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PV Perspective of Impacts on Downstream Extreme Rainfall Event of a Tibetan Plateau Vortex Collaborating with a Southwest China Vortex

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The TRMM-based rainfall data are available at https://disc.gsfc.nasa.gov/datasets/TRMM_3B42_7/summary?keywords="3B42"%20"3%20hours". The MERRA-2 data were downloaded from https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/. This research was jointly supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB40000000) and the National Natural Science Foundation of China (41730963 and 41876020). The authors are grateful to the anonymous reviewers for their valuable comments. Special thanks are due to Prof. B. J. HOSKINS for his enthusiastic discussions and instructive suggestions on the draft


doi: 10.1007/s00376-021-1027-9

  • An extreme rainfall event occurred over the middle and lower reaches of the Yangtze Basin (MLY) during the end of June 2016, which was attributable to a Tibetan Plateau (TP) Vortex (TPV) in conjunction with a Southwest China Vortex (SWCV). The physical mechanism for this event was investigated from Potential Vorticity (PV) and omega perspectives based on MERRA-2 reanalysis data. The cyclogenesis of the TPV over the northwestern TP along with the lower-tropospheric SWCV was found to involve a midtropospheric large-scale flow reconfiguration across western and eastern China with the formation of a high-amplitude Rossby wave. Subsequently, the eastward-moving TPV coalesced vertically with the SWCV over the eastern Sichuan Basin due to the positive vertical gradient of the TPV-related PV advection, leading the lower-tropospheric jet associated with moisture transport to intensify greatly and converge over the downstream MLY. The merged TPV−SWCV specially facilitated the upper-tropospheric isentropic-gliding ascending motion over the MLY. With the TPV-embedded mid-tropospheric trough migrating continuously eastward, the almost stagnant SWCV was re-separated from the overlying TPV, forming a more eastward-tilted high-PV configuration to trigger stronger ascending motion including isentropic-gliding, isentropic-displacement, and diabatic heating-related ascending components over the MLY. This led to more intense rainfall. Quantitative PV diagnoses demonstrate that both the coalescence and subsequent re-separation processes of the TPV with the SWCV were largely dominated by horizontal PV advection and PV generation due to vertically nonuniform diabatic heating, as well as the feedback of condensation latent heating on the isentropic-displacement vertical velocity.
    摘要: 2016年6月底,长江中下游地区发生的一次极端降雨事件主要归因于高原涡和西南涡的协同影响。利用MERRA-2再分析资料,本文从位势涡度(PV)和垂直速度发展的角度探讨了这一事件发生的内部物理机制。在中高纬罗斯贝波列的影响下,我国西部和东部对流层中层发生了大尺度环流重构,这直接影响了青藏高原西北部上空高原涡以及东部对流层低层西南涡的生成。随后,由于高原涡东移导致局地正的PV平流随高度的增加而增强,高原涡在四川盆地东部与西南涡发生垂直合并,同时引起对流层低空急流的显著加强,其带来的水汽进一步向长江中下游地区输送和辐合。合并的高原涡-西南涡系统导致了对流层上层气块沿等熵面滑动引起的上升运动的发展。随着高原涡嵌入对流层中层的高度槽,并不断东移,西南涡移动较小,并与上层的高原涡再次分离,形成了向东更加倾斜的大值PV结构,激发了下游更强的上升运动,包括沿等熵面滑动的垂直速度分量、等熵面位移导致的垂直速度分量,以及与非绝热加热有关的垂直速度分量,最终导致了极端强降水。PV的定量诊断表明,在高原涡和西南涡合并与再分离过程中,PV收支主要受到水平PV平流以及垂直非均匀加热的影响,凝结潜热的释放对等熵位移导致的垂直速度分量存在显著的反馈作用。
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  • Figure 1.  Geopotential height (thick black contours; units: gpm), horizontal wind (gray vectors; units: m s−1), and PV (color shading with respect to left color bar; units: PVU, 1 PVU = 10−6 K m2 s−1 kg−1; the 1-PVU contours are highlighted by thin black curves) on the 500-hPa isobaric surface at (a) 1800 UTC 28 June, (b) 1800 UTC 29 June, (c) 0600 UTC 30 June, and (d) 0600 UTC 1 July 2016. Blue solid circles (dashed black curves) mark the center position of the TPV (the location of the trough-line) at 500 hPa. (e)–(h) Same as (a)–(d), but for the 700-hPa geopotential height (contours; units: gpm) and vertically integrated (1000–300 hPa) water vapor flux (hollow vectors; units: kg m−1 s−1). Red solid circles (dashed black curves) mark the center position of the SWCV (the location of the trough-line) at 700 hPa. The color shadings (with respect to right color bar) in (g) and (h) respectively show the 24-hour accumulated rainfall (units: mm) from 0600 UTC 29 June to 0600 UTC 30 June and from 0600 UTC 30 June to 0600 UTC 1 July 2016. The red rectangle in each panel denotes the key region (29.5°–33°N, 113°–119°E) representing the middle and lower reaches of the Yangtze Basin (MLY) where the extreme rainfall event occurred. The blue rectangles in (c) and (g) denote the eastern Sichuan Basin (ESB) region. The Tibetan Plateau with terrain altitude above 3000 m is outlined by thick gray curve.

    Figure 2.  (a) Longitude–time cross section of TRMM-derived rainfall rate averaged over the latitudinal band (29.5°–33°N) of the MLY key region (color shading, units: mm h−1) from 0000 UTC 29 June to 2100 UTC 01 July 2016. The dashed red lines show the western and eastern boundaries of the MLY key region. (b) Pressure–time cross section of area-averaged PV (color shading; units: PVU), equivalent potential temperature (θe, solid gray curves, units: K), and vertical velocity ($ \omega $, dashed black contours, units: Pa s−1) over the MLY key region. The abscissa refers to Coordinated Universal Time (UTC).

    Figure 3.  Pressure–longitude cross sections (30°–32°N) of PV (color shading and contours; units: PVU; the 1-PVU contours are highlighted by black solid curves), zonal-vertical circulation (vectors; zonal wind in m s−1 and vertical motion (multiplied by a factor of −50) in Pa s−1, reference vector is given at bottom right), and magnitude of horizontal water vapor flux (purple contours; units: 10−3 kg m−1 Pa−1 s−1) superimposed on the potential temperature (dashed curves; units: K) during the coalescence stage of the TPV with the SWCV over the ESB region for (a) 1800 UTC 29 June, (b) 0000 UTC 30 June, (c) 0600 UTC 30 June, and during the re-separation stage of the TPV from the SWCV over the MLY key region for (d) 1200 UTC 30 June, (e) 1800 UTC 30 June, and (f) 0000 UTC 01 July 2016. The gray shading shows the terrain altitude associated with the Tibetan Plateau. The blue and red bold solid lines marked along the abscissa represent the zonal ranges of the ESB region and MLY key region, respectively.

    Figure 4.  Pressure–longitude cross sections (30°–32°N) of (a) local PV tendency (color shading; units: 10−5 PVU s−1) and its forcing terms (color shading; units: 10−5 PVU s−1) in Eq. (1) due to (b) horizontal PV advection, (c) vertical PV advection, (d) horizontal diabatic heating, and (e) vertical diabatic heating for the coalescence stage of the moving-off TPV with the SWCV around 0000 UTC 30 June 2016. Black contours show the actual PV distribution at 0000 UTC 30 June (indicated by several contours of 0.8, 1.5, and 2.2 PVU) in each panel. (f)–(j) Same as (a)–(e), but for the re-separation stage of the TPV–SWCV at 0900 UTC 30 June 2016. The gray shading shows the terrain altitude associated with the Tibetan Plateau. The blue and red bold solid lines marked along the abscissa represent the zonal ranges of the ESB region and MLY key region, respectively.

    Figure 5.  Pressure–time cross sections of area-averaged (a1–a2) MERRA-2 data-provided vertical velocity ($ {\omega }_{\rm{rea}} $, contours; units: Pa s−1) along with the sum ($ {\omega }_{\rm{total}} $, color shading; units: Pa s−1) of recalculated vertical velocity components $ {\omega }_{\rm{ID}} $, $ {\omega }_{\rm{IG}} $, and $ {\omega }_{Q} $, (b1–b2) $ {\omega }_{\rm{ID}} $ (color shading; units: Pa s−1), (c1–c2) $ {\omega }_{\rm{IG}} $ (color shading; units: Pa s−1; green contours refer to its zonal component $ {\omega }_{{\rm{I}}{\rm{G}}-x} $, while red contours refer to its meridional component $ {\omega }_{{\rm{I}}{\rm{G}}-y} $, only the magnitude equal to 0.05 or −0.05 Pa s−1 is plotted for each component of $ {\omega }_{\rm{IG}} $), (d1–d2) $ {\omega }_{Q} $ (color shading; units: Pa s−1), and (e1–e2) area-averaged rainfall rate (bars; units: mm h−1) together with area-averaged magnitude of vertically integrated (1000–300 hPa) water vapor flux (IWVF; black lines; units: 102 kg m−1 s−1) over (a1–e1) ESB region, and (a2–e2) MLY key region, respectively. The abscissa refers to Coordinated Universal Time (UTC).

