**1. Introduction**

The Tibetan Plateau (TP) is located in Southwestern China. It is the highest plateau in the world. It is known as the third pole of the Earth and is also the source area of many rivers [1–4]. For the same troposphere height in summer, the moisture content over the plateau is much higher than that in the other surrounding areas. The sensible heating of the plateau is an important reason for the abrupt change in the East Asian circulation, which plays an important role in modulating the East Asian monsoon [5–10]. Ye [11] pointed out that the southeastern part of the plateau is an exceedingly high humidity center in summer compared with the surrounding areas. The plateau serves the function

**Citation:** Li, M.; Wang, L.; Chang, N.; Gong, M.; Ma, Y.; Yang, Y.; Chen, X.; Han, C.; Sun, F. Characteristics of the Water Vapor Transport in the Canyon Area of the Southeastern Tibetan Plateau. *Water* **2021**, *13*, 3620. https://doi.org/10.3390/w13243620

Academic Editor: Maria Mimikou

Received: 9 November 2021 Accepted: 12 December 2021 Published: 16 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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of transferring the water vapor from the south to the east, and the strength of this effect directly affects the drought and flood conditions in the middle and lower reaches of the Yangtze River [11–14]. Previous studies have also shown that the southeastern part of the plateau is a high value center of the total water vapor in summer [15–19]. Qu and Zhang [19] studied the distribution of the summer water vapor flux field in East Asia and concluded that there are three water vapor transport channels in East Asia in July. The first is from the Bay of Bengal and the east coast of India to China; the second is from Southern and Southeastern China to Eastern China; and the third channel trends east-west, from East Asia to China [19]. Therefore, it is crucial to study the surface flux and its influence on the water vapor transport in the southeastern part of the plateau to gain a better understanding of the land–atmosphere interactions and their influence on the high-increasing water vapor transport on the plateau.

In recent years, the Lagrangian method has been gradually applied to the study of water vapor transport. Massacand et al. inferred the mesospheric humidity source of heavy precipitation on the southern side of the Alpine area by examining the specific humidity along the back trajectories [20]. Bertò et al. used the Lagrangian trajectory model (i.e., the HYSPLIT model) to analyze the water vapor source during a heavy precipitation event in Trentino, Italy, in 2002 [21]. They found that the main water vapor channel was transported from subtropical Africa to Trentino through the Mediterranean. James et al. investigated the change in the net water along a large number of backward trajectories to identify the water source in the flooded areas of the Elbe River in August 2002 [22]. Sodemann and Stohl [23] employed the recently developed Lagrangian moisture source diagnostic of Sodemann et al. [24] to determine the seasonality of moisture sources for all of Antarctica over a 5-year period. Previous studies indicate that the moisture source and transport path can change rapidly during a precipitation event [25,26]. Using the Lagrangian method, Jiang et al. (2013) studied the characteristics of the moisture contributions during the boreal summer over the Yangtze River valley (YRV) [27]. Chu et al. (2021) focused on the effect of water vapor transport processes on the variations in the seasonal mean rainfall over East China [28]. Chen and Luo (2018) used the Lagrangian model to explore the paths and sources of the water vapor carried to Southern China (SC) during the pre-flood season [29]. Moreover, based on a Lagrangian model, Sun and Wang (2014) quantitatively calculated the water vapor transport from every water vapor source to Eastern China during 2000–2009 [30].

The progress in meteorology research on the TP depends to a large extent on the development of various data about the plateau. With the launch of the three Field Observation Experiments of Atmospheric Science on the Tibetan Plateau, the research data about the plateau have been gradually improved [31–34]. In addition, it has been reported that even along the same latitudinal belt, the atmospheric circulation patterns [35] and the surface heat fluxes [36–38] regulating the moisture transport to the western TP are different from those of the eastern TP. The canyon area in southeastern Tibet is an important channel for water vapor transport from the Bay of Bengal to the south of the plateau to mainland China. The heat flux anomaly over the plateau affects the vertical movement and convergence and divergenceover the plateau, which leads to anomalies in the height field and wind field in East Asia [18]. The changes in the surface flux cause the changes in the annular flow field over the region, and they affect the water vapor transport. To study the influence of the changes in the surface flux on the water vapor transport in the upper layer, the singular value decomposition (SVD) method was used to analyze the correlation between the water vapor flux divergence field and the surface heat fluxes fields and to separate multiple coupling modes from the two element fields to the greatest extent possible to reveal the temporal and spatial relationships between the water vapor flux divergence field and the surface heat flux fields.

In this study, the water vapor transport characteristics were analyzed using the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT)\_v4 backward trajectory model at Danka and Motuo stations in the canyons in the southeastern TP from November 2018 to

October 2019. The contribution rates of the different water vapor paths were quantitatively analyzed to further deepen our scientific understanding of the water vapor transport paths on the TP. Then, using ERA-5 reanalysis data and the characteristics of the high-altitude water vapor transport, the impact of the changes in the surface fluxes on the water vapor transport was analyzed using SVD. The results help reveal the source of the water vapor and the mechanism by which the Earth-atmosphere interactions influence the water vapor transport on the TP. 2018 to October 2019. The contribution rates of the different water vapor paths were quantitatively analyzed to further deepen our scientific understanding of the water vapor transport paths on the TP. Then, using ERA-5 reanalysis data and the characteristics of the high-altitude water vapor transport, the impact of the changes in the surface fluxes on the water vapor transport was analyzed using SVD. The results help reveal the source of the water vapor and the mechanism by which the Earth-atmosphere interactions influence the water vapor transport on the TP.

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#### **2. Data and Methods 2. Data and Methods**

*2.1. Study Area* 

#### *2.1. Study Area*

The study area was the canyon area in the southeastern TP, and the research stations were Danka Station (29.89◦ N, 95.68◦ E, a.s.l. (above sea level) 2701 m) and Motuo Station (29.31◦ N, 95.32◦ E, a.s.l. 1154 m). Danka station is located in the northwestern part of Bomi County, Nyingchi City, Tibet Autonomous Region, on the southern bank of the Palongzangbo River Valley, and the underlying surface is mainly grassland. Motuo Station is located in the lower reaches of the Yarlung Zangbo River, Motuo County, and the underlying surface is mainly grassland. The topography of the observation area and the distribution of observation sites are shown in Figure 1. The study area was the canyon area in the southeastern TP, and the research stations were Danka Station (29.89° N, 95.68° E, a.s.l. (above sea level) 2701 m) and Motuo Station (29.31° N, 95.32° E, a.s.l. 1154 m). Danka station is located in the northwestern part of Bomi County, Nyingchi City, Tibet Autonomous Region, on the southern bank of the Palongzangbo River Valley, and the underlying surface is mainly grassland. Motuo Station is located in the lower reaches of the Yarlung Zangbo River, Motuo County, and the underlying surface is mainly grassland. The topography of the observation area and the distribution of observation sites are shown in Figure 1.

**Figure 1.** Topography of the study area and locations of the observation sites, Solid dots indicate the site location. **Figure 1.** Topography of the study area and locations of the observation sites, Solid dots indicate the site location.

#### *2.2. Data*

*2.2. Data* 


horizontal resolution of the data is 0.1° × 0.1°. The time range of the data used in this

study is from 1989 to 2019.

