1 Introduction

The Eurasian continent is the predominant area for snow cover in the Northern Hemisphere, where winter snow accounts for 60-65% of the total snow extent. The topography of Eurasian continent is complex, leading to a highly uneven and variable spatial distribution of snow cover. The region exhibits prolonged snow accumulation, notably in northern Russia, where snow persists for eight months or longer (Robinson et al. 1993; Brown and Robinson 2010). Most current studies on snow cover in Eurasia focus on specific regions, such as Siberia and the Tibetan Plateau (TP) (Wu and Qian 2003; Shen et al. 2020). The snow depth in western and eastern Eurasia exhibit opposite trends, characterized by a west-east dipole pattern (Wu et al. 2014; Zhang et al. 2017). Significant changes have occurred in the extent of snow cover, the number of snow days, and the snow properties of both the TP and the Eurasian continent, which are affected by global warming. The period of snow cover is generally shortened, accompanied by an earlier onset of spring snowmelt. Increasing local extreme snowfall events leads to a more inhomogeneous snow cover distribution. Over the past 30 years, snow cover in Eurasia has declined by around 10% (Kang et al. 2010; Che et al. 2019; Yao et al. 2019). The decrease in spring snow cover across Eurasia has contributed to the severe droughts in northern and northeastern China (Wu et al. 2009; Yao et al. 2022). Moreover, the rising frequency of summer heat waves in Europe may also be strongly linked to the decline in the Eurasian snow cover and Arctic sea ice (Zhang et al. 2020).

The changes in winter and spring snow cover across Eurasia play an important role in the weather and climate of East Asia in subsequent seasons (Wu et al. 2007; Jia et al. 2018; Shen et al. 2020; Chen et al. 2023). Zhao (1984) initially identified a negative relationship between winter and spring snow cover in Eurasia and the intensity of East Asian summer monsoon, along with the summer rainfall in the Yangtze-Huaihe Valley from 1971 to 1980. The spring snow cover in Western Siberia is the key zone affecting precipitation in southern China (Wu and Kirtman 2007). The winter snow cover anomalies in Eurasia have a significant positive correlation with the precipitation anomalies in South China and North China during late summer (Yang and Xu 1994; Wu and Kirtman 2007), while demonstrating a negative correlation with the precipitation anomalies in western and Northeast China (Sankar-Rao et al. 1996; Zuo et al. 2012). There are also different results indicating that the snowy winters in Eurasia are conducive to the northward movement of the rain belt. The positive correlation between winter Eurasian snow cover and summer precipitation in China is observed in North China, Northeast China, and Southwest China, while a negative correlation emerges in the Yangtze-Huaihe Valley and most of Northwest China (Chen and Song 2000a, b). Furthermore, a notable negative correlation exists between winter snow cover across Eurasia and the Mei-yu rainfall in Jiangsu, whereas the relationship with summer rainfall along the Yangtze River is weak (Cao 1994; Liu et al. 2014).

Winter and spring Eurasian snow cover is widely recognized as a key predictor of summer monsoon and precipitation in East Asia (Yim et al. 2010; Zuo et al. 2011; He et al. 2018; Jia et al. 2018; Yang et al. 2021; Zhang et al. 2021a). Wu et al. (2009) highlighted that less spring snow water equivalent (SWE) in western Eurasia and excessive SWE in eastern Eurasia and the TP frequently correlated with decreased summer rainfall in North and Northwest China. On interdecadal time scales, the intensified spring snowmelt in Western Siberia is strongly linked to a meridional quadrupole summer rainfall pattern, with excessive rainfall in South China and the Huang-Huai River region and less rainfall in the middle and lower reaches of Yangtze River Valley and Inner Mongolia-northeastern China (Cheng et al. 2022). Zhang et al. (2008) pointed out that the interdecadal transition of spring snow cover in the Eurasian continent in the late 1980s not only influenced the interdecadal transition of the summer climate in eastern China but also was closely related to the interdecadal transition of spring precipitation in southern and eastern China in the late 1980s. After the late 1980s, the precipitation in eastern and southern China increased significantly. Wu and Kirtman (2007) suggested a positive correlation between spring snow cover anomalies in Western Siberia and spring rainfall in southern China, with the correlation to summer rainfall being comparatively weaker, based on analysis using multiple snow datasets.

