Xiuping YAO^1,3,,,
Qin ZHANG²,
Xiao ZHANG³

Corresponding author: Xiuping YAO,yaoxp@cma.gov.cn;

1.China Meteorological Administration Training Centre, Beijing 100081, China
2.Zibo Meteorological Bureau of Shandong Province, Zibo 255048, China
3.State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing 100081, China
Manuscript received: 2019-12-23
Manuscript revised: 2020-06-14
Manuscript accepted: 2020-06-16
Abstract:By employing NCEP?NCAR 1°×1° reanalysis datasets, the mechanism of the easterlies vortex (EV) affecting the short-term movement of the subtropical anticyclone over the western Pacific (WPSA) in the mei-yu period is examined using potential vorticity(PV) theory. The results show that when the EV and the westerlies vortex (WV) travel west/east to the same longitude of 120°E, the WPSA suddenly retreats. The EV and WV manifest as the downward transport of PV in the upper troposphere, and the variation of the corresponding high-value regions of PV significantly reflects the intensity changes of the EV and WV. The meridional propagation of PV causes the intensity change of the EV. The vertical movement on both sides of the EV is related to the position of the EV relative to the WPSA and the South Asian high (SAH). When the high PV in the easterlies and westerlies arrive at the same longitude in the meridional direction, the special circulation pattern will lower the position of PV isolines at the ridge line of the WPSA. Thus, the cyclonic circulation at the lower level will be strengthened, causing the abnormally eastward retreat of the WPSA. Analysis of the PV equation at the isentropic surface indicates that when the positive PV variation west of the EV intensifies, it connects with the positive PV variation east of the WV, forming a positive PV band and making the WPSA retreat abnormally. The horizontal advection of the PV has the greatest effect. The contribution of the vertical advection of PV and the vertical differential of heating is also positive, but the values are relatively small. The contribution of the residual was negative and it becomes smaller before and after the WPSA retreats.
Keywords: mei-yu period,
easterlies vortex,
western Pacific subtropical anticyclone,
potential vorticity,
diagnostic analysis
摘要:本文利用NCEP/NCAR 1°×1°分辨率资料，从位涡理论角度研究了梅雨期热带东风带扰动影响西太平洋副热带高压（简称西太副高）东西向异常活动的机制。结果表明：梅雨期东/西风带扰动（EV/WV）向西/东相向运动，到达同一经度120°E时，西太副高出现突然东退。在对流层高层东/西风带扰动均对应正位涡异常，在其移动过程存在高位涡下传，其正位涡值可较好地反映东/西风带扰动的强度变化；东风带扰动东西两侧的垂直运动在西太副高东退前后发生转变，与西太副高、南亚高压和东风带扰动的相对位置配置有关；西太副高东退时，东/西风扰动的高PV在经向上的不断接近，使西太副高脊线上的等1pvu等值线位置降低，强迫低层气旋式环流增强，使西太副高东退。等熵面位涡收支诊断表明，348K等熵面上东风带扰动西侧正PV局地变化开始加强，并与西风带扰动东侧的正PV局地变化在经向上连成带状时，西太副高异常东退。其中，位涡的水平平流项作用最大；位涡的垂直平流项和加热的垂直微分项贡献也为正，但数值相对较小；余差项贡献为负，在副高东退前后，余差项变小，有利于西太副高东退。
关键词:梅雨期,
西太副高,
东风带扰动,
位涡,
诊断分析

