图  1  （a）南疆地区地形图片，（b）2019年9月9日18时（协调世界时，下同）至9月10日18时24小时降水量（单位：mm，来源为Cmorph资料）分布

Figure  1.  (a) Picture of the terrain in southern Xinjiang, (b) 24-h accumulated precipitation (units: mm) observed by Cmorph data from 1800 UTC 9 September to 1800 UTC 10 September 2019

图  2  2019年9月10日00时（a）200 hPa位势高度（黑色实线，单位：dagpm）、风速（填色，单位：m s⁻¹），（b）500 hPa位势高度（黑色实线，单位：gpm）、风速（填色，单位：m s⁻¹），（c）650 hPa相当位温（黑色实线，单位：K）、水汽通量散度辐合（填色，单位：10⁻⁹ kg cm⁻² s⁻¹ hPa⁻¹），（d）700 hPa风矢量（风向杆，单位：m s⁻¹）、风速（填色，单位：m s⁻¹）。图b、c中的红色矩形区域表示降水区，图d中的绿色箭头表示水汽输送方向

Figure  2.  (a) Geopotential height (black lines, units: dagpm) and wind speed (shadings, units: m s⁻¹) at 200 hPa, (b) geopotential height (black lines, units: gpm) and wind speed (shadings, units: m s⁻¹) at 500 hPa, (c) equivalent potential temperature (black lines, units: K) and convergence (shadings, units: 10⁻⁹ kg cm⁻² s⁻¹ hPa⁻¹) of moisture flux divergence at 650 hPa, (d) wind (barbs, units: m s⁻¹) and wind speed (shadings, units: m s⁻¹) at 700 hPa at 0000 UTC 10 September 2019. In Figs. b, c, red rectangles represent precipitation area; in Fig. d, the green arrow represents direction of water vapor transport

图  3  2019年9月9日18时至9月10日00时（a）Cmorph资料、（b）WRF模式模拟的6小时累积降水量（单位：mm）；2019年9月9日23时（c）云顶亮温（单位：°C），（d）Cmorph资料、（e）WRF模式模拟的1 h累积降水量（单位：mm）。蓝色矩形框区表示天山南坡降水区域

Figure  3.  (a) Cmorph data and (b) WRF simulated 6-h accumulated precipitation (units: mm) during 1800 UTC 9 September to 0000 UTC 10 September 2019; (c) TBB (black body temperature, units: °C), 1-h accumulated precipitation (units: mm) from (d) Cmorph data and (e) WRF simulated at 2300 UTC 9 September 2019. The blue rectangles represent the precipitation area of the southern slope of the Tianshan Mountains

图  4  2019年9月9日南疆暴雨雷达组合回波（单位：dBZ）分布：（a）18时；（b）19时；（c）20时；（d）21时；（e）22时；（f）23时。实线表示对流线东西走向，虚线表示对流线南北走向

Figure  4.  Distributions of composite radar reflectivity (units: dBZ) of heavy rain in southern Xinjiang at (a) 1800 UTC, (b) 1900 UTC, (c) 2000 UTC, (d) 2100 UTC, (e) 2200 UTC, (f) 2300 UTC on 9 September 2019. The solid (dashed) lines represent the east–west (south–north) trend of the streamline

图  5  2019年9月9日（a）21时、（b）22时、（c）23时位涡波作用密度的绝对值垂直积分平均（阴影，单位：10⁻⁷ K s⁻¹）与雷达组合回波（等值线，单位：dBZ）的水平分布，图5a–c中蓝色直线分别经过76°E、76.5°E、77°E，分别为图6a–c剖面所在位置

Figure  5.  Horizontal distributions of the averaged vertical integrated absolute potential vorticity wave-activity density (shadings, units: 10⁻⁷ K s⁻¹) and composite radar reflectivity (isolines, units: dBZ) at (a) 2100 UTC, (b) 2200 UTC, (c) 2300 UTC on 9 September 2019. In Figs. 5a–c, the blue lines go through 76°E, 76.5°E, 77°E, corresponding to the locations of the sections in Figs. 6a–c

