**2. Materials and Methods**

#### *2.1. Data*

Daily and 6-h horizontal winds and air temperature were derived from the reanalysis of the European Center for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) products [42], spanning the 40-yr period from 1979 to 2018. The dataset we obtained is a spatially gridded one that has a fixed horizontal resolution of 1◦ × 1◦ and 37 vertical levels. Daily and 6-h horizontal winds and air temperature (2.5◦ × 2.5◦ and 17 vertical levels) were also obtained from the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) [43] for the period of January 1979–December 2018. It is noted that the key results presented later in this paper are not sensitive to the selection of reanalysis datasets. Following Curio et al. [44], the relative vorticity was calculated from the wind field and was employed to represent the vortices. Interpolation methods were used to obtain a spatial resolution of 1◦ × 1◦ and a temporal resolution of 1 h, if necessary.

The daily precipitation in East Asia for the period of 1 January 1979 to 31 December 2018 was obtained from the CPC precipitation dataset [45]. We selected this period to match the duration of the ERA-Interim and NCEP/NCAR datasets. The APHRO\_MA\_025deg\_V1003R1 product based on the APHRODITE rain gauge data precipitation dataset for the 1979–2015 period was also used in this study [46]. Both precipitation datasets have a fixed horizontal resolution of 0.5◦ × 0.5◦. In the following section, we will demonstrate that the results relevant to precipitation are not sensitive to the selection of the precipitation datasets.

#### *2.2. Spatial Fourier Transform to Derive the AVS Pattern*

The relative vorticity and horizontal wind field were divided into the AVS-related component and other wave-related components using the Fourier transform, which has been widely applied in wave analysis [47,48]. In this study, the spatial lowpass filtered relative vorticity captured the AVS related to the Tibetan Plateau. The spatial domain was 60◦ E–120◦ W, 10◦ S–80◦ N. The components with a meridional wavelength shorter than 7–9◦ and a zonal wavelength shorter than 14–18◦ were filtered out. We chose these thresholds due to the distances between neighboring vortices in the AVS being longer than these wavelength thresholds.

#### *2.3. The AVS-Related Precipitation and Heavy Rain Days*

Mesoscale cyclonic activities could trigger substantial precipitation. Previous studies have attempted to determine the precipitation associated with mesoscale cyclonic activities. Some studies use a fixed-radius scheme to identify the precipitation related to mesoscale cyclonic activities [44,49]. However, other studies use the outermost closed contour (OCC) to detect the affected precipitation [50]. The domain of mesoscale cyclonic activities is naturally defined by the region covered by the outermost closed contour (OCC) in the

potential height or relative vorticity fields. In addition, the precipitation within the coverage of the OCC is defined as related to mesoscale cyclonic activities.

To determine the precipitation associated with the AVS, in this study, following Hanley and Caballero [50], we used the region covered by the OCC instead of a fixed radius to detect the precipitation affected by cyclonic activities in the AVS. The OCC of the AVS was defined as the contour where the spatial Fourier-filtered relative vorticity was zero. The AVS-related precipitation was determined over 110–120◦ E, 125–130◦ E, and 130–145◦ E, respectively. These three regions represent East China, the Korean Peninsula, and Japan, respectively.

#### **3. Results**

#### *3.1. Topography of the Tibetan Plateau and Surrounding Meteorological Conditions*

The Tibetan Plateau spans the region of approximately 26~40◦ N, 73~105◦ E. The grid of (40◦ E, 32◦ N) is located upstream of the Tibetan Plateau with an elevation of only 500 m and serves as a reference coordinate grid for the Tibetan Plateau. Figure 2 displays the mean seasonal cycle of the zonal wind at that grid. Strong westerlies prevail over the upstream region and over almost the whole troposphere from 1000 hPa to 100 hPa for a whole year. The minima of the westerlies occurred over the boreal summer.

**Figure 2.** Vertical-temporal distributions of climatological mean values of the zonal wind at the grid (40◦ E, 32◦ N) during 1979–2018 (unit: m/s).