The climatic effect of snow cover is realized through its albedo effect and hydrological effect (Robinson et al. 1993; Xu et al. 2021). As a critical element of surface conditions, snow cover anomalies impact the energy balance by altering the surface albedo. However, the albedo effect is operative solely during snowy seasons. The hydrological effect extends into the post-snow season through the “memory” of soil moisture, which has a delayed impact on summer precipitation change. It is considered more important (Xu et al. 2021). Spring is the season of transition from winter to summer. The spring snowmelt directly increases soil moisture and impacts the diabatic heating from the ground (Sun et al. 2021). Nozawa and Fujiwara (2017) suggest that the decrease in snow-melted water suppresses the evaporation of soil moisture as snow vanishes, leading to land surface warming, heightened sensible heat flux, and warming of the middle and upper atmosphere, subsequently influencing changes in atmospheric circulation.

This study first analyzed the spatial distribution and interdecadal variability of Eurasian snow cover using high-resolution remote sensing products and reanalysis data. Then, based on the three precipitation datasets, the relationship between EOF1 and EOF2 of winter and spring snow cover in Eurasia and the precipitation in China are identified, respectively. Possible physical mechanisms of snow cover anomalies affecting precipitation in China are discussed, offering compelling support for exploring potential predictors of summer precipitation variability in China. The paper is organized as follows. Section 2 describes the datasets and methods used in this study. Section 3 presents the spatial distribution of snow depth in Eurasia, its relationship with precipitation in China, and possible physical mechanisms. Section 4 explores the effects of other factors. The conclusions are reported in Sect. 5.

2 Data and methods

2.1 Snow depth data

Long-term series of daily snow depth in Euroasia (1980–2016) dataset was used in this study to analyze the spatial distribution of snow cover. The dataset is produced by a passive microwave remote sensing inversion method, covering Eurasia from 1980 to 2016, with a daily temporal resolution and a horizontal resolution of 0.25° × 0.25° (Che et al. 2008). The algorithm considers the temporal and spatial variation of snow characteristics. It establishes the dynamic relationship between the brightness temperature difference of multiple frequencies and the measured snow depth in space and season. Long-term series onboard data are obtained from three sensors: SMMR, SSM/I, and SSMI/S (Dai et al. 2015). The daily snow depth is composed of a matrix of 720 × 332, with each value representing a grid of 0.25° × 0.25°. The relative deviation of snow depth data in Eurasia is within 30% through the validation of the measured stations (Dai et al. 2017).

The Global Land Data Assimilation System (GLDAS) incorporates ground- and satellite-based observations to provide optimized and near-re real-time surface state variables. GLDAS data with a monthly temporal resolution and a spatial resolution of 0.25° × 0.25° from 1980 to 2016 were utilized as supplemental data for snow depth.

2.2 Precipitation data

Three gridded precipitation datasets from 1980 to 2016 were used in this study. The monthly precipitation observations are derived from the CN05.1 gridded dataset, constructed based on the interpolation from over 2400 observing stations in China at a spatial resolution of 0.25° × 0.25° (Wu and Gao 2013). Compared to the EA05 (0.5° latitude-longitude grid over East Asia) (Xie et al. 2007) and APHRO (Asian Precipitation—Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources) (Yatagai et al. 2009) precipitation data, the CN05.1 dataset demonstrates excellent performance in regions of eastern China with a high density of observing stations (Xu et al. 2009; Wu et al. 2017). The CN05.1 data is also the most accurate near-surface meteorological data for China, featuring high spatial resolution that effectively captures the actual changes of each meteorological variable.

The Global Precipitation Climatology Centre (GPCC) has developed a global gridded precipitation dataset from approximately 86,100 ground-based observations worldwide, using the SPHEREMAP interpolation method. This data is advantageous because it combines data from meteorological observation stations, hydrological monitoring stations, and some regional datasets (Becker et al. 2013). The GPCC precipitation dataset uses far more global stations than any other dataset (Schneider et al. 2013). The latest version of GPCC precipitation data (Full Data Monthly Version 2022) is used in this paper with a horizontal resolution of 0.25° × 0.25°.

The monthly precipitation data of the Climate Prediction Center Merged Analysis of Precipitation (CMAP) is obtained by combining the rainfall recorder, satellite-based observations, and the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis data. It has a horizontal resolution of 2.5° × 2.5°. The CMAP precipitation is widely used in long-term climate studies. The dataset can be downloaded for free from https://psl.noaa.gov/data/gridded/data.cmap.html. For clarity of discussion, the three precipitation datasets will be denoted as CN05.1, GPCC, and CMAP, respectively. The average precipitation for December-January-February, March-April-May, and June-July-August was calculated as the winter, spring, and summer precipitation in China, respectively.

