**1. Introduction**

The Rossby wave (RW) propagation caused by external forcing is one of the mechanisms leading to the configuration of wave trains called teleconnection. In the northern hemisphere (NH), a favorable area with RW-forming dynamic conditions is located in East Asia [1,2]. The Rossby wave pattern at the upper troposphere generally manifests as Rossby wave train of atmospheric response to one or more local wave sources [3–5]. In the NH midlatitudes, the source of RW may be related to topography, marine–terrestrial contrast, or transient baroclinic systems [6]. Ye and Zhu [7] believe that both topographic and diabatic heating play an important role in the climatological atmospheric teleconnections along the westerly jet stream, especially the large troughs over East Asia and the east coast of North America. Previous studies of Rossby wave source (RWS) have shown that most of the strong RWS are located in the subtropical zone on the seasonal timescales, although most of the upper divergent flow regions are located near the equator. Because the divergent flow is greater at the edge of the greatest divergence zone and the absolute vorticity gradient is larger at higher latitudes [2,8,9], these all provide conditions for RWS formation

**Citation:** Ding, Y.; Sun, X.; Li, Q.; Song, Y. Interdecadal Variation in Rossby Wave Source over the Tibetan Plateau and Its Impact on the East Asia Circulation Pattern during Boreal Summer. *Atmosphere* **2023**, *14*, 541. https://doi.org/10.3390/ atmos14030541

Academic Editors: Xiaolei Zou, Guoxiong Wu and Zhemin Tan

Received: 8 February 2023 Revised: 7 March 2023 Accepted: 8 March 2023 Published: 11 March 2023

**Copyright:** © 2023 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/).

in the subtropics. Therefore, RWS may be associated with both local forcing and absolute vorticity advection caused by atmospheric diabatic heating. Plumb [10] shows that the main forcing of the quasi-stationary wave originates from the topographic influence over the Tibetan Plateau (TP), as well as interaction of the diabatic heating with transient flows over the Pacific, Northwest Atlantic, and Siberia by diagnosing the wave activity flux in the NH winter.

Ye [11] first applied the RW energy dispersion theory to the study of the atmospheric circulation change mechanism. Previous studies have shown that the energy propagation process of Rossby waves along the westerly jet in the NH summer is an important dynamic mechanism for the development of high-latitude trough in East Asia, and its downstream effect is also an important driver of flood disasters in China [12–15]. On the interdecadal timescale, there is a Rossby wave train in the midlatitudes. The eastward propagation of wave energy has a significant impact on the precipitation pattern in the middle and lower reaches of the Yangtze River basin [16,17]. The Tibetan Plateau, as the steepest and most complex terrain on the Earth and the region with the strongest land–atmosphere interaction in the NH midlatitudes, has a great influence on regional and global climate [18–20]. Moreover, its local thermal forcing can directly affect the downstream atmospheric circulation and rainfall pattern [21–23]. Previous studies have shown that the surface turbulent heat flux in the southeastern TP plays an important role in regulating Meiyu and rainstorm in the Yangtze River Basin [24–27]. There is also a close relationship between the variation of snow cover in different regions of the TP and the atmospheric circulation [28–31]. In addition, the anomalous diabatic heating over the TP can trigger Rossby waves propagating westward and eastward along the extratropical westerly jet to change the large-scale climate on the interannual scale [32–34].

The above studies on the impact of RWS mainly focus on the seasonal and interannual timescales and discuss the RW role on persistent circulation anomaly and corresponding precipitation pattern in East Asia. However, where is the key area of RW energy dispersion in the NH summer on interdecadal scale? What is the physical mechanism of the Rossby wave train excited from the TP on the precipitation anomaly in East Asia? All these are worthy of further discussion. Thus, we analyze the interdecadal variability and spatial distribution of the TP-RWS in summer during 1900 to 2010. In addition, the causes of the TP-RWS and its effects on the anomalous circulation in East Asia are discussed so as to understand the physical mechanism of precipitation anomalies associated with TP-RWS. Section 2 of the manuscript introduces the data and methods used. Section 3 analyzes the interdecadal variability of the TP-RWS and its impact on the East Asia Circulation Pattern. Conclusions and discussion are shown in Sections 4 and 5, respectively.

