Subseasonal swing of cold and warm extremes between Eurasia and North America in winter of 2020/21: initiation and physical process

Eurasia and North America experienced a robust subseasonal swing of surface air temperature (SAT) extremes in 2020/21 winter, featuring severe cold (warm) extremes over Eurasia before (after) 15 January and conversely over North America. This sharp subseasonal swing of intercontinental cold and warm extremes exerted considerable severe impacts on human activities and the global economy. Here we examined the initiation and physical process based on data analyses. Our results show annual cycle (AC) anomalies of SAT caused this subseasonal alternating of temperature extremes in two regions. The AC anomalies of SAT are regulated by the phase transition of the North-Pacific-Oscillation-like (NPO-like) circumglobal Rossby wave (CRW) train. Unprecedented warming sea surface temperature over midlatitude Northwest Atlantic in early winter initiated a positive phase of the NPO-like CRW train, via eddy-mediated physical processes and the resultant feedback of sea ice loss over the Barents-Kara Seas. While, the subsequent downward feedback of stratospheric processes resulted in the negative phase of the NPO-like CRW pattern in late winter. This work advances the understanding of the subseasonal predictability of SAT extremes from impacts of AC anomalies and intercontinental seesawing.


Introduction
In a winter with weak seasonal mean anomalies of surface air temperatures (SATs), frequent and alternative occurrences of both bitterly cold waves and extremely warm spells are commonplace (Geng et al 2017, Ma et al 2018, Dai and Fan 2022. Observations show that the subseasonal variability of wintertime SATs is distinct under the frequent influence of largescale recurrent circulation patterns, also referred to as 'weather regimes' (Gong and Ho 2004, Cattiaux et al 2010, Lin 2018. Dramatic swings between persistent cold and warm spells sometimes occur within a winter. For example, western Europe was exposed to more than two weeks of exceptionally cold conditions after a mild start during the winter of 2011/12 (de Vries et al 2013); China witnessed remarkable temperature volatility during the winter of 2007/08, featured by a warm early winter contrasting with a severely cold and snowy late winter (Liu et al 2012); East Asia and northern Europe experienced an extreme cold spell during mid-to-late January 2016 after remarkably warmer than normal SATs (Geng et al 2017). Large-scale extreme cold spells assailed Eurasia and North America in the early and late boreal winter of 2020/21 (Yu et al 2022, Zhang et al 2022a, 2022b. In early winter, when Eurasia persistently suffered from a severe cold spell, North America experienced unusually mild weather. However, this pattern reversed in late winter (Cohen et al 2021, Coumou 2021. These seesaw temperature extremes exerted considerable impact on human activities and the global economy (WMO 2022).
The conspicuous subseasonal variability of winter SATs can alter the risks of regional extreme cold and warm episodes (Katz and Brown 1992), which directly affects sectors of energy demand, transport disruption and social emergency protection systems. This subseasonal variability falls in a 'gap' between weather forecasting and long-range climate prediction. Because of the influence of both the initial conditions of the atmosphere and the more slowly evolving boundary conditions, how to improve the subseasonal predictability remains a great challenge (Vitart et al 2017, White et al 2017, Mariotti et al 2020. In recent decades, considerable progress has been achieved in identifying the potential sources of subseasonal predictability, associated with dynamical processes and the forecast skill (Vitart et al 2017, Lang et al 2020, Xiang et al 2020. Of which, the activity of stratosphere polar vortex, sea surface temperature (SST), and sea ice have been considered major potential sources of subseasonal predictability due to their persistent and slowly varying circulation anomalies (Baldwin et al 2003, Kim et al 2014, Geng et al 2017, White et al 2017. It was suggested that warmer SST anomalies along the Gulf Stream can excite an Atlantic-Eurasian (EU) teleconnection that amplify over the Barents Sea region via interacting with sea-ice anomaly and enhance cold anomalies over Eurasia (Sato et al 2014, Wang et al 2019, Jin et al 2020. While, low Barents-Kara Sea sea ice can induce a weakening of the stratospheric polar vortex and subsequently result in low temperatures in mid-latitudes via downward influence at the subseasonal timescale (Kim et al 2014. Coinciding with the case of 2020/21, the observed sea ice cover in the Barents-Kara Seas and SST in the midlatitude Northwest Atlantic were the lowest and highest on record in December 2020, followed by a major sudden stratospheric warming event in January 2021 (Zhang et al 2022b). However, whether the co-occurrence of these events was a coincidence or there was a physical linkage remains unknown. Here, we intend to explore the initiation and physical processes regulating the subseasonal swing of intercontinental opposite SAT anomalies during the winter of 2020/21. Our results suggest that the unprecedented Northwest Atlantic warming caused a positive EU-like pattern and triggered the subsequent operation of multiple feedback mechanisms, resulting in a subseasonal swing of intercontinental temperature extremes in winter of 2020/21. Our result provides an important implication for the subseasonal predictability of extreme temperature events based on the impact of annual cycle (AC) anomalies and intercontinental seesawing.

