Dynamic Trigger and Moisture Source of Two Typical Meiyu Front Rainstorms Associated with Eastward-Moving Cloud Clusters from the Tibetan Plateau

青藏高原东移云团影响下游暴雨的触发维持机制及水汽输送特征分析

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  • Corresponding author: Yi DENG, yi.deng@eas.gatech.edu
  • Funds:

    Supported by the National Natural Science Foundation of China (41620104009 and 41975058), Science and Technology Funds of Hubei Meteorological Bureau (2022Y25 and 2022Z02), and Joint Open Project of Key Laboratory of Meteorological Disaster, Ministry of Education & Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology (KLME202106). Yi DENG is in part supported by the U.S. National Science Foundation (AGS-2032532) and NOAA (NA20OAR4310380)

  • doi: 10.1007/s13351-022-1179-2

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  • Eastward-moving cloud clusters from the Tibetan Plateau (TP) often trigger heavy rainfall events in the Yangtze River basin in summer. Forecasting these events in an operational environment remains a challenging task. Here, dynamical diagnosis and a Lagrangian trajectory model are used to analyze the background atmospheric circulation, maintenance mechanism, and moisture transport of two Meiyu front rainstorms (MYFR) during 30 June–2 July 2016 and 17–19 June 2018 associated with eastward-moving cloud clusters from the TP. It is shown that in both cases heavy rainfall is characterized by semi-continuous rainbelts extending from the eastern TP to the Yangtze River valleys with eastward-spreading convective clouds weakening and strengthening alternately from the eastern TP to downstream regions. Following the track of positive water vapor advection, centers of positive vorticity propagate downstream through the Sichuan basin. The baroclinic thermodynamic–dynamical interaction and the barotropic non-equilibrium force work against each other in the development of the MYFR. Specifically, during the early stage of precipitation development, the barotropic non-equilibrium force dominates, while during the period of heavy precipitation the baroclinic thermodynamic–dynamical interaction dominates. The convergence associated with the baroclinic thermodynamic–dynamical interaction guarantees the persistence of heavy precipitation. Compared to the climate mean state (1988–2018), both MYFR events associated with eastward-moving cloud clusters from the eastern TP are characterized by increased moisture transport from the southwest. One of the major paths of moisture transport in both cases is along the south side of the TP, directly connected to the eastward movement of cloud clusters.
    青藏高原云团东移常常引发长江流域强降水,这类暴雨的预报是业务难点之一。利用动力诊断方程和拉格朗日轨迹模式,从定性和定量角度揭示了梅雨期两个高原东移云团引发下游暴雨个例的环流背景、触发维持机制和水汽输送特征。TBB变化表明,对流云团从高原东部到下游江淮地区逐渐东传并交替减弱和增强。正涡度大值中心在正水汽平流引导下,从高原东侧经四川盆地向下游传播。斜压热动力相互作用与正压非平衡强迫在梅雨锋暴雨发生与发展阶段的变化相反。强降水初期,正压强迫占主导;而在强降水持续期,斜压强迫占主导作用,其激发的辐合增长保障了强降水天气的持续。暴雨过程的水汽输送相对于气候态更多来自西南方向,其中一条明显的沿高原南侧的气流与东移云团有关。
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  • Fig. 1.  Precipitation rate (mm day−1) averaged from (a) 0800 BT 30 June to 0800 BT 2 July 2016 and (b) 0800 BT 17 to 0800 BT 19 June 2018, and Hovmöller (time–longitude) diagram for (c, d) rain rate (mm h−1) and (e, f) TBB (°C) at (c, e) 31°N between 29 June and 3 July 2016 and (d, f) 33°N between 16 and 20 June 2018.

    Fig. 2.  Average 500-hPa geopotential height (black contours; gpm; the green lines denote the troughs), 200-hPa geopotential height (shading; gpm), upper-level jet greater than 20 m s−1 (red vectors), and 850-hPa winds exceeding 12 m s−1 (blue barbs) (a) from 0800 BT 30 June to 0800 BT 3 July 2016 and (b) from 0800 BT 17 to 0800 BT 20 June 2018.

    Fig. 3.  The equivalent potential temperature (θe) (black contours; K), specific humidity (shading; g kg−1), and winds (vectors; m s−1) at 850 hPa from 0800 BT 30 June to 1400 BT 1 July 2016. The “L” indicates the southwest vortex.

    Fig. 4.  Locations of Meiyu front (thick black line) and precipitation (shading; mm) from 0800 BT 30 June to 1400 BT 1 July 2016. Contours are the frontal intensity ($\dfrac{\partial \mathit{\theta }_{\rm{e}}}{\partial \mathit{y}}$; K km−1) at 850 hPa; θe is equivalent potential temperature.

    Fig. 5.  Height–longitude cross section of specific cloud liquid water content (colors; 104 kg m−3) and cloud ice water content (contour; 105 kg m−3) at 31°N at 6-h intervals between 0800 BT 30 June and 1400 BT 1 July 2016. The red box marks the heavy rainfall area and gray shading illustrates the topography.

    Fig. 6.  Height–longitude cross section of relative vorticity (colors; 105 s−1) and water vapor advection (contours; g kg−1) at 31°N from 0800 BT 30 June to 1400 BT 1 July 2016 at a 6-h interval. The red box highlights the heavy rainfall area and gray shading illustrates the topography.

    Fig. 7.  Distributions of the barotropic non-equilibrium force (black dashed line; 10−10 s−2) at 850 hPa at (a) 0800 BT 30 June, (b) 1400 BT 30 June, (c) 2000 BT 30 June, and (d) 0200 BT 1 July 2016. Black shadings mark topography under 850 hPa.

    Fig. 8.  As in Fig. 7, but for distributions of the baroclinic thermodynamic–dynamical interaction term (black dashed lines; 10−10 s−2).

    Fig. 9.  Starting locations in the heavy rainfall area used in the backward trajectory simulation during (a) 30 June–2 July 2016 and (b) 17–19 June 2018.

    Fig. 10.  Spatial distributions of air parcel specific humidity (shaded; g kg−1) and number of air parcels (contour) seven days before reaching the heavy rainfall area for (a) climatic mean of 30 June–2 July between 1988 and 2018, (b) 30 June–2 July 2016, (c) climatic mean of 17–19 June between 1988 and 2018, and (d) 17–19 June 2018.

    Fig. 11.  Cluster analysis of backward trajectories for (a) climatic mean of 30 June–2 July between 1988 and 2018, (b) 30 June–2 July 2016, (c) climatic mean of 17–19 June between 1988 and 2018, and (d) 17–19 June 2018. The numbers indicate the percentage contribution of water vapor in each channel.

    Fig. 12.  Schematic summarizing the major atmospheric circulation systems during 2016 and 2018 MYFR cases associated with eastward-moving cloud clusters from the TP (SCS: South China Sea, BOB: Bay of Bengal, YHRV: Yangtze–Huai River valley).

    Fig. B1.  Distributions of the barotropic non-equilibrium force (black dashed line; 10−10 s−2) at 850 hPa at (a) 0800 BT 17 June, (b) 1400 BT 17 June, (c) 2000 BT 17 June, and (d) 0200 BT 18 June 2018. Black shadings mark topography under 850 hPa.

    Fig. B2.  As in Fig. B1, but for distributions of the baroclinic thermodynamic–dynamical interaction term (black dashed lines; 10−10 s−2).

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Dynamic Trigger and Moisture Source of Two Typical Meiyu Front Rainstorms Associated with Eastward-Moving Cloud Clusters from the Tibetan Plateau

    Corresponding author: Yi DENG, yi.deng@eas.gatech.edu
  • 1. Hubei Key Laboratory for Heavy Rain Monitoring and Warning Research, Institute of Heavy Rain, China Meteorological Administration, Wuhan 430205, China
  • 2. School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta 30314, USA
  • 3. Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson 85718, USA
Funds: Supported by the National Natural Science Foundation of China (41620104009 and 41975058), Science and Technology Funds of Hubei Meteorological Bureau (2022Y25 and 2022Z02), and Joint Open Project of Key Laboratory of Meteorological Disaster, Ministry of Education & Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology (KLME202106). Yi DENG is in part supported by the U.S. National Science Foundation (AGS-2032532) and NOAA (NA20OAR4310380)

Abstract: Eastward-moving cloud clusters from the Tibetan Plateau (TP) often trigger heavy rainfall events in the Yangtze River basin in summer. Forecasting these events in an operational environment remains a challenging task. Here, dynamical diagnosis and a Lagrangian trajectory model are used to analyze the background atmospheric circulation, maintenance mechanism, and moisture transport of two Meiyu front rainstorms (MYFR) during 30 June–2 July 2016 and 17–19 June 2018 associated with eastward-moving cloud clusters from the TP. It is shown that in both cases heavy rainfall is characterized by semi-continuous rainbelts extending from the eastern TP to the Yangtze River valleys with eastward-spreading convective clouds weakening and strengthening alternately from the eastern TP to downstream regions. Following the track of positive water vapor advection, centers of positive vorticity propagate downstream through the Sichuan basin. The baroclinic thermodynamic–dynamical interaction and the barotropic non-equilibrium force work against each other in the development of the MYFR. Specifically, during the early stage of precipitation development, the barotropic non-equilibrium force dominates, while during the period of heavy precipitation the baroclinic thermodynamic–dynamical interaction dominates. The convergence associated with the baroclinic thermodynamic–dynamical interaction guarantees the persistence of heavy precipitation. Compared to the climate mean state (1988–2018), both MYFR events associated with eastward-moving cloud clusters from the eastern TP are characterized by increased moisture transport from the southwest. One of the major paths of moisture transport in both cases is along the south side of the TP, directly connected to the eastward movement of cloud clusters.