To determine whether meteorological conditions around the Tibetan Plateau favor the generation of vortex street shedding, two dimensionless indices were employed here to measure the basic flow parameters: the Froude number (*Fr*) and Reynolds number (*Re*). Etling [27] showed that a stable vortex street on the lee side of an obstacle can exist when the Froude number (*Fr*) is smaller than 0.4 and the Reynolds number (*Re*) falls in a particular range. The particular range of Reynolds numbers (*Re*) for the generation of vortex street shedding was suggested to be 50–105 for different horizontal sizes of the obstacle [25].

The Froude number is the dimensionless ratio of flow inertia to gravitational forces. The parameter is relevant in the description of stratified atmospheric flows. Here, we calculate the streamlines of the air parcels that flow over and around the obstacle separately [51]. The flow below the level of the partitioning streamline, referred to as dividing streamline height, is regarded as a quasi-2D streamline in horizontal planes.

When the vertical profile of wind speed and stratification is given, the dividing streamline height *hc* can be calculated based on an implicit expression derived by Snyder et al. [51]:

$$0.5 \text{l}I^2(h\_c) = \int\_{h\_c}^{h\_m} N^2(z)(h\_m - z)dz\tag{1}$$

where *U(z)* is the vertical profile of upstream wind speed, *hm* is the average height of the Tibetan Plateau that is felt by the large-scale flow (average height of Tibetan Plateau plus its boundary layer depth), which is approximately 5000 m, and *N(z)* is the Brunt-Väisälä frequency. The dividing streamline height *hc* is then used to calculate the Froude number in the slowly varying (approximated as constant) upstream velocity and stratification [27]:

$$Fr = 1 - \frac{h\_c}{h\_m} \tag{2}$$

Note that this equation of *Fr* is different from its glossary definition; this equation of *Fr* is derived based on laboratory experiments [51] and was recommended to calculate *Fr* in the real atmosphere [27]. Figure 3 plots the climatological mean of the dividing streamline height *hc* for various seasons. The dividing streamline height *hc* falls in the range of 3500 m to 4000 m (approximately 600–700 hPa), indicating that the Froude number varies from 0.2 to 0.3 and falls in the range of Froude numbers that could support vortex shedding year-round. The value of dividing streamline height coincides well with the results revealed by numerical experiments, which illustrates that the westerly flowing around the Tibetan Plateau dominates the flowing over in the middle-low troposphere [52]. At the dividing streamline height level, the diameter of the Tibetan Plateau is approximately 1000 km year-round. The upstream velocity for the Tibetan Plateau at that level is observed to be approximately 8 m/s in summer and 15 m/s in other seasons.

**Figure 3.** Red line: The seasonal variation in the climatological mean of the height of the dividing streamline *hc* of the Tibetan Plateau (unit: m). Black lines mark 1 standard deviation. The blue line is the threshold above which the stable AVS could exist.

Using the above values, we can estimate the Reynolds number, the dimensionless ratio of inertial force to viscous force, for various seasons. The Reynolds number is defined as:

$$Re = \frac{\mathcal{U}\_o d}{\upsilon} \tag{3}$$

where *Uo* is the upstream velocity, *d* is the obstacle (cylinder) diameter, and *ν* is the kinematic viscosity of the fluid. A value of *ν* = 1000 m2/s was used in this study, as suggested by Thomson et al. [25]. The estimated *Re* is approximately 1.5 × <sup>10</sup><sup>4</sup> in winter and 0.8 × <sup>10</sup><sup>4</sup> in summer. The estimated *Re* is below the upper threshold (105) at which the vortex street with a predominant frequency can exist, suggesting that the Reynolds number falls in the range of Reynolds numbers that could support vortex shedding year-round.

#### *3.2. Characteristics of the AVS on the Leeward Side of the Tibetan Plateau*

The analysis in Section 3.1 revealed that the meteorological conditions around the Tibetan Plateau are favorable for the generation of vortex street shedding year-round. What are the characteristics of the AVS on the leeward side of the Tibetan Plateau? In this study, the focus is placed on the downstream AVS, far beyond the sharp downhill region.

