
<sec id="s2-1">
<title>2.1 Data</title>
<p>The present study focuses on the area ranging within 20&#x2013;27&#xb0;N and 105&#x2013;120&#xb0;E, which includes almost all of South China, except for Hainan Province. The datasets used in this study include surface and radiosonde observations in South China during April-June of 2008&#x2013;2021 provided by the China Meteorological Administration (CMA). Surface observations with 1-h temporal resolution from 188 national surface stations (red dots in <xref ref-type="fig" rid="F1">Figure 1</xref>) are used for identifying heavy rainfall events. The radiosonde data is obtained from 14 sounding stations in South China (blue crosses in <xref ref-type="fig" rid="F1">Figure 1</xref>). The sounding stations are endowed with an advanced L-band radiosonde system, capable of meticulously profiling atmospheric parameters such as temperature, atmospheric pressure, relative humidity (RH), and wind characteristics with a remarkable vertical resolution of &#x223c;10 m (<xref ref-type="bibr" rid="B25">Guo et al., 2016</xref>; <xref ref-type="bibr" rid="B35">Jiang et al., 2017</xref>; <xref ref-type="bibr" rid="B51">Miao et al., 2018</xref>). The conventional detection time of the L-band radiosondes is 0800 LST and 2000 LST, and additionally observations at 0200 LST and 14 LST are performed depending on the special weather conditions or test requirements.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The distribution of the terrain height of South China, sounding sites (blue crosses), and near-surface meteorological stations (red dots).</p>
</caption>
<graphic xlink:href="feart-13-1598866-g001.tif">
<alt-text content-type="machine-generated">Topographic map of southern China showing elevation levels with a color gradient from green (low) to brown (high). Red dots and blue X marks indicate specific locations. Latitude and longitude lines provide geographic context.</alt-text>
</graphic>
</fig>
<p>To identify the cold fronts and diagnose the atmospheric conditions for WSHR and FHR events, ERA5 (<xref ref-type="bibr" rid="B30">Hersbach et al., 2020</xref>) is used in this study. ERA5 data have a time interval of 1 h and horizontal grid spacing of 0.25 &#xd7; 0.25 latitude-longitude with 37 pressure levels and surface. In addition, the tropical cyclone (TC) best-track dataset provided by CMA (<xref ref-type="bibr" rid="B72">Ying et al., 2014</xref>; <xref ref-type="bibr" rid="B44">Lu et al., 2021</xref>) is used to exclude the days affected by TCs.</p>
</sec>
<sec id="s2-2">
<title>2.2 Identification and categorization of heavy rainfall events</title>
<p>In this study, daily precipitation is defined as the total precipitation recorded during the period from 2000 to 2000 LST. A heavy rainfall event in South China is characterized by at least five of the 188 stations reporting daily precipitation exceeding 50 mm day<sup>&#x2212;1</sup>. The time when the hourly precipitation reaches (below) 0.1 mm/h is defined as the start (end) time of the heavy rainfall event. Heavy rainfall events due to TCs are excluded if there are any observational stations in South China within the effective radius of TCs on a day in the pre-summer rainy season. The effective radius is 500 km in this study, according to previous studies (<xref ref-type="bibr" rid="B36">Lee et al., 2010</xref>; <xref ref-type="bibr" rid="B23">Gu et al., 2017</xref>).</p>
<p>Generally, WSHR events occur independently of synoptic fronts and under weak synoptic-scale forcing, while FHR events are closely associated with synoptic fronts. To define WSHR and FHR events, the first step is to identify the fronts. In this study, the locations of fronts are analyzed by forecasters who subjectively locate fronts using a combination of the horizontal gradient of potential temperature (<inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#x2207;</mml:mo>
<mml:mi mathvariant="normal">&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) and wind observations in the surface and 925 hPa layers (<xref ref-type="bibr" rid="B60">Thomas and Schultz, 2019</xref>; <xref ref-type="bibr" rid="B67">Wu et al., 2020a</xref>; <xref ref-type="bibr" rid="B74">Zeng et al., 2023</xref>). If frontal features are clear in surface analyses, we locate the fronts based on the hourly surface observations (mainly by significant potential temperature gradients). Otherwise, we define the fronts mainly based on the 925 hPa directional wind shear (significant difference in wind direction) and potential temperature gradients. The second step is to define WSHR and FHR events. Only WSHR and FHR events with a duration of more than 6 h are selected. WSHR events are defined as heavy rainfall that occurs &#x3e;200 km ahead of the front line or in weakly forced synoptic environments (<xref ref-type="bibr" rid="B33">Huang et al., 1986</xref>). FHR events refer to the heavy rainfall that appears within 200 km of the front. To adequately describe the preconvective conditions for both WSHR and FHR events, we focus exclusively on heavy rainfall events that affected sounding stations. Under the constraints of these conditions, 132 WSHR events and 84 FHR events are identified in South China from 2008 to 2021. There are 125 WSHR-only cases, 77 FHR-only cases, and 7 cases of both WSHR and FHR. <xref ref-type="fig" rid="F2">Figure 2</xref> shows the locations of fronts (925 hPa wind shears) during a pure FHR event, a pure WSHR event, and a hybrid event with coexisting FHR and WSHR.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Distribution of precipitation and the circulation at <bold>(A)</bold> 1600 LST on 21 April 2017, <bold>(B)</bold> 0800 LST on 7 May 2017 and <bold>(C)</bold> 0800 LST on 10 May 2013: 925 hPa wind field (each bar represent 4 m s<sup>&#x2212;1</sup>) and daily cumulative precipitation (shaded, mm). The solid brown lines represent the positions of the front lines. The blue dots represent the stations where heavy rainfall occurred.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g002.tif">
<alt-text content-type="machine-generated">Weather maps showing rainfall distribution and wind patterns over a geographic region for three different dates in 2017 and 2013. Each map uses color gradients from blue to red to indicate increasing rainfall from 10 to 100 millimeters. Arrows display wind direction and intensity.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-3">
<title>2.3 Proximity sounding and physical parameters</title>
<p>To investigate the features of the environmental deviation between WSHR and FHR events, a precise understanding of how to determine the preconvective soundings is essential. Soundings too close to heavy rainfall events are excluded because the environmental conditions may have been altered by the convective feedback (<xref ref-type="bibr" rid="B55">Potvin et al., 2010</xref>). The present study selects the closest soundings prior to 2 h before the start time of heavy rainfall events. For instance, the start time of the pure FHR event (<xref ref-type="fig" rid="F2">Figure 2A</xref>) is at 1600 LST on 21 April, the sounding data collected at 0800 LST on 21 April were selected for analysis of FHR events. When both FHR and WSHR events occur simultaneously, the following procedure is adopted: First, the type of heavy rainfall event experienced at each station is identified. Subsequently, the sounding data corresponding to the time closest to the onset of the heavy rainfall event is selected, based on the start time of the heavy rainfall.</p>
