Modulation of the impact of winter-mean warm Arctic-cold Eurasia pattern on Eurasian cold extremes by the subseasonal variability

Utilizing ERA5 data, this study provides evidence that both the winter-mean state and subseasonal variability (SSV) of the warm Arctic-cold Eurasia (WACE) pattern significantly influence the frequency of cold extremes in Eurasia. The positive phase of winter-mean WACE (WACEMean) or a stronger SSV of WACE (WACESSV) corresponds to a higher occurrence of cold extremes over central Eurasia and East Asia. Furthermore, the study reveals that the impact of WACEMean on the cold extremes is modulated by WACESSV. During years characterized by a positive WACEMean and enhanced WACESSV, the associated winter-mean anticyclonic anomalies, combined with amplified subseasonal circulation fluctuations over the northern Eurasia continent, contribute to a significant increase in the blocking frequency over the Ural–Siberia region. This, in turn, contributes to an intensified occurrence of cold extremes in central Eurasia and East Asia. In contrast, during the years with a positive WACEMean but reduced WACESSV, in the absence of significant changes in the subseasonal circulation fluctuations, the winter-mean anticyclonic anomalies over the northern Eurasia continent do not exert a significant impact on Ural–Siberian blocking frequency by themselves. Consequently, there are no notable anomalies in the frequency of cold extremes over central Eurasia and East Asia. Finally, this study reveals that the differences in the distribution of the frequency anomalies in the blocking between the two sets of years are attributed to the constructive and destructive superposition of anomalies in subseasonal circulation fluctuations related to the WACEMean and WACESSV.


Introduction
Global warming has been suggested to alter the probabilities of temperature extremes occurring worldwide, leading to increased heatwaves and decreased cold waves (Stott et al 2004, Alexander et al 2006, Peterson et al 2012, Schoetter et al 2015, Screen et al 2015, Herring et al 2016).However, from the late 1980s through the early 2010s, the Northern Hemisphere mid-latitudes, particularly Eurasia region, have experienced a cooling trend and an increase in high-impact cold extremes despite ongoing global temperature rise (Overland et al 2011, Cohen et al 2012, Zhang et al 2012, Johnson et al 2018).In densely populated East Asia, the extreme cold events have not only become more frequent but also stronger and longer-lasting (Woo et al 2012, Tang et al 2013, Sun et al 2016), causing significant disruptions to economies and societies in the region (Gong et al 2014, Wu et al 2017).
The cooling anomalies observed over Eurasia region are closely linked to pronounced warming anomalies in the Arctic, forming a distinct pattern known as the 'warm Arctic-cold Eurasia' (WACE) pattern (Overland et al 2011, Cohen et al 2014).Since the mid-2000s, the winter-mean WACE pattern (WACE Mean ) has consistently shown a persistent positive phase, contributing significantly to the increased occurrence of severe winters in Eurasia (Mori et al 2014, Wang et al 2020b).However, there is ongoing debate regarding whether the changes in the magnitude and polarity of the WACE Mean can be attributed to Arctic sea ice loss (Blackport and Screen 2020, Cohen et al 2020, Zappa et al 2021).Some studies suggest that Arctic sea ice loss contributes to the changes observed in the WACE Mean (Wu et al 2011, 2015, 2022, Mori et al 2014, 2019, Outten et al 2023).Specifically, the background conditions associated recent rapid loss of Arctic sea ice and subsequent rapid Arctic warming favor the more frequent occurrence of Ural blocking highs and intensified Siberian highs, leading to increased occurrence of severe winters (Honda et al 2009, Liu et al 2012, Cohen et al 2014, Mori et al 2014, 2019, Yao et al 2017).However, a significant number of studies based on models have questioned the impact of sea ice on the WACE Mean (Sun et al 2016, Blackport and Screen 2021, Komatsu et al 2022).These studies have found little impact of sea ice on midlatitude variability and multidecadal trends during winter (Ogawa et al 2018, Koenigk et al 2019), or they have detected midlatitude responses to sea ice loss that are much weaker compared to internal variability (Screen et al 2013, McCusker et al 2016, Sun et al 2016).In this context, the changes in the WACE Mean may primarily result from internal variability within the extratropical atmosphere (Sun et al 2016, Jin et al 2020, Wang and Chen 2022).Regardless of whether the change in WACE Mean is driven by sea ice loss, the upper-level Ural blocking highs and the surface Siberian highs are important factors influencing the variability of the WACE Mean (Mori et al 2014).These circulation features are also dominant factors associated with cold extremes in Eurasia, particularly in East Asia (Zhang et al 1997, Wang et al 2010, Park et al 2011, Cheung et al 2012).Hence, changes in the phase of the WACE Mean potentially have implications for modulating Eurasian cold extremes.
