Interannual Influences of the Surface Potential Vorticity Forcing over the Tibetan Plateau on East Asian Summer Rainfall

The influences of interannual surface potential vorticity forcing over the Tibetan Plateau (TP) on East Asian summer rainfall (EASR) and upper-level circulation are explored in this study. The results show that the interannual EASR and associated circulations are closely related to the surface potential vorticity negative uniform leading mode (PVNUM) over the TP. When the PVNUM is in the positive phase, more rainfall occurs in the Yangtze River valley, South Korea, Japan, and part of northern China, less rainfall occurs in southern China, and vice versa. A possible mechanism by which PVNUM affects EASR is proposed. Unstable air induced by the positive phase of PVNUM could stimulate significant upward motion and a lower-level anomalous cyclone over the TP. As a result, a dipole heating mode with anomalous cooling over the southwestern TP and anomalous heating over the southeastern TP is generated. Sensitivity experiment results regarding this dipole heating mode indicate that anomalous cooling over the southwestern TP leads to local and northeastern Asian negative height anomalies, while anomalous heating over the southeastern TP leads to local positive height anomalies. These results greatly resemble the realistic circulation pattern associated with EASR. Further analysis indicates that the anomalous water vapor transport associated with this anomalous circulation pattern is responsible for the anomalous EASR. Consequently, changes in surface potential vorticity forcing over the TP can induce changes in EASR.

The TP, as the highest and broadest plateau on Earth, has increasingly attracted the attention of climatologists due to its large dynamic and thermodynamic effects on the cli-mate of Asia. Previous studies have demonstrated that the thermal forcing of the TP can greatly impact the Asian summer monsoon system (e.g., Flohn, 1957;Yeh et al., 1957;Ye and Gao, 1979;Yanai et al., 1992;Wu et al., , 2007Wu et al., , 2012Wu et al., , 2018Xu et al., 2015). For example, Wu et al. ( , 2007 indicated that sensible heating over the TP is the major driver of monsoon rainfall over the Asian continent. The strong surface sensible heating over the TP during boreal spring can affect the subsequent summer monsoon rainfall (Zhao and Chen, 2001;Duan et al., 2005). The onset, formation, and evolution of the Asian summer monsoon are closely related to the thermal forcing of the TP (Wu and Zhang, 1998;Hsu and Liu, 2003). Moreover, some studies have examined the mechanical effects of the TP on the Asian summer monsoon system. Hahn and Manabe (1975) documented that the South Asian summer monsoon would not reach inland Asia if the TP were removed. More complex experiments, considering increasing TP heights from zero to its contemporary height (Chen et al., 1999;Liu, 1999;Kitoh, 2004;Jiang et al., 2008), have indicated that Asian summer monsoon rainfall shifts northward from the Indian Ocean to inland Asia as TP height increases. Certain studies (Liu and Yin, 2002;Liang et al., 2005) have illustrated that the onset and evolution of the Asian summer monsoon is also sensitive to the location and height of the TP. However, little insight is given about the intrinsic combined effects of dynamic and thermodynamic forcing of the TP in the literature. Potential vorticity (PV; Rossby, 1940;Ertel, 1942), which inherently combines atmospheric dynamics and thermodynamics, is an ideal indicator of the combined dynamic and thermodynamic conditions of the TP. Most previous studies have focused on atmospheric interior PV. Its impacts on general circulation structure (e.g., Hoskins, 1991), rainstorms, and cold air activities (e.g., Wu et al., 1995;Wu and Cai, 1997;Zhao and Ding, 2009) and its interannual relation to ozone (Danielsen, 1968;Allaart et al., 1993;Folkins and Appenzeller, 1996;Sandhya et al., 2015) and Rossby wave breaking (Folkins and Appenzeller, 1996;Ryoo et al., 2013;Bowley et al., 2019) are the main areas of interest. However, instead of atmospheric interior PV, some studies (e.g., Hoskins, 1991) highlight the importance of surface PV, especially surface PV over the TP, based on the impermeability theorem McIntyre, 1987, 1990). For example, the elevated TP is one of the most prominent surface PV sources in the world (Sheng et al., 2021). In particular, the surface PV over the TP (TPPV) could exert a prominent influence on the TP vortex (Sheng et al., 2021) and downstream rainfall and extreme cold events Yu et al., 2019;Zhang et al., 2021). Although surface PV is known to be of great importance, the influence of surface TPPV forcing on EASR is still a knowledge gap.
This study aims to illustrate the interannual impact on EASR of the surface TPPV forcing associated with the intrinsic combined effect of the dynamics and thermodynamics of the TP. The remainder of the paper is organized as follows. Section 2 presents the data, method, and model. In sec-tion 3, the relationships of surface TPPV forcing with EASR and EASR-related circulation are presented. Section 4 analyzes the possible mechanism of how surface TPPV forcing affects EASR. Finally, conclusions and discussion are provided in section 5.
2. Data, method, and model 2.1. Data Monthly mean data on the hybrid σ-p model level obtained from MERRA2 (Rienecker et al., 2011;Lucchesi, 2012) are used to calculate surface PV and surface static stability. Variables include air temperature, zonal and meridional wind, and pressure.
Additional data used in this study include monthly outgoing longwave radiation (OLR) from the polar-orbiting series of satellites of the National Oceanic and Atmospheric Administration (Liebmann and Smith, 1996), monthly land precipitation from the Climatic Research Unit (Mitchell and Jones, 2005), and monthly specific humidity and zonal, meridional, and vertical wind on pressure level from MERRA2.
The study period is 1980-2017. The horizontal resolution of all MERRA2 data is 0.625° × 0.5° (longitude × latitude). The horizontal resolutions of the OLR and precipitation data are 2.5° × 2.5° and 0.5° × 0.5°, respectively. Climate mean values calculated over June, July, and August (JJA) are used to represent the boreal summer condition.

