1 Introduction

Central Asia, across Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, Uzbekistan, and part of northwest China (Huang et al. 2014), located in Asian drylands and characterized by arid to semi-arid climates, has scarce precipitation and significant evaporation. In Central Asia, climate changes altered the water balance of the region which has a great impact on socio-economic development (Ma et al. 2021). The freshwater availability is closely related to the occurrence and amount of snowfall in Central Asia (Dietz et al. 2014). According to Chen et al. (2016), as the main water suppliers in arid and semi-arid regions, the mountains provide the main water resources for Central Asia in the form of glacier and snow water (Wang and Zhang 2019; Yao et al. 2019). These findings indicate that investigations of snowfall in Central Asia, a region highly sensitive to global climate change, are important for local hydrology, ecological protection, and economic development.

Previous studies have shown that most Asian dryland climatic patterns have changed from warm-dry to warm-wet conditions since the 1980s (Hu et al. 2002; Yao et al. 2021). Snowfall and extreme snowfall events in northern Xinjiang have experienced a significant increase during the past decades (Sun et al. 2010; Wang et al. 2017; Zhou et al. 2018; Yang et al. 2020). Therefore, in the content of the warm and wet background in Asian drylands, the characteristics of interannual variability of precipitation anomalies and the possible reasons are particularly important. Most previous studies suggest that anomalous atmospheric circulation and sea surface temperature (SST) anomalies are responsible for precipitation anomalies in Central Asia. For example, based on the results of CESM, Li et al. (2022) verified that the North Atlantic SST anomaly enhances the two wave trains along the North Atlantic jet and the Asian-African jet, favoring extreme snowfall in Central Asia. The quasi-stationary wave train in mid-to high-latitude Eurasia that is closely related to the east Atlantic/western Russia (EA/WR) pattern and the negative North Atlantic Oscillation (NAO) could deepen the Lake Balkhash trough and lead to increased extreme precipitation in eastern Central Asia, which is also adjusted by high-latitude North Atlantic SST anomalies (Ma et al. 2021). Apart from the influence of the North Atlantic, the Pacific SST anomaly could also exert significant effects on the Eurasian climate. Recent studies proposed that the thermal effect of the North Pacific Victoria mode (VM) could stimulate anomalous circumglobal wave train, which propagates eastward and deepens the Central Asian vortices, favoring the development of related heavy snowfall in Central Asia (Chen et al. 2022). Besides the impact of SST anomalies, climate changes in Asian drylands are associated with snow cover reduction over the Tibetan Plateau (Zhang et al. 2021), the westerly variations (Schiemann et al. 2008; Huang et al. 2013; Chen et al. 2019a), the polar vortex (Kim and Choi 2021; Zhang et al. 2022), Arctic Oscillation (AO) and other forcing sources (Chen et al. 2019b; Sun et al. 2021). Li and Fan (2022) indicated that the dominant patterns of winter surface air temperature anomalies over Central Asia are modulated by AO, stratospheric polar vortex, NAO, and the Ural blocking pattern. Previous studies indicate that cold events over Central Asia are related to the weakening of the polar vortex which affects the Central Asian climate by modulating the Siberian high (Kim and Choi 2021). In addition, changes in polar vortex position, i.e., a shift of the Arctic polar vortex towards the Eurasian continent, could further enhance cooling and snowfall over Eurasia (Zhang et al. 2016; Huning and AghaKouchar 2020). Furthermore, water vapor transport, strong cold advection, and synoptic-scale wave activity over the midlatitudes of Eurasia are also responsible for extreme precipitation events in Eurasia (Wen et al. 2009; Chen and Zhai 2013; Ding and Li 2017; Chen et al. 2019b; Zhang et al. 2021). Sun et al. (2021) reported that increased synoptic-scale wave activity may lead to increased snowfall frequency over northeastern–northwestern China during winter. Notwithstanding the aforementioned studies, few studies have focused on the dominant modes of the interannual variability of winter snowfall in Central Asia and the associated anomalous atmospheric circulation is still not clear. Considering the sequential dryland warming, it is important to understand winter snowfall variability and its associated physical processes in Central Asia.

