Introduction

Significant fluctuations in surface air temperature (SAT) have attracted increasing attention due to their potential links to extreme weather and climate events1,2,3. In particular, the increased frequency and intensity of SAT anomalies over Eurasia and North America exert substantial influences on agriculture, ecosystems, economics, and human health1,4,5,6. For example, the record-breaking cold winters of 2009/10 over Eurasia and 2013/14 over North America resulted in extensive damage to traffic and agriculture and significantly affected people’s lives1,7. Therefore, understanding SAT variability over Eurasia and North America is of great interest.

Previous studies indicated that the local atmospheric circulation could control the variation in the SAT over the Eurasia and North America8,9,10,11. For example, the Arctic Oscillation (AO), which is the dominant atmospheric mode over the mid-to-high-latitude Northern Hemisphere (NH), may exert substantial influences on the climate and weather in the Eurasia and North America by modulating atmospheric circulations10. The lower boundary forcings, like snow cover, may also significantly impact the climate in the NH12,13. Snow cover may impact SAT anomalies through both the snow-albedo effect and the snow-hydrological effect14,15,16.

Besides, it has been well documented that variations in sea surface temperature (SST) in the tropical Pacific associated with El Niño–Southern Oscillation (ENSO) can influence the winter SAT over North America and East Asia by modulating the atmospheric teleconnection17,18,19,20,21. Specifically, the Pacific–North American (PNA) atmospheric teleconnection pattern induced by ENSO can act as an atmospheric bridge linking the SST forcing over the tropical Pacific to the winter SAT over North America17,19. The winter SAT anomaly pattern over North America associated with ENSO is traditionally characterized by a north–south dipole-like feature with negative anomalies over the southeastern U.S. and positive anomalies over northwestern North America22. Furthermore, during El Niño, an anomalous anticyclone over the western North Pacific (WNP) may result in increased winter SAT over parts of East Asia since anomalous southwesterlies to the northwest flank of the anticyclone bring warmer air from lower latitudes20.

Beyond the tropics, SST anomalies in the extratropical oceans have been reported to play a crucial role in the SAT variability over Eurasia and North America. For instance, the North Atlantic SST anomalies, North Atlantic tripole SST mode in particular, coupled with the North Atlantic Oscillation (NAO) during boreal winter and spring seasons23,24, are closely linked to the SAT variability over Eurasia and North America4,11,25. While these relationships have been extensively studied, the impact of SST anomalies in the extratropical North Pacific on the interannual SAT variability over Eurasia and North America still remains unclear.

Anomalous SST over the North Pacific mainly exhibits two distinct anomaly patterns associated with the Pacific Decadal Oscillation (PDO)26,27 and the Victoria mode (VM)28, respectively. The PDO is a prominent SST variability over the North Pacific with the “regime shifts” on the decadal time scale, which has been studied extensively for its wide-ranging impacts on the global climate and marine and terrestrial ecosystems29,30,31. Besides the PDO, the VM, defined as the second dominant mode of SST anomalies in the North Pacific, has received increasing attention over the recent two decades due to its significant climate impacts28,32. Several recent studies have pointed out that the VM has a significant impact on the climate variability over the surrounding and remote regions, such as ENSO, the Pacific Intertropical Convergence Zone summer precipitation, and tropical cyclone genesis over the WNP32,33,34. While the profound influence of the VM on the climate variability over the pan-North Pacific has been extensively studied, works about its impact on SAT variability over Eurasia and North America are limited. To address this knowledge gap, here, we elucidate the influence of the VM on the interannual SAT variability in winter-spring seasons over Eurasia and North America based on observational datasets and numerical experiments, which could help improve our understanding of the role of extratropical North Pacific SST anomalies in the mid-to-high-latitude climate.