Method
Surface PV is calculated as follows (Sheng et al., 2021): u, v) where and is the specific volume and absolute vorticity in the hybrid σ-p coordinate system, respectively. The g is gravity, which is 9.8 m s −2 , p is pressure, is potential temperature, f is the Coriolis parameter, is horizontal wind, and h indicates that the horizontal difference is carried out at the hybrid σ-p level. The surface PV is obtained from the two bottom levels at the hybrid σ-p level. More details about the calculation of surface PV can be found in Sheng et al. (2021).
The surface static stability is calculated as , where and are obtained from the two bottom levels at the hybrid σ-p level.
The horizontal water vapor flux (WVF) is calculated as follows: where q is specific humidity. Statistical methods, including linear regression, linear correlation, Student's t-test, empirical orthogonal function (EOF), and multivariate EOF (MVEOF), are used in this study. The linear trends and decadal variation (more than nine years) in the data are removed to highlight the interannual variability.

Model
The linear baroclinic model (LBM) (Watanabe et al., 1999;Watanabe and Kimoto, 2000) is employed to investigate the responses of the upper-level circulation to the surface PV forcing over the TP. The model used in this study has 20 σ vertical levels. Each horizontal level is represented by spherical harmonics with a resolution of T42. More details about the model description can be found in Watanabe and Jin (2003). The LBM is a time-varying model that linearizes the basic state based on primitive equations. We take boreal summer climatology as the basic state in this study. Since dissipation terms including biharmonic horizontal diffusion, weak vertical diffusion, Newtonian damping, and Rayleigh friction are adopted, the model response reaches its steady state at approximately 14 days. Therefore, we use the results averaged from the last 15 days in the 30-day integration for analysis.

