**3. The Guiding Role of Theory of Rossby Wave Energy Dispersion in the Study on the Dynamical Processes of the Variabilities of the East Asian Summer Monsoon System**

Under the guidance of the theory of Rossby wave energy dispersion, the research on the dynamical processes of the variabilities of the East Asian summer monsoon system has been in recent years, especially on the interannual and interdecadal variabilities of the EAP pattern and "Silk Road" teleconnection wave trains and their effects on the variability of summer monsoon precipitation in eastern China.

*3.1. The Guiding Role of the Theory of Rossby Wave Energy Dispersion in the Study on the Dynamical Processes of the Interannual Variability of the East Asian Summer Monsoon System* 3.1.1. Dynamical Influence of the EAP Pattern Teleconnection Wave Train on the Interannual Variability of the East Asian Summer Monsoon System

In summer, the monsoon is prevalent in East Asia. Due to the obvious interannual variability of the monsoon, severe droughts and floods often occur in the eastern part of China. Therefore, the causes of the interannual variability of the East Asian summer monsoon system and summer monsoon precipitation in China are important research topics.

The dynamical processes of the interannual variability of the East Asian summer monsoon system have been an interesting research topic for many scholars in East Asia since the 1980s. Nitta [13] firstly proposed that there is an anti-correlated oscillation, or the Pacific-Japan (PJ) oscillation, between the summer atmospheric circulation anomalies over the tropical western Pacific around the Philippines and those around Japan. Kosaka and Nakamura [20,32] also investigated the dynamics of the PJ oscillation. Under the guidance of the theory of Rossby wave energy dispersion, our research group [14–17,33] systematically studied the influence of strong heat sources formed by convective activities and the SST in the tropical western Pacific Ocean around the Philippines on the East Asian summer monsoon system and summer precipitation in eastern China from observational facts, theory and numerical simulations, respectively. These studies show that there is a distribution of teleconnection wave train of atmospheric circulation anomalies over the tropical western Pacific Ocean through East Asia and the Okhotsk Sea to Alaska and the west coast of North America in summer, which is referred as the East Asia/Pacific (EAP) pattern teleconnection wave train. These studies revealed that, as shown in Figure 3a, when the western Pacific warm pool is in a warm state and the convective activities over the tropical western Pacific around the Philippines are strong, there is a cyclonic circulation anomaly over the tropical western Pacific around the Philippines. Meanwhile, there is an anticyclonic circulation anomaly over Japan and the Yangtze and Huaihe River basins in China, i.e., the western Pacific subtropical high shifts northward. There is a cyclonic circulation anomaly that extends from north China towards the Okhotsk Sea. Under this condition, the plum rains over the Yangtze and Huaihe River basins are weak. In contrast, when the western Pacific warm pool is in a cold state and the convective activities over the tropical western Pacific around the Philippines are weak, as shown in Figure 3b, there is an anticyclonic circulation anomaly around the Philippines. There is a cyclonic circulation anomaly over Japan and the Yangtze and Huaihe River basins in China; that is, the West Pacific subtropical high shifts southward. In this configuration, strong plum rains often cause floods in the Yangtze River and Huaihe River basins. Due to the EAP pattern teleconnection wave train, the summer monsoon precipitation anomalies in eastern China often show a distribution of "+, −, +" or "−, +, −" tripole pattern wave train from south to north.

**Figure 3.** Schematic map of the relationships among the thermal state of the West Pacific warm pool (0◦–14◦ N, 130◦–150◦ E), the convective activities around the Philippines, the West Pacific subtropical high and the summer monsoon rainfall anomaly in the Yangtze River and the Huai River valleys in the (**a**) warm and (**b**) cooling states of the West Pacific warm pool (From Huang and Sun [17]).

It can also be studied from the EOF analysis of summer monsoon precipitation that the distributions of summer precipitation anomalies in eastern China are similar to the EAP pattern teleconnection. Our research group recently conducted the EOF analysis of the summer precipitation in eastern China using data for 60 years from 1961 to 2020. Figure 4a–d show the spatial distribution and corresponding temporal coefficients of summer precipitation in eastern China from 1961 to 2020, respectively. As shown in Figure 4a, the first mode of summer precipitation in eastern China shows a meridional tripole structure, which is similar to the EAP pattern. Additionally, as shown in Figure 4c, the first main mode of the variability of summer monsoon precipitation in eastern China shows a 2–3 year period. This is closely related to the meridional tripole distribution of the first mode of zonal water vapor transports in East Asia in summer [34].