    Figure 6.  Evolutions of area-averaged vertical velocity (ω; black curve; units: Pa s−1) and its components $ {\omega }_{\rm{ID}} $ (green curve; units: Pa s−1), $ {\omega }_{\rm{IG}} $ (red curve; units: Pa s−1), and $ {\omega }_{Q} $ (blue curve; units: Pa s−1) over the ESB region at (a) 300 hPa and (b) 700 hPa. (c) and (d) same as (a) and (b), but for the MLY key region. The omega components contributing to local rainfall are shaded. The abscissa refers to Coordinated Universal Time (UTC).

    Figure 7.  Same as Fig. 6, but for the area-averaged $ {\omega }_{\rm{ID}} $ (dashed green curve; units: Pa s−1) and its dynamical forcing term of PV advection (−F1, dotted black curve; units: 10−17 Pa−1 s−3) and thermodynamic forcing term of diabatic heating (−F2, dashed black curve; units: 10−17 Pa−1 s−3) at 700 hPa over (a) ESB region and (b) MLY key region according to Eq. (10). The abscissa refers to Coordinated Universal Time (UTC).

    Figure 8.  Schematic diagram showing the 2016 MLY extreme rainfall event stages with the TPV and/or SWCV (cyclonic arrows) behavior and concomitant variations in PV (arbitrary polygons indicated by black solid or dashed curves represent the high PV equal to 1 PVU), vertical motion (upward arrows denote ascending motion and downward arrows signify descending motion) along the isentropic surfaces (concave-downward and convex-upward solid blue curves), and diabatic heating (red shading). The dashed curves denote the distribution of PV (dashed black lines) and isentropes (dashed blue lines) in the next moment. Red (black) parallelograms denote the MLY key region (ESB region). Vertical cross sections are averaged between 30°–32°N across the central key region. The gray shading shows the range and height of the Tibetan Plateau with terrain altitude greater than 1500 m. (a) Stage for the TPV moving off the TP in conjunction with the development of the SWCV. (b) Stage for the TPV coalescing with the SWCV over the ESB region to trigger upper-tropospheric ascending motion and to enhance lower-tropospheric convergent water vapor flux over the downstream MLY key region. (c) Stage for the MLY extreme rainfall peak, during which the TPV was re-separated from the SWCV to generate the strengthened water vapor flux and stronger ascending motion in terms of the lower-tropospheric isentropic-gliding vertical velocity ($ {\omega }_{\rm{IG}} $) and diabatic heating-related vertical velocity ($ {\omega }_{Q} $) over the MLY key region. (d) Stage for the extreme rainfall weakening, during which the TPV disappeared and the SWCV decayed.

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Manuscript received: 12 January 2021
Manuscript revised: 21 May 2021
Manuscript accepted: 31 May 2021
通讯作者: 陈斌, bchen63@163.com
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PV Perspective of Impacts on Downstream Extreme Rainfall Event of a Tibetan Plateau Vortex Collaborating with a Southwest China Vortex

    Corresponding author: Jiangyu MAO, mjy@lasg.iap.ac.cn
  • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China

Abstract: An extreme rainfall event occurred over the middle and lower reaches of the Yangtze Basin (MLY) during the end of June 2016, which was attributable to a Tibetan Plateau (TP) Vortex (TPV) in conjunction with a Southwest China Vortex (SWCV). The physical mechanism for this event was investigated from Potential Vorticity (PV) and omega perspectives based on MERRA-2 reanalysis data. The cyclogenesis of the TPV over the northwestern TP along with the lower-tropospheric SWCV was found to involve a midtropospheric large-scale flow reconfiguration across western and eastern China with the formation of a high-amplitude Rossby wave. Subsequently, the eastward-moving TPV coalesced vertically with the SWCV over the eastern Sichuan Basin due to the positive vertical gradient of the TPV-related PV advection, leading the lower-tropospheric jet associated with moisture transport to intensify greatly and converge over the downstream MLY. The merged TPV−SWCV specially facilitated the upper-tropospheric isentropic-gliding ascending motion over the MLY. With the TPV-embedded mid-tropospheric trough migrating continuously eastward, the almost stagnant SWCV was re-separated from the overlying TPV, forming a more eastward-tilted high-PV configuration to trigger stronger ascending motion including isentropic-gliding, isentropic-displacement, and diabatic heating-related ascending components over the MLY. This led to more intense rainfall. Quantitative PV diagnoses demonstrate that both the coalescence and subsequent re-separation processes of the TPV with the SWCV were largely dominated by horizontal PV advection and PV generation due to vertically nonuniform diabatic heating, as well as the feedback of condensation latent heating on the isentropic-displacement vertical velocity.

摘要: 2016年6月底,长江中下游地区发生的一次极端降雨事件主要归因于高原涡和西南涡的协同影响。利用MERRA-2再分析资料,本文从位势涡度(PV)和垂直速度发展的角度探讨了这一事件发生的内部物理机制。在中高纬罗斯贝波列的影响下,我国西部和东部对流层中层发生了大尺度环流重构,这直接影响了青藏高原西北部上空高原涡以及东部对流层低层西南涡的生成。随后,由于高原涡东移导致局地正的PV平流随高度的增加而增强,高原涡在四川盆地东部与西南涡发生垂直合并,同时引起对流层低空急流的显著加强,其带来的水汽进一步向长江中下游地区输送和辐合。合并的高原涡-西南涡系统导致了对流层上层气块沿等熵面滑动引起的上升运动的发展。随着高原涡嵌入对流层中层的高度槽,并不断东移,西南涡移动较小,并与上层的高原涡再次分离,形成了向东更加倾斜的大值PV结构,激发了下游更强的上升运动,包括沿等熵面滑动的垂直速度分量、等熵面位移导致的垂直速度分量,以及与非绝热加热有关的垂直速度分量,最终导致了极端强降水。PV的定量诊断表明,在高原涡和西南涡合并与再分离过程中,PV收支主要受到水平PV平流以及垂直非均匀加热的影响,凝结潜热的释放对等熵位移导致的垂直速度分量存在显著的反馈作用。

    • During boreal summer, a kind of shallow low-pressure system often arises over the Tibetan Plateau (TP) and is commonly called the Tibetan Plateau Vortex (TPV; Ye and Gao, 1979; Lhasa Project Group on Qinghai-Xizang Plateau Meteorology, 1981). The typical spatial scale of the TPV is only 400–800 km in the horizontal direction and 2–3 km in the vertical direction, with the maximum positive vorticity usually occurring around 500 hPa near the surface of the TP (Ye and Gao, 1979; Lhasa Project Group on Qinghai-Xizang Plateau Meteorology, 1981). TPVs are observed to originate generally over the western half of the TP (Li et al., 2011, 2014), but most of them decay or disappear over the eastern half within 12–24 hours (Wang et al., 2009). A few TPVs can last for several days over or while moving off of the TP under certain environmental conditions, and the moving-off TPVs can directly or indirectly cause extreme weather events such as heavy rainstorms to take place over downstream regions of eastern China (Ye and Gao, 1979; Li, 2002; Ma et al., 2020).

      The moving-off TPVs are found to have some relevance to the lower tropospheric vortexes over the eastern and southeastern flanks of the TP in southwestern China (Chen et al., 2004; Cheng, 2016; Li et al., 2017). Such vortexes are commonly referred to as Southwest China Vortexes (SWCVs), with the strongest cyclonic center occurring mostly around 700 hPa or 850 hPa (Wang et al., 1993; Cheng et al., 2016). SWCVs are important mesoscale to synoptic-scale systems that occur during summer and not only bring about locally intense rainfall over southwestern China (Wang et al., 1993; Chen et al., 2004) but also lead to downstream heavy rainfall over even wider swaths of eastern China as they migrate large distances eastward (Zhao et al., 2007; Chen et al., 2015; Wang and Liu, 2017). For instance, the record-breaking rainstorm event over Henan Province in May 2013 was caused by the eastward movement of a SWCV, resulting in severe damage to crops and houses (Wang and Liu, 2017).

