The sudden stratospheric warming in January 2021

Using the ERA5 reanalysis, sea surface temperature and sea ice observations, and the real-time multivariate Madden–Julian index, this study explores a sudden stratospheric warming (SSW) in January 2021, its favorable conditions, and the near surface impact. Wavenumbers 1 and 2 alternately contributed to the total eddy heat flux from mid-December 2020 to late January 2021, and the wavenumber 2 during the onset period nearly split the stratospheric polar vortex. In mid-December 2020 and during the 2021 New Year period (1–5 January 2021), a blocking developed over the Urals, which enhanced the local ridge and the climatological wavenumber 2. Composite results confirm that the Arctic sea ice loss in autumn and La Niña favor the deepening of the high latitude North Pacific low and the increase of the Urals height ridge, which together enhance the planetary waves and hence disturb the stratospheric polar vortex. However, the Madden–Julian oscillation (MJO) in the tropics was dormant in mid-to-late December 2020 and early January 2021, and the well-established statistical relationship between the MJO convection over the western Pacific and the SSW is not applicable to this special case. The cold air outbreak in China during the 2021 New Year period before the January 2021 SSW onset is not explained by the SSW signal which developed in the stratosphere. In contrast, the downward-propagating signal reached the near surface in mid-February 2021, which may contribute to the cold air outbreak in US and may help to explain the extreme coldness of Texas in middle February.


Introduction
On average, sudden stratospheric warming (SSW) occurs 6 or 7 times every decade in the Arctic stratosphere , Rao et al 2019b. The model evidence has confirmed that the SSWs might increase with global warming, but such an increase is insignificant (Ayarzagüena et al 2018(Ayarzagüena et al , 2020. Arctic stratospheric air temperatures increase by 40-60 K within a week, and in a major SSW the circumpolar jet reverses to easterlies (Charlton and Polvani 2007, Hu et al 2014, Butler et al 2015. The weakening and distortion of the Arctic polar vortex during the SSW is projected onto the negative phase of the Northern Annular Mode/Arctic Oscillation (NAM/AO) (Baldwin andDunkerton 1999, 2001), which tends to propagate downward and can affect the near surface. Therefore, SSW events can serve to improve the near surface predictability associated with the negative phase of the AO .
In the last three years, both the Antarctic and Arctic polar stratospheres witnessed a huge variation in their circulation and temperature. Specifically, two major SSWs were observed over the Arctic stratosphere in February 2018 and January 2019, respectively , Lee and Butler 2019, Rao et al 2019a, Lu et al 2021. The February 2018 SSW has been reported to be triggered by the blocking in the Urals and Alaska, which disrupt the zonal circulation in mid-to-high latitudes and amplify the climatological wave amplitudes , Overland et al 2020. The January 2019 SSW occurred under several favorable conditions, including the solar minima, easterly winds of the quasi-biennial oscillation (QBO), moderate El Niño, and active convection over the marine continent and western Pacific during the Madden-Julian Oscillation (MJO) phase 6 by enhancing upward propagation of extratropical planetary waves (Rao et al 2019a). The different configurations of the favorable conditions , Rao et al 2019a, 2020a and morphologies of the polar vortex (Butler et al 2020) for the February 2018 and January 2019 SSWs explain their different predictability, with the latter having greater predictability with a longer lead time than the former in most subseasonal to seasonal forecast systems.
Compared to the NH, very few SSWs take place in the SH due to weaker planetary waves, owing to the even distribution of oceanic water in high latitudes of the SH. Hitherto, only two SSWs (i.e. September 2002 and 2019) have been observed in the SH (Hu 2020, Shen et al 2020, Rao et al 2020b. Although no SSW event was observed in the 2019/20 boreal winter, an extremely strong stratospheric polar vortex coupled with Arctic ozone loss appeared in March 2020 (Rao andGarfinkel 2020, 2021b).
The 2020/21 winter was very different, with a major SSW on 5 January, attracting wide attention in the media (Lee 2021 and references therein). However, tropospheric precursors for this SSW are not widely explored in literature, and favorable conditions triggering this event are not yet clearly understood either. Not all SSWs show a successful downward propagation of the negative NAM/AO signal from the stratosphere to the troposphere (Karpechko et al 2017), so the relationship between the SSW and the near surface predictability is still uncertain. The January 2021 warming event adds another case to the limited sample of historical SSWs, which provides an additional opportunity for studying the downward propagation of the stratospheric SSW signal and its impact on the near surface. The general characteristics of this SSW deserve special report and careful study.