<p>To explore the connections between heavy rainfall and thermodynamic characteristics in the troposphere in South China, an analysis of 15 sounding-derived parameters (<xref ref-type="table" rid="T1">Table 1</xref>) is conducted. Among these parameters, T<sub>d850</sub>, T<sub>d500</sub>, T<sub>d100</sub>, and PWAT demonstrate the water vapor condition, &#x3b8;<sub>e100</sub>, &#x394;&#x3b8;<sub>e950,500</sub>, CAPE, KI, SI, and TT indicate the stability of the atmosphere, while LCL and WCD represent the thermodynamic state. Additionally, WS<sub>0-1km</sub>, WS<sub>0-3km</sub>, and WS<sub>0-6km</sub> characterize the dynamic features in the lower and middle troposphere. All the selected characteristics are frequently used as indicators for heavy rainfall forecasts and are closely associated with the generation and formation of heavy rainfall (<xref ref-type="bibr" rid="B20">Dyson et al., 2015</xref>).</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Listing of all sounding-derived parameters used in the analysis.</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#989494">
<th align="center">Symbols</th>
<th align="center">Parameter descriptions and equations</th>
<th align="center">Units</th>
<th align="center">References</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">T<sub>d100</sub>
</td>
<td align="center">Average dew point temperature in the 100 hPa above ground level</td>
<td align="center">&#xb0;C</td>
<td align="center">
<xref ref-type="bibr" rid="B11">Craven et al. (2002)</xref>
</td>
</tr>
<tr>
<td align="center">T<sub>d850</sub>
</td>
<td align="center">Dew point temperature at 850 hPa</td>
<td align="center">&#xb0;C</td>
<td align="center">
<xref ref-type="bibr" rid="B27">Harnack et al. (1998)</xref>
</td>
</tr>
<tr>
<td align="center">T<sub>d500</sub>
</td>
<td align="center">Dew point temperature at 500 hPa</td>
<td align="center">&#xb0;C</td>
<td align="center">
<xref ref-type="bibr" rid="B27">Harnack et al. (1998)</xref>
</td>
</tr>
<tr>
<td align="center">&#x3b8;<sub>e100</sub>
</td>
<td align="center">Mean layer equivalent potential temperature in the 100 hPa above ground level</td>
<td align="center">K</td>
<td align="center">
<xref ref-type="bibr" rid="B53">Omotosho et al. (2000)</xref>
</td>
</tr>
<tr>
<td align="center">&#x394;&#x3b8;<sub>e950,500</sub>
</td>
<td align="center">Mean layer equivalent potential temperature lapse rate: &#x394;&#x3b8;<sub>e950,500</sub> &#x3d; &#x3b8;<sub>e950</sub> &#x2212; &#x3b8;<sub>e500</sub>
</td>
<td align="center">K</td>
<td align="center">
<xref ref-type="bibr" rid="B57">Schultz et al. (2000)</xref>
</td>
</tr>
<tr>
<td align="center">PWAT</td>
<td align="center">Precipitable water<break/>
<inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mtext>PWAT</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mn>0</mml:mn>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:msubsup>
<mml:mi>q</mml:mi>
<mml:mo>&#x2206;</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, where <italic>P</italic>
<sub>0</sub> is surface pressure</td>
<td align="center">mm</td>
<td align="center">
<xref ref-type="bibr" rid="B27">Harnack et al. (1998)</xref>
</td>
</tr>
<tr>
<td align="center">KI</td>
<td align="center">K index<break/>
<inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mtext>KI</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>850</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>500</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mn>850</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>700</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mn>700</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">&#xb0;C</td>
<td align="center">
<xref ref-type="bibr" rid="B29">Henry (2000)</xref>
</td>
</tr>
<tr>
<td align="center">CAPE</td>
<td align="center">Convective available potential energy<break/>
<inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:mtext>CAPE</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mo>&#x222b;</mml:mo>
<mml:mtext>LFC</mml:mtext>
<mml:mtext>EL</mml:mtext>
</mml:msubsup>
<mml:mi>B</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>d</mml:mi>
<mml:mi>z</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">g</mml:mi>
<mml:msubsup>
<mml:mo>&#x222b;</mml:mo>
<mml:mtext>LFC</mml:mtext>
<mml:mtext>EL</mml:mtext>
</mml:msubsup>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi>T</mml:mi>
<mml:mi>v</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:mover accent="true">
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfrac>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>d</mml:mi>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">J kg<sup>-1</sup>
</td>
<td align="center">
<xref ref-type="bibr" rid="B4">Brooks et al. (2003)</xref>
</td>
</tr>
<tr>
<td align="center">TT</td>
<td align="center">Total Totals<break/>
<inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mtext>TT</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>850</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>500</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mn>850</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>500</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">K</td>
<td align="center">
<xref ref-type="bibr" rid="B52">Miller (1972)</xref>
</td>
</tr>
<tr>
<td align="center">SI</td>
<td align="center">Showalter index: <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mtext>SI</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>500</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mtext>LCL</mml:mtext>
<mml:mn>500</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">&#xb0;C</td>
<td align="center">
<xref ref-type="bibr" rid="B58">Showalter (1953)</xref>
</td>
</tr>
<tr>
<td align="center">WCD</td>
<td align="center">Warm cloud depth: <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mtext>WCD</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mtext>LCL</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">m</td>
<td align="center">
<xref ref-type="bibr" rid="B49">Market et al. (2003)</xref>
</td>
</tr>
<tr>
<td align="center">LCL</td>
<td align="center">Lifting condensation level</td>
<td align="center">m</td>
<td align="center">
<xref ref-type="bibr" rid="B11">Craven et al. (2002)</xref>
</td>
</tr>
<tr>
<td align="center">WS<sub>0-1km</sub>
</td>
<td align="center">Bulk wind shear: magnitude of vector difference between 0 and 1 km</td>
<td align="center">m s<sup>-1</sup>
</td>
<td align="center">
<xref ref-type="bibr" rid="B15">Doswell et al. (1996)</xref>
</td>
</tr>
<tr>
<td align="center">WS<sub>0-3km</sub>
</td>
<td align="center">Bulk wind shear: magnitude of vector difference between 0 and 3 km</td>
<td align="center">m s<sup>-1</sup>
</td>
<td align="center">
