*3.2. The Mechanisms Contributing to Interdecadal Variations in the TP-RWS*

Since the large-scale divergent flow is directly related to anomalous diabatic heating of the atmosphere, we calculate the correlation map of the atmospheric heat source (Q1) with the TP-RWS in order to explore the possible causes of the TP-RWS interdecadal variations (Figure 5). It is worth noting that two Q1 key areas occur over the plateau, which are located in the northwestern TP (Pamirs plateau) and southeastern TP. When the interdecadal TP-RWS intensifies, the atmospheric heating characteristics over the two regions are significantly different, that is, the anomalous Q1 in northwestern TP is mainly found between the near-ground plateau and 300 hPa in the troposphere, while the Q1 in southeastern TP is more pronounced from 500 hPa to 200 hPa. The regional climate of Pamir Plateau and Tarim Basin are mainly characterized by drought, with less rainfall due to the faint water vapor imported from the tropical Indian Ocean. Meanwhile, the giant mountains in southeastern TP are mainly affected by the monsoon and moist water vapor

from the tropical ocean in summer, resulting in abundant water vapor being lifted here, which is conducive to the occurrence of deep convection [49,50]. Therefore, dynamical mechanisms contributing to the interdecadal variations in TP-RWS may be different in northwestern and southeastern TP.

**Figure 3.** The standardized time series of Rossby wave source over the TP (\*−1; dotted lines) and its 10−year low−pass filtering value (solid lines) in summer of 1900−2010. The red and black lines are results from the ERA−20C and NCEP−20C reanalysis datasets, respectively. The RWS\*−1 represents the intensity of negative Rossby wave source over the TP.

**Figure 4.** Regression coefficients between interdecadal TP−RWS series (the same as Figure 3) and the RWS (shading) and divergent wind component (vectors; unit: m·s−1) derived from ERA−20C during 1900−2010. The cross−hatched areas indicate coefficients above the 95% confidence level.

**Figure 5.** (**a**) Spatial correlations between interdecadal TP−RWS series (the same as Figure 3) and the atmospheric heat source (Q1) derived from ERA−20C during 1900−2010. (**b**) Vertical profile of correlation coefficients between the TP−RWS and the Q1 over northwestern TP (red solid line) and the Q1 over southeastern TP (blue solid line). The cross−hatched areas indicate coefficients above the 95% confidence level. The black rectangles in (**a**) denote the northwestern and southeastern TP.

The components of RWS, i.e., the vortex stretching term (RWS-S1) and the absolute vorticity advection term caused by divergent flow (RWS-S2), can be used to determine the causes of interdecadal TP-RWS during 1900 to 2010. From Formula (1), RWS-S1 is mainly determined by absolute vorticity and strong divergence, and the RWS-S2 is directly related to absolute vorticity gradient and the divergent wind component. In general, strong atmospheric heating can lead to circulation changes, which can be understood as the local influence of the RWS-S1 term on Rossby wave source. Moreover, other regions also can affect the RWS through large-scale divergent flow, which can be used as a horizontal distribution rebalancing of absolute vorticity by RWS-S2 term. The time series of TP-RWS sub-items have obvious interdecadal changes in summer from 1900 to 2010 (Figure 6). Both RWS-S1 and RWS-S2 are closely related to TP-RWS on the interdecadal scale, with correlation coefficients of 0.81 and 0.67, respectively. By comparison, RWS-S1 seems to play a more dominant role. However, the correlation coefficient between RWS-S1 and RWS-S2 is only 0.14, which indicates that their interdecadal evolutions are independent of each other. Furthermore, we find that the interdecadal Q1 fluctuations over northwestern and southeastern TP also represent significant differences with correlation coefficient of −0.05 only. Meanwhile, similar interdecadal temporal variations exist between TPRWS-S1 and northwestern TP-Q1 and between TPRWS-S2 and southeastern TP-Q1, with the correlation coefficients reaching 0.60 and 0.51, respectively. These results show that the TPRWS-S1 and TPRWS-S2, which cause interdecadal variation of TP-RWS, have independent changes along with the related atmospheric diabatic heating in different regions over the TP. Therefore, the interdecadal TP-RWS can be regarded as a result of the joint contribution of Q1 over northwestern and southeastern TP by different dynamical mechanisms.