      During the summer of 2016, a series of persistent heavy rainfall events occurred within and south of the middle and lower reaches of the Yangtze Basin (MLY, Shao et al., 2018; Zhang et al., 2021); one record-breaking heavy rainfall event took place from 30 June to 6 July. Specifically, the weekly accumulated rainfall amount for some stations in Hubei and Anhui provinces exceeded 500 mm, with a maximum amount even greater than 1000 mm in the downtown areas of Wuhan City. This long-lasting rainfall event led to devastating floods and severe casualties of more than 330 people, with economic losses of at least $22 billion (U.S. dollars), becoming the second largest weather-related natural disaster in Chinese history (Zhou et al., 2018). The most intense rainfall was observed around 2100 UTC 30 June, with the 24-hour (from 0600 UTC 30 June to 0600 UTC 1 July) accumulated rainfall amount being greater than 160 mm and occurring mostly over the Hubei–Anhui–Jiangxi provinces (29.5°–33°N, 113°–119°E) within the MLY (Fig. 1h). As such, this target domain is selected as a key region to represent the MLY in examining the dynamical mechanism of the strongest rainfall event during the sub-period from 30 June to 1 July 2016. Following Ma et al. (2020), this strongest rainfall event over the MLY key region for the sub-period from 0600 UTC 30 June to 0600 UTC 1 July was thus deemed as an extreme MLY rainfall event in the present study. Ma et al. (2020) linked the occurrence of this extreme rainfall event with the potential vorticity (PV) advection associated with an eastward migrating TPV. Through the quantitative diagnostics for the PV-related omega equation, they found that during the event the strong ascending motion was dynamically induced by the PV advection increasing with height, and the positive PV advection in the middle-upper troposphere was produced because the off-TP TPV was advected by westerlies toward the MLY region (cf. Figs. 1bd). However, they did not examine the contributions of the TPV-related diabatic heating feedback and the low-level SWCV (Figs. 1fh) located over the middle Yangtze River during this extreme event.

      Figure 1.  Geopotential height (thick black contours; units: gpm), horizontal wind (gray vectors; units: m s−1), and PV (color shading with respect to left color bar; units: PVU, 1 PVU = 10−6 K m2 s−1 kg−1; the 1-PVU contours are highlighted by thin black curves) on the 500-hPa isobaric surface at (a) 1800 UTC 28 June, (b) 1800 UTC 29 June, (c) 0600 UTC 30 June, and (d) 0600 UTC 1 July 2016. Blue solid circles (dashed black curves) mark the center position of the TPV (the location of the trough-line) at 500 hPa. (e)–(h) Same as (a)–(d), but for the 700-hPa geopotential height (contours; units: gpm) and vertically integrated (1000–300 hPa) water vapor flux (hollow vectors; units: kg m−1 s−1). Red solid circles (dashed black curves) mark the center position of the SWCV (the location of the trough-line) at 700 hPa. The color shadings (with respect to right color bar) in (g) and (h) respectively show the 24-hour accumulated rainfall (units: mm) from 0600 UTC 29 June to 0600 UTC 30 June and from 0600 UTC 30 June to 0600 UTC 1 July 2016. The red rectangle in each panel denotes the key region (29.5°–33°N, 113°–119°E) representing the middle and lower reaches of the Yangtze Basin (MLY) where the extreme rainfall event occurred. The blue rectangles in (c) and (g) denote the eastern Sichuan Basin (ESB) region. The Tibetan Plateau with terrain altitude above 3000 m is outlined by thick gray curve.

      Figure 2.  (a) Longitude–time cross section of TRMM-derived rainfall rate averaged over the latitudinal band (29.5°–33°N) of the MLY key region (color shading, units: mm h−1) from 0000 UTC 29 June to 2100 UTC 01 July 2016. The dashed red lines show the western and eastern boundaries of the MLY key region. (b) Pressure–time cross section of area-averaged PV (color shading; units: PVU), equivalent potential temperature (θe, solid gray curves, units: K), and vertical velocity ($ \omega $, dashed black contours, units: Pa s−1) over the MLY key region. The abscissa refers to Coordinated Universal Time (UTC).

      For the mesoscale to synoptic-scale system such as the TPV or SWCV, except for variations in relative vorticity, changes in vertical velocity are crucial to its development and movement (Hoskins et al., 1985). Hoskins et al. (2003) linked the omega variation with the PV forcing, reexamining how the vertical motion is generated even in the presence of diabatic heating under the quasigeostrophic or the semigeostrophic frameworks. The components of vertical velocity associated with the system development were found to satisfy an omega equation with forcing determined from the relative advection of interior PV and boundary temperature as well as diabatic heating effect.

      Ma et al. (2020) only investigated the impact of the TPV-related PV advection on the MLY extreme rainfall event from 30 June to 1 July 2016 (or “MLY extreme rainfall event” in short), without examining the contribution of the SWCV and its combined effect with the TPV. Therefore, the objective of the present study is to explore the downstream influences on this MLY extreme rainfall event of the TPV in conjunction with the SWCV from a PV perspective. Based on the PV–omega equation, the different components of vertical motion arising from PV forcing are also examined to reveal the dynamical mechanism of how the upstream TPV migrated eastward to coalesce and re-separate with the SWCV, thereby explaining the cause for the MLY extreme rainfall event.

      Section 2 introduces the data and methods used in this study. Section 3 describes the MLY extreme rainfall event in association with the TPV and SWCV. Section 4 analyzes the downstream impact of the two vortexes on the MLY extreme rainfall event from a PV perspective, and different ascending components of vertical velocity related to PV are examined in section 5. Finally, a summary and discussion are given in section 6.

    2.   Data and methods
    • The 3-hourly gridded satellite-observed rainfall data with a spatial resolution of 0.25° longitude × 0.25° latitude are provided by the National Aeronautics and Space Administration’s Tropical Rainfall Measuring Mission (TRMM, Huffman et al., 2007). The atmospheric circulation data including air temperature, wind field, PV, geopotential height, and specific humidity are extracted from Version 2 of the Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) products produced by the Global Modeling and Assimilation Office (Gelaro et al., 2017), which are available at 3-hour intervals. The MERRA-2 reanalysis data include 42 isobaric surfaces from 1000 hPa to 0.1 hPa, with a horizontal resolution of 0.625° longitude × 0.5° latitude.

    • Generally, a TPV is defined as a local minimum in the geopotential height field at 500 hPa appearing over the TP, with one or more closed geopotential height contours or cyclonic winds in the vicinity of three neighboring weather stations (Lhasa Project Group on Qinghai-Xizang Plateau Meteorology, 1981). In combination with the method for defining the surface cyclone (Wernli and Schwierz, 2006), the present study defines the TPV center as a local minimum of the 500-hPa geopotential height within closed or semi-closed height contours, with the maximum relative vorticity in cyclonic flow during the TPV generated and migrated eastward over the TP and before it incorporated into the downstream 500-hPa trough of geopotential height fields. For convenience of describing and highlighting its subsequent effect on the MLY extreme rainfall event during and after the TPV merged into the 500-hPa height trough, we still tracked this vortex system and continued to call it as the TPV, except that the TPV center was determined as a local minimum within the trough corresponding to maximum relative vorticity. Similarly, the SWCV center is defined on the 700-hPa isobaric surface with local minimum geopotential height together with maximum relative vorticity.

    • The PV equation in the isobaric coordinate system can be expressed as follows (Ertel, 1942; Hoskins et al., 1985; Hoskins, 1991, 1997, 2015):

      where P is Ertel PV and is the dot product of the absolute vorticity vector for unit mass and the potential temperature gradient: $ P=\alpha {\boldsymbol{\xi }}_{\rm{a}} \cdot {\bf{\nabla}} \theta $, α is the specific volume, $ {\boldsymbol{\xi }}_{\rm{a}} $ is the three-dimensional absolute vorticity, θ is the potential temperature, and $ {\bf{\nabla}} $ is the three-dimensional gradient operator in xyp space. $ {\boldsymbol{V}}_{\rm{h}} $ is the horizontal wind vector (u, v), and $ \omega $ is the vertical velocity. $ {{\bf{\nabla}} }_{\rm{h}} $ is the horizontal gradient operator, $ {\boldsymbol{k}} $ is a unit vertical vector, and $ \zeta $ is the vertical relative vorticity. g is the gravitational acceleration, $ \dot{\theta } $ is the diabatic heating rate, and $ {\boldsymbol{F}} $ is frictional acceleration in the momentum equation. The left-hand side of Eq. (1) refers to the local rate of change of PV or the PV tendency, while the five terms on the right-hand side refer from first to fifth to the horizontal and vertical PV advection, the PV generation by the horizontally and vertically nonuniform diabatic heating, as well as the PV dissipation by the frictional effect, respectively. In this study, every term except the last one of Eq. (1) was calculated to show the dynamical and thermodynamical processes contributing to the net PV tendency during the MLY extreme rainfall event, revealing the relative importance of different processes in forcing PV redistribution and resultant vertical motion (as discussed in section 4). Note that the PV dissipation associated with frictional force is not analyzed here because its effect is relatively small in free atmosphere for the synoptic-scale event.