<xref ref-type="bibr" rid="B15">Doswell et al. (1996)</xref>
</td>
</tr>
<tr>
<td align="center">WS<sub>0-6km</sub>
</td>
<td align="center">Bulk wind shear: magnitude of vector difference between 0 and 6 km</td>
<td align="center">m s<sup>-1</sup>
</td>
<td align="center">
<xref ref-type="bibr" rid="B15">Doswell et al. (1996)</xref>
</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Statistical characteristics of WSHR and FHR events</title>
<p>To understand the seasonal climatology for WSHR and FHR events, <xref ref-type="fig" rid="F3">Figure 3</xref> shows the semi-monthly variation of rainfall amount and the occurrence of WSHR and FHR events during the pre-summer rainy season from 2008 to 2021. Each month is broken down into two 15/16 periods called early and late. The mean rainfall amount of WSHR events peaks in early May, while FHR events exhibit a maximum rainfall amount in late June, and the former is greater than the latter from April to early June. The frequency of WSHR events increases gradually from April to June. As WSHR events are closely associated with warm and moist conditions, with the onset of the East Asian summer monsoon in late May, the warm and moist flow may contribute to more favorable conditions for WSHR events (<xref ref-type="bibr" rid="B71">Yihui and Chan, 2005</xref>). While WSHR events exhibit higher frequency in late June, the rainfall amount is less compared to earlier periods. It is likely associated with changes in convective organization during the monsoon progression. As East Asian summer monsoon establishes, the low-level flow becomes warmer and more moisture-saturated. This environment favors more frequent but less organized convective systems with shorter durations, leading to higher frequency but lower accumulated rainfall. In contrast, the occurrence of FHR events increased in April, with peak values in early May. FHR events decrease from early May to June as the East Asian summer monsoon progresses and the warm, moist air dominates while cold air decays over South China (<xref ref-type="bibr" rid="B9">Chen et al., 2021</xref>). The rainfall amount of FHR events increases from early May to late June but the frequency decreases. Although the frequency of cold fronts decreases after East Asian summer monsoon establishes, it is prone to produce more intense FHR events under the warmer and more humid environment in South China once a front occurs.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Semi-monthly variation of mean rainfall amount and occurrence frequency of WSHR and FHR events with orange and blue bars representing WSHR and FHR events, respectively. The red (blue) dotted line represents the occurrence frequency of WSHR (FHR) events.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g003.tif">
<alt-text content-type="machine-generated">Bar and line chart comparing FHR and WSHR precipitation and frequency from April to June. FHR precipitation decreases while WSHR increases overall. Both FHR and WSHR frequencies rise, with WSHR showing a more significant increase by June.</alt-text>
</graphic>
</fig>
<p>Previous studies have revealed that the diurnal variations of precipitation in South China vary in different areas (<xref ref-type="bibr" rid="B8">Chen et al., 2018</xref>; <xref ref-type="bibr" rid="B82">Zhong, 2020</xref>). A statistical analysis by <xref ref-type="bibr" rid="B8">Chen et al. (2018)</xref> shows that during the pre-summer (May-June) season from 1998 to 2014, the morning rainfall peak was more pronounced over the South China coastal area, whereas afternoon and nocturnal rainfall were dominant on land and in the northern inland region, respectively. <xref ref-type="bibr" rid="B21">Fu et al. (2023)</xref> illustrated that FHR events mainly start around 0000 LST, while the start time of WSHR events is relatively evenly distributed from 2300 to 0300 LST. FHR events are likely to end in the morning and noon, while WSHR events prefer to end in the afternoon. This study focuses on the frequency of diurnal variations of the rainfall peak time of two heavy rainfall events. As shown in <xref ref-type="fig" rid="F4">Figure 4</xref>, WSHR events exhibit a peak in the morning (0800 LST), while the peak time of FHR events is mainly concentrated between 0100 and 0500 LST, with the peak at 0400 LST. For coastal areas, the peak for WSHR events is mainly caused by the coastal terrain and land-sea distribution in southern China, which strengthens the nighttime land breeze, combined with the strengthening of the LLJs in the early morning (<xref ref-type="bibr" rid="B8">Chen et al., 2018</xref>; <xref ref-type="bibr" rid="B1">Bai et al., 2019</xref>; <xref ref-type="bibr" rid="B17">Du and Chen, 2019a</xref>; <xref ref-type="bibr" rid="B18">Du and Chen, 2019b</xref>; <xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>). For inland areas, the interaction between the LLJs and local terrain effects may be conducive for WSHR events (<xref ref-type="bibr" rid="B56">Pu et al., 2022</xref>; <xref ref-type="bibr" rid="B80">Zhang S. et al., 2022</xref>). In contrast, the rainfall peak time of FHR events is found at night (0400 LST), which is possibly attributed to two mechanisms: the intensification of BLJs at night and the frontogenesis caused by the diabatic process (<xref ref-type="bibr" rid="B6">Chen et al., 2007</xref>; <xref ref-type="bibr" rid="B24">Guan et al., 2020</xref>). The frontogenesis is dominated by the diabatic heating process during the frontal precipitation (<xref ref-type="bibr" rid="B62">Wang et al., 2022</xref>). The sensible cooling over the cloud-free areas at the cold side of the front increases the temperature gradient and causes frontogenesis, which results in the peak time of FHR events at night (<xref ref-type="bibr" rid="B6">Chen et al., 2007</xref>).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Diurnal variation of frequency for the peak time of WSHR and FHR events. Orange and blue bars represent WSHR and FHR events, respectively.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g004.tif">
<alt-text content-type="machine-generated">Bar chart comparing the frequency of two metrics, FHR in blue and WSHR in orange, across different times labeled in local solar time (LST) from 0 to 24 hours. Frequency ranges from 0 to 0.12. Peaks are visible in the early morning and evening hours for both metrics.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Differences in sounding paraments between WSHR and FHR events</title>
<sec id="s3-2-1">
<title>3.2.1 Humidity</title>
<p>