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The location and intensity of the subtropical anticyclone over the western Pacific (WPSA) can directly affect the weather in China and its consequences, especially the flooding during the mei-yu period over the Yangtze River?Huaihe River Basin (Liu et al., 2013). Therefore, research on the WPSA has always been an important subject for Chinese meteorologists. Before the 1980s, Huang et al. (Huang and Yu, 1962; Huang, 1963, 1978; Huang and Tang, 1978) conducted numerous studies on the evolution of the WPSA. Some researchers have pointed out that the WPSA is not just a complex system with dynamic properties (Wu et al., 2002). In the late 1970s, the tropical meteorology research group at the Institute of Atmospheric Physics, Chinese Academy of Sciences (Group on Tropical Meteorology, Institute of the Atmospheric Physics, Academia Sinica, 1977), summarized the research progress on the evolution of the WPSA in summer and proposed that the WPSA is a deep system in the troposphere that is closely related to high-latitude weather systems and the South Asian high (SAH). Since the 1990s, the formation mechanism of the subtropical high and its interannual variation have been further studied. The complete form of the vertical vorticity tendency equation is an effective tool for understanding the formation and variation of the WPSA. It not only has the dynamic terms of the traditional equation, but also the internal forcing terms of the atmospheric thermodynamic structure and the external forcing term of heating and friction. Liu et al. (2001) demonstrated the effect of deep convective heating on the WPSA by using the complete form of the vertical vorticity tendency equation and numerical simulation. When the atmospheric circulation is adjusted in the diabatic heating, thermal adaptive equilibrium is established between vorticity generation, friction dissipation and potential vorticity flowing out of the source region, accompanied by the phenomenon of overcurrent. The theory of “two-stage thermal adaptation” (Wu et al., 2000) can well explain that the SST anomaly in the northern Indian Ocean can lead to the anomaly of the WPSA. In the first stage of thermal adaptation, SST anomalies over the Indian Ocean form low-level cyclonic circulation and convective precipitation occurs in the south airflow to the east of the circulation. In the second stage, the extension of the WPSA over 500 hPa is strengthened. Since 2000, the relationships of the WPSA anomaly with the atmospheric circulation in the tropical area and the westerlies have been given more attention, especially the rule of the interaction of the short-term variation of the WPSA with the westerlies system and tropical waves (Wu et al., 2003).
The concept of potential vorticity (PV) can be traced back to the studies of Rossby (1940) and Ertel (1942). Ertel’s PV is defined as ${P_{\rm{E}}} = \alpha {{{\zeta }}_\alpha } \cdot \nabla \theta $, where ${\rm{\alpha}} $ is specific volume, and ${{{\zeta }}_\alpha }$ and $\theta $ denote three-dimensional absolute vorticity and potential temperature, respectively. Hoskins (1991) pointed out that positive PV disturbances in the stratosphere can extend downward to the middle troposphere and induce the cyclonic circulation, which can pass through the entire troposphere down to the near-surface. It was also demonstrated that the downward transport of PV disturbances in the upper troposphere or stratosphere can induce the development of cyclones in the lower troposphere and over the ground. When the positive PV disturbance at the upper level moves to the lower troposphere or the baroclinic zone on the ground, it can cause disturbances of the potential temperature at the lower level. Davis and Emanuel (1991) made the point that the development of the upper-level PV is strongly influenced by the anomalies at the lower level, which has developed and further deepened Hoskins’ theory of the downward transport of PV. Since PV is conserved for the air parcel in the inviscid and adiabatic baroclinic atmosphere, it can be regarded as another physical quantity denoting the air-parcel movement, just like the potential temperature and specific humidity. The usage of PV in tracking the trajectory of cold air provides a new tool for operational weather forecasts. According to the viewpoint of PV, the atmospheric structure can be regarded as the superposition of the upper-level cyclone and anticyclone around the positive and negative PV anomalies, and the low-level cyclone and anticyclone around the positive and negative PV anomalies (Shou, 2010). The subtropical high in summer, which is a powerful anticyclone, as well as the surrounding SAH, westerlies and easterlies systems, manifest as PV anomaly regions with different positive/negative signs and sizes, which are closely related to changes in weather.
Yao et al. (2007, 2008) found that the easterlies vortex (EV) in the upper troposphere moved westward and the westerlies vortex (WV) moved eastward during 22?25 June 2003, which caused the short-term eastward retreat of the WPSA and terminated the first rainstorm during the mei-yu period over the Yangtze River?Huaihe River Basin. This phenomenon confirms the close relationship between the WPSA and the easterly systems in the low latitudes. The EV is a synoptic-scale system with a deep vertical scale and a “warm up and cold down” structure. The strength and structure of the EV changes before and after the eastward retreat of the WPSA. According to composite analysis of several cases (Zhang et al., 2010), the positive PV variations in the EV and the WV join together and form a belt-like zone before and after the eastward retreat of the WPSA. Vorticity advection, vertical motion and heterogeneous heating all play important roles. Further research on thermal forcing (Sun et al., 2013; Yao and Sun, 2016) has shown that the distribution and intensity of the diabatic effect near the EV leads to the retreat of the WPSA. The above studies have shown that the dynamic and thermal mechanisms are two interrelated factors, which are both important in the short-term movement of the WPSA influenced by the EV. As a comprehensive physical quantity containing both thermodynamic and dynamic factors, PV probably plays an important role in the short-term movement of the WPSA. Studies in recent years have also shown that the existence of the Tibetan Plateau leads to a unique exchange of substances in the stratosphere and troposphere over East Asia in summer (Xia et al., 2016). The diabatic heating of the Tibetan Plateau can cause a surrounding circulation anomaly in the troposphere (Ren et al., 2014; Wu et al., 2015). Thus, an examination of the thermodynamic and dynamic effects of the Tibetan Plateau on the movement of the WPSA is of important scientific value. Combined with the above facts and research results, the forcing effect of the EV in the upper troposphere over the tropics on the short-term zonal movement of the WPSA is explored more deeply in this paper, and the causes are also discussed from the perspective of PV.