The structure of the paper is organized as follows. Following the introduction, data and methods are described in section 2. Section 3 displays the evolution of the circulation and temperature anomalies during this SSW. Section 4 explores the possible precursors for this SSW event, and the near surface response is also discussed. Finally, conclusions are summarized in the section 5.

Data and methodology
The daily ERA5 reanalysis is used in this study, downloaded at a 1 • (latitude) ×1 • (longitude) horizontal resolution and 37 pressure levels from 1000 to 1 hPa (Hersbach et al 2020). Variables analyzed in this study include the geopotential height (Z), zonal and meridional winds (u, v), and air temperature at pressure levels. The monthly sea ice concentration and sea surface temperature (SST) version 1 from 1979 to 2020 are obtained from the Met Office Hadley Centre, with a horizontal resolution of 1 • × 1 • (Rayner et al 2003). The climatology of those variables is calculated as the long-term mean during 1979-2020. Anomalies refer to the deviations of daily data in 2021 from the climatology.
Given the relationship between the tropical MJO and SSWs (Garfinkel et al 2012), the real time multivariate MJO index (Wheeler and Hendon 2004) is used to test the tropical conditions for the January 2021 SSW, which is available from the Australian Bureau of Meteorology (www.bom.gov.au/ climate/mjo/graphics/rmm.74toRealtime.txt). Considering that the vertical component (F z ) of the Eliassen-Palm flux is approximately proportional to the transient eddy heat flux (Andrews et al 1987), the eddy heat flux (v * T * ) is calculated using the daily meridional wind and temperature from the ERA5 reanalysis. The overbar means the zonal average, and the superscript asterisk means the zonal deviation.

Evolution of the stratosphere-troposphere coupling
The height-temporal evolutions of the circumpolar zonal wind at 60 • N, polar cap temperature anomalies, and polar cap height anomalies are shown in figure 1. Based on the first day when the daily-mean circumpolar westerly was reversed to easterly, a major SSW event occurred in the Arctic stratosphere on 5 January, 2021 (figures 1(a) and (d)). The zonal wind at 60 • N/10 hPa (figure 1(d)) oscillated around zero: easterly winds appeared from 5 to 20 January for 14 days (with a 2 days westerly interruption) and 2 days from February 1 to 2 (also see Lee et al 2021), much longer than the mean duration of easterlies for all SSWs (i.e. 8 days) (Rao and Garfinkel 2021a). The relatively long persistence time of easterlies during this SSW might reflect a persistent strong dynamical forcing, which overwhelms the nonadiabatic cooling effect during this period. The daily-mean circumpolar westerlies in the upper stratosphere reversed to easterlies around 31 December 2020 (figure 1(a)). The easterly anomalies formed since 26 December 2020, and they covered a thick vertical extent from 500 hPa to 10 hPa. The easterly anomalies increased rapidly after 3 January 2021 and reach two maxima (−40 m s −1 ) on 6 and 16 January 2021 above 5 hPa, respectively. The easterly anomalies started on 26 December 2020 and ended on 16 February 2021 at 10 hPa with a persistence time of 53 days.
Consistent with the circumpolar wind evolution, the Arctic stratosphere warms suddenly after 31 December 2020 (anomalies: ∼5 K). The temperature anomalies at 10 hPa developed to the maximum (>25 K) around 4 January 2021, with an abrupt increase of 20 K in five days. Furthermore, the positive temperature anomalies in the polar cap lasted for 38 days throughout 31 December until 6 February 2021 at 10 hPa ( figure 1(b)). Warm temperature anomalies primarily developed above 200 hPa. According to the geostrophic wind principle, the reversal of zonal wind is connected with rising of the polar cap geopotential height. Therefore, positive standardized height anomalies were observed to develop several days before the SSW onset and strengthen after the onset. Strong positive geopotential height anomalies were present in both the troposphere and stratosphere after the SSW, with two periods of particularly strong apparent downward propagation: one during 25-31 January and the other during 7-13 February (figure 1(c)). The metric of the standardized polar cap height anomalies is actually a substitute for the NAM index but with the sign reversed (Baldwin andThompson 2009, Rao et al 2020a). In summary, the January 2021 SSW is characterized by its long-lasting time and a possible downward impact.

