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To examine the influence of the local geomorphology in Taizhou City, we chose σ = 0.954 (a height of about 400–500 m) as a representative level for nearsurface horizontal flow. Results show that the vortices are in good correspondence with the next 10minute hail fallout zone. Figure 9 shows the streamline and the convergence during the next 10minute accumulated hail precipitation at TT (the northern part of the Taizhou City). The next 10minute hail fallout zone moved as the mesoγ vortices shifted along the convergence line. At 0720 UTC (Fig. 9a), there was a persistent southwesterly flow existing at the south of the TT region. A convergence line (the red dashed line) was located at the north of the TT region. Besides, there had just been a flow confluence at the generation location of vortex “V1” (the red circle in Fig. 9a). Vortex “V1” first occurred at the west of Longxi at 0730 UTC (Fig. 9b). The convergence line (the red dashed line) at that time was still located at the north of the TT region. The simulated vortex and convergence line pattern are similar to those of the observed result (Fig. 3a). At 0740 UTC, the convergence line moved southward and merged with the mesoγ vortex. The convergence strength at the west of Longxi increased. “V1” was still stabilized at the west of Longxi (Fig. 9c), which was also at the bottom of valley and similar to observed mesoγ vortex, and was accompanied by a convergence center. The next 10minute accumulated hail precipitation amount showed that the hail fallout zone was strongly correlated with “V1.” With the movement of the convective systems, the convergence also continued to shift southeastward. At 0750 UTC, “V1” moved to Longxi (Fig. 9d) and was accompanied by a convergence increase. In addition, it was followed by the next 10minute hail precipitation amount center. Then, “V1” started to fade, and another vortex “V2” formed at its eastern strong convergence zone at 0800 UTC (Fig. 9e). The vorticity intensity of “V2” exceeded 1 × 10^{−3} s^{−1}. The hail fallout zone at the next 10 minutes of 0800 UTC showed that the second hail precipitation amount center was located at the location of “V2.” Subsequently, “V2” moved northeastward, in accordance with the northeastward movement of the hail fallout zone (figure not shown).
Figure 9. Wind streamlines at σ = 0.954, the amount of hail accumulated over next 10 minutes (mm; rainbow colormap), surface convergence field (× 10^{−4} s^{−1}; blue colormap), and terrain elevations (yellow colormap; same as Figs. 2, 3, 7; omitted here). (a) 0720 UTC, (b) 0730 UTC, (c) 0740 UTC, (d) 0750 UTC, and (e) 0800 UTC. The letters denote the names of the mesonet stations. The red dashed line in (a) and (b) indicates the convergence line. The rectangular box in (b) indicates the area covered by the flow region in Fig. 12. M–N in (c) indicates the crosssection location of Fig. 13.
To better examine the evolution of the nearsurface vortices, we chose the “V1” vortex as a representative sample. The time–height series of “V1” (Fig. 10) described the average of 9point (3 km × 3 km) center of the vortex (we defined the vortex center according to the streamline at σ = 0.954). Figure 10a shows the change of vorticity and divergence at the initial region. The above analysis showed that “V1” initially formed at 0730 UTC. The result suggested that positive vorticity existed before convergence. Although there was no obvious vortex existing in the streamline field, the positive vorticity already existed. At 0640 UTC, there was no storm occurring near the TT region. The positive vorticity center existed at 0700–0710 UTC. After the occurrence of the positive vorticity center, a convergence center was generated. Figure 10b shows the elements at the vortex center, which indicates the evolution of vortex. At the onset stage of the vortex, positive vorticity originated at the near surface, which indicated that the nearsurface vortex was derived from the nearsurface flow. Gradually, the positive vorticity center extended upward, and negative vorticity appeared after 0800 UTC. As shown in Fig. 9, “V1” started to fade at 0810 UTC at the level of σ = 0.954 (the third level), which is mutual agreement with this time–height plot. The convergence field shows that the vortex formed in the convergence zone. After “V1” appeared, the convergence increased significantly, and the maximum convergence reached −3.6 × 10^{−3} s^{−1}. During the “V1” fading period, the convergence decreased. Obviously, the relationship between the vorticity and the divergence field reflected a feedback mechanism between vorticity and convergence.