Previous research has delved into the impact of the WACE Mean on the winter-mean climate anomalies and the frequency of cold extremes in the Eurasia region (Mori et al 2014, 2019, Wang et al 2020a).Notably, the variation in the WACE pattern has been observed on subseasonal timescale in addition to the seasonal timescale (Yao et al 2017, Kim et al 2021).This highlights the necessity to investigate the influence of the subseasonal variability of the WACE pattern (WACE SSV ), as changes at this timescale can have significant implications for society and ecosystems, particularly if they lead to altered extreme events (Katz and Brown 1992, Schär et al 2004, Martineau et al 2020, van der Wiel and Bintanja 2021).Consequently, this research also aims to examine whether changes in the WACE SSV can modify the relationship between the WACE Mean and the frequency of cold extremes in Eurasia.By doing so, valuable insights can be gained into the complex mechanisms by which the WACE pattern influences cold extremes in Eurasia.

Data and methods
This study primarily utilizes daily and monthly reanalysis data from the European Centre for Medium-Range Weather Forecasts reanalysis version 5 (ERA5) dataset (Hersbach et al 2020).The daily and monthlymean variables are derived from hourly data and include surface air temperature (SAT), sea level pressure (SLP) and 500 hPa geopotential height (Z500).The selected temporal and spatial ranges are from January 1950 to March 2023, with a resolution of 1 • × 1 • .In a study conducted by Yu et al (2021), it was found that the ERA5 temperature field shows good consistency with buoy observations, although there may be some warm biases present.This confirms the reliability of ERA5 data in accurately reflecting climate variations in the Arctic region.
The calculation of daily anomalies for any variable was conducted using the following procedure: firstly, a 10 d low-pass filter was applied to the daily mean atmospheric data in order to eliminate fluctuations associated with synoptic-scale baroclinic waves.Subsequently, for a specific date, an anomaly field was defined as the deviation of the lowpass filtered field for that particular date from the daily climatological-mean annual cycle.In order to quantify the strength of subseasonal variability (SSV), the standard deviation of the daily anomalies was calculated for each grid point during the winter season (December-February, DJF) for each year.This methodology aligned with the approach presented in Nakamura (1996).To identify cold extreme dates, the daily SAT anomalies were compared to the 5th percentile of the distribution of SAT anomalies for the winter season spanning from 1950/51 to 2022/23.Cold extreme dates were determined as instances when the SAT anomaly fell below this threshold, using the methodology employed in Martineau et al (2020).Blocking events in this study were defined following the method used in previous studies (Liu et al 2012, Tang et al 2013).Specifically, blocking events were identified as intervals when the daily SLP anomalies were higher than 1.5 standard deviations from the climatological mean for each grid cell, persisting for a minimum duration of five consecutive days.
To extract the WACE pattern, an empirical orthogonal function (EOF) analysis was employed, as done in previous studies (Mori et al 2014, Wang et al 2020a).In this study, the EOF analysis was applied to the daily SAT anomalies during winter, covering the region from 0 • to 180 • E and 30 • to 90 • N, over the period from 1950/51 to 2022/23.To ensure equal weighting of areas in the analysis, the SAT anomalies were weighted by the cosine of latitude, providing equal weightage to individual grid points (North et al 1982).The two leading EOF patterns explained approximately 33% of the total variance.The first leading EOF pattern (EOF1) accounted for 20% of the total variance and showed SAT anomalies associated with the Arctic oscillation (AO) (figure S1(a)).The second leading EOF pattern (EOF2) accounted for 13% of the total variance and exhibited the typical WACE anomaly pattern, featuring pronounced warming over the Barents-Kara region and significant cooling spreading over the central and eastern parts of the Eurasian continent (figure S1(b)).Therefore, the second principal component (PC2) was considered as the WACE index.Subsequently, the winter-mean state and SSV of the WACE pattern were quantified as the WACE Mean index and WACE SSV index, respectively.The WACE Mean index represents the average value of daily WACE index during the winter season of each year.On the other hand, the WACE SSV index is calculated as the standard deviation of the daily WACE index during the winter season for each year.

