Case study on the formation of a torrential‐rainfall‐producing southwest vortex: Backward trajectory analyses and sensitivity simulations

The southwest vortices (SWVs) are a unique type of mesoscale vortex that frequently induce torrential rainfall in China. In this study, we focused a long‐lived quasi‐stationary SWV, which was the primary system for producing an extremely heavy rainstorm within/around Sichuan (the maximum hourly precipitation was ~103.8 mm) in Mid July 2021. After reproduced the SWV's formation by using Weather Research and Forecasting model, we conducted trajectory analyses and topography sensitivity simulations to understand the effects of complicated topography on the vortex's formation. It is found that, the regions south and southwest of the SWV acted as the most important source regions for the air clusters that formed the SWV (proportion ≥ 65%), and the air clusters originated from the upper layer contributed the most (≥60%). Of these, the air clusters sourced from the upper layer southwest and south of the SWV played the most important role in the SWV's formation, as their increase in cyclonic vorticity and their contributions to trajectory number and vorticity were all much larger than those of the others. Sensitivity simulations indicated that, detailed topography features around the Sichuan Basin were crucial in determining the structure, intensity and precipitation of the SWV, whereas, the topography features were not a decisive factor for the SWV's formation. In summary, our findings are useful to enrich the current understanding of the SWVs' formation, which would be helpful to improve the related forecasts.

Numbers: 42075002, U20A2097; Innovation Team Fund of Southwest Regional Meteorological Center, China Meteorological Administration, Grant/Award Number: XNQYCXTD-202202; Open Grants of the State Key Laboratory of Severe Weather, Grant/Award Number: 2021LASW-A06; Fund of Heavy Rain and Drought-Flood Disasters in Plateau and Basin Key Laboratory of Sichuan Province, Grant/Award Number: SZKT202001