Figure 10. Time–height plots. Vorticity (× 10^{−4} s^{−1}; shaded) and divergence (× 10^{−4} s^{−1}; contour) (a) at the vortex initial region, and (b) of the mesoγ vortex.
To further examine the physical processes responsible for the development of the vortex, the budget of vertical vorticity is a favored approach (e.g., Zhang, 1992; Knievel and Johnson, 2003; Wang et al., 2016). The vertical vorticity equation can be written as follows:
$$\frac{{\partial {\rm{\zeta }}}}{{\partial t}} \!=\!  \left({u\frac{{\partial {\rm{\zeta }}}}{{\partial x}} \!+\! v\frac{{\partial {\rm{\zeta }}}}{{\partial y}}} \right)  \left({w\frac{{\partial {\rm{\zeta }}}}{{\partial z}}} \right)  {\rm{\zeta }}\left({\frac{{\partial u}}{{\partial x}} \!+\! \frac{{\partial v}}{{\partial y}}} \right) \!+\! \left({\frac{{\partial w}}{{\partial x}}\frac{{\partial v}}{{\partial z}}  \frac{{\partial w}}{{\partial y}}\frac{{\partial u}}{{\partial z}}} \right),$$ (1) where u, v, and w are the wind components, and ζ is the vertical vorticity (
${\rm{\zeta }} = \partial v/\partial x  \partial u/\partial y$ ). The terms on the righthand side of Eq. (1) represent vorticity changes due to horizontal advection, vertical advection, stretching, and tilting, respectively. The lefthand side of Eq. (1) indicates the change in the vertical vorticity. Based on the foregoing analysis, “V1” originated along the convergence line; therefore, the vertical stretching of the vorticity on “V1” must have played an important role in its genesis. Moreover, the conjunction of the outflow of the severe convective storm and the topographic convergence line may have acted to tilt the vortex line so that the tilting generation of the vorticity was also important. Vorticity budget analysis illustrated that the vertical vorticity tilting and stretching are significant factors for the generation of mesoγ vortices (e.g., Trier et al., 1997; Kosiba et al., 2013; Markowski and Richardson, 2017). The results of the vorticity budget (Fig. 11) also show that the stretching (Fig. 11c) and tilting (Fig. 11d) terms were more important than the others (Figs. 11a, b), particularly at low levels. The accuracy of the vorticity budget was examined by comparing the value of the sum of the terms on the righthand side of Eq. (1) (Fig. 11e) and the tendency of local relative vorticity (Fig. 11f). These two factors were similar. The residual of the local relative vorticity and the sum of the terms on the righthand side (Fig. 11g) suggest that the residual term exhibited two weak positive centers at 0750 and 0800 UTC. The residual term is complex; it includes the numerical error, frictional effect term, and so on. Xu et al. (2015) treated the residual term as the frictional effect term. They found that the surface drag was important for mesovortex genesis. In this case, the center at 0750 UTC probably contained the frictional effect. It was more likely that the other center was the numerical error. As the position of this center was high, the effect of surface drag should be very weak. It was also reasonable that the numerical error increased with the increasing calculation time. However, the residual term was small compared with the stretching and tilting terms. Therefore, it was not given considerable attention. The analysis of the vorticity budget also indicated that the stretching and tilting effects were dominant in our case (compared to the contributions of the horizontal advection and vertical advection). At the onset stage (0730 UTC), stretching was a major factor in the generation of the lowlevel vortex, whereas tilting had a weak negative effect. “V1” formed in a convergence region, and the depth of the convergence region was over 2 km; therefore, it was possible that stretching played an important role at the onset stage of the mesoγ vortex. However, the skewT plot (Fig. 8a) indicates that the near surface wind and vertical wind shear were very weak and that lowlevel updraft near the surface (Fig. 12a) was small. These factors indicated that tilting was not important at the onset stage. During the development stage of the vortex, stretching maintained a positive contribution to the vortex. The positive stretching center had good correspondence with the lowlevel positive vorticity center; this indicated that stretching was a key factor in the life span of this vortex. The positive contribution of the tilting effect mostly occurred at the stage of positive vorticity development upward (after 0750 UTC), when the updraft increased obviously. This indicated that the storm might help tilt the vortex line and help the vortex develop upward. In addition, at a relatively high level (above the 0.74 km), both the stretching term and the tilting term provided a positive contribution to help develop positive vorticity.Figure 11. Time–height plots of the terms in the vorticity budget Eq. (1). (a) Horizontal advection term, (b) vertical advection term, (c) stretching term, (d) tilting term, (e) the sum of terms on the righthand side of Eq. (1), (f) change of vertical vorticity, and (g) the residual term (× 10^{−6} s^{−2}; shaded).