Influence of WACE Mean and WACE SSV on Eurasian cold extremes
To investigate the climatic influence of the WACE Mean and WACE SSV , we analyze the regressed anomalies of winter-mean SAT (SAT Mean ), SSV of SAT (SAT SSV ), and cold extreme frequency onto the normalized WACE Mean index and WACE SSV index, respectively.As depicted in figures 1(a) and (d), the regressed patterns of SAT Mean on the normalized WACE Mean index and WACE SSV index exhibit distinct differences.Additionally, the associated anomalous patterns of SAT SSV with the two indices are also markedly different (figures 1(b) and (e)).However, the positive values of both indices demonstrate an increasing tendency in the frequency of cold extremes over central Eurasia and East Asia (figures 1(c) and (f)).These changes in cold extreme frequency, which are associated with the WACE Mean , are primarily driven by the variations in SAT Mean .When the WACE Mean is in its positive phase, cold extremes occur more frequently in regions of central Eurasia and East Asia where SAT Mean is colder, while they are less frequent in the Barents-Kara Sea regions where SAT Mean is warmer (figures 1(a) and (c)).In contrast, the regressed pattern of SAT SSV onto the normalized WACE Mean index is very different from the regressed pattern of cold extreme frequency (figures 1(b) and (c)).This suggests a limited influence of associated anomalous SAT SSV on the frequency of extreme cold events.
On the other hand, a stronger WACE SSV corresponds to a significant enhancement in SAT SSV but no significant changes in the SAT Mean in central Eurasia and East Asia (figures 1(d) and (e)).A study conducted by Song et al (2018) has emphasized the crucial role of subseasonal variations in triggering cold events in East Asia, with more than half of the temperature anomalies attributed to these variations.In this context, a stronger SAT SSV , which corresponds to a wider range of subseasonal SAT fluctuations, can also increase the likelihood of cold extremes.Therefore, even in the absence of significant reductions in SAT Mean , the enhanced SAT SSV in central Eurasia and East Asia, associated with a stronger WACE SSV , also contributes to an increased likelihood of cold extreme in these regions (figures 1(d)-(f)).Furthermore, it is observed that a stronger WACE SSV corresponds to enhanced SAT SSV over the Barents-Kara Sea region, but it does not have a significant impact on the frequency of cold extremes in this particular region ( figures 1(e) and (f)).This can likely be attributed to the primary influence of other factors, such as WACE Mean , in determining extreme cold events in the Arctic region, as depicted in figures 1(a) and (c).Furthermore, although a stronger WACE SSV corresponds to a decrease in SAT Mean anomalies over high-latitude regions of the Eurasian continent, these SAT Mean anomalies do not translate into changes in the frequency of cold extremes (figures 1(d) and (f)).
As previous studies have indicated, variations in SAT on both subseasonal and seasonal timescales over the Eurasian continent are closely linked to changes in atmospheric circulation anomalies (Wang andChen 2014, Song andWu 2017).Therefore, further investigation was conducted into the changes in the anomalies of winter-mean atmospheric circulation and the strength of the subseasonal circulation fluctuations, represented by the SSV of SLP (SLP SSV ) and Z500 (Z500 SSV ). Figure 2 displays the regressed anomalies of winter-mean SLP (SLP Mean ), SLP SSV and blocking frequency onto the standardized time series of WACE Mean index and WACE SSV index, respectively.We observe that the positive phase of WACE Mean is associated with positive anomalies in SLP Mean over the Ural-Siberian region (figure 2(a)).This indicates a strengthening of the surface Siberian High, which is a direct dynamical factor to link warm Arctic to cold Eurasia (Wu et al 2015, Wu 2017, Wu and Ding 2023).Meanwhile, there are significant increases in winter-mean Z500 (Z500 Mean ) around the Ural Mountains during the positive phase of WACE Mean (figure S3(a)).These findings are consistent with previous research conducted by Mori et al (2014).Additionally, we observed that the strength of the subseasonal circulation fluctuations over the Ural region, represented by the SLP SSV and Z500 SSV , tends to be more pronounced during the positive phase of WACE Mean (figures 2(b) and S3(b)).The amplification of subseasonal circulation fluctuations may be attributed to the fact that the positive phase of WACE Mean corresponds to reduced temperature gradients (figure 1   of blocking events occurring over the Ural-Siberian region (figure 2(c)).