图  6  2019年9月9日位涡波作用密度垂直分布（阴影，单位：10⁻⁸ K s⁻¹ m⁻¹）：（a）21时沿76°E（图5a蓝色直线）剖面；（b）22时沿76.5°E（图5b蓝色直线）剖面；（c）23时沿77°E（图5c蓝色直线）剖面。灰色实线为地形高度线（单位：km），绿色柱为1 h累积降水量（单位：mm），黑色等值线为雷达回波（单位：dBZ）

Figure  6.  Vertical distributions of potential vorticity wave-activity density (shadings, units: 10⁻⁸ K s⁻¹ m⁻¹) along (a) 76°E (the blue line in Fig. 5a) at 2100 UTC, (b) 76.5°E (the blue line in Fig. 5b) at 2200 UTC, and (c) 77°E (the blue line in Fig. 5c) at 2300 UTC on 9 September 2019. The gray solid line is the terrain (units: km), the green bar represents the 1-h precipitation (units: mm), and the black line denote the radar reflectivity (units: dBZ)

图  7  2019年9月9日（a）21时、（b）22时、（c）23时位涡波作用方程各强迫项水平平均（单位：10⁻⁹ K m s⁻²）以及各强迫项之和（黑色线）的垂直廓线。红色线：$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$；绿色线：$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$；蓝色线：$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$；紫色线：$\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$。$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A3}}}}$较其他项小两个量级，已忽略。不同时刻的水平平均为该时刻四条对流线各自小区域（图5中的红色框区域）平均后的均值

Figure  7.  Vertical profiles of the horizontal averaged total forcing (black lines, units: 10⁻⁹ K m s⁻²) of potential vorticity wave-activity relation and its components at (a) 2100 UTC, (b) 2200 UTC, and (c) 2300 UTC on 9 September 2019. The red, green, blue, and purple lines represent $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$ (the divergence of the wave-activity density flux by the basic flow), $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$ (the flux divergence of part of first-order perturbation potential vorticity by perturbation flow), $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$ (divergence of the differences between perturbation advection and averaged perturbation advection ), and $\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$ (the exchange between the basic-state potential vorticity and averaged wave-activity density), respectively. $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A3}}}}$ (the divergence of the coupling of ageostrophic perturbation wind and perturbation potential temperature) is ignored due to its small magnitude. The horizontal averaged quantities in certain time is obtained by firstly conducing the average respectively over the four small regions corresponding to the four convective lines (red boxes in Fig. 5) and then doing an average to the four averaged results

图  8  2019年9月9日（a）21时、（b）22时、（c）23时位涡波作用方程总强迫（阴影，单位：10⁻⁹ K s⁻²）与雷达组合回波（等值线，单位：dBZ）的水平分布。图b中红色虚线表征波作用强迫大于6×10⁻⁹ K s⁻²区域，红色箭头表征波作用强迫中心区

Figure  8.  Horizontal distributions of the total forcing (shadings, units: 10⁻⁹ K s⁻²) of potential vorticity wave-activity relation and composite radar reflectivity (isolines, units: dBZ) at (a) 2100 UTC, (b) 2200 UTC, and (c) 2300 UTC on 9 September 2019. In Fig. b, regions with the forcing larger than 6×10⁻⁹ K s⁻² are enclosed by the red dotted lines. The red arrow indicates the center of the forcing

图  9  2019年9月9日22时（a）0.25～6 km、（b）6～12 km高度平均的位涡波作用方程总强迫（阴影，单位：10⁻⁹ K s⁻²）与雷达组合回波（等值线，单位：dBZ）的水平分布。红色实线为未来1 h（23时）45 dBZ等值线（参考图8c），以表征对流线的变化趋势。图a中，红色虚线区域是对流区位涡波作用方程总强迫大于0的区域

Figure  9.  Horizontal distributions of the total forcing (shadings, units: 10⁻⁹ K s⁻²) of potential vorticity wave-relation equation averaged over (a) 0.25–6 km and (b) 6–12 km and composite radar reflectivity (isolines, units: dBZ) at 2200 UTC on 9 September 2019. The solid red lines represent the shape of the 45-dBZ contours (refer to Fig. 8c) in the following 1 h (2300 UTC), which characterizes the changing trend of convective lines. In Fig. a, the red dashed line indicates the positive area of the total forcing of potential vorticity wave-relation equation

图  10  2019年9月9日22时0.25～6 km平均的（a）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$、（b）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$、（c）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$、（d）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$与雷达组合回波（等值线，单位：dBZ）的水平分布。红色虚线表征对流区波作用强迫大于0的区域，红色实线为未来1 h（23时）45 dBZ等值线

