Roles of eddy generation and jet characteristics in setting the annual cycle of Siberian storm track

The Siberian storm track is one of the drivers of the East Asian extreme weather events. Using the daily JRA‐55 reanalysis data from 1980 to 2021, this study examines roles of eddy generation and jet characteristics in setting the annual cycle of Siberian storm track. It is found that there are two peaks of Siberian storm track intensity in boreal spring and autumn. The possible reason for such an annual cycle is explored by analyzing the maximum Eady growth rate over the Siberian region and jet characteristics. The stronger Siberian Eady growth rate in boreal spring and autumn, favoring a stronger baroclinic eddy generation, could contribute to the stronger intensity of Siberian storm tracks in these two seasons. Furthermore, the Siberian jet stream cores during boreal spring and autumn are located north of 50° N and resembles more an eddy‐driven jet. While in winter, the subtropical jet stream enhanced and the eddy‐driven jet becomes relatively weaker, which is less efficient to generate midlatitude baroclinic eddies. Besides, the eddy‐driven jet can modulate the horizontal wave propagations from upstream, which also plays a role in amplifying the spring and autumn Siberian storm tracks.

Considerable progress has been made to understand the annual cycles of NPST and NAST because of their strong intensity and wide impacts. In North Atlantic, the storm tracks are strongest in boreal winter, accompanied with the strong baroclinicity in the same season. Relative to winter, both the storm tracks and baroclinity are weakest in summer. This can be explained by the classical baroclinic instability theory. However, as noted by previous studies, the storm tracks in North Pacific are reduced in midwinter, relative to autumn and spring, despite the stronger winter baroclinicity and westerlies. This phenomenon is referred to the midwinter suppression in previous studies and has been attributed to the upstream seeding effect, local diffusivity efficiency, and eddy life cycle time scale (Chang, 2003).
Baroclinic instability has long been recognized as the main factor for occurrence and development of extratropical cyclones and anticyclones, and its changes are the key for understanding the storm track variations (Charney, 1947;Eady, 1949;Harvey et al., 2014;Lindzen & Farrell, 1980;O'Gorman, 2010;O'Gorman & Schneider, 2008;Woollings et al., 2012). Previous studies have suggested that the region with high maximum Eady growth rate is the main area for generating baroclinic eddies. The growth of midlatitude baroclinic eddies becomes stronger as the baroclinic instability increases (Eady, 1949;Nie et al., 2013;Robinson, 2000). Variations of storm track intensity may also be related to jet characteristics. As suggested by previous studies, the intensity of storm track is positively correlated with the intensity of the eddy-driven jet stream. Below the velocity threshold of 45 mÁs À1 , the storm track intensity is increased as the jet strengthens (Montoya Duque et al., 2021;Nakamura, 1992).
Less attention has been paid to annual cycle of the Siberian storm track which is one of the most important trajectory paths for the boreal winter cold surge in East Asia. Previous studies have shown that more than half of the cold air processes and extreme weather in China come from Siberia. The changes in the storm track and the cooperation of other systems have an impact on the extreme low temperature events in China (see Figure S1; Han et al., 2008;Hu & Huang, 1997;Lu, 2001;Ren et al., 2007;Rogers, 1997;Wen et al., 2006). In addition, since the Siberian storm track is located upstream of the NPST, understanding its annual cycle may also help to explain the annual cycle of the latter according to the "upstream seeding effect" theory. Therefore, examining the annual cycle of Siberian storm tracks and understanding its dynamical reason is of great importance for both the extreme weather prediction and improved understanding of the midwinter suppression phenomenon. In this study, we will examine the climatic annual cycle of Siberian storm tracks and provide a possible physical explanation for it. The paper is organized as follows. Section 2 describes data and method. The annual cycle of Siberian storm tracks is provided in Section 3 and physical explanation is provided in Section 4. Section 5 presents the summary and discussion.