The positive WACE SSV index is associated with positive SLP Mean anomalies over the Ural region and increased SLP SSV anomalies over the Ural-Siberian region (figures 2(d) and (e)).These anomalies also contribute to an increased likelihood of blocking events occurring over the Ural-Siberian region (figure 2(f)).The variations in the WACE SSV are highly correlated with changes in both SLP SSV and Z500 SSV (figures 2(e) and S3(d)).However, in the corresponding winter-mean anomalies, only significant changes are observed in SLP Mean and not in Z500 Mean (figures 2(d) and S3(b)).The SLP Mean anomalies associated with a stronger WACE SSV display characteristics similar to the negative phase of AO (figure 2(d)).This finding is consistent with previous research indicating that the negative wintermean AO is associated with an enhancement in subseasonal temperature variability in Eurasia (Gong andHo 2004, Jeong andHo 2005).
In summary, the SLP Mean and SLP SSV anomalies associated with both WACE Mean and WACE SSV contribute to altering the likelihood of events over the Ural-Siberian region.Since blocking events in this region play a vital role in the occurrence of cold extremes across central Eurasia and East Asia (Yao et al 2017, Ma et al 2018), the probability of experiencing cold extremes in these regions undergoes significant changes associated with variations in both WACE Mean index and WACE SSV index.

Modulation of the influence of WACE Mean on Eurasian cold extremes by WACE SSV
The aforementioned findings suggest that both of the WACE Mean and WACE SSV can significantly impact extreme cold events in central Eurasia and East Asia.Importantly, since the interannual variations of these two factors are independent, with a correlation coefficient of only 0.14 between the detrended time series of the two indices, their effects on the Eurasian cold extremes can be either consistent or contrasting.To investigate whether the WACE SSV can modulate the influence of the WACE Mean on Eurasian cold extremes, the years with a positive WACE Mean index were divided into two groups: +WACE Mean /+WACE SSV years when the normalized WACE SSV index is larger than zero, and +WACE Mean /−WACE SSV years when the WACE SSV index is less than zero.This resulted in 18 yr identified as +WACE Mean /+WACE SSV years and 19 yr as +WACE Mean /−WACE SSV years.Figures 3(a This finding suggests that, when the WACE SSV index is negative, the positive phase of the WACE Mean no longer promotes the occurrence of cold extremes over Eurasia.Therefore, it can be concluded that the WACE SSV greatly modulates the influence of the WACE Mean on Eurasian cold extremes. In consideration of the crucial role played by blocking events over the Ural-Siberian region in driving Eurasian cold extremes, we further examined the composite anomalies of blocking frequency during the +WACE Mean /+WACE SSV years and +WACE Mean /−WACE SSV years.As depicted in figures 3(c) and (d), the differences in the distribution of cold extreme frequency anomalies between the two sets of years can be attributed to variations in the frequency of blocking events over the Ural-Siberian region.Figure 3(c) shows a significant increase in blocking frequency over the Ural-Siberian region during +WACE Mean /+WACE SSV years, corresponding to the heightened occurrence of cold extremes observed across central Eurasia and East Asia.Conversely, figure 3(d) shows no significant change in Ural-Siberian blocking frequency during +WACE Mean /−WACE SSV years, resulting in no significant anomalies in the frequency of cold extremes in Eurasia.These results suggest that the modulation by the WACE SSV influences the frequency of blocking events over the Ural-Siberian region.This modulation, in turn, affects the occurrence frequency of cold extremes in central Eurasia and East Asia.