Therefore, the current study aims to improve the understanding of the interannual variability of winter (December–February) snowfall events over Central Asia and investigate the associated physical mechanisms. The rest of this paper is organized as follows: Sect. 2 describes data and methods; in Sect. 3, leading modes of winter snowfall frequency in Central Asia are investigated; in Sect. 4, the underlying mechanisms of leading modes are analyzed; conclusions and discussion are provided in Sect. 5.

2 Data and methods

2.1 Data

The hourly mean reanalysis data of snowfall, sea level pressure (SLP), and the monthly mean reanalysis of precipitation, temperature, vertically integrated water vapor transport (WVT), zonal and meridional winds, geopotential height, and vertical velocity are extracted from the latest European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis product, i.e., the ERA5 (Hersbach et al. 2020), which has a horizontal resolution of 0.25° × 0.25°. The snowfall in ERA5 is the sum of large-scale snowfall and convective snowfall, which has been widely used to estimate snowfall variation (Liu et al. 2019; Wang et al. 2019; Taszarek et al. 2020; Lin and Chen 2022). The ERA5 hourly snowfall data (0:00–23:00) were accumulated as daily snowfall in this study. For each grid point, if the daily snowfall is larger than 0.1 mm, this day would be recognized as a snowfall day. For a given year, the number of snowfall days in winter (December–February, DJF) is defined as the frequency of snowfall in that year.

The monthly SST data used in this study is derived from the Met Office Hadley Centre observation data sets (Rayner et al. 2003), which has a horizontal resolution of 0.5° × 0.5°. The monthly Nino-3.4 indices which are defined as the regional-averaged SST (5° N–5° S, 170°–120° W) are derived from the NOAA Climate Prediction Center (https://www.esrl.noaa.gov/psd/data/climateindices/list/).

2.2 Method

In this study, an empirical orthogonal function (EOF) analysis is used to analyze the leading modes of interannual variability of the snowfall frequency over Central Asia, and the eigenvalue separation of EOF was evaluated by North's significance test (North et al. 1982).

The wave activity flux (WAF) is applied to illustrate the wave-like activity in this study (Takaya and Nakamura 2001). The WAF is written as follows:

$$ {\text{W}} = \frac{P}{{2\left| {\overline{\user2{U}}} \right|}}\left\{ {\begin{array}{*{20}c} {\overline{u}\left( {v^{^{\prime}2} - \psi^{\prime}v_{x}^{^{\prime}} } \right) + \overline{v}\left( { - u^{^{\prime}} v^{\prime} + \psi^{\prime}u_{x}^{^{\prime}} } \right)} \\ {\overline{u}\left( { - u^{\prime}v^{\prime} + \psi^{\prime}u_{x}^{^{\prime}} } \right) + \overline{v}\left( {u^{^{\prime}2} + \psi^{\prime}u_{y}^{^{\prime}} } \right)} \\ {\frac{{f_{0} R_{a} }}{{N^{2} H_{0} }}\left[ {\overline{u}\left( {v^{\prime}T^{\prime} - \psi^{\prime}T_{x}^{^{\prime}} } \right) + \overline{v}\left( { - u^{^{\prime}} T^{\prime} - \psi^{\prime}T_{y}^{^{\prime}} } \right)} \right]} \\ \end{array} ,} \right. $$

where U = (u, v), f0, Ra, N, H0, and \({T}^{\mathrm{^{\prime}}}\) represent the horizontal wind velocity, the Coriolis parameter at 45°N, gas constant for dry air, Brunt–Vaisala frequency, scale height, and perturbed air temperature, respectively; P = (pressure/1000 hPa); The subscript x (y) denotes a derivative in the zonal (meridional) direction. Overbars and primes denote climatological mean and perturbations, respectively.

In this study, to investigate planetary-scale wave activity, 3-D Plumb flux for all wave components is calculated (Plumb 1985; Eq. (4) in Nath et al. 2014). The Lanczos filter (Duchon 1979) is used to calculate the 2–7-day bandpass filtered daily SLP whose variance is used to quantify the synoptic-scale wave activity (Woollings et al. 2012; Nishii et al. 2015; Sun and Wang 2017). Considering that this study focuses on interannual variability, the linear trends in the data during 1979–2021 are removed before all computations.