2.3 Reanalysis data

The monthly geopotential height and wind field data obtained from the NCEP/NCAR are utilized, and the grid spacing is 2.5° × 2.5°. This data is available for free download from https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.derived.pressure.html. The remaining data are derived from the fifth generation European Reanalysis (ERA5), provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Bell et al. 2021; Hersbach et al. 2023). It includes the monthly mean vertical velocity, surface heat flux data with a horizontal resolution of 0.1° × 0.1° and the soil moisture in four layers with depths of 0–7 cm, 7–28 cm, and 28–100 cm.

2.4 Methods

The empirical orthogonal function (EOF) method takes the time series of the field as the analysis object. It extracts the primary feature quantities by analyzing the structural features of matrix data. The EOF decomposes the time-varying meteorological element field into a spatial component and a temporal component that are orthogonal to each other. In EOF, the eigenvectors of the covariance matrix are also called spatial eigenvectors (spatial modes). The ith eigenvector is called the ith mode. The spatial modes reflect, to some extent, the spatial distribution characteristics of the meteorological element field. The principal component (PC) corresponds to the temporal variation, also called the time coefficient, which reflects the change in weight of the corresponding spatial mode over time.

The geopotential height anomalies are calculated from the actual value minus the climatic state, as are anomalies for other meteorological elements. Correlation analyses were also conducted to investigate the relationship between Eurasian snow depth and precipitation in Eastern China. Given the emphasis on the interdecadal time scales, a 6-year low-pass Lanczos filter (Duchon, 1979) is applied to extract the interdecadal components of the raw data. Furthermore, the statistical significance of the correlation and regression analyses is assessed using the Student’s t-test.

The horizontal wave activity flux (WAF) is calculated based on the method by Takaya and Nakamura (2001) outlined.

3 Results

3.1 Distribution of snow depth in Eurasia

Figure 1 shows the spatial distribution of snow depth in Eurasia from 1980 to 2016 based on remote sensing observations. Eurasia experiences seasonal variations in multi-year average snow depths, with the entire continent nearly devoid of snow cover during summer, except for the western TP. Extensive snow cover occurs on the surface throughout spring, autumn, and winter. The spatial distribution of snow depth exhibits clear latitudinal zonation, with average snow depth increasing progressively with latitude. During winter, characterized by the most extensive and deepest snow cover, the high-value center of multi-year average snow depth resides in central and western Siberia, reaching over 70 cm. Moreover, the average snow depth in the 50–70°N region of Eurasia exceeds 20 cm. The high snow depths in China are predominantly found in the TP, Northeast China, northern Xinjiang, and the Tianshan Mountains. The snow depth diminishes gradually south of 50°N. In the southern Yangtze River region, even during winter, the multi-year average snow depth remains below 1 cm. During the spring, snow depth in the 50–70°N region of Eurasia significantly decreases compared to winter, especially in western Siberia, where rapid melting results in snow depth plummeting to no more than 50 cm. In contrast, the snow cover on the TP has remained relatively stable. Snow cover across Eurasia is more extensive and deeper in spring than autumn. During the autumn, the highest snow depths, which do not exceed 33 cm, are found between central and western Siberia. At this time, the eastern and western TP are snow-covered, whereas the interior of TP is either snow-free or has a thin snow covering.

Fig. 1
figure 1

Spatial distribution of snow depth in Eurasia from 1980 to 2016 based on remote sensing observation during (a) spring (MAM), (b) summer (JJA), (c) autumn (SON), and (d) winter (DJF)

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Snow depth from GLDAS was also analyzed for spatial distribution, shown in the Supplementary material (Fig. S1). The comparison indicates a general consistency between the snow cover variations derived from the GLDAS data and those observed through remote sensing. Notably, the maximum snow depth calculated by GLDAS is significantly higher than the observed values, especially during winter, by about 10–16 cm. Moreover, the observed snow depth ranging from 1 to 25 cm in the central and eastern TP is significantly higher than that of the GLDAS. Given the consistency between satellite-observed snow depth and previous conclusions, the subsequent analysis is predicated on these observations.