    • Following Hoskins et al. (2003), Wu et al. (2020) divided the vertical velocity ($ \omega $) in the quasigeostrophic diabatic thermodynamic equation into three components, including the isentropic-displacement vertical velocity ($ {\omega }_{\rm{ID}} $), the isentropic-gliding vertical velocity ($ {\omega }_{\rm{IG}} $), and the diabatic heating-related vertical velocity ($ {\omega }_{\rm{Q}} $):

      where

      and

      where $ {\Theta } $ is a standard potential temperature distribution averaged over a horizontal domain and a period of interest, $ {{\Theta }}_{p} $ is the vertical gradient of $ {\Theta } $, $ {\boldsymbol{V}}_{{\rm{g}}} $ is the horizontal geostrophic velocity, $ {\boldsymbol{C}} $ is a constant horizontal velocity at which the reference frame moves, and the others are used following their conventional meteorological notations ($ {\boldsymbol{C}} $ is relatively small compared to the geostrophic wind, so it is not considered in calculating $ {\omega }_{\rm{IG}} $ for this case study). Dynamically, according to Hoskins et al. (2003), the component $ {\omega }_{\rm{ID}} $ represents the rate of vertical displacement of a particle that is stationary in the horizontal relative to the moving isentropic surface, and it is associated with the development of the thermal field. The component $ {\omega }_{\rm{IG}} $ depicts the vertical motion of a particle moving along a sloping isentropic surface, and it is associated with the thermal structure as well as the horizontal quasigeostrophic flow. However, the component $ {\omega }_{Q} $ is basically dependent on atmospheric diabatic heating (Wu et al. 2020). Based on the work of Hoskins et al. (2003), Wu et al. (2020) further derived another form of omega equation relating $ {\omega }_{\rm{ID}} $ to quasigeostrophic PV ($ {q}_{{\rm{g}}} $) for a diabatic atmosphere (see their Eq. 14). In their $ {\omega }_{\rm{ID}} $ equation, the source term is proportional to the vertical derivative of the horizontal advection of $ {q}_{{\rm{g}}} $ [namely $ f\partial \left({\boldsymbol{V}}_{{\rm{g}}} \cdot {\bf{\nabla}} {q}_{{\rm{g}}}\right)/\partial p $] plus a diabatic term [-$ {f}^{2}{\partial }^{2}\left(\dot{\theta }/{{\Theta }}_{p}\right)/\partial {p}^{2} $]. Charney and Stern (1962) showed that in z- (or p-) coordinates, the local rate of change and horizontal advection of quasigeostrophic PV ($ {q}_{{\rm{g}}} $) are proportional to the local rate of change and horizontal advection of Ertel PV (P) in θ-coordinates. Hoskins and James (2014) further proved that in the limit of small Rossby number Ro, large Richardson number Ri, and when $ {\rm{R}}{{\rm{i}}^{ - 1}} \ll {\rm{Ro}} $,

      In the isobaric and isentropic coordinate systems,

      It follows that

      The weather system under current consideration is dominated by an isolated region of large PV, and the tilt of isentropic surfaces is small in both the longitudinal and latitudinal directions, as shown in Fig 3. Thus, the second term on the right-hand side of the above formula can be neglected, and we can reach the following approximation:

      Figure 3.  Pressure–longitude cross sections (30°–32°N) of PV (color shading and contours; units: PVU; the 1-PVU contours are highlighted by black solid curves), zonal-vertical circulation (vectors; zonal wind in m s−1 and vertical motion (multiplied by a factor of −50) in Pa s−1, reference vector is given at bottom right), and magnitude of horizontal water vapor flux (purple contours; units: 10−3 kg m−1 Pa−1 s−1) superimposed on the potential temperature (dashed curves; units: K) during the coalescence stage of the TPV with the SWCV over the ESB region for (a) 1800 UTC 29 June, (b) 0000 UTC 30 June, (c) 0600 UTC 30 June, and during the re-separation stage of the TPV from the SWCV over the MLY key region for (d) 1200 UTC 30 June, (e) 1800 UTC 30 June, and (f) 0000 UTC 01 July 2016. The gray shading shows the terrain altitude associated with the Tibetan Plateau. The blue and red bold solid lines marked along the abscissa represent the zonal ranges of the ESB region and MLY key region, respectively.

      Because in the limit of small Rossby number for large-scale atmospheric motion, the wind vector can be replaced by geostrophic wind, in this case, the omega equation for $ {\omega }_{\rm{ID}} $ in a diabatic atmosphere can be approximately expressed as:

      Eq. (10) indicates that isentropic-displacement vertical velocity $ {\omega }_{\rm{ID}} $ is forced by the vertical gradient of Ertel PV advection and the vertical structure of atmospheric diabatic heating. The boundary condition is imposed by assuming zero vertical pressure velocity on the boundary so that warm horizontal advection or diabatic heating on horizontal boundary will result in in situ isentropic-displacement descent, and vice versa. The solution of $ {\omega }_{\rm{ID}} $ depends on both the internal forcing on the right-hand side of Eq. (10) (particular solution) and the boundary forcing (general solution). This study focuses only on the impacts of internal forcing. For convenience of presentation, the first and second terms on the right-hand side of this equation are represented respectively by F1 and F2. The quantitative analyses using Eqs. (2) to (5) will be given in section 5.

    3.   Basic features of the extreme MLY rainfall event associated with the TPV and SWCV
    • As introduced in section 1, the focus of this study is on the extreme rainfall event over the MLY key region (red rectangles in Fig. 1) for the period of 30 June to 1 July 2016. Thus, Fig. 1 shows the 500-hPa and 700-hPa circulation evolutions before and during this extreme event from 1800 UTC 28 June to 0600 UTC 1 July 2016 to illustrate the large-scale flow reconfiguration relating to the TPV and SWCV.

      Note in Fig. 1a that almost two days before the event, an extraordinarily strong western Pacific subtropical high (WPSH) was present in the middle troposphere on 1800 UTC 28 June, with an unprecedented intensity characterized by the 5910-gpm contour located west of the southeastern coast of China. To the north of the zonal ridge line of the WPSH around 25°N, there was a meridionally-elongated large-scale westerly trough in the midlatitudes around 115°E (Fig. 1a). Thus, the strong northwesterlies behind the trough intruded southward to reach south of 30°N over central China, while the southwesterlies prevailed in front of the trough over eastern China, with discrete high PV greater than 1 PVU (1 PVU = 1 × 10−6 K kg−1 m2 s−1). On the other hand, there was an almost closed cyclonic circulation over the western and central TP at 1800 UTC 28 June (Fig. 1a), signifying the existence of a TPV. Meanwhile, some areas with high PV greater than 1.2 PVU were observed to exist around the TPV or within the entire trough zone over the TP, indicating that the TPV had already formed. Data analysis indicates that this TPV had formed at 1800 UTC 27 June (Ma et al. 2020). Its formation mechanism will be given in a separate study.

      Similar to 500 hPa, the westward-extended WPSH was also evident at 700 hPa (Fig. 1e), with strong southwesterlies on its northwestern side transporting moisture toward the south of the MLY key region, as evidenced by a poleward-directed corridor of strong vertically integrated water vapor flux (Simmonds et al., 1999). Note that the midlatitude trough elongating southward into the key region and its upstream ridge at 700 hPa (Fig. 1e) were located east of the corresponding trough and ridge at 500 hPa (Fig. 1a), clearly reflecting the baroclinic structure of Rossby waves in the middle and lower troposphere. Note also that in the lower troposphere a shallow trough existed over Sichuan Basin along 104°E between 25°N and 30°N (Fig. 1e), which facilitated the subsequent cyclogenesis of a SWCV (Fig. 1f).

      With the TPV migrating continually eastward to reach the eastern edge of the TP by 1800 UTC 29 June (Fig. 1b), the TPV-related northeast–southwest oriented trough of the previous day (Fig. 1a) at 500 hPa was transformed into a narrow and zonally-elongated trough (cyclonic shear line), accompanied by extraordinarily high PV greater than 3 PVU locally (Fig. 1b), indicating that the TPV was intensified concomitantly. Meanwhile, another shallow off-TP trough was generated to the northeast of the TPV (Fig. 1b), forming a typical flow pattern of "Northern trough and Southern vortex", as suggested by previous studies such as Yu and Gao (2008). Consequently, the southwesterlies in front of these two troughs were evidently strengthened (Fig. 1b) due to an enhanced horizontal gradient of the geopotential height relative to the WPSH at 500 hPa. In turn, such warm and moist southwesterlies were conducive to the further intensification and subsequent movement of the TPV (Figs. 1b and 1c), as suggested by Li et al. (2011, 2014). In correspondence with the intensified TPV (Fig. 1b), a SWCV formed at 700 hPa in northeastern Yunnan province with the vortex center around 26°N and 104°E (Fig. 1f), because more moisture was transported to the north of 30°N along the periphery of the eastern TP, as evidenced by southwesterly water vapor flux (Fig. 1f).