<xref ref-type="fig" rid="F5">Figure 5</xref> shows boxplots of moisture parameters for WSHR and FHR events. The T<sub>d100</sub> is a parameter that represents the low-level atmospheric vapor condition. The distributions of T<sub>d100</sub> exhibit considerable overlaps between WSHR and FHR events. As shown in <xref ref-type="fig" rid="F5">Figure 5A</xref>, their 25th percentiles are 19.6 &#xb0;C and 20.1 &#xb0;C, and their 75th percentiles are 22.6 &#xb0;C and 22.4 &#xb0;C, both respectively. These results suggest that T<sub>d100</sub> shows no significant differences between WSHR and FHR events, indicating that both WSHR and FHR events are initiated in a favorable low-level moist environment. The abundant low-level water vapor of FHR and WSHR events may be associated with BLJ, which favor the preconvective environment to produce heavy rainfall through transporting moisture (<xref ref-type="bibr" rid="B40">Liang et al., 2019</xref>; <xref ref-type="bibr" rid="B43">Liu et al., 2020</xref>; <xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>; <xref ref-type="bibr" rid="B74">Zeng et al., 2023</xref>). In this sense, our result agrees with the previous literature.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Box-and-whisker plots of <bold>(A)</bold> T<sub>d100</sub>, <bold>(B)</bold> T<sub>d850</sub>, <bold>(C)</bold> T<sub>d500</sub>, <bold>(D)</bold> PWAT from FHR and WSHR events over South China. The boxes represent the 25th&#x2013;75th percentiles (interquartile range), whiskers extend to the minima and maxima, and the bars in the boxes indicate the 50th percentiles (median). Red (blue) cross represents the mean value of each parameter of WSHR (FHR) events.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g005.tif">
<alt-text content-type="machine-generated">Four box-and-whisker plots comparing FHR and WSHR data sets. (A) Td1000 shows temperature ranges with FHR and WSHR around 18-24 &#xB0;C. (B) Td850 displays 5-20 &#xB0;C ranges. (C) Td500 illustrates -60 to 0 &#xB0;C ranges. (D) PWAT depicts 30-80 mm ranges. FHR is blue, WSHR is red.</alt-text>
</graphic>
</fig>
<p>The T<sub>d850</sub> shows the water vapor content in the low-level troposphere. The interquartile range of T<sub>d850</sub> are 16.3 &#xb0;C&#x2013;19.1 &#xb0;C and 15.9 &#xb0;C&#x2013;17.9 &#xb0;C for FHR and WSHR events, respectively (<xref ref-type="fig" rid="F5">Figure 5B</xref>). The T<sub>d850</sub> median is higher in FHR events (17.5 &#xb0;C) than in WSHR events (16.6 &#xb0;C). The T<sub>d850</sub> between FHR and WSHR events are statistically different with <italic>p</italic> &#x3c; 0.01 (two-tailed Welch&#x2019;s <italic>t</italic>-test, (<xref ref-type="bibr" rid="B65">Welch, 1947</xref>); <xref ref-type="table" rid="T2">Table 2</xref>), although the distributions overlap somewhat. Some previous case studies demonstrated that the water vapor conditions in the lower mid-level of FHR are critical to the development of frontal convective system (<xref ref-type="bibr" rid="B48">Luo et al., 2020</xref>; <xref ref-type="bibr" rid="B70">Yang et al., 2023</xref>). WSHR events also tend to occur in an environment with high humidity (<xref ref-type="bibr" rid="B5">Chen and Zhang, 2021</xref>; <xref ref-type="bibr" rid="B26">Han et al., 2021</xref>). <xref ref-type="bibr" rid="B38">Li and Du (2021)</xref> suggested that synoptic-system-related low-level jet (SLLJ) is more associated with FHR events, which is a possible reason for the higher water content at 850 hPa in FHR events.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Listing of the mean values and <italic>p</italic>-Value of the <italic>t</italic>-test for FHR and WSHR events for all sounding-derived parameters.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Parameters</th>
<th align="center">FHR</th>
<th align="center">WSHR</th>
<th align="center">
<italic>p</italic>-Value</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">T<sub>d100</sub>
</td>
<td align="center">20.9</td>
<td align="center">21.0</td>
<td align="center">0.722</td>
</tr>
<tr>
<td align="center">T<sub>d850</sub>
</td>
<td align="center">17.5</td>
<td align="center">16.6</td>
<td align="center">
<bold>0.007</bold>
</td>
</tr>
<tr>
<td align="center">T<sub>d500</sub>
</td>
<td align="center">&#x2212;14.2</td>
<td align="center">&#x2212;10.7</td>
<td align="center">0.017</td>
</tr>
<tr>
<td align="center">PWAT</td>
<td align="center">58.2</td>
<td align="center">59.7</td>
<td align="center">0.237</td>
</tr>
<tr>
<td align="center">&#x3b8;<sub>e100</sub>
</td>
<td align="center">353.5</td>
<td align="center">351.8</td>
<td align="center">0.222</td>
</tr>
<tr>
<td align="center">&#x394;&#x3b8;<sub>e950,500</sub>
</td>
<td align="center">13.3</td>
<td align="center">10.6</td>
<td align="center">0.044</td>
</tr>
<tr>
<td align="center">KI</td>
<td align="center">37.0</td>
<td align="center">36.5</td>
<td align="center">0.504</td>
</tr>
<tr>
<td align="center">CAPE</td>
<td align="center">1507.0</td>
<td align="center">1454.3</td>
<td align="center">0.710</td>
</tr>
<tr>
<td align="center">TT</td>
<td align="center">44.9</td>
<td align="center">43.7</td>
<td align="center">
<bold>0.003</bold>
</td>
</tr>
<tr>
<td align="center">SI</td>
<td align="center">&#x2212;1.8</td>
<td align="center">0.0</td>
<td align="center">
<bold>0.000</bold>
</td>
</tr>
<tr>
<td align="center">WCD</td>
<td align="center">4497.2</td>
<td align="center">4698.5</td>
<td align="center">
<bold>0.001</bold>
</td>
</tr>
<tr>
<td align="center">LCL</td>
<td align="center">602.7</td>
<td align="center">379.2</td>
<td align="center">
<bold>0.000</bold>
</td>
</tr>
<tr>
<td align="center">WS<sub>0-1km</sub>
</td>
<td align="center">7.1</td>
<td align="center">8.1</td>
<td align="center">0.064</td>
</tr>
<tr>
<td align="center">WS<sub>0-3km</sub>
</td>
<td align="center">12.0</td>
<td align="center">10.9</td>
<td align="center">0.072</td>
</tr>
<tr>
<td align="center">WS<sub>0-6km</sub>
</td>
<td align="center">14.7</td>
<td align="center">10.9</td>
<td align="center">
<bold>0.000</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>In bold, <italic>p</italic>-Values equal to or lower than 0.010.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The T<sub>d500</sub> is a parameter that assesses mid-level water vapor content for precipitation. For FHR events, most values range from &#x2212;19.7 &#xb0;C to &#x2212;6.3 &#xb0;C, which is broader than the range for WSHR events, whose 25th and 75th percentiles are &#x2212;12.4 &#xb0;C and &#x2212;5.1 &#xb0;C, respectively (<xref ref-type="fig" rid="F5">Figure 5C</xref>). The mean value of T<sub>d500</sub> for WSHR events is about 25% higher than that for FHR events. The differences between WSHR and FHR events are statistically significant at a 98% level of confidence, with <italic>p</italic> &#x3c; 0.02, despite some overlap between the interquartile ranges (<xref ref-type="table" rid="T2">Table 2</xref>). Thus, T<sub>d500</sub> effectively discriminates between WSHR and FHR events. WSHR events tend to occur in a higher mid-level humidity environment. Since WSHR events occur more frequently in June and FHR events peaks at early May, the higher humidity at mid-level troposphere in WSHR events is related to the warm-moisture air fed by southwesterly monsoonal flows after the onset of East Asia summer monsoon. The higher humidity at midtroposphere in WSHR events may reduce the evaporation and increase the precipitation rate. For FHR events, the drier midtroposphere indicates that the air requires deeper lifting to reach saturation than WSHR events (<xref ref-type="bibr" rid="B15">Doswell et al., 1996</xref>).</p>