| DATA AND METHODS
The 6-hourly reanalysis data from 1980 to 2021 from the Japan Meteorological Agency (JRA-55) are used here. The data have a horizontal resolution of 2.5 Â 2.5 . Monthly standard deviation of the 24-h difference filtered daily meridional velocity at 300 hPa is used to indicate monthly storm track intensity Wallace et al., 1988). Specifically, where N is the sample size of month, and v 0 the synoptic anomaly of the meridional wind. As discussed in previous studies , the 24-h difference filter highlights the synoptic variability with time scales of 1.2-6 days.
To assess the atmospheric baroclinicity in different months, we use the maximum Eady growth rate that is proportional to the vertical shear of the background westerlies and inversely proportional to the atmospheric static stability. According to Eady (1949), the maximum Eady growth rate can be written as: where f is the Coriolis parameter, N is the 6-hourly Brunt-Väisälä frequency, V is the 6-hourly zonal wind, the overbar in Equation (2) denotes averaging over 1 month or season. z the height, and σ the maximum Eady growth rate. The vertical derivatives of wind speed at 850 hPa are obtained by central difference between 875 and 825 hPa. We define the region of 45 N-65 N, 60 E-100 E as the Siberian storm track key region. And storm track intensity indices are calculated as the normalized monthly or seasonal mean storm track intensity averaged over the key region at 300 hPa. To test the robustness of storm track intensity index, we also perform empirical orthogonal function (EOF) analysis to the seasonal mean storm track intensity in the key region. To analyze the annual cycle of jet stream and Eady growth rate, we first calculate the monthly mean zonal wind and Eady growth rate averaged over the key region (45 N-65 N, 60 E-100 E) and then normalize these fields by monthly standard deviation after removing the annual mean. Figure 1 first shows spatial distributions of the climatological storm track intensity in different months of the whole year. Over the Siberian region, the storm tracks exhibit a pronounced annual cycle, with the strongest intensity in October, and the weakest in June and July. More particularly, the Siberian storm tracks during March and April are isolated and have a moderate intensity and have connected with the downstream NPST. During June and July, the storm tracks disappear. Beginning from August, the Siberian storm tracks become stronger and spatially connected with the upstream NAST. The intensity reaches the strongest in October and then decays in boreal winter. Since the storm track is strongest over 60 E-100 E, 45 E-65 N, we apply a spatial average of storm track intensity over this key region to analyze the annual cycle of Siberian storm track in the following.

| CLIMATOLOGY OF THE SIBERIAN STORM TRACKS
To explicitly examine seasonal variations of Siberian storm track positions, Figure 2a shows the annual cycle of storm track intensity zonally averaged over 60 -100 E. It is clear that the storm track exhibits two peaks throughout the year, with a stronger one in autumn and the other in spring. Furthermore, the latitudinal positions of Siberian storm tracks are more poleward in autumn and winter, with the center located around 55 N, while the center of storm tracks is slightly southward during spring. Figure 2b further displays the annual characteristics of Siberian storm track intensity meridionally averaged over 45 -65 N. From July to F I G U R E 1 Monthly-mean climatological distribution of the storm track during 1980-2020 at 300-hPa (shading, unit: m 2 Ás À2 ). The green frame represents the typical area of Siberian storm tracks (45 -65 N, 60 -100 E).
October, the storm track center gradually moves westward, reaching 60 E in October, and from October to next May, the storm track center moves eastward, up to 85 E in April. Clearly, the more northeastward the centers of Siberian storm track are, the stronger their intensity is.
The variance percentage explained by the first EOF is more than 48% and the highest at 63% in the four seasons, so the corresponding first time series (PC1) can be well used to represent intensity variations of the Siberian storm tracks. Correlation between the defined the Siberian storm tracks intensity index and PC1 reaches 0.99, and exceeds the statistical significance at the 99% confidence level of the Student t test. Such a high correlation indicates that the defined index can represent the intensity variation of the Siberian storm track very well.

| POSSIBLE CAUSES FOR THE ANNUAL CYCLE OF SIBERIAN STORM TRACKS
We further explore the possible reason for shaping the distinct annual cycle of Siberian storm tracks from the perspectives of eddy generation and jet characteristics. Previous studies of synoptic eddy dynamics have suggested that the occurrence and development of eddies is significantly related to the baroclinic growth rate quantifying the eddy generation (Charney, 1947;Eady, 1949;Lim & Wallace, 1991;Lindzen & Farrell, 1980;Park et al., 2010). Some studies have pointed out that the winter suppression of NPST is closely related to jet characteristics (Chang, 2001;Harnik & Chang, 2004;Nakamura, 1992;Nakamura & Sampe, 2002). Figure 2c shows the monthly variations of the Siberian storm track intensity index and the maximum Eady growth rate index at different pressure levels. The maximum Eady growth rate at 850-500 hPa has two peaks in boreal spring and autumn. Comparing the two peaks, the maximum Eady growth rate is consistently varying with the storm track index, except that the baroclinicity is stronger in spring than autumn. This indicates that the annual cycle of Eady growth rate may help explain the annual cycle of Siberian storm track activities. As compared to the dry Eady growth rate in Figure 2c, the moist Eady growth rate in Figure S2c seems to better match the seasonal cycle of storm track intensity. The maximum Eady growth rate can affect the production of baroclinic synoptic eddies and thus the storm track strength. Interestingly, the baroclinic growth rate is significantly weakened in winter, which may be one of the reasons for the winter suppression of the Siberian storm track. This is essentially different from the strong baroclinicity but weak storm track activity in North Pacific.

| The maximum Eady growth rate
To examine specific distributions of the baroclinic growth rate in different months, Figure 3 shows its climatology at 850 hPa in April, July, October, and January. In April, the maximum Eady growth rates are observed in the Siberia. In July, the maximum Eady growth rate decreases over the Siberia but increased slightly over the southern Siberia. In October, the maximum Eady growth rate increases over Siberia again. In January, the maximum Eady growth rate over Siberia slightly decreases. Previous studies have suggested that the region with high maximum Eady growth rate is the main area for generating eddies. The annual cycle of spatial pattern of maximum Eady growth rate indicates that the stronger storm track in spring and autumn is closely related to the baroclinic eddy generation in Siberia (Eady, 1949;Nie et al., 2013;Novak et al., 2018;Robinson, 2000).