Data
The daily and monthly atmospheric field data are from the Japanese 55-year Reanalysis (JRA-55) (Kobayashi et al 2015), the daily and monthly SST data are from the National Oceanic and Atmospheric Administration (NOAA) high-resolution Optimum Interpolation SST version 2.1 dataset (Banzon et al 2020) and Extended Reconstructed SST version 5 (ERSST v5, Huang et al 2017), and the daily and monthly sea ice concentration (SIC) data on a grid of 25 km × 25 km are from the NOAA/national snow and ice data center (NSIDC) Climate Data Record of Passive Microwave SIC, version 4 (Meier et al 2021).

Harmonic analysis
Due to intrinsic nonlinearities in the climate system, the response of the Earth's climate system to periodic solar forcing is not the same year after year but is an amplitude-frequency modulated AC (Wu et al 2008, Stine et al 2009, Yu et al 2022. Following Yu et al (2022), we conducted a harmonic decomposition using the Fourier transform to identify the AC (periods longer than 90 days), intraseasonal oscillation (ISO, periods of 10-90 days) and synoptic variation (periods shorter than 10 days) from the original field. The yearly AC component is defined as the annual mean plus the first three harmonics of the raw daily data from 1 July to the following 30 June, omitting 29 February in leap years, whereas ISO and synoptic components are defined as the sum of the 4th to 36th harmonics and residual, respectively. The AC anomaly is defined as the difference between the yearly AC and the climatological mean AC.

Statistical analysis
The statistical significance of the linear regressions and correlations were calculated using a two-tailed Student's t test with the effective degrees of freedom estimated following Kosaka et al (2012). To determine the major modes of SAT variation, we performed an empirical orthogonal function (EOF) analysis of AC anomalies of SAT poleward 20 • N after being weighted by the square root of the cosine of the latitude. We calculated the wave activity flux (WAF), which is parallel to the local group velocity of stationary Rossby wave and can be used to depict the propagation of the atmospheric wave train, using the method of Plumb (1985). Rossby wave source was calculated following Sardeshmukh and Hoskins (1988) to detect the origin of the wave train. The Eady growth rate (Lindzen and Farrell 1980) was calculated to diagnose the changes in baroclinicity. The geopotential height tendency induced by transient eddies was diagnosed following Lau and Holopainen (1984).