青藏高原东移云团影响下游暴雨的触发维持机制及水汽输送特征分析

青藏高原云团东移常常引发长江流域强降水,这类暴雨的预报是业务难点之一。利用动力诊断方程和拉格朗日轨迹模式,从定性和定量角度揭示了梅雨期两个高原东移云团引发下游暴雨个例的环流背景、触发维持机制和水汽输送特征。TBB变化表明,对流云团从高原东部到下游江淮地区逐渐东传并交替减弱和增强。正涡度大值中心在正水汽平流引导下,从高原东侧经四川盆地向下游传播。斜压热动力相互作用与正压非平衡强迫在梅雨锋暴雨发生与发展阶段的变化相反。强降水初期,正压强迫占主导;而在强降水持续期,斜压强迫占主导作用,其激发的辐合增长保障了强降水天气的持续。暴雨过程的水汽输送相对于气候态更多来自西南方向,其中一条明显的沿高原南侧的气流与东移云团有关。
    • Flooding in the Yangtze–Huai River valleys caused by Meiyu front rainstorms (MYFR) can be a destructive meteorological event in China. Precipitation during Meiyu events is often related to eastward-moving cloud clusters from the Tibetan Plateau (TP), and has different characteristics compared to other rainfall in the region. Most convective cloud systems associated with torrential rain in the Yangtze–Huai River valley during 1998 and 1991 could be traced back to systems originated from the TP and its surrounding areas (Ninomiya, 2000; Wang et al., 2003). From the eastern part of the TP to a thousand kilometers eastward, there is a significant phase-to-east phenomenon of rainfall diurnal variation, such as diurnal peaks of precipitation first appear at the east edge of the TP from the afternoon to early evening, then in the late evening to the next early morning over the Meiyu front in middle and lower Yangtze River basins (Bao et al., 2011; Xu and Zipser, 2011; Zhang et al., 2014). This pattern is consistent with lower atmospheric convergence systems from the steep eastern part of the TP moving eastward to the middle reaches of the Yangtze River (Sun and Zhang, 2012; Jin et al., 2013; Chen et al., 2014; Li et al., 2014). However, a systematic analysis of the atmospheric circulation characteristics of heavy rains in the Yangtze–Huai River valley induced by eastward-moving cloud clusters is still lacking.

      There have been numerous studies of the occurrence, development, and maintenance mechanisms of MYFR (Chen et al., 1998; Sun et al., 2010; Bao et al., 2011; Zhao, 2015; Fu et al., 2016; Sha et al., 2018; Sugimoto, 2020). The diabatic heating and dynamic forcing over the TP can affect planetary large-scale (including monsoon) circulation, which in turn affects precipitation in the Yangtze–Huai River valley (Tanaka et al., 2001; Wang et al., 2012). In addition, the eastward movement of TP convective cloud clusters produces a southwest vortex in the Sichuan basin, and often triggers convective activity on the Meiyu front of the Yangtze River basin (Yasunari and Miwa, 2006; Wang et al., 2011). Chen et al. (2009), based on the further refined divergence equations, demonstrated that a barotropic non-equilibrium force is the triggering mechanism for heavy rainfall, and that the baroclinic thermodynamic–dynamical interaction dominates the maintenance of precipitation. However, it is unclear how the eastward-moving cloud clusters from the TP trigger the heavy rains in the Yangtze–Huai River valley.

      Availability of water vapor is an important condition for the occurrence of heavy rainfall during Meiyu periods (Lu et al., 2014; Sun and Wang, 2015; Li et al., 2016; Xu et al., 2017; Sugimoto, 2020). Located in the upstream area of eastern China, the TP has an important effect on water vapor transport in the Yangtze–Huai River valley, thus on drought and flood events in the region (Xu et al., 2015). The TP has been known as an important water vapor “transport station” on the western boundary of the Meiyu belt in the Yangtze River basin (Xu et al., 2002). Warm and humid airflows from the Indian Ocean and the South China Sea are lifted up by the terrain, providing favorable conditions for the development of convective clouds in the central part of the TP (Huang and Cui, 2015). Most of the water vapor transported to the Yangtze–Huai River valley is from the south along the west flank of northwestern Pacific subtropical high, coming from both the tropical western Pacific and Indian monsoon region. The summertime rainfall over the Yangtze–Huai River valley is closely related with the water vapor transport from the south (Zhang, 2001). Some water vapor is transported with eastward airflow from the TP; the influence of the atmosphere from the TP on downstream regions mainly involves precipitation (Xu et al., 2004; Chen et al., 2012). Fu et al. (2006) also found that there is strong convection in the TP and its surrounding areas in summer, which carries moisture downstream and produces precipitation. Lagrangian models have been developed to determine the moisture origin or sink by calculating backward or forward trajectories of air parcels residing over the target region. Several models such as Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) (Stein et al., 2015) or Flexible Particle (Stohl et al., 2005) can calculate back trajectories.

      However, previous studies have largely ignored the question of how background circulations feed smaller-scale systems that directly trigger Meiyu frontal rainstorms; nor have they analyzed the role of eastward-propagating cloud clusters from the TP in moisture transport. The main purpose of this study is to answer two questions: (a) how do the background circulations feed smaller-scale systems that directly trigger precipitation in the Meiyu season; and (b) what are the characteristics of moisture transport by eastward-propagating cloud clusters from the TP? The ultimate goal of our work is to improve our understanding of the atmospheric circulation conditions and moisture transport characteristics of MYFR to improve the monitoring and prediction of these destructive rainstorms.

      The rest of the paper is organized as follows. The data and analysis methods are described in Section 2. In Section 3, we present the characteristics of typical Meiyu frontal rainstorms in 2016 and 2018. In Section 4, we describe the initiation and maintenance characteristics of MYFR. Using Lagrangian trajectory analysis, we describe moisture transport associated with the MYFR in Section 5. Finally, the discussion and conclusions are given in Section 6.

    2.   Data and methods
    • We use the ECMWF ERA-Interim 6-h reanalysis product (with 0.5° horizontal resolution and 37 vertical levels ranging from 1000 to 1 hPa) (ERA-Interim; Dee et al., 2011) for synoptic analysis and dynamical diagnosis of the Meiyu season (June–July) of 2010–2018. Variables used include geopotential height, wind, specific humidity, cloud liquid water content, and cloud ice water content. In addition, we use hourly precipitation observations from the Climate Prediction Center morphing technique for the production of global precipitation estimates (CMORPH) and brightness temperature of blackbody data of the Fengyun-2E satellite (with 0.1° resolution) from the China Meteorological Administration (CMA) to investigate the evolution of precipitation and convection activities.

    • We apply the HYSPLIT (Stein et al., 2015) model to the NCEP–NCAR reanalysis data to identify the origins and destinations of the air masses. The subset of this data is available from the Air Resources Laboratory (ARL), NOAA in a format suitable for transport and dispersion calculations using HYSPLIT. The variables used by HYSPLIT included the geopotential height, temperature, zonal wind, meridional wind, and the specific humidity. These variables from NCEP/NCAR show a similar synoptic-scale pattern with ERA-Interim reanalysis data. Three-dimensional back trajectories were calculated to track the sources of low- to midlevel (850–700 hPa) moisture at each grid point. The Lagrangian methodology has been successfully applied in studies of the source of moisture in many regions of the world (Izquierdo et al., 2012; Yang et al., 2014; Salih et al., 2015; Jiang et al., 2017; Yang et al., 2019).

    3.   Characteristics of MYFR associated with eastward-moving cloud clusters from the eastern TP
    • The Meiyu front rainband often stretches thousands of kilometers across East Asia and the western Pacific (Ninomiya, 2000). The criteria used to select heavy rainfall cases are: (1) it should be influenced by Meiyu front and (2) it needs to be affected by clouds moving eastward from the TP. We determined the Meiyu front rainstorm events affected by clouds moving eastward from the TP by using Fengyun-2E satellite data and hourly observation station precipitation data from the National Meteorological Information Center of China Meteorological Administration. The blackbody temperature (TBB) threshold of ≤ −30°C is used, and the positions of convective cloud and precipitation areas are mainly detected by eyes. From 2010 to 2018, a total of 20 events (e.g., 3–7 June 2010, 10–12 June 2011, 3–5 July 2012, 26–30 June 2013, 15–18 June 2015, 6–8 June 2016, 14–16 June 2016, 14–18 July 2016, 30 June–2 July 2016, 17–19 June 2018, and so on) have been analyzed; qualitatively similar results are found for these events. Here, we focus on two classic MYFR events.

      From 30 June to 2 July 2016, a wide-spread, heavy precipitation event occurred in the middle and lower reaches of the Yangtze River region during the Meiyu period (Fig. 1a). Twenty-seven national basic stations in Hubei Province recorded precipitation exceeding the extreme precipitation standard, and the daily precipitation hit high records at three stations (24-h accumulated precipitation reached 272.5, 285.2, and 263.0 mm at Jingmen, Macheng, and Jiangxia stations, respectively).