Figure  10.  Horizontal distributions of (a) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$, (b) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$, (c) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$, and (d) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$ averaged over 0.25–6 km and composite radar reflectivity (isolines, units: dBZ) at 2200 UTC on 9 September 2019. The red dashed lines indicate the positive area of the forcing components, and the solid red lines denote the shape of the 45-dBZ contours in the following 1 h (2300 UTC)

图  11  2019年9月9日22时沿76.7°E的（a）位涡波作用方程总强迫，（b）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$，（c）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$中的分项$ - \partial \left( {\bar u{A_1}} \right)/\partial x $、（d）$- \left[ {\partial \left( { - \bar u\partial {{\theta '}_{\rm{e}}}/\partial x} \right)/\partial x} \right]\left( {\partial v'/\partial z} \right)$的垂直分布，单位：10⁻⁸ K s⁻² m⁻¹。黑色等值线为雷达回波（单位：dBZ），灰色实线为地形高度线（单位：km），绿色柱为1 h累积降水量（单位：mm），下同

Figure  11.  Vertical distributions of (units: 10⁻⁸ K s⁻² m⁻¹) (a) the total forcing of potential vorticity wave-relation equation, (b) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$, (c) component $ - \partial \left( {\bar u{A_1}} \right)/\partial x $ of $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$, (d) component $- \left[ {\partial \left( { - \bar u\partial {{\theta '}_{\rm{e}}}/\partial x} \right)/\partial x} \right]\left( {\partial v'/\partial z} \right)$ of $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A1}}}}$ along 76.7°E at 2200 UTC on 9 September 2019. The black lines denote the radar reflectivity (units: dBZ), the gray solid lines denote the terrain (units: km), the green bars denote the 1-h precipitation (units: mm), the same below

图  12  2019年9月9日22时（a）6 km高度扰动广义位温（阴影，单位：K）和环境大气平均流场水平分布（等值线，单位：m s⁻¹），（b）沿76.7°E的扰动经向风速垂直分布（阴影，单位：m s⁻¹）

Figure  12.  (a) Perturbation-generalized potential temperature (shadings, units: K) at 6-km height and basic state wind stream (isolines, units: m s⁻¹) and (b) vertical distribution of perturbation meridional wind speed along 76.7°E at 22 UTC on 9 September 2019

图  13  2019年9月9日22时沿76.53°E的（a）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$、（b）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$中的分项$- \partial \left[ {w'\left( {\partial \bar u/\partial z} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)} \right]/\partial z$、（c）$- \left( {\partial w'/\partial z} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)\left( {\partial \bar u/\partial z} \right)$、（d）$- w'\left[ {\partial \left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)/\partial z} \right]\left( {\partial \bar u/\partial z} \right)$的垂直分布，单位：10⁻⁸ K s⁻² m⁻¹

Figure  13.  Vertical distributions (units: 10⁻⁸ K s⁻² m⁻¹) of (a) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$, (b) component $- \partial \left[ {w'\left( {\partial \bar u/\partial z} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)} \right]/\partial z$, (c) component $- \left( {\partial w'/\partial z} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)\left( {\partial \bar u/\partial z} \right)$, and (d) component $- w'\left[ {\partial \left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)/\partial z} \right]\left( {\partial \bar u/\partial z} \right)$ of $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A2}}}}$along 76.53°E at 2200 UTC on 9 September 2019

图  14  2019年9月9日22时沿76.48°E的（a）$\nabla \cdot {\boldsymbol{F}}$、（b）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$、（c）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$中的分项$\partial \left[ {w'\left( {\partial {{\theta '}_{\rm{e}}}/\partial z} \right)\left( {\partial \bar u/\partial z} \right)} \right]/\partial y$和（d）$\left\{ {\partial \left[ {w'\left( {\partial {{\theta '}_{\rm{e}}}/\partial z} \right)} \right]/\partial y} \right\}\left( {\partial \bar u/\partial z} \right)$的垂直分布，单位：10⁻⁸ K s⁻² m⁻¹