Climatic indices
The cold (warm) extremes were defined as the days with daily SAT anomalies lower (higher) than the 10th (90th) percentile value of the daily SAT anomaly distribution during the entire analysis period. The leading EOF mode of 500 hPa geopotential height anomalies poleward of 20 • N in the winters (december-january-february, DJF) of 1958/1959-2020/2021 is an annular mode (see supplementary figure S1(a)), which resembles the Arctic Oscillation (AO) identified by Thompson and Wallace (1998). The second mode features a nonannular circumglobal Rossby wave (CRW) train (supplementary figure S1(b)) with an EU-like pattern over the Atlantic-Eurasia sector (Wang et al 2019) and a North-Pacific-Oscillation-like (NPO-like) pattern over the Pacific-North-America (PNA) sector (Linkin and Nigam 2008). Here, we refer to EOF1 and EOF2 as the AO and circumglobal-NPO (CNPO) patterns, respectively. The daily AO (CNPO) index was then computed by projecting the AO (CNPO) pattern onto the daily 500 hPa geopotential height anomalies.

Dominant mode of the AC anomalies of SAT and the circulation regime
In the winter of 2020/21, most of the high-latitude regions in the northern hemisphere (NH) experienced a warm seasonal mean SAT anomaly mainly due to Arctic-amplified warming, and robust warming appeared over northeastern Canada and the Barents-Kara Seas (figure 1(a)). The seasonal SAT mean in Siberia stands out as the most below normal, but it is still within the normal fluctuation range. Except for the Mediterranean, weak seasonal mean SAT anomalies appeared in most midlatitude regions, but warm and cold extremes more frequently coexisted over Eurasia and North America, resulting in extremely positive standard deviation anomalies of the daily SAT ( figure 1(b)). The large daily SAT variability was dominated by the anomalous AC component (supplementary figure S2), implying a strong subseasonal phase transition of AC SAT anomalies in this winter (figure 1). The daily SAT averaged over the NH midlatitude exhibited the polarity of AC anomalies, which changed from a strongly negative phase in early winter to an extremely positive phase in late winter over Eurasia and conversely over North America (figures 1(c) and (d)). Superimposed by the ISO component, Eurasia experienced an unusual cold surge and excessively warm weather in early and late winter. In contrast, North America suffered from extremely warm and cold SATs in early and late winter. Figure 1(e) shows the EOF analysis of the AC anomalies of the daily SAT poleward of 20 • N in the winter of 2020/21. EOF1 accounted for 63.8% of the total variance and showed a dipole pattern in the Western Hemisphere, where larger negative and positive loadings appear over eastern Eurasia and the Barents-Kara Seas, respectively. In the Eastern Hemisphere, the warmer AC SAT anomalies dominated most of the North American continent. The principal component (PC1) changed from the positive to negative phase in mid-January, which implies an intercontinental alternation of cold spell from eastern Eurasia to North America, characterized by a subseasonal out-of-phase change in this winter (figure 1(f)). The time series of PC1 was significantly correlated with the time evolution of the AC SAT anomalies averaged over North America and eastern Eurasia, with zero contemporaneous correlation coefficients (r) of 0.58 and −0.86, respectively. The maximum r of −0.88 (0.67) between PC1 and the anomalous AC SAT over Eurasia (North America) was observed when PC1 lags (leads) the Eurasia (North America) SAT index by four (five) days. The zero contemporaneous r between the AC anomalous indexes of SAT in eastern Eurasia and North America was −0.55, and the maximum r of −0.72 was calculated when the Eurasia AC index leads North America by six days. All of the above correlation coefficients were statistically significant at the 0.01 level. Figure 2 shows the PC1-regressed anomalous circulation in winter of 2020/21. During the cold spell dominating Eurasia, the entire northern Eurasia was occupied by a large-scale positive SLP anomaly (shading in figure 2(a)). Two ridges over the higher SLP extended southward along the Ural Mountains and eastern flank of the Tibetan Plateau. Accordingly, northerly surface winds prevailed over northern Asia, enhancing the southward invasion of the cold wave. As a result of the southerly winds over Europe, warmer SAT anomalies appeared over the Barents and Kara Seas. During the warm spell dominating North America, Alaska exhibited a strongly negative SLP, while a weakly enhanced SLP center appeared over the western United States. The resulting large zonal SLP gradient enhanced the southerlies over the west coast of North America, carrying relatively warm and moist air to the continent.
In the mid-troposphere, the PC1-regressed circulation anomalies featured a CRW train pattern consisting of the EU-like and NPO-like wave trains over the Atlantic-EU and Pacific-American sections. Two strongly anomalous anticyclones were situated over the central North Atlantic and northern Siberia, and two cyclonic centers were located over Western Europe and East Asia. This resembled the positive phase of the EU teleconnection pattern. In the PNA section, two anomalous anticyclones were situated over the subtropical North Pacific and North America, and a strongly anomalous cyclone was located near Alaska. This resembled the positive phase of the NPO teleconnection pattern. The anomalous anticyclone and cyclone over the Ural Mountains and East Asia enhanced the Ural blocking high and East Asian trough, respectively. The counterparts over Alaska and North America suppressed the Alaska blocking high and North American trough, respectively. This anomalous CRW train pattern highly resembled the CNPO pattern, defined as the EOF2 of wintertime smoothed monthly anomalous H500 over the extratropical NH (supplementary figure S1(b)). In addition, the PC1-regressed CRW train exhibited a  mostly equivalent barotropic structure except over East Asia and eastern North America. It emanated from an anticyclonic center over the North Atlantic with a strongly anomalous upper-level Rossby wave source ( figure 2(b)), which matched the positive SST anomalies over the midlatitude North Atlantic and thus indicated the potential forcing of the underlying SST anomalies.