      Figure 1.  Precipitation rate (mm day−1) averaged from (a) 0800 BT 30 June to 0800 BT 2 July 2016 and (b) 0800 BT 17 to 0800 BT 19 June 2018, and Hovmöller (time–longitude) diagram for (c, d) rain rate (mm h−1) and (e, f) TBB (°C) at (c, e) 31°N between 29 June and 3 July 2016 and (d, f) 33°N between 16 and 20 June 2018.

      The second heavy rainfall event occurred during 17–19 June 2018 (Fig. 1b). Sichuan, Chongqing, Shaanxi, Henan, and Hubei experienced strong convective weather including heavy rains, thunder, and strong winds. Precipitation intensity peaked on 18 June 2018, and over 60 stations reported rainstorms or heavy rainstorms in the Yangtze–Huai River valley. The maximum hourly rainfall intensity occurred at Dangyang station (30.49°N, 111.47°E; 43.5 mm) in Hubei Province, and the daily precipitation at this station was 155.7 mm.

      The two MYFR processes were characterized by long and continuous rainbelts extending from the eastern TP to the Yangtze–Huai River valley. The two events differ only in that the MYFR event in 2016 was more south trend, along the southeastern part of the TP, across southern Sichuan basin, to the middle and lower reaches of the Yangtze River. The rainbelt of the 2018 event was further north, reaching from the eastern part of the TP to the Huaihe River basin. The East Asian summer monsoon and related seasonal rainbelts have significant variability at intraseasonal timescales (Ding and Chan, 2005). Many events are induced by eastward-moving cloud clusters. To illustrate the typical evolution of the precipitation associated with these rainstorms, we use the 2016 and 2018 events as examples. A Hovmöller time–longitudinal diagram of CMORPH rain rate data for 29 June–2 July 2016 shows the eastward movement of precipitation in Fig. 1c. Precipitation started at 2000 BT (Beijing Time) 29 June at the southeastern edge of the TP to the Sichuan basin (99°–105°E) with a rain rate of approximately 6 mm h−1. After 0800 BT 30 June, the precipitation intensity gradually increased and heavy rainfall center began to shift eastward. At 0800 BT 1 July, the hourly precipitation intensity in some areas of the middle reaches of the Yangtze River exceeded 20 mm h−1. Over the course the same day, the Jiangxia station (30.21°N, 114.2°E) recorded 263.0 mm day−1 of precipitation, which exceeded its historical record. After 0800 BT 2 July, the heavy rainfall center continued to move eastward to the lower reaches of the Yangtze River. The MYFR during 17–19 June 2018 also involved eastward movement of the rainbelt from the eastern TP to downstream areas (Fig. 1d), but precipitation intensity is weaker than 2016 event. Based on the above analysis, these two typical MYFR events were selected for in-depth analysis.

    • The above analysis indicates that MYFR precipitation shows significant eastward shift along the eastern side of the TP to eastern China. Sun and Zhang (2012) showed that the rainbelt is generally accompanied by the development of a mesoscale convective system (MCS). On satellite images, the Meiyu front often appears a long cloud belt or low-value TBB belt extending from the Yangtze River to the Japanese archipelago, which can produce a temporally and spatially uneven precipitation distribution on the ground (Fu et al., 2016).

      Figures 1e and 1f show the eastward-moving cloud systems during the MYFR processes in a Hovmöller time–longitudinal diagram, where areas with TBB ≤ −30°C represent convective cloud activities with a longer life history; evidence of this statement also can be found in some other studies (Esmaili et al., 2016). At 2000 BT 29 June 2016, strong convective cloud activity (TBB ≤ −60°C) occurred over the central part and the eastern part of the TP (85°–102°E). In the afternoon of 30 June, the convective cloud system from the TP moved eastward to the Sichuan basin (105°E) and weakened. At the same time, there was new convective clouds development on the eastern part of the Sichuan basin, which continued to strengthen as the system moved east. In the evening of 30 June, the convective clouds reached 110°E and weakened again. When the cloud clusters moved over the middle reaches of Yangtze River in the early morning of 1 July, they became stronger with the development of new convective clouds. It can be seen that with the eastward movement of cloud clusters from the TP, the convective cloud system continuously strengthened and weakened, leading to strong precipitation in the middle and lower reaches of the Yangtze River. Because the eastward movement of convective cloud clusters over the plateau will stimulate new convective systems in the lower reaches of Yangtze River basin under the action of topographic forcing. The east–west rainfall centers are related to the propagation of precipitation systems downstream of the eastern TP, which is consistent with earlier founding (Yasunari and Miwa, 2006).

      Similarly, although the rainbelt of the MYFR event during 16–19 June 2018 was further northward, the convective cloud system from the TP continuously strengthened and weakened, leading to strong precipitation in the Yangtze–Huai River valley. Strong convective cloud activity occurred in the morning of 16 June at the east edge of the TP (97°–102°E, as shown in Fig. 1f), but this weakened during the evening. New convective cloud developed on the east of the TP during the morning of 17 June before it moved eastward. The cloud clusters weakened as they traversed the northern part of the Sichuan basin at night. However, with the eastward shift of the southwest China vortex, the convective cloud system strengthened again. In the afternoon of 18 June, the low vortex cloud system strengthened and TBB decreased. The low vortex cloud system moved eastward and began to affect the Yangtze–Huai River valley (Fig. 1f).

      The TBB evolutions of the two MYFR events described above indicate that the convective cloud clusters gradually moved from the eastern TP to the Yangtze–Huai River valley and alternately weaken and strengthen, which is in good agreement with the occurrence and evolution of precipitation. We next investigate what characteristics of large atmospheric circulation caused heavy rainfall.

      At the 200-hPa level, the South Asia high of the MYFR from 30 June to 2 July 2016 extended from the TP to the east coast of China (Fig. 2a), and there existed a westerly jet on the north side of the South Asia high. The Meiyu front rainbelt was located in the region of anticyclonic shear near the north edge of the South Asia high, on the south side of the westerly jet. At 500 hPa, there were two cut-off lows located over the western side of Lake Baikal and in Northeast China, respectively. Meanwhile, a synoptic ridge system dominated over Lake Baikal in the middle latitudes. The 5880-m isohypse of the subtropical high pressure was stably maintained over Southeast China.

      Figure 2.  Average 500-hPa geopotential height (black contours; gpm; the green lines denote the troughs), 200-hPa geopotential height (shading; gpm), upper-level jet greater than 20 m s−1 (red vectors), and 850-hPa winds exceeding 12 m s−1 (blue barbs) (a) from 0800 BT 30 June to 0800 BT 3 July 2016 and (b) from 0800 BT 17 to 0800 BT 20 June 2018.

      At the 850-hPa level, the winds indicate that the southwest vortex gradually moved eastward (Fig. 3). Additionally, the equivalent potential temperature (θe) reached 350 K in the middle reaches of the Yangtze River at 2000 BT 30 June (Fig. 3a), indicating high temperatures and humidity at low levels, and from 30 June to 1 July coincided with the eastward movement of heavy rainfall. The warm and humid airflows around the subtropical high were located over the middle and lower reaches of the Yangtze River. Figure 4 shows the frontal intensity and locations of Meiyu front at 850 hPa and 6 h-total precipitation (Li et al., 2018). An important feature of the Meiyu front is its strong humidity gradient across the front; it benefits heavy precipitation in these areas (Fig. 4). The low-level jet around the subtropical high conveyed warm and humid air to the central and eastern part of Hubei Province. The maximum wind speed of the jet axis exceeded 20 m s−1 (Fig. 3d), and the tongue of high humidity [dewpoint temperature (Td) ≥ 19°C at 850 hPa, not shown] and Meiyu front extended from Chongqing to Hubei Province (Figs. 4a–d). The low-level jet and boundary layer jet continuously transported water vapor to the regions of precipitation. From 30 June to 2 July, precipitable water over the middle reaches of the Yangtze River exceeded 60 mm, and the specific humidity at the 850-hPa level exceeded 14 g kg−1 (Fig. 3). These circulation features collectively drive humid and warm air masses to the region producing conditions favoring heavy rainfall.

      Figure 3.  The equivalent potential temperature (θe) (black contours; K), specific humidity (shading; g kg−1), and winds (vectors; m s−1) at 850 hPa from 0800 BT 30 June to 1400 BT 1 July 2016. The “L” indicates the southwest vortex.

      Figure 4.  Locations of Meiyu front (thick black line) and precipitation (shading; mm) from 0800 BT 30 June to 1400 BT 1 July 2016. Contours are the frontal intensity ($\dfrac{\partial \mathit{\theta }_{\rm{e}}}{\partial \mathit{y}}$; K km−1) at 850 hPa; θe is equivalent potential temperature.

      The 500-hPa circulation field of the 16–19 June 2018 event also showed two cut-off lows and one synoptic ridge system at high latitudes (Fig. 2b). However, the further south of the rainbelt in 2016 event should be related with a more southward extension of the trough over northeastern China compared to the trough in 2018 event.