According to the research of Yao et al. (2008), during 22?25 June 2003, the WPSA first advanced westward and then retreated eastward significantly, which directly led to the occurrence and interruption of the first rainstorm over the Yangtze River?Huaihe River Basin. During this process, the disturbance in the easterlies keeps advancing westward, while the disturbance in the westerlies keeps advancing eastward. The WPSA begins to retreat eastward abnormally when the two disturbances arrive at the same longitude at the border of sea and land. As PV is conserved on the isentropic surface for adiabatic, frictionless flow, the analysis of variables on the isentropic surface can track the source region and evolutionary characteristics of the weather system more clearly than that on the geopotential height surface. In the following section, we use NCEP?NCAR reanalysis data to make isentropic potential vortex maps to investigate the PV distribution characteristics during 22?25 June 2003. In this paper, the isentropic surfaces of 348 K and 330 K are selected, which are roughly located near the levels of 200 hPa and 500 hPa at the middle and high latitudes, respectively. Thus, the characteristics of the middle and upper troposphere can be well represented.
Figure 1 shows the distributions of the PV and wind field on the isentropic surfaces of 348 K and 330 K during 22?25 June 2003. On the isentropic surface of 348 K, it can be seen that the SAH corresponds to the low PV. Meanwhile, in the westerlies, the high PV first moves eastward, then propagates to the lower latitudes along the east side of the SAH, and finally moves westward forming a high-PV belt in the tropical region. The large-scale closed circulation system formed in this process is the EV. On the 330-K isentropic surface, the WPSA corresponds to the low PV while the EV corresponds to the high PV. On 22 June (Fig. 1a), the SAH extends eastward to 160°E, and the high PV in the EV centered near 140°E and 17.5°N moves westward. The strong steering flow in the south of the SAH imports high PV at the rear of the EV into the disturbance from the northeast, which further intensifies the disturbance. The high PV corresponding to the WV at 110°E constantly moves eastward. On the 330-K isentropic surface (Fig. 1b), the 588-dagpm contour is obviously bent at the position of the EV, and the WPSA extends westward to 112°E. On 23 June, the main body of the SAH strengthens. A westerlies trough moves to the same longitude as the EV. Meanwhile, the high PV corresponding to the westerlies trough is transported southward by the north wind in the east of the SAH and propagates to the lower latitude. Together with the continuous involvement of the high PV on the east side of the EV, the development of the EV reaches its maximum intensity. At the same time, the high PV corresponding to the WV moves eastwards and equatorward. On the 330-K isentropic surface at the low level, the range of the high-PV zone on the north side of the WPSA increases rapidly. The 0.5-PVU line expands southward to the vicinity of 30°N, and the WPSA extends westward beyond 110°E. On 24 June, influenced by the north wind on the east side of the SAH, the WV with high PV continues to invade into the lower latitudes, forming an independent high-PV center, which is basically close to the EV in the meridional direction. On the 330-K isentropic surface, the WV corresponds to an independent high-PV value region, and the 0.5-PVU line at its south side expands southward to 27°N. The main body of the WPSA retreats to east of 130°E. On 25 June, with the strengthening and eastward extending of the SAH, the high PV corresponding to the WV continues to move eastward, and then deviates from the main body of the SAH and moves northeastward. Meanwhile, the EV moves westward, followed by the westward extension of the WPSA.
Figure1. PV fields (shading; units: 10^?6 m² s^?1 K kg^?1) and potential height fields (red dotted line and white thick solid isoline; units: dagpm) on the 348-K (left) and 330-K (right) isentropic surfaces from 22 to 25 June 2003.


It can be seen that the high PV corresponding to the WV moves southeastward, getting closer to the EV, which regularly moves westward. When the high PV corresponding to the EV and that corresponding to the WV basically reach the same longitude in the meridional direction, it causes the abnormal eastward retreat of the WPSA, and the process is accompanied by the southward movement of the high PV in the lower troposphere. The movement and evolution of the high PV corresponding to the EV and WV are related to the SAH, and the change in the EV intensity is also affected by the high-latitude system.