3.2 Winter snow depth variability in Eurasia and its relationship with precipitation in China

Fig. 2
figure 2

(a) Spatial pattern of the first EOF mode of winter snow depth in Eurasia during 1980–2016 and (b) the normalized time series corresponding to the first principal component

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The spatial and temporal characteristics of snow depth in Eurasia are complicated. An EOF analysis was performed on the long-term snow depth series for winter and spring in Eurasia. An EOF analysis was conducted on the winter-spring snow cover with the largest snow extent and depth based on the long-term snow depth series in Eurasia. The first three EOF modes of winter snow depth account for 24.4%, 10.2%, and 6.1% of the total variance, respectively. According to North et al. (1982), these three modes are well separated from each other. Figure 2 shows the spatial pattern of the first EOF mode (EOF1) of winter snow depth in Eurasia, representing the climatic state. The snow depth variations in Eurasia generally agree with the results shown in Fig. 1, with the larger anomalies between central and western Siberia. The principal component of EOF1 (PC1) in Fig. 2b shows a decreasing trend, mainly indicating a global warming signal. Combining the spatial pattern of EOF1 shows that global warming noticeably impacts the snow cover distribution in Eurasia during 1980–2016. Since the time series shows a decreasing trend, it is known that there is an overall decreasing trend in the snow cover in Eurasia. The winter snow depth in Eurasia increased until 1992, followed by a decrease, as shown in Fig. 3a.

Fig. 3
figure 3

Anomalies of (a) winter and (b) spring snow depth observations averaged in Eurasia from 1980–2016

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The spatial distribution and corresponding time series of the second EOF mode (EOF2) of winter snow depth across Eurasia are presented in Fig. 4. The spatial pattern of EOF2 is characterized by a west-east dipole pattern, with a positive center located in northern Lake Baikal and a negative center in the region between eastern Europe and the Western Siberian Plain. It is worth noting that the snow cover on the TP reveals a lack of clear regional distribution characteristics. It generally agrees with the findings of Zhang et al. (2017) regarding snow cover distribution in Eurasia. The principal component of EOF2 (PC2) in Fig. 4b displays noticeable interannual and interdecadal variations in this pattern. It also implies that the snow cover in Eurasia can impact local or global weather and climate patterns, especially at the interannual and interdecadal scales, through the spatial characteristics of the EOF2 of Eurasian snow depth.

Fig. 4
figure 4

(a) Spatial pattern of the second EOF mode of winter snow depth in Eurasia, and (b) the normalized time series corresponding to the second principal component (black line) and the normalized time series of the third EOF mode of summer precipitation in China (blue line)

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To investigate the potential relationship between Eurasian snow cover and precipitation in China at the interdecadal scale, the PC2 was correlated with the winter precipitation from CN05.1, GPCC, and CMAP (Fig. S2). The spatial correlations derived from these three datasets exhibit a high level of consistency in Eastern China. The results indicate that snow cover distribution across Eurasia plays an important role in regulating the winter precipitation in China and, to some extent, impacts the precipitation in the lower-middle reaches of the Yangtze River and South China. Notably, the precipitation in the eastern TP showed opposite trends compared to that in the western and southern TP.

Fig. 5
figure 5

The correlation coefficients between the PC2 of winter snow depth (SD) in Eurasia and the summer precipitation in China from (a) CN05.1, (b) GPCC, and (c) CMAP. Dotted areas denote the correlations that are statistically significant at the 0.05 level. And (d) spatial pattern of the third EOF mode of summer precipitation in China

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Many studies have indicated a strong correlation between the winter snow cover anomalies in Eurasia and the summer climate of East Asia. A meridional quadrupole structure is identified in the northern and southern regions of East Asia by correlating summer precipitation with the principal component of EOF2 of winter snow depth in Eurasia. Specifically, enhanced rainfall in Northeast China and the lower-middle reaches of the Yangtze River is associated with reduced rainfall in the Yellow River basin and southern China (Fig. 5a). The spatiotemporal features of summer precipitation in China are further analyzed using CN05.1 precipitation spanning from 1980 to 2016. The first three EOF modes account for 17.1%, 14.0%, and 8.4% of the total variance, respectively, and they are separated from each other. It was observed that the spatial pattern of the third EOF mode (EOF3) of summer precipitation in China closely resembles the meridional quadrupole structure of the correlations between the EOF2 of Eurasian snow depth and China summer precipitation (Fig. 5d). The correlation coefficient between the PC3 of summer precipitation in China and the PC2 of winter snow depth is 0.49, which reached the 95% confidence level based upon a Student’s t test (Fig. 4b). It indicates that there is a significant correlation between winter snow depth anomalies in Eurasia and summer precipitation in China. Comparatively, the GPCC data demonstrate higher consistency with the observed precipitation distribution characteristics. The CMAP precipitation, on the other hand, performs slightly worse, likely attributable to its coarser resolution. In Northwest China, the correlation of CMAP precipitation is not very significant.