Initiation of the CRW by the warming SST in North Atlantic Ocean
The PC1-regressed SSTa exhibited a tripolar structure over the North Atlantic, with stronger warming in the midlatitude Northwest Atlantic, sandwiched by colder anomalies in the subpolar North Atlantic and weak cold anomalies in the subtropical latitudes. The area-mean AC of daily SSTa over the midlatitude Northwest Atlantic (30 • -48 • N, 40 • -70 • W) was highly correlated with PC1 (figures 1(f) and 2(g)), with a zero contemporaneous r of 0.95. It should be noted that the AC of SST in early winter has persistently set new records since 1981 over the midlatitude Northwest Atlantic (red dots in figure 2(g)). The meridional SST gradient was enhanced and reduced to the north (south) of the warm SSTa over the Northwest Atlantic. As a result, the low-level baroclinicity revealed by the Eady growth rate was enhanced (reduced) over the high (mid)-latitude North Atlantic (figure 2(c)). Accordingly, the activity of the transient eddies was enhanced (reduced) to the north (south) of the climatological-mean North Atlantic storm track (figure 2(d)). Therefore, eddy vorticity forcing induced a positive geopotential height tendency (figure 2(e)), which possibly initiated the anticyclonic center and wave source of the CRW train ( figure 2(b)).
To verify the effect of AC SST warming over the midlatitude North Atlantic in historical winters, we calculated regression of atmospheric components against the normalized, detrended and three-monthsmoothed monthly SST anomalies averaged over the midlatitude Northwest Atlantic during the winters of 1958/59-2019/20 (figure 3). The atmospheric baroclinicity increased significantly over the high-latitude North Atlantic due to the increased meridional SST gradient over the Northwest Atlantic ( figure 3(a)). The activity of the transient eddy was enhanced significantly to the north of the climatological storm track ( figure 3(b)). A significant barotropic anticyclonic tendency was induced over the North Atlantic via the resultant eddy vorticity forcing (figure 3(c)), which resulted in the Atlantic source of the EU-like wave train (figure 3(e)). The anomalous anticyclone, as part of the eastward propagating wave train over northern Siberia, reduced the local SIC (figure 3(d)), which in turn reinforced the anomalous anticyclone by the turbulent heat flux from the ocean to the atmosphere and excited the WAF moving southeastward to the North Pacific (figure 3(f)). Combined with the strong Pacific jet and thermal contrast between colder Asia and warmer North Pacific in climatology, an NPO-like circulation pattern developed and was maintained over the PNA sector. In general, the response of the remarkable anomalous circulation of the positive CNPO-like train to the historical warm SST anomalies in the midlatitude Northwest Atlantic resembled the anomalous AC-related circulation regime in the early winter of 2020/21, implying that the observed positive CNPO-like train in the early winter of 2020/21 was possibly driven by the extremely warming SST over the Northwest Atlantic.