**Figure 4.** (**a**,**b**) Spatial distributions and (**c**,**d**) corresponding time coefficient series of the first and second components of EOF analysis of summertime (JJA) rainfall in eastern China for 1961–2020. The sold and dashed lines in Figure 4a,b indicate positive and negative values, respectively, and EOF1 and EOF2 explain 11.1% and 8.8%, respectively.

Huang et al. [35] used the EAP pattern teleconnection of atmospheric circulation anamolies to further explain the causes of the interannual variability of the summer precipitation in eastern China. This study showed that the spatial distribution of the variabilities of summer precipitation and East Asian summer monsoon water vapor transport fluxes in eastern China appears a meridional tripole distribution with a quasi-biennial period. The interannual variability with the quasi-biennial period maybe caused by the planetary wave train (i.e., EAP pattern teleconnection wave train) generated by the interannual variation of thermal forcing over the tropical western Pacific warm pool. Figure 5 shows the distribution of 500 hPa geopotential height anomalies regressed from the PC1. As shown in Figure 5, we can see that the summer monsoon circulation anomalies over East Asia and the tropical western Pacific exhibit a meridional tripole structure from south to north, and this distribution resembles the EAP pattern teleconnection wave train.

**Figure 5.** Distribution of summertime 500 hPa height anomalies over East Asia regressed by the time coefficients of EOF1 of summertime 500 hPa height for 1961–2020. Solid and dashed lines indicate positive and negative height anomalies, respectively, and areas with confidence level over 95% are shaded. Data of geopotential height fields is from the NCEP/NCAR reanalysis data [30].

To reflect the interannual variability of the EAP pattern teleconnection wave train and its influence on the interannual variability of summer monsoon precipitation in the Yangtze and Huaihe River basins, Huang G. [36] defined an EAP index from the distribution of the EAP pattern teleconnection wave train. This index is calculated with the standardized seasonal-mean (June-July-August) 500 hPa height anomaly at three different grid points (20◦ N, 125◦ E; 40◦ N, 125◦ E; 60◦ N, 125◦ E), which can well measure the strength of the East Asian summer monsoon and describe the interannual variability of summer rainfall and surface air temperature in East Asia. This index has a significantly negative correlation not only with summer monsoon precipitation in the Yangtze and Huaihe River basins in China but also with summer precipitation in Korea. Moreover, this index has a positive correlation with summer precipitation in North and South China. This shows that this index can describe the interannual variability of precipitation caused by East Asian summer monsoon. Figure 6 shows the wavelet analysis of the EAP index for 60 summers (June to August) recently calculated by using the definition of Huang G. [36] and the NCEP/NCAR reanalysis data from 1961 to 2020. From Figure 6, it can be seen that this index shows the interannual variability with the 2–3 year period from the 1970s to the late 1990s and from 2015 onward, which indicates that the interannual variability of East Asian summer monsoon precipitation with the 2–3 year period is closely related to the interannual variability of the EAP pattern teleconnection wave train.

**Figure 6.** Wavelet analysis (*Y*-axis denotes periods, units: year; the curve on the right panel denotes the global wavelet spectrum; shading depicts power spectrum significant beyond 95% level based on the Chi-square test) of the EAP index calculated by using the definition in Huang G. [36] and 500 hPa height fields of the NCEP/NCAR reanalysis data [30] for 1961–2020.

3.1.2. Dynamical Influence of the "Silk Road" Pattern Teleconnection Wave Train on the Interannual Variability of the East Asian Summer Monsoon System