3 Leading modes of snowfall frequency in Central Asia

Figure 1 shows the first two leading EOF modes of snowfall frequency in winter over Central Asia during 1979–2021. The leading EOF1 mode and second mode (EOF2) passed North’s significance test and accounted for approximately 47.1% and 14.1% of the total variance, respectively. The EOF1 is basically characterized by positive anomalies over entire Central Asia, except for a few areas of negative anomalies over the Tarim basin (Fig. 1a). The EOF2 exhibits a meridional dipole pattern which is characterized by positive anomalies over northwestern Central Asia and negative anomalies over the other region (Fig. 1c). The PC1 of snowfall frequency shows a significant positive phase during 1988–1994 and 2013–2020 (Fig. 1b), suggesting an increased snowfall frequency over Central Asia in the two periods, which is consistent with the shift from warm-dry to warm-wet over Northwest China since 1987 (Shi et al. 2002, 2003). The PC2 of snowfall frequency shows a significant positive phase during the 2000s and a negative phase during the 2010s (Fig. 1d).

Fig. 1
figure 1

a EOF1 and c EOF2 of interannual variability of snowfall frequency in winter over Central Asia. b, d are the detrended and standardized principal component (PC) time series, respectively. Top-right corners in a, c are the corresponding percentage of explained variance to the total variance

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4 Drivers and mechanism for the dominant modes of snowfall frequency

4.1 Mechanism of the EOF1 of snowfall frequency

To investigate the associated circulation anomalies with respect to the interannual variation of snowfall frequency over Central Asia, the regressed pressure vertical velocity field at 500 hPa, vertical integrated WVT, and divergence of vertically integrated WVT against the PC1 during 1979–2021 are presented in Fig. 2. In correspondence to a positive phase of EOF1, ascending anomalies in the troposphere which contribute to positive snowfall frequency occur in the Central Asia except for Xinjiang (Fig. 2a). In addition, the interannual variability of winter snowfall frequency is associated with an anomalous northwesterly WVT branch crossing the western boundary of Central Asia and an anomalous southwesterly WVT branch crossing the southern boundary of Central Asia, which conveys moisture anomalies from western Europe and Indian Ocean into Central Asia (Fig. 2b). These two WVT branches convergence over the western Central Asia, which may contribute to the positive snowfall frequency anomalies in DJF (Fig. 2c). The ascending anomalies and anomalous WVT favor transport of water vapor into Central Asia, thus, leading to enhanced snowfall frequency.

Fig. 2
figure 2

Anomalies of a 500-hPa vertical velocity (unit: Pa s–1), b vertically integrated WVT (units: kg m–1 s–1), and c vertically integrated WVT divergence (units: kg m–2 s–1) regressed on the standardized PC1 in DJF during 1979–2021. The dots in a, c, and shading in b denote where the anomalies are significant at the 90% confidence level based on the Student’s t test

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To illustrate the pressure vertical velocity and WVT anomalies associated with the interannual variability of winter snowfall frequency, Fig. 3 shows the geopotential height anomalies and wave activity flux in the troposphere regressed on the detrended and standardized PC1. The geopotential height at 200 hPa and 850 hPa are characterized by negative anomalies in northwestern Atlantic and Central Asia, and positive geopotential height anomalies centered in the mid-latitude North Atlantic (Fig. 3a, b). Evidently, there is a wave train in the troposphere stimulated from the midlatitude North Atlantic which propagates eastward (Fig. 3a, b). The wave train is also characterized by anomalous cyclones centered in northern Atlantic and northern Central Asia, and anticyclones over northwestern Europe and eastern Eurasia (Fig. 3c). The wave train divides into two branches near western Eurasia (Fig. 3a, b). The north wave train travels to Central Asia and eastern Asia, inducing negative geopotential height anomalies and ascending motions over Central Asia (Fig. 3a). The south wave train propagates eastward and southeastward to the northern Indian Ocean (Fig. 3b). These two wave trains are prominent in both the lower (850 hPa) and upper (200 hPa) troposphere (Fig. 3a, b). Recent studies proposed that the Central Asian climate may also be regulated by Pacific SSTA (Sun et al. 2019; Zhu et al. 2020; Chen et al. 2022), it is worth noting that there may be a wave train propagating from the eastern tropical Pacific to the North Atlantic in the upper troposphere (Fig. 3a). Therefore, the SST anomalies over tropical Pacific and northern Atlantic associated with the anomalous wave train may play an important role for inducing the associated atmospheric teleconnection over Central Asia (Sun et al. 2019; Chen et al. 2022).