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

The atmospheric data used in this paper are from the ERA-20th Century (ERA-20C) monthly reanalysis dataset provided by the European Center for Medium Range Weather Forecasting (ECMWF) for 1900 to 2010 [35]. In order to compare the calculation results, we also use monthly atmospheric variables of the 20th Century Reanalysis (NCEP-20C) from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) for 1836 to 2015 [36]. The horizontal resolution of the two datasets is 1◦ × 1◦, and the rectilinear grid numbers are 181 × 360. The data include wind field (V), temperature (T), geopotential height (H), vertical velocity (ω), and specific humidity (q) of 27 layers from 1000 hPa to 100 hPa. In addition, the surface sensible heat flux (SHTFL), total cloud cover (TCC), snow albedo (ASN), and surface pressure are used. The centennial precipitation data used in our study are based on the global terrestrial meteorological grid dataset established by the University of East Anglia (CRU\_ts4) from 1901 to 2010, with a horizontal resolution of 0.5◦ × 0.5◦. The monthly land precipitation data provided by the Global Precipitation Climatology Centre (GPCC) for 1900–2010 are also used, with a horizontal resolution of 0.25◦ × 0.25◦. The 2500 m terrain height is selected as the criteria for calculating the regional average over the TP. In this study, interdecadal variation denotes

the time series of TP-RWS and other physical quantities remove the linear trend during 1900 to 2010 in summer, and then perform 10-year low-pass filtering.

According to the derivation of Sardeshmukh and Hoskins [4,8] based on the nonlinear vorticity equation, the Rossby wave source (RWS) on a horizontal level can be calculated as:

$$RWS = -\nabla \cdot (f + \zeta) V\_{\chi} = -(f + \zeta)D - V\_{\chi} \cdot \nabla (f + \zeta) \tag{1}$$

where the RWS represents Rossby wave source. The *f* and ζ are planetary vorticity and relative vorticity, respectively, and absolute vorticity is the sum of the two. *D* represents the horizontal divergence *<sup>∂</sup><sup>u</sup> <sup>∂</sup><sup>x</sup>* <sup>+</sup> *<sup>∂</sup><sup>v</sup> <sup>∂</sup><sup>y</sup>* and *V<sup>χ</sup>* is the divergent component of the horizontal wind. The divergent wind component is calculated by inverting the Laplacian operator in spherical harmonic space after computing the divergence. The Formula (1) shows that time-averaged vorticity can be considered as a combination of the vortex stretching term (RWS-S1) produced by local strong divergence and the absolute vorticity advection term (RWS-S2) caused by large-scale divergent flow [2]. When an anomalous vorticity diverges outward, the local vorticity decreases, and this vorticity divergence center is called the vortex source region. The converse is the vortex sink area. Therefore, analyzing the RWS distribution and its variability can help to understand the origin and physical mechanism of planetary wave generation and atmospheric changes [37].

The method of calculating Q1 in this study is based on the inverted algorithm of Yanai et al. [38]:

$$Q\_1 = C\_P \left[ \frac{\partial T}{\partial t} + V \cdot \nabla T + \left( \frac{P}{P\_0} \right)^k \omega \frac{\partial \theta}{\partial P} \right] \tag{2}$$

where T is temperature, V is horizontal wind vector, ω is vertical velocity, and θ is the potential temperature. k = R/Cp, where R and CP are dry atmospheric constant and isobaric specific heat capacity, respectively. All these variables are in p co-ordinates; thus, Q1 at each isobaric layer can be calculated.