| The jet stream characteristics
Here, we examine roles of the annual cycle of jet stream characteristics in shaping Siberian storm track seasonality. Figure 2d further shows the annual cycle of jet stream intensity at different heights in Siberia accompanied with the storm track intensity. The jet intensity has two peaks in spring and autumn, which is consistent with the storm tracks. Figure 4 further shows the vertical structure of jet streams in four typical months. There are two parts of jet streams over the key region: a strong subtropical jet and an eddy-driven jet in midlatitude. As shown in Figure 4, the spring and autumn jet streams in Siberia are centered north of 50 N and resembles more an eddy-driven jet (Figures 4a and 5c). In summer, with the subtropical jet moving northward, the part of eddy-driven jet disappears (Figure 4b), consistent with the observed weakest storm tracks in summer. While in winter, as shown in Figure 4d, the subtropical jet stream becomes strongest and the eddy-driven jet is weaker, which is less efficient to generate midlatitude baroclinic eddies (Yuval et al., 2018). Meanwhile, the wind speed of midlatitude westerly is weaker, compared to spring and autumn. Therefore, the annual cycle of Siberian storm track is closely related to that of the jet characteristics, which is clearly indicated by the in-phase relationship between the Siberian storm track and jet stream intensity. In particular, that the midlatitude jet stream becomes relatively weaker in boreal winter may be responsible for the corresponding weakening of the Siberian storm track. On the one hand, the jet stream, can affect the local eddy generation through altering meridional temperature gradient following the thermal wind balance. On the other hand, the jet stream can affect the horizontal wave propagation by acting as a waveguide. Furthermore, there could be a possible feedback between the jet stream and storm tracks. According to the zonal momentum budget, the eddy-driven jet is mostly affected by eddy momentum flux convergence. The latter is strongly affected by both eddy generation associated with storm track and eddy dissipation. (Baker et al., 2017;Chen et al., 2007Chen et al., , 2013Mbengue & Schneider, 2018;Nie et al., 2016Nie et al., , 2022, which deserves further studies for the Siberian storm tracks. It is also interesting to note that the storm track intensity matches better with the jet stream than the Eady growth rate. This is because the jet stream can modulate the horizontal wave propagation. Figure 5 shows the mean E-vector and its divergence in four seasons. It is clear that the horizontal E-vector in the key region is strongest in autumn, while the local eddy generation is relatively weaker in this season. This suggests that horizontal wave propagation plays an important role in strengthen the autumn storm tracks over Siberia.

| CONCLUSIONS AND DISCUSSIONS
Many progresses have been made to understand the annual cycle of oceanic storm tracks in Northern Hemisphere. Less attention was paid to the continental storm tracks. In this study, we provided an explicit examination of annual cycle of Siberian storm tracks. There is a north-south vacillation with a range of about 5 in the location of the Siberian storm tracks, reaching the northernmost in winter and southernmost in summer during 1 year. It is found that the intensity of storm tracks has two peaks in autumn and spring. The Siberian storm track annual cycle is closely related to the local baroclinic eddy generation and jet characteristics. The strong baroclinicity in spring and autumn, giving rise to more active eddy generation, play a major role in shaping the annual cycle of storm tracks. In addition, the jet characteristics may play an important role in affecting the annual cycle. During spring and autumn, the eddy-driven jet is the strongest, and are consistent with strong baroclinic eddy generation. In contrast, during midwinter, the subtropical jet strengthens and eddy-driven jet is weak, and thus F I G U R E 5 Horizontal distribution of the E vector (vector, 25 m 2 Ás À2 ) and its divergence (shading, 10 À5 mÁs À2 ) for the four seasons of spring (a) summer, (b) autumn, (c) and winter (d)  not favoring strong baroclinic eddy generation. Furthermore, the jet stream can act as a wave guide, which induce the wave packets from upstream to enhance the autumn Siberian storm tracks. These results indicate that the variability of the Siberian storm track may be related to its upstream large-scale atmospheric circulation pattern, which is worthy of examination. The Siberia region is to the north of the Tibetan Plateau, and the baroclinicity may also be affected by the seasonal thermal difference varying due to the plateau effect, making the baroclinicity stronger in spring and autumn but weaker in winter and summer. And the relatively stronger baroclinicity in spring and autumn is related to meridional temperature gradient instead of static stability ( Figure S2). Note that the storm track latitude in different seasons may also affect the annual cycle of storm track intensity. Future work will be conducted to analyze the relationship between the seasonality of Tibetan Plateau heating anomaly and Siberian storm tracks.

SUPPORTING INFORMATION
Additional supporting information can be found online in the Supporting Information section at the end of this article.