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3.1. Vertical structural characteristics and evolution

According to the study of Yao et al. (2008), the structure and intensity of the EV itself also changes when it affects the short-term movement of the WPSA. Some of these changes occur prior to the short-term movement of the WPSA, which has a certain predictive effect.
In order to reveal the structural characteristics of the EV in the PV field, the vertical-cross-section distribution of the dry PV is discussed without considering the influence of water vapor. Figure 2 shows the longitude?height cross section of the PV and the potential temperature along the center of the EV. It can be seen that the high-value region of PV above 200 hPa is wave-like. There is a PV tongue extending to the lower level at the longitude of the EV, and this PV anomaly is distributed symmetrically along the zero line of the meridional wind in the EV. The isentropic surfaces converge to the center of the EV, indicating that the EV is a region with large-value static stability, which also has a structure that is warmer at the upper level and colder at the lower level. Here, 1 PVU is regarded as the characteristic line that represents the activity of the high-value region of PV. From the figure, it is clear that the PV anomaly region continuously moves westward. Before the WPSA retreats eastward, the lowest position of the high-value region of PV locates at about 250 hPa on 22 June and it extends down to about 300 hPa on 23 June, accompanied by the significant strengthening of PV in the upper troposphere. At this time, the isentropic surface closes strongly inward, resulting in an increase of the distance between the upper and lower isentropic surfaces over the EV center, a decrease of the static stability, and a strengthening of the cyclonic circulation. Therefore, the downward transport of the high PV is beneficial to the enhancement and vertical expansion of the EV. After the WPSA retreats, the PV anomaly region shrinks up slightly, corresponding to the decrease in the intensity and range of the EV.
Figure2. Vertical profiles of PV (shading; units: 10^?6 m² s^?1 K kg^?1), meridional wind (solid line; units: m s^?1) and potential temperature (dotted line; units: K) field on (a) 22, (b) 23, (c) 24 and (d) 25 June.


According to the analysis in section 2, the development of the EV is accompanied by the entry of the external high PV. In order to illustrate the influence of the high-PV transport from the high latitudes on the intensity change of the EV, the evolution of the meridional PV transport north of the EV (near 25°N) on the 348-K isentropic surface is analyzed by using the equation ${T_{\theta,y}} = {v_\theta }{(\partial {P_\theta }/\partial y)_\theta }$(Fig. 3), where ${v_\theta }$ is the meridional wind speed on the isentropic surface, ${\left({\partial {P_\theta }/\partial y} \right)_\theta }$ is the meridional PV transport on the isentropic surface. From 0000 UTC 21 June, the high PV corresponding to the EV strengthens and moves westward continuously, the central maximum intensity reaches 4 PVU at 0000 UTC 23 June, and then weakens during the westward movement. The large-value area of ${T_{{\rm{\theta }},{\rm{y}}}}$ above 1 PVU appears near 137°E from 1200 UTC 21 June to 1200 UTC 23 June, indicating that there is a continuous southward transport of PV on the east side of the SAH. When the EV moves to the vicinity of 137°E, its intensity increases rapidly due to the transport of the positive PV. When the EV continues to move westward, the meridional transport of PV decreases, and the intensity of the EV weakens.
Figure3. Evolution of PV along 17.5°N (solid line; units: 10^?6 m² s^?1 K kg^?1) and meridional PV conveying ${T_{\theta,y}}$ (shading; 10^?6 m s^?1 K kg^?1) along 25°N on the 348-K isentropic surface.


The above analyses show that the high-value anomaly of PV in the upper troposphere or lower stratosphere corresponds to the location of the EV. The maintenance of the EV is the result of the downward transport of PV from the upper troposphere. Also, its central intensity is determined by the intensity of the downward transport of PV and the meridional propagation of the positive PV from the high latitudes.