To answer this question, in Figure 4a–d, we display four cases of the spatial structure of the Fourier-filtered relative vorticity and horizontal wind over the leeward side of the Tibetan Plateau. These four cases are displayed for the spring, summer, autumn, and winter seasons. Clearly, the Fourier-filtered relative vorticity fields in various seasons all bear close resemblance to that of the classic von Kármán vortex-street patterns observed in laboratory flow experiments and illustrated in Figure 1. The double row of counter-rotating vortex pairs appears on the leeward side of the Tibetan Plateau, confirming a well-defined AVS pattern related to the Tibetan Plateau. The cyclonic vortices and anticyclonic vortices in the wake of the Tibetan Plateau are generated over the Sichuan Basin and Gansu Province, respectively, and then both propagate eastward toward the Pacific Ocean, with the trail persisting a considerable distance downstream of the Tibetan Plateau. Note that the AVSs discussed here are mostly generated by the portion of the mean flow split horizontally by the Tibetan Plateau at the upstream and merged downstream, not by the portion that overflows the Tibetan Plateau.

The spatial structures of the AVS showed seasonal variations. A common feature that emerged between spring and winter is that the centerlines connecting the centers of a cyclonic-anticyclonic vortex pair all have an approximately west-east orientation. The propagating direction of rotating vortex pairs in these seasons follows that of westerlies, consistent with the results in Horváth et al. [16]. However, the centerlines connecting the centers of a cyclonic-anticyclonic vortex pair in summer and early autumn have a southwestnortheast orientation. Notably, a strong anticyclonic circulation was located over the western Pacific (Figure 4b,c), which was termed the western Pacific subtropical anticyclone (WPSA). The WPSA penetrates northwards in summer, and the strong southwesterlies along its western edge may favor the southwest-northeast propagation direction of the AVS in summer and early autumn. Thus, the differences in the centerline orientation among various seasons may be related to the difference in the position of the WPSA.

A question that naturally follows is whether the AVS pattern was simply a coincidence or a consequence of using Fourier filtering. Our further analysis of the historical data without filtering eliminates the possibility of these artifacts. Figure 4e,h displays the spatial structure of the raw relative vorticity field of the four cases listed in Figure 4a–d. The AVS structure can still be distinguished in the raw field of these cases. The spatial patterns of unfiltered relative vorticity share similar spatial structures of their corresponding filtered field, with the filtered field explaining approximately 66% to 76% of the raw field among various seasons (Figure 4e–h vs. Figure 4a–d).

Figure 5a–c displays the spatiotemporal evolution of daily relative vorticity at 700 hPa (without filtering) over the downstream region of the Tibetan Plateau (110–120◦ E) from February to April of 1981, 1984, and 1992. The AVS structure remains robust in the raw data; the double row of counter-rotating vortex pairs alternately appeared in the region between 25–40◦ N, with the centerline located at 32◦ N, which is the central line of the Tibetan Plateau (Figure 5a–c). In this double-row pattern, each vortex is opposite the center of the spacing between the two vortices in the other row, and the lateral spacing is roughly equal to the cross-stream diameter of the Tibetan Plateau. Another noticeable feature is that the vortex pairs are generated at a predominant period of approximately 3–4 days and then propagate downstream to the Pacific at a similar, steady speed (Figure 5a–f). The above features suggest that the double row of counter-rotating vortex pairs over the leeward side of the Tibetan Plateau in the unfiltered field exists in various seasons, and this structure also bears a close resemblance to that of the classic von Kármán vortex-street patterns observed in laboratory flow experiments and illustrated in Figure 1.