Fig. 3
figure 3

Anomalies of a 200-hPa geopotential height (shaded, unit: gpm) and the wave activity flux (vector, unit: m–2 s–2), b 850-hPa geopotential height (shaded, unit: gpm) and the wave activity flux (vector, unit: m–2 s–2), and c 500-hPa horizontal wind (unit: m s–1) regressed on the standardized PC1 in DJF during 1979–2021. The dots in a and b denote where the geopotential height anomalies are significant at the 90% confidence level based on the Student’s t test. Shading in c denote where the horizontal wind are significant at the 90% confidence level based on the Student’s t test

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Previous studies have proposed that variations of NAO (Wang et al. 2013) and North Atlantic SST (Bothe et al. 2012; Lu et al. 2020; Ma et al. 2021; Li et al. 2022) have a close relationship with atmospheric circulations over Central Asia, the geopotential height anomalies in Fig. 3a, b also exhibit a positive NAO pattern. Thus, the roles of NAO and North Atlantic SST in the modulation of snowfall frequency in Central Asia are further examined. The correlation coefficient between the PC1 and the NAO index is 0.3 (significant at the 90% confidence level). However, the wave trains regressed on the NAO index in winter are not significant (figure not shown), which suggests that the NAO may be insufficient to stimulate the wave train that impacts the snowfall frequency in Central Asia. Thus, more work is needed to refine the influence of North Atlantic SST on snowfall frequency in Central Asia. As presented in Fig. 4a, a positive phase of EOF1 of snowfall frequency is associated with positive SST anomalies over the mid-latitude North Atlantic and negative SST anomalies over the high- and low-latitude North Atlantic (Fig. 4a). To further investigate the relationship between North Atlantic SST and snowfall in Central Asia, an Atlantic SST index is defined (ATL-SST-I = SST [40°–65° N, 70°–30° W]–SST [0°–22.5° N, 70°–20° W]–SST [20°–40° N, 100°–60° W]). The correlation coefficient between the ATL-SST-I and the PC1 is 0.42 (Fig. 4b), which is significant at the 90% confidence level. Actually, previous studies demonstrate that the air-sea interaction over the North Atlantic is complex, and the high-latitude SST anomalies may be insufficient to stimulate deep convection (Deng et al. 2018). Besides, Chen et al. (2020b) have demonstrated that the NAO-related atmospheric circulation anomalies may contribute to the North Atlantic tripole SST anomalies via modulating surface heat fluxes, and the North Atlantic tripole SST changes can also lead to a NAO-like atmospheric anomaly. Therefore, the interaction between the North Atlantic SST and the NAO may be responsible for atmospheric circulations over Central Asia.

Fig. 4
figure 4

Anomalies of a sea surface temperature (unit: K) regressed on the standardized PC1 in DJF during 1979–2021. b The standardized time series of Atlantic SST and PC1 in DJF during 1979–2021. The dots denote where the anomalies are significant at the 90% confidence level based on the Student’s t test. The green rectangular represent significant areas of SSTA that are used to define the ATL-SST-I

