PV Perspective of Impacts on Downstream Extreme Rainfall Event of a Tibetan Plateau Vortex Collabora

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2. Data and methods

2.1. Data

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2.1. Data

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.

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2.2. Methods

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2.2. Methods

2.2.1. Identification for the TPV and SWCV

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2.2.1. Identification for the TPV and SWCV

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.

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2.2.2. PV equation

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2.2.2. PV equation

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.

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2.2.3. Vertical motion decomposition

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2.2.3. Vertical motion decomposition

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:

Figure3. 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

3.1. Middle and lower tropospheric flow configurations

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3.1. Middle and lower tropospheric flow configurations

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).

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3.2. Dynamical and thermodynamical conditions before and during the extreme rainfall event

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3.2. Dynamical and thermodynamical conditions before and during the extreme rainfall event

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 (θ_e > 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. 1a–d. 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 (θ_e 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

4.1. PV evolution associated with the TPV and SWCV

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4.1. PV evolution associated with the TPV and 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. 3d–f), 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.

Figure4. 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.

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4.2. Quantitative PV diagnosis

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4.2. Quantitative PV diagnosis

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. 4f–j) 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.