      Both MYFR events clearly involved eastward movement of the weather system from the TP to downstream regions. To further explore the impact of eastward-moving cloud clusters on precipitation, as the corresponding results for the 2018 event are qualitatively similar to 2016 case, so the 2016 event is used as an example, we show in Fig. 5 the vertical distribution of specific cloud liquid water content (CLWC) and cloud ice water content (CIWC) from the TP to the Yangtze River basin during the MYFR event in 2016. At 0800 BT 30 June 2016 (Fig. 5a), convective cloud clusters developed vigorously at the eastern edge of the TP. Highest values of CLWC (exceeding 3 × 10−4 kg m−3) are mainly found at the 500-hPa level. CIWC is distributed at higher levels, in the upper troposphere at 200–400 hPa. CIWC has two local maxima over the eastern edge of the TP and the Sichuan basin exceeding 1 × 10−4 kg m−3. At 1400 BT 30 June (Fig. 5b), with the cloud clusters moving eastward, the CLWC and CIWC large value centers moved eastward from the TP to the west side of the Sichuan basin. The value of CLWC decreased, while CIWC slightly increased. At 2000 BT 30 June (Fig. 5c), the CLWC and CIWC centers moved further eastward; the area of maximum CIWC reached the middle reaches of the Yangtze River and CLWC decreased. From 0200 to 0800 BT 1 July, CLWC and CIWC increased rapidly over the eastern part of Hubei Province (Figs. 5d, e; red boxes). The large value areas gradually became more concentrated and the height of peak values decreased. At this time, heavy rainfall occurred in this region. Meanwhile, a new high value area of CIWC appeared in the middle of the TP and extended eastward. After 1400 BT 1 July (Fig. 5f), the CLWC and CIWC centers moved further eastward to the lower reaches of the Yangtze River, and CLWC over the eastern part of Hubei Province decreased.

      Figure 5.  Height–longitude cross section of specific cloud liquid water content (colors; 104 kg m−3) and cloud ice water content (contour; 105 kg m−3) at 31°N at 6-h intervals between 0800 BT 30 June and 1400 BT 1 July 2016. The red box marks the heavy rainfall area and gray shading illustrates the topography.

      Changes in CLWC and CIWC are directly related to the vertical motion of air masses and to weather system. At 0800 BT 30 June 2016 (Fig. 6a), there was positive vorticity in the middle and lower troposphere over the eastern part of the TP, indicating stretching of the air column and pronounced ascending motion in the clouds. As the air masses rose and condensed to release latent heat, convective cells formed and CLWC and CIWC increased (Fig. 5a) in a region corresponding to the low TBB region in Fig. 1e. At the same time, water vapor advection below the middle troposphere was positive over the middle and upper reaches of the Yangtze River (108°–114°E). Previous studies have shown (Wu et al., 1995; Gao et al., 2004; Chen, 2007) that positive water vapor advection is conducive to the excitation of positive relative vorticity development, which tends to lead to new convective organization. It can be seen in Figs. 6b–f that positive water vapor advection gradually moved eastward and developed. Meanwhile, the area of maximum positive relative vorticity moved from the eastern side of the TP to the middle and lower reaches of the Yangtze River under the guidance of positive water vapor advection. This led to the development of the TP cloud clusters on an eastward path, and thus affected heavy rainfall. Li et al. (2017, 2020) have proposed that the TP vortex triggers a southwest vortex, and then the TP vortex emigrates from the TP and affects the MYFR with the southwest vortex together.

      Figure 6.  Height–longitude cross section of relative vorticity (colors; 105 s−1) and water vapor advection (contours; g kg−1) at 31°N from 0800 BT 30 June to 1400 BT 1 July 2016 at a 6-h interval. The red box highlights the heavy rainfall area and gray shading illustrates the topography.

      For the case in 2018, the rainbelt was located further northward and the convective cloud system from the TP to the Yangtze–Huai River valley continuously strengthened and weakened. The CLWC and CIWC had large values over the northeastern edge of the TP where strong convective activity occurred in the morning of 16 June (figures were not shown). The cloud liquid and ice water content decreased during the evening, but increased again from 17 to 19 June when the cloud clusters were moving eastward. Moreover, during 17–18 June, from east of the TP to the Yangtze–Huai River valley, the positive value of water vapor advection gradually moved eastward and intensified. Meanwhile, the center of positive vorticity also propagated eastward guided by the positive water vapor advection.

    4.   Mechanisms of MYFR initiation and maintenance
    • The above two cases analysis demonstrates that heavy precipitation systems over the Yangtze River basin can be affected by eastward-moving cloud clusters from the TP. We next explore the dynamic mechanisms responsible for the initiation and maintenance of MYFR. Weather analysis shows that different configurations of the atmospheric thermal and the dynamic field will cause different evolutions of divergence fields which are keys for determining atmospheric vertical motion thus clouds formation and rainfall. Therefore, it is desirable to consider a new divergence equation involving coupling of the thermodynamic field and the dynamical field. Chen et al. (2009) used the relationship between the thermodynamic field and the dynamic field and derived a new divergence equation which includes the forcing of ageostrophic Q-vector coupling with vertical wind shear:

      $$\begin{aligned}[b] \frac{{\partial {{D}}}}{{\partial {{t}}}} &= - {\nabla ^2}{{E}} + {\boldsymbol{k}} \cdot [\nabla \times ({{f}} + \zeta ) {\boldsymbol{V}} ] \\ & + \frac{1}{\sigma }\left( {2 {\boldsymbol{Q}} - {{{f}}^2}\frac{{\partial {{{\boldsymbol{V}}_{\rm{a}}}} }}{{\partial {{p}}}}} \right) \cdot \frac{{\partial {\boldsymbol{V}} }}{{\partial {{p}}}} - \omega \frac{{\partial {{D}}}}{{\partial {{p}}}} , \end{aligned} $$ (1)

      where ${\boldsymbol{Q}} = \dfrac{1}{2}\left[ {{{f}}\left( {\dfrac{{\partial {{v}}}}{{\partial {{p}}}}\dfrac{{\partial {{u}}}}{{\partial {{x}}}} - \dfrac{{\partial {{u}}}}{{\partial {{p}}}}\dfrac{{\partial {{v}}}}{{\partial {{x}}}}} \right) - {{h}}\dfrac{{\partial {\boldsymbol{v}} }}{{\partial {{x}}}} \cdot \nabla {\theta _{\rm{e}}}} \right] {\boldsymbol{i}} + \dfrac{1}{2}\Bigg[ {{f}}\Bigg( \dfrac{{\partial {{v}}}}{{\partial {{p}}}}$$\dfrac{{\partial {{u}}}}{{\partial {{y}}}} - \dfrac{{\partial {{u}}}}{{\partial {{p}}}} \dfrac{{\partial {{v}}}}{{\partial {{y}}}} \Bigg)- {{h}}\dfrac{{\partial {\boldsymbol{v}} }}{{\partial {{y}}}} \cdot \nabla {\theta _{\rm{e}}} \Bigg] {\boldsymbol{j}}$ is the wet ageostrophic forcing vector, ${E}=\mathrm{\varnothing }+\dfrac{{\boldsymbol{V}}\cdot{\boldsymbol{V}}}{2}$ is pressure energy, and ${D}=\nabla \cdot {\boldsymbol{V}}$ is horizontal divergence.

      In practical weather forecast analysis, more attention is paid to the increase or decrease of convergence intensity in the middle and lower troposphere, which is the maximum convergence level. Therefore, at the maximum convergence level $\dfrac{\partial {D}}{\partial {p}}=0$, and Eq. (1) is simplified as:

      $$ \frac{{\partial {{D}}}}{{\partial {{t}}}} = - {\nabla ^2}{{E}} + {\boldsymbol{k}} \cdot [\nabla \times ({{f}} + \zeta ) {\boldsymbol{V}} ] + \frac{1}{\sigma }\left( {2 {\boldsymbol{Q}} - {{{f}}^2}\frac{{\partial {{{\boldsymbol{V}}_{\rm{a}}}} }}{{\partial {{p}}}}} \right) \cdot \frac{{\partial {\boldsymbol{V}} }}{{\partial {{p}}}} . $$ (2)

      Here, the variation of the divergence field is determined by the barotropic non-equilibrium forcing (non-equilibrium between mass and wind) $-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+{\zeta }\right){\boldsymbol{V}}\right]$ and the baroclinic coupled forcing between Q vector and vertical wind shear (the baroclinic thermodynamic–dynamical interaction) $\dfrac{1}{\mathrm{\sigma }}\left(2{\boldsymbol{Q}}-{{f}}^{2}\dfrac{\partial {{\boldsymbol{V}}_{\mathrm{a}}}}{\partial {p}}\right)\cdot \dfrac{\partial {\boldsymbol{V}}}{\partial {p}}$ (Chen et al., 2009). The details of this method are described in Appendix A. The geostrophic adaptation process of mesoscale motion is realized by adjusting the divergence field. Continuous heavy rainfall is often associated with an energy front that forms through strong baroclinic pressure (Chen et al., 2014). Both of the two terms can arouse the change of divergence. Convergence increases when the barotropic non-equilibrium forcing is negative, which is conducive to the initiation of rainstorms. Similarly, airflow convergence also increases when the baroclinic thermodynamic–dynamical interaction is negative, which helps the maintenance of heavy rainfall. Since the two MYFR events were similarly characterized by variations in the divergence field, we will again use the 2016 event as an example to illustrate the dynamical forcing responsible for the evolution of lower tropospheric convergence. The details of 2018 event are described in Appendix B.