Figure  14.  Vertical distributions (units: 10⁻⁸ K s⁻² m⁻¹) of (a) $\nabla \cdot {\boldsymbol{F}}$, (b) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$, (c) component $\partial \left[ {w'\left( {\partial {{\theta '}_{\rm{e}}}/\partial z} \right)\left( {\partial \bar u/\partial z} \right)} \right]/\partial y$ and (d) component $\left\{ {\partial \left[ {w'\left( {\partial {{\theta '}_{\rm{e}}}/\partial z} \right)} \right]/\partial y} \right\}\left( {\partial \bar u/\partial z} \right)$ of $\nabla \cdot {{\boldsymbol{F}}_{{\rm{Aex}}}}$ along 76.48°E at 2200 UTC on 9 September 2019

图  15  2019年9月9日22时4.5 km高度的（a）扰动位温（阴影，单位：K）、扰动风场（箭头，单位：m s⁻¹）以及（b）扰动垂直速度（阴影，单位：m s⁻¹）的水平分布，（c）沿76.48°E的扰动广义位温（阴影，单位：K）和垂直流场（箭头，经向风单位：m s⁻¹，垂直速度单位：10⁻¹ m s⁻¹）垂直分布

Figure  15.  Horizontal distributions of (a) perturbation-generalized potential temperature (shadings, units: K) and perturbation wind field (arrows, units: m s⁻¹), (b) vertical-perturbation vertical velocity at 4.5-km height, (c) vertical distributions of perturbation-generalized potential temperature (shadings, units: K) and vertical circulation (arrows, meridional wind units: m s⁻¹, vertical velocity units: 10⁻¹ m s⁻¹) along 76.48°E at 2200 UTC on 9 September 2019

图  16  2019年9月9日22时沿76.38°E的（a）$\nabla \cdot {\boldsymbol{F}}$、（b）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$、（c）$\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$中的分项$- \partial \left[ {v' \cdot \nabla u'\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)} \right]/\partial z$和（d）$- \left( {\partial v'/\partial z} \right)\left( {\partial u'/\partial y} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right) - v'\left[ {\partial \left( {\partial u'/\partial z} \right)/\partial y} \right]\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)$的垂直分布，单位：10⁻⁸ K s⁻² m⁻¹

Figure  16.  Vertical distributions (units: 10⁻⁸ K s⁻² m⁻¹) of (a) $\nabla \cdot {\boldsymbol{F}}$, (b) $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$, (c) component $- \partial \left[ {v' \cdot \nabla u'\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)} \right]/\partial z$, and (d) component $- \left( {\partial v'/\partial z} \right)\left( {\partial u'/\partial y} \right)\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right) - v'\left[ {\partial \left( {\partial u'/\partial z} \right)/\partial y} \right]\left( {\partial {{\theta '}_{\rm{e}}}/\partial y} \right)$ of $\nabla \cdot {{\boldsymbol{F}}_{{\rm{A4}}}}$ along 76.38°E at 2200 UTC on 9 September 2019

图  17  2019年9月9日22时沿75.38°E的（a）扰动纬向风速（阴影，单位：m s⁻¹）、（b）扰动经向风速（阴影，单位：m s⁻¹）、（c）扰动广义位温（阴影，单位：K）和垂直流场（箭头，经向风单位：m s⁻¹，垂直速度单位：10⁻¹ m s⁻¹）垂直分布

Figure  17.  Vertical distributions of (a) perturbation zonal wind speed (shadings, units: m s⁻¹), (b) perturbation meridional wind speed (shadings, units: m s⁻¹), (c) perturbation-generalized potential temperature (shadings, units: K) and vertical circulation (arrows, meridional wind units: m s⁻¹, vertical velocity units: 10⁻¹ m s⁻¹) and along 76.38°E at 2200 UTC on 9 September 2019

图  18  根据波作用方程诊断的南疆暴雨组织化概念模型。红色箭头为上升流，蓝色箭头为下沉流，深蓝色箭头框为纬向基本气流，虚线箭头为扰动纬向风，蓝色虚线为低层扰动气流形成的锋面或辐合线

Figure  18.  Concept model of the organization process diagnosed from the wave-activity relation equation in southern Xinjiang. The red arrow indicates ascending flow, the blue arrow indicates descending flow, the dark blue arrow box is zonal basic flow, the dashed arrow is the perturbation zonal flow, the blue dashed line is the front or convergence line formed by the low-level perturbation flow