Lagged regressions with respect to (left) the inverted vortex index and (right) wave index in two reanalyzes and four models. (a and b) Z10 averaged over the polar cap (north of 60°N; meter), (c and d) Arctic Oscillation index, and (e and f) North American surface air temperature (SAT) index. Positive lags indicate that the stratospheric indices lead the other variables. Positive values of the North American SAT index indicate cooling over North America (Figure 1d). The lines in red, blue, plum, purple, black and gray represent CAM6‐PAMIP, MIROC6‐PAMIP, CAM6‐AMIP, WACCM‐AMIP, European Centre for Medium‐Range Weather Forecasts Interim reanalysis and Japanese 55‐year Reanalysis (JRA‐55), respectively. Solid parts of the lines represent regression coefficients significant at the 95% confidence level based on the student's t‐test. The light blue shading denotes the 2.5%–97.5% confidence interval estimated using JRA‐55 data.

Lagged regressions with respect to (left) the inverted vortex index and (right) wave index in two reanalyzes and four models. (a and b) Z10 averaged over the polar cap (north of 60°N; meter), (c and d) Arctic Oscillation index, and (e and f) North American surface air temperature (SAT) index. Positive lags indicate that the stratospheric indices lead the other variables. Positive values of the North American SAT index indicate cooling over North America (Figure 1d). The lines in red, blue, plum, purple, black and gray represent CAM6‐PAMIP, MIROC6‐PAMIP, CAM6‐AMIP, WACCM‐AMIP, European Centre for Medium‐Range Weather Forecasts Interim reanalysis and Japanese 55‐year Reanalysis (JRA‐55), respectively. Solid parts of the lines represent regression coefficients significant at the 95% confidence level based on the student's t‐test. The light blue shading denotes the 2.5%–97.5% confidence interval estimated using JRA‐55 data.

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Plain Language Summary A weak polar vortex in the winter stratosphere is likely associated with cold spells at the surface, yet there are large uncertainties in predicting surface cold events based on stratospheric signals. This study introduces a new method to separate stratospheric variability into the leading modes of zonally symmetric and asymm...

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... These wave events are associated with alternating NAM anomalies (Ding et al., 2022) like during wQBO SSWs, and may partly explain the weak overall NAM signals during wQBO when averaged over the winter season. ...
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Plain Language Summary Roughly every other winter the polar stratosphere (15–50 km) in the Northern Hemisphere experiences a rapid and significant warming. These sudden stratospheric warming (SSW) events collapse the polar vortex, that is, the wintertime eastward wind surrounding the pole. After collapse, in the following weeks, the disturbances produced by the SSW reach the lower stratosphere and may penetrate into the troposphere (0–15 km), affecting the surface weather. In this study, we show that statistically significant surface changes, such as warming in the Middle East and Eastern Canada and cooling in Northern Eurasia, are observed in the late winter in those winters when SSW occurs. Conversely, opposite temperature changes are common in the late winter in those winters when the polar vortex does not collapse. Surface temperature changes reflect the state of the vortex state more closely when equatorial stratospheric winds are westward. These findings are valuable, for example, for regional temperature forecasting by using seasonal predictions of the polar vortex.
... Numerous studies have explored the impacts of strength of stratospheric polar vortex (SPV) on the tropospheric and even surface climate and weather anomalies (Baldwin & Dunkerton, 2001;Ding et al., 2022;He et al., 2024;Hu et al., 2021Hu et al., , 2024Lu et al., 2021;Nakagawa & Yamazaki, 2006;Zhang et al., 2022). The weakening of the SPV was suggested to lead to a decrease in surface air temperature (SAT) in East Asia Huang & Tian, 2019;Kolstad et al., 2010;Liu et al., 2023;Orsolini et al., 2018;Woo et al., 2015). ...