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According to Deng et al. (2018), the North Atlantic SST may indirectly affect the wave trains related to the circum-global teleconnection through the westerly jet over North Atlantic. Here, the impact of the North Atlantic SST and the NAO-like atmospheric anomaly on the Central Asian anomalous circulation is explored. Based on the climatic mean SST gradient, there is a large SST gradient area in the mid-latitude North Atlantic (Fig. 5a). The triple SST anomalies in the North Atlantic could lead to a negative meridional SST gradient around 20° N–30° N and positive meridional SST gradient around 40° N–50° N (Fig. 5a). The change of meridional SST gradient can induce southward shifted westerlies by impacting the meridional gradient of 1000- to 300-hPa layer thickness (Brayshaw et al. 2008). The anomalous SST cooling along 10° N and 50° N decreases the layer thickness between 1000- and 300-hPa while the anomalous SST warming along 30° N increases the layer thickness between 1000- and 300-hPa (Fig. 5b). Accordingly, the meridional layer thickness gradient increases around 30°N and decreases around 50° N (Fig. 5b). Based on the principle of thermal wind, anomalous westerly winds, and easterly wind are observed around 20° N and 45° N, respectively (Fig. 5c) (Li et al. 2020). Thus, the climatological westerly jet is decelerated and induces a 300-hPa anomalous anticyclone on its northern edge (Fig. 5d, e). In addition, SST cooling in the northern tropical Atlantic results in a 700-hPa anomalous anticyclone over the subtropical North Atlantic via a Rossby wave–type atmospheric response (Chen et al. 2020a). The ATL-SST index-related 700-hPa wind anomalies bear a close resemblance to the positive phase of winter NAO, with a significant cyclonic anomaly over the high latitudes and a significant anticyclonic anomaly over the midlatitudes (Fig. 5f). The NAO-like dipole atmospheric anomaly, in turn, helps to maintain the ATL-SST anomaly via modulating surface heat fluxes in winter (Chen et al. 2020a). The anomalous anticyclone in the troposphere associated with NAO and the ATL-SST anomalies may further influence the circum-global teleconnection which can induce an anomalous cyclone over Central Asia (Fig. 5d, e). In general, the interaction between the North Atlantic SST and the NAO affects the subtropical jet stream, which in turn affects circum-global teleconnection and leads to snowfall frequency anomalies in Central Asia.

Fig. 5
figure 5

a Wintertime climatological meridional SST gradient (\(\partial \) SST/\(\partial \) y; contour, unit: 10–5 K m−1) and SST gradient (shaded, unit: 10–5 K m−1), b layer thickness between 1000- and 300-hPa (contour, unit: gpm) and its meridional gradient (shaded, unit: gpm m−1), c anomalies of 200-hPa zonal wind (unit: m s−1), d anomalies of 300-hPa wind and meridional wind (unit: m s−1), and e anomalies of 700-hPa wind and meridional wind (unit: m s−1) regressed on the standardized time series of ATL-SST-I in DJF during 1979–2021. The dots in a–c, and black contours in d, e denote where the anomalies are significant at the 90% confidence level based on the Student’s t test. The green thick line in c delineates the axis of the climatological westerly jet here

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To explore the potential forcing sources of circum-global teleconnection, the simultaneous SST regression in the Pacific against PC1 was conducted in Fig. 6. The results indicate that an El Niño-like condition in the tropical Pacific SST anomalies occurs in the positive phase of the dominant mode of EOF1. The correlation coefficient between the Nino-3.4 index and PC1 is 0.43 (Fig. 6b), which is significant at the 90% confidence level. Further, the regressed geopotential height anomalies and wave activity flux against the time series of the Nino-3.4 index were presented in Fig. 6c, d. Evidently, the atmosphere–ocean interactions over the eastern tropical Pacific may partly contribute to the atmospheric wave train in the northern hemisphere, which is consistent with previous study (Chen et al. 2020b). The wave train originated from the eastern tropical Pacific may propagate eastward and induce a negative geopotential height anomaly in Central Asia and contribute to increased snowfall frequency in winter (Fig. 6c, d).