Next, we calculate correlation maps between the two sub-terms of RWS and multiple meteorological elements on the interdecadal scale. As shown in Figure 7, the contribution of TPRWS-S1 to TP-RWS mainly occurs over the Pamir Plateau, which is characterized by both strong divergence and anomalous absolute vorticity. In addition, significant negative snow albedo and increased surface sensible heat flux are observed along the northwestern TP. Since the albedo of snow cover is significantly greater than that of other underlying surfaces (e.g., soil, forest, grass, and water), the albedo decreases when the snow melts, resulting in more solar radiation absorbed by the ground and the net radiation increases. The processes enhance surface sensible heat flux and lead to an increased Q1 over northwestern TP in the middle and lower troposphere. Therefore, the main contribution component of TP-RWS in northwestern TP is TPRWS-S1, which is caused by interdecadal variations in snow cover. In addition, we find that the snow albedo associated with the TPRWS-S1 shows a spatial east–west dipole-like pattern over the TP. This feature has also been observed in the study of the plateau snow cover [51,52]. In contrast, the main effect of TPRWS-S2 on TP-RWS is manifested in southeastern TP (Figure 8) due to the strong absolute vorticity advection caused by deep convection. A strong divergence is accompanied by the meridional northward flow in southeastern TP. This process excites disturbance in vorticity field, which is conducive to the RWS-S2 formation at the upper troposphere. Thus, the interdecadal TP-RWS variations during boreal summer are a synergistic result of the snow cover related to the vortex stretching term in northwestern TP and the deep convection related to the absolute vorticity advection term in southeastern TP.

**Figure 6.** The standardized interannual and interdecadal time series of TP−RWS components (\*−1; red lines) and the Q1 over the northwestern and southeastern TP (black lines) in summer of 1900−2010. (**a**) The vortex stretching term RWS−S1 and the northwestern TP−Q1 (60–80◦ E, 32–45◦ N), (**b**) the absolute vorticity advection term RWS−S2 and the southeastern TP-Q1 (80–105◦ E, 27–35◦ N).

In summary, the interdecadal variation in TP-RWS is closely related to atmospheric diabatic heating over northwestern and southeastern TP. The interdecadal variations in snow cover over the TP result in divergence and absolute vorticity anomalies by affecting atmospheric heating from TP surface to the middle troposphere, and then contribute to the TP-RWS by vortex stretching term. On the other hand, due to latent heat release of deep convection in southeastern TP, the TP-RWS can be formed and maintained through absolute vorticity advection caused by large-scale divergent flow in the middle and upper troposphere. Therefore, although the TP-RWS manifests as a whole, the causes of its interdecadal variations are not the same in northwestern and southeastern TP.

**Figure 7.** The correlation coefficients between interdecadal TPRWS−S1 series (the same as Figure 6a) and (**a**) the RWS (shading) and divergent wind component (vectors), (**b**) the divergence (shading) and absolute vorticity (contours) at 200 hPa, (**c**) snow albedo, (**d**) surface sensible heat flux derived from ERA−20C during 1900−2010. The cross-hatched areas indicate coefficients above the 95% confidence level. The black rectangles represent the northwestern TP.

**Figure 8.** The correlation coefficients between interdecadal TPRWS−S2 series (the same as Figure 6b) and (**a**) the RWS, (**b**) divergent wind component (vectors) and absolute vorticity gradient (shading) at 200 hPa, (**c**) precipitation, (**d**) total cloud cover derived from ERA−20C during 1900−2010. The crosshatched areas indicate coefficients above the 95% confidence level. The black rectangles represent the southeastern TP.

#### *3.3. Impacts of the Interdecadal TP-RWS on East Asia Circulation Pattern*

The interdecadal TP-RWS in JJA have a significant impact on the downstream atmospheric circulation and precipitation. From the correlation maps between TP-RWS and the land precipitation (Figure 9), an enhanced RWS corresponds to more JJA rainfall over the TP, especially in the southeastern and northwestern TP. These two regions are consistent with the atmospheric diabatic heating areas in the above section. For East Asia, the TP-RWS interdecadal variation corresponds to a clear tripole rainfall pattern. When the intensity of TP-RWS is relatively strong, the regions from the Huang-huai River Basin to the southern Korean Peninsula and the southern part of the Japan Island are accompanied by moisture anomalies, while the South China and North China are usually dry. By comparing different reanalysis results of TP-RWS and precipitation datasets, we find that there are significant relationships between the interdecadal TP-RWS and the precipitation in the Huang-huai River Basin. All the results show that the JJA rainfall in the north of the Yangtze River increases, while the precipitation in South China is suppressed.

**Figure 9.** The correlation coefficients between interdecadal TP−RWS (same as Figure 3) and global terrestrial precipitation. The interdecadal TP−RWS in (**a**,**c**) and (**b**,**d**) are from ERA−20CR and NCEP−20C, respectively. The precipitation data in (**a**,**b**) and (**c**,**d**) are from CRU\_ts4 and GPCC, respectively. The cross−hatched areas indicate coefficients above the 95% confidence level. Black boxes indicate the key areas of interdecadal precipitation.