... White et al. (2019) revealed that splitting events exhibit a near-instantaneous and barotropic response from the stratosphere to the troposphere, whereas displacement events have stronger long-term impacts. Ding et al. (2022) highlighted asymmetric modes of SPV contributing to cooling in North America. ...
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Using long‐term reanalysis data, extreme cold events (ECEs) over East Asia are categorized into long‐duration ECEs (L‐ECEs, lasting more than 7 days) and short‐duration ECEs (S‐ECEs, lasting 3–7 days) according to the duration of ECEs during boreal winters from 1959/1960 to 2019/2020. Our results show that L‐ECEs over East Asia exhibit greater intensity, higher frequency, and longer persistence than S‐ECEs. On annual average, L‐ECEs are 1.8 K colder, contribute over 60% of total ECE days, and dominate in longer durations, persisting beyond day 5 and lasting up to 12 days. L‐ECEs in East Asia are attributed to the extension of the stratospheric polar vortex (SPV) toward the Atlantic‐Euro region. This SPV extension tends to enhance the Atlantic‐Euro trough, which is coupled with a strengthened and persistent Eurasian teleconnection pattern and a strengthened Ural ridge and East Asia trough during the decay of ECEs (after day 3). The strengthened East Asia trough, accompanied with cyclonic circulation, facilitates the transport of cold air from higher to lower latitudes. This process makes the ECEs more persistent and longer in duration, potentially developing into L‐ECEs. The findings of this study provide valuable insights into the linkages between the extension of the SPV and ECEs over East Asia from a long‐term climate statistics perspective instead of relying solely on case‐by‐case analysis. This study may offer a valuable new predictor for forecasting long‐lasting ECE events over East Asia.
... Due to the strengthening of large-scale planetary waves, the winter stratospheric polar vortex undergoes a rapid weakening, which is accompanied by a sudden stratospheric warming (SSW) (Baldwin et al., 2021). The polar vortex perturbed by planetary waves produces a zonally asymmetric pattern in the SSW effects observed in air temperature, winds, total ozone content (TOC), and tropopause altitude (Ding et al., 2022;Kidston et al., 2015;Thompson and Wallace, 2000). Due to the quasi-stationary wave (QSW) structure, the SSW influence is often manifested as persistent extreme cold weather in certain regions, such as Northern Europe, East Asia or North America (Kolstad et al., 2022;Lü et al., 2020;Smith and Polvani, 2014;Thompson and Wallace, 2000;Tomassini et al., 2012). ...
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This paper analyzes the four severe cooling events in Changchun, Northeast China, in January for selected years. The events in the absence of sudden stratospheric warmings were chosen. This excludes the possible effects of warm stratospheric anomalies in the polar vortex region, which may affect midlatitudes. The meridional profiles and maps for the coldest and warmest days of January are compared using the temperature and ozone data from observations and reanalysis. Based on the vertical temperature structure compared to the coldest–warmest days, the lower stratosphere–surface thermal coupling was analyzed, which has not been studied previously. It has been shown that (i) temperature increases by 5–10C in the lower stratosphere, (ii) lowering the tropopause by about 2–3 km, (iii) pushing the cold midtropospheric layer from climatological about 3 km to the surface with formation of the midlatitude temperature minimum, and (iv) a decrease in surface temperature in Changchun by 15–24C, concurrently occurred on the coldest days compared to the warmest days. Cold air in the region of the midlatitude minimum temperature, merging with the cold air of higher latitudes, contributes to the formation of the cold air outbreak pattern. The main elements of stratospheric and tropospheric dynamics (quasi-stationary and traveling planetary waves, zonally asymmetric Brewer-Dobson circulation, deformation of the tropopause, and tropospheric isotherms) involved in extreme cooling events are analyzed. Because of the positive correlation between total ozone and temperature in the lower stratosphere, extremely high total ozone over the midlatitude region may serve as an indicator of warm stratospheric anomaly and possible downward thermal forcing. HIGHLIGHTS • Stratosphere–troposphere coupling and cold air outbreak in the pre-SSW wintertime. • Transformation of the temperature and ozone profiles in the four extreme coolings. • Anomalous stratosphere warming and tropopause descent lead to extremely cold weather.