## *2.3. Water Vapor Transport Trajectory Model (HYSPLIT\_v4)*

The HYSPLIT\_v4 model is a professional model for calculating and analyzing the transport and diffusion trajectories of air pollutants. It was jointly developed by the Air Resources Laboratory of the National Oceanic and Atmospheric Administration (NOAA) of the United States and the Australian Meteorological Service in the past 20 years [39,40]. The HYSPLIT\_v4 model is a mixed Eulerian-Lagrangian model, in which the Lagrangian method is used for the advection and diffusion. The model is usually used to track the movement direction of the particles or gas carried by the airflow, and it can be used to forecast the wind situation in real time, to analyze precipitation, and to study the trajectory. In this study, the HYSPLIT\_v4 model was used to simulate the water vapor transport from November 2018 to October 2019 at Danka and Motuo stations in the canyon area of southeastern Tibet, and the water vapor transport trajectory was studied. The model uses 11-day backward water vapor transport trajectory simulation, and the top height of the model is 10 km. The characteristics of the water vapor trajectories in different seasons were obtained.

#### *2.4. Singular Value Decomposition (SVD) Method*

The SVD method is based on the maximum covariance between two element fields. It is an effective diagnostic analysis method for studying the correlation structure of two fields. It is suitable for climate diagnostic analysis and for studying the teleconnections between large-scale meteorological fields. Compared with typical correlation analysis methods, the singular value decomposition method can maximally separate the independent coupling distribution patterns of the two meteorological fields. These distribution patterns reveal the spatial relationship and the temporal correlation between the two meteorological fields in order to determine the real teleconnection pattern and the key area of influence. From the spatial distribution pattern of the modal anisotropy correlation, we found the large value region of anisotropy correlation coefficient in the left and right fields, which represents the key region of the interactions between the left and right fields. The anisotropy correlation coefficients between the two meteorological element fields can be used to analyze their relationship. The Monte Carlo method was used to test the significance of the SVD results.

#### **3. Results Analysis**

### *3.1. Water Vapor Transport Trajectories in the Canyon Area in Southeastern Tibet*

Figure 2 shows the water vapor transport track at Danka Station and Motuo Station during the non-Asian monsoon season (non-AMS) (i.e., spring) for 11 days (the map projection is the Lambert projection). The northwest air flow is the main water vapor source at the two stations in the non-AMS. Seven percent of the water vapor at Danka Station came from the northeastern part of the Pacific Ocean, passed over Canada, passed over the Arctic Ocean, turned to the northwest over the Norwegian Sea, and reached Danka Station. Similarly, Motuo Station received a small amount of water vapor from the northern Pacific, 25% from India, 40% from the northwest path, and 32% from the nearby area to the west. Compared with the spring atmospheric circulation pattern on the TP, strong westerlies occurred to the south of the plateau during spring and were the main water vapor transport channels in the southeastern gorge area of Tibet. The high terrain of the plateau affected the wind flow around this latitude, forming a pattern characterized by a southern trough and a northern Ridge. The northwestward air flow of the northern ridge delivered about 40% of the water vapor to southeastern Tibet during the non-AMS. Based on the height of the water vapor transmission channels, the water vapor transmission channel in the southwest was below 3000 m, while the water vapor transmission channel in the west and the northwest water vapor transport height reached 4500 m.

Compared with the sources of water vapor transport during the non-AMS (spring), and the main water vapor source path of the two stations came from the southwest air flow (Figure 3). During the Asian monsoon season (AMS) (i.e., summer), 20% of the water vapor at Danka Station came from the northwest path and 80% came from the southwest,

AMS.

mainly from the Arabian Sea and the Bay of Bengal, whereas almost all of the water vapor at Motuo station came from the Arabian Sea. The height of the water vapor transmission path between the two stations through the Bay of Bengal was less than 1500 m. During this period, the South Asian Monsoon prevailed on the plateau, and the southwest winds at this time made a major contribution to the water vapor transport from the Bay of Bengal to this area, forming a main water vapor transport channel over southeastern Tibet and into inland China. *Water* **2021**, *13*, x FOR PEER REVIEW 5 of 23

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**Figure 2.** Eleven-day backward water vapor transport trajectories for Danka station and Motuo station during the non-**Figure 2.** Eleven-day backward water vapor transport trajectories for Danka station and Motuo station during the non-AMS. into inland China.

**Figure 3. Figure 3.**  Eleven-day backward water vapor transport trajectories for Danka station and Motuo station during the AMS. Eleven-day backward water vapor transport trajectories for Danka station and Motuo station during the AMS.

The water vapor transport in the canyon area of the southeastern TP is closely related to the Asian monsoon climate. Correlation analysis was conducted between the water vapor transport path and the circulation field, ground heating, and water vapor flux during the non-AMS and AMS in order to determine the mechanism by which the monsoon climate affects the water vapor transport path in the canyon area of the southeastern TP.

**Figure 3.** Eleven-day backward water vapor transport trajectories for Danka station and Motuo station during the AMS.

#### *3.2. Effect of Surface Fluxes on Water Vapor Transport*

3.2.1. Relationship between Sensible Heat Flux and Water Vapor Flux Divergence in the Canyon Area of Southeastern Tibet

Based on the results of the water vapor transport simulation obtained using the HYSPLIT\_v4 backward trajectory model (see Section 3.1), the water vapor transport in the canyon area of the southeastern TP exhibited significant climate characteristics during the AMS. In this section, we analyze the spatial relationship of the temporal correlation between the sensible heat and water vapor flux divergence from the perspective of the variations in the AMS. The water vapor flux divergence is a very important meteorological factor, which characterizes the water vapor transport. The SVD method was used to calculate the correlation coefficient (R) between the first four pairs of singular vector covariance contributions (SCFs), the cumulative covariance contributions (CSCFs), and the expansion coefficient. The time span was from 1989 to 2019 (Table 1).

**Table 1.** SVD results of sensible heat field and water vapor flux divergence field.


As can be seen from Table 1, the cumulative covariance contributions of the first four pairs of the coupling modes of the sensible heat and the water vapor flux divergence in each season and the whole year were greater than 78%, the covariance contribution rate of the first two modes was greater than 58%, and it reached 94.49% during the AMS, indicating that the first two pairs of coupling modes represent most of the characteristics of the sensible heat field and the water vapor flux divergence. In addition, the first two modes passed the 95% Monte Carlo test, so in this section, the first two coupling modes of the sensible heat field and the water vapor flux divergence field in southeastern Tibet are analyzed.