<p>The PWAT gives an account of the total atmospheric water vapor contained in a vertical column above a specific sensor. As presented in <xref ref-type="fig" rid="F5">Figure 5D</xref>, there is a high degree of overlap in PWAT between WSHR and FHR events. The 25th percentiles for WSHR and FHR are 51 mm and 56 mm, respectively, while the 75th percentiles are 65 mm and 66 mm. These results are consistent with the findings of <xref ref-type="bibr" rid="B5">Chen and Zhang (2021)</xref>, indicating that both WSHR and FHR events need abundant water vapor for their formation.</p>
</sec>
<sec id="s3-2-2">
<title>3.2.2 Instability parameters</title>
<p>The equivalent potential temperature (&#x3b8;<sub>e</sub>) is a parameter of both moisture and temperature, which represents the convective instability of a specific layer within the troposphere (<xref ref-type="bibr" rid="B57">Schultz et al., 2000</xref>). <xref ref-type="fig" rid="F6">Figure 6A</xref> shows that WSHR and FHR events exhibit similar &#x3b8;<sub>e100</sub> values, with 75% of both soundings higher than 348 K. It indicates that the lowest 100 hPa layer over South China is warm and moist with high &#x3b8;<sub>e</sub>, which favors the occurrence of WSHR and FHR events in South China.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>As Figure 5, but <bold>(A)</bold> for &#x3b8;<sub>e100</sub>, <bold>(B)</bold> for &#x394;&#x3b8;<sub>e950,500</sub>, <bold>(C)</bold> for KI, <bold>(D)</bold> for CAPE, <bold>(E)</bold> for TT, <bold>(F)</bold> for SI.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g006.tif">
<alt-text content-type="machine-generated">Six box plots comparing FHR and WSHR for different meteorological parameters. (A) Potential temperature at 100 hPa, (B) Temperature difference 950 to 500 hPa, (C) K-index, (D) Convective available potential energy, (E) Total totals index, (F) Showalter index. Blue represents FHR, and red represents WSHR, with each plot showing variations in distribution and central tendency.</alt-text>
</graphic>
</fig>
<p>The atmosphere is considered as convectively unstable if &#x394;&#x3b8;<sub>e</sub> &#x3e;0 over a sufficiently deep layer. Consequently, the &#x394;&#x3b8;<sub>e950,500</sub> value is calculated to investigate the instability in the lower troposphere. Around 50% of WSHR events have &#x394;&#x3b8;<sub>e950,500</sub> values greater than 10.3 K, and more than 61% of FHR events exceed 10.3 K. The median &#x394;&#x3b8;<sub>e950,500</sub> is higher in FHR events (14.53 K) than in WSHR events (10.28 K). The median &#x394;&#x3b8;<sub>e950,500</sub> of FHR events is very close to the 75th percentile of &#x394;&#x3b8;<sub>e950,500</sub> for WSHR events, which reflects that stronger vertical instability in frontal environments (<xref ref-type="fig" rid="F6">Figure 6B</xref>). There are significant differences between WSHR and FHR events, with a confidence level of 96%. This difference is linked to drier mid-tropospheric conditions (T<sub>d500</sub>) in FHR events, which enhance the &#x3b8;<sub>e</sub> contrast between the warm-moist boundary layer and the mid-troposphere. These results suggest that FHR events require a stronger unstable environment for their formation.</p>
<p>The K index (KI) is an integrative indicator of atmospheric stability and moisture, which comprises a temperature difference term and two moisture-related terms (<xref ref-type="bibr" rid="B29">Henry, 2000</xref>; <xref ref-type="bibr" rid="B20">Dyson et al., 2015</xref>). The KI values for WSHR and FHR events are comparable. As shown in <xref ref-type="fig" rid="F6">Figure 6C</xref>, the 25th to 75th percentiles of KI for FHR events range from about 35 &#xb0;C to 41 &#xb0;C, while for WSHR events the 25th to 75th percentiles range from 35 &#xb0;C to 38 &#xb0;C. Therefore, there are no significant differences between WSHR and FHR events.</p>
<p>CAPE is an energy-based measure of atmospheric potential instability that is widely recognized as an indicator of convective instability (<xref ref-type="bibr" rid="B3">Brooks et al., 1994</xref>; <xref ref-type="bibr" rid="B37">Lepore et al., 2015</xref>). CAPE is proportional to the kinetic energy, which a parcel can obtain from its environment due to buoyancy&#x2019;s contribution to vertical acceleration. Higher CAPE values indicate greater potential for strong updrafts, which favors the occurrence of rainfall. The medians of CAPE for both WSHR and FHR events are around 1100 J kg<sup>&#x2212;1</sup>. The 25th-75th percentile of CAPE for WSHR and FHR events range from 99 J kg<sup>&#x2212;1</sup> to 2189 J kg<sup>&#x2212;1</sup> and 404 J kg<sup>&#x2212;1</sup>&#x2013;2266 J kg<sup>&#x2212;1</sup>, respectively. The distribution of CAPE exhibits a high degree of overlap (<xref ref-type="fig" rid="F6">Figure 6D</xref>), indicating CAPE may not be useful in distinguishing whether FHR or WSHR events occur. These results are consistent with previous findings (<xref ref-type="bibr" rid="B14">Dong et al., 2019</xref>; <xref ref-type="bibr" rid="B74">Zeng et al., 2023</xref>).</p>
<p>The Total Totals Index (TT) is a parameter that is highly relevant in the forecasting of thunderstorms and other convective events. According to the threshold given by the Weather Forecast Office in North America, TT below 45 &#xb0;C is an unfavorable environment for thunderstorm formation, whereas TT above 50 &#xb0;C encourages the development of thunderstorms. Applying these figures to our database, we find that 44% of FHR events and 32% of WSHR events exceed 45 &#xb0;C, and only three FHR events and one WSHR event surpassed 50 &#xb0;C, which is consistent with <xref ref-type="bibr" rid="B39">Li et al. (2021)</xref>. Compared to WSHR events, FHR events prefer to occur with a higher TT environment, which accounted for stronger instability. WSHR and FHR events are statistically different at a 99% level of confidence, although the distributions overlap somewhat (<xref ref-type="fig" rid="F6">Figure 6E</xref>). Therefore, TT allows us to differentiate between WSHR and FHR events.</p>
<p>The Showalter Index (SI) is defined as the temperature difference between 500 hPa and the temperature of an air parcel in a pseudo-adiabatic ascent from 850 hPa to 500 hPa. A negative SI value indicates an unstable environment. The median of SI for FHR events is &#x2212;1.7 &#xb0;C, lower than that of WSHR events, which is &#x2212;1 &#xb0;C (<xref ref-type="fig" rid="F6">Figure 6F</xref>). 87% of FHR events occurred under unstable conditions (SI &#x3c; 0), with 59.5% in moderate (SI from &#x2212;3 &#xb0;C to 0 &#xb0;C) instability and 14.3% in severe (SI &#x2264; &#x2212;4 &#xb0;C) instability, respectively. In contrast, 65.2% of WSHR events occurred in moderate instability, while only 2.3% in severe instability. There are significant differences between WSHR and FHR events, with a confidence level of 99%. This suggests that FHR events are associated with greater instability than WSHR events, and SI shows skillful discrimination between WSHR and FHR events.</p>