... The 10 hPa geopotential height anomalies 129 linked to strong stratospheric wave events during wQBO and eQBO years share similar patterns, 130featuring an NA ridge and a Eurasian trough(Figures 1a-1b). This wave-1 pattern is largely in 131 phase with the wave-1 climatology and reinforces the climatological wave-1 via constructive 132 wave interference(Ding et al., 2022;Smith & Kushner, 2012). We note that on day 10, the ridge ...
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Extreme stratospheric wave activity has been linked to surface cold extremes over North America, but little is known whether the Quasi-biennial Oscillation (QBO) plays a role in this linkage. Here, by comparing strong stratospheric wave events during the westerly phase (wQBO) with those during the easterly phase (eQBO), we show that the cooling signature following strong wave events depends on the QBO phase in observations. During wQBO, strong wave events are followed by an increased risk of North American cold extremes and a vertical structure shift from a westward phase tilt to an eastward tilt. However, strong wave events under eQBO do not change the cold risk nor alter the vertical tilt. We further examine this dependence on QBO in QBO-resolving climate models, finding that the cooling signature of strong wave events in models is largely insensitive to QBO phases. This insensitivity is suggested to be linked to model biases in the stratospheric wave representation.
... Increasing evidence shows that some continental CAOs can even occur during positive SNAM events (e.g. Garfinkel et al. 2017;Waugh et al. 2017;Kretschmer et al. 2018;Huang and Tian 2019;Zhou et al. 2021;Millin et al. 2022;Ding et al. 2022;Finke et al. 2023). Moreover, recent studies have identified that the polar vortex anomaly descending to the lower stratosphere leads to the most robust tropospheric response (e.g., Gerber et al. 2009;Hitchcock et al. 2013;Runde et al. 2016;Cai et al. 2016;Karpechko et al. 2017;Rupp and Birner 2021). ...
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A Stratospheric Northern Annular Mode (SNAM) phase-based composite analysis reveals that continental Cold Air Outbreaks (CAOs) can occur during both positive and negative SNAM events. CAOs tend to occur over Asia, characterized by a meridional-dipole surface temperature anomaly pattern (cold midlatitudes and warm high-latitudes) when the SNAM index is decreasing or the stratospheric polar vortex is weakening, but over North America and Europe with a meridionally-homogeneous pattern when the SNAM index is increasing or the stratospheric polar vortex is strengthening. While the decreasing SNAM is dominated by a stronger stratospheric poleward warm branch (WB-ST) of the isentropic meridional mass circulation and vice versa, the CAOs always follow a stronger tropospheric poleward warm branch (WB-TR) and an equatorward cold branch (CB) of the isentropic meridional mass circulation. The correspondence between the stronger/weaker WB-ST and stronger/weaker WB-TR&CB during majority of SNAM phases (referred to as stratosphere-troposphere coupling regimes) is responsible for the CAOs in Asia. During the remaining phases (stratosphere-troposphere decoupling regimes), in accompany with a weaker/stronger WB-ST, the WB-TR&CB are stronger/weaker and relates to the CAOs occurred in North America and Europe. The coupling regimes when the stratospheric polar vortex is weakening/strengthening are mainly attributed to the E-P flux convergence/divergence from the middle troposphere to the lower stratosphere, the larger wave amplitude throughout the column, and anomalous tropospheric wave flux mainly in the Asia in subpolar latitudes. The decoupling regimes, however, are mainly related to the anomalous westward-tilting of waves and the wave flux reflection toward the North America or Europe.