**Figure 4.** (**a**–**d**) Fourier filtered horizontal structure of 4 cases in daily relative vorticity at 700 hPa for the period of boreal (**a**) spring (16 March 1992), (**b**) summer (1 August 1991), (**c**) autumn (15 September 2002), and (**d**) winter (15 February 2005) (unit: s−1). The green line marks the topography of the Tibetan Plateau. The vector exhibited the Fourier filtered 700 hPa horizontal wind field. (**e**–**h**) Same as (**a**–**d**) but for the unfiltered field replacing the Fourier filtered field.

#### *3.3. The Properties of the AVS on the Leeward Side of the Tibetan Plateau*

To further confirm that the AVSs developing on the leeward side of the Tibetan Plateau can be interpreted as the atmospheric analog of the classic von Kármán vortex street, various properties of AVSs were calculated to compare with those in previous studies of smaller obstacle caused AVS. These properties are summarized in Tables 1 and 2.

**Figure 5.** (**a**–**c**) Hovmöller diagram of daily relative vorticity at 700 hPa averaged over 110–120◦ E (unit: 10−<sup>5</sup> s<sup>−</sup>1) for the period of February to April (winter to spring) in (**a**) 1981, (**b**) 1984, and (**c**) 1992. The straight line in panel a is used to represent 32◦ N, which is roughly the central line of the Tibetan Plateau. Precipitation averaged over 110–120◦ E was also exhibited by the purple lines (2 levels of 5 mm/day and 15 mm/day). (**d**–**f**) Hovmöller diagram of daily relative vorticity at 700 hPa averaged over 28–32◦ N from March to April in (**a**) 1981, (**b**) 1984, and (**c**) 1992 (unit: 10−<sup>5</sup> s<sup>−</sup>1).

**Table 1.** Characteristic values for the vortex streets of the leeward side of the Tibetan Plateau for 12 cases in spring and winter. The characteristic values include vortex spacing *a*, vortex width *h*, and aspect ratio *h/a*, AVS vortex shedding period *Te*, the propagation velocity of the AVS patterns *Ue*, the undisturbed wind velocity *Uo*, the Reynolds number *Re*, and the Strouhal number *S*.


The aspect ratio *h/a* (see Figure 1) is a basic property of an AVS. Laboratory experiments show that a stable vortex formed on the lee side of an obstacle is characterized by 0.28 < *h/a* <0.52 [19]. The aspect ratio *h/a* of AVS recorded in previous studies falls in the

range of 0.15–0.8 [25]. Rows 2–4 in Table 1 display the vortex spacing *a*, vortex width *h*, and aspect ratio *h/a*, respectively. In this study, the dimensions of the AVS can be measured directly based on the position of extreme points. Considering that the longer shedding period may cause an increasingly disordered AVS structure, only the two westernmost vortex pairs in each case were used to calculate the aspect ratio *h/a*. The aspect ratio *h/a* in the 12 AVS cases listed in Table 1 mainly falls into the range of 0.2 to 0.59, which is comparable to that observed by previous studies. From Table 1, one can see that the vortex spacing *a* varies from 2478 km to 3807 km. Moreover, the average AVS width *h* is 1055 km, which is roughly equal to the cross-stream diameter of the Tibetan Plateau.

Another property that can be identified directly is the AVS vortex shedding period *Te* (Figure 5a–c). *Te* was defined as the difference between the timing of the maximal value in consecutive cyclonic vortices in the relative vorticity field at 700 hPa in the latitude-time diagram (row 7 of Table 1). Three properties of AVS can be calculated based on *Te*: (1) The propagation velocity of the AVS patterns, *Ue*, (2) the ratio between the vortex propagation velocity *Ue* and the undisturbed wind velocity *Uo* (referred to as *Ue/Uo* below), and (3) the Strouhal number *S*.

Following Chopra and Hubert [20], The AVS propagation velocity *Ue* is defined as:

$$dL\_{\mathfrak{c}} = \frac{a}{T\_{\mathfrak{c}}} = af \tag{4}$$

where *f* is the vortex shedding rate (or frequency), *Ue* is the vortex propagation velocity and is defined as *a* divided by *Te*, and *Te* is the vortex shedding period. From Table 1, one can see that the vortex shedding period *Te* falls in the range from 50 to 137 h, and these values are also approximately one to two orders of magnitude greater than those observed by previous studies. From Table 1, *Ue* was estimated to fall into the range between 5.7 m/s and 17.8 m/s. These values are comparable to those observed in previous studies.