<p>The &#x394;&#x3b8;<sub>e950,500</sub>, TT, and SI statistically significantly discriminates well between FHR and WSHR events. In contrast, &#x3b8;<sub>e100</sub>, KI, and CAPE exhibit limited utility in distinguishing between FHR and WSHR events. The distributions of the humidity and instability parameters above indicate the differences between FHR and WSHR events. In general, heavy rainfall is produced by deep moist convection that develops within a favorable preconvective environment in the presence of three essential ingredients: moisture, instability, and lift (<xref ref-type="bibr" rid="B15">Doswell et al., 1996</xref>). The differences in &#x394;&#x3b8;<sub>e950,500</sub> may link to the drier mid-troposphere in FHR events, which enhance the &#x3b8;<sub>e</sub> contrast between the warm-moist boundary layer and the mid-troposphere. The &#x3b8;<sub>e100</sub> and KI mainly show thermodynamic characteristics below 700 hPa. They may not be useful in distinguishing FHR and WSHR events due to small difference in temperature and humidity conditions between FHR and WSHR events.</p>
</sec>
<sec id="s3-2-3">
<title>3.2.3 Dynamic parameters</title>
<p>Vertical wind shear is a critical factor influencing the organization and structural characteristics of heavy rainfall, as it helps to decouple the updraft and downdraft flows (<xref ref-type="bibr" rid="B20">Dyson et al., 2015</xref>). Previous studies have demonstrated that lower vertical wind shear corresponds to a decreased likelihood of raindrop evaporation, promoting efficient precipitation (<xref ref-type="bibr" rid="B12">Davis, 2001</xref>).</p>
<p>WS<sub>0-6km</sub> values greater than 10 m s<sup>&#x2212;1</sup> and 20 m s<sup>&#x2212;1</sup> are considered favorable environments for multicell storms and supercells, respectively (<xref ref-type="bibr" rid="B50">Markowski and Richardson, 2010</xref>). Strong vertical wind shear facilitates the organization of convection into mesoscale convective systems (<xref ref-type="bibr" rid="B64">Weisman and Klemp, 1982</xref>). As illustrated in <xref ref-type="fig" rid="F7">Figure 7A</xref>, a large fraction of both WSHR and FHR events are associated with WS<sub>0-6km</sub> below 20 m s<sup>&#x2212;1</sup>. FHR events exhibit higher quartiles than WSHR events, with a median WS<sub>0-6km</sub> for FHR events of 13.2 m s<sup>&#x2212;1</sup>, compared to 10.0 m s<sup>&#x2212;1</sup> for WSHR events. The 25th percentile of WS<sub>0-6km</sub> for FHR events is 10.9 m s<sup>&#x2212;1</sup>, which is larger than the median WS<sub>0-6km</sub> for WSHR events (10.0 m s<sup>&#x2212;1</sup>). And the median of WS<sub>0-6km</sub> for FHR events is close to the 75th percentile of WS<sub>0-6km</sub> for WSHR events, which suggests that FHR events tend to be accompanied by stronger vertical wind shear. These results are consistent with <xref ref-type="bibr" rid="B74">Zeng et al. (2023)</xref>. The distributions of WS<sub>0-6km</sub> are statistically significant at the 99% confidence level, with <italic>p</italic> &#x3c; 0.001 (<xref ref-type="table" rid="T2">Table 2</xref>), illustrating that WS<sub>0-6km</sub> is a good discriminator for these two types of heavy rainfall. It indicates that FHR events develop in an environment with stronger vertical wind shear than WSHR events. Strong vertical wind shear is conducive to the formation of tilted structures in convective systems, separating updrafts from precipitation particles. The separation of updrafts and downdrafts generated by the gravitational drag of precipitation particles is beneficial for the development of convective systems. Thus, the lifetime of the convective systems has been extended (<xref ref-type="bibr" rid="B31">Houze, 2004</xref>; <xref ref-type="bibr" rid="B54">Pilorz et al., 2016</xref>). In addition, the vertical wind shear promotes the concentration of water vapor carried by updrafts in the middle and lower troposphere, which is beneficial for improving precipitation efficiency and increasing the probability of short-term heavy rainfall. <xref ref-type="bibr" rid="B43">Liu et al. (2020)</xref> suggested that the more intense cold or quasi-stationary front accompanied by the stronger geostrophic southerly winds within both jets over inland and coastal south China is, the more rainfall over the inland region is favored. Thus, synoptic conditions with high WS<sub>0-6km</sub> are conducive for the initiation of FHR.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>As Figure 5, but <bold>(A)</bold> for WS<sub>0-6km</sub>, <bold>(B)</bold> for WS<sub>0-3km</sub>, <bold>(C)</bold> for WS<sub>0-1km</sub>.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g007.tif">
<alt-text content-type="machine-generated">Three box-and-whisker plots compare wind speeds at different altitudes. Plot (A) shows WS from zero to six kilometers; (B) from zero to three kilometers; (C) from zero to one kilometer. Each plot differentiates between FHR in blue and WSHR in red.</alt-text>
</graphic>
</fig>
<p>The distributions of WS<sub>0-3km</sub> exhibit considerable overlaps between WSHR and FHR events (<xref ref-type="fig" rid="F7">Figure 7B</xref>). The 25th to 75th percentile of WS<sub>0-3km</sub> for FHR events range from 8.7 m s<sup>&#x2212;1</sup>&#x2013;15.2 m s<sup>&#x2212;1</sup>, whereas the 25th and 75th percentile values for WSHR events are 7.9 m s<sup>&#x2212;1</sup> and 13.3 m s<sup>&#x2212;1</sup>, respectively. These values are consistent with the results presented in <xref ref-type="bibr" rid="B74">Zeng et al. (2023)</xref>. It implies that WS<sub>0-3km</sub> shows no significant differences between WSHR and FHR events, with both event types characterized by weak-to-moderate shear (5&#x2013;20 m s<sup>&#x2212;1</sup>).</p>
<p>Previous studies have revealed that strong low-level wind shear is unfavorable for torrential rain (<xref ref-type="bibr" rid="B50">Markowski and Richardson, 2010</xref>; <xref ref-type="bibr" rid="B79">Zhang Q. et al., 2022</xref>). <xref ref-type="fig" rid="F7">Figure 7C</xref> shows that the median and mean values of WS<sub>0-1km</sub> for FHR events are lower than those of WSHR events. For FHR events, the 25th and 75th percentiles are 5.0 m s<sup>&#x2212;1</sup> and 9.1 m s<sup>&#x2212;1</sup>, respectively. This interval is similar to that of WSHR events, whose 25th and 75th percentiles are 5.3 m s<sup>&#x2212;1</sup> and 10.5 m s<sup>&#x2212;1</sup>. The differences in WS<sub>0-1km</sub> values are not statistically significant, illustrating that both WSHR and FHR events are characterized by weak WS<sub>0-1km</sub> in most cases.</p>
<p>In addition to bulk wind shear, the vertical wind profiles of WSHR and FHR events are compared. For FHR events, the mean wind speed increases gradually from near the surface to 200 hPa, with the maximum wind speed reaching 19.6 m s<sup>-1</sup> (<xref ref-type="fig" rid="F8">Figure 8A</xref>). The low-level wind speed for WSHR events increases from 2 m s<sup>&#x2212;1</sup>&#x2013;9.8 m s<sup>&#x2212;1</sup> below 850 hPa. From 800 hPa to 350 hPa, the wind speed maintains a relatively stable range of 10&#x2013;12 m s<sup>&#x2212;1</sup>, while above 300 hPa, it increases further to 15 m s<sup>&#x2212;1</sup>. The wind directions of WSHR and FHR events veer with altitude from the boundary layer to midtroposphere, transitioning through south-southeasterly, southerly, south-westerly, and westerly directions. This veering indicates strong warm advection, with an average 900&#x2013;800 hPa wind speed of 6&#x2013;10 m s<sup>&#x2212;1</sup> from the southwest. WSHR events have greater wind speed and warm advection in the lower troposphere. The stronger low-level wind favors the low-level disturbance, which can cause significant low-level convergence and the initiation of convective systems (<xref ref-type="bibr" rid="B10">Chen et al., 2023</xref>). The warm advection is conducive to the formation of warm and humid environmental conditions and the deeper thickness of the warm cloud layer for convection triggering.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>