... Recently, several studies used the cluster analysis and the empirical orthogonal function method to identify the SPV stretching events (Cohen et al., , 2022Ding et al., 2022Ding et al., , 2023, Liang Z et al., 2023 and found that their reflective mechanism and tropospheric response closely resemble those of reflecting SSWs (Matthias & Kretschmer, 2020;Messori et al., 2022;Shen et al., 2023;Zou et al., 2024). Further efforts have been made to unveil possible causes and impacts of the SPV stretching events. ...
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Plain Language Summary Stratospheric polar vortex (SPV) stretching events are characterized by a zonally asymmetric pattern of lower stratospheric variability with positive height anomalies over northern Eurasia and negative anomalies over Canada. In this study, we mainly focus on the SPV stretching events that occurred from October to November, and this is because the surface cooling over high‐latitude Eurasia following these events is associated with the stratospheric pathway. Here, the autumn events can be categorized into lower (LoSIC/BKSIC) and higher (HiSIC/Ctrl) sea ice groups based on observations and simulations. We further demonstrate that lower BKS sea ice conditions are favorable for intensified upward propagation of waves into the stratosphere in the Euro‐Siberian sector prior to the onset of SPV stretching events, and subsequently affect the geometry of the SPV (SPV stretching pattern). The stratospheric wave‐2 ridge anomalies migrate downward to the mid‐troposphere 30–40 days following SPV stretching onset, leading to the enhancement of the Arctic‐North European high and attendant colder Eurasia. These results emphasize the critical modulating role of Arctic sea ice in the Eurasian cooling response to SPV stretching events.
... The increasing frequency of weak SPV states can account for nearly 60% of the cooling region over midlatitude Eurasia; this proportion rises to about 80% when El Niño-Southern Oscillation variability is included, indicating that persistent weak SPV and tropical variability together contribute to Eurasian cooling (Kretschmer et al. 2018a). Besides the SPV stretching events, an empirical orthogonal function method is applied to extract the planetary wave-1 pattern associated with stratospheric variability, which features a high surface pressure anomaly over Alaska and a low anomaly over eastern North America, thus favoring cold surges over North America via stratosphere-troposphere interactions (Ding et al. 2022(Ding et al. , 2023. ...
... With the increasing importance of weak SPV, most existing literature appears to emphasize the crucial role of SSWs in Eurasian and North American coldness (e.g., Hall et al. 2021;Kodera et al. 2016;Xu et al. 2022;Zhang et al. 2020), the SPV stretching events and related surface responses are only marginally mentioned in several studies (Cohen et al. , 2022Ding et al. 2022Ding et al. , 2023Kretschmer et al. 2018b;Liang et al. 2023;Matthias and Kretschmer 2020;Messori et al. 2022;Shen et al. 2023). However, the occurrence probability of SSWs is less than that of SPV stretching events Liang et al. 2023). ...
... For autumn SPV stretching events, the downward extension of stratospheric signals during the early stage directly results in negative AO/NAO-like anomalies and thereby the first cold anomalies in northern Eurasia. This pattern is broadly consistent with the lagged effect of the planetary wave-1 pattern (Ding et al. 2022(Ding et al. , 2023 and the features of the Eurasia-weakened pattern notified by Liang et al. (2023). The deepening of the East Asian trough and the increase of the Ural high associated with stratospheric wave activity during the late stage are favorable for the second cold surge in high-latitude Eurasia and mid-latitude East Asia respectively. ...