      Subsequently, the TPV moved completely away from the TP to reach the Sichuan Basin and was embedded in a northeast–southwest elongated 500-hPa trough at 0600 UTC 30 June (Fig. 1c). This moving-off TPV resulted in a wide range of locally moderate rainfall along its migrating path over the southern TP as well as the large downhill terrain area during the period from 0600 UTC 29 June to 0600 UTC 30 June (as shown in Fig. 1g). According to Zheng et al. (2013), the diabatic latent heating ahead of a vortex not only intensifies the local vertical vorticity but also affects the migrating direction of the vortex (as discussed further in section 4). In response to the moving-off TPV (Fig. 1c), the SWCV developed explosively with a local minimum of geopotential height less than 3070 gpm (Fig. 1g). The centers of these two vortexes were located within almost the same domain over the Eastern Sichuan Basin (ESB, 29.5°–33°N, 105°–108°E), indicating that the SWCV coalesced vertically with the TPV to form a deep cyclonic circulation system. Thus, this ESB domain (shown as blue rectangles in Figs. 1c and 1g) is defined as another key region to demonstrate the coalescence process of these two vortexes in the following sections. On the other hand, such a deepened SWCV also sped up the southwesterlies on its eastern side, which worked in conjunction with the eastward-propagating and southward-extending midlatitude trough to cause the water vapor flux to veer right, favoring the moisture transport towards the MLY (Fig. 1g). Noticeably, the TPV migrated drastically across the MLY key region to the coastal area from 0600 UTC 30 June to 0600 UTC 1 July (Fig. 1d), whereas the SWCV moved less, indicating that the TPV was re-separated from the SWCV. The almost stagnant SWCV was connected with the 700-hPa trough to the north in such a way that the low-level jet stream (LLJ) between the SWCV and WPSH became stronger (Fig. 1h), resulting in enhanced moisture convergence over the MLY key region and extremely intense rainfall during this 24-hour period (Fig. 1h). Note also that the TPV was mainly incorporated with the southern segment of the 500-hPa trough over eastern China during the heavy rainfall episode (Figs. 1c and 1d), thus the midlatitude Rossby wave acted as a carrier to propagate the TPV. In fact, the extreme rainfall event resulted mostly from the downstream impacts of the TPV together with the SWCV (as discussed below).

    • For the MLY key region, as shown in Figs. 1g and 1h, the extreme rainfall happened mostly during the period when the TPV re-separated from the SWCV. Figure 2a illustrates the longitude-time cross section (averaged along the key-region latitudes) of 3-hourly rainfall rate. The rainfall belt originated from at least 106°E and then propagated eastward into the MLY key region, corresponding to the eastward-moving TPV. Note from Fig. 2a that the heavy rainfall over the MLY key region started after 0600 UTC 30 June when the two vortexes were merged vertically around 106°E, suggesting an important role of the SWCV coalescing with the overlying TPV in generating the MLY extreme rainfall event (as discussed below).

      Since the rainfall occurrence depends on ascending motion of warm and moist air, the pressure-time cross section of the area-averaged equivalent potential temperature and vertical velocity over the MLY key region is investigated and shown in Fig. 2b. Note that before 0600 UTC 30 June, very warm and moist air was present in the lower troposphere, as evidenced by large-value equivalent potential temperature (θe > 334 K below 700 hPa). Importantly, the equivalent potential temperature decreased with increasing height in the lower troposphere (below 700 hPa), indicating that the low-level atmosphere was thermodynamically unstable to vertical motion and that regional convection could be likely to develop.

      As expressed dynamically in Eq. (10), the isentropic-displacement vertical motion ($ {\omega }_{\rm{ID}} $), as one of vertical velocity components, is induced partly by the vertical gradient of horizontal PV advection. The MLY key region was dominated by westerlies, especially in the middle and upper troposphere, before and during the extreme event, as shown in Figs. 1ad. The vertical configuration of area-averaged PV is displayed in Fig. 2b to demonstrate the relationship of ascending motion with PV behavior (particularly with TPV-related PV advection). Note that over the MLY key region, although high-value PV existed in the upper troposphere (above 400 hPa) before 1800 UTC 29 June (Fig. 2b), ascending motion was difficult to be induced because the upper-tropospheric atmosphere was very stable (θe increases with height). However, evident ascending motion (vertical velocity < −0.2 Pa s−1) first occurred in the middle-upper troposphere (150–500 hPa) beginning 0000 UTC 30 June (Fig. 2b), accompanied by high PV (greater than 0.6 PVU) in the middle troposphere (300–500 hPa). Subsequently, ascending motion extended downward and intensified, with the strongest ascending motion (Fig. 2b) corresponding well with the most intense rainfall (Fig. 2a) over the MLY key region around 2100 UTC 30 June. Notably, the mid-tropospheric high PV (Fig. 2b) was associated with the presence and eastward propagation of the TPV from 0000 UTC 30 June onwards, as shown in Figs. 1c and 1d. In fact, the mid-tropospheric high PV (Fig. 2b) reflected that the horizontal PV advection by prevailing westerlies was greater in the middle troposphere than in the lower troposphere, thus inducing considerable ascending motion (cf. Fig. 3) and resultant rainfall (Fig. 2a). Of course, such ascending motion also included other components ($ {\omega }_{\rm{ID}} $ and $ {\omega }_{\rm{Q}} $) of vertical velocity (as discussed below).

    4.   Downstream impacts of the TPV in coalescence with and re-separation from the SWCV
    • The above analyses indicate that the coalescence and re-separation of the TPV–SWCV system have an important impact on the variations in downstream circulation. To clarify the vertical interactions of the TPV with the SWCV and their influences on the extreme rainfall event, Fig. 3 illustrates pressure–longitude cross sections of PV fields as well as the zonal–vertical circulation averaged along the conjunct track (30°–32°N) of the two vortexes during the period from 1800 UTC 29 June to 0000 UTC 1 July. Note in Fig. 3a that the TPV exhibited a slightly eastward-tilted high-PV column over the eastern edge of the TP between 98°E and 103°E from the surface to 300 hPa, corresponding to the arrival of the TPV on 1800 UTC 29 June (Fig. 1b), with a maximum PV center greater than 2 PVU indeed located at 500 hPa. Moist air was transported upward by strong ascending motion, with large horizontal water vapor fluxes greater than 5 × 10−3 kg m−1 Pa−1 s−1 occurring above 400 hPa within and ahead of the TPV center. As shown in Fig. 1b, such large water vapor fluxes around the eastern TP resulted mostly from the 500-hPa southwesterlies. Note that another center of larger water vapor fluxes existed over the MLY key region, especially below 700 hPa (Fig. 3b), which was caused by low-level southwesterlies on the northwestern side of the WPSH (Fig. 1f).

      Six hours later, the high-PV column of the TPV was far from the high-altitude platform of the eastern TP (Fig. 3b), and the intensity of the TPV was evidently enhanced. Below and ahead of the TPV-related high-PV column, a weak PV zone associated with the SWCV was present around 105°E (Fig. 3b), accompanied by large water vapor fluxes greater than 1 × 10−2 kg m−1 Pa−1 s−1. As such, the SWCV-generated ascent in the middle and lower troposphere happened to superimpose with the TPV-related updrafts in the middle and upper troposphere, further enhancing the ascending motion in the entire troposphere (Fig. 3b), resulting in locally heavy rainfall over the ESB region (Fig. 2a). Obviously, such considerable ascending motion consisted of different components ($ {\omega }_{\rm{ID}} $ and $ {\omega }_{\rm{IG}} $) of vertical velocity, as expressed in Eqs. (3) to (4). In turn, such strong rainfall-related diabatic latent heating subsequently induced stronger ascending $ {\omega }_{Q} $, as in Eq. (5). How these vertical velocity components were dynamically generated will be discussed in section 5.