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3.2. Vertical motion

Hoskins et al. (Hoskins, 1974; Hoskins et al., 1985) proposed the concept of “potential vorticity substance”, considering the isentropic surface as a semi-transparent film, which can be freely passed through by ordinary air substances, but on which the “potential vorticity substance” could only make two-dimensional motion. Therefore, not only can PV theory explain the occurrence and development of cyclones, but its conservation on the isentropic surface cloud can also provide an interpretation of the change in vertical motions occurring on both sides of the positive PV anomaly at the upper level. The vertical motion on the west (east) side of the EV changes from subsidence (ascent) to ascent (subsidence) before and after the eastward retreat of the WPSA, which could be used to predict the short-term retreat of the WPSA (Yao and Sun, 2016). The inversion of the EV’s vertical motion is discussed from the viewpoint of PV.
Based on the PV viewpoint (Hoskins et al., 2003), the $\omega $ equation can be deduced as $W = {W_{{\rm{IU}}}} + {W_{{\rm{ID}}}}$, where the isentropic up-glide is ${W_{{\rm{IU}}}}$ and the isentropic displacement is ${W_{{\rm{ID}}}}$. If the system maintains a constantly thermal structure, the vertical velocity of the system depends on the isentropic up-glide ${W_{{\rm{IU}}}}$. When none of the reference system is stable, the ${W_{{\rm{IU}}}}$ tends to dominate the vertical motion field (Hoskins, 2015). Since the vertical motion of the system is related to the velocity of the reference system, ${W_{{\rm{IU}}}}$ mainly depends on the relative airflow on the isentropic surface. According to the above analysis, the isentropic surface and cyclone circulation are relatively stable during the process of the westward advection of the PV anomaly corresponding to EV. Figure 4 is the vertical profile of PV on the isentropic surface. With 1 PVU as the characteristic line, the intensity of relative airflow can be roughly determined according to the position of the PV anomaly. Taking the EV center as the origin of the reference system, before the WPSA retreats eastward, the EV, which is located on the south side of the WPSA, is in the relatively strong easterly airflow at the lower level, but in the relatively weak westerly airflow at the upper level. The continuous shrinkage of the isentropic surface forces the airflow above the anomaly to ascend (descend) at the east (west) side. The airflow under the anomaly shows the same motion state as well. In addition, connected with the shear, the poleward side of the isentropic surface tilts upward, forcing the poleward-moving air on the east side of EV to rise and the equatorward-moving air on the other side to sink. After the WPSA retreats eastward, the EV, which is located on the south side of the SAH, is in a relatively strong easterly airflow at the upper level and the easterly airflow becomes very weak at the lower level, causing the air at the east (west) side of the EV to move down (up). From the meridional cross section along the EV center (Figs. 4d and e), it is found that the isentropic surface north of the EV lowers significantly after the eastward retreat of the WPSA because of the SAH, especially the 350-K surface, which falls to 250 hPa at around 30°N. The isentropic surface becomes low in the north and high in the south, resulting in the poleward-moving air on the east (west) side of the EV to move down (up).
Figure4. Vertical cross section of vorticity (shading; units: 10^?5 s^?1), PV (isolines; units: 10^?6 m² s^?1 K kg^?1) and vertical circulation (vectors; units: 10^?2 Pa s^?1 along 17.5°N on (a) 23, (b) 24 and (c) 25 June. Meridional cross section of PV (shading), isentropic temperature (white isolines; units: K) and the zonal anomalous height field (black isolines; units: gpm) along the center of EV at (d) 0000 UTC 23 June and (e) 0600 UTC 24 June.


In conclusion, the EV is a deep tropical system, whose vertical movement depends on the ambient airflow. The changes in vertical motion on both sides of the EV are closely related to the relative positions of the EV with the WPSA and the SAH. This can be well explained by the “isentropic up-glide”.

Figure 5a shows the vertical cross section of PV and potential temperature along the center of the WV on 23 June. Different from the tropical region, the wave-like high-PV region of the WV lies below 200 hPa, which is significantly lower than the altitude of the EV. The position of the WV also corresponds to a high-PV tongue and the downward transport of high PV is more obvious than that corresponding to the EV. The isentropic surfaces gather in the center of the PV anomaly area, combined with a strong upward (downward) movement on the east (west) side. Figure 5b shows the PV evolution in the center of the WV. On 22 June, the lowest point of the characteristic line is at 300 hPa. At 0000 UTC 23 June, the high PV propagates downward to 700 hPa, strengthening the cyclonic circulation at the lower level. After 1200 UTC 24 June, the characteristic line of 1 PVU is located at 500?700 hPa. Seen from the 500-hPa wind field (figure not shown), a center of south wind appears at the lower level on the east side of the WV on 23 June, and an independent north-wind center forms on the west side of the WV on 24 June, indicating that a system independent of the upper level appears at the lower level. To further illustrate the process of the downward transport of PV corresponding to the WV, a latitude?height cross section is made along the center of WV (Fig. 5d). It can be seen that the tropopause at the latitude of the SAH gets remarkably uplifted, accompanied by the low PV and a strong concave-down isentropic surface. At 0000 UTC 23 June, the meridional gradient of the high PV in the south of the WV is very large, and its intersection angle with the isentropic surface is nearly perpendicular below 200 hPa. Under such configuration, the air with high PV in the stratosphere, which locates in the north of the tropopause-breaking zone under the adiabatic condition, is transported southward to the lower troposphere along the concave-down isentropic surface (Ren et al., 2014). As seen in Fig. 5c, the strong anticyclone of the SAH determines that a northerly airflow is maintained at its east side and an upper-level jet stream appears on its north side. The right side of the exit region of the jet stream is conducive to the downward movement. Meanwhile, the strong north wind and downward movement are favorable for the PV transport through the tropopause. The intrusion of high PV could trigger the cyclonic circulation and severe convection at the lower level. As the WV moves eastward, it gradually breaks away from the influence of the SAH. The isentropic surface on the south side of the WV tends to be flat, and the southward and downward transport of PV corresponding to the WV gradually weakens, indicating that the PV transport of the WV is related to the SAH. In contrast, the PV downward transport of the westerlies system over the Pacific Ocean is much weaker (Fig. 4d), mainly due to the fact that the SAH in this region corresponds to the weaker negative PV and the weaker concave-down degree of isentropic surfaces.
Figure5. (a) Vertical cross section of PV (shading; units: 10^?6 m² s^?1 K kg^?1), meridional wind (isolines; units: m s^?1), isentropic temperature (dashed lines; units: K) and vertical circulation (vectors; units: 10^?2 Pa s^?1 along the center of the WV on 23 June. (b) Evolution of PV along the center of the WV. (c) Divergence (shading; units: 10^?5 s^?1), full wind speed (contours; units m s^?1) and wind field at 200 hPa. (d) Meridional cross section of PV (shading), potential temperature (white isolines; units: K) and the zonal anomalous height field (black isolines; units: gpm) along the center of the WV at 0000 UTC 23 June.