3.3 Spring snow depth variability in Eurasia and its relationship with precipitation in China

The first three EOF modes of spring snow depth in Eurasia account for 22.6%, 11.5%, and 7.3% of the total variance, respectively. These three modes are separated from each other. The spatial pattern of the first EOF mode (EOF1) of spring snow depth reflects an overall decreasing trend in Eurasia (Fig. 6), consistent with the results of winter snow depth. The center is located in central and western Siberia, indicating a significant decrease in spring snow depth in this region. The corresponding principal component of EOF1 indicates a shift from a negative to a positive time coefficient in the late 1980s, suggesting a shift from increasing and decreasing snow depth across Eurasia. As illustrated in Fig. 3b, spring snow depth in Eurasia decreased after 1988.

Fig. 6
figure 6

(a) Spatial pattern of the first EOF mode of spring snow depth in Eurasia from 1980 to 2016 and (b) the normalized time series corresponding to the first principal component

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The second EOF mode of spring snow depth in Eurasia reveals that the high-value centers are also predominantly concentrated in the middle and high latitudes, featuring a clear meridional wave train distribution characterized by a “negative-positive-negative” pattern (Fig. 7a). Specifically, apart from a negative center positioned between eastern Europe and the Western Siberian Plain and a positive center near the western Lake Baikal, there is an additional negative center in the north of Central Sibirian plateau. Examining the time series of the second EOF mode of spring snow depth also shows that the time coefficient shifted from negative to positive in the late 1980s, corresponding to a slight increase in snow depth in central and western Eurasia. Following this period, the time series reverted to negative, leading to a decrease in snow cover in these regions. It indicates that spring snow cover in Eurasia also displays significant interdecadal variability. Then, spring and summer precipitation from 1980 to 2016 are utilized for correlation analysis with the PC2 of spring snow depth in Eurasia. The relationship between spring snow depth anomalies and spring precipitation in southeastern China is exactly the opposite of that in central China (Fig. S3). The China summer precipitation regressed onto the PC2 of Eurasian spring snow depth also displays a meridional quadrupole pattern, with excessive precipitation over the regions of the Yangtze River basin, Northeast China, and eastern TP and deficient precipitation over the Yellow River basin, southern China, and southern TP (Fig. 8). This pattern is also more similar to the one in Fig. 5. It is consistent with the findings of Zuo et al. (2012), who emphasized that the feedback of mid-to-high latitude snow cover on atmospheric circulation further impacts summer precipitation in Eastern China. The reduction of Eurasian snow cover in spring leads to a decrease in heat flux upward from the ground, an increase in heat flux downward into the soil, and an increase in the boundary layer height.

Fig. 7
figure 7

(a) Spatial pattern of the second EOF mode of snow depth in spring over the Eurasian continent and (b) the normalized time series of the second principal component

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Fig. 8
figure 8

The correlation coefficients between the PC2 of spring snow depth (SD) in Eurasia and the summer precipitation in China from (a) CN05.1, (b) GPCC, and (c) CMAP. Dotted areas denote the correlations that are significant at the 0.05 level

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3.4 Possible physical mechanisms

From the above analysis, it is clear that there is a significant correlation between winter and spring snow depth anomalies in Eurasia and Eastern China summer precipitation. Subsequently, the following section focuses on the possible physical mechanisms by which the winter-spring snow depth anomalies in Eurasia impact Eastern China summer precipitation. Previous studies have demonstrated that Eurasian snowmelt directly increases soil moisture and influences soil temperatures in various Siberian regions during the warm season, decreasing surface air temperatures and diabatic heating of the troposphere. Figure 9 displays the regressed 0–100 cm soil moisture anomalies during summer onto the normalized time series of the second principal component of winter and spring snow depth in Eurasia. It is clear that the contrast in soil moisture anomalies between the east and west corresponds to the pattern of snow cover anomalies, particularly illustrated in the spring snow cover shown in Fig. 7a. The snow cover anomalies between eastern Europe and the Western Siberian Plain coincide with more pronounced negative soil moisture anomalies, whereas positive soil moisture anomalies are observed in the vicinity of Lake Baikal. The combination of snow cover and soil moisture anomalies underscores the substantial hydrological effect of snow cover, with excessive (less) snow cover leading to more (less) snowmelt and, thus, wetter (drier) soils. However, soil moisture anomalies are more influenced by localized spring snowmelt than by winter snowmelt. The soil moisture pattern in Eurasia extends into the following summer, influenced by the long-term memory of surface hydrological conditions in the region.