The variability of the East Asian summer monsoon system is influenced not only by the heat of the tropical western Pacific but also by the subtropical jet over Asia. The results studied by previous studies [18,19,21] demonstrated the existence of a wave train in the meridional wind variability in the upper troposphere from West Asia to East Asia. Later, Enomoto et al. [37] referred to this teleconnection wave train as the "Silk Road" pattern teleconnection. Therefore, the anomalies of East Asian summer monsoon precipitation with the meridional tripole or meridional dipole distribution may be influenced not only by the EAP pattern teleconnection but also by the Silk Road pattern teleconnection propagating along the upper tropospheric subtropical jet stream from West Asia to East Asia. Tao and Wei [38] suggested that the "Silk Road" pattern teleconnection has an important influence on the northward or southward movement of the western Pacific subtropical high and the East Asian summer monsoon rainfall belt. Hsu and Lin [39] and Kosaka et al. [40] also suggested that the Silk Road pattern teleconnection has an important influence on the western Pacific subtropical high and the northward or southward movement of and the summer monsoon rainfall belt. Hsu and Lin [39] and Kosaka et al. [40] further noted that the distribution of the summer precipitation anomalies with the tripole pattern is related not only to the EAP pattern teleconnection but also to the Silk Road pattern teleconnection propagating along the subtropical jet over Asia. Huang et al. [41] studied the dynamical processes of the variability of East Asian summer monsoon precipitation in terms of water vapor transports and showed that the variability of the East Asian summer monsoon precipitation is driven by a combination of the EAP pattern teleconnection wave train and the Silk Road pattern teleconnection wave train.

#### *3.2. The Guiding Role of the Theory of Rossby Wave Energy Dispersion in the Study on the Dynamical Processes of the Interdecadal Variability of the East Asian Summer Monsoon System*

The East Asian summer monsoon system not only has significant interannual variability but also obvious interdecadal variability. Due to the influence of interdecadal variability of the East Asian summer monsoon system, there is significant interdecadal variability in summer precipitation in eastern China. The result studied by Huang et al. [41] showed that the summer monsoon precipitation in eastern China experienced three significant interdecadal variations from the 1970s to the beginning of the 21st century. Recently, our research group analyzed the interdecadal variability of summer precipitation in eastern China using the summer precipitation data from 1961 to 2020 (Figure 7). The result shows that during 1961–1976, the summer precipitation anomalies in eastern China exhibited a "+, −, +" meridional tripole distribution from south to north, i.e., there was more precipitation in southern and northern China and less precipitation in the Yangtze River basin. However, during 1978–1992, the summer precipitation anomalies in eastern China appeared to have the opposite meridional distribution to those during 1961–1976. In the period from 1977 to 1992, the summer precipitation anomalies in eastern China appeared to have the opposite distribution of the meridional tripole pattern from 1961 to 1977, i.e., the meridional tripole pattern of "−, +, −", when the summer precipitation in southern and northern China decreased, while the summer precipitation in the Yangtze River basin increased. However, from 1999 to 2010, the summer monsoon precipitation anomaly in eastern China changed from a meridional tripole distribution to a meridional dipole distribution, i.e., appeared a feature with floods in southern China and droughts in northern China. Recently, our analysis also shows that there has been an additional variation in the interdecadal variability of summer precipitation pattern in eastern China since 2011, the summer precipition anomalies appear a meridional "+, −, +" tripole, i.e., more summer precipitation in northern and southern China and less summer precipitation in the Yangtze and Huaihe River basins.

**Figure 7.** Distribution of summertime (JJA) rainfall anomalies (percentage) averaged for 110◦–120◦ E in eastern China with latitude and time. Solid and dashed lines indicate positive and negative anomalies, respectively, and positive anomalies are shaded. Data of precipitation is from the dataset of precipitations at 822 observational stations in China.