Figure 4 shows the results of the SVD anisotropy correlation analysis between the standardized anomaly of the sensible heat field and the standardized anomaly of the water vapor flux divergence field during the non-AMS. The first mode (Figure 4a,b) shows that the sensible heat in the southwestern and southwestern parts of southeastern Tibet was mainly positive. There was a significant negative value on the southern boundary line, and the values in the central and eastern regions were negative. In the corresponding water vapor flux divergence field, there was a positive center of the water vapor flux divergence on the southern boundary of the plateau and a negative region in the west. Except for the sporadic negative anomaly regions in the eastern, southern, and central parts of southeastern Tibet, the other regions were positive. Figure 4e,f show that the correlation coefficient between the sensible heat and water vapor flux divergence of the first mode is 0.93. There is a significant positive correlation between the sensible heat flux field and the water vapor flux divergence field. This indicates that during the non-AMS, when the sensible heat of the western and southwestern parts of the southeastern Tibet increased (decreased) and the sensible heat of the eastern and central parts of the southeastern Tibet decreased (increased), the water vapor flux divergence in the eastern part of Tibet decreased (increased), while it increased (decreased) in the central and eastern regions. From the second type of modal space, we can see that the sensible heat field was significantly negative in the Hengduan Mountains on the southeastern part of the TP, and there was a positive area in the northeast. The negative anomaly area in the northeastern part of southeastern Tibet corresponded to the water vapor flux divergence, and the rest

of the areas were in the same positive region. The two large value areas corresponded to each other. The correlation coefficient between the sensible heat field and the whole water vapor flux divergence field of the second mode reached 0.91, indicating that when the sensible heat of the northeast area increased (decreased) during the non-AMS, the sensible heat in the rest of the areas decreased (increased), the water vapor flux divergence in the northeastern region decreased (increased), and it increased (decreased) in the rest of the areas. were in the same positive region. The two large value areas corresponded to each other. The correlation coefficient between the sensible heat field and the whole water vapor flux divergence field of the second mode reached 0.91, indicating that when the sensible heat of the northeast area increased (decreased) during the non-AMS, the sensible heat in the rest of the areas decreased (increased), the water vapor flux divergence in the northeastern region decreased (increased), and it increased (decreased) in the rest of the areas.

decreased (increased), the water vapor flux divergence in the eastern part of Tibet decreased (increased), while it increased (decreased) in the central and eastern regions. From the second type of modal space, we can see that the sensible heat field was significantly negative in the Hengduan Mountains on the southeastern part of the TP, and there was a positive area in the northeast. The negative anomaly area in the northeastern part of southeastern Tibet corresponded to the water vapor flux divergence, and the rest of the areas

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**Figure 4.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the spring sensible heat field and the water vapor flux divergence field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of **Figure 4.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the spring sensible heat field and the water vapor flux divergence field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second mode of the sensible heat field; (**d**) the second mode of the water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF time series in (**e**,**f**).

The AMS is the main season for water vapor transport. The results of the SVD analysis of the sensible heat and the water vapor flux divergence fields during the AMS show that the cumulative variance contribution of the first four modes of the two fields reached 94.49%, which represents most of the characteristics of the sensible heat and the moisture flux divergence fields during the AMS (Table 1). The first mode of the SVD analysis of the summer surface flux field and the moisture flux divergence field shows that the sensible heat field was a negative region with a uniform type, and there was a significant negative value region on the southern and eastern boundaries of the plateau (Figure 5a–d). The whole water vapor flux divergence field was clearly positive in southeastern Tibet. The correlation coefficient between the sensible heat and the moisture flux divergence of the first mode was 0.94 during the AMS, indicating that there was a clear positive correlation between the sensible heat and the water vapor flux divergence fields. That is, when the sensible heat decreased (increased) during the AMS, the water vapor flux divergence increased (decreased), and the large negative area on the southern boundary and the southeast boundary was the key area and affected the whole water vapor flux divergence during the AMS. The contribution of the second mode's covariance was 11.43%, and the significant positive area of the sensible heat field was located in the northern part of southeastern Tibet. The negative value area was located in the southwest, while the right field was opposite to this distribution. The correlation coefficient for the sensible heat and water vapor flux divergence fields was 0.93, exhibiting a positive correlation, indicating that the sensible heat field in the canyon area of southeastern Tibet increased in the northeast during the AMS. In addition, when it decreased in the southwest, the water vapor flux divergence field decreased in the northeast and increased in the southwest. The time series changes in the sensible heat and the water vapor flux divergence fields of the first two modes were basically synchronous (Figure 5e,f), and the fluctuation amplitude was large.

3.2.2. Relationship between the Latent Heat and the Water Vapor Flux Divergence in the Canyon Area of Southeastern Tibet

In this section, the SVD method is used to investigate the spatial relationship between the latent heat field and the water vapor flux divergence field. The latent heat field is the left field, and the water vapor flux divergence field is the right field. The covariance contribution (SCF), cumulative covariance contribution (CSCF), and correlation coefficient (R) of the first four pairs of singular vectors in each season were calculated (Table 2).


**Table 2.** SVD results of latent heat field and water vapor flux divergence field.

The cumulative covariance contributions of the first four pairs of coupling modes of the latent heat flux and the water vapor flux divergence in each season and the whole year were greater than 78%. The covariance contributions of the first two modes were greater than 57% and 93.64% during the AMS, respectively. It indicated that the first two pairs of coupling modes represent most of the characteristics of the latent heat flux and the water vapor flux divergence field (Table 2). The first two modes passed the 95% Monte Carlo test, so in this section, the first two coupling modes of the latent heat and water vapor flux divergence field in southeastern Tibet are analyzed.

**Figure 5.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the sensible heat field and the water vapor flux divergence field in southeastern Tibet during the AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second modal of the sensible heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF time series in (**e**,**f**). **Figure 5.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the sensible heat field and the water vapor flux divergence field in southeastern Tibet during the AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second modal of the sensible heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF time series in (**e**,**f**).

3.2.2. Relationship between the Latent Heat and the Water Vapor Flux Divergence in the Canyon Area of Southeastern Tibet In this section, the SVD method is used to investigate the spatial relationship between the latent heat field and the water vapor flux divergence field. The latent heat field is the Figure 6a–d shows the results of the SVD analysis of the normalized anomalies of the latent heat field and the water vapor flux divergence field during the non-AMS. From spatial distribution of the first mode, we can see that there was a positive region in the latent heat field, except for in the western region. The remaining areas were negative.

There were remarkably positive values in the eastern and southern parts of the plateau. There was a negative value in the western part of the whole water vapor flux divergence field, and there were sporadic negative anomaly centers in the other areas. The correlation coefficient between the latent heat field and the water vapor flux divergence field of the first mode was 0.95, indicating that the two fields had a good positive correlation. That is, when the latent heat in southeastern Tibet decreased (increased) in the southwestern and eastern areas and the latent heat increased (decreased) in the west, the water vapor flux divergence increased (decreased) in the southwest and east and decreased (increased) in the west. In the second modal spatial distribution, the latent heat field was negative in the northwest and positive in the southeast, and the negative value of the whole water vapor flux divergence field was positive in the northeast. That is, when the sensible heat in southeastern Tibet was weak (strong) in northwest-southeast direction, the water vapor flux divergence field was strong (weak) in southwest-northeast direction. Based on the time series curve of the first mode and the second mode of the two fields, the correlations were 0.95 and 0.86, respectively (Figure 6e,f). The fluctuation trend was basically consistent, and the first mode time series exhibited an upward trend.

Figure 7a–d show the first mode of the spatial distribution of the latent heat field and the water vapor flux divergence field in southeastern Tibet during the AMS. It can be concluded that the latent heat field and the water vapor flux divergence field exhibited good consistent distributions, and the latent heat field during the AMS was negative. The significant negative centers were located on the plateau and the eastern and southern boundaries. The whole water vapor flux divergence field was a positive region. The positive centers were located in the southern and central parts of southeastern Tibet. The correlation coefficient for the first mode of the latent heat field and the water vapor flux divergence field was 0.94 during the AMS. There was a significant positive correlation. This shows that the water vapor flux divergence increased (decreased) when latent heat decreased in southeastern Tibet during the AMS. The second modal spatial distribution pattern was drawn as follows. When the latent heat field in southwestern Tibet increased in the southwest and decreased in the northeast, the water vapor flux divergence field in the total-column was reversed. Based on the corresponding time series of the first mode and the second mode, the change trend was more consistent, and the correlation coefficients reached 0.94 and 0.93, respectively, exhibiting the same phase of change (Figure 7e,f).