| INTRODUCTION
Under global warming, torrential rainfall shows increasing trends in its intensity and frequency, resulting in huge economic losses worldwide (IPCC, 2023;Tradowsky et al., 2023).Torrential rainfall is one of the most important natural disasters in China (Song, 2018), which causes huge economic losses every year.Due to their great impacts, torrential rainfall events had formed a research focus for decades (Luo et al., 2020).Numerous previous studies had confirmed that, the mesoscale vortices (Fu et al., 2020) played a crucial role in inducing torrential rainfall events in China (Cheng et al., 2016;Fu et al., 2022;Li & Deng, 2013;Tao, 1980;Zhao et al., 2004).Over the Yangtze River, there are a total of three source regions for mesoscale vortices (Feng et al., 2019;Fu et al., 2022;Zhang et al., 2015).Of these, the mesoscale vortices formed around the Sichuan Basin were defined as the southwest vortices (SWVs; Lu, 1986).The SWVs are a unique type of vortex in China (in terms of source regions, formation/evolution mechanisms and structures), with their generation and evolution comprehensively affected by the topographies of the Tibetan Plateau and Sichuan Basin (Wang & Tan, 2014).According to statistics, in terms of the intensity, frequency and coverage area of precipitation, the SWVs are second only to typhoon and residual low pressure, ranking second in importance (Li et al., 2021).
Southwest China (Sichuan Province and surrounding regions; Figure 1a) is one of the most densely populated areas in the world.Under a warming climate, the SWVs pose a more serious threat to this region.For instance, in 2020 summer, the SWVs were abnormally active, which caused the highest precipitation in the past 70 years within/around Sichuan Basin (Fu et al., 2021).Therefore, improving the forecasts of the SWVs is of great importance.However, as the SWVs mainly form around the Sichuan Basin, which is located east of the Tibetan Plateau (Figure 1a), complicated topographies exert notable effects on the SWVs' formation.This makes forecasting the SWVs challenging (Li, 2021).To this end, a few studies (they are limited in number) were conducted to clarify the effects from the complicated topography on SWVs' formation.For instance, Wang and Tan (2014) pointed out that, the Hengduan mountain (southeast of the Tibetan Plateau) generated a vorticity stream by turning the southwesterly wind, and the Sichuan Basin enhanced the second vorticity stream by stretching and tilting the airflow sourced over the Tibetan Plateau.The merging of the two vorticity streams contributed to the SWV's formation.Yang et al. (2023) found that, the Yunnan-Guizhou Plateau played an important role in the SWV's formation, as the air clusters mainly enhanced in their cyclonic vorticity and convergence as they descended along the topography of the plateau, both of which were favorable for the SWV's formation.As the mentioned above show, for different types of SWVs, the effects from topography were notably different.As there are various types of SWVs, which differ from each other remarkably in their precipitation intensity, life span, displacement, and structure (Feng et al., 2016;Fu et al., 2015;Fu et al., 2014;Lu, 1986;Yu & Gao, 2017;Zhang et al., 2019), to reach a more comprehensive understanding of the effects from the complicated topography on SWVs' formation requires more case studies.
From July 14, 2021 to July 16, 2021, under the joint influences of a low-level shear line and a SWV, Sichuan Basin experienced an eye-catching torrential rainfall event (Figure 1c), during which an hourly precipitation peak of 103.8 mm appeared in Guangyuan City.This event had resulted in serious economic losses and notable social impacts.The SWV in this event was belonged to the quasi-stationary type (Fu et al., 2014), which accounted for the largest proportion among all SWV types (Feng et al., 2016).In order to enrich the current understanding of the SWVs, the primary scientific purpose of this study was to investigate the effects of the complicated topography within/around Sichuan Basin on the formation of the SWV during the torrential rainfall event.The remainder of the present article is structured shows the domain (shading; m) for the simulation.Panel (b) illustrates the simulated 36-h accumulated precipitation (shading; mm).Panel (c) is the same as (b) but for the station observation."A," "B," and "C" mark the rain bands in the simulation, and "a," "b," and "b" mark the rain bands in the observation.Panel (d) shows the simulated geopotential height at 500 hPa (blue contour; gpm) and 700 hPa (shading; gpm) 12 h before the SWV's formation, where the thick dashed black line represents the trough line of the 500-hPa trough, and the thick dashed brown line denotes the trough line of the 700-hPa trough.Panel (e) is the same as (d) but for the ERA5 reanalysis data.The shading area over the Tibetan Plateau (i.e., the white region in panel (d)) should be ignored as it is the extrapolation data from the ERA5 model.
as follows: Section 2 shows the data and methods used in this paper; Section 3 presents an overview of the event and simulation validation; Section 4 provides detailed results of the trajectory analyses and sensitivity simulations; and finally, a conclusion and discussion is reached in Section 5.

| Data
The hourly station observational precipitation data from the China Meteorological Administration (CMA) was used to analyze the rainfall event and to validate the simulation results.The 12-h sounding data and hourly surface observational data were used for analysis nudging in the simulation (Skamarock et al., 2008).The hourly, 0.25 Â 0.25 ERA5 reanalysis dataset (Hersbach et al., 2020) provided by the European Centre for Medium-Range Weather Forecasts were used for synoptic analyses, simulation validation, and simulation.

| Model configuration
As the weather research and forecasting (WRF) model is skillful for forecasting heavy rainfall events (Alizadeh-Choobari, 2018;Alizadeh-Choobari & Gharaylou, 2017;Fu et al., 2019), in this study, we used WRF version 4.4.2(Skamarock et al., 2008) to simulate the torrential rainfall event.Initial and boundary conditions were derived from the ERA5 reanalysis dataset with a 0.25 Â 0.25 spatial resolution and an hourly temporal resolution.We also used the soundings and hourly surface observations for analysis nudging (Skamarock et al., 2008).Only one domain (Figure 1a), which covered both the central and southern sections of China, was used in the simulation.The horizontal resolution of the domain was 3 km, with a total of 999 Â 900 grids.There were 51 vertical levels in the simulation with the model top fixed at 50 hPa.The physical schemes used in the simulation included the WRF Single Moment six-class scheme (Hong & Lim, 2006) for microphysics, and the Yonsei State University scheme (Noh et al., 2001) for planetary boundary layer processes.The Noah land surface model (Skamarock et al., 2008), the Goddard shortwave radiation scheme (Chou & Suarez, 1999), and the RRTM longwave radiation scheme (Mlawer et al., 1997) were also employed in the simulation.The simulation was initiated at 0000 UTC July 14, 2021, and terminated at 0000 UTC July 17, 2021 (i.e., ran for a total of 72 h).The spin-up time was 6 h, and we did not consider the spatial spin-up in the analysis to minimize the edge effects.