According to the previous analysis, during the eastward retreat of the WPSA, the southward movement of the high-PV zone appears near the south side of the WV at 30°N in the lower troposphere, which is in favor of the eastward retreat of the WPSA. This phenomenon can be reflected by the PV column with the center intensity greater than 1 PVU in the vertical cross section (Fig. 5d). Its formation may be attributable to the fact that the eastern margin of the SAH narrows and weakens under the pressure of high PV corresponding to the EV and the WV (Figs. 1c and e), which leads to the weakening in the intensity of the negative PV in the upper troposphere on the isentropic surface and the strengthening of the cyclonic circulation at the lower level, and further maintenance of the upward movement at 30°N. The condensation latent heat released by precipitation can lead to the generation of a cyclonic PV anomaly in the lower troposphere, which may be the cause of the generation of high PV in the lower troposphere (Brennan et al., 2008).

In order to further reveal the activity of the EV and WV in the PV field and their forcing mechanism on the WPSA, the relationship between the intensity change of the WPSA in the PV field and the high PV anomaly of the EV and WV is analyzed as follows.
Figure 6 shows the cross section along the line between the centers of the EV and WV, and the ridge line of the WPSA is marked by the zero line of zonal wind. It can be seen that, while the high PV anomaly of the WV moves eastward, it continuously extends from the upper troposphere to the lower troposphere. Since the data are the daily mean, the positive large-value (about 330 K) PV area on the south side of the WV in the vertical direction is actually the reflection of the high-PV zone at 30°N in the middle troposphere. When the high PV anomalies of the EV and WV approach the same longitude, the distance between them is the shortest. Along the ridge line of the WPSA, the position of the WPSA corresponds to the abnormal low-value area of columnar PV. On 22 June, the isoline of 0.5 PVU is below 345 K on the ridge line of the WPSA, and there is a low-PV anomaly center at 350 K on its west, corresponding to the location of the SAH. On 23 June, under the effect of ambient wind, the high PV corresponding to the EV tilts northward at the lower level. As the high PV anomalies of the EV and WV approach each other, the columnar low PV anomalies intensify and narrow in the whole atmosphere, and a low-value center appears at the lower level. On the ridge line of the WPSA, the 0.5-PVU line is raised to 350 K, corresponding to the enhanced westward movement of the WPSA. On 24 June, the distance between the high PV anomalies of the EV and WV continues to decrease as the EV becomes more inclined to the north at the lower level. The columnar structure of the low PV anomaly begins to fracture from the middle, while the high PV anomaly of the EV intrudes into the ridge line of the WPSA, leading to the rapid eastward retreat of the WPSA.
Figure6. Vertical cross section of PV (isolines; values in the shaded region are greater than 0.5 PVU; units: 10^?6 m² s^?1 K kg^?1) along the line between the centers of the EV and WV from 22 to 25 June. The dotted line represents the zero line of zonal wind.


It can be seen that the low PV anomaly on the ridge line of WPSA first intensifies and then weakens during the process that the high PV anomalies of the WV and EV move toward each other. The intensity variation is consistent with the variation of the 588-dagpm contour of the WPSA at 500 hPa. According to Hoskins (1974), anticyclonic circulations would appear above and below the negative PV anomaly of the upper level. According to the principle of PV conservation, when the negative PV anomaly intensifies, the distance between the upper and lower isentropic surfaces would be shortened, the static stability would increase, and the anticyclonic circulation would strengthen. Therefore, the WPSA would strengthen when the positive PV anomaly on the ridge of the WPSA decreases, and vice versa. Therefore, it is more intuitive and simpler to discuss the intensity change of the WPSA via the change in the PV anomaly at high altitude. Why, then, does the variation in the PV anomaly corresponding to the WPSA at the upper level appear and how does the high PV anomalies of the EV and WV affect the intensity change of the WPSA? The above analyses only focus on the change in the intensity of the WPSA between the PV anomalies of the EV and the WV. Further discussion is conducted about the change in the PV distribution on the fixed isentropic surface to reveal the causes for the short-term east?west movement of the WPSA.