      Water vapor transport is mainly concentrated in middle and lower troposphere, and the barotropic non-equilibrium force and the baroclinic thermodynamic–dynamical interaction also occur at middle and lower troposphere, so these variables are shown at 850 hPa. Figure 7 shows the distribution of the barotropic non-equilibrium forcing during the 2016 MYFR. Prior to the heavy rainfall in the middle and lower reaches of the Yangtze River (0800–1400 BT 30 June, Figs. 7a, b), when the eastward-moving cloud clusters are still near the Sichuan basin, Anhui Province and eastern Hubei Province were controlled by positive values of barotropic non-equilibrium forcing. In contrast, the upper reaches of the Yangtze River to the western part of Hubei Province were controlled by negative values, which indicates that the atmospheric state was unstable, with the intensity gradually increasing from west to east. At 2000 BT 30 June (Fig. 7c), the value of barotropic non-equilibrium forcing over Hubei and Anhui provinces decreased to −3 × 10−8 s−2. The atmospheric motion was in a strong non-equilibrium state, which favored geostrophic adjustment and stimulated the rapid growth of convergence. The rainstorm occurred in the eastern Hubei Province in the early morning of 1 July. At the time when rainstorm became strong (0200 BT 1 July), the value of barotropic non-equilibrium forcing rapidly increased to −2 × 10−9 s−2 (Fig. 7d). Strong convective activity was seen developing over the eastern Hubei Province and Anhui Province in satellite imageries of eastward-moving clouds (figure not shown). This indicates that with the development of eastward-moving convection, the barotropic non-equilibrium forcing of atmospheric motion weakened and almost reached a quasi-equilibrium state. After 1400 BT 1 July, the convective cloud clusters remained strong, and the heavy rainfall in the eastern Hubei Province lasted until 2000 BT. In the initial stage of this MYFR, the barotropic non-equilibrium forcing preceded the development of precipitation and was strongest at the start of heavy rainfall.

      Figure 7.  Distributions of the barotropic non-equilibrium force (black dashed line; 10−10 s−2) at 850 hPa at (a) 0800 BT 30 June, (b) 1400 BT 30 June, (c) 2000 BT 30 June, and (d) 0200 BT 1 July 2016. Black shadings mark topography under 850 hPa.

      The distribution of the coupled forcing of baroclinic ageostrophic and the wind vertical shear during the MYFR is shown in Fig. 8. At 0800 BT 30 June (Fig. 8a), before the rainstorm occurred, the Sichuan basin and most of the Yangtze River basin were controlled by a region of positive baroclinic forcing. This indicates that the impact of the baroclinic thermodynamic–dynamical interaction on divergence was small in the rainstorm area, and was not conducive to convection. At 1400 BT (Fig. 8b), with the cloud clusters moving eastward, the zone of negative baroclinic forcing began to appear in the middle and upper reaches of the Yangtze River. As the stability of the atmosphere decreased after convection development, the value of σ dropped significantly. With the energy front significantly strengthened, the baroclinic forcing in the eastern Hubei Province further expanded and strengthened before the weakening during the evening of 30 June (Fig. 8c). At 0200 BT 1 July (Fig. 8d), as a result of a reduction in σ and the combined effect of the low-level jet and the energy front, the eastern part of Hubei Province and Anhui Province were controlled by a negative zone of baroclinic forcing, and the central intensity exceeded −2 × 10−8 s−2. Such strong forcing can continuously stimulate convective convergence at low levels of the troposphere. At 1400 BT 1 July, precipitation intensity began to weaken. In addition, the low-level jet weakened and the energy front disappeared, resulting in an area of positive baroclinic forcing over the eastern Hubei Province (not shown), which was not conducive to the maintenance of strong precipitation.

      Figure 8.  As in Fig. 7, but for distributions of the baroclinic thermodynamic–dynamical interaction term (black dashed lines; 10−10 s−2).

      The analysis outlined above shows that during the MYFR the baroclinic thermodynamic–dynamical interaction and the barotropic non-equilibrium force worked against each other during the development of the rainstorm. In the early stage of heavy precipitation, before the eastward-moving cloud clusters arriving, the baroclinic forcing was small, while the barotropic non-equilibrium forcing dominated. When affected by the cloud clusters, the precipitation intensified and the baroclinic forcing dominated. The convergence stimulated by baroclinic forcing guaranteed the persistence of heavy precipitation.

    5.   Lagrangian analysis of moisture transport during the MYFR
    • The above analysis shows that as the convective cloud clusters gradually moved eastward from the eastern TP to the Yangtze–Huai River valley, they experienced further development, weakening, and re-enhancement. These cloud clusters were characterized by sufficient water vapor supply and strong ascending motion. The forcing of ascending motion has been analyzed in Sections 3 and 4. Here, we further investigate the different characteristics of water vapor path and moisture source between climate mean state and two MYFR events.

    • The NOAA HYSPLIT model allows a user to simultaneously release parcels from all points within a user-specified matrix at a given time and height (Stein et al., 2015). The target area for this analysis was defined as two boxes over Yangtze–Huai River valley (28°–32°N, 110°–116°E for 2016 MYFR event; 31°–34°N, 106°–114°E for 2018 MYFR event, red points in Fig. 9). The HYSPLIT model was run to calculate 168-h (7-day) backward air trajectories. The modeling periods are from 0800 BT 30 June to 0200 BT 3 July and from 0800 BT 17 to 0200 BT 20 June from 1988 to 2018 with an integration time step of 6 h. The target region was divided into 1° × 1° grid points which serve as the starting locations for the back trajectories. For both two MYFR events, parcels were released at the level of 3000 and 1500 m (approximately 700 and 850 hPa); these levels are associated with the main moisture transport paths from the east of the TP. All parcels were integrated backward in time for 7 days. Outputs were recorded every 6 h with variables indicating the position (latitude, longitude, and altitude) and meteorological parameters (specific humidity) (Jiang et al., 2017).

      Figure 9.  Starting locations in the heavy rainfall area used in the backward trajectory simulation during (a) 30 June–2 July 2016 and (b) 17–19 June 2018.

    • We can clearly identify the distribution of water vapor through statistical analysis of simulated backward trajectories of parcels reaching the heavy rainstorm region during MYFR periods (Drumond et al., 2011). In Fig. 10, we show the trajectories of air parcels and the associated field of specific humidity seven days before they reached the target area. Figure 10a shows that the water vapor in climate mean during the period 30 June–2 July 1988–2018 can be tracked southward to the equatorial Indian Ocean, eastward to the western Pacific Ocean, northward to Siberia, and westward to Europe seven days prior to it reaching the target area. The water vapor distribution is relatively scattered. Highest values of specific humidity (exceeding 30 g kg−1) are found in the northern part of the Indian Ocean to the Bay of Bengal. For the MYFR period 30 June–2 July 2016 (Fig. 10b), the water vapor is tracked southward to the equatorial Indian Ocean and the Bay of Bengal. The center of large values (exceeding 70 g kg−1) was mainly located from the eastern part of the Bay of Bengal to the Indo-China Peninsula. Over the western Pacific Ocean and central Asia there was only a small amount of water vapor supply to the MYFR. In contrast with the climatological condition, the 2016 MYFR event distribution has more water vapor concentrate over the south of the TP.

      Figure 10.  Spatial distributions of air parcel specific humidity (shaded; g kg−1) and number of air parcels (contour) seven days before reaching the heavy rainfall area for (a) climatic mean of 30 June–2 July between 1988 and 2018, (b) 30 June–2 July 2016, (c) climatic mean of 17–19 June between 1988 and 2018, and (d) 17–19 June 2018.

      For the 2018 MYFR event, the climatic distribution of water vapor during the period 17–19 June 1988–2018 is mainly concentrated in the Indo-China Peninsula and Eurasia (Fig. 10c). Because the target area is more northward than that of 2016 MYFR event, moisture source regions also locate more northward. Different from the climatological condition, during the period 17–19 June 2018 (Fig. 10d), the large value areas of water vapor mainly distribute near the Arabian Sea–Bay of Bengal and southeast of China. It is worth mentioning that the large center of water vapor is further south than that of the air parcels because the southwesterly airflow carried more specific humidity, a lot of air parcels come from western China (Figs. 10a, c), that could be an important moisture source while having a low mean humidity.

      To further investigate differences in water vapor source and transport path between the MYFR events and the climatic mean, cluster analysis was used to classify the air particle trajectories into different channels and the quantitative water vapor contribution of each channel was calculated. The fractional contribution of water vapor (Qcon) carried by each channel in Fig. 11 is calculated as:

      Figure 11.  Cluster analysis of backward trajectories for (a) climatic mean of 30 June–2 July between 1988 and 2018, (b) 30 June–2 July 2016, (c) climatic mean of 17–19 June between 1988 and 2018, and (d) 17–19 June 2018. The numbers indicate the percentage contribution of water vapor in each channel.

      $$ {Q_{\rm{{con}}}} = \sum\limits_1^m {{q_{}}} /\sum\limits_1^n {{q_{}}}, $$ (3)

      where q is the specific humidity carried by each individual trajectory, m is the number of clustered trajectories for each channel, and n is the total number of computed trajectories. Water vapor is lost or replenished as a result of precipitation or evaporation during the transport, so the contribution is evaluated at the final locations of each channel.