One question that arises is the possible mechanism responsible for the difference in blocking frequency anomalies between the +WACE Mean /+WACE SSV and +WACE Mean /−WACE SSV years.To understand this, we examine the composite patterns of SLP Mean and SLP SSV anomalies for the +WACE Mean /+WACE SSV and +WACE Mean /−WACE SSV years in figure 4, considering their crucial role in altering blocking frequency.In figures 4(a) and (b), +WACE Mean /+WACE SSV and +WACE Mean /−WACE SSV exhibit pronounced increases in SLP Mean anomalies in the northern of the Eurasian continent.These anomalies closely resemble the regression pattern associated with the positive WACE Mean shown in figure 2(a).This suggests that the constructive and destructive superposition of the SLP Mean anomalies related to the WACE Mean and WACE SSV plays a limited role in explaining the differences in blocking frequency anomalies.However, there are substantial differences in the composite patterns of SLP SSV anomalies between the two groups.In +WACE Mean /+WACE SSV years, the constructive superposition of SLP SSV anomalies related to the WACE Mean and WACE SSV leads to a significant enhancement of SLP SSV over the Ural-Siberia region.This enhancement aligns closely with the regions of positive SLP Mean anomalies (figures 4(a) and (c)).Consequently, the combined effect results in an increase in the frequency of blocking events in the region.In contrast, during +WACE Mean /−WACE SSV years, the destructive superposition of SLP SSV anomalies leads to no significant changes in SLP SSV over the northern Eurasian continent (figure 4(d)).Without a notable enhancement in subseasonal SLP fluctuations, the increase in SLP Mean alone does not seem sufficient to influence the blocking frequency over the northern Eurasian region.These findings indicate that the differences in the distribution of blocking frequency anomalies in the Ural-Siberian region can be partly attributed to the constructive and destructive superposition of SLP SSV anomalies related to the WACE Mean and WACE SSV .b), but for the SLPSSV (hPa).The dotted areas denote the anomalies that are significant at the 95% confidence level according to the Student's t-test.

Summary and discussion
Utilizing ERA5 data, this study has found that both the WACE Mean and WACE SSV play significant roles in shaping cold extremes over Eurasia.The frequency of cold extremes in Eurasia shows an increasing tendency associated with the positive WACE Mean , primarily driven by variations in SAT Mean .Regions with colder SAT Mean , such as central Eurasia and East Asia, exhibit more frequent cold extremes.Additionally, a stronger WACE SSV corresponds to an enhancement of SAT SSV in Eurasia, particularly in central Eurasia and East Asia.This wider range of subseasonal SAT fluctuations also contributes to an increased likelihood of extreme events in these regions.
The study further reveals that the WACE SSV modulates the influence of the WACE Mean on Eurasian cold extremes.Specifically, during years with both a positive WACE Mean and enhanced WACE SSV (+WACE Mean /+WACE SSV years), there is a notable increase in the occurrence of cold extremes over central Eurasia and East Asia.Conversely, during years with a positive WACE Mean but reduced WACE SSV (+WACE Mean /−WACE SSV years), the anomalies in cold extreme frequency diminish.These differences can be attributed to changes in blocking frequency over the Ural-Siberian region.The +WACE Mean /+WACE SSV years exhibit a significant increase in blocking frequency, corresponding to the heightened occurrence of cold extremes in central Eurasia and East Asia.However, the +WACE Mean /−WACE SSV years show no significant changes in blocking frequency, leading to no significant anomalies in cold extreme frequency in this region.
An analysis of the underlying mechanisms reveals that the constructive and destructive superposition of SLP SSV associated with the WACE Mean and WACE SSV play a crucial role in shaping the blocking frequency over Ural-Siberian region.During +WACE Mean /+WACE SSV years, due to the constructive superposition of SLP SSV anomalies related to the WACE Mean and WACE SSV , there is an enhancement of subseasonal SLP fluctuations over the Ural-Siberia region, closely aligned with the regions of positive winter-mean SLP anomalies.This combined effect leads to an increase in blocking activity and the occurrence of cold extremes.Conversely, during +WACE Mean /−WACE SSV years, the destructive superposition of the SLP SSV anomalies associated with WACE Mean and WACE SSV results in no significant changes in subseasonal SLP fluctuations over the northern Eurasian continent.In the absence of a substantial enhancement in subseasonal SLP fluctuations, the increase in SLP Mean is not sufficient to significantly alter the blocking frequency over the northern Eurasian region.