Fig. 6
figure 6

Anomalies of a sea surface temperature regressed on the standardized PC1 in DJF during 1979–2021. b The standardized time series of the Nino-3.4 index and PC1 in DJF during 1979–2021. Anomalies of c 300-hPa geopotential height (shaded, unit: gpm) and the wave activity flux (vector, unit: m–2 s–2), d 700-hPa geopotential height (shaded, unit: gpm) and the wave activity flux (vector, unit: m–2 s–2) regressed on the standardized time series of Nino-3.4 index in DJF during 1979–2021. The dots in a denote where the SST anomalies are significant at the 90% confidence level based on the Student’s t test. The dots in c, d denote where the geopotential height anomalies are significant at the 90% confidence level based on the Student’s t test

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The above results suggest that the NAO and SST anomalies over the North Atlantic and eastern tropical Pacific play important roles in modulating the EOF1 of snowfall frequency in Central Asia. The zonal wave train pattern is a possible mechanism for the linkage between the tropical Pacific SST and the EOF1 of snowfall frequency in Central Asia. Meanwhile, the interaction between the NAO and the North Atlantic SST anomalies may influence the zonal wave train by modulating the SST gradient and further affect the westerlies and the circum-global teleconnection. In addition, the partial correlation coefficient between the Nino-3.4 index and PC1 is 0.38, which is 0.36 between the ATL-SST-I and the PC1. In another word, the SST anomalies in the eastern tropical Pacific have a larger contribution to EOF1 of snowfall frequency than the North Atlantic SST.

4.2 Mechanism of the EOF2 of snowfall frequency

To investigate the underlying mechanisms of the EOF2, the regressed vertical velocity field at 500 hPa, vertically integrated water vapor transport, and divergence of vertically integrated water vapor transport against the PC2 during 1979–2021 were presented in Fig. 7. In the positive phase of EOF2 of snowfall frequency, anomalous ascending motions related to positive snowfall frequency occur in northern Central Asia and anomalous descending motions related to negative snowfall frequency occur in southern Central Asia (Fig. 7a). Correspondingly, there is a westerly WVT anomaly and convergence of the vertically integrated WVT over northern Central Asia and northerly WVT anomalies and divergence of the vertically integrated WVT over southern Central Asia (Fig. 7b, c). The anomalous pressure vertical velocity and WVT are closely related to the negative geopotential height anomalies over northern Central Asia and the positive geopotential height anomalies over southern Central Asia (Fig. 7d).

Fig. 7
figure 7

Anomalies of a 500-hPa vertical velocity (unit: Pa s–1), b vertically integrated WVT (units: kg m–1 s–1), c vertically integrated water vapor flux divergence (units: kg m–2 s–1), and d 700-hPa geopotential height anomalies (unit: gpm) regressed on the standardized PC2 in DJF during 1979–2021. The dots in a, c, d, and shading in b denote where the anomalies are significant at the 90% confidence level based on the Student’s t test

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The factors responsible for the geopotential height anomalies associated with the EOF2 of snowfall frequency need to be further examined. Sun et al. (2021) demonstrated that the synoptic-scale wave activity over the midlatitudes of Eurasia may induce a cyclone and anomalous convergence of water vapor in the lower troposphere and result in large-scale intense snowfall in northwestern China during winter (Gulev et al. 2001; Sun and Wang 2017; Sun et al. 2021; Wang et al. 2009). To examine the impact of the synoptic-scale wave activity on the interannual variability of snowfall frequency over Central Asia, the synoptic-scale wave activity anomalies regressed on the standardized PC2 are computed. As shown in Fig. 8a, corresponding to a positive phase of the EOF2 of snowfall frequency, the positive SLP variance (SLP_var) anomalies occur over northern Central Asia, negative SLP_var anomalies occur over southern Central Asia. In general, positive SLP_var anomalies indicate increased synoptic-scale wave activity which may lead to increased snowfall frequency and vice versa (Sun et al. 2021). In mid-latitudes, increased synoptic-scale wave activity is attributed to increased atmospheric baroclinicity which is associated with an increased meridional temperature gradient (Sun et al. 2021). To examine the meridional temperature gradient, pressure–latitude cross section of temperature and geopotential height anomalies averaged within 40°E–100°E regressed on the standardized PC2 are provided in Fig. 8b, c. As shown in Fig. 8b, there is a prominent positive air temperature anomaly over the mid-latitude regions (40° N–60° N) for 1000–400 hPa. The positive temperature anomaly in Central Asia may increase the meridional temperature gradient in northern Central Asia and decrease the meridional temperature gradient in southern Central Asia. Besides, the result indicates that a positive phase of the EOF2 of snowfall frequency corresponds to an anomalous cold low in the troposphere (1000–300 hPa) between 50° N and 70° N and an anomalous warm high in the troposphere (1000–300 hPa) between 30° N and 50° N (Fig. 8c). Thus, the dipolar anomaly of the tropospheric geopotential height favors the anomalous warming around 50° N, enhancing meridional temperature gradient in northern Central Asia. The atmospheric baroclinicity and synoptic-scale wave activity in northern Central Asia increase due to the increased meridional temperature gradient which is conducive to the occurrence of the dipole mode of snowfall frequency in Central Asia. In addition, the subsidence anomalies in southern Central Asia and anomalous ascending motions in northern Central Asia (Fig. 7a), which play a key role in the occurrence of the dipole mode of snowfall frequency in Central Asia, result from the dipole mode of the anomalous geopotential height in the troposphere.