Fig. 9
figure 9

Summer 0–100 cm soil moisture anomalies (color shading; m3 m− 3) regressed onto the PC2 of (a) winter and (b) spring snow depth in Eurasia. Dotted areas denote the correlations that are significant at the 0.05 level

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Snowmelt induces soil moisture anomalies that have a prolonged impact on diabatic heating by altering the percentage of latent heat and sensible heat at the surface. To analyze the impact of soil moisture on surface thermal conditions in summer, the net radiation, surface sensible heat flux, and latent heat flux regressed onto the normalized time series of the second principal component of winter snow depth in Eurasia were investigated (Fig. 10). The net radiation at the surface is enhanced between eastern Europe and the Western Siberian Plain and weakened near Lake Baikal. These changes in net radiation further result in an increase in sensible heat flux and a reduction in latent heat flux between eastern Europe and the Western Siberian Plain, as well as a decrease in sensible heat flux and a slight increase in latent heat flux in the vicinity of Lake Baikal. Similar conclusions can be drawn regarding the distribution of net radiation, sensible heat flux, and latent heat flux regressed onto the PC2 of spring snow depth in Eurasia (Fig. S4). Notably, remarkably different changes in sensible and latent heat fluxes are observed in the southern and northern regions of Lake Baikal, highlighting a more pronounced reduction in the latent heat flux. The similarity of the pattern of sensible heat flux anomalies to the Eurasian snow cover distribution and summer soil moisture anomalies implies that the local energy balance is influenced by the Eurasian snow cover anomalies.

Fig. 10
figure 10

Summer (a) net radiation, (b) surface sensible heat flux, and (c) latent heat flux anomalies (color shading; W m− 2) regressed onto the PC2 of winter snow depth in Eurasia. Dotted areas denote the correlations that are significant at the 0.05 level

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Figure 11 illustrates the atmospheric thermal features over the Eurasian continent associated with winter snow depth. It can be seen that during the summer, surface air temperature increases significantly in the dry regions of eastern Europe and the Western Siberian Plain and decreases significantly in the humid regions around Lake Baikal. These anomalous surface thermal forcings can lead to a warmer or cooler atmosphere in the lower troposphere. The same is true for the effect of spring snow depth in Eurasia (Fig. S5). Zhang et al. (2017) demonstrated that the near-surface thermal conditions and the meridional north-south dipole structure of the net radiation anomalies shown in Fig. 10a enhance atmospheric baroclinicity by affecting the temperature gradient.

Fig. 11
figure 11

Summer surface air temperature anomalies (color shading; ℃) regressed onto the PC2 of winter snow depth in Eurasia. Dotted areas denote the correlations that are significant at the 0.05 level

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At 200 hPa, a strengthened subtropical westerly jet extending from Lake Baikal to northern China, along with the easterly wind anomalies in the north of the subtropical westerly jet, are shown in Fig. 12a. At the 500 hPa geopotential height, anomalous cyclonic and anticyclonic patterns were observed in the north and south, respectively, of the exit area of the East Asian subtropical westerly jet. Furthermore, there is a notable mid-latitude Eurasian wave train from the Western Siberian Plain to the Northwestern Pacific, featuring a negative center positioned over Mongolia and a positive center over the Western Siberian Plain. These results indicate that the westerly wind anomalies in the upper troposphere, induced by winter snow cover anomalies, provide conducive dynamic conditions for the emergence of the north-south dipole and Eurasian wave train patterns in the mid- to high-latitude regions of East Asia. The 200-hPa zonal wind and 500 hPa geopotential height anomalies regressed onto the PC2 of spring snow depth in Eurasia show nearly identical patterns (Fig. S6). Then, the vertical velocity in summer regressed onto the PC2 of winter snow depth in Eurasia, revealing a distinct descending motion in the troposphere over eastern Europe and the Western Siberian Plain, corresponding to an ascending motion in the western Lake Baikal (Fig. 13). Low-level moisture originating from wet soil can be lifted to the high level through the ascending flow under the background of in-situ low-level cyclonic circulation (Dirmeyer et al. 2014). Simultaneously, the latent heat released during this process could also contribute to the development of cyclonic circulation (Zhang et al. 2003). It enhances the linking of surface thermal forcing and mid- and upper-level circulation anomalies.