The above section points out that abnormal PV changes in the upper troposphere can stimulate the intensity changes of the WPSA whose main body locates in the middle and lower troposphere. In this section, the horizontal distribution and the evolution of PV anomalies at high altitude are preliminarily analyzed by using the PV equation. In the selection of the isentropic surface, considering that the eigenvalue 1 PVU is located in the upper troposphere, whose variation is more suitable to reflect the changes in the anomalies of both positive and negative PV, we chose 348 K as the reference isentropic surface.
The Ertel PV equation with quasi-hydrostatic approximation (Bluestein, 1992) is given as follows:
where A is the local variation, B is the horizontal advection, C is the vertical advection, D is the vertical differential term of heating, E is the horizontal differential term of heating, and F is the friction term. The expression of PV on the isentropic surface is $P = - {\zeta _{\alpha,\theta }}g\left({{{\partial \theta }/ {\partial p}}} \right)$, in which ${\zeta _{a,\theta }} = ({\zeta _\theta } + f)$ is the absolute vorticity on the isentropic surface and $ - g(\partial \theta /\partial p)$ is the static stability. On any isentropic surface, under the adiabatic and frictionless condition, all terms associated with heating and friction in Eq. (1) are zero; only the terms of A and B are left, which means that the horizontal advection determines the local change in PV, and the PV contour will be advected unalterably with its magnitude unchanged. Therefore, the horizontal advection of PV is regarded as the conservation term and the residual terms as non-conservation terms.

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6.1. Local variation of PV

According to the above analysis, the EV and WV both correspond to the funnel-shaped high PV anomalies at high altitude, while the WPSA corresponds to the low PV anomaly. Figure 7 shows the local variation of PV at 348 K from 22 to 25 June, representing the intensity change and moving direction of the PV anomaly. Before the eastward retreat of the WPSA, the local variation of negative (positive) PV corresponding to the east (west) side of the EV strengthens, indicating that the intensity of the positive PV anomaly corresponding to the EV strengthens while moving westward. The east (west) side of the WV corresponds to the local variation of the positive (negative) PV, and the positive center moves towards the southeast side of the WV center while developing, indicating that the WV has been continuously strengthening and tends to move equatorward. On 23 June, the weak local variation of positive PV in the WPSA begins to weaken, and the area corresponding to the negative local variation appears on the south of the local-variation positive center of PV corresponding to the WV, which is beneficial to the development of the low-level anticyclonic circulation and the westward extension of the WPSA. However, due to the close proximity and enhanced development of the positive PV anomalies of the EV and WV, the low PV anomaly corresponding to the WPSA is squeezed into the belt-like distribution by the positive PV anomalies on the north and south sides. As the EV and WV move toward each other, when they reach the same longitude, the local-variation centers of positive PV on the east side of the EV and west side of the WV are connected. A belt-like zone with positive local variation of PV is formed to the west of 130°E, which enhances the positive PV anomaly over the WPSA west of 130°E and is not beneficial to maintaining the anticyclonic circulation. The intensity of the WPSA decreases, indicating an abnormally eastward retreat at 500 hPa. On 25 June, the high PV anomaly of the EV (WV) continues to move westward (eastward), and the positive local-variation center of the positive PV anomaly also moves to the west (northeast). The WPSA begins to develop westward along with the negative local variation area of PV on the east side of EV.
Figure7. Distribution of PV (shaded area is the region with PV larger than 1 PVU; units: 10^?6 m² s^?1 K kg^?1) and the local variation of PV $\partial P/\partial t$ (units: 10^?6 m² s^?2 K kg^?1) on the 348-K isentropic surface from 22 to 25 June.


It can be seen that the short-term movement of the WPSA is related to the evolution of the positive PV anomalies of the EV and WV at the high level. Due to the enhancement of the positive PV anomaly at the high level, the distance between the isentropic surfaces at the upper and lower levels decreases, the static stability increases, and the cyclonic circulation weakens, which leads to the weakening of the WPSA. Next, to further explore the causes for the short-term movement of the WPSA, the budget of the PV equation on the 348-K isentropic surface is analyzed before and after the eastward retreat of WPSA.