      Figure 11a shows the climate mean distribution of water vapor transport channels from 30 June to 2 July 1988–2018. Channel 1 originates in the eastern part of Europe and reached the target area via central Asia; the water vapor transport contribution of this channel is 23%. This channel is located near the westerly jet which is associated with strong winds, so this transport path is the longest. Channel 2 has the largest contribution to water vapor transport at 61%. It originates from the central Indian Ocean and entered China through the Bay of Bengal and the northern part of the Indo-China Peninsula. Channel 3 is from the western Pacific and the South China Sea and is clustered based on southeast airflow. The water vapor transport contribution is 16% and the transport distance is the shortest.

      For the MYFR event from 30 June to 2 July 2016, all the three water vapor transport channels come from the southwest (Fig. 11b). Channel 1 originates from the southern part of the Bay of Bengal, arriving at the heavy rainfall area via the Indo-China Peninsula and the Yunnan–Guizhou Plateau. This channel has the largest contribution to water vapor transport, accounting for 56%. Channel 2 is the Indian Ocean channel, which is clustered by the cross-equatorial airflow between 50° and 70°E. Water vapor enter the Yangtze River basin from the Indian Ocean through the Bay of Bengal and the western South China Sea; the contribution of this channel is 25%. Channel 3 is clustered by the airflow on the south side of the TP. It originated from the northern part of the Indian Peninsula, passing through the southwest of the TP and Southwest China, before reaching the middle reaches of the Yangtze River; the contribution of this channel to water vapor transport is 19%. These channel routes indicate that the 2016 MYFR event is induced by eastward-moving cloud clusters from the eastern side of the TP. The path of the water vapor channel 3 is very close to the path of eastward-moving cloud clusters. Although the contribution of water vapor transport is not the largest, the analysis shows that air masses were carrying water vapor downstream from the east side of the TP.

      The other MYFR event has similar characteristic for climatic mean and the case in 2018. There are two water vapor transport channels originating from northwest during 17–19 June 1988–2018, and the third channel originates in the Bay of Bengal (Fig. 11c). During 17–19 June 2018, all the three water vapor transport channels come from the south (Fig. 11d). Channel 1 is clustered by the airflow on the south side of the TP. It originates from the Indian Ocean, passes through Indian Peninsula and southwest of the TP, and at last reaches Yangtze–Huai River valley. Similar to 2016 MYFR event, the path of this channel is also very close to the path of the eastward-moving cloud clusters.

      In summary, moisture transport for the middle and lower reaches of Yangtze River is divided into southwestward, northwestward, and southeastward. There is more water vapor transport from the southwest direction in the MYFR of 2016 and 2018 than that in the climatic mean. This is consistent with the presence of a strong southwesterly wind during the two MYFR events, as shown in the above results regarding atmospheric circulation conditions (Fig. 2). The moisture flows of channel 3 in 2016 MYFR event and channel 1 in 2018 MYFR event on the south side of the TP are guided by the eastward-moving cloud clusters because the paths of the water vapor channels in 2016 and 2018 are very close to the path of the eastward-moving cloud clusters (Figs. 11b, d).

    6.   Discussion and conclusions
    • This paper examines two typical MYFR involved with eastward-moving cloud clusters from the TP. The characteristics of the spatial and temporal distributions of precipitation and the background circulation were analyzed. We also used a dynamic diagnosis equation to reveal the triggering and maintenance mechanisms for MYFR events, and adopted a Lagrangian trajectory model to quantify moisture sources of the two MYFR. The main conclusions are as follows:

      (1) The MYFR events in 2016 and 2018 occurred and developed along the southeastern part of the TP, the southern Sichuan basin, and the Yangtze–Huai River valley. Changes in brightness temperature indicate that convective systems over the TP move eastwards and trigger the formation of the southwest vortex moved along the Meiyu front with the eastward propagation of a small leading trough to the northeast. Under its influence, an area of high positive vorticity also moves from the eastern side of the TP to the middle and lower reaches of the Yangtze River, and induces a series of convective systems and heavy rainfalls along Meiyu front. Specifically, the upwelling of moisture source from the south helps to sustain the elevated layer of conditionally unstable air, while the moisture transport into the convective zone further yields instability for growing convection. Such processes are strongly regulated by low level jet highlighting the monsoon flow that strengthens convective instability, more than moisture supply and ascending motion, for supporting the warm-season rainfall systems (Fig. 12).

      Figure 12.  Schematic summarizing the major atmospheric circulation systems during 2016 and 2018 MYFR cases associated with eastward-moving cloud clusters from the TP (SCS: South China Sea, BOB: Bay of Bengal, YHRV: Yangtze–Huai River valley).

      (2) During the development and maintenance stage of MYFR, the baroclinic thermodynamic–dynamical interaction $\bigg( \dfrac{1}{{\sigma }}\left(2{\boldsymbol{Q}}-{{f}}^{2}\dfrac{\partial {{\boldsymbol{V}}_{\mathrm{a}}}}{\partial {p}}\right)\cdot \dfrac{\partial {\boldsymbol{V}}}{\partial {p}}\bigg)$ and the barotropic non-equilibrium force ($-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+\zeta \right){\boldsymbol{V}}\right]$) show opposite change. In the early stage of heavy precipitation, the barotropic non-equilibrium force dominates, while during strong precipitation the baroclinic thermodynamic–dynamical interaction dominates. The convergence associated with the baroclinic force guarantees the persistence of heavy precipitation. This relationship between the baroclinic thermodynamic–dynamical interaction and heavy precipitation is one of the major mechanisms responsible for the maintenance of heavy precipitation.

      (3) Backward trajectory analysis showed that there is more water vapor transport from the southwest in the 2016 and 2018 MYFR events than what would be expected based on a 30-yr climatology. One of the airflow paths south of the TP was related to the eastward-moving cloud clusters.

      Cloud clusters from the TP continuously weakened and strengthened as they moved eastward. New convection systems (such as the southwest vortex) emerge in the Sichuan basin when convective clouds move out from the TP. The positive vortex disturbance produced by the TP convection system can promote the formation of the southwest vortex (Fu et al., 2018). The mesoscale vortex plays apparent roles in triggering and organizing moist convection along the Meiyu front, while diabatic heating from moist convection is essential in the development and strengthening of the mesoscale vortex. The nocturnal development of the mesoscale vortex and convective activity are further enhanced by the development of a strong nocturnal low level jet (LLJ) over the plains just south of the Meiyu front (Sun and Zhang, 2012). The dynamics and moisture transport of the background circulation were crucial to the triggering and maintenance of precipitation (Wei et al., 2012). This study has provided an effective method to understand the relationship between precipitation and upstream clouds. The complex energy conversion that exists in the complex terrain near Sichuan basin needs further investigation. Future work will also examine the genesis mechanism of the initial MYFR vortex that eventually develops into a mature MYFR storm.

      Acknowledgments. The authors are thankful to the Editor and anonymous reviewers for their constructive comments.

    Appendix A: A new divergence equation
    • As shown in Chen et al. (2009), in pressure coordinate, the atmospheric motion equation can be written as

      $$ \frac{\partial {\boldsymbol{V}}}{\partial {t}}+\left({\boldsymbol{V}}\cdot \nabla \right){\boldsymbol{V}}+{\omega }\frac{\partial {\boldsymbol{V}}}{\partial {p}}-f{\boldsymbol{V}}\times {\boldsymbol{k}}=-\nabla \varphi , \tag{A1}$$
      $$ \frac{\partial {\theta }_{\mathrm{e}}}{\partial {t}}+\left({\boldsymbol{V}}\cdot \nabla \right){\theta }_{\mathrm{e}}+{\omega }\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}=0 ,\tag{A2} $$
      $$ \nabla \cdot {\boldsymbol{V}}+\frac{\partial {\omega }}{\partial {p}}=0 , \tag{A3}$$

      where V is two-dimensional wind vector, ω is vertical velocity, f is Coriolis parameter, θe = θexp($ \dfrac{Lq}{{C}_{p}T} $) is equivalent potential temperature (L is condensation latent heat coefficient, q is specific humidity, Cp is heat capacity at constant pressure, and T is temperature), and $\nabla =\dfrac{\partial }{\partial {x}}{\boldsymbol{i}}+\dfrac{\partial }{\partial {y}}{\boldsymbol{j}}$.

      $$ \frac{\partial {D}}{\partial {t}}=-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+{\zeta }\right){\boldsymbol{V}}\right]-\nabla {\omega }\cdot \frac{\partial {\boldsymbol{V}}}{\partial {p}}-{\omega }\frac{\partial {D}}{\partial {p}} , \tag{A4}$$

      where ${D}=\nabla \cdot {\boldsymbol{V}}$ is divergence, and ${E}=\mathrm{\varnothing } +\dfrac{{\boldsymbol{V}}\cdot {\boldsymbol{V}}}{2}$ is pressure energy. Equation (A4) is the traditional divergence equation. This equation shows that the factors affect divergence are only wind (V, ω) and mass (E), but no thermal force (θe). It is different to analyze the impact of atmospheric thermal force and stratification on the divergence.