3.2.3. Relationships between the Surface Sensible Heat, Latent Heat, and Northward Water Vapor Flux

According to the trajectory simulation results of the HYSPLIT\_v4 11-day backward trajectory, the source of the water vapor transport was closely related to the changes in the atmospheric circulation situation. The source of the water vapor transport was quite different during the non-AMS and the AMS. During the non-AMS, the water vapor in southeastern Tibet mainly came from a westward path, while during the AMS, the water vapor mainly came from a southwestward path, accounting for a relatively small number of westward paths. Therefore, the surface fluxes and the water vapor flux to the north and east in winter and summer are discussed in this section. Similarly, the surface sensible heat flux and the latent heat flux were taken as the left field in the SVD, the water vapor flux to the north and the water vapor flux to the east were taken as the right field, and the time period was from 1989 to 2019. The covariance contribution (SCF), cumulative covariance contribution (CSCF), and correlation coefficient (R) between the expansion coefficients of the first four pairs of singular vectors are shown in Table 3. The north (east) water vapor flux refers to the horizontal water vapor velocity of a column of air extending from the Earth's surface to the top of the atmosphere. A positive value represents the flux from the west (south) to the east (north). The mean cumulative variance contribution of the first mode to the SVD analysis of the surface flux and the northward and eastward vapor fluxes exceeded 61%. This represents the main characteristics of the relationship between the two physical quantity fields. The first mode passed the 95% level, so the first mode was analyzed in this section. The first four pairs of modal results are shown in Table 3.

**Figure 6.** SVD analysis and corresponding time coefficients of the surface latent heat field and the water vapor flux divergence field in southeastern Tibet during the non-AMS (**a**) the first mode of the latent heat field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second mode of the latent heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The black solid line is the boundary of the Tibetan Plateau in (**a**–**d**). The red solid line is SSHF time series and the blue solid line is VIMDF in (**e**,**f**) time series. **Figure 6.** SVD analysis and corresponding time coefficients of the surface latent heat field and the water vapor flux divergence field in southeastern Tibet during the non-AMS (**a**) the first mode of the latent heat field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second mode of the latent heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The black solid line is the boundary of the Tibetan Plateau in (**a**–**d**). The red solid line is SSHF time series and the blue solid line is VIMDF time series in (**e**,**f**).

Figure 7a–d show the first mode of the spatial distribution of the latent heat field and the water vapor flux divergence field in southeastern Tibet during the AMS. It can be concluded that the latent heat field and the water vapor flux divergence field exhibited good consistent distributions, and the latent heat field during the AMS was negative. The

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significant negative centers were located on the plateau and the eastern and southern boundaries. The whole water vapor flux divergence field was a positive region. The positive centers were located in the southern and central parts of southeastern Tibet. The correlation coefficient for the first mode of the latent heat field and the water vapor flux divergence field was 0.94 during the AMS. There was a significant positive correlation. This shows that the water vapor flux divergence increased (decreased) when latent heat decreased in southeastern Tibet during the AMS. The second modal spatial distribution pattern was drawn as follows. When the latent heat field in southwestern Tibet increased in the southwest and decreased in the northeast, the water vapor flux divergence field in the total-column was reversed. Based on the corresponding time series of the first mode and the second mode, the change trend was more consistent, and the correlation coefficients reached 0.94 and 0.93, respectively, exhibiting the same phase of change (Figure 7e,f).

**Figure 7.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the latent heat field and the water vapor flux divergence field in southeastern Tibet in summer. (**a**) the first mode of the latent heat field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second mode of the latent heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF in (**e**,**f**) time series. **Figure 7.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the latent heat field and the water vapor flux divergence field in southeastern Tibet in summer. (**a**) the first mode of the latent heat field; (**b**) the first mode of water vapor flux divergence field; (**c**) the second mode of the latent heat field; (**d**) the second mode of water vapor flux divergence field; (**e**) the first mode; and (**f**) the second mode. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF time series in (**e**,**f**).

3.2.3. Relationships between the Surface Sensible Heat, Latent Heat, and Northward Wa-

According to the trajectory simulation results of the HYSPLIT\_v4 11-day backward trajectory, the source of the water vapor transport was closely related to the changes in

ter Vapor Flux


**Table 3.** SVD Analysis of surface flux and northward water vapor flux in Southeast Tibet.

For the first mode of the SVD analysis of the sensible heat and moisture during the non-AMS (Figure 8a,b), the results show that the sensible heat field was negative in both the southeast boundary and the southern part of the plateau, and the northern region was a positive anomaly, which was the key area affecting the northward water vapor flux during the same period. The northward water vapor flux field was positive, except for in the western region of the plateau, and the center of the positive anomaly was located in the central region. The correlation coefficient of the first mode was 0.78, indicating that there was a positive correlation between the sensible heat and the northward vapor flux. When the sensible heat increased in northeastern Tibet and decreased in southeastern Tibet and the southern part of the plateau, the water vapor flux in most parts of the plateau increased to the north and decreased to the west, and vice versa. From the corresponding time series (Figure 8e), it can be seen that the overall change trends of the surface flux and the northward water vapor flux were roughly the same. The fitting degree before 2008 was worse than that after 2008, and there were large fluctuations in 2009 and 2013.

There was also a significant coupling mode between the latent heat and northward water vapor flux during the non-AMS (Figure 8c,d). In the first mode, the contribution of the variance was 78.52%, and the correlation coefficient of the latent heat and the northward water vapor flux fields reached 0.8. The distribution characteristics of the time series were similar to those of the sensible heat field. The first mode was similar to the first mode of the sensible heat and the plateau's northward moisture flux. The difference is that in the sensible heat field, the values were negative in northern and northwestern Tibet, while the northward water vapor flux field moved eastward. However, the whole plateau was still a positive anomaly, and the western part was negative. The correlation coefficient of the first mode was 0.8. This shows that when the surface latent heat increased in the western, central, southern, and eastern parts of the plateau in winter, the northward water vapor flux increased in most parts of the plateau and decreased in the western part, and vice versa (Figure 8f).

During the AMS, the relationship between the surface flux field and the northward water vapor flux field was more pronounced. There were significant coupling modes between the sensible and latent heat fluxes and the northward water vapor transport flux during the AMS, and the correlation coefficients were 0.83 and 0.85, respectively (Figure 9e,f). The sensible and latent heat flux fields had consistent positive values (Figure 9a,c). The large values were located in the eastern part of southeastern Tibet and the southern boundary of the plateau, which were the key areas in which the summer climate influenced the northward water vapor flux. The northward water vapor flux field was basically positive on the main part of the plateau, and the area with the largest positive value was in the southern part of southeastern Tibet. There was a good positive correlation between the surface sensible and latent heat fluxes and the northward water vapor flux, that is, when the sensible and latent heat fluxes increased (decreased) in the eastern part of southeast Tibet and the southern boundary of the plateau during the AMS, the northward water vapor flux in the main part of the plateau increased, especially in southeastern Tibet, and decreased in the Himalayas in southern Tibet. It can be seen from the time series diagram

*Water* **2021**, *13*, x FOR PEER REVIEW 15 of 23

that the change trend of the surface flux field in southeastern Tibet was consistent with that of the northward water vapor flux field during the AMS (Figure 9e,f).