Fig. 12
figure 12

(a) The 200-hPa zonal wind (color shading; m s− 1) and (b) 500 hPa geopotential height (color shading; gpm) anomalies in summer regressed onto the PC2 of winter snow depth in Eurasia. Climatological zonal winds with speed > 20 m s-1 are enclosed by the black lines in (a). Dotted areas denote the correlations that are significant at the 0.05 level

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Fig. 13
figure 13

The longitude-pressure section of vertical velocity (Pa s-1) in summer (JJA) averaged along 50–65°N regressed onto the PC2 of winter snow depth in Eurasia

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Figure 14 displays the 500 hPa streamfunction and WAF anomalies during the summer. Notable positive streamfunction anomalies are observed between eastern Europe and the Western Siberian Plain. It is attributed to the winter-spring snow cover anomalies and enhanced thermal heating. At middle and high latitudes, WAFs spread from the North Atlantic to eastern Europe. The wave train strengthened significantly in the Western Siberian Plain. It then splits into two branches, one continuing latitudinal propagation at high latitudes and the other shifting to East Asia, which impacts precipitation in Eastern China. The enhanced propagation pattern is attributed to thermal forcing associated with winter-spring snow cover and soil moisture anomalous. The persistence of the wave propagation is mainly related to the consecutive surface thermal forcings. The process by which Eurasian snow cover affects soil moisture and summer precipitation in China is illustrated in Fig. 15.

Fig. 14
figure 14

The 500 hPa streamfunction (color shading; m2 s− 1) and the associated wave activity flux (vectors; m2 s− 2) anomalies in summer regressed onto the PC2 of winter snow depth in Eurasia

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Fig. 15
figure 15

The 500 hPa streamfunction (color shading; m2 s− 1) and the associated wave activity flux (vectors; m2 s− 2) anomalies in summer regressed onto the PC2 of winter snow depth in Eurasia

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4 Discussion of the effects of other factors

Anomalies in Eurasian snow cover can trigger an anomalous mid-latitude Eurasian wave train. The near-surface thermal anomalies associated with Eurasian spring snow cover anomalies induce an anomalous meridional temperature gradient. The atmospheric response to the surface thermal conditions increases the local 1000 − 500 hPa thickness, enhancing the Eurasian wave train (Zhang et al. 2017). Besides, strong positive (negative) upper-level divergence appears over the right (left) side of the exit region of the upper-level jet, combined with favorable water vapor conditions, leading to an anomalous distribution of Eastern China summer precipitation (Cheng et al. 2022).

Snow cover anomalies in winter across the Eurasian continent significantly influence atmospheric circulation during the same period (Zhang et al. 2016). At this time, the anticyclone over Siberia has strengthened, the East Asian trough has deepened significantly, and there is a notable stronger in winter monsoon activity in East Asia. The influence of snow cover anomalies in various Eurasian regions on precipitation in China varies significantly (Wu and Kirtman 2007; Wu et al. 2009; Wang et al. 2019). Studies have proposed that less snow cover in western Eurasia, more snow cover in eastern regions, and heightened snow accumulation on the TP, correspond to a decrease in summer precipitation in North China (Wu et al. 2009). The less spring snow cover in western Eurasia tends to be accompanied by a wetter south-drier north pattern over eastern China, and vice versa (Zhang et al. 2021a). Furthermore, the impact of different snow cover spatial modes on summer precipitation in East Asia is significantly different. The second EOF mode of Eurasian snow cover in winter and spring is more closely related to East Asian summer precipitation than the first EOF mode (Figs. 5 and 8). It is consistent with the conclusion of Yim et al. (2010). The relationship between the Eurasian snow cover and the East Asian climate is also affected by other atmospheric factors and lower boundary forcing, such as ENSO, Arctic Oscillation (AO), and North Atlantic Oscillation (NAO) (Zhang et al. 2021b). The NAO stimulates the Rossby wave train in the middle and high latitudes of the Northern Hemisphere in the following spring by affecting the dipole pattern of the Eurasian snow cover anomalies, finally leading to excessive spring precipitation in the middle and lower reaches of the Yangtze River (Han and Zhang 2021).