Alternate pulses of wavenumber 1 and wavenumber 2
To explain the occurrence of this SSW and compare the contribution by planetary wavenumbers 1 and 2, the eddy heat flux at 100 hPa and 300 hPa areaaveraged over 45 • -75 • N is shown in figures 1(e) and (f). Persistent and long-lasting total eddy heat flux occurred before the onset of the January 2021 SSW, and three peaks should be noted at 100 and 300 hPa (i.e. around 12 December, 27 December and 1 January). Those three pulses are contributed by different planetary waves, with the first peak by wavenumber 2, the second peak by wavenumber 1, and third peak by wavenumber 2 again. Eddy heat flux pulses by wavenumbers 1 and 2 appears alternately, weakening the stratospheric polar vortex persistently. Upward propagation of planetary waves was enhanced before the onset date of this warming event, but such an enhancement did not stop soon after the SSW began. The zonal winds in the troposphere and lower stratosphere were still westerlies and the zero winds were around 50 hPa after the SSW onset. The presence of westerlies in the lower stratosphere denotes a more baroclinic structure during this SSW ( figure 1(a)). Previous studies suggest that the persistence of eddy heat flux is more important for decelerating the zonal mean zonal winds than the strength of the eddy heat flux pulses themselves (Polvani and Waugh 2004). From 5 to 25 January, the total waves in mid-tohigh latitudes were still active to produce large eddy heat flux, mainly contributed by wavenumber 1. The strong wave activities especially in the upper troposphere might explain the long-lasting period of this warming event. Therefore, it is reasonably revealed that the onset of this event and its exceptional persistence is due to the alternate dominance of wavenumbers 1 and 2, which still continued after the SSW onset as the westerlies in the lower stratosphere did not reverse soon.
To reveal the variation of the stratospheric polar vortex shape associated with the change in the eddy heat flux pulse in figures 1(e) and (f), the height and its anomalies in the Northern Hemisphere at 10 hPa and 500 hPa during several wave pulse periods are shown in figure 2. The morphology of the stratospheric polar vortex can be disturbed and affected by the tropospheric wave pulses. The first pulse period from 14 to 16 December 2020 was denoted by the elongation of the stratospheric polar vortex toward Arctic Eurasia and Arctic Canada in the stratosphere (two anomalous lows were identified over Arctic Eurasia and Arctic Canada, and an anomalous high developed in the Pacific sector; figure 2(a)) as the tropospheric height anomaly is nearly in phase with the climatological wavenumber 2 (figure 2(d)). In the second stage from 23 to 29 December, the North Pacific high (and its anomaly) center moved slightly westward to Kamchatka Peninsula in the stratosphere (figure 2(b)) while the Aleutian low deepened and the North Atlantic height rose in the troposphere (figure 2(e)). The third stage from 1 to 4 January 2021 was identified with an anomalous wavenumber 2 pattern in the stratosphere (figure 2(c)) and the Urals height rose again in the troposphere (figure 2(f)).
In the fourth stage from 9 to 21 January 2021 the negative height anomalies in midlatitudes are zonally symmetric, indicating the development of the negative NAM in the stratosphere (figure 2(g)); the negative height anomalies over North Pacific and its neighboring area still persisted and intensified the climatological wavenumber 1 in the troposphere ( figure 2(j)). In the fifth stage from 23 January to 3 February 2021, the stratospheric polar vortex was still located over the Barents Sea, but with a more circular shape and narrower coverage (figure 2(h)); the tropospheric negative height anomalies over East Asia and North Atlantic, as well as the positive height anomalies over the Urals and Northeast Pacific strengthen the climatological wavenumber 2 ( figure 2(k)). In the sixth stage from 6 to 14 February 2021, a gradual recovery of the stratospheric polar vortex was observed (figure 2(i)) as an annular mode response pattern developed in the troposphere (figure 2(l)).