| Trajectory analysis
We used the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model (Stein et al., 2015) for tracking the air clusters that formed the SWV at the time when the vortex formed.The HYSPLIT model was provided by the National Oceanic and Atmospheric Administration.It was a complete system for computing simple air parcel trajectories, as well as the associated complex transport, dispersion, chemical transformation, and deposition.In this event, the SWV formed at 1800 UTC July 15, 2021 (Section 3.1), which was defined as the formation time.According to 700-hPa stream field and vorticity associated with the SWV, a key region (28.5-31.5 o N, 102.5-106E; the purple box shown in Figure 2a) that mainly covered the central area of the vortex was determined.We divided the key region evenly with an interval of 0.1 .After removing the location that was located beneath the terrain, there was a total of 1072 air clusters (Figure 2d), which were used in the backward trajectory analyses.The backward tracking was initiated at 1800 UTC July 15, 2021 (i.e., the formation time) and run for 36 h to cover the whole formation stage of the SWV.In order to determine the main sources of the air clusters that formed the SWV, we determined nine subregions relative to the vortex's key region (purple lines in Figure 2c).In addition, relative to 700 hPa (around 3000 m), we divided the air column into three layers: lower layer (height < 2500 m), middle layer (2500 m ≤ height ≤ 3500 m), and upper layer (height > 3500 m).

| Overview of the event
From July 14, 2021 to July 16, 2021, under the joint influences of a low-level shear line and a SWV, a series of torrential rainfall events hit Sichuan Basin and surrounding regions (Figure 1c), and caused severe flash floods and urban waterlogging.Heavy precipitation mainly appeared in 12 cities (which were mainly located in northeast Sichuan Province): Guangyuan, Mianyang, Deyang, Ya'an, Meishan, Leshan, Bazhong, Nanchong, Suining, Ziyang, Neijiang, and Zigong.From 2000 UTC July 14, 2021 to 2000 UTC July 16, 2021, for Sichuan Province, there were 1132 observational stations with an accumulated precipitation of 50-99.9mm, 1044 stations with an accumulated precipitation of 100-249.9 mm, and 18 stations with an accumulated precipitation of 250 mm and above.Among them, there were three observational stations at which an accumulated precipitation of above 300 mm appeared (they were all located within Guangyuan City): Mengzi (332.8 mm), Zhongling (318.9 mm), and Yingcui (302.1 mm).Moreover, the maximum hourly precipitation during this event was 103.8 mm in Maoqiao (Guangyuan City), implying that this event was an extremely heavy rainstorm.
During the torrential rainfall event, a middle-level shortwave trough maintained east of the Tibetan Plateau (Figure 1d,e).Warm advection appeared ahead of the trough (not shown), which promoted ascending motions through quasi-geostrophic forcings (Holton, 2004).In addition, there was a lower-tropospheric trough (Figure 1d,e), which was situated south of Sichuan.The low-level jet associated with this trough contributed to maintaining the lower-level convergence.Under the favorable background environment discussed above, a SWV formed within the Sichuan Basin at 1800 UTC July 15, 2021 (Figure 2a,b) and lasted for $33 h.After formation, as the steering flow was weak, the vortex mainly maintained a quasi-stationary behavior (Fu et al., 2014).According to previous studies (Fu et al., 2019;Markowski & Richardson, 2010), a vortex can contribute to precipitation mainly through two dynamical effects: (i) maintaining/enhancing ascending motions, and (ii) maintaining/enhancing lower-level convergence.In this event, overall, the precipitation intensity showed consistent variation features with the SWV's intensity (the correlation coefficient between the key-region averaged precipitation and vorticity was $0.63), implying that the SWV acted as the primary system for inducing the heavy precipitation during this event.
F I G U R E 2 Panel (a) shows the simulated stream (black line), cyclonic vorticity (shading; 10 À5 s À1 ), and wind above 4 m s À1 (a full wind bar is 4 m s À1 ) at 700 hPa (when the vortex formed).Thick green lines outline the terrain higher than 3000 m.Panel (b) is the same as (a) but for the ERA5 reanalysis, where the gray shading outlines the terrain higher than 3000 m.Panel (c) shows the locations of the air clusters (small black boxes) that formed the vortex (24-h before the formation of the vortex), where shading is terrain (m), and thick purple lines show the division of the regions relative to the vortex's key region.Panel (d) shows the tracks of the air clusters that formed the vortex, where shading is vorticity (10 À5 s À1 ), and the small closed boxes and open circles mark the starting and ending locations of the backward tracking, respectively.