In this study, blocking events were defined as positive SLP anomalies that persist for an extended period.Previous studies have commonly used the two-dimensional blocking index, calculated using meridional gradients of Z500, to detect blocking events (Davini et al 2012, Wang et al 2021).Applying this method, we also observed a significant increase in the frequency of blocking events around the Ural Mountains during the positive phase of the WACE Mean or with a stronger WACE SSV .However, it is important to note that the positive anomalies in blocking frequency, determined by meridional gradients of Z500, are primarily observed in the Ural region and do not extend to the Siberian region (figure S4).Furthermore, the modulation of the influence of the WACE Mean on blocking events by the WACE SSV remains evident even when using the method of meridional height gradients (figure S5), enhancing the reliability and robustness of our conclusions.
Our study highlights the importance of understanding the mechanisms driving changes in WACE SSV .Previous studies have indicated a decrease in SAT SSV over northern high latitudes during winter due to the decreased meridional temperature gradients associated with Arctic amplification (Screen 2014, Collow et al 2019, Blackport et al 2021, Dai and Deng 2021).Blackport et al (2021) further suggested that the decreasing SAT SSV in the northern extratropics is attributed to human influence.However, it is worth noting that the weakening in SAT SSV primarily occurs in high-latitude regions and not in central Eurasia and East Asia, indicating limited impact from anthropogenic forcing on WACE SSV .Previous studies have emphasized the influence of the winter-mean AO on SAT SSV in East Asia, based on observed statistical connections (Gong andHo 2004, Jeong andHo 2005).This highlights the potential impact of the atmospheric mean flow on WACE SSV , given the close linkage between WACE SSV and SAT SSV in East Asia.However, it is important to note that the change in WACE SSV cannot be simply attributed to the anomalous atmospheric mean flow.This is because changes in the self-interaction among associated subseasonal eddies can also alter the seasonal-mean flow (Cai and Van Den Dool 1994, Feldstein 2002, 2003).Therefore, further investigation is necessary to better understand the relationship between the winter-mean flow and WACE SSV .
(a)) and a more meandering jet, which are favorable for the development of subseasonal Rossby waves (Francis and Vavrus 2012, Liu et al 2012, Tang et al 2013).The presence of positive winter-mean anticyclonic anomalies, coupled with a wider range of subseasonal fluctuations in atmospheric circulation, results in an increased probability

Figure 1 .
Figure 1.Regressed anomalies of (a) SATMean ( • C), (b) SATSSV ( • C) and (c) cold extreme frequency (%) onto the standardized time series of WACEMean index.(d)-(f) are the same as (a)-(c), but for the regressed anomalies onto the standardized time series of WACESSV index.The dotted areas denote the anomalies that are significant at the 95% confidence level according to the Student's t-test.

Figure 2 .
Figure 2. Regressed anomalies of (a) SLPMean (hPa), (b) SLPSSV (hPa) and (c) blocking frequency (%) onto the standardized time series of WACEMean index.(d)-(f) are the same as (a)-(c), but for the regressed anomalies onto the standardized time series of WACESSV index.The dotted areas denote the anomalies that are significant at the 95% confidence level according to the Student's t-test.
) and (b) examines the composite frequency anomalies of cold extremes during +WACE Mean /+WACE SSV years and +WACE Mean /−WACE SSV years.The composite anomalies during +WACE Mean /+WACE SSV years exhibit a well-organized and statistically significant pattern.Notably, a significant increase in the frequency of cold extremes can be observed over central Eurasia and East Asia during +WACE Mean /+WACE SSV years (figure 3(a)).In contrast, during +WACE Mean /−WACE SSV years, the anomalies of the cold extreme frequency nearly disappear over the Eurasian continent (figure 3(b)).

Figure 3 .
Figure 3. Composite anomalies of cold extreme frequency (%) for (a) +WACEMean/+WACESSV and (b) +WACEMean/−WACESSV years, respectively.(c), (d) are the same as (a), (b), but for the blocking frequency (%) anomalies.The dotted areas denote the anomalies that are significant at the 95% confidence level according to the Student's t-test.
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