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The weak stratospheric polar vortex (SPV) is usually linked to Northern Hemisphere cold spells. Based on the fifth generation of ECMWF atmospheric reanalysis and WACCM model experiments, we use K-means cluster analysis to extract the zonally asymmetric pattern of October-February stratospheric variability, which involves a stretched SPV and hence leads to cold surges in Northern Hemispheric mid-latitudes. There are contrasting effects and mechanisms between autumn (October–November) and late winter (February) SPV stretching events. In October, anomalies in the stratospheric circulation affect the near-surface 16–20 days after the weakening of the SPV. This contributes to a shift in the North Atlantic Oscillation (NAO) towards its negative phase, leading to cold anomalies over northern Eurasia. Together with the weakening of planetary wave-1 during days 31–40, the second stratosphere–troposphere coupling strengthens the East Asian trough and the Siberian high, resulting in Eurasian high-latitude cooling. For November, the suppressed upward propagation of wave-1 during days 11–15 is conducive to anomalous high pressure over northern Europe and thereby European cooling through a stratospheric pathway, while for days 21–30, the weakening of propagating wave-2 over Eastern Europe intensifies the mid-latitude wave train through a tropospheric pathway, favorable for cold temperatures in mid-latitude East Asia. In contrast, the late winter SPV stretching events and the attendant Eurasian coldness during 11–25 days are likely to have been simultaneously driven by the long-lived European high anomaly, which enhanced the upward-propagating tropospheric waves into the stratosphere and thus favored SPV stretching. It indicates that the tropospheric pathway, rather than the stratospheric pathway, plays a dominant role in cold Eurasia following February SPV stretching events.
... Distinct Eurasian and North American cooling signatures follow zonally symmetric and asymmetric subseasonal modes of the stratospheric polar vortex (X. Ding et al., 2022;Kretschmer et al., 2018). The subseasonal "stretched" stratospheric polar vortex variations modified by abnormal states of Arctic sea ice and Eurasian snow cover is linked with the recent winter extreme cold across parts of Asia and North America (Cohen et al., 2021). ...
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Plain Language Summary In spring 2022, extremely cold and warm spells alternately affected eastern China (EC) and caused drastic temperature whiplash events, featured by the enhanced subseasonal variability of surface air temperature (SAT). We find the subseasonal SAT variability is directly associated with the Eurasian wave train, and its intensity is correlated with sea ice concentrations (SICs) over the Barents‐Kara Seas (BK) in previous winter. Increased SICs reduce the heat transfer from ocean to atmosphere, induce a cyclone anomaly aloft, and diminish the climatological planetary wavenumber‐1 component. The weakened upward wave activity flux strengthens the stratospheric polar vortex, which spreads downward until spring. Hence, the polar front jet in the North Atlantic is enhanced, and the meridional temperature gradient in northern Europe increases, providing a favorable background for atmospheric disturbance development. The North Atlantic wave train propagates farther eastward after gaining more kinetic energy from the accelerated jet and intensifies the following Eurasian wave train. Due to stronger local baroclinic energy conversion, the Eurasian wave train further strengthens, resulting in enhanced subseasonal SAT variability over EC. Therefore, the extremely increased winter BK SICs could be a useful initial signal for the probability of temperature whiplash events over EC in the following spring.
... They argue that the tropospheric circulation regime associated with NA cold spells only acts as a precursor for the suppressed planetary wave-1 (a wave structure with one crest and one trough at a latitude circle) activity in the stratosphere. Ding et al. (2022Ding et al. ( , 2023, in contrast, show that strong stratospheric wave activity precedes positive NAO-like NA cooling at the surface with a 10-day lag. The divergent conclusions underscore that the surface impacts of stratospheric waves remain an area of active research. ...
... However, many of these studies only analyzed reanalyzes, and the sensitivities of these methods are unclear when applied to climate models. Ding et al. (2022) measure stratospheric wave activity with a simple metric based on the EOF analysis of the zonally asymmetric component of 10 hPa geopotential height, which can be readily applied to climate models. Ding et al. (2023) further show the impact of extreme stratospheric wave events on NA cold spells consistently across reanalysis and Coupled Model Intercomparison Project Phase 6 (CMIP6) ensemble means. ...
... We define extreme stratospheric wave events based on the EOF analysis of 10 hPa geopotential height for ERA5 and individual CMIP6 models, as in Ding et al. (2022). After removing the zonal mean, EOF is applied to the zonally asymmetric component of geopotential height at 10 hPa north of 20°N, weighted by the square root of the cosine of latitudes. ...