The current findings do not completely agree with the relative importance of snow cover over the TP and Eurasia. Snow cover anomalies over the TP and Western Siberia play crucial roles in influencing the East Asian summer monsoon (Qian et al. 2010; Duan et al. 2012). Li and Wang (2011) proposed that the winter and spring snow cover anomalies over the TP have an opposite effect to that of the Eurasian snow cover on summer precipitation in China. The persistence of large-scale snow cover in key areas of the TP serves as an important “influence source” that affects China’s climate and the East Asian atmospheric circulation (Xu et al. 2015). Anomalous winter and spring snow cover on the TP causes anomalous heat sources, affecting the moisture transport path and intensity from the ocean to the land. This dynamic modulates the spatiotemporal evolution of precipitation in Eastern China, characterized by “North floods-South droughts” and “North droughts-South floods” (Xu et al. 2015). Consequently, the impact of the Eurasian snow cover on East Asian precipitation is quite complicated.

This paper presents a diagnostic analysis of the relationship between Eurasian snow cover and precipitation in China using the observed data. The results can serve as a reference for further analyses of this relationship. Still, they are insufficient to clarify the mutual influence between the two. Additionally, the impact of Eurasian snow cover on weather and climate change in East Asia has not been fully understood. For the East Asian monsoon and summer rainfall in China, is the influence of the TP or the Eurasian snow cover more important? What are the mechanisms of their synergistic effects and respective contributions? There is still a need for in-depth research and discussion. Next, we will continue to strengthen the study of snow cover anomalies on the TP and the Eurasian continent and their relationship with precipitation in China. We will also identify the key areas where snow cover anomalies affect the prediction of summer rainfall in China. It will be an important reference for exploring the mechanism of East Asian monsoon changes and improving the accuracy of short-term climate prediction in China.

5 Conclusion

The study commenced by analyzing the spatiotemporal characteristics of snow cover across the Eurasian continent utilizing high-resolution snow depth data. An EOF analysis was then performed on the winter and spring with the greatest snow depth in Eurasia. The results indicate a significant seasonal variation in the multi-year average snow depth across the TP and the Eurasian continent, with a large range of snow cover in spring, autumn, and winter. Notably, the average snow depth in winter exceeds 20 cm in the 50–70°N region of Eurasia.

The winter and spring snow cover in Eurasia not only shows a decreasing trend due to global warming (the first EOF mode, its variance accounted for 24.4% and 22.6% of the total variance) but also exhibits significant interdecadal variation (the second EOF mode, its variance accounted for 10.2% and 11.5% of the total variance). In the spatial distribution of the second EOF mode, the snow cover in the north of 50°N in Eurasia presents a west-east dipole pattern. From the principal component corresponding to the second EOF mode of winter snow depth, it exhibits significant interdecadal variations. The snow cover in Eurasia plays a crucial role in regulating the winter precipitation in China. It influences precipitation in the middle and lower reaches of the Yangtze River and South China, resulting in an opposite trend of precipitation in the eastern TP to that in the western and southern TP. Additionally, it was observed that the spatial correlation pattern between the EOF2 of Eurasian snow depth and summer precipitation in China closely resembles the meridional quadrupole structure of the third EOF mode of summer precipitation in China. This pattern is characterized by excessive rainfall in Northeast China and the lower-middle reaches of the Yangtze River, and less rainfall over the Yellow River basin and southern China. The spatiotemporal characteristics of the first EOF mode of spring snow depth in Eurasia are consistent with those of winter snow depth, indicating an overall decrease in spring snow depth across Eurasia. Moreover, the influence of the second EOF mode of spring snow depth on summer rainfall in China should not be neglected. The spatial pattern of summer precipitation regressed onto the PC2 of spring snow depth in Eurasia also shows the meridional quadrupole structure mentioned above.

The physical mechanisms by which winter-spring snow depth anomalies in Eurasia affect summer precipitation in Eastern China are similar. Decreased snow depth in Eurasia during the winter and spring directly leads to diminished soil moisture, increasing net radiation and sensible heat flux at the surface. The meridional distribution of surface temperature also exhibits a dipole pattern, closely resembling the second EOF mode of snow cover. Changes in surface temperature further strengthen the meridional temperature gradient, leading to enhanced subtropical westerly jet in the upper troposphere. At 500 hPa geopotential height, an anomalous cyclone and an anomalous anticyclone occurred north and south of the jet exit area, respectively. The Eurasian snow cover anomalies pattern triggered an anomalous mid-latitude Eurasian wave train, which strengthened significantly in the Western Siberian Plain. It then splits into two branches, one continuing to propagate eastward at high latitudes and the other shifting towards East Asia, thereby impacting precipitation in Eastern China. This work indicates that the second EOF mode of Eurasian snow cover can impact the precipitation variability in Eastern China during the same period and in summer on an interdecadal scale.