Results

Observed relationship between the VM and the SAT over Eurasia and North America

The development and peak of the VM typically occur in the winter-spring seasons (December–May, DJFMAM)32. To investigate the relationship between the VM and the SAT over Eurasia and North America during the period 1950–2020, we calculated the correlation between the DJFMAM-averaged SAT anomalies over the NH and the VM index (see Method). It is noteworthy that the VM is partly forced by the North Pacific Oscillation (NPO)-like atmospheric variability32. To remove the effect of the NPO and isolate the internal variability of the VM, linear regression was performed with respect to the NDJFMA-averaged NPO index prior to analysis. The correlation map of the SAT anomalies with the VM index during winter-spring seasons is illustrated in Fig. 1a, which is characterized by anomalous positive and negative SAT over mid-to-high-latitude east-central Eurasia and eastern North America, respectively, along with negative SAT anomalies over the north of the Indian peninsula. The spatial feature of this correlation map manifests as a tripole pattern over the NH, which is similar to the first EOF (EOF1) mode of the winter-spring SAT interannual variability over the NH (Fig. 1b). Despite the somewhat eastward and westward shifts in the centers of the SAT anomalies related to the VM over mid-to-high-latitude Eurasia and North America, respectively, compared with that of the EOF1 mode, the two spatial patterns closely resemble each other, as supported by their strong correlation (R = 0.71; significant at the 99% confidence level). To focus on SAT variability related to the VM over mid-to-high-latitude Eurasia and North America, we defined a simple index, referred to as the EANA index, as the difference between the normalized winter-spring SAT anomalies averaged over mid-to-high-latitude east-central Eurasia (90°–140°E, 47°–72°N) and eastern North America (95°–65°W, 47°–72°N). Corresponding to the spatial resemblance between the SAT anomaly pattern related to the VM and the EOF1 mode of the SAT variability over the NH, the EANA index is closely linked to the first PC (PC1) associated with the EOF1 mode of the interannual SAT variability over the NH (Fig. 1c), as indicated by their high temporal correlation coefficient of 0.85 (significant at 99% confidence level).

Fig. 1: Relationship between the VM and the interannual SAT variability over the North Hemisphere during winter-spring seasons.
figure 1

a The winter-spring surface air temperature (SAT) anomalies in NH obtained by correlating the SAT anomalies with the normalized VM index during 1950–2020 based on the NCEP-1 datasets. b The winter-spring SAT anomalies in NH obtained by correlating the SAT anomalies with the normalized PC time series of the first leading mode of the SAT anomalies in NH. c The time series of the first leading normalized PC (bar) and the EANA index (solid black line). d The time series of the VM (blue line) and the EANA (red line) indices. Oblique lines in a and b indicate the 95% confidence level based on a two-tailed Student’s t test, respectively. In c and d, the correlation coefficients are given in the lower left corner of each panel. The black boxes in a and b denote mid-to-high-latitude eastern Eurasia (90°–140°E, 47°–72°N) and eastern North America (95°–65°W, 47°–72°N), respectively.

Full size image

Figure 1d shows the time series of the winter-spring VM and EANA indices. Conspicuous interannual variability can be found in these two indices with a strong correlation between them (R = 0.52, significant at the 99% confidence level). We observed a similar correlation when using the ERA5 data (not shown), indicating the robustness of our analysis. The preliminary correlation analyses suggest that the VM is closely linked to the SAT over mid-to-high-latitude Eurasia and North America. Previous studies have revealed that the NH SAT can be significantly influenced by the AO10,35, NAO8,9,11,25, ENSO18,20,21 and Eurasian snow cover12,13. To minimize interference from these climate factors, we conducted a partial correlation analysis to isolate the climatic influence of the VM. As shown in Supplementary Fig. 1, there is little change in the regions of significant correlation when these winter-spring signals are removed. These results suggest that the VM plays a key role in SAT anomalies over mid-to-high-latitude Eurasia and North America that is linearly independent of the aforementioned climate factors. In the following section, we will explore the plausible mechanisms underlying this teleconnection.