      Note in Fig. 3b that the high-PV column of the TPV tended to be advected eastward by the horizontal westerlies, and the westerlies were stronger in the middle-upper troposphere than in the lower troposphere, causing the TPV to completely merge with the underlying SWCV to form a deep high-PV system over the downstream region at 0600 UTC 30 June (Fig. 3c). The SWCV, which was manifested by high PV in lower troposphere, was intensified significantly by 0600 UTC (Fig. 3c) compared with 0000 UTC (Fig. 3b), indicating the great effect of the TPV on the development of the underlying SWCV. The merged TPV–SWCV then caused the flow amplification in the midtroposphere over eastern China around 0600 UTC 30 June (as shown in Fig. 1c), triggering significant downstream development of ascending motion (Fig. 3c). As a result, extreme rainfall began over the MLY key region (Fig. 2a). Note in Fig. 3c that the isentropic surfaces, especially in the upper troposphere, formed as a concave distribution around the merged system. As suggested by Hoskins et al. (1985), an isolated tropospheric high-PV forcing could induce warm temperature anomalies above the PV forcing center and cold anomalies below the center due to the thermal wind relationship (see their Fig. 8). Therefore, in addition to the airmass rising along the sloping surfaces in the meridional direction (as discussed later in section 5), the contractive isentropic surfaces around the merged PV system guide the airmass to climb in strong westerlies, inducing distinct ascending $ {\omega }_{\rm{IG}} $ above 400 hPa over the MLY key region (Fig. 3c). Such phenomenon in the PV-induced flow structure can be seen in Hoskins et al. (2003) and Hoskins (2015). The ascending $ {\omega }_{\rm{ID}} $ was also noted to exist over the Sichuan Basin between 104°E and 106°E (Fig. 3c), which coincided with the vertical distribution of the middle-upper tropospheric positive horizontal PV advection located over the underlying negative PV advection (Fig. 4b) as well as the diabatic heating feedback (Fig. 4e) according to Eq. (10). As suggested by Ma et al. (2020), this positive vertical gradient of horizontal PV advection could induce strong ascending $ {\omega }_{\rm{ID}} $ locally and facilitate the intensification of the SWCV. This eastward-tilted vertical distribution of high PV became more significant during the MLY extreme rainfall event (Figs. 3df), with the TPV center re-separating from the low-level SWCV after 0600 UTC 30 June, inducing stronger ascending motion over the MLY key region, thereby producing more intense rainfall.

      Figure 4.  Pressure–longitude cross sections (30°–32°N) of (a) local PV tendency (color shading; units: 10−5 PVU s−1) and its forcing terms (color shading; units: 10−5 PVU s−1) in Eq. (1) due to (b) horizontal PV advection, (c) vertical PV advection, (d) horizontal diabatic heating, and (e) vertical diabatic heating for the coalescence stage of the moving-off TPV with the SWCV around 0000 UTC 30 June 2016. Black contours show the actual PV distribution at 0000 UTC 30 June (indicated by several contours of 0.8, 1.5, and 2.2 PVU) in each panel. (f)–(j) Same as (a)–(e), but for the re-separation stage of the TPV–SWCV at 0900 UTC 30 June 2016. The gray shading shows the terrain altitude associated with the Tibetan Plateau. The blue and red bold solid lines marked along the abscissa represent the zonal ranges of the ESB region and MLY key region, respectively.

    • To substantiate the relative importance of the PV advection-related dynamical factors in causing the TPV to coalesce with and re-separate from the SWCV through PV redistribution, a quantitative PV budget was performed based on Eq. (1) to calculate the net PV tendency and its components created by horizontal and vertical PV advection as well as nonuniform diabatic heating at 0000 UTC 30 June and 0900 UTC 30 June.

      As shown in Fig. 4a, net positive PV tendency occurred ahead of the high-PV column (indicated by solid lines) of the TPV before the coalescence of the two vortexes, with net negative PV tendency in the rear, signifying that the high-PV column would develop eastward, with the low-level vortex intensifying concurrently over the ESB region. For the forcing terms contributing to the net PV tendency, there was strong positive horizontal PV advection ahead of the high-PV column of the TPV above 500 hPa extending to 150 hPa over the ESB region (Fig. 4b), accompanied by strong negative PV advection to its west and east. The PV tendency component created by the vertical gradient of diabatic heating had positive values in the lower troposphere over the ESB region (Fig. 4e), indicating the essential role of diabatic heating in the creation of high PV. Obviously, such newly generated high PV will be advected upward by vertical PV advection under strong ascending motion (Fig. 3b), with positive anomalies above the centers of both the TPV and SWCV and negative anomalies below (Fig. 4c). However, the PV tendency component created by the horizontal gradient of diabatic heating was negative (positive) ahead of (within) the high-PV column (Fig. 4d), which partly offset the positive horizontal PV advection (Fig. 4b). This made it clear that the TPV–SWCV coalescence resulted mostly from positive horizontal and vertical PV advection ahead of the high-PV column as well as the low-level PV generation by the nonuniform vertical diabatic heating, which also explain the rapid eastward movement of the TPV after 0000 UTC 30 June as shown in Fig. 3c.

      The PV budget diagnoses (Figs. 4fj) for the TPV–SWCV re-separation stage around 0900 UTC 30 June show that the net positive tendency in the middle-upper troposphere (Fig. 4f) over the western MLY key region (around 115°E) similarly resulted from the middle-upper tropospheric positive horizontal PV advection (Fig. 7g), while negative PV advection dominated in lower troposphere due to intense southerlies ahead of the SWCV transporting negative PV anomalies northward (this type of southerlies can be seen in Fig. 1g). This occurs because of atmospheric PV being spatially distributed with high values in the north and low values in the south (not shown). However, the net positive PV tendency in the lower troposphere (Fig. 4f) responsible for the intensification of the local SWCV was ascribed to the PV generation by nonuniform vertical diabatic heating (Fig. 4j). Note that the diabatic heating-generated PV component within 400–700 hPa (Fig. 4j) was completely offset by negative vertical PV advection (Fig. 4h). Thus, the TPV was then re-separated from the low-level SWCV due to the dominating horizontal PV advection (Fig. 3d). In fact, moderate rainfall over the MLY key region happened to begin after 0600 UTC 30 June, with the most intense rainfall concentrating from 0900 UTC 30 June to 1200 UTC 1 July (Fig. 2a). These facts reinforce the importance of the coalescence of the TPV with SWCV and their subsequent re-separation for the extreme rainfall event.

    5.   Evolution of different $ \omega $ components in relation to PV
    • As shown in Fig. 3, the development of ascending motion over the MLY key region depended closely on the evolution of the vertically eastward-tilted high-PV distribution after the TPV–SWCV coalescence. To reveal the dynamical mechanisms from PV forcing for ascending motion occurrences before and during the extreme rainfall event, the different components of vertical motion were recalculated based on Eqs. (2) to (5). Note in Figs. 1a1d that the TPV was mostly embedded in the 500-hPa trough as part of a synoptic-scale disturbance, with the SWCV being incorporated with the 700-hPa synoptic-scale trough (Figs. 1g and 1h). Therefore, such decompositions of the vertical velocity in a quasigeostrophic framework were suitable for the TPV- and SWCV-merged synoptic-scale process. Figure 5 displays pressure–time cross sections of area-averaged total vertical velocity $ \omega $, its recalculated components $ {\omega }_{\rm{ID}} $, $ {\omega }_{\rm{IG}} $, $ {\omega }_{Q} $, and resultant rainfall over the ESB region and the MLY key region (cf. Figs. 1c and 1g). Note in Figs. 5a15a2 that for each of the two regions, the strong ascending motion indicated by blue shading was consistent with that denoted by dashed contours, suggesting that the total vertical velocity represented by the sum of the three recalculated components agreed well with what was provided by the MERRA-2 reanalysis data. Note also that the duration of strong ascending motion (Figs. 5a15a2) corresponded well to that of significant rainfall (Figs. 5e15e2) for the two regions.

      Figure 5.  Pressure–time cross sections of area-averaged (a1–a2) MERRA-2 data-provided vertical velocity ($ {\omega }_{\rm{rea}} $, contours; units: Pa s−1) along with the sum ($ {\omega }_{\rm{total}} $, color shading; units: Pa s−1) of recalculated vertical velocity components $ {\omega }_{\rm{ID}} $, $ {\omega }_{\rm{IG}} $, and $ {\omega }_{Q} $, (b1–b2) $ {\omega }_{\rm{ID}} $ (color shading; units: Pa s−1), (c1–c2) $ {\omega }_{\rm{IG}} $ (color shading; units: Pa s−1; green contours refer to its zonal component $ {\omega }_{{\rm{I}}{\rm{G}}-x} $, while red contours refer to its meridional component $ {\omega }_{{\rm{I}}{\rm{G}}-y} $, only the magnitude equal to 0.05 or −0.05 Pa s−1 is plotted for each component of $ {\omega }_{\rm{IG}} $), (d1–d2) $ {\omega }_{Q} $ (color shading; units: Pa s−1), and (e1–e2) area-averaged rainfall rate (bars; units: mm h−1) together with area-averaged magnitude of vertically integrated (1000–300 hPa) water vapor flux (IWVF; black lines; units: 102 kg m−1 s−1) over (a1–e1) ESB region, and (a2–e2) MLY key region, respectively. The abscissa refers to Coordinated Universal Time (UTC).