Leading mode of surface TPPV, EASR, and upperlevel circulation
EOF analysis is applied to analyze the dominant temporal and spatial features of the surface TPPV, EASR, and circulation over East Asia during boreal summer for the 1980-2017 period. Figure 1a shows the first leading mode of the EOF (EOF1) on the summer surface TPPV. The variation in surface PV on the southern slope and in the southeastern corner of the TP has the opposite sign to that in the main TP platform. Although the signs of the surface PV in the two areas are opposite, the southern area is quite small. In general, the distribution of EOF1 on surface PV shows a negative uniform mode (PVNUM). The corresponding normalized first principal component of the EOF pattern (PC1) is defined as the surface PV index (PVSI; red line), as shown in Fig. 1d. The variance percentage explained by the first leading mode is 36%. Figure 1b shows the EOF1 of EASR. The corresponding normalized PC1 is defined as the precipitation index (PreI; blue dashed line), as shown in Fig. 1d. The maximum variation center of EASR occurs in the Yangtze River valley, South Korea, Japan (YKJ), and southern China. The variation in EASR in YKJ has the opposite sign to that in southern China. There is also a relatively weak dipole variation mode in northern China. The dominant mode of EASR obtained in this study is generally consistent with that obtained by Zuo et al. (2011).
Using the NCEP-NCAR reanalysis over midlatitude Asia in JJAS (i.e., June, July, August, and September) from 1948 to 1998, Wu (2002) identified an interannual dominant pattern in the upper-level winds called the midlatitude Asian summer (MAS) pattern. The MAS pattern in his study features two anomalous cyclones, with one centered at (37.5°N, 65°E) and the other centered at (42.5°N, 130°E). Following Wu (2002), we applied MVEOF analysis to the 200-hPa wind anomaly to reveal the dominant circulation mode over midlatitude Asia during boreal summer. The domain for the MVEOF analysis is (20°-60°N, 50°-150°E), and the result is not sensitive to the domain. The first leading mode of MVEOF (MVEOF1) is shown in Fig. 1c, and the corresponding normalized PC1 is defined as the midlatitude Asian summer index (MASI; black dashed line) shown in Fig. 1d. Figure 1c shows two anomalous cyclones, one centered northwest of the TP and one centered over northeastern Asia. In between the two large cyclones is an anticyclone over the southeastern corner of the TP. The anticyclone identified in this study is more prominent than that in Wu (2002), which is partly because of the different reanalysis data and partly because of the different periods. From high to low latitudes, the positive MAS generally shows a "CCA" pattern (i.e., cyclone-cyclone-anticyclone pattern). Correspondingly, the negative MAS generally shows an "AAC " pattern (i.e., anticyclone-anticyclone-cyclone pattern).
To investigate the relationship of surface TPPV forcing with the EASR and upper-level circulation over East Asia, Fig. 1d shows the time series of PVSI, MASI, and PreI. PVSI shows significant correlations with PreI and MASI, with yield correlation coefficients of 0.56 and 0.74 (both passing the 0.05 significance level), respectively. These results indicate that the EASR and the leading mode of circulation (i.e., MAS pattern) over East Asia are closely related to the surface TPPV forcing.