Local surface heat flux effects associated with the VM

Building upon the aforementioned results, this section further investigates the surface heat flux and atmospheric circulation anomalies associated with the VM to elucidate their role in the formation of the SAT anomalies over mid-to-high-latitude Eurasia and eastern North America. The observed similarities between the spatial distribution of surface net heat flux (NHF) and SAT anomalies over mid-to-high-latitude Eurasia and North America (Fig. 2a and Supplementary Fig. 2) suggest that changes in surface heat fluxes are closely related to the formation of SAT anomalies. While the NHF anomalies over eastern North America are relatively weak, there are notable positive NHF anomalies over mid-to-high-latitude east-central Eurasia (Fig. 2a).

Fig. 2: Anomalies of the winter-spring surface heat flux associated with the VM.
figure 2

Anomalies of DJFMAM a NHF, b SWR, c SHF, d LWR, e LHF, and f TCC (W m–2) obtained by regression on the normalized VM index. Stippled regions denote anomalies significant at the 95% confidence level according to the Student’s t test. Positive (negative) values indicate heat fluxes are downward (upward), which contribute to positive (negative) SAT anomalies. Boxes indicate the domain to represent mid-to-high-latitude eastern Eurasia and eastern North America, respectively.

Full size image

Our results reveal that the shortwave radiation (SWR) and sensible heat flux (SHF) associated with the VM have a positive contribution to the NHF anomalies over mid-to-high-latitude east-central Eurasia (Fig. 2b, c), whereas the longwave radiation (LWR) and latent heat flux (LHF) associated with the VM have an opposite effect (Fig. 2d, e). The positive SWR and negative LWR anomalies over mid-latitude Eurasia can be attributed to decreased TCC anomalies (Fig. 2f), which increase downward SWR anomalies and reduce downward LWR anomalies. The decreased TCC anomalies are consistent with anomalous lower-level divergence (Supplementary Fig. 2), which could lead to anomalous downward motion. In addition, the SHF is an important contributor to the NHF anomalies over mid-to-high-latitude Eurasia (Fig. 2c). The positive SHF anomalies over this region may be explained by southwesterly wind anomalies (Supplementary Fig. 2) that bring warmer air from lower latitudes, increasing the land–air temperature difference. As the warm and dry air from the mid-latitude inland east-central Eurasia has a lower humidity compared to that over the land, the land–atmosphere humidity difference may be increased, contributing partly to upward LHF anomalies over mid-to-high-latitude east-central Eurasia (Fig. 2e). Taken together, these results indicate that the surface heat fluxes associated with the VM contribute to SAT anomalies over mid-to-high-latitude east-central Eurasia, while the surface heat fluxes associated with the VM may not explain the formation of SAT anomalies over eastern North America.

Role of atmospheric circulation in linking the VM and SAT anomalies

The above analyses reveal that the anomalous surface heat fluxes associated with the VM have an important contribution to the formation of SAT anomalies over mid-to-high-latitude Eurasia. However, changes in SAT are not only influenced by surface heat fluxes but also by atmospheric circulation. Thus, anomalous atmospheric circulation may play a significant role in the linkage between the winter-spring SAT over mid-to-high-latitude Eurasia and eastern North America and the VM. In order to make this issue clear, we first checked the anomalous atmospheric circulation associated with the variation in SAT by regressing geopotential heights at 200-hPa and 850-hPa on the EANA index (Fig. 3). The anomalous geopotential heights at 200-hPa (Fig. 3a) and 850-hPa (Fig. 3b) associated with the EANA index exhibit a similar pattern over mid-to-high-latitude NH, indicating an equivalent barotropic vertical structure. The regression pattern manifests as a wave pattern over the NH and anomalous positive and negative geopotential heights are observed over mid-to-high-latitude east-central Eurasia and eastern North America, respectively, corresponding to SAT anomalies. We note that these anomalous geopotential height patterns are closely align with the geopotential height anomalies associated with the VM (Fig. 4), supported by the strong correlation of the anomalous patterns (R = 0.87 and R = 0.88 for geopotential heights at 200-hPa and 850-hPa, respectively; significant at the 99% confidence level). The robust correlations between the atmospheric circulations associated with the EANA and the VM indices suggest that the wave pattern of atmospheric teleconnections serves as a crucial mechanism linking the VM and change in the SAT over mid-to-high-latitude Eurasia and eastern North America. Therefore, we hypothesize that the wave pattern acts as an atmospheric bridge connecting the VM and circulation associated with SAT anomalies over mid-to-high-latitude Eurasia and eastern North America.