      Equation (A2) can be differential operated by $\dfrac{\partial }{\partial {x}}$ and $\dfrac{\partial }{\partial {y}}$ to

      $$ \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }_{\mathrm{e}}\right)+\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}+\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}}+\left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\cdot \nabla \omega=0 .\tag{A5} $$

      On the isobaric surface, it would be

      $$ \nabla {\theta }_{\rm{e}}=\frac{\left|\nabla {\theta }_{\rm{e}}\right|}{\left|\nabla {\theta }\right|}\nabla {\theta } .\tag{A6} $$

      From $\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {x}}=\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {T}}\dfrac{\partial {T}}{\partial {x}}$ and $\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {y}}=\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {T}}\dfrac{\partial {T}}{\partial {y}}$, we can get

      $$\hspace{72pt} \nabla {\theta }_{\mathrm{e}}=\frac{\partial {\theta }_{\mathrm{e}}}{\partial {T}}\nabla {T} ,\tag{A7} $$
      $$\hspace{72pt} \nabla {\theta }=\frac{\partial {\theta }}{\partial {T}}\nabla {T} , \tag{A8}$$
      $$\hspace{72pt} \frac{\left|\nabla {\theta }_{\mathrm{e}}\right|}{\left|\nabla {\theta }\right|}=\frac{\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {T}}}{\dfrac{\partial {\theta }}{\partial {T}}} . \tag{A9}$$

      Because $ \dfrac{Lq}{{C}_{p}T}\ll 1 $,

      $$ \theta_{{\rm{e}}}=\theta_{{\rm{exp}}} \left(\frac{Lq}{{C}_{p}T}\right)=T{\left(\frac{1000}{p}\right)}^{{K}_{d}}\left(1+\frac{Lq}{{C}_{p}T}\right) ,\tag{A10} $$
      $$ \frac{\partial {\theta }_{\mathrm{e}}}{\partial {T}}={\left(\frac{1000}{p}\right)}^{{K}_{d}}\left(1+\frac{L}{{C}_{p}}\frac{\partial {q}}{\partial {T}}\right) , \tag{A11}$$
      $$ \frac{\partial {\theta }}{\partial {T}}={\left(\frac{1000}{p}\right)}^{{K}_{d}} ,\tag{A12} $$

      where Kd = R / Cp. Using Eqs. (A11) and (A12), Eq. (A9) can be written as

      $$ \frac{\left|\nabla {\theta }_{\mathrm{e}}\right|}{\left|\nabla {\theta }\right|}=1+\frac{L}{{C}_{p}}\frac{\partial {q}}{\partial {T}}=1+\frac{L[L-{C}_{L}\left({T}-273.16\right)]{q}}{{C}_{p}{R}_{w}{T}^{2}}=\lambda , \tag{A13}$$

      where CL = 2.38 J (g K)−1, Rw = 0.46 J (g K)−1, Cp = 1.00 J (g K)−1, and L = 2501 J g−1. Using Eq. (A13), Eq. (A6) can be written as

      $$ \nabla {\theta }_{\rm{e}}=\lambda \left(T\right)\nabla {\theta } . \tag{A14}$$

      Then Eq. (A14) becomes

      $$ \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }_{\rm{e}}\right)=\lambda \left(T\right)\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }\right)+\nabla {\theta }\frac{\mathrm{d}\lambda \left(T\right)}{\mathrm{d}{t}} . \tag{A15}$$

      Under the adiabatic condition

      $$ \frac{\mathrm{d}}{\mathrm{d}{t}}\nabla {\theta }_{\rm{e}}=\lambda \left(T\right)\frac{\mathrm{d}}{\mathrm{d}{t}}\nabla {\theta } . \tag{A16}$$

      Equation (A5) can be written as

      $$ \lambda \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }\right)+\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}+\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}}+\left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega=0 .\tag{A17} $$

      Here the geostrophic wind was identified as

      $$ \frac{\partial {V}_{{\rm{g}}}}{\partial p}=\frac{R}{pf}{\nabla T\times {{\boldsymbol{k}}}=\frac{R}{pf}\left(\frac{p}{1000}\right)}^{\frac{R}{{C}_{p}}}\nabla {\theta }\times {{\boldsymbol{k}}} , \tag{A18}$$

      where R = 287 J (kg K)−1, Cp = 1005 J (kg K)−1, and we can get

      $$ {\nabla {\theta }=\frac{pf}{R}\left(\frac{p}{1000}\right)}^{-\frac{R}{{C}_{p}}}{{\boldsymbol{k}}}\times \frac{\partial {V}_{{\rm{g}}}}{\partial p} . \tag{A19}$$

      Then Eq. (A19) becomes

      $$ \begin{aligned}[b] & {\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }\right)=\frac{pf}{R}\left(\frac{p}{1000}\right)}^{-\frac{R}{{C}_{p}}}{{\boldsymbol{k}}}\times \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {V}_{{\rm{g}}}}{\partial p}\right)\\ & \quad\quad + \Bigg(1-\frac{R}{{C}_{p}}\Bigg)\frac{f}{R}{\left(\frac{p}{1000}\right)}^{-\frac{R}{{C}_{p}}}\frac{\mathrm{d}p}{\mathrm{d}{t}}{{\boldsymbol{k}}}\times \left(\frac{\partial {V}_{{\rm{g}}}}{\partial p}\right) . \end{aligned}\tag{A20}$$

      In practical, the orders of magnitude of first term and second term on the right-hand side of Eq. (A20) are 10−9 km−1 s−1 and 10−10 km−1 s−1, so Eq. (A20) can be written as

      $$ {\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\nabla {\theta }\right)=\frac{R}{pf}\left(\frac{p}{1000}\right)}^{-\frac{R}{{C}_{p}}}{{\boldsymbol{k}}}\times \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {V}_{{\rm{g}}}}{\partial p}\right) .\tag{A21}$$

      Then Eq. (A17) can be written as

      $$\begin{aligned}[b] & {\lambda \frac{pf}{R}\left(\frac{p}{1000}\right)}^{-\frac{R}{{C}_{p}}}\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {V}_{{\rm{g}}}}{\partial p}\right)\times {{\boldsymbol{k}}}=\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}\\ & \quad\quad +\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}}+\left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega . \end{aligned}\tag{A22}$$

      We define ${h}={\dfrac{R}{p}\left(\dfrac{p}{1000}\right)}^{\frac{R}{{C}_{p}}}$, then Eq. (A22) can be written as

      $$ \frac{\lambda f}{h}\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {{{\boldsymbol{V}}}_{{\rm{g}}}}}{\partial p}\right)\times {{\boldsymbol{k}}}=\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}+\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}}+\left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega . \tag{A23}$$

      Using the geostrophic wind $ \nabla$ϕ = fVg × k, Eq. (A1) can be expressed as

      $$ \frac{\partial {\boldsymbol{V}}}{\partial {t}}+\left({\boldsymbol{V}}\cdot \nabla \right){\boldsymbol{V}}+{\omega }\frac{\partial {\boldsymbol{V}}}{\partial {p}}=f({\boldsymbol{V}}-{{{\boldsymbol{V}}}_{{\rm{g}}}})\times {{\boldsymbol{k}}} . \tag{A24}$$

      Define ${{{\boldsymbol{V}}}_{{\rm{a}}}}={\boldsymbol{V}}-{{{\boldsymbol{V}}}_{{\rm{g}}}}$, where ${{{\boldsymbol{V}}}_{{\rm{a}}}}$ is geostrophic deviation, Eq. (A24) can be written as

      $$ \frac{\partial }{\partial {t}}\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\right)+\frac{\partial }{\partial {p}}\left[\left({\boldsymbol{V}}\cdot \nabla \right){\boldsymbol{V}}\right]+\frac{\partial }{\partial {p}}\left({\omega }\frac{\partial {\boldsymbol{V}}}{\partial {p}}\right)=f\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}\times {{\boldsymbol{k}}} .\tag{A25} $$

      Then Eq. (A25) becomes

      $$ \frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\right)+\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\cdot \nabla \right){\boldsymbol{V}}-{D}\frac{\partial {\boldsymbol{V}}}{\partial {p}}=f\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}\times {{\boldsymbol{k}}} . \tag{A26}$$

      Using Eq. (A26) $\times \; \dfrac{\lambda f}{h}{{\boldsymbol{k}}}$, we can get

      $$ \frac{\lambda f}{h}\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {\boldsymbol{V}}}{\partial p}\right)\times {{\boldsymbol{k}}}=-\frac{\lambda {f}^{2}}{h}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}-\frac{\lambda f}{h}\Bigg[\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\cdot \nabla \right){\boldsymbol{V}}-{D}\frac{\partial {\boldsymbol{V}}}{\partial {p}}\Bigg]\times {{\boldsymbol{k}}} .\tag{A27} $$

      Using Eq. (A27) minus Eq. (A23), it becomes

      $$ \begin{aligned}[b] & \frac{\lambda f}{h}\frac{\mathrm{d}}{\mathrm{d}{t}}\left(\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial p}\right)\times {{\boldsymbol{k}}}=-\frac{\lambda {f}^{2}}{h}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}-\frac{\lambda f}{h}\left[\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\cdot \nabla \right){\boldsymbol{V}}-{D}\frac{\partial {\boldsymbol{V}}}{\partial {p}}\right]\\ & \quad \quad \times {{\boldsymbol{k}}}-\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}-\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}}-\left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega . \\[-10pt] \end{aligned}\tag{A28}$$