**Figure 8.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and northward water vapor flux field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the northward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the northward water vapor flux field; (**e**) the sensible heat flux and northward water vapor flux field; and (**f**) the latent heat flux and northward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMD in (**e**,**f**) time series. **Figure 8.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and northward water vapor flux field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the northward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the northward water vapor flux field; (**e**) the sensible heat flux and northward water vapor flux field; and (**f**) the latent heat flux and northward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**<sup>d</sup>**). The solid red line is SSHF time series and the solidblue line is VIMD time series in (**e**,**f**).

During the AMS, the relationship between the surface flux field and the northward water vapor flux field was more pronounced. There were significant coupling modes between the sensible and latent heat fluxes and the northward water vapor transport flux

9e,f). The sensible and latent heat flux fields had consistent positive values (Figure 9a,c). The large values were located in the eastern part of southeastern Tibet and the southern boundary of the plateau, which were the key areas in which the summer climate influenced the northward water vapor flux. The northward water vapor flux field was basically positive on the main part of the plateau, and the area with the largest positive value was in the southern part of southeastern Tibet. There was a good positive correlation between the surface sensible and latent heat fluxes and the northward water vapor flux, that is, when the sensible and latent heat fluxes increased (decreased) in the eastern part of southeast Tibet and the southern boundary of the plateau during the AMS, the northward water vapor flux in the main part of the plateau increased, especially in southeastern Tibet, and decreased in the Himalayas in southern Tibet. It can be seen from the time series diagram that the change trend of the surface flux field in southeastern Tibet was consistent with

that of the northward water vapor flux field during the AMS (Figure 9e,f).

**Figure 9.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and northward water vapor flux field in southeastern Tibet during the AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the northward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the northward water vapor flux field; (**e**) the sensible heat flux and northward water vapor flux field; and (**f**) the latent heat flux and northward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMDF time series in (**e**,**f**).

3.2.4. Influences of the Surface Sensible Heat and Latent Heat on the Water Eastward Vapor Flux

Table 4 shows the contribution rates and correlation coefficients of the first four pairs of principal component modes of the variance for the SVD analysis of the surface fluxes and eastward water vapor flux in southeast Tibet. It can be seen that the contribution rate of the cumulative variance of the first four pairs was greater than 97%, and there was a significant coupling mode. The analysis period was from 1989 to 2019. Similarly, the first mode of the SVD analysis passed the 95% level Monte Carlo test, so the first mode was mainly analyzed.


**Table 4.** SVD Analysis of surface flux and eastward water vapor flux in Southeast Tibet.

It can be seen from the time series diagram of the surface fluxes and the eastward water vapor flux during the non-AMS that the trends of the two-time series were quite consistent (Figure 10). The sensible heat and eastward water vapor flux exhibited fluctuating upward trends during the non-AMS, while the latent heat and eastward water vapor flux exhibited fluctuating downward trends. Figure 10e,f show the first mode of the corresponding time series of the SVD anisotropy between the surface fluxes and the eastward vapor flux during the non-AMS. Figure 10a,b show that the surface sensible heat field was negative in the northwest and positive in the southeast. The negative region was located at the boundary of the southeast plateau, and the eastward water vapor flux field was consistent as a whole. The main body of the plateau and the northern part of the plateau were positive. The high value area was located in the eastern part of Qinghai Province on northern part of the TP, and the southern part of the Himalayas was a consistent negative value area. The correlation coefficient between the sensible heat and the first mode of the eastward water vapor flux was 0.80, indicating that there was a positive correlation between the surface fluxes and the eastward water vapor flux fields. That is, when the sensible heat increased in the southeast and decreased in the northwest in the winter, the eastward water vapor flux increased over the plateau and decreased in the Himalayas, and vice versa.

It can be seen from Figure 10c,d that the latent heat had a good consistency. The positive high value area was located on the southeastern boundary of the plateau, and there was a small negative value area in the southeastern part. In the eastward water vapor flux field, the main body of the plateau and the area to the north were negative value areas, the high value area was in the Qinghai area on the northeastern part of the TP, and the positive area was in the southern part of the Himalayas, with a distribution opposite that of sensible heat field. The correlation coefficient of the first mode of the latent heat flux and the eastward vapor flux fields reached 0.79, which indicates that when the southeast latent heat accumulation increased in the southeast, the overall water vapor flux to the east decreased and that in the Himalaya Mountains increased, and vice versa.

The spatial distribution of the first mode of the SVD analysis of the sensible heat and latent heat fluxes during the AMS was consistent. In the first mode, the sensible and latent heat fields in southeast Tibet were positive, and the two large positive areas were located in southeastern Tibet (Figure 11a,c). This shows that this area was the key area in which the surface flux affected the eastward water vapor flux during the AMS. The eastward water vapor flux field was positive in the main part of the plateau and the Himalayas, and there were negative areas in the northwest and southwest (Figure 11b,d). The maximum positive area was located in southeastern Tibet, which corresponded well with the maximum positive area of the surface fluxes. There were significant coupling modes between the eastward water vapor flux and the sensible heat flux and latent heat flux during the AMS, and the correlation coefficients were 0.77 and 0.85, respectively. That is, when the sensible heat and latent heat fluxes increased in southeastern Tibet during the AMS, the water vapor flux from the main part of the plateau and the Himalayas to the east

increased, and vice versa. It can be seen from the time series diagram that the change trend corresponded well and the fluctuation range was large (Figure 11e,f). latent heat accumulation increased in the southeast, the overall water vapor flux to the east decreased and that in the Himalaya Mountains increased, and vice versa.

**Figure 10.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and eastward water vapor flux field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the eastward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the eastward water vapor flux field; (**e**) the sensible heat flux and eastward water vapor flux field; and (**f**) the latent heat flux and eastward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMD in (**e**,**f**) time series. **Figure 10.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and eastward water vapor flux field in southeastern Tibet during the non-AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the eastward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the eastward water vapor flux field; (**e**) the sensible heat flux and eastward water vapor flux field; and (**f**) the latent heat flux and eastward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The solid red line is SSHF time series and the solid blue line is VIMD time series in (**e**,**f**).

The spatial distribution of the first mode of the SVD analysis of the sensible heat and latent heat fluxes during the AMS was consistent. In the first mode, the sensible and latent heat fields in southeast Tibet were positive, and the two large positive areas were located

in southeastern Tibet (Figure 11a,c). This shows that this area was the key area in which the surface flux affected the eastward water vapor flux during the AMS. The eastward water vapor flux field was positive in the main part of the plateau and the Himalayas, and there were negative areas in the northwest and southwest (Figure 11b,d). The maximum positive area was located in southeastern Tibet, which corresponded well with the maximum positive area of the surface fluxes. There were significant coupling modes between the eastward water vapor flux and the sensible heat flux and latent heat flux during the AMS, and the correlation coefficients were 0.77 and 0.85, respectively. That is, when the sensible heat and latent heat fluxes increased in southeastern Tibet during the AMS, the water vapor flux from the main part of the plateau and the Himalayas to the east increased, and vice versa. It can be seen from the time series diagram that the change trend

corresponded well and the fluctuation range was large (Figure 11e,f).