Fig. 3: The atmospheric circulation associated with the EANA index.
figure 3

a Regressed anomalous pattern of DJFMAM 200hPa geopotential height (shading; units: m) and horizontal winds (vectors; units: m s–1) with respect to the EANA index. b As a but for 850 hPa. Areas with regression significant at the 95% level are shown. The wind anomalies are shown only when the zonal or meridional wind anomalies are significant at the 95% confidence level. Boxes indicate the domain to represent mid-to-high-latitude eastern Eurasia and eastern North America, respectively.

Full size image
Fig. 4: The atmospheric circulation associated with the VM index.
figure 4

a Regressed anomalous pattern of DJFMAM 200 hPa geopotential height (shading; units: m) and horizontal winds (vectors; units: m s–1) with respect to the VM index. b As a but for 850 hPa. Areas with regression significant at the 95% level are shown. The wind anomalies are shown only when the zonal or meridional wind anomalies are significant at the 95% confidence level. Boxes indicate the domain to represent mid-to-high-latitude eastern Eurasia and eastern North America, respectively.

Full size image

To test our hypothesis, we calculated the anomalous Rossby wave activity fluxes regressed on the VM (Fig. 5). The results suggest that strong Rossby wave activity fluxes originate from the WNP, propagate eastward across North America, and then turn southeastward to western Europe. Furthermore, two branches of the Rossby wave activity fluxes originating from western Europe are identified. The first branch is a poleward-orientated wave train, initially going northeastward to the Barents–Kara Seas and then southeastward to mid-to-high-latitude east-central Eurasia, which contributes to the positive geopotential height anomalies observed in this region. The second branch propagates from western Europe, penetrating South Asia, and turns northeastward to mid-to-high-latitude east-central Eurasia, but mainly remains confined to East Asia. In addition, it is noted that the Rossby wave train associated with the VM originate from the WNP and propagate northwards to northern East Asia, contributing to the positive geopotential height anomalies in situ, which is in alignment with the previous finding36. These findings provide further support for the proposed hypothesis that the wave pattern serves as an atmospheric bridge linking the VM and the circulation associated with SAT anomalies over mid-to-high-latitude Eurasia and eastern North America.

Fig. 5: Anomalies of the DJFMAM wave activity flux (vectors; unit: m2 s–2) and Z200 (shading; unit: m) regressed on the VM index.
figure 5

Dotted areas indicate that the regressions are significant 95% confidence level. The wave activity flux anomalies are shown only when the zonal or meridional component is significant at the 95% confidence level. The green stars denote the center of the cyclonic/anticyclonic anomalies. Boxes indicate the domain to represent mid-to-high-latitude eastern Eurasia and eastern North America, respectively.

Full size image

Quantitively, the two branches of the Rossby wave train (RWT) were depicted by using two indices, referred to as the RWT1 and RWT2, which were defined based on the averaged geopotential height at 200-hPa in the centers of the cyclonic/anticyclonic anomalies along the wave train (see Fig. 5). It is clear that the RWT1 and RWT2 indices have a significant correlation (R = 0.64 and 0.66, respectively, significant at the 99% confidence level) with the VM index during winter-spring (Fig. 6a, b). Moreover, the correlation coefficients between the EANA index and the RWT1 and RWT2 indices reach 0.80 and 0.81, respectively, which are also significant at the 99% confidence level (Fig. 6c, d). Together with the immediate relationship of the anomalous wave pattern of the atmospheric circulation with the VM and the SAT anomalies, it is certainly possible that the wave pattern acts as a crucial link between the VM and the SAT over mid-to-high-latitude Eurasia and eastern North America. Consequently, our results indicate that the VM-induced anomalous atmospheric wave trains play an important role in the formation of atmospheric circulation anomalies, which ultimately result in notable SAT anomalies over mid-to-high-latitude Eurasia and eastern North America.