| Simulation validation
For the background environment, the simulation had reproduced the middle-level shortwave trough east of the Tibetan Plateau and the lower-level trough south of Sichuan well (not shown).As Figure 2a,b show, the simulation reproduced the SWV formation at 1800 UTC July 15, 2021, but of a stronger intensity in cyclonic vorticity and wind speed.The simulated vortex center was located in a lower latitude ($1 ) than that of the ERA5-derived SWV, and the horizontal range of the simulated SWV was larger.Overall, the correlation coefficient of the simulated horizontal wind field and the ERA5 horizontal wind field within the key region of the SWV was $0.78, implying that the simulation was highly consistent with the ERA5 reanalysis data.From Figure 1b, the simulation had generated three rain bands in the eastern section of Sichuan ("A"-"C").Of these, the rain bands "A" and "B" were consistent with the rain bands "a" and "b" shown in Figure 1c, whereas, the rain band "C" was located southwest of the rain band "c."In addition, we calculated the threat score (TS; Etherton and Santos, 2008) for different rainfall intensity, and it was found that for the 36h accumulated precipitation, the TS was $0.54, and for the heavy rainfall, the TS was $0.29.In summary, as discussed above, the simulation had reasonably captured the key features during the SWV's formation and thus could be used for a further study.

| Trajectory analyses
In order to clarify the air clusters directly accounted for the SWV's formation, we designed the backward tracking method presented in Section 2.3.There was a total of 1072 trajectories with their initial locations all located within the SWV's key region (Figure 2d).As Table 1 shows, all nine subregions (Figure 2c) acted as sources for the air clusters that formed the SWV at its formation time.Of these, the subregion South contributed the most in trajectory number ($35.0%),Southwest ranked second ($30.7%), and Inside ranked third ($10.3%).In the vertical direction, air clusters sourced from the upper layer had the largest proportion ($61.2%),those originated from lower and middle layers ranked second and third, respectively.This was notably different from the situation documented in Feng et al. (2019), as for that SWV, air clusters sourced from the lower layer contributed the most.Overall, in this event, for the lower layer, the subregion Inside had the largest proportion, for the middle layer, Southwest contributed the most, and for the upper layer, South ranked first (Table 1).
For the subregions South, Southwest and Inside, which in total accounted for $76% in trajectory number, we analyzed the variations in their averaged vorticity from À36 h to 0 h (i.e., the formation time).Overall, these air clusters' vorticity experienced complicated variations during this period (Figure 3a).Compared the vorticity of the air clusters at the SWV's formation time, we found that, the upper layer of the southwest type (SW_UP), the upper layer of the south type (SS_UP), the middle layer of the southwest type (SW_MI), and the lower layer of the south type (SS_LO) ranked first to fourth.They made a total contribution of $78.2% in vorticity (Figure 3c), which was larger than their contribution in trajectory number ($57.0%;Table 1).Due to their relative higher contributions, in this study, we mainly focused on these four primary types of air clusters.For the four primary types of air clusters, their variations in vorticity showed a significant increasing trend during the period from À12 h to 0 h (Figure 1b), implying that this period was crucial for the SWV's formation.Of the four primary types of air clusters, the maximum increasing trend appeared in the SW_UP ($0.86 Â 10 À5 s À1 h À1 ), and that of the SS_UP ranked second ($0.38 Â 10 À5 s À1 h À1 ).In addition, these two types of air clusters ranked first and second both in their contributions to trajectory number and vorticity (Figure 3c), with their sum proportions of $44.3% and $56.7%, respectively.This means that the SW_UP and SS_UP played the most important role in the SWV's formation.