Favorable conditions for occurrence of the January 2021 SSW
Previous studies (Rao et al 2019a, Baldwin et al 2021 revealed that favorable conditions for occurrence of the NH SSWs include the easterly QBO around 30-50 hPa, moderate El Niño, and solar minimum. However, the 2020/21 winter was not in the easterly QBO phase or in the warm El Niño-Southern Oscillation (ENSO) state; only the solar activities are still during a minimum period of the 11 year cycle (not shown). Figure 3 displays several metrics that might contribute to the tropospheric variations in January 2021, including ENSO, Arctic sea ice, and the MJO. The January 2021 SSW is preceded by the moderately cold ENSO state (La Niña) in the eastern equatorial Pacific (figures 3(a) and (d)). Statistics in Rao et al (2019a) show that both moderate El Niño and La Niña increase the probability of the SSW occurrence compared to the neutral ENSO state. The warm SST anomalies (maximum: ∼2.6 • C) in North Pacific might not explain the strengthening of the Aleutian low in January 2021 (figures 3(d) and (f)), as Hu and Guan (2018) established that warm North Pacific SSTs usually weaken the intensity of the local low center. The coldest SST anomalies in the eastern Pacific can reach −1.8 • C (figure 3(d)), although the area-weighted SST anomaly in the Niño3.4 region is moderately strong (−1.0 • C; figure 3(a)). The composite height anomalies at 500 hPa associated with La Niña is shown in figure 3(g), and 15 La Niña winters for the composite are selected (i.e. the SST anomalies in Niño3.4 region are lower than −0.5 • C for three consecutive wintertime months, November-January;1984/85, 1985/86, 1989/90, 1996/97, 1999/2000, 2000/01, 2001/02, 2006/07, 2008/09, 2009/10, 2011/12, 2012/13, 2017/18, 2018/19, and 2020. A negative Pacific-North American pattern was detected in the La Niña composite, but the positive height anomalies shift equatorward and are not situated over high-latitude North Pacific. It is negative height anomalies that developed over Aleutian Islands ( figure 3(g)). Therefore, negative height anomalies over Aleutian Islands are observed during both El Niño and La Niña, implying the asymmetric impact of ENSO on the extratropical circulation (Domeisen et   In addition, the January 2021 SSW also followed widespread Arctic sea ice loss in autumn (figure 3(e)), particularly over the Barents-Kara Sea (BK, 10 • -110 • E, 65 • -85 • N). The detrended autumn Barents-Kara Sea ice density index from 1982 to 2020 is shown in figure 3(b), which is the areaaveraged sea ice density over 10 • -110 • E, 65 • -85 • N (Screen 2017). In the 2020 autumn, the coverage of Barents-Kara Sea ice was significantly reduced. It is reported that sea ice loss in the Barents-Kara Sea during early winter usually strengthens the upward propagation of planetary waves and disturbs the stratospheric polar vortex in January (Kim et al 2014, Sun et al 2015, although the observed impact of sea ice might be inflated by the effects of atmospheric circulation variability on sea ice (Blackport and Screen 2021). Eight autumns with large Barents-Kara sea ice loss (i.e. the index is lower than −0.5σ) are evident : 1983, 1984, 1985, 1995, 2012, 2016, 2018 and 2020. The composite 500 hPa height anomalies in the following January of heavy Barents-Kara sea ice loss in autumn are shown in figure 3(h), resembling the observed pattern in January 2021 (figure 3(f)). Namely, the negative height anomalies over North Pacific and positive height anomalies at 500 hPa over Barents-Kara Sea is possibly associated with the Barents-Kara Sea ice loss in the preceding autumn.
In summary, the persisting wave activities in the troposphere from late-December 2020 to late-January 2021 can be associated with the moderate La Niña and the heavy ice loss over the Arctic. In contrast, the MJO was fairly weak within two weeks before the SSW onset (figure 3(c)). The convection over the western Pacific was enhanced during late January and February, much later than the SSW onset (see MJO phases 6 and 7 in figure 3(c)).

Possible surface impact of the January 2021 SSW
As the zonal-mean signal associated with the SSW propagates downward to the troposphere, the near surface responds (Rao et al 2020a, Lu et al 2021. Composite results in previous studies  show that the near surface temperature patterns before and after the SSW onset are not the same: cold anomalies form over the Eurasian continent before the SSW onset, while both North Eurasian and North American continents are cold in the following 1-2 month after the SSW onset. The 2 meter temperature (t2m) anomalies are shown in figure 4 during the January 2021 SSW. The composite results in previous studies are still true for the January 2021 SSW event. Namely, in the pre-SSW to onset periods (figures 4(a) and (b)), North Eurasia is anomalously cold, while warm anomalies develop in Canada. The pre-SSW temperature pattern is not likely a response to the stratospheric variation, but a tropospheric variation itself. A nationwide cold surge struck China during the 2021 New Year (figure 4(b)), and the cold anomalies during this period in Asia develop further equatorward than those during 21-30 December (figure 4(a)). The cold air outbreak in China during 31 December-10 January was mainly caused by the development of the Urals blocking, which enhances the meridional circulation in the downstream area, East Asia (see the local positive height anomalies in figure 2(f)).