Fig. 6: Relationship between the Rossby wave trains and the VM and EANA indices.
figure 6

a, b Scatterplot of the winter-spring VM index with the RWT1 and RWT2 indices, respectively. c, d As for a, b but for scatterplot of the winter-spring RWT1 and RWT2 indices with the EANA index, respectively. The correlation coefficients are given in the lower right corner of each panel.

Full size image

To better understand the origin of the VM-induced anomalous wave activity fluxes, anomalous RWS at 200-hPa associated with the VM was analyzed. The climatological zonal winds at 200-hPa are overlaid as contours. The anomalous RWS is pronounced over the WNP, which presents significantly positive RWS anomalies over the southeast of Japan extending to the central North Pacific (Fig. 7a). Previous studies have indicated that the planetary vortex stretching term \(-f{D}_{\chi }\) contributes overwhelmingly to the RWS, which actually reflect the variation in divergence \({D}_{\chi }\) but with opposite signs37,38. Furthermore, the RWS anomalies are essentially in agreement with the precipitation anomalies over the WNP associated with the VM (Fig. 7b). These findings suggest that significant negative (positive) precipitation anomalies and the related upper tropospheric convergence (divergence) anomalies over the WNP play a crucial role in inducing the upper-tropospheric RWS anomalies. Notably, the positive RWS anomalies over the southeast of Japan are located near the East Asian westerly jet (EAWJ) core. Previous studies have suggested that disturbances near the EAWJ core tend to propagate eastward zonally to the downstream area in a Rossby wave pattern since the jet can act as a wave guide39. Therefore, the anomalous RWS over the southeast of Japan associated with the VM could induce atmospheric circulation anomalies and further impact winter-spring SAT anomalies over mid-to-high-latitude Eurasia and eastern North America through wave propagation.

Fig. 7: Anomalies of the winter-spring RWS and precipitation regressed on the VM index.
figure 7

a RWS anomalies (shading, unit: 3×10^–10 s^–2). b Precipitation anomalies (unit: mm day^–1). In a, the climatological 200-hPa zonal winds (contours, unit: m s^–1) obtained by the DJFMAM-averaged 200-hPa zonal winds during 1981–2010 are also presented. Dotted areas indicate the anomalies significant at the 95% confidence level. Boxes indicate the domain to represent western North Pacific.

Full size image

The VM impact on the SAT anomalies simulated by numerical experiments

The observational results elucidate an underlying mechanism responsible for the impact of the VM on winter-spring SAT anomalies over mid-to-high-latitude Eurasia and eastern North America. However, the results have limitations due to the influences of internal climate variabilities. To make a stronger case that the VM SST anomalies cause some important part of the SAT anomalies over Eurasia and North America, rather than merely being associated with it, we performed numerical experiments with CAM5. Supplementary Fig. 3a displays the simulated anomalous SAT responses to the winter-spring VM obtained by the difference between the Sensitivity and the Control experiments. It is evident that notable positive and negative SAT anomalies appear over mid-to-high-latitude Eurasia and eastern North America, respectively. While the simulated center of the SAT anomalies over mid-to-high-latitude Eurasia shifts westward compared with the observations, the spatial pattern of the simulated SAT anomalies over mid-to-high-latitude NH shares characteristics with the observed composite differences of the SAT anomalies between positive and negative VM events (Supplementary Table 1) shown in Supplementary Fig. 3b. This is further supported by the strong correlation of the SAT anomaly patterns (R = 0.68; significant at the 99% confidence level). Thus, these results confirm the key role of the VM in inducing winter-spring SAT anomalies over mid-to-high-latitude Eurasia and eastern North America.