Feedback of rapid sea ice loss in the Barents-Kara Seas
The anomalous westerly winds on the northern flank of the anticyclone over the North Atlantic intensified the eastward transport of relatively warm and moist ocean air (figures 2(b) and 3(e)). Meanwhile, the southerly winds on the western flank of the anticyclone of the CRW train led to the anomalous poleward transport of warm air, which resulted in rapid sea ice melting in the Barents-Kara Seas (figures 2(f) and 3(d)). The sea ice declined concurrently with negative turbulent heat anomalies (figures 2(f) and 3(d)) and an implication of more heat flux from the ocean to the atmosphere and warming the local SAT and air temperatures aloft. The feedback forcing of sea ice loss amplified the anomalous anticyclone over northern Siberia, as indicted by the Rossby wave source and increased WAF from the Barents-Kara Sea-Ural Mountain ridge southeastward to Siberia (figures 2(b), 3(e) and (f)). Consequently, a meridional dipole circulation structure was formed with cyclonic and anticyclonic anomalies over northern and southern East Asia. The anomalous westerly over East Asia acing on the zonal gradient of climatological temperature between the colder Asia and the warmer Pacific can trigger the growth of a positive NPO (Sung et al 2021). Ultimately, the CRW train resembles the positive phase of the EU and NPO-like circulation regimes, which favors extremely cold and warm SATs over eastern Eurasia and North America, respectively.

Wave reflection in the stratosphere
The positive phase of the CNPO pattern interfered constructively with climatological planetary waves of the zonal wavenumber-1 component. The superposition of the anomalous anticyclone and cyclone over the North Atlantic and subpolar Pacific on the ridge and trough of the climatological planetary wavenumber-1 component, respectively ( figure 4(a)). The amplitude of the planetary wavenumber-1 component was thus increased, and the upward injection of planetary wave activity into the stratosphere was enhanced  ( figure 4(b)), implying stronger wave reflection from the stratosphere to the troposphere. The tropospheric planetary waves consequently amplified and shifted eastward, leading to an anomalous anticyclone over Alaska (supplementary figure S3), favoring the occurrence of a negative NPO pattern. Along with the persistently positive anomaly of the CNPO pattern in the early winter of 2020/21 (figure 4(c)), the positive upward WAF anomaly over eastern Siberia persisted for approximately two months (figure 4(d)). After the peak time of the positive CNPO index on approximately 2 January 2021, the upward WAF anomaly over eastern Siberia weakened, while the downward WAF over Canada strengthened (figures 4(c) and (d)). A tropospheric anticyclonic anomaly subsequently occurred over Alaska and gradually became stronger (supplementary figure   S4). The CNPO index transitioned into a negative phase and reached extreme negative conditions when the downward WAF over Canada reached its maximum (figures 4(c) and (d)). As a response to the transition from an anomalous anticyclone (cyclone) into cyclone (anticyclone) over Ural Mountain (Alaska), a cold (warm) Eurasia (America) in early winter correspondingly turned into a warm (cold) Eurasia (North America) in late winter.