**Figure 11.** (**a**–**d**) SVD analysis and (**e**,**f**) corresponding time series of the surface flux field and eastward water vapor flux field in southeastern Tibet during the AMS. (**a**) the first mode of the thermal field; (**b**) the first mode of the eastward water vapor flux field; (**c**) the first mode of the latent heat field; (**d**) the first mode of the eastward water vapor flux field; (**e**) the sensible heat flux and eastward water vapor flux field; and (**f**) the latent heat flux and eastward water vapor flux field. The solid black line is the boundary of the Tibetan Plateau in (**a**–**d**). The red solid line is SSHF time series and the blue solid line is VIMD time series in (**e**,**f**).

## **4. Summary and Conclusions**

In this study, the 11-day backward trajectories of two observation stations located in the southeastern Tibetan Canyon from November 2018 to October 2019 were analyzed using the HYSPLIT\_v4 backward trajectory model. Then the SVD method was used to analyze the relationships between the sensible heat and latent heat and the water vapor flux divergence in the southeastern Tibet gorge region. Due to the effects of the atmospheric circulation patterns and seasonal heat fluxes, the patterns of the moisture sources for southeastern Tibet exhibited significant seasonal differences. The main conclusions of this study are as follows.


Our results show that the source of water vapor in the study area is different in different seasons, which will provide a certain theoretical basis for further research on the extreme precipitation of the Tibetan Plateau in the future. It is of great value to further study the different source areas and density of water vapor sources to improve extreme precipitation forecasts. In addition, some questions remain to be addressed. For example, this article only analyzes the seasonal characteristics of water vapor sources in southeastern Tibet from 2018 to 2019, only the data of the past 30 years is selected for analysis. Why

were there large fluctuations in 2009 and 2013, whether the VIMDF is mainly influenced by the surface thermal effect on the TP, and whether the relationship is regulated by other external forcing factors, such as sea surface temperature (SST). Cui et al. (2015) pointed out that during the positive phase of the North Atlantic Oscillation (NAO) in winter, it can inspire a stable downstream Rossby wave train, inducing the Asian subtropical westerly jet to intensify and the India-Burma trough to deepen, and it also increases the snow depth on the TP in winter, followed by a positive SSHF anomaly in spring in most areas of the TP [41]. What are the synergetic effect and contribution rates of the NAO and the SSHF on the TP? These issues need further study.

**Author Contributions:** M.L., L.W., N.C. and Y.Y. mainly wrote the manuscript and were responsible for the research design, data preparation and analysis. Y.M. and M.L. supervised the research, including methodology development, as well as manuscript structure, writing and revision. ML drafted the manuscript. F.S., M.G., X.C. and C.H. prepared the data and wrote this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was financially supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No. 2019QZKK0103).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The global data assessment system (GDAS) data were obtained from the National Centers for Environmental Prediction (NCEP) of the United States (https://www. ready.noaa.gov/gdas1.php, accessed on 8 September 2020). The NCEP/NCAR reanalysis data were obtained from the NCEP of the United States. We used the air temperature (air), u wind speed (uwnd), v wind speed (vwnd), and relative humidity (Rhum) data as the input for HYSPLIT\_v4, and the horizontal resolution of the data is 2.5◦ × 2.5◦ (https://psl.noaa.gov/data/gridded/data. ncep.reanalysis.html, accessed on 10 May 2020). The variables used in the reanalysis of the ERA-5 data (https://www.ecmwf.int/en/about/media-centre/science-blog/2017/era5-new-reanalysisweather-and-climate-data, accessed on 18 October 2020).

**Acknowledgments:** This work was financially supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (Grant No. 2019QZKK0103), the National Natural Science Foundation of China (Grant No. 41675106, 41805009), National key research and development program of China (2017YFC1505702) and Scientific Research Project of Chengdu University of Information Technology (KYTZ201721).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Rongxiang Tian 1,2,\* , Yaoming Ma 3,4,5 and Weiqiang Ma 3,4,5**


**Abstract:** The Indian Ocean and East Asia are the most famous monsoonal regions, and the climate of East Asia is affected by the change in wind direction due to monsoons. The vertical motion of the atmosphere is closely related to the amount of precipitation in whichever particular region. Climate diagnosis and statistical analysis were used to study the vertical motion of air over the Indian Ocean and its relationship with the climate in East Asia. The vertical motion of air over the Indian Ocean had a significant correlation with the climate in China—especially with precipitation in the Tibetan Plateau and the Yangtze River Basin—as a result of the interaction of the vertical motion of air from the Indian Ocean, the Tibetan Plateau and the subpolar region in the Northern Hemisphere. The vertical motion over the Indian Ocean was weakened from 1981 to 2010, except at a height of 500 hPa in winter. The vertical motion of air over the Indian Ocean had a period of 7–9 years in summer and 9–12 years in winter. An ascending motion was dominant over most of the Indian Ocean throughout the year and the central axis of the ascending motion changed from a clockwise rotation from winter to summer to a counterclockwise rotation from summer to winter as a result of the monsoonal circulation over the Indian Ocean. These results will provide a theoretical reference for a comprehensive understanding of the climate in Asia and contribute to work on climate prediction in these regions.

**Keywords:** Indian Ocean; East Asia climate; vertical motion of air; Tibetan Plateau

## **1. Introduction**

The Indian Ocean and East Asia have a monsoonal climate [1]. The Indian Ocean is surrounded by continental regions. There are different radiation and energy balances between the land and ocean as a result of the different natures of the underlying land and ocean surfaces (e.g., the heat capacity and albedo, etc.), and these balances change with the seasons. Different pressure fields are produced in different seasons, which generate a seasonal change in the wind field, namely, monsoons [1,2]. The summer monsoon brings abundant precipitation, while the winter monsoon brings drought and little rain. In terms of the influence of the change in wind direction due to the monsoon on the climate, there has been much research concerning the influence of change in the horizontal wind field on climate, while the relationship between climate and change in the vertical wind field has not received enough attention. The vertical motion of air is the result of both thermal and dynamic action [3], and can be directly linked to precipitation. Heating of the underlying surface can be expressed directly as the vertical motion of air [4]. The characteristics and intensity of vertical motion in the atmosphere are closely related to precipitation. Precipitation is associated with updrafts and drought is associated with

**Citation:** Tian, R.; Ma, Y.; Ma, W. Vertical Motion of Air over the Indian Ocean and the Climate in East Asia. *Water* **2021**, *13*, 2641. https:// doi.org/10.3390/w13192641

Academic Editor: Aizhong Ye

Received: 15 August 2021 Accepted: 19 September 2021 Published: 25 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

downdrafts [5]. For example, on a temporal scale, short-term vertical motion is associated with small-scale precipitation—such as typhoons (hurricanes) and rainstorms—whereas long-term vertical motion is associated with large-scale rainy weather (mostly low-pressure areas) and droughts (mostly high-pressure areas) [6]. On a spatial scale, areas of ascent in the Hadley circulation correspond to low pressure and a rainy zone in the meridional direction, such as the region of ascending air near the equator, whereas areas of descending air correspond to high pressure and arid zones (e.g., the subtropical arid region) [7,8]. The area of ascent related to the Walker and anti-Walker circulations [9] corresponds to the rainy zone around the equator, whereas the area of descending air corresponds to regions with only small amounts of rain in the zonal direction [10,11].