      As discussed in the previous sections, the interaction of the TPV and SWCV exerts great effect on the downstream circulation. Such a downstream effect of the merged TPV–SWCV system can be understood according to the spatiotemporal evolutions of the vertical velocity components. Note in Figs. 5b15b2 and 5c15c2 that ascending $ {\omega }_{\rm{IG}} $ basically occurred in the middle and upper troposphere, while ascending $ {\omega }_{\rm{ID}} $ was mainly concentrated in the lower troposphere. Therefore, a contrastive evolution of different vertical velocity components on 300 hPa and 700 hPa over the ESB region and the MLY key region occurred, as shown in Fig. 6. Over the ESB region, apparent zonal $ {\omega }_{\rm{IG}} $ equal to −0.15 Pa s−1 is observed in the middle and upper troposphere earlier than 1800 UTC 29 June (Fig. 5c1 and Fig. 6a), which corresponds to the ascending motion along the sloping isentropic surface within and ahead of the eastward-titled high-PV column around 300 hPa (Fig. 3a). Under sufficient water vapor supply (Fig. 5e1), this ascending $ {\omega }_{\rm{IG}} $ indeed produced considerable rainfall at least greater than 1 mm h−1 over the ESB region (Fig. 5e1). In turn, the rainfall-released latent heating generated ascending $ {\omega }_{Q} $ in the upper troposphere immediately (Figs. 5d1 and Fig. 6a). On the other hand, the ascending $ {\omega }_{\rm{ID}} $ appeared in the lower troposphere after 0900 UTC 29 June (Fig. 5b1 and Fig. 6b). To examine the forcing factors for the low-level ascending $ {\omega }_{\rm{ID}} $, Fig. 7 shows the temporal evolutions of the area-averaged 700-hPa $ {\omega }_{\rm{ID}} $ and forcing terms based on Eq. (10) over each of the two target regions. For the ESB region (Fig. 7a), the ascending $ {\omega }_{\rm{ID}} $ from 0900 UTC to 1800 UTC 29 June (Fig. 6b) was largely induced by a positive vertical gradient of horizontal PV advection (Fig. 7a), with partial contribution from the diabatic heating. The combination of $ {\omega }_{\rm{IG}} $, $ {\omega }_{\rm{ID}} $, and $ {\omega }_{Q} $ indeed facilitated the local rainfall to increase after 1800 UTC 29 June (Fig. 5e1). As the rainfall intensity increased (Fig. 5e1), $ {\omega }_{Q} $ became stronger, forming a positive feedback between rainfall and $ {\omega }_{Q} $ (Figs. 5d1 and 5e1). Therefore, $ {\omega }_{Q} $ predominated the rest of the rainfall process over the ESB region after 2100 UTC 29 June (Figs. 6a and 6b) with an extremely strong intensity greater than −0.6 Pa s−1. However, according to Eq. (5), the rainfall-released condensation latent heating in turn acted as a feedback forcing to dominate the subsequent variation of local $ {\omega }_{\rm{ID}} $. This is reflected by the significant weakening of the ascending $ {\omega }_{\rm{ID}} $ at the 700 hPa level, which was due to enhanced diabatic heating forcing during the middle and later parts (1800 UTC 29 June to 1800 UTC 30 June) of the local rainfall event (Fig. 7a). Thus, strong feedback of the diabatic heating resulted in a shallow ascending $ {\omega }_{\rm{ID}} $, mainly concentrated between 500 hPa and 700 hPa over the ESB region (Fig. 5b1).

      Figure 6.  Evolutions of area-averaged vertical velocity (ω; black curve; units: Pa s−1) and its components $ {\omega }_{\rm{ID}} $ (green curve; units: Pa s−1), $ {\omega }_{\rm{IG}} $ (red curve; units: Pa s−1), and $ {\omega }_{Q} $ (blue curve; units: Pa s−1) over the ESB region at (a) 300 hPa and (b) 700 hPa. (c) and (d) same as (a) and (b), but for the MLY key region. The omega components contributing to local rainfall are shaded. The abscissa refers to Coordinated Universal Time (UTC).

      Figure 7.  Same as Fig. 6, but for the area-averaged $ {\omega }_{\rm{ID}} $ (dashed green curve; units: Pa s−1) and its dynamical forcing term of PV advection (−F1, dotted black curve; units: 10−17 Pa−1 s−3) and thermodynamic forcing term of diabatic heating (−F2, dashed black curve; units: 10−17 Pa−1 s−3) at 700 hPa over (a) ESB region and (b) MLY key region according to Eq. (10). The abscissa refers to Coordinated Universal Time (UTC).

      Figure 8.  Schematic diagram showing the 2016 MLY extreme rainfall event stages with the TPV and/or SWCV (cyclonic arrows) behavior and concomitant variations in PV (arbitrary polygons indicated by black solid or dashed curves represent the high PV equal to 1 PVU), vertical motion (upward arrows denote ascending motion and downward arrows signify descending motion) along the isentropic surfaces (concave-downward and convex-upward solid blue curves), and diabatic heating (red shading). The dashed curves denote the distribution of PV (dashed black lines) and isentropes (dashed blue lines) in the next moment. Red (black) parallelograms denote the MLY key region (ESB region). Vertical cross sections are averaged between 30°–32°N across the central key region. The gray shading shows the range and height of the Tibetan Plateau with terrain altitude greater than 1500 m. (a) Stage for the TPV moving off the TP in conjunction with the development of the SWCV. (b) Stage for the TPV coalescing with the SWCV over the ESB region to trigger upper-tropospheric ascending motion and to enhance lower-tropospheric convergent water vapor flux over the downstream MLY key region. (c) Stage for the MLY extreme rainfall peak, during which the TPV was re-separated from the SWCV to generate the strengthened water vapor flux and stronger ascending motion in terms of the lower-tropospheric isentropic-gliding vertical velocity ($ {\omega }_{\rm{IG}} $) and diabatic heating-related vertical velocity ($ {\omega }_{Q} $) over the MLY key region. (d) Stage for the extreme rainfall weakening, during which the TPV disappeared and the SWCV decayed.

      More importantly, because the middle tropospheric air temperature was increasing due to rainfall-released condensation latent heating, the isentropic surfaces became more concave over the ESB region, leading to more sloping isentropic surfaces prevailing over the downstream key region, as illustrated in Fig. 3b. However, prior to the coalescence of the TPV and SWCV, the northwesterlies dominated the middle and upper troposphere over the key region (cf. Fig. 1b). Due to the sloping meridional distribution of isentropic surfaces (not shown), the meridional component of such northwesterlies could have induced descending $ {\omega }_{\rm{IG}} $ in the upper troposphere before 2100 UTC 29 June (red solid lines in Fig. 5c2), which offset the zonal ascending $ {\omega }_{\rm{IG}} $ (dashed green lines) to a great extent. After the TPV exited the TP, the downstream flow experienced a rapid redistribution (Fig. 1c) in which the northwesterlies were replaced by southwesterlies that induced stronger zonal ascending $ {\omega }_{\rm{IG}} $ over the key region (Fig. 5c2). As such, ascending $ {\omega }_{\rm{IG}} $ similarly appeared first in the upper troposphere over the key region at 2100 UTC 29 June (Figs. 5c2 and 6c).