Huang et al. [41] investigated the dynamic process of the interdecadal variability of summer precipitation in eastern China and noted that the interdecadal variability of summer precipitation in eastern China is closely related to the interdecadal variability of the teleconnection wave trains of the summer atmospheric circulation anomalies over East Asia, especially in regards to the interdecadal variability of the EAP pattern teleconnection wave train, which plays an important role in the variabilities of summer precipitation in eastern China. Recently, it is analyzed that the interdecadal variability of summer wholelayer water vapor transport fluxes between 1000 and 300 hPa using the NCEP/NCAR reanalysis data of water vapor transport fluxes over the Eurasian region from 1961 to 2020. Figure 8a–d show the 1000–300 hPa whole-layer water vapor transport fluxes averaged for the summers of 1977–1992, 1993–1998, 1999–2010, and 2011–2020, respectively. In Figure 8a, the anomalies of water vapor transport fluxes over Southeast Asia and East Asia appeared as a "cyclone-anticyclone-cyclone" tripole anomaly pattern during 1977–1992, i.e., there was an EAP-like pattern teleconnection wave train. And there was a strong southward water vapor transport anomaly in the eastern part of China. This finding indicates that the East Asian summer monsoon weakened. In addition, the anomalies of water vapor transport fluxes from the Caspian Sea through central Asia to North China appeared the distribution of "cyclone-anticyclone-cyclone", those are similar to the distribution of the Silk Road-like pattern teleconnection wave train. In contrast, the anomalies of summer water vapor transport fluxes over East Asia during 1993–1998 (see Figure 8b) showed a somewhat different distribution from Figure 8a, i.e., anomalies of water vapour transport fluxes over Southeast Asia and East Asia appeared the dipole pattern distribution of "anticyclone-cyclone". This finding indicates that the East Asian summer monsoon became stronger during this period. Moreover, the "anticyclone-cyclone-anticyclone-cyclone" pattern anomalies of water vapour transport fluxes from the Caspian Sea to North China were similar to the Silk Road pattern teleconnection wave train. However, comparing Figure 8c with Figure 8a,b, it is obvious that the distributions of the anomalies of water vapor transport fluxes along the zonal direction over Eurasia or along the meridional direction over East Asia significantly changed during the period from 1999 to 2010. During this period, the anomaly distribution of water vapor fluxes over East Asia appeared the meridional dipole pattern, and the anomaly distribution of water vapor fluxes over Eurasia showed an "anticyclone-cyclone-anticyclone-cyclone" pattern, which is similar to the Silk Road pattern teleconnection wave train. In addition, Figure 8c shows that there was the southward water vapor transport flux anomalies extending from the northeast region to the southwest region of China, which indicates that the East Asian summer monsoon became weak again during this period, which weakens the water vapor transport to the northeast and north China. Therefore, the persistent droughts occurred in these regions in different degrees during summer. However, there was a strong northward water vapor transport

flux anomaly from the southeast coastal area of China to the east of the Huaihe River basin, which caused significant increase of the summer precipitation and severe floods in these regions during this period. Recently, the result analyzed by our research group shows that during 2011–2020, as shown in Figure 8d, the southward water vapor transport flux anomalies over the northeast to southwest region of China were smaller than those during 1999–2011, while the northward water vapor transport fluxes over the southeast coast of China to the Yellow River and Huaihe River regions in China were strengthened. This caused the increase of the summer precipitation in northern China and the water vapor transport flux anomalies from Southeast Asia to the northeast region of China along the eastern part of China. The water vapor transport flux anomalies from Southeast Asia along the eastern part of China to the northeast part of China appeared the distribution of "anticyclone-cyclone-anticyclone", which is similar to the EAP-like pattern teleconnection wave train. And the water vapor transport flux anomalies from the Caspian Sea to East Asia appeared the "anticyclone-cyclone-anticyclone-cyclone" distribution, which is the Silk Road-like pattern teleconnection distribution.

**Figure 8.** Anomaly distributions of summertime (JJA) water vapor transport fluxes integrated from 1000 hPa to 300 hPa over the Eurasian continent, averaged for (**a**) 1977–1992, (**b**) 1993–1998, (**c**) 1999–2010, and (**d**) 2011–2020. Data of water vapor and wind fields are from the NCEP/NCAR reanalysis data for 1961–2020 [30].

From the above analyses of the spatial distribution of the interdecadal variability of summertime water vapor transport fluxes over Eurasia, we can see that the interdecadal variability in summer monsoon precipitation over eastern China since the 1970s is closely related to not only the interdecadal variability of the distribution of the EAP pattern teleconnection wave train propagating along the meridional direction in East Asia but also related to the interdecadal variability of the Silk Road teleconnection wave train propagating along the subtropical jet in the upper troposphere over the Eurasian subtropics. Both wave trains are formed by the propagations of quasi-stationary planetary waves in the spherical atmosphere.

In summary, the interannual and interdecadal variabilities of summer monsoon precipitation and whole-layer water vapor transport in eastern China may be result of joint action of the interannual and interdecadal variabilities of the EAP pattern teleconnection wave train propagating along the meridional direction over East Asia and the Silk Road pattern teleconnection wave train propagating along the subtropical regions from West

Asia to East Asia. Therefore, the theory of Rossby wave energy dispersion proposed by academician Ye provides an important scientific basis for short- and medium-term weather forecasting but also a new idea for short-term summer climate prediction.