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Extreme stratospheric wave activity has been suggested to be connected to surface temperature anomalies, but some key processes are not well understood. Using observations, we show that the stratospheric events featuring weaker‐than‐normal wave activity are associated with increased North American (NA) cold extreme risks before and near the event onset, accompanied by less frequent atmospheric river (AR) events on the west coast of the United States. Strong stratospheric wave events, on the other hand, exhibit a tropospheric weather regime transition. They are preceded by NA warm anomalies and increased AR frequency over the west coast, followed by increased risks of NA cold extremes and north‐shifted ARs over the Atlantic. Moreover, these links between the stratosphere and troposphere are attributed to the vertical structure of wave coupling. Weak wave events show a wave structure of westward tilt with increasing altitudes, while strong wave events feature a shift from westward tilt to eastward tilt during their life cycle. This wave phase shift indicates vertical wave coupling and likely regional planetary wave reflection. Further examinations of CMIP6 models show that models with a degraded representation of stratospheric wave structure exhibit biases in the troposphere during strong wave events. Specifically, models with a stratospheric ridge weaker than the reanalysis exhibit a weaker tropospheric signal. Our findings suggest that the vertical coupling of extreme stratospheric wave activity should be evaluated in the model representation of stratosphere‐troposphere coupling.
... These two types of stratospheric impacts on the surface can be distinguished by the sign of lower-stratospheric meridional heat flux during the recovery stage of SSWs 24,25 , clustering analysis 3,26-28 , or empirical orthogonal function (EOF) analysis 29,30 . Particularly, Cohen et al. 3 argues that stratospheric polar vortex stretching involving planetary wave reflection is linked to North American cold spells such as the February 2021 Texas cold wave. ...
... This indicates that strong stratospheric wave activity can serve as a sub-seasonal predictor for cold air outbreaks over North America. In contrast to the persistent weather regimes associated with stratospheric polar vortex events [12][13][14][15][16][17][18][19] or lower-stratospheric wave reflection events 3,26 , we substantiate an emerging linkage between extreme stratospheric wave events and the intraseasonal fluctuations between warm and cold snaps over North America [29][30][31] . We further support this linkage through idealized nudging simulations in the Specified Chemistry Whole Atmosphere Community Climate Model (SC-WACCM4) 39 , which suggests that the vertical wave coupling plays a key role in the North American cold extremes following strong stratospheric wave events. ...
... Strong and weak wave events are identified by extreme percentiles of the wave index, which is defined as the leading principal component of the zonally asymmetric component of geopotential height at 10 hPa for the extended boreal winter from November to March in ERA5 reanalysis and CMIP6 models (see details in Methods). The corresponding EOF mode of 10-hPa geopotential height features a transient planetary wave-1 pattern, with the positive phase amplifying the climatological wave pattern through constructive wave interference and the negative phase weakening the climatological wave via destructive interference 29 (Supplementary Fig. 1). Consecutive days above the 95th percentile of the wave index are referred to as strong wave events, and the days below the 5th percentile are termed weak wave events. ...
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Extreme cold events over North America such as the February 2021 cold wave have been suggested to be linked to stratospheric polar vortex stretching. However, it is not resolved how robustly and on which timescales the stratosphere contributes to the surface anomalies. Here we introduce a simple measure of stratospheric wave activity for reanalyses and model outputs. In contrast to the well-known surface influences of sudden stratospheric warmings (SSWs) that increase the intraseasonal persistence of weather regimes, we show that extreme stratospheric wave events are accompanied by intraseasonal fluctuations between warm and cold spells over North America in observations and climate models. Particularly, strong stratospheric wave events are followed by an increased risk of cold extremes over North America 5–25 days later. Idealized simulations in an atmospheric model with a well-resolved stratosphere corroborate that strong stratospheric wave activity precedes North American cold spells through vertical wave coupling. These findings potentially benefit the predictability of high-impact winter cold extremes over North America.