Within the following month after the SSW onset when the SSW signals mainly developed in the stratosphere and upper troposphere, cold anomalies still persisted in high latitudes of Russia due to tropospheric variability and warm anomalies gradually diminished in large parts of North America (figures 4(c) and (d)). In the second month after the January 2021 SSW onset, the downward-propagating signals seemed to reach the near surface (figure 1). The negative NAM developed at near surface, which had appeared before the SSW onset ( figure 1(c)). The extremely cold wave in Texas and the cold air outbreak in US were related to the near surface negative NAM in mid-to-late February ( figure 4(e)). The composite MJO phase 7 also corresponds to a significant cold pattern in Canada and central US (figure 4(f)), which additionally explains the cold anomalies in large parts of the US.

Summary
Using the ERA5 reanalysis, the SST and sea ice observations, and the real-time multivariate MJO index, the evolution of the January 2021 SSW event, favorable conditions for the occurrence of this case, and its surface impact are explored in this study. The main conclusions are as follows.
(a) In December 2020, the upward propagation of planetary wave energy progressively accumulated in the extratropical stratosphere, denoted by the alternate wavenumber 1 and wavenumber 2 eddy heat flux pulses. In mid-December 2021, the wavenumber 2 pulse dominated the total eddy heat flux in the circumpolar region. In late-December 2020, the wavenumber 1 forcing strengthened and continued to accumulate the total eddy heat flux. In the 2021 New Year period, the wavenumber 2 redeveloped and the stratospheric polar vortex elongated and possessed two anomalous low centers, and the circumpolar westerlies reversed to easterlies. The persistent alternate wavenumber 1 and wavenumber 2 forcing in December 2020 led to a large stratospheric perturbation. Owing to the continuous wave forcings, the zonal wind deceleration began nearly one week earlier before the SSW onset, and the circumpolar easterly anomalies and negative NAM signal also preceded the SSW onset by nearly one week. (b) Previous studies show that the composite eddy heat flux decrease rapidly after the SSW onset ; in contrast, the wave forcing did not stop after the January 2021 SSW onset. Consistent with the long-lasting period of the eddy heat flux pulse after its onset, this SSW lasted for ∼2 months. After the SSW onset, large negative NAM-like signals propagated downward to the near surface during late-January and mid-February. (c) In mid-December 2020 and during the 2021 New Year period (1-5 January 2021), enhanced wavenumber 2 was observed to propagate from the troposphere to the stratosphere, explaining the elongation and two anomalous low centers of stratospheric polar vortex. A blocking commonly developed over the Urals in these two periods, which enhances the local ridge and the climatological wavenumber 2. In late December 2020 and during the post-SSW period, an anomalous low appeared over North Pacific, which favors the deepening of the local trough and the climatological wavenumber 1.
(d) Favorable conditions for the occurrence of the SSW in January 2021 include the BK sea ice loss in the preceding autumn and the cold SST state in tropical Pacific (i.e. a La Niña developed in the 2020/21 winter). Composite 500 hPa height anomaly patterns in January for the BK sea ice loss in autumn and La Niña are highly consistent with the observed circulation anomaly in January 2021. Both conditions favor the deepening of the high latitude North Pacific low and the rising of the Urals ridge. In contrast, the tropical convection over western Pacific associated with the MJO phase 6 is fairly weak in the pre-SSW and onset periods. (e) Cold air outbreak in China during the 2021 New Year period is not solely due to the stratospheric variation, because the SSW signal mainly developed in the stratosphere and did not reach the near surface. This cold surge was mainly related to the synchronous upstream blocking development over the Urals. In contrast, the second downward-propagating signal reached the near surface in middle February 2021, which together with the MJO phase 7 are consistent with the cold air outbreak in the US and associated extreme coldness of Texas in middle February.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).