**Table 2.** Characteristic values for the vortex streets of the leeward side of the Tibetan Plateau for 12 cases in summer. The characteristic values include vortex spacing *a*, vortex width *h*, and aspect ratio *h/a*, AVS vortex shedding period *Te*, the propagation velocity of the AVS patterns *Ue*, the undisturbed wind velocity *Uo*, the Reynolds number *Re*, and the Strouhal number *S*.


The ratio *Ue/Uo* is a common choice to estimate *Uo* when directly measuring *Uo* is difficult. Following Chopra and Hubert [20], as well as Li et al. [4], the ratio *Ue/Uo* and the aspect ratio *h/a* satisfy the following equation:

$$(2B - A) \left(\mathcal{U}\_{\varepsilon}/\mathcal{U}\_{o}\right)^{2} + (2A - 3B) \left(\frac{\mathcal{U}\_{\varepsilon}}{\mathcal{U}\_{o}}\right) + \left(B - A + \frac{B}{4A}\right) = 0\tag{5}$$

where *A =coth (πh/a)* and *B =πh/a*. The analytical solution shows that the ratio *Ue/Uo* equals 0.75 if the aspect ratio *h/a* is close to 0.39. In previous studies, the ratio *Ue/Uo* fell in a range of 0.7 to 0.85 [25]. In our study, the ratio *Ue/Uo* in the 12 AVS cases mainly falls into the range of 0.54 to 0.88, and the estimated *Uo* varies from 7.3 m/s to 28.4 m/s (Table 1).

The Strouhal number, *S*, is an essential dimensionless quantity in the description of oscillating flows. It can be considered a normalized shedding frequency, defined as:

$$S = \frac{d}{T\_\epsilon \mathcal{U} I\_o} \tag{6}$$

where *Uo* is the upstream velocity, *d* is the crosswind island diameter at dividing streamline height *hc*, and *Te* is the shedding period between two consecutive like-rotating vortices. Laboratory experiments show that the Strouhal number *S* varies from 0.12 to 0.21 when the Reynolds number *Re* is smaller than 10<sup>4</sup> [53]. In this study, the Strouhal number *S* fluctuated within the broad range of 0.13–0.28, which is consistent with the conclusions in previous studies.

In a nonrotating, unstratified fluid, the nature of the wake only depends on the Reynolds number, which is the dimensionless ratio of inertial force to viscous force. In Section 3.1, the Reynolds number, *Re*, was estimated to be O (104). In this study, the Reynolds number *Re* fluctuated within the broad range of 0.73 × <sup>10</sup>4–2.41 × 104, which is consistent with our previous estimation.

When the wake on the leeward side of the Tibetan Plateau was characterized by an AVS with a southwest-northeast orientation, many AVS properties changed considerably (Table 2). The distinctions in the AVS properties for these two periods can be summarized as follows: (1) The aspect ratio *h/a* in the subtropical AVS increased to 0.38–0.77. The increases in the aspect ratio *h/a* were mainly caused by the shortening of vortex spacing *a*. (2) The AVS propagation velocity *Ue* declined to 2.5–7.0 m/s, which mainly resulted from the decrease in upstream velocity in boreal summer. The Reynolds number, *Re*, was thereby decreased to 0.35 × 104–1.17 × <sup>10</sup>4, and the average AVS vortex shedding period *Te* increased to 114 h.

Thus, the above results indicate that the AVS on the leeward side of the Tibetan Plateau can be interpreted as the atmospheric analog of classic von Kármán vortex streets in various seasons.