Figure 12. The threedimensional (3D) perspective from southerly or southwesterly flow of the “V1” vortex. (a) 0730 UTC and (b) 0750 UTC. The blue and red tubes indicate the flow directions. The flows are from the blue tubes to the red tubes. The greenshaded region denotes the updraft region, and the redshaded region denotes the downdraft region.

The evolution of the 3D flow was shown in Fig. 12, and we used this to indicate the variations of u, v, and w. The display region of this 3D flow was depicted by the black box in Fig. 9b. Figure 12a shows the 3D flow, which was at the center of vortex “V1” in TT at 0730 UTC. According to the horizontal streamline analysis at that time (Fig. 9), “V1” was at the bottom of the valley and had not merged with the convergence line caused by the severe convective system. As shown in Fig. 12a, there was an obvious turbulence near the surface; however, the intensity of updraft was not strong. After 10 min, there was a significant updraft of all the parcels at the center of “V1,” which indicated that the existence of the lowlevel vortex enhanced the local updraft. At that time, “V1” and the northern convergence line merged, and the vorticity of “V1” increased. The 3D flow indicated that these parcels were initiated by over mountain flows and the outflow from the storm along the nearsurface convergence line. The lowlevel vortex then formed more completely. At 0750 UTC (Fig. 12b), the flow rotated and ascended simultaneously. The updraft showed a pronounced enhancement. In the meantime, followed by hailshooting, there was a downdraft zone at the hailshooting zone (the redshaded region).

To analyze the vertical structure of “V1” and the relevant convective cell, we plotted the crosssection along M–N (Fig. 9c). As shown in Fig. 13a, the nearsurface mesoγ vortex “V1” was located near the strong echo wall, the nearsurface flows (the cold outflow from the convective system and the warm easterly flow) converged over “V1,” and a strong updraft was tilted to the convective system reaching its top. A WER existed in association with “V1.” According to the abovementioned analysis, the existence of “V1” may help enhance the updraft. The maximum reflectivity to the west of the WER exceeded 50 dBZ and extended to the ground. Another strong echo center of 42 dBZ appeared aloft between 6 and 12km altitude and extended to the overhang. The overhang was prominent, and a roll circulation occurred in the overhang region, allowing the external airflow to be well mixed with the airflow in the convective system. The divergence field along the crosssection (Fig. 13b) shows an obvious convergence region over “V1”; the maximum convergence exceeded −2 × 10^{−3} s^{−1}. Moreover, a divergence region was observed at the top of the convective system. This pattern of lowlevel convergence and upperlevel divergence could help to promote the development of the storm system. The potential temperature crosssection (Fig. 13c) showed that “V1” was located in the high potential temperature region, which contained high levels of unstable energy. This high potential temperature region corresponded to the strong convergence region and the strong echo region. In addition, the heights of 0 and −20°C isothermal lines were appropriate for hail. Under the promotion of powerful updraft, graupel was found to be broadly and horizontally widespread between the 0°C isothermal line and the top of the convective cloud. The hailmixing ratio was mainly located in the strong updraft region in front of the strong echo column. This strong updraft contributed to maintenance of the growth of the hailstones.
Figure 13. Vertical crosssections along “M–N” shown in Fig. 9c. (a) Radar reflectivity (dBZ; shaded) and winds (arrows denote the composition of along the crosssectional wind and the vertical wind); (b) divergence (× 10^{−4} s^{−1}; shaded), velocity (m s^{−1}; contour), and winds (arrows denote the composition of along the crosssectional wind and the vertical wind); and (c) potential temperature (K; shaded), graupel mixing ratio (g kg^{−1}; contour with red lines), hailmixing ratio (g kg^{−1}; contour with green lines), and the thin black lines represent the isotherm lines of −20 and 0°C. The red star indicates the location of the mesoγ vortex.