Relationship of surface TPPV forcing with EASR
and associated circulation Figure 2 shows the spatial pattern of the correlation coef-ficients between the PVSI and EASR anomalies. The pattern ( Fig. 2) is similar to EOF1 of EASR (Fig. 1b). A negative correlation appears in southern China, whereas positive correlations are observed in YKJ. A positive correlation, but with a small area, appears in part of northern China. The correlation coefficients in these regions are significant at the 0.05 significance level. A weak negative correlation is seen in the area south of northern China (approximately 42°N), but this correlation is not significant. These results indicate that the positive phase of PVNUM is associated with more rainfall in YJK and part of northern China and less rainfall in southern China, and the negative phase of PVNUM is related to the opposite rainfall pattern.
To understand the comprehensive three-dimensional relationship between surface TPPV forcing and EASR, the correlation patterns between the PVSI, PreI, and circulation anomalies at different levels are shown in Fig. 3. Figures 3a-c show correlation coefficients between PVSI and circulation at different levels. Corresponding to the positive (negative) PVNUM, at 200 hPa (Fig. 3a), two anomalous cyclones (anticyclones) appear at middle latitudes at approximately 40°N. One center is located northwest of the TP, and the other is located in northeastern China (Fig. 3a). In addition to these two anomalous cyclones (anticyclones), an anomalous anticyclone (cyclone) center appears at the southeastern corner of the TP. This configuration generally shows the MAS pattern (Fig. 1b). Except for the anomalous cyclone (anticyclone) over the northwestern TP at 850 hPa (Fig. 3c), this equivalent barotropic pattern can also be seen at the middle (Fig.  3b) to lower (Fig. 3c) levels. The correlation between PreI and circulation (Figs. 3d-3f) closely resembles Figs. 3a-c, which further confirms that surface TPPV forcing is significantly related to EASR. In addition, comparing Figs. 3a-c and Figs. 3d-f reveals that the MAS pattern plays an important role in the connection between surface TPPV forcing and EASR.

Possible mechanism of the surface TPPV forcing affecting the EASR
To investigate the possible mechanism of surface TPPV forcing affecting EASR, the LBM is employed in this section to examine the response of upper circulation to the anomalous heating related to surface TPPV forcing.

Diagnostic analysis
Surface PV is closely related to the static stability within the surface layer. Figure 4a shows the correlation coefficient between PVSI and static stability anomalies. The correlation between the PVSI and horizontal wind anomalies at the surface and vertical motion (omega) anomalies at 500 hPa are shown in Fig. 4b. Corresponding to the positive phase of PVNUM, the anomalous static stability over the whole TP is significantly negative (Fig. 4a). This result means that the air within the surface layer over the TP is anomalously statically unstable. As a result, the anomalous omega is significantly negative, accompanied by anomalous upward motion occurring at the main body of the TP (Fig. 4b). Consequently, a significant anomalous cyclonic circulation is generated at the surface south of the TP (Fig. 4b).
The negative phase of PVNUM corresponds to the opposite situation of surface static stability and circulation pattern.
The anomalous south and north winds associated with the anomalous circulation to the south of the TP (Fig. 4b) induced by surface TPPV forcing could lead to anomalous heating over the TP. Figure 5 shows the correlation coefficient between PVSI and OLR (Fig. 5a) and regressed rainfall anomalies against PVSI (Fig. 5b) to examine the distribution of anomalous heating. A dipole mode of the OLR anomalies is clearly observed in Fig. 5a. Corresponding to the positive phase of PVNUM, positive OLR anomalies cover the southwestern TP to northern India. The highest negative OLR anomalies mainly occur on the eastern TP, whereas the highest positive OLR anomalies mainly occur on the western TP. The anomalous cyclonic circulation (Fig. 4b), with cool and divergent flow to its western part and wet, warm flow to its eastern part, accounts for this clear dipole mode of the OLR (Fig. 5a). Consistent with the OLR, the rainfall anomalies also show a dipole mode (Fig. 5b) with less rainfall over the southwestern TP and northern India and more rainfall over the eastern TP. The rainfall anomalies indicate that the strongest negative and positive condensational heating anomalies occur at the southwestern TP to northern India and the eastern TP, respectively. Corresponding to the negative phase of PVNUM, the situation is opposite.