<bold>(A)</bold> Vertical profile of mean wind direction and speed for WSHR and FHR events, <bold>(B)</bold> vertical profile of the wind speed difference between FHR and WSHR events. Short barbs represent wind strengths of 5 m s<sup>&#x2212;1</sup> and long barbs 10 m s<sup>&#x2212;1</sup>.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g008.tif">
<alt-text content-type="machine-generated">Two-panel chart comparing wind speeds at various pressures. Panel A shows wind speed profiles for FHR and WSHR with colors from blue to red indicating speeds from 1 to 16 meters per second. Panel B displays the wind speed difference between FHR and WSHR in a bar chart format, with red indicating positive and blue indicating negative differences. Pressure is measured in hectopascals.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F8">Figure 8B</xref> presents the wind speed differences between FHR and WSHR events. The largest difference between WSHR and FHR events is at 400 hPa in the upper troposphere, which is 4.1 m s<sup>&#x2212;1</sup>. In FHR events, the wind speed in the upper troposphere is 3&#x2013;4 m s<sup>&#x2212;1</sup> larger than that in WSHR events. The combination of frontal lifting, stronger wind shear, and abundant water vapor creates favorable conditions for the initiation of convective systems. In contrast, WSHR events have stronger mean winds than FHR events under 800 hPa, particularly in the <italic>v</italic> component, where winds are about 1.5 m s<sup>&#x2212;1</sup> stronger. Strong southerly winds might favor the preconvective environment to produce WSHR by transporting more moisture.</p>
<p>Some previous cases studies demonstrated that the underestimated southerlies in the lower troposphere result in the northeastward shifted shear line and the absent moisture channel at the boundary layer in a forecast of WSHR event (<xref ref-type="bibr" rid="B77">Zhang et al., 2022b</xref>). Attributed to these atmospheric circulation biases, the accumulated warm and moist energy is weaker at the boundary layer, which leads to weaker intensities of precipitation in the forecast. <xref ref-type="bibr" rid="B75">Zhang and Meng (2019)</xref> suggested that the QPF skill of WSHR events with LLJs is lower than that without LLJs. The QPF skill of WSHR events with LLJs is significantly correlated with the forecast accuracy of the LLJs, especially at 925 hPa. WSHR events are characterized by stronger wind than FHR events in the low-level troposphere and a close relationship with LLJs. Future numerical prediction for WSHR events need to improve the low-level wind and warm advection. The forecast uncertainties of FHR primarily stem from the SLLJ and the convergence of cold and warm air masses (<xref ref-type="bibr" rid="B38">Li and Du, 2021</xref>). Improving the prediction skill of frontal lifting and the wind shear can enhance the numerical prediction of FHR events. Assimilating more wind observations in the numerical model may correct the wind speed and wind direction, which helps to improve the QPF skill of WSHR and FHR events.</p>
</sec>
<sec id="s3-2-4">
<title>3.2.4 Warm cloud height and LCL height</title>
<p>The warm cloud depth (WCD) is defined as the difference in height between the lifting condensation level and the freezing level (0 &#xb0;C isotherm) (<xref ref-type="bibr" rid="B20">Dyson et al., 2015</xref>). WCD is closely related to high precipitation rates. Several previous studies showed that WSHR events usually occur in environments with thick warm cloud layers (<xref ref-type="bibr" rid="B28">He et al., 2021</xref>; <xref ref-type="bibr" rid="B56">Pu et al., 2022</xref>; <xref ref-type="bibr" rid="B79">Zhang Q. et al., 2022</xref>). <xref ref-type="fig" rid="F9">Figure 9A</xref> shows that both WSHR and FHR events have high WCD values, with 97% of these events exceeding 3.3 km. Moreover, a significant difference exists between WSHR and FHR events. For FHR events, most WCD values range from 4216 m to 4821 m, while WSHR events have higher 25th and 75th percentiles of 4531 m and 4985 m, respectively. WSHR events are characterized by high precipitation efficiency, which may be associated with the collision and coalescence of raindrops (warm rain process) in deep warm clouds (<xref ref-type="bibr" rid="B12">Davis, 2001</xref>; <xref ref-type="bibr" rid="B26">Han et al., 2021</xref>; <xref ref-type="bibr" rid="B79">Zhang Q. et al., 2022</xref>; <xref ref-type="bibr" rid="B63">Wang et al., 2025</xref>).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>As Figure 5, but <bold>(A)</bold> for WCD, <bold>(B)</bold> for LCL.</p>
</caption>
<graphic xlink:href="feart-13-1598866-g009.tif">
<alt-text content-type="machine-generated">Two boxplots comparing FHR and WSHR for two variables: (A) shows WCD in meters, ranging from 3000 to 6000, with FHR having higher values; (B) shows LCL in meters, ranging from 0 to 1800, with FHR having higher values. Blue represents FHR and red represents WSHR.</alt-text>
</graphic>
</fig>
<p>The lifting condensation level height (LCL) is defined as the height at which water vapor condenses, as well as the height of the stratus cloud base. The distributions of LCL associated with the WSHR and FHR are shown in <xref ref-type="fig" rid="F9">Figure 9B</xref>. The median and mean values of LCL for WSHR events are consistently lower than those for FHR events, with a significant discrepancy observed at a confidence level of 99% (<xref ref-type="table" rid="T2">Table 2</xref>). Based on these results, LCL discriminates well between WSHR and FHR events.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 Summary</title>
<p>Using surface meteorological observations, ballon-sounding measurements, and ERA5 reanalysis data, heavy rainfall events during the pre-summer rainy season from 2008 to 2021 were classified into WSHR and FHR events. This study investigates the differences in statistical and preconvective environmental characteristics between WSHR and FHR events. The major findings can be summarized as follows:</p>
<p>The monthly frequency of WHSR events in South China increases from April to June. The occurrence frequency of FHR events demonstrates an unimodal pattern, peaking in early May. The mean rainfall amount of WSHR events peaks in early May, whereas FHR events have a maximum rainfall amount in late June. The peak occurrence time of WSHR events in South China is in the morning (0800 LST), whereas the FHR events tend to peak in the early morning (0400 LST).</p>