| Sensitivity simulations
The SWVs' formation was affected notably by the topographies within/around the Sichuan Basin (Wang & Tan, 2014;Yang et al., 2023).From Section 4.1, we found that the subregions Southwest, South, and Inside ranked top threes both in their contributions to trajectory number and vorticity.Therefore, the topographies in these three regions may exert important effects on the SWV's formation.To verify this hypothesis, we first defined the F I G U R E 3 Panel (a) shows the averaged vorticity (10 À5 s À1 ) of different types of air clusters during the period from À36 h (i.e., 36 h before the vortex formation) to 0 h (i.e., the time when the vortex formed), where the green dashed box marks the period from (e) CTRL (f) SW75 ( g simulation described in Section 2.2 as the control (CTRL) run; then, we lowered the topographies within the subregions of Southwest, South, and Inside to 75% of their respective original values, while kept all other configurations the same to the CTL run (initial and boundary conditions for the sensitivity runs were regenerated by using the modified topography).Correspondingly, the sensitivity runs were defined as the SW75, S75, and IN75 runs, respectively.
From Figure 4a-d, the accumulated precipitation before the SWV's formation was sensitive to the topographies within the three subregions, particularly for the rainfall within the key region.For the key-region averaged precipitation, that of the SW75 run was enhanced, whereas, those of the S75 and IN75 runs were reduced.From the stream filed and vorticity, it could be found that, for all three sensitivity runs, the SWV could form within the key region (Figure 4e-h), but of different intensity and locations.This means that, for the SWV in this event, detailed topography features were not a decisive factor for its formation.Overall, the SW75 run showed an enhanced key-region cyclonic vorticity, whereas, the key-region cyclonic vorticity of the S75 and IN75 runs was reduced.In addition, the contrast in the SWVs' vorticity was consistent with the contrast in their precipitation (Figure 4).
Changes in SWVs' intensity and precipitation were directly related to the changes in the air clusters that formed the SWVs.As Figure 3c-h shows, the air clusters' trajectories of the CTRL run were different from those in sensitivity runs.For the four primary types of air clusters, their contributions changed notably in sensitivity runs (Figure 3d).Of these, the SW75 run showed the smallest changes in all four primary types of air clusters (Figure 3d), implying that the SWV's formation in this event was relatively insensitive to the topography within the subregion Southwest.Of the four primary types, the SS_UP increased by $5.4% (Figure 3d) in trajectory number and $8.7% in cyclonic vorticity, whereas, the remaining three types all decreased in their contributions.Therefore, the enhancement of the SWV's intensity in the SW75 run (Figure 4f) was mainly due to the increase of the SS_UP's contributions.
For the S75 run, the four primary types showed the largest changes among the three sensitivity simulations.This indicates that, the SWV's formation in this event was the most sensitive to the topography within the subregion South.Of the four primary types of air clusters, the SS_UP decreased by $41.8% in their trajectory number (Figure 3d) and $34.7% in cyclonic vorticity, which dominated the weakening of the SWV's intensity (Figure 4e-h).In contrast, other three types of air clusters mainly increased in their contributions, of which the most notable increase appeared in the SW_UP (Figure 3d).However, the increase in cyclonic vorticity related to the SS_LO, SW_UP, and SW_MI could not offset the decrease associated with the SS_UP.For the IN75 run, changes of the four primary types were also notable, implying that the SWV's formation in this case was also sensitive to the topography within the subregion Inside.Of these, the SS_UP increased by $36.3% in trajectory number (Figure 3d), and the SW_UP increased by $6.1%.In contrast, both the SS_LO and SW_MI decreased in their trajectory number and cyclonic vorticity.This was crucial for the weakening of the SWV's intensity.