      As discussed above, the ascending $ {\omega }_{\rm{IG}} $ would certainly trigger the development of $ {\omega }_{Q} $ over the MLY key region in the upper troposphere at 0000 UTC 30 June (Fig. 5d2 and Fig. 6c) with the gradually reinforced water vapor flux (Fig. 5e2). Note that the subsequent diabatic heating release in the upper troposphere exerted great feedback on $ {\omega }_{\rm{ID}} $, with descending $ {\omega }_{\rm{ID}} $ in the upper troposphere and ascending $ {\omega }_{\rm{ID}} $ below (Fig. 5b2). This can be demonstrated by the forcing terms for the lower tropospheric ascending $ {\omega }_{\rm{ID}} $ around 0600 UTC 30 June over the key region (Figs. 6d and 7b), with the contribution of diabatic heating to $ {\omega }_{\rm{ID}} $ predominating over that of the vertical gradient of PV advection (Fig. 7b). At the same time, the TPV merged with the SWCV at 0600 UTC 30 June, and ascending $ {\omega }_{\rm{IG}} $ prevailed throughout the entire middle and upper troposphere from 200 hPa to 600 hPa (Fig. 5c2). As a result, ascending $ {\omega }_{Q} $ also deepened immediately (Fig. 5d2) in response to the latent heat release caused by the enhanced vertical motion (Fig. 5a2). On the other hand, after the re-separation of the TPV and SWCV, the vertical configuration of rainfall-related diabatic heating continually manufactured considerable positive PV over the key region in the lower troposphere (as discussed in section 4), which resulted in slightly convex isentropic surfaces below the PV center (Fig. 3e). Thus, strong southerlies led air parcels to glide upward along the isentropic surfaces, as manifested by evident meridional ascending $ {\omega }_{\rm{IG}} $ in the lower troposphere afterwards (red dashed lines in Fig. 5c2). The lower tropospheric ascending motion promoted the rapid development of $ {\omega }_{Q} $ (Fig. 6d), ultimately resulting in the subsequent extreme rainfall event due to drastic ascending motion in the entire troposphere (Fig. 5a2) with increased water vapor supply (Fig. 5e2) driven by the LLJ (Fig. 1h). To understand the relative importance of dynamical and thermodynamical contributions to local ascending motion, different components ($ {\omega }_{\rm{IG}} $, $ {\omega }_{\rm{ID}} $, and $ {\omega }_{Q} $) of total vertical velocity ($ \omega $) in the middle troposphere (averaged between 300–700 hPa) are calculated for the peak of the extreme rainfall event over the MLY from 0900 UTC 30 June to 0300 UTC 1 July (Fig. 5e2). $ {\omega }_{Q} $ was noted to contribute 93% to total ascending motion, indicating that the thermodynamical effect played a dominant role. The next largest contributor, the $ {\omega }_{\rm{IG}} $-related dynamic process, contributed 11% to the total ascending motion. However, $ {\omega }_{\rm{ID}} $ reflected descent, contributing −5% to the total ascending motion.

      However, the extreme ascending $ {\omega }_{Q} $ and rainfall were weakened by some internal factors. For the decaying episode (after 0600 UTC 30 June) of the rainfall process over the ESB region (Fig. 5e1), the zonal component of $ {\omega }_{\rm{IG}} $ exhibited significant descending motion in the middle and upper troposphere (Fig. 5c1), which partially counteracted ascending $ {\omega }_{Q} $ (Fig. 5d1) to weaken the total ascending motion (Fig. 5a1). This was mainly because the isentropic surfaces became downsloping behind the eastward-moving TPV, leading air parcels to migrate eastward and downward. Although water vapor was still sufficient (Fig. 5e1), reduced ascending motion (Fig. 5a1) resulted in the rainfall gradually decreasing (Fig. 5e1). The descending motion (Fig. 5a1) also weakened the SWCV (Fig. 3f), directly influencing the direction and intensity of water vapor flux in the LLJ towards the MLY key region. As a result, the water vapor flux over the key region began to decrease after 2100 UTC 30 June (Fig. 5e2). As the eastward movement of the TPV resulted in descending $ {\omega }_{\rm{IG}} $ over the key region in upper troposphere (Fig. 5c2), the ascending $ {\omega }_{Q} $ was considerably reduced (Fig. 5d2). Thus, the rainfall over the MLY key region decayed dramatically, with the intensity decreasing to around 1 mm h−1 after 1500 UTC 1 July (Fig. 5e2).

    6.   Summary and discussion
    • During the summer of 2016, a long-lasting rainfall episode occurred from 30 June to 6 July over the MLY key region, leading to locally devastating floods. Within this long-lasting episode, the most intense rainfall arose during the first stage (30 June–1 July 2016), which was strongly affected upstream by both the midtropospheric TPV and the lower-tropospheric SWCV. Therefore, the present study focuses on the first stage as an extreme MLY rainfall event, examining the dynamical mechanism for the occurrence and evolution of the event through PV diagnostics and omega decompositions. Large-scale circulation evolutions demonstrated that although the SWCV was generated later than the TPV, their subsequent coalescence and re-separation played an important role in generating the extreme rainfall event. Thus, the physical processes for the TPV activities and its interactions with the SWCV as well as their relative contributions to the event can be understood from four distinct stages as shown in Fig. 8, including how the TPV-related PV advection affected the vertical velocity and how the merged and re-separated TPV–SWCV system facilitated the LLJ-related moisture transport and even stronger ascending motion over the downstream MLY. The major findings are summarized as follows:

      Before the extreme rainfall event, the TPV was initially formed within a 500-hPa geopotential height trough over the northwestern TP around 1800 UTC 27 June and then migrated eastward, which resulted in the large amplification of the downstream meridional disturbance. When the moving TPV arrived at the eastern slope of the TP, it manifested as a slightly eastward-tilted high-PV column. Considerable ascending motion was induced ahead by a positive vertical gradient of horizontal PV advection created by the TPV-related high PV, giving rise to moderate rainfall locally and resultant diabatic latent heating, which also facilitated the development of the SWCV over the ESB region (Fig. 8a). Because the SWCV-related nonuniform vertical diabatic heating was also conducive to PV generation in the lower troposphere (as diagnosed by the PV budget), the SWCV-related low-level PV generation together with the TPV-related midtropospheric PV advection favored these two vortexes to coalesce vertically around 0600 UTC 30 June (Fig. 8b). The merged TPV–SWCV acted as a high-PV forcing feature and caused the middle-upper tropospheric isentropic surfaces to become concave downward over the ESB region. This enabled the airmass to glide along the upward-sloping isentropic surfaces over the MLY key region, generating the strong isentropic-gliding ascending motion ($ {\omega }_{\rm{IG}} $). At the same time, the enhanced SWCV as a part of the merged TPV–SWCV system led to an increase in the pressure gradient between it and the WPSH. Thus, the lower-tropospheric southwesterly LLJ was enhanced and able to increase water vapor flux towards the MLY key region (Fig. 8b), enabling locally heavy rainfall.

      Because the PV generation caused by the nonuniform diabatic heating in middle-upper troposphere was mostly offset by negative vertical PV advection, the net positive tendency in the middle-upper troposphere over the western MLY key region largely resulted from the positive horizontal PV advection, while negative PV advection was dominant in the lower troposphere due to intense southerlies in front of the SWCV transporting negative PV anomalies northward. Consequently, the TPV was re-separated from the low-level SWCV (Fig. 8c). The two re-separated high-PV systems favored even stronger isentropic gliding ($ {\omega }_{\rm{IG}} $) and diabatic heating-generated ascending motion ($ {\omega }_{Q} $) over the MLY key region, thereby producing subsequent extreme rainfall. As the TPV continued to move eastward and decay (Fig. 8d), descending $ {\omega }_{\rm{IG}} $ behind the TPV occurred successively over the ESB region and then the key region, which significantly weakened the SWCV. The rainfall was then suppressed due to both the weakened ascending motion and water vapor supply. During the rainfall process, the isentropic-displacement ascending motion ($ {\omega }_{\rm{ID}} $) was largely affected by the feedback of the diabatic heating, thereby influencing the rainfall. It was the very positive cooperation between the TPV and SWCV that resulted in the extreme rainfall event over the MLY key region.

      It should be noted that the present study only analyzes how the internal PV forcing and diabatic heating affect the development and variation of atmospheric vertical ascent and the associated precipitation. The validity of the omega equation analysis in the paper depends on the conditions for the quasigeostrophic equations: small Rossby number and small static stability differences from a basic stratification that is a function of p only. Because these conditions are not strictly satisfied in the TPV case study, the results of the analysis should be viewed as a qualitative indication of the processes involved. Besides, how the boundary forcing influences the development and variation has not been touched upon and deserves further investigation. In addition to the extreme rainfall stage of 1200 UTC 30 June–1200 UTC 12 July that was mainly examined in the present study, the subperiod of 4–5 July experienced the second most intense rainfall within the long-lasting rainfall period from 30 June to 6 July over the MLY key region. Given that this long-lasting period of rainfall was actually a wet episode of a quasi-biweekly oscillation of the Yangtze rainfall in summer 2016 (Zhang et al., 2021), we will explore how and to what extent the quasi-biweekly disturbances affect the above synoptic-scale extreme rainfall events based on multiscale interactions in the future.

      Acknowledgements. The TRMM-based rainfall data are available at https://disc.gsfc.nasa.gov/datasets/TRMM_3B42_7/summary?keywords="3B42"%20"3%20hours". The MERRA-2 data were downloaded from https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/. This research was jointly supported by the National Natural Science Foundation of China (Grant Nos. 41730963 and 41876020) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB40000000). The authors are grateful to the anonymous reviewers for their valuable comments. Special thanks are due to Prof. B. J. HOSKINS for his enthusiastic discussions and instructive suggestions on the draft.ns on the draft.

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