Sensitivity experiments
The response of upper-level circulation to the negative heating anomaly over northern India has been examined in Wei et al. (2014). Because the lower latitude of the negative heating anomaly over northern India (Fig. 5b) is far away from the westerly jet (light green shading in Fig. 7) at high latitudes in the north, the associated atmospheric response regarding the negative heating anomaly over northern India is trapped south of 40°N (Wei et al., 2014;see their Fig. 8), exhibiting a zonal dipole mode with an anomalous cyclone to the west of 80°E and an anomalous anticyclone to the east of 80°E. There are some differences between the circulation caused by the negative heating anom-aly over northern India (Wei et al., 2014;see their Fig. 8) and the MAS pattern (Fig. 3) related to EASR. Hence, regarding the negative heating anomalies centered on the southwestern TP and northern India, we focus on the southwestern TP in this study.
Based on the diagnostic analysis of heating anomalies induced by surface TPPV forcing, three groups of experiments are conducted. Expt1 is an experiment of positive heating over the southeastern TP (Expt1, Figs. 6a-b). Expt2 is an experiment of negative heating over the southwestern TP (Expt2, Figs. 6c-d). Expt3 is an experiment of combined positive and negative heating over the southeastern and southwestern TP, respectively (Expt3, Fig. 6e). According to the reanalysis, the heating centers are at 30°N, 99°E and 32°N, 75°E in Expt1 and Expt2, respectively. The peaks of the ideal heating profiles in Expt1 and Expt2 are 1.0 K d −1 and  -1.0 K d −1 , respectively. The peaks in the heating profile are at σ= 0.6 and σ= 0.4 in Expt1 and Expt2, respectively. Since the LBM is a linear model, the heating configuration (Fig. 6e) and atmospheric response (Fig. 7c) in Expt3 are linear combinations of Expt1 and Expt2.
The atmospheric responses are shown in Fig. 7. In Expt1 (Fig. 7a), the positive heating anomaly over the eastern TP triggers a local anomalous anticyclone and high height at 200 hPa. The anomalous high is strengthened locally with slight northward and westward dispersion. In Expt2 (Fig. 7b), the negative heating anomaly over the southwestern TP stimulates a local anomalous cyclone and low height at 200 hPa. Compared with Wei et al. (2014), because the location of the negative heating center over the southwestern TP is farther north than that over northern India, the anomalous cyclone could trigger waves in the west-erly jet and lead to an anomalous cyclone downstream over northeastern China. In Expt3 (Fig. 7c), the response of atmospheric circulation with the "CCA" pattern is very similar to the MAS pattern related to EASR (Figs. 3d-f). These results indicate that the dipole heating mode induced by surface TPPV forcing can lead to a realistic MAS pattern, which is important for the formation of the anomalous EASR.

Influence of circulation anomalies on EASR
The above results indicate that surface TPPV forcing can lead to the formation of the MAS pattern. In this section, we examine how the MAS pattern affects the EASR anomalies.
Rainfall anomalies are related to water vapor transport anomalies and their divergence at the lower level. Since atmo- spheric moisture is mainly concentrated at the middle to lower levels, Fig. 8 shows the correlation between PVSI and WVF and its divergence at 500 hPa (Fig. 8a) and 850 hPa (Fig. 8b). Generally, the anomalous WVF (Fig. 8) shows an equivalent barotropic structure. This equivalent barotropic structure markedly resembles the MAS pattern. Corresponding to the positive phase of PVNUM, the anomalous cyclonic WVF (Fig. 8) over northeastern China embedded in the MAS pattern converges water vapor over South Korea and Japan and, cooperating with the southern anticyclonic WVF, converges the wet, warm southwesterly flow and dry, cold northerly wind to the Yangtze River valley. In addi-tion, an anomalous convergence of WVF (Fig. 8) occurs in part of northern China. Hence, the EASR over YKJ and part of northern China is greater than normal (Fig. 2). Although the WVF transfers water vapor to southern China, the WVF is divergent. Thus, the EASR over southern China is lower than normal (Fig. 2). Corresponding to the negative phase of PVNUM, the situation is opposite. These results indicate that the WVF anomalies related to the MAS pattern are responsible for the EASR anomalies.