| CONCLUSION AND DISCUSSION
An extremely heavy rainstorm hit Sichuan and surrounding regions from July 14, 2021 to July 16, 2021, and resulted in serious economic losses and notable social impacts.One of the most striking features of this event was that, a quasi-stationary SWV maintained for $33 h and acted as a crucial factor for inducing the heavy rainfall.After reproduced the SWV's formation by using the WRF model, we conducted trajectory analyses and sensitivity simulations to understand the effects of the complicated topography within/around Sichuan Basin on the formation of the SWV.Main findings are as follows: in the horizontal direction, all subregions surrounding the key region acted as the sources for the air clusters that formed the SWV, of which, the subregions South and Southwest contributed the most and second most, respectively.In the vertical direction, air clusters originated from the upper layer accounted for the largest proportion, and those originated from lower and middle layers ranked second and third, respectively.Among all types of air clusters, the SW_UP, SS_UP, SW_MI, and SS_LO made a total contribution of $78.2% in vorticity and $57.0% in trajectory number.These four primary types of air clusters showed a significant increase in their cyclonic vorticity from À12 h to 0 h, which directly rendered the SWV's formation.Of these, the SW_UP and SS_UP played the most important role in the SWV's formation, as their increase in cyclonic vorticity and their contributions to trajectory number and vorticity were all much larger than those of the others.Sensitivity simulations show that, although the detailed topography features were not a decisive factor for the SWV formation, they could modify the structure, intensity and precipitation of the SWV.Overall, the SWV's formation in this event was the most sensitive to the topography within the subregion South, as the SWV showed the most notable changes in the S75 run.After lowering the topography within the subregion South, the SWV weakened by $30.4% in intensity, which mainly due to the decrease of the SS_UP in trajectory number and cyclonic vorticity.The SWV's intensity was also sensitive to the topography within the subregion Inside, whereas, it was relatively insensitive to the topography within the subregion Southwest.
For this particular event, the SWV's formation was affected by the subregion South most notably, and the air clusters originated from the upper layer were the most important.For similar events, improving the forecast accuracy of the regions south of Sichuan Basin (e. g., by assimilated surface observation data), and improving the forecast accuracy of the upper troposphere (e. g., by assimilated soundings and satellite data) would be useful to improve the forecast of the SWVs.However, as previous studies show, different types of SWVs may show notably different features during their formation stage.Therefore, the limitation of a case study's F I G U R E 4 Panels (a-d) illustrate the simulated 36-h accumulated precipitation (shading; mm) for the control (CTRL), SW75, S75, and IN75 runs, respectively.Panels (e-h) show the simulated stream field (black line), cyclonic vorticity (shading; 10 À5 s À1 ), and wind above 4 m s 1 (a full wind bar is 4 m s-1 ) at 700 hPa (when the vortex formed) for the CTRL, SW75, S75, and IN75 runs, respectively.Purple boxes mark the key region of the vortex, and the purple numbers in panels (e-h) show the key region averaged vorticity (10-5 s-1 ).
representativeness should be taken into consideration when understanding the results of this study.In addition, how the detailed topographies affected the production/extinction of the cyclonic vorticity of the four primary types of air clusters is also helpful to understand the SWV's formation.This will be investigated in a future study.
) S75 (h) IN75-12 h to 0 h.SS_UP = the upper layer of the south type; SS_MI = the middle layer of the south type; SS_LO = the lower layer of the south type; SW_UP = the upper layer of the southwest type; SW_MI = the middle layer of the southwest type; SW_LO = the lower layer of the southwest type; IN_UP = the upper layer of the inside type; IN_MI = the middle layer of the inside type; IN_LO = the lower layer of the inside type.Panel (b) is the same as (a) but for the four types of air clusters during the period from À12 h to 0 h, and the linear trends of the vorticity variations are also shown.Panel (c) shows the contributions (%) in trajectory number and key-region averaged vorticity of the four types of air clusters.Panel (d) shows the contributions (%) in trajectory number of the four types of air clusters in different simulations.Panels (e-h) illustrate the trajectories (shading is the height of air clusters; m) of different simulations, where the small closed boxes and open circles mark the starting and ending locations of the backward tracking, respectively.