The large-scale circulation differences between the Sensitivity and the Control runs provide further evidence that the anomalous atmospheric wave trains induced by the VM can cause SAT anomalies over mid-to-high-latitude Eurasia and eastern North America. Similar to observational results, the simulated geopotential heights at 200-hPa (Supplementary Fig. 4a) and 850-hPa (Supplementary Fig. 4b) anomalies over mid-to-high latitude NH show a barotropic vertical structure, which exhibits an anomalous atmospheric Rossby wave pattern. The high-level positive and negative geopotential height anomalies of the Rossby wave dominate mid-to-high-latitude east-central Eurasia and eastern North America, respectively. Actually, there are some distinctions between the observation and the simulation in the Rossby wave propagation (Fig. 5 and Supplementary Fig. 5a). Compared with the observation (Fig. 5), the simulated wave activity fluxes train propagates from the WNP, penetrating eastern North America, and turns to mid-to-high latitude Eurasia with only one branch of wave train (Supplementary Fig. 5a). This wave train has seven cyclonic/anticyclonic anomalies centered at the WNP, eastern North America, eastern North Atlantic, western North Atlantic, western Europe, the Barents–Kara Seas, and mid-to-high latitude Eurasia, respectively. Despite these discrepancies, the wave train induced by the VM is generally well simulated. Furthermore, the anomalous RWS associated with the VM over the WNP are also reasonably simulated (Supplementary Fig. 5b). These results support that the significant role of VM in driving SAT anomalies over mid-to-high latitude Eurasia and eastern North America through atmospheric wave propagation.

Discussion

In this study, we focused primarily on the impact of the VM on the interannual variation in winter-spring SAT over the mid-to-high-latitude NH and the physical mechanisms responsible for this impact by using observations and numerical model experiments. Our findings indicate a strong relationship between the interannual variation in SAT over the mid-to-high-latitude NH and the VM during winter-spring, which is characterized by an opposite-sign dipole pattern with positive SAT anomalies over mid-to-high-latitude east-central Eurasia and negative SAT anomalies over eastern North America.

A diagnostic analysis of surface heat fluxes suggests that the formations of the SAT anomalies over the mid-to-high-latitude east-central Eurasia are tightly connected to the changes in surface heat fluxes associated with the VM, featured by a significant increase in downward surface NHF anomalies over large parts of mid-to-high-latitude east-central Eurasia. In contrast, change in surface heat fluxes associated with the VM has a limited effect on the formation of SAT anomalies over eastern North America due to the relatively weak surface NHF anomalies in this region. Moreover, the VM-induced anomalous atmospheric circulations play a crucial role in the formation of notable SAT anomalies over mid-to-high-latitude east-central Eurasia and eastern North America. As summarized by the schematic diagram in Fig. 8, the negative SST anomalies associated with the VM over the WNP are linked to negative precipitation and upper-tropospheric wind convergence anomalies in situ, which induce significant positive RWS anomalies near the East Asian westerly jet core. These RWS anomalies act as disturbances that propagate eastward, exciting a wave train-like pattern. The high-level positive and negative geopotential height anomalies of the Rossby wave dominate mid-to-high-latitude east-central Eurasia and eastern North America, respectively, leading to the variation in SAT anomalies. Therefore, the VM can influence SAT anomalies over mid-to-high-latitude east-central Eurasia and eastern North America via the propagation of Rossby wave trains.

Fig. 8: Schematic diagram of the VM influencing the winter-spring seasons SAT variability over the mid-to-high-latitude Eurasia and North America.
figure 8

The red and blue shading over the North Pacific denotes the positive VM. The blue (red) box filled with blue (red) oblique lines indicates the negative (positive) SAT anomalies in eastern North America (mid-to-high-latitude eastern Eurasia). The gray vectors over eastern North America and mid-to-high-latitude eastern Eurasia indicate the cyclone and anticyclone, respectively. The shaded blue (red) arrow indicates the winter-spring anomalous upward (downward) flows related to the VM. The orange (sky blue) circles with “A” (“C”) represent the positive (negative) the geopotential height anomalies at 200 hPa, the indicator of the atmospheric bridge. The yellow oval indicates the Rossby wave source related to the VM.