In addition, the three-dimensional T-N wave flux derived by Takaya and Nakamura [39,40] based on the Plumb wave flux [10] is used in our study to describe the Rossby wave energy propagation. These elements are able to better describe the Rossby wave disturbance along the westerly jet in zonal inhomogeneous flow [41]. The formula is expressed as follows:

$$\mathcal{W} = \frac{p \cos \varphi}{2|\mathcal{U}|} \begin{Bmatrix} \frac{\mathcal{U}}{a^2 \cos^2 \varphi} \left[ \left(\frac{\partial \varphi'}{\partial \lambda}\right)^2 - \Psi' \frac{\partial^2 \varphi'}{\partial \lambda^2} \right] + \frac{V}{a^2 \cos \varphi} \left[ \frac{\partial \psi'}{\partial \lambda} \frac{\partial \psi'}{\partial \varphi} - \Psi' \frac{\partial^2 \varphi'}{\partial \lambda \partial \varphi} \right] \\\ \frac{\mathcal{U}}{a^2 \cos \varphi} \left[ \frac{\partial \psi'}{\partial \lambda} \frac{\partial \psi'}{\partial \varphi} - \Psi' \frac{\partial^2 \psi'}{\partial \lambda \partial \varphi} \right] + \frac{V}{a^2} \left[ \left(\frac{\partial \psi'}{\partial \varphi}\right)^2 - \Psi' \frac{\partial^2 \psi'}{\partial \varphi^2} \right] \\\ \frac{f\_0^2}{N^2} \left\{ \frac{\mathcal{U}}{a \cos \varphi} \left[ \frac{\partial \psi'}{\partial \lambda} \frac{\partial \psi'}{\partial z} - \Psi' \frac{\partial^2 \psi'}{\partial \lambda \partial z} \right] + \frac{V}{a} \left[ \frac{\partial \psi'}{\partial \varphi} \frac{\partial \psi'}{\partial z} - \Psi' \frac{\partial^2 \psi'}{\partial q \partial z} \right] \right\} \end{Bmatrix} \tag{3}$$

where the *ϕ*, *λ*, Φ, and *a* represent the latitude, longitude, geopotential, and radius of the Earth, respectively. *z* is the vertical co-ordinates of the log *p*. *ψ* = <sup>Φ</sup> *<sup>f</sup>* is the disturbance of quasi-geostrophic stream function relative to the climatology. The basic flow *U* represents the climate average.

#### **3. Results**

## *3.1. Interdecadal Variation in Rossby Wave Source over the Tibetan Plateau*

In the June–July–August (JJA) period, a Rossby wave source clearly appears along the upper tropospheric westerly jet over East Asia and the extratropical Pacific, which is much stronger than that in the tropics (Figure 1a). In the North Hemisphere (NH), the Asian Monsoon–Tibet Plateau region exhibits a strong negative RWS and the North Africa and Mediterranean Sea are positive RWS regions. In addition, the eastern subtropical Pacific and the Atlantic Ocean showed weak RWSs. The RWSs in the Southern Hemisphere are mainly located over the South Indian Convergence Zone, South Pacific, and South Atlantic. These are consistent with previous studies [2,9,42]. For the JJA mean, the intertropical

convergence zone moves towards the Northern Hemisphere, and its associated heavy rainfall (Figure 1b) extends northeast from East Asia and the Northwest Pacific. Meanwhile, there is a strong divergent flow and velocity potential center over the Asian monsoon region, which corresponds to its strong convection. The divergence flow radiates outward from East Asia and extends into Eurasia and the Pacific. The concurrence of large-scale divergence at 200 hPa and deep convection indicates that the velocity potential center at the upper troposphere in the NH is largely caused by diabatic heating over the Asian monsoon region [43], while North Africa occurs as a net radiation sink in summer, resulting in continuous cooling as a powerful cold source [44]. This distribution of heat and cold sources forms a divergent/convergent field center over the Asian monsoon region and the Mediterranean Sea. According to Formula (1), negative RWS sources over the Asian summer monsoon region in Figure 1a are formed. Previous studies have shown that these large-scale heating forcings and their RWSs play important roles in forming and maintaining atmospheric circulation over East Asia and the North Pacific [45,46].