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6.2. Evolution of each term in the PV equation

Figures 8 and 9 show the distributions of each term in the PV equation [Eq. (1)] before and after the eastward retreat of the WPSA. In the calculation, it is found that among them, the effects of the horizontal advection and residual are the greatest, while those of the vertical advection and residual terms are slightly weaker. The horizontal distribution of the advection terms of PV is very similar to that of the local variation of PV, which increases (decreases) on the west side of the EV (WV) and decreases (increases) on the east side. This shows that the conservation terms make an important contribution to the local variation of PV on both sides of the EV and WV. However, it is noted that the value of the conservation term is much larger than that of the local variation, especially for the positive PV variation on the west (east) side of the EV (WV), which necessarily requires an equilibrium from the non-conservation terms. Before the WPSA retreats eastward (Fig. 8), the positive PV variation on the west side of the EV not only comes from the advection term, but also from the vertical advection term and the vertical differential term of heating, which make the PV variation on the east (west) side of EV tend to be negative (positive). However, the distribution of the residual term is opposite, thus weakening the distribution of the PV variation mentioned above. For the WV, the intensity of the PV variation on the east (west) side caused by the PV advection is greater, but the vertical advection, vertical differential of heating and the residual term all tend to weaken the effect of the conservation term. After the WPSA retreats eastward (Fig. 9), the negative variation of PV disappears between the EV and the WV, and their corresponding positive variations get through from north to south. The distribution of the advection term clearly reveals this characteristic, similar to that of the PV variation. The remaining non-conservation terms are quite different from those before the eastward retreat of the WPSA. The distributions of vertical advection in the EV and the WV both correspond to the positive variation of PV. The vertical differential term of heating becomes negative (positive) on the left (right) side of the WV, while it shows a positive value corresponding to the EV. Contrary to the advection term, the residual term has the effect of offsetting the advection term.
Figure8. Distribution of PV (shading; units: 10^?6 m² s^?1 K kg^?1) and the terms (a) B, (b) C, (c) D and (d) E+F in Eq. (1) (solid and dotted isolines; units: 10^?6 m² s^?2 K kg^?1) on the 348-K isentropic surface on 23 June.


Figure9. As in Fig. 8 but on 24 June.


It can be seen that the PV at the upper level is not conserved due to the existence of residual and diabatic heating, and its local variation is related to the horizontal and vertical advection of PV, the vertical differentiation of heating and the residual. Although the horizontal advection term of PV—namely, the conservation term—describes well the distribution of the two regions of the positive PV variation in the north and south before and after the eastward retreat of WPSA, the intensity is inconsistent with the PV-variation field and requires corrections from the non-conservation terms.
It is worth noting that we only diagnose the nature of how the EV affects the WPSA by using PV in this paper. For better application in manual and numerical prediction, the influence of the WV and EV’s strength and position on the WPSA’s short-term movement needs to be considered. Therefore, in future research work, we will consider using numerical sensitivity experiments to examine the impact of the two systems, so as to further study the quantitative contributions of the WV and EV.

Based on a case in 2003, this paper explains the process and mechanism of how the EV impacts the short-term abnormal eastward retreat of the WPSA by using the theory of PV. The main conclusions are as follows.
On the 348-K isentropic PV diagram, the north wind on the east side of the SAH leads the high PV corresponding to the westerlies to move southeastward, forming the WV, which reaches the same longitude as the high PV corresponding to the EV, and the WPSA is forced to retreat eastward abnormally. The SAH plays an important role in the movement and evolution of these two systems.
The EV corresponds to the high PV in the upper troposphere, and its maintenance is the result of PV downward transport at the upper level. The intensity of the EV center depends on the intensity of PV downward transport, which is related to the meridional propagation of PV at high latitude. The change in vertical motion on both sides of the EV depends on the relative position between the WPSA and the SAH. The WV is controlled by the positive PV anomaly area. Under the configuration of the isentropic surface and the PV surface at the east edge of the SAH, the PV anomaly at the upper level is transported downward, which promotes the growth of cyclonic circulation at the lower level of the WV. The weakening of the SAH in the meridional direction is beneficial to the development and southward movement of high PV at the middle and lower levels over the Yangtze River?Huaihe River Basin.
When the WPSA retreats eastward, the high PV corresponding to the EV and the WV continuously approach each other in the meridional direction and the position of the 1-PVU isoline on the ridge of the WPSA is lowered, which forces the enhancement of cyclonic circulation at the lower level and leads to the abnormally eastward retreat of the WPSA at 500 hPa.
Before the WPSA retreats eastward, the positive PV variation on the west side of the EV begins to strengthen. When the positive PV variations in the EV and the WV join together and form a belt-like zone, the WPSA retreats abnormally. The budget analyses of isentropic PV show that the horizontal advection of the PV has the greatest effect. The contribution of the vertical advection of PV and the vertical differential of heating is also positive, but the values are relatively small. The contribution of the residual was negative and it becomes smaller before and after the WPSA retreats.
Acknowledgements. This study was supported by the National Natural Science Foundation of China (Grant Nos. 41775048, 91937301, 41775050 and 91637105), the National Key R&D Program of China (Grant No. 2018YFC1507804), and the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No. 2019QZKK0105).