Full size image

This paper improves our understanding of the climate impacts of the VM, which provides insights into the key role of the VM in the interannual SAT variability over the mid-to-high-latitude Eurasia and North America. In general, significant interannual SAT variability may be linked to extreme weather and climate events, which exert substantial influences on ecosystems, human health, and socioeconomic development. Therefore, further investigation is necessary to determine the extent to which the VM affects downstream extreme events by altering the interannual SAT variability over the mid-to-high-latitude NH.

In addition, we noted that the interannual variability of the VM undergoes a remarkable interdecadal change, with decreased variability from the early 1960s to the early 1980s and increased variability from the early 1980s to the late 2000s (Supplementary Fig. 6). This finding is in good agreement with the conclusions of Ding et al. 32. As expected, the interdecadal changes in the VM variability are generally consistent with its connection with the SAT anomalies over mid-to-high-latitude Eurasia and North America (Supplementary Fig. 6), suggesting that a stronger VM tends to have more profound impacts on the NH climate. However, the physical mechanisms responsible for the interdecadal change in the VM remain unknown. Thus, further investigation is required to understand the potential mechanisms responsible for decadal variations in the VM.

Methods

Datasets and methods

This study employs monthly mean SAT, sea level pressure (SLP), geopotential heights, horizontal winds, net shortwave radiation flux, net longwave radiation flux, net sensible heat flux, net latent heat flux at the surface, and total cloud cover (TCC). All the above variables are derived from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis 140. The SAT, SLP, geopotential heights and horizontal winds have a horizontal resolution of 2.5° × 2.5°. The heat fluxes and TCC are on a T62 Gaussian grid. The convention for surface heat fluxes is positive for downward flux. To verify the robustness of the results, the SAT data from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) are also employed41. The monthly mean SST dataset used in this study is provided by the Met Office Hadley Centre Global Sea Ice and Sea Surface Temperature dataset with a horizontal resolution of 1° × 1°42. The precipitation data were obtained from the National Oceanic and Atmospheric Administration (NOAA) Precipitation Reconstruction (PREC) dataset43. The snow cover data are from the ERA5 with a horizontal resolution of 1° × 1°41. In this study, we focus on the time period is 1950-2020.

To describe the VM variability, following Ding, et al. 32, the VM index is defined as the second principal component (PC) associated with the second empirical orthogonal function (EOF) mode of SST anomalies in the North Pacific poleward of 20°N. The North Pacific Oscillation44 index is defined as the PC2 associated with the EOF2 of the SLP anomalies over 120°E–80°W, 20°–60°N45. The Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO) indices are obtained from the NOAA Climate Prediction Center (CPC) website (http://www.cpc.ncep.noaa.gov/data/indices). The Niño3.4 index, which is used to represent ENSO variability, is defined by SST anomalies averaged over the 5°S–5°N, 170°–120°W region. Following Jia, et al. 12, the snow cover (SC) index is defined as averaging SC over the central-eastern Eurasia (40°–70°N, 80°–140°E). These indices from 1950 to 2020 are all linearly detrended and standardized using population standard deviations.

Our analysis is conducted for the December–May (DJFMAM), which corresponds to winter–spring seasons. To better isolate the interannual variation, a 9-yr high-pass fast Fourier transform (FFT) filter is applied to the data to obtain the interannual variability (other filters such as 10- and 11-yr low-pass filters do not change the conclusion). All data sets are linearly detrended in an effort to avoid possible influences associated with global warming signal. A two-tailed t-test is used to analyze the statistical significance of the results.