Fig. 8
figure 8

Anomalies of DJF mean a SLP_var (unit: hPa2), latitude-pressure section of the b temperature (unit: K), and c geopotential height (unit: gpm) averaged within 40° E–100° E regressed on the standardized PC2 during 1979–2021. The dots denote where the anomalies are significant at the 90% confidence level based on the Student’s t test

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But what causes this temperature and geopotential anomaly in the troposphere? As can be seen in Fig. 8b, c, the possible mechanism may be the stratosphere-troposphere interaction, since the geopotential height anomalies in the troposphere extend into the stratosphere in Central Asia. Since planetary waves play a crucial role in the stratosphere-troposphere coupling, three-dimensional Plumb flux at 50 hPa during winter is shown in Fig. 9. As presented in Fig. 9a, in climatology, the upward propagation of Plumb flux is very strong during winter and is centered above the northeast Eurasia continent. The horizontal component of Plumb wave activity flux propagates eastward from Europe to Greenland and the northern Atlantic in winter, confirming the results of those from Wei et al. (2021). The three-dimensional Plumb fluxes regressed on the standardized PC2 are shown in Fig. 9b, c. There are two distinct centers of upward wave activity fluxes over the North Atlantic and North Pacific corresponding to a positive phase of the EOF2 of snowfall frequency (Fig. 9b). Notably, there are apparent downward propagation of Plumb fluxes over northern Eurasia (Fig. 9b). Further, a longitude-height section of the Plumb flux at 60° N is conducted, the downward propagation of Plumb flux is strong around 45° E–90° E, which corresponds to Central Asia (Fig. 9c). These results indicate that there are strong wave reflections around 45° E–90° E which can help to strengthen the coupling of atmospheric circulation in the stratosphere and the troposphere. As demonstrated by Gong et al. (2019) and Wei et al. (2021), the wave reflection may be related to the stratospheric polar vortex. Focusing on the climate variations in the stratosphere, on the positive phase of EOF2 of snowfall frequency, the polar vortex is strengthened in winter with two censers located in northeastern and northwestern Eurasia and the westerly wind in the high latitudes of the stratosphere accelerate (Fig. 9d, e). Therefore, the northwestern center of the stratospheric polar vortex may be related to the downward propagation of Plumb flux and the wave reflections. Thus, the regional mean of 50-hPa geopotential height within 0° E–60° E, 60° N–75° N is calculated to represent the intensity of the northwestern center of the stratospheric polar vortex. The correlation coefficient between 50-hPa geopotential height index and PC2 exceeds 90% confidence level, indicating that the dipole mode of snowfall frequency in Central Asia is closely related to the shift of the polar vortex in the stratosphere.