**Figure 1.** Distribution of global (**a**) Rossby wave source (shading; unit: 10−<sup>10</sup> s−2) and divergent wind component (vectors; unit: m·s<sup>−</sup>1), and (**b**) precipitation (unit: mm·day<sup>−</sup>1) in June−August of 1900−2010. The green contours in (**a**,**b**) represent the 2.5km topography height of the Tibetan Plateau.

How the RWSs have changed during boreal summer over the past 110 years and what physical processes they are associated with are the main concerns in this study. The NH summer RWS variability has exhibited prominent differences, as exemplified by the RWS variance patterns on interannual and interdecadal timescales in Figure 2. Notably, the maximum variability of RWSs on both timescales occurs over the northwestern TP, and the fluctuations are also large over the northeast of China and near the Mediterranean Sea. The interdecadal spatial distributions of NH RWS variabilities are very consistent with those on the interannual timescale. Furthermore, the TP-RWS variance on interdecadal timescale accounts for 22.3% of that in raw from 1900 to 2010. All these indicate that the northwestern TP, including most parts of the Eurasian continent, is the anomalous RWS fluctuation region. As the largest plateau and strongest heat source in boreal summer, the changes in TP thermal conditions may lead to the interdecadal RWS anomalies over this region.

Figure 3 shows the JJA interannual and interdecadal RWS time-series over the TP (topographic height above 2500 m) of 200 hPa from 1900 to 2010. It can be seen that the TP-RWS in the upper troposphere is characterized by multidecadal variations. From the perspective of intensity changes, the TP-RWS showed continuous strong periods during the early 20th century, the 1920s to 1940s, the 1950s to 1970s, and after 2000. Accordingly, the temporal series turned into weak periods during the 1910s to 1920s, 1940s to 1950s, and from the 1970s to the end of the 20th century. Moreover, the TP-RWS variation shows multidecadal differences in the recent 110 years. In the first half of the 20th century, it oscillated in longer periods and, after the late 1950s, decadal variations were more evident. These may be affected by the joint influence of various internal forcing oscillations, as well as the increasing instability of the climate system since global warming [47,48]. The NCEP-20C datasets from 1900 to 2015 are also used to calculate TP-RWS time evolution in order to reduce the uncertainty of calculation results from different datasets. The temporal correlation of TP-RWS between ERA-20C and NCEP-20C datasets reaches 0.72 on the interannual scale, which is 0.69 on the interdecadal scale, and they both pass the 99% confidence test. Therefore, the selected ERA-20C data in this paper can accurately reflect the variations in TP-RWS. Furthermore, in order to explore the spatial distribution characteristics with the TP-RWS interdecadal evolution in the past 110 years, we calculate one-point correlation between the TP-RWS anomalies and large-scale divergent flow in the NH summer (Figure 4). When the interdecadal intensity of TP-RWS increases, the corresponding maximum RWS area appears over the northwestern TP, which is accompanied by a strong divergence center at the upper troposphere. Meanwhile, the RWS in the south of the TP, especially in the northwestern Indo–China Peninsula, shows a weakly negative correlation with the RWS in the whole plateau. The above results show that, as a key area of the interdecadal RWS fluctuations in boreal summer, the causes of the TP-RWS and its influences are worth studying.

**Figure 2.** Spatial distribution of the RWS variance (unit: 10−<sup>10</sup> s−4) during boreal summer of 1900–2010 (**a**) on an interannual timescale and (**b**) on an interdecadal timescale (black box indicates the key area of the RWS variance 65–90◦ E, 30–45◦ N).