#### *3.4. Impacts of the AVS on Precipitation over the Wake of the Tibetan Plateau*

Obviously, cyclonic activities in the AVS caused substantial precipitation (Figure 5a–c). A question that naturally follows is how much precipitation over the wake of the Tibetan Plateau can be closely tied to the AVS. To answer this question, we compared the spatiotemporal evolution of precipitation and cyclonic activities and calculated the relationship between heavy rain days and AVS-related cyclonic activities over East China, Japan, and the Korean Peninsula.

Figure 6 exhibits the seasonal variation in the climatological mean of the rainband and positive vorticity over 110–120◦ E, 125–130◦ E, and 130–145◦ E for the whole year. The rainband with precipitation exceeding 4 mm/day over these three regions began in the temporal span of March to September and the spatial span of the south to 32◦ N, and then the rainband penetrated northwards in the subtropics, propagating from 25◦ N to 40◦ N. Such a spatiotemporal structure was largely shared by that of positive relative vorticity. The correlation coefficients for the spatiotemporal domain were 0.178 (5691 samples, *p* < 0.01), 0.133 (*p* < 0.01), and 0.124 (*p* < 0.01).

The similarity between the seasonal evolution of the climatological mean was further supported by a single case. Figure 7 presents the seasonal meridional evolution of the rainband and positive vorticity over 110–120◦ E for the period from February to September 1983. The spatiotemporal structure of the rainband bears a close resemblance to that of positive vorticity. The correlation coefficients for the spatiotemporal domain were 0.164 (5691 samples, *p* < 0.01).

**Figure 6.** Hovmöller diagram of (**a**–**c**) daily precipitation derived from CPC datasets (unit: mm) and (**d**–**f**) daily relative vorticity at 850 hPa (unit: 10−<sup>6</sup> s−1) averaged over (**a**,**d**) 110–120◦ E, (**b**,**e**) 125–130◦ E, and (**c**,**f**) 130–145◦ E. The results were smoothed by a pentad temporal domain. Gray represents missing records.

**Figure 7.** Hovmöller diagram of (**a**) daily relative vorticity at 850 hPa (unit: 10−<sup>6</sup> s<sup>−</sup>1) and (**b**) daily precipitation derived from CPC datasets (unit: mm) for the period from February to September 1983 averaged over 110–120◦ E. The results were smoothed by a pentad temporal domain.

How much precipitation and how many heavy rain days can be closely tied to the AVS in the leeside wake of the Tibetan Plateau? Figures 8 and 9 present the proportion of precipitation (Figure 8) and heavy rain days (Figure 9, defined as daily precipitation exceeding 8 mm/day) that can be closely tied to AVS (characterized by positive vorticity in the Fourier filtered field). A common feature that emerged in these three regions is that 80–90% of heavy rain days were accompanied by positive vorticity in AVS, which means that the seasonal variations in AVS are closely tied to the heavy rain days in the main rainband. Moreover, 80–90% of the total precipitation in the main rainband is closely tied to the seasonal variations in AVS. Our study reveals that the impact of the Tibetan Plateau on precipitation can be in a larger region (a scale of a few thousand kilometers) downstream of the Tibetan Plateau and that this impact is facilitated by the AVS. The AVS provides a favorable cyclonic environment for precipitation. When other low-value weather systems march to the cyclic vortex region of the AVS, precipitation can significantly increase.

**Figure 8.** Hovmöller diagram of the (**a**–**c**) monthly precipitation and (**d**–**f**) the ratio of the monthly precipitation closely tied to AVS to the total monthly precipitation averaged over (**a**,**d**) 110–120◦ E, (**b**,**e**) 125–130◦ E, and (**c**,**f**) 130–145◦ E. White represents missing records of land precipitation.

**Figure 9.** Hovmöller diagram of (**a**–**c**) the yearly frequency of heavy rain days (defined as daily precipitation exceeding 8 mm/day) and the ratio of (**d**–**f**) the number of heavy rain days closely tied to AVS to the total number of heavy rain days averaged over (**a**,**d**) 110–120◦ E, (**b**,**e**) 125–130◦ E, and (**c**,**f**) 130–145◦ E. White represents missing records of land precipitation.