Discussion
Our results demonstrate that the CRW train associated with the subseasonal swing of intercontinental SAT extremes in winter of 2020/21 is initiated by the warming North Atlantic. It has been suggested that, a positive phase of the EU wave train over the Atlantic-EU section is usually accompanied by a positive phase of the Pacific-North-America or Western-Pacific (PNA or WP) circulation pattern over the PNA section (Wallace and Gutzler 1981, Harnik et al 2016, Song et al 2016, Sung et al 2021. Through eddy-mediated physical processes, the SSTa over the midlatitude North Atlantic can produce a Rossby wave source that propagates eastward over the EU continent (Li 2004, Bueh and Nakamura 2007, Wang et al 2019. Therefore, our result is consistent with previous studies that addressed the importance of the warm North Atlantic SST in the alteration of Arctic-EU wave train. Meanwhile, the stratospheretroposphere dynamical coupling process we presented is supported by the previous studies. The warming SSTs over the North Atlantic could modulate the subseasonal variability in SATs over eastern Eurasia and North America, which carry important implications for the predictability of extreme temperature events on subseasonal time scale. The AO is a large-scale circulation pattern that influences weather in the NH (Thompson and Wallace 1998). Observations have shown that there are more cold air outbreaks and extreme warm events than usual during the negative phase of the AO. The cold air outbreaks and regional extreme warmth are associated with a meandering jet stream when it dips southward or northward. The AO mostly had an extremely negative phase in the winter of 2020/2021 (figure 4(c)), which may also have contributed to the intercontinental seesawing temperature extremes. El Niño and Southern Oscillation (ENSO) represents the strongest year-to-year fluctuation of the global climate system and is a dominant predictability source of global climate (Timmermann et al 2018, Mariotti et al 2020. It was suggested that the La Niña (cold ENSO events with anomalously cold conditions over eastern tropical Pacific) contributed to the extreme cold events from East Asia to North America in winter 2020/21 (Zheng et al 2022, Zhang et al 2022a, Zhang et al 2022b. Thus, the synergistic effect of the warm Northwest Atlantic and the cold tropical Pacific (La Niña) on the subseasonal swing of intercontinental temperature extremes in winter of 2020/21 requires additional investigation.

Conclusion
During the 2020/21 boreal winter, a subseasonal swing of cold and warm spells attacked Eurasia and North America and caused a robust alternating of SAT extremes in these two regions. We investigated its initiation and physical process and found that the cold and warm extremes were mainly regulated by the AC SAT anomalies, which was associated with the subseasonal phase transition of a CRW train. Figure 5 shows a schematic of the initiation and physical processes. This CRW was initiated by the extreme warming SST over the midlatitude Northwest Atlantic in early winter, amplified by the feedback of sea ice loss over the Barents-Kara Seas, and its phase was changed by the wave reflection in the stratosphere in late winter.
The extreme warming SST over the Northwest Atlantic produced a strong anomalous anticyclone overhead by altering the transient eddy activities and the resultant vorticity forcing and excited an eastward-propagating wave train. The anomalous anticyclone of the wave train over the Barents-Kara Seas promoted the local loss of sea ice. The loss of sea ice in turn amplified the anomalous anticyclone by increasing the upward turbulent heat flux and excited the southeastward WAF. The resulting CWR resembled the positive phase of the EU and NPO teleconnection patterns and facilitated cold (warm) spells over eastern Eurasia (North America) in early winter. The positive NPO-like CRW pattern interacted constructively with the climatological planetary waves, enhanced the amplitude of the planetary wavenumber-1 component and the associated upward propagation over northeastern Eurasia, consequently weakening the stratospheric vortex. Meanwhile, mainly due to the intensified interaction between the planetary wavenumber-1 and wavenumber-2 components, the downward propagation of the planetary waves in Canada was stronger. Along with the subsequent strong wave reflection over Canada, the NPO-like CRW train was involved in the opposite phase in late winter. Correspondingly, the anomalous anticyclone over northern Asia favored a warm spell and extremely warm SAT anomalies over eastern Eurasia, while the anomalous cyclone over North America indicated that the strengthening of the North American trough favored a cold spell and extremely cold SATs over North America.
All data that support the findings of this study are included within the article (and any supplementary files).