Fig. 9
figure 9

a Climatological distribution of the Plumb wave activity flux (unit: m2 s−2) at 50 hPa in winter (DJF). The shadings are the vertical component of the Plumb fluxes, the vectors are the horizontal component, with only magnitude larger than 4 shown. b Plumb wave activity fluxes (unit: m2 s−2) at 50 hPa (only magnitude larger than 0.05 shown), c Longitude–height section of Plumb wave activity flux at 65° N (unit of horizontal component: m2 s−2, unit of vertical component: 102 m2 s−2), d 50-hPa geopotential height anomalies (unit: gpm), and e 50-hPa zonal wind (unit: m s–1) in DJF regressed on the standardized PC2 during 1979–2021. The dots in d and shading in e denote where the anomalies are significant at the 90% confidence level based on the Student’s t test

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The above results suggest an impact of the troposphere-stratosphere interaction on the EOF2 of snowfall frequency. The enhanced northwestern center of the stratospheric polar vortex may induce more planetary wave reflection from the stratosphere to the troposphere, which lead to a positive (negative) geopotential height anomaly in southern (northern) Central Asia. The increased synoptic-scale wave activity over northern Central Asia associated with the negative geopotential height anomaly may largely account for the increased snowfall frequency over northern Central Asia and vice versa. The anomalous anticyclone and anomalous cyclone may lead to descending motions and ascending motions, respectively, which further induce decreased snowfall frequency over northern Central Asia and increased snowfall frequency over southern Central Asia.

5 Conclusions

This study has investigated the leading modes of interannual variation of snowfall frequency over Central Asia. The EOF1 of interannual variation of snowfall frequency is characterized by a homogeneous pattern over Central Asia, with maximum anomaly loading over northwestern Central Asia. The second mode of the interannual variability of the snowfall frequency showed a dipole mode characterized by reversed anomalies of snowfall frequency over northern Central Asia and southern Central Asia. The underlying mechanisms of EOF1 and EOF2 are different. The result indicates that the EOF1 of snowfall frequency in Central Asia is closely associated with the NAO and the SST anomalies over the North Atlantic and eastern tropical Pacific. A positive SST anomaly in the eastern tropical Pacific may stimulate a zonal wave train in the northern hemisphere which propagates eastward and induce a negative geopotential height anomaly in Central Asia. The negative geopotential height anomaly associated with anomalous ascending motions and anomalous northwesterly WVT can contribute to increased snowfall frequency in Central Asia. Besides, the zonal wave train is also influenced by the interaction between the NAO and the triple SST anomalies in the North Atlantic. The layer thickness between 1000- and 300- hPa decreases along 10° N and 50° N and increases along 30° N due to the triple SST anomalies in the North Atlantic. The change of meridional layer thickness gradient can induce anomalous westerly winds around 20° N. The southward westerly jet may further strengthen the zonal wave train in the troposphere and deepen the anomalous cyclone over Central Asia.

As for the EOF2, the results suggest that the polar vortex in the stratosphere and troposphere-stratosphere interaction play important roles in modulating the interannual variation of EOF2 of snowfall frequency in Central Asia. The enhanced northwestern center of the polar vortex in the stratosphere may induce more planetary wave reflection from the stratosphere to the troposphere and induce a positive (negative) geopotential height anomaly in southern (northern) Central Asia. The negative and positive geopotential height anomaly may induce increased and decreased synoptic-scale wave activity over northern and southern Central Asia, respectively. The pressure vertical velocity anomalies and anomalous synoptic-scale wave activity associated with the geopotential height anomalies can further induce decreased snowfall frequency over northern Central Asia and increased snowfall frequency over southern Central Asia.

This study proposes several factors that may influence the interannual variability of snowfall frequency in Central Asia, including the eastern central Pacific SST anomalies, the air-sea interaction over the North Atlantic, the polar vortex in the stratosphere, and the troposphere-stratosphere interaction. However, these finds are obtained by statistical analysis and are not sufficient, the climates in Eurasian are also modulated by many other factors such as the snow cover over the Tibetan Plateau (Zhang et al. 2021), the SST anomalies in the warm-pool region (Lu et al. 2020), sea ice anomalies in the Barents Sea–Kara Sea region (Sun et al. 2021). Besides, the reason why the PC1 shifted from negative to positive since the 1990s remains unclear, the interdecadal variation of snowfall frequency in central Asia needs further investigation.