In order to reveal the causes of the close relationship between TP-RWS and precipitation in East Asia, the Asia–Pacific atmospheric circulation anomaly associated with the TP-RWS is further discussed and analyzed in this study. As shown in Figure 10, significant negative geopotential height anomalies are observed at the middle and low troposphere over northwestern TP, Huang-huai River Basin, and the southern part of Japan, while positive geopotential heights appear over the southeastern TP and the northwestern Pacific Ocean. The stream function field at 850 hPa in the southern TP and East Asia is dominated by anomalous cyclonic circulation, and the centers are located in eastern India and Bangladesh, the Indochina Peninsula, and the Huang-huai River Basin. The prevailing southerly and easterly winds in the northwestern Pacific Ocean and the Huang-huai River Basin are attributed to the anomalous cyclonic circulation at the lower troposphere in East Asia, which lead to the water vapor convergence and upward movement at the middle and lower troposphere. The above circulation pattern provides favorable water vapor

transmission and dynamic conditions for the occurrence of precipitation in these regions, which increase the precipitation in the Huang-huai River Basin, South Korea, and Japan.

**Figure 10.** The correlation coefficients between interdecadal TP-RWS (same as Figure 3) and (**a**) geopotential height (shading) and water vapor transport flux (vectors) at 600 hPa, (**b**) stream function (shading) and horizontal wind field (vectors) at 850 hPa from 1900 to 2010. The cross−hatched areas indicate coefficients above the 95% confidence level.

We further discuss the spatial distribution of the relationship between interdecadal TP-RWS and related wave-activity flux. A prominent characteristic is that the TP-RWS triggers a zonal wave train along the northwestern TP to the North Pacific (Figure 11a). The geopotential height in northwestern TP, eastern TP, East Asia, and the northwestern Pacific Ocean correspond to negative, positive, negative, and positive wave train anomalies, respectively. As shown in Figure 11b, strengthening TP-RWS is accompanied by an anomalous wave activity flux originating over the northwestern TP and propagating eastward along the westerly jet stream to the East Asia and northwestern Pacific. This anomalous wave flux also has a tendency to spread southward but to a lesser extent. Moreover, we investigate the vertical structure to further explore the teleconnection pattern associated with interdecadal TP-RWS. A significant zonal wave train can be seen from the TP to the northwestern Pacific, and the strongest wave flux is located over the western TP, accompanied by a Rossby wave spreading downstream to East Asia and the North Pacific. In addition, the TP-RWS teleconnection pattern exhibits an equivalent barotropic structure at the vertical profile. It is worth noting that the anomalous wave activity excites from the TP has obvious characteristics of propagating from the upper troposphere to the lower troposphere over East Asia. Accompanied by the low pressure over the Huang-huai River Basin to Japan Island, the TPRWS-excited teleconnection is conducive to the strengthening ascent movement at the middle and lower troposphere.

**Figure 11.** (**a**) The correlation coefficients between interdecadal TP−RWS (same as Figure 3) and the geopotential height (shading) and T−N wave flux (vectors) at 200 hPa. Vertical profiles of correlation coefficients between interdecadal TP-RWS and (**b**) the geopotential height and T−N wave flux, (**c**) the vertical velocity averaged along 28−45◦ N from 1900 to 2010. The cross-hatched areas indicate coefficients above the 95% confidence level.

Previous studies have shown that the Atlantic multidecadal oscillation (AMO) can modulate the intensity of the East Asian summer monsoon by exciting teleconnection wave train [53–56]. The interannual variation in deep convection in the southeastern TP is also closely associated with the AMO [57,58]. In order to distinguish the effects of TP-RWS and AMO on East Asia, we calculate the partial correlation between interdecadal TP-RWS and the atmospheric circulation without AMO series in the Northern Hemisphere (Figure 12). Consistent with Figure 11, the zonal wave train excited by interdecadal TP-RWS propagating from northwestern TP to East Asia is still clear and the corresponding circulation intensity over East Asia and Northwest Pacific is significantly strengthened. Therefore, it is reasonable to believe that the TP-RWS during 1900 to 2010 can stimulate an equivalent barotropic zonal wave train that travels eastward along the westerly jet to the northwest Pacific and exhibits "low-high-low-high" geopotential height anomalies at the vertical profile. Furthermore, the pattern is conducive to the upward movement and precipitation over the Huang-huai River Basin.

**Figure 12.** (**a**) Partial correlation coefficients between interdecadal TP−RWS (same as Figure 3) and the geopotential height (shading) and T−N wave flux (vectors) at 200 hPa (remove interdecadal AMO). Vertical profiles of partial correlation coefficients between interdecadal TP−RWS and (**b**) the geopotential height and T−N wave flux, (**c**) the vertical velocity averaged along 28−45◦ N from 1900 to 2010. The cross−hatched areas indicate coefficients above the 95% confidence level.