      As $\dfrac{\mathrm{d}}{\mathrm{d}{t}}\left(\dfrac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial p}\right)\approx 0$, Eq. (A28) can be written as

      $$ \begin{aligned}[b] & \left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega=-\frac{\lambda {f}^{2}}{h}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}-\frac{\lambda f}{h}\left[\left(\frac{\partial {\boldsymbol{V}}}{\partial {p}}\cdot \nabla \right){\boldsymbol{V}}-{D}\frac{\partial {\boldsymbol{V}}}{\partial {p}}\right] \\ & \quad \quad \times{{\boldsymbol{k}}}-\left(\frac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{i}}}-\left(\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {\theta }_{\mathrm{e}}\right){{\boldsymbol{j}}} . \end{aligned}\tag{A29}$$

      As $-\dfrac{\lambda f}{h}\left[\left(\dfrac{\partial {\boldsymbol{V}}}{\partial {p}}\cdot \nabla \right){\boldsymbol{V}}-{D}\dfrac{\partial {\boldsymbol{V}}}{\partial {p}}\right]\times {{\boldsymbol{k}}} = \dfrac{\lambda f}{h}\left(\dfrac{\partial {v}}{\partial {p}}\dfrac{\partial {u}}{\partial {x}}- \dfrac{\partial {u}}{\partial {p}}\dfrac{\partial {v}}{\partial {x}}\right)\;{{\boldsymbol{i}}}$$+ \dfrac{\lambda f}{h} \left(\dfrac{\partial {v}}{\partial {p}}\dfrac{\partial {u}}{\partial {y}}-\dfrac{\partial {u}}{\partial {p}}\dfrac{\partial {v}}{\partial {y}}\right){{\boldsymbol{j}}}$, Eq. (A29) can be expressed as

      $$\begin{aligned}[b] & \left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega=-\frac{{f}^{2}}{h}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}+\frac{1}{h}\Bigg\{\left[{f}\left(\frac{\partial {v}}{\partial {p}}\frac{\partial {u}}{\partial {x}}-\frac{\partial {u}}{\partial {p}}\frac{\partial {v}}{\partial {x}}\right)-\frac{h}{\lambda }\frac{\partial {\boldsymbol{V}}}{\partial {x}}\right.\\ & \quad \quad \cdot \nabla {{\theta }}_{\mathrm{e}}\Bigg]{{{\boldsymbol{i}}}}+ \left[{f}\left(\frac{\partial {v}}{\partial {p}}\frac{\partial {u}}{\partial {y}}-\frac{\partial {u}}{\partial {p}}\frac{\partial {v}}{\partial {y}}\right)-\frac{h}{\lambda }\frac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {{\theta }}_{\mathrm{e}}\right]{\boldsymbol{j}}\Bigg\} .\\[-10pt] \end{aligned}\tag{A30}$$

      Define ${\boldsymbol{Q}}=\dfrac{1}{2}\left[{f}\left(\dfrac{\partial {v}}{\partial {p}}\dfrac{\partial {u}}{\partial {x}}-\dfrac{\partial {u}}{\partial {p}}\dfrac{\partial {v}}{\partial {x}}\right)-\dfrac{h}{\lambda }\dfrac{\partial {\boldsymbol{V}}}{\partial {x}}\cdot \nabla {{\theta }}_{\rm{e}}\right]{\boldsymbol{i}}+\dfrac{1}{2}$$\Bigg[{f}\Bigg(\dfrac{\partial {v}}{\partial {p}}\dfrac{\partial {u}}{\partial {y}} -\dfrac{\partial {u}}{\partial {p}} \dfrac{\partial {v}}{\partial {y}}\Bigg)-\dfrac{h}{\lambda }\dfrac{\partial {\boldsymbol{V}}}{\partial {y}}\cdot \nabla {{\theta }}_{\rm{e}}\Bigg]{\boldsymbol{j}}$, Eq. (A30) can be written as

      $$ \left(\frac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}\right)\nabla \omega=-\frac{{f}^{2}}{h}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}+\frac{2}{h}{\boldsymbol{Q}} .\tag{A31} $$

      Define ${\sigma }=-{h}\dfrac{\partial {\theta }_{\mathrm{e}}}{\partial {p}}$, Eq. (A31) can be written as

      $$ \nabla \omega=\frac{{f}^{2}}{{\sigma }}\frac{\partial {{{\boldsymbol{V}}}_{{\rm{a}}}}}{\partial {p}}-\frac{2}{{\sigma }}{\boldsymbol{Q}} .\tag{A32} $$

      So, Eq. (A4) can be expressed as

      $$\begin{aligned}[b] \dfrac{\partial {D}}{\partial {t}}&=-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+{\zeta }\right){\boldsymbol{V}}\right]\\ & + \dfrac{1}{{\sigma }}\left(2{\boldsymbol{Q}}-{{f}}^{2}\frac{\partial {{\boldsymbol{V}}_{\mathrm{a}}}}{\partial {p}}\right)\cdot \frac{\partial {\boldsymbol{V}}}{\partial {p}}-{\omega }\frac{\partial {D}}{\partial {p}} . \end{aligned}\tag{A33}$$

      In practical weather forecast analysis, more attention is paid to the increase or decrease of convergence intensity in the middle and lower troposphere, which is the maximum convergence level. Therefore, at the maximum convergence level $\dfrac{\partial {D}}{\partial {p}}=0$, Eq. (A33) is simplified as:

      $$ \frac{\partial {D}}{\partial {t}}=-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+{\zeta }\right){\boldsymbol{V}}\right]+\frac{1}{{\sigma }}\left(2{\boldsymbol{Q}}-{{f}}^{2}\frac{\partial {{\boldsymbol{V}}_{\mathrm{a}}}}{\partial {p}}\right)\cdot \frac{\partial {\boldsymbol{V}}}{\partial {p}} .\tag{A34} $$

      The variation of the divergence field is determined by the barotropic non-equilibrium forcing (non-equilibrium between mass and wind) $-{\nabla }^{2}{E}+{\boldsymbol{k}}\cdot \left[\nabla \times \left({f}+{\zeta }\right){\boldsymbol{V}}\right]$ and the baroclinic coupled forcing between Q vector and vertical wind shear (the baroclinic thermodynamic–dynamical interaction) $\dfrac{1}{\mathrm{\sigma }}\left(2{\boldsymbol{Q}}-{{f}}^{2}\dfrac{\partial {{\boldsymbol{V}}_{\mathrm{a}}}}{\partial {p}}\right)\cdot \dfrac{\partial {\boldsymbol{V}}}{\partial {p}}$.

    Appendix B: Mechanisms of MYFR initiation and maintenance for 2018 event
    • Figure B1 shows the distribution of the barotropic non-equilibrium forcing during the 2018 MYFR. When the eastward-moving cloud clusters are still near the east of the TP, Shaanxi and Henan provinces prior to the heavy rainfall were controlled by positive or small negative values of barotropic non-equilibrium forcing. It can be seen that the intensity of unstable gradually increasing from west to east (0800–1400 BT 17 June, Figs. B1a, b). At 2000 BT 17 June (Fig. B1c), the values over Shaanxi and Henan provinces decreased to −2 × 10−8 s−2. The atmospheric motion was in a strong non-equilibrium state, which favored geostrophic adjustment and stimulated the rapid growth of convergence. The rainstorm occurred in the southern Shaanxi Province in the early morning of 18 June. At the time when rainstorm became strong (0200 BT 18 June), the value of barotropic non-equilibrium forcing rapidly becomes positive (Fig. B1d). This indicates that with the development of eastward-moving convection, the barotropic non-equilibrium forcing of atmospheric motion weakened and almost reached a quasi-equilibrium state. After 0200 BT 18 June, the convective cloud clusters remained strong, and the heavy rainfall in the southern Henan Province lasted until 1400 BT. The situation of initial stage in 2018 MYFR case is similar to 2016 case.

      Figure B1.  Distributions of the barotropic non-equilibrium force (black dashed line; 10−10 s−2) at 850 hPa at (a) 0800 BT 17 June, (b) 1400 BT 17 June, (c) 2000 BT 17 June, and (d) 0200 BT 18 June 2018. Black shadings mark topography under 850 hPa.

      The distribution of the coupled forcing of baroclinic thermodynamic–dynamical interaction term during 2018 case is shown in Fig. B2. At 0800 and 1400 BT 17 June (Figs. B2a, b), before the rainstorm occurred, the northeast of the TP and most of the Shaanxi and Henan provinces were controlled by a region of positive baroclinic forcing. This indicates that the impact of the baroclinic thermodynamic–dynamical interaction on divergence was small in the rainstorm area, and was not conducive to convection. At 2000 BT (Fig. B2c), with the cloud clusters moving eastward, the zone of negative baroclinic forcing began to appear in the southern Shanxi and northern Henan Province. Moreover, the baroclinic forcing further expanded and strengthened over the eastern Henan. At 0200 BT 18 June (Fig. B2d), the whole of Henan Province and southern Shaanxi Province were controlled by a negative zone of baroclinic forcing, and the central intensity exceeded −1 × 10−8 s−2. Such strong forcing can continuously stimulate convective convergence at low levels of the troposphere.

      Figure B2.  As in Fig. B1, but for distributions of the baroclinic thermodynamic–dynamical interaction term (black dashed lines; 10−10 s−2).

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