Conclusion and discussion
The present study investigates the relationship between the surface PV forcing over the TP and EASR and the associated circulation on the interannual timescale and the possible mechanism. The main conclusions obtained from the results are described as follows.
The correlation between the time series of the leading mode of the surface PV forcing over the TP (i.e., PVNUM) and EASR and the leading mode of upper-level circulation (i.e., MAS pattern) are as high as 0.56 and 0.74, respectively. Moreover, the circulation related to PVNUM greatly resembles the circulation associated with EASR. These results indicated that the interannual EASR and related upperlevel circulation over East Asia are closely linked to the surface PV forcing over the TP, and the MAS pattern plays an important role in the PVNUM affecting EASR. Diagnostic analysis indicates that the positive phase of PVNUM could lead to unstable air within the surface layer over the TP. As a result, anomalous upward motion and cyclonic circulation are generated over the TP. Induced by cyclonic circulation, a dipole heating mode with anomalous cooling over the southwestern TP and anomalous heating over the southeastern TP appeared. Sensitivity experiments prove that the dipole heating mode associated with the surface PV forcing over the TP can trigger the MAS pattern related to EASR anomalies. The MAS pattern converges water vapor to the Yangtze River valley, South Korea, Japan, and part of northern China and diverges water vapor over southern China. Therefore, the EASR over the Yangtze River valley, South Korea, Japan, and part of northern China is greater than normal, and that over southern China is lower. The negative phase of PVNUM is related to the opposite rainfall and circulation pattern. Consequently, the surface PV forcing over the TP exerts a significant influence on EASR by changing the air static stability within the surface layer over the TP and causing the dipole heating mode and the subsequent anomalous water vapor transport related to the MAS pattern.
The aforementioned major mechanism is briefly shown schematically in Fig. 9. In summary, PVNUM triggers lower-level cyclonic circulation by reducing the surface static stablity (Fig. 9b). The dipole heaing mode induced by this cyclonic circulation could lead to anomalous circulation at the upper level (Fig. 9a). As a result, the anomalous water vapor transport (Fig. 8) embedded in the upper-level anomalous circulation is responsible for EASR anomalies   Previous studies (e.g., Wu, 2002) show that the MAS pattern is related to the Indian summer monsoon. We calculated the concurrent correlation coefficient between the MASI and Indian summer monsoon index (defined by Wang et al., 2001) and found that the correlation coefficient reaches -0.45, passing the 0.05 significance test; however, when the index of the surface TPPV forcing (i.e., PVSI, red line in Fig. 1d) is removed, it is reduced to -0.28, which does not pass the significance test. This result further confirms the important role of surface TPPV forcing on EASR. ENSO is the most prominent interannual signal in climate systems. We also calculated the correlation between the summer PVSI and NINO3.4 index (SST averaged over the region 5°S-5°N, 170°-120°W; https://psl.noaa.gov/ data/climateindices/list/) in the preceding winter and concurrent summer. The coefficients are 0.21 and -0.18, respectively, which do not pass the significance test, meaning that the relationship between surface TPPV forcing and EASR is unaffected by ENSO. It should be noted that some studies (e.g., Guan et al., 2015) suggested that North Atlantic Oscillation, Pacific Decadal Oscillation, and Atlantic Multidecadal Oscillation have great impact on surface air temperature, which is related to surface PV. The role of these decadal oscillations in the interdecadal variation of surface TPPV will be investigated in the future.
The present study only focuses on the impacts of the TP on monsoon rainfall over East Asia. The complicated Asian summer monsoon system, greatly affected by the TP, includes the South Asian summer monsoon and the East Asian summer monsoon. Research on the relationship between the PV anomaly over the TP and monsoon rainfall, as well as wind fields over the Asian region will be conducted in the future. In this study, although the simple model (e.g., LBM) clearly shows the impact of surface TPPV forcing on EASR, it is still necessary to use a fully coupled model to examine the surface TPPV-rainfall-circulation feedback to understand the interactions between the surface TP forcing and EASM system. Furthermore, with the help of the PV budget equation, the relative importance of dynamic PV advection, PV generation due to diabatic heating, and friction effects to the variation of surface PV will be quantificationally answered, which will greatly advance our understanding of the TP's impacts.