The wave activity flux46 is used to investigate the stationary Rossby wave propagation induced by the VM, which can capture instantaneous wave propagation. It is parallel to the local group velocity of a stationary Rossby wave train in the Wentzel–Kramers–Brillouin approximation. Only the horizontal components of this WAF are used in this study. The horizontal flux is calculated according to the following equation:

$$W=\frac{P}{2{\rm{|}}\vec{U}{\rm{|}}}\left\{\begin{array}{c}U\left({{v}^{{\prime} }}^{2}-{\psi }^{{\prime} }{{v}^{{\prime} }}_{x}\right)+V(-{u}^{{\prime} }{v}^{{\prime} }+{\psi }^{{\prime} }{{u}^{{\prime} }}_{x})\\ U\left(-{u}^{{\prime} }{v}^{{\prime} }+{\psi }^{{\prime} }{{u}^{{\prime} }}_{x}\right)+V({{u}^{{\prime} }}^{2}+{\psi }^{{\prime} }{{u}^{{\prime} }}_{y})\end{array}\right.$$
(1)

where P, \(\vec{U}\) = (U, V), ψ′ and \(\vec{V}\)′ = (u′, v′) denote relative pressure (pressure/1000 hPa), basic state wind velocity, perturbation geostrophic stream-function and perturbed wind velocity, respectively. We calculated the basic state by using the 1981–2010 climatology and the perturbation means the anomalies of variables, which are calculated relative to the 1981–2010 climatology.

We defined the two indices to quantitively depict two branches of the Rossby wave train (RWT) associated with the VM, referred to as the RWT1 and RWT2, which were calculated based on the averaged geopotential height at 200-hPa in the centers of the cyclonic/anticyclonic anomalies along the wave train according to the following formulas:

$${RWT}1=\,-Z\left(33^\circ N,\,170^\circ W\right)+Z\left(55^\circ N,\,160^\circ W\right)-Z\left(66^\circ N,\,80^\circ W\right)+Z\left(53^\circ N,\,5^\circ E\right)-Z\left(75^\circ N,\,60^\circ E\right)+Z\left(50^\circ N,\,130^\circ E\right)$$
(2)
$${RWT}2=\,-Z\left(33^\circ N,\,170^\circ W\right)+Z\left(55^\circ N,\,160^\circ W\right)-Z\left(66^\circ N,\,80^\circ W\right)+Z\left(53^\circ N,\,5^\circ E\right)-Z\left(28^\circ N,\,100^\circ E\right)+Z\left(50^\circ N,\,130^\circ E\right)$$
(3)

where Z is the geopotential height anomalies at 200-hPa.

To investigate the source of the Rossby waves, following Sardeshmukh and Hoskins47, we adopt the barotropic vorticity equation to describe the Rossby wave source (RWS):

$$S=\,-\nabla \left(\vec{{V}_{\chi }}{\zeta }_{a}\right)=\,-f{D}_{\chi }-\zeta {D}_{\chi }-\vec{{V}_{\chi }}\cdot \nabla (f+\zeta )$$
(4)

where S is the source/sink of the Rossby wave; \(\vec{{V}_{\chi }}\) denotes the divergent wind vector, \({\zeta }_{a}\) is the absolute vorticity, f and \(\zeta\) are the planetary vorticity and relative vorticity, respectively, and \({D}_{\chi }\) is the horizontal divergence. This equation indicates that the divergence of vorticity flux contributes to the generation of the RWS38.

Experimental design

To examine the impact of the VM on the SAT over Eurasia and North America, we performed several modeling experiments based on the CAM548, which has 30 hybrid sigma-pressure vertical levels with a horizontal resolution of 0.937° × 1.25° (latitude × longitude). The climatological monthly mean SST, as a reference state, was used to force the atmospheric model (Control). In addition, we added the composite difference of SST anomalies between positive and negative VM events (defined as years when the DJFMAM-averaged VM index was greater than 1.0 positive standard deviation and less than 1.0 negative standard deviation, respectively; see Supplementary Fig. 7) on the DJFMAM climatological SST anomalies in the extratropical North Pacific (Sensitivity). Each experiment was integrated for 40 years, and only the last 30 years of the integrations were taken for analyses to avoid any influence of the initial conditions.