<p>To identify the crucial parameters that can improve the prediction of WSHR and FHR events, 15 metrics were evaluated based on 132 and 84 proximity soundings for WSHR and FHR backgrounds, respectively. Generally, both WSHR and FHR events occur in moist environments. The middle level of WSHR events is moister than those of FHR events, while the lower troposphere of FHR events has more water vapor than WSHR events. In contrast to the WSHR background, the environment for FHR events is characterized by stronger atmospheric instability, with three parameters (&#x394;&#x3b8;<sub>e950,500</sub>, TT, and SI) showing significant differences between WSHR and FHR events. Although CAPE is typically used to reflect the environmental instability for heavy rainfall events in previous studies (e.g., <xref ref-type="bibr" rid="B61">Wang et al., 2014</xref>; <xref ref-type="bibr" rid="B66">Wu and Luo, 2016</xref>; <xref ref-type="bibr" rid="B41">Liu et al., 2018</xref>), it proves indistinguishable between WSHR and FHR events. The dynamic environments of both WSHR and FHR events are associated with moderate to severe wind shear, with FHR events exhibiting stronger WS<sub>0-6km</sub> than WSHR events. The composite wind profiles rotate clockwise from boundary layer to midtroposphere in both WSHR and FHR events, indicating that these events are associated with strong warm advection. The wind speed for FHR events increases gradually from 1000 hPa to 200 hPa. WSHR events exhibit greater wind speed below 800 hPa than FHR events, while the wind speed in the upper troposphere for FHR events is 3&#x2013;4 m s<sup>&#x2212;1</sup> larger than that in WSHR events. Moreover, WCD and LCL display significant differences between WSHR and FHR events. WSHR events are characterized by deeper WCD and lower LCL than FHR events.</p>
<p>WSHR events occur in environments with weakly synoptic forcing. The preconvective environment of WSHR events is characterized by moister mid-level troposphere, deeper warm cloud layer, lower LCL, and stronger warm advection environment than FHR events. These differences are likely enhanced warm rain processes in WSHR events, potentially providing more cloud droplets for raindrops to collect. Stronger southerly winds and the warm advection in the low-level troposphere for WSHR events can transport more incoming water vapor and deepen the thickness of the warm cloud layer to develop heavy rain. In contrast, FHR events are primarily forced by synoptic-scale frontal lifting, leading to widespread convective systems around the frontal area. FHR events tend to occur with greater low-level moisture, stronger instability, stronger 0&#x2013;6 km wind shear, and stronger wind in the upper troposphere. The coexistence of warm, humid air in the lower layer and dry air in the mid-troposphere enhances the equivalent potential temperature gradient, thereby increasing convective instability (<xref ref-type="bibr" rid="B83">Ninomiya and Shibagaki, 2007</xref>). The synoptic lifting provided by the fronts acts as the triggering mechanism that efficiently releases this instability. Moderate to severe vertical wind shear is conducive to the formation of tilted structures in convective systems and promotes the concentration of water vapor carried by updrafts in the middle and lower troposphere, which contributes to the maintenance of convective organization.</p>
<p>To improve the QPF skill for WHSR and FHR events, significant efforts need to be made according to different key environmental parameters. <xref ref-type="bibr" rid="B45">Luo and Chen (2015)</xref> suggested that prediction could be significantly improved when the initial fields of moisture, wind, and temperature were changed together for an extreme rainfall event in East China. Convection-permitting ensemble forecasts of a double-rainbelt event in South China revealed that the FHR event is sensitive to the synoptic forcing, and its sensitive area mainly locates near the frontal system, while the coastal boundary layer jet and water vapor from the South China Sea govern WSHR processes. The choice of microphysical scheme is critical for the convective initiation for the WSHR event (<xref ref-type="bibr" rid="B70">Yang et al., 2023</xref>). Based on previous studies and the results of this study, future numerical prediction for WSHR requires improving the prediction skill of WCD, LCL, T<sub>d500</sub>, and the wind at low-level troposphere by choosing more appropriate microphysics schemes (<xref ref-type="bibr" rid="B75">Zhang and Meng, 2019</xref>; <xref ref-type="bibr" rid="B77">Zhang et al., 2022b</xref>; <xref ref-type="bibr" rid="B69">Xiao et al., 2025</xref>). The simulation capabilities of different microphysics schemes for the heavy rainfall event can be evaluated and improved by using polarimetric radar, soundings, and surface observation data. For FHR events with strong synoptic forcing, data assimilation of wind and moisture needs to be improved to reduce initial errors and further decrease forecast errors. The influence of initial conditions of wind and moisture on the development of FHR events can be further discussed in the future.</p>
<p>In summary, this study analyzes the temporal characteristics and the preconvective environments of WSHR and FHR events over South China. These results enhance our understanding of the different skillful parameters for WSHR and FHR events. However, an in-depth discussion of the initiation and formation mechanisms of heavy rainfall, particularly WSHR, has not been conducted. Future studies should focus on the relationships between the statistical characteristics and the initiation mechanisms of the two types of events to better understand the intrinsic patterns of different types of heavy rainfall. Additionally, employing numerical simulations to assess the relative importance of different parameters should be considered in future studies to improve the numerical prediction of heavy rainfall in South China.</p>
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<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s6">
<title>Author contributions</title>
<p>YW: Validation, Writing &#x2013; review and editing, Investigation, Formal Analysis, Software, Methodology, Data curation, Visualization, Resources, Conceptualization, Writing &#x2013; original draft, Project administration, Funding acquisition. DyW: Visualization, Software, Writing &#x2013; review and editing, Supervision, Resources. DhW: Funding acquisition, Resources, Validation, Supervision, Writing &#x2013; review and editing, Software.</p>
</sec>
<sec sec-type="funding-information" id="s7">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This work was supported by the Science and Technology Development Fund of Macao Special Administrative Region (Grant No. 0009/2024/RIB1).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
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<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
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<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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