The upward motion of air over the Indian Ocean and the downward motion of air over the surrounding continents form many vertical circulations [12] which affect the amount of precipitation. Bjerknes [13] studied the relationship between the vertical motion of the atmosphere and precipitation over India as early as 1910 and showed that the vertical motion of air over India is closely related to the amount of precipitation in the northern side of the Indian Ocean. On the western side of the Indian Ocean, the vertical motion of air over Africa is also closely related to the local precipitation, and has led to droughts in Africa during the last century [14,15]. Since China is on the path of the Indian monsoon, there has been much research on the influence of change in the horizontal wind field on climate in China [16,17], while the research on the relationship between the vertical movement of air from the Indian Ocean and the climate of faraway China is rare.

We investigated the effects of the vertical motion of air over the Indian Ocean on the climate in East Asia. We aimed to find out whether the vertical motion of air associated with the Indian Ocean monsoonal circulation plays a role in the formation of and change in the climate of East Asia.

The research results are of significance to understand comprehensively the climate of East Asia and make more accurate climate forecasts. The paper is organized as follows: Section 2 describes the data and methods. The results and discussion are presented in Sections 3–5. The study concludes with a brief summary in Section 6.

#### **2. Data and Methods**

#### *2.1. Data*

Data for the monthly mean vertical wind speed were obtained from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis dataset [18] with a resolution of 2.5◦ × 2.5◦ . Twelve pressure levels were used for the Indian Ocean (1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150 and 100 hPa). Precipitation data from 839 meteorological stations were provided by the China Meteorological Administration. The surface air temperature and atmospheric pressure were extracted from the Scientific Data Center for the Cold and Arid Regions of China surface meteorological datasets with a temporal and spatial resolution of 0.1◦ × 0.1◦ . The monthly mean data which were calculated by using these datasets form the basis of the analytical approach.

Taking into consideration the remote connection between the equatorial Indian Ocean's sea surface temperature and the East Asian climate [19], the location of the Indian Ocean was taken as (25◦ S–30◦ N, 20◦ E–125◦ E) and the location of China as (15◦ N–55◦ N, 70◦ E–145◦ E). The time period measured was 1981–2010. Due to the horizontal wind at 850 hPa, the vertical motion of air (omega) at 500 hPa and the sea surface temperature play an important role in some regions in the Indian Ocean, while outgoing longwave radiation and the vertical motion of air (omega) at 500 hPa dominate for other regions in the occurrence of extreme rainfall [20]. The sea surface temperature anomaly (dipole event) over the Indian Ocean also has a good correlation with the geopotential height of 500 hPa, and is closely related to the precipitation anomaly in China during summer [21,22]. Therefore, the vertical motions of 500 hPa and 850 hPa over the Indian Ocean are selected. We studied the correlation between vertical movement over the Indian Ocean in January as

well as June and the climate in East Asia, since the Indian Ocean summer monsoon erupts in June while January is the beginning of winter [23].

To determine the reliability of the data, we compared the vertical motion of air in the NCEP, ERA-Interim (produced by the European Center for Medium-Range Weather Forecasts) and JRA-55 (from the Japan Meteorological Agency) datasets over the Indian Ocean and the Tibetan Plateau and found that they had almost identical systems and centers [24]. It is therefore reasonable to analyze the vertical motion of air using the NCEP data.

## *2.2. Methodology*

To diagnose and analyze the vertical motion of air over the Indian Ocean, we used empirical orthogonal function (EOF) analysis [25,26] to decompose the vertical velocity in winter (December–February), summer (June–August), January and June. The vertical velocity fields were decomposed into products of space function and time function by EOF decomposition. EOF analysis can be used to decompose the original data field, anomaly field and standardization field of vertical velocity. The results of decomposing different data fields are different in climatic significance. Because we performed orthogonal function decomposition on the original vertical velocity field, the first eigenvector (the spatial distribution) represents the average state (main pattern) of the vertical velocity field in the study area (explanation variance is large), and the corresponding time coefficient represents the time variation characteristics of the main pattern. The calculation of the EOF is as follows:

$$X\_{M \times N} = V\_{M \times P} \times T\_{P \times N} \tag{1}$$

where *XM*×*<sup>N</sup>* is a data matrix of the original vertical velocity composed of *N* observations of *M* spatial points. *V* are eigenvectors and T are eigenvalues. We used the first eigenvector in the analysis. To determine whether the first eigenvector has a physical meaning, we used the rule suggested by [26] to test the results:

$$e\_{\dot{\jmath}} = \lambda\_{\dot{\jmath}} \left(\frac{2}{N}\right)^{\frac{1}{2}} \tag{2}$$

where *e<sup>j</sup>* is the error range of the eigenvalue *λ<sup>j</sup>* and *N* = 30 is the sample size. When the adjacent eigenvalues satisfied *λ<sup>j</sup>* − *λ<sup>j</sup>* + 1 ≥ *e<sup>j</sup>* , we considered that the EOFs corresponding to these two eigenvalues were significant.

The time series of the corresponding main pattern in winter and summer was used to extract the periodic variation signals of the spatial distribution pattern using Morlet wavelet analysis [27–29].

The continuous wavelet transform *W<sup>X</sup> n* (*s*) on a scale s of a discrete time series *x<sup>n</sup>* (*n* = 1, . . . , *N*) with uniform time steps *δt* was defined as the convolution of *x<sup>n</sup>* with the scaled and translated version of the wavelet function ψ<sup>0</sup> :

$$\mathcal{W}\_{n}^{X}(s) = \sqrt{\frac{\partial t}{s}} \sum\_{n'=0}^{N-1} \mathbf{x}\_{n'} \boldsymbol{\upmu}\_{0}^{\*} \left[ \frac{(n'-n)\partial t}{s} \right] \tag{3}$$

where \* indicates the complex conjugate, *N* is the total number of data points in the time series and (*∂t*/*s*) 1/2 is the factor used to normalize the wavelet function, such that every wavelet function has a unit energy at each wavelet scale s.

By transforming the wavelet scale *s* and localizing along the time index *n*, we obtained a diagram showing the fluctuation characteristics of the time series at a certain scale and its variation with time—that is, the wavelet power spectrum [27,28,30]. The Morlet wavelet is not only non-orthogonal, but is an exponential complex-valued wavelet regulated by a Gaussian distribution defined as:

$$
\psi\_0(t) = \pi^{-1/4} e^{i\omega\_0 t} e^{-t^2/2} \tag{4}
$$

where *t* is the dimensionless time and *ω*<sup>0</sup> is the dimensionless frequency. When *ω*<sup>0</sup> = 6, the wavelet scale s is basically equal to the Fourier period (*λ* = 1.03 s) [30], so the scale term and the periodic term can be substituted for each other. Then the wavelet power spectrum *<sup>W</sup><sup>X</sup> n* (*s*) 2 is calculated.

To eliminate edge effects (i.e., the cone of influence), we used red noise processes as the background spectrum to test the statistical significance of the wavelet power spectrum [27–29]. Values outside the cone of influence were estimated at the 95% confidence level on each scale. Correlation analyses were conducted between the time series of the primary pattern and the meteorological indices (surface air temperature, atmospheric pressure and precipitation) in January and June; *t*-tests were used to verify the statistical results.

#### **3. Vertical Motion of Air over the Indian Ocean**

#### *3.1. Distribution of the Vertical Velocity of Air*

Figure 1a shows that upward motion of atmosphere (negative) is dominant over the Indian Ocean throughout the year. The central axis of upward motion (the connection line of the upward motion center) not only moves along the meridian from north to south, but also rotates with the seasons: the central axis is at about 10◦ S in spring, 7.5◦ S in autumn and 10◦ S in winter. The axis rotates clockwise from winter to summer and counterclockwise from summer to winter.

There are two ascending centers in the Indian Ocean in spring and summer. In spring, the two centers are located at about (10◦ S, 72.5◦ E) and (10◦ S, 100◦ E), whereas in summer they are located at (0, 60◦ E) and (6◦ S, 90◦ E).

There is only one rising center in the Indian Ocean in autumn and winter. From autumn to winter, the rising center of the South Indian Ocean moves not only longitudinally, but also latitudinally. The center moves from (7.5◦ S, 80.5◦ E) in autumn to (10◦ S, 72◦ E) in winter. There is a center of subsidence in the northern Arabian Sea in spring, autumn and winter, but not in summer.

In the Bay of Bengal region of the North Indian Ocean, subsidence is dominant in winter and spring, whereas ascent is dominant in summer and autumn. This is because the Bay of Bengal is surrounded on three sides by land: the highest plateau in the world, the Tibetan Plateau, lies to the north; the Indian subcontinent lies to the west; and the Central South Peninsula lies to the east.

#### *3.2. Distribution Characteristics of Atmospheric Vertical Motion over the Indian Ocean*

Since an EOF analysis decomposes the original vertical velocity of the air, the spatial distribution of the principal mode represents the average distribution feature of the vertical velocity of air, and its time series represents the time-varying characteristics of the average distribution of the vertical velocity of air. Here, the explanatory variances of the principal modes for vertical motion at 850 and 500 hPa over the Indian Ocean in summer were 93% and 90%, respectively, and therefore their spatial distribution can be used to fully represent the average distribution of vertical motion at these altitudes (Figure 1b).

From Figure 1c, we know that these time coefficients are all greater than zero. This may be because we decomposed the original vertical velocity (X matrix in Equation (1)) by EOF analysis; the time series of the principal mode came to the first quadrant after EOF decomposition (coordinate rotation) [31–35]. Analysis of the principal mode showed that in summer, the vertical motion was relatively weak at 850 hPa and that there was only one center of ascending motion in the east (6◦ S, 90◦ E). The center of upward motion at 500 hPa was also located at (6◦ S, 90◦ E) (Figure 1b), which shows that the center between upper and lower layers is symmetric.

The explanatory variances in the principal modes for vertical motion at 850 and 500 hPa over the Indian Ocean in winter are 88 and 85%, respectively. There are two centers of ascending motion at 850 hPa (8◦ S, 61◦ E) and (10◦ S, 72◦ E), but only one center of ascending motion at 500 hPa (12◦ S, 74◦ E) in winter, which shows that they are asymmetric.

*Water* **2021**, *13*, x FOR PEER REVIEW 5 of 14

**Figure 1.** Distribution of the vertical velocity of air over the Indian Ocean. (**a**) Vertical velocity at 500 hPa in spring (March–May), summer (June–August), autumn (September–November) and winter (December–February). The yellow line delineates the central axis of upward motion. (**b**) Spatial distribution of the primary EOF-analyzed pattern for the vertical velocity at 500 and 850 hPa in summer and winter; all values passed North's significance test. (**c**) Temporal variation in the primary pattern of the vertical velocities at 500 and 850 hPa in summer and winter. (**d**) Wavelet power spectrum of the temporal coefficients of the primary pattern of the vertical velocity at 500 hPa in both summer and winter. The red line delineates the cone of influence and the yellow areas show confidence levels > 95%. **Figure 1.** Distribution of the vertical velocity of air over the Indian Ocean. (**a**) Vertical velocity at 500 hPa in spring (March–May), summer (June–August), autumn (September–November) and winter (December–February). The yellow line delineates the central axis of upward motion. (**b**) Spatial distribution of the primary EOF-analyzed pattern for the vertical velocity at 500 and 850 hPa in summer and winter; all values passed North's significance test. (**c**) Temporal variation in the primary pattern of the vertical velocities at 500 and 850 hPa in summer and winter. (**d**) Wavelet power spectrum of the temporal coefficients of the primary pattern of the vertical velocity at 500 hPa in both summer and winter. The red line delineates the cone of influence and the yellow areas show confidence levels > 95%.

There are two ascending centers in the Indian Ocean in spring and summer. In spring, the two centers are located at about (10° S, 72.5° E) and (10° S, 100° E), whereas in summer they are located at (0, 60° E) and (6° S, 90° E). There is only one rising center in the Indian Ocean in autumn and winter. From au-The Arabian Sea and the Bay of Bengal are dominated by the upward motion of air in summer, but by the downward motion of air in winter, as they are strongly affected by the thermal differences between the continents and the oceans.

tumn to winter, the rising center of the South Indian Ocean moves not only longitudinally, but also latitudinally. The center moves from (7.5° S, 80.5° E) in autumn to (10° S, 72° E) in winter. There is a center of subsidence in the northern Arabian Sea in spring, autumn Analysis of the time coefficients of the principal modes (Figure 1c) shows that the vertical motion at 850 and 500 hPa had a downward trend in summer from 1981 to 2010, which indicated that the vertical motion over the Indian Ocean weakened over time,

and winter, but not in summer.

especially at 850 hPa. It has been suggested previously that global warming may weaken atmospheric motion [36]. The situation is different in winter. The vertical upward motion of air over the South Indian Ocean and the vertical subsidence of air over the North Indian Ocean both decreased at 850hPa over time. By contrast, the vertical motion at 500 hPa was enhanced—that is, the upward vertical motion of air in the South Indian Ocean and the downward vertical motion of air in the North Indian Ocean increased.

#### *3.3. Period of Vertical Motion of Air*

Because the explanatory variances of the principal modes at 500 hPa in summer and winter are 90 and 85%, respectively, they can be used to fully represent the distribution of the mean vertical motion of air over the Indian Ocean. We used the time coefficients of the principal mode to carry out wavelet analysis to understand the periodic variation in vertical motion over the Indian Ocean.

The distribution of the principal mode of the vertical velocity of air over the Indian Ocean in summer had a period of about 7–9 years from 1990 to 2010. The variances all passed the 95% reliability test. The periodic oscillation in winter was 9–12 years from the early 1990s to around 2003 and 2–3 years from 1987 to 1991. Both variances passed the 95% significance test (Figure 1d).

#### **4. Relationship between the Vertical Motion of Air and the Climate in East Asia**

The onset of the Indian monsoon in the Indian Ocean occurs in June. To understand the correlation between the climate in China and the vertical motion of air over the Indian Ocean, we analyzed the relationship between the temporal coefficients of the principal modes of the EOF analysis (explanatory variance 73%) for the vertical motion at 500 hPa over the Indian Ocean and the surface air temperature as well as the atmospheric air pressure in June. In addition, the monthly mean precipitation from the respective 839 meteorological stations in China is used to correlate with the time coefficient of the primary mode of the vertical motion of air at 500 hPa over the Indian Ocean; 839 correlation coefficients are obtained. Then, Figure 2a,b are formed by the correlation coefficients from 839 stations. For comparison, we also studied the correlation in January (explanatory variance 81%) and used the T-test to verify the correlation coefficient between them.
