The dynamical evolution of Sudden Stratospheric Warmings of the Arctic winters in the past decade 2011–2021

In this study, we analyse the dynamical evolution, and identify the major warming (MW) and minor warming events of the past 11 Arctic winters (2010/11–2020/21). During the period, MW is found in 4 winters and is in January for 2012/13, 2018/19 and 2020/21 and in February for 2017/18. A major final warming is observed in the year 2015/16. The most severe MW occurred in the 2012/13 winter, for which a rise in temperature of about 30 K is found at 60° N. The investigation of tropospheric wave forcings for the period reveals that the MW in 2012/13 and 2017/18 is forced by the combined activity of waves 1 and 2, whereas the MW in 2018/19 and 2020/21 is driven by wave 1. Studies have shown that the frequency of Sudden Stratospheric Warming (SSW) in the Arctic has been increasing since 1957/58, which is about 1.1 MWs/winter during 1998/99–2009/10. However, this frequency decreases to 0.36 MWs/winter in the period 2010/11–2020/21 and 0.74 MWs/winter in 1998/99–2020/21. An inverse relationship is observed between the period of occurrence of SSWs and total column ozone (TCO) in the Arctic for the past 11 winters (2010/11–2020/21). For instance, the temperature in the lower stratosphere in January, in which most warmings occur, shows a statistically significant high positive correlation (0.79) with the average TCO in January–March. Therefore, this study assists in understanding the relationship between inter-annual variability of ozone and the occurrence of SSWs. Major warmings (MWs) of the past decade occurred mostly in January and then in February. A decreasing trend in the occurrence of MWs in the past decade, 0.36 MWs/winter. The warming occurrences in the stratosphere make lower ozone depletion. A positive correlation exists between lower stratospheric temperature and total ozone. Major warmings (MWs) of the past decade occurred mostly in January and then in February. A decreasing trend in the occurrence of MWs in the past decade, 0.36 MWs/winter. The warming occurrences in the stratosphere make lower ozone depletion. A positive correlation exists between lower stratospheric temperature and total ozone.


Introduction
The presence of Sudden Stratospheric Warming (SSW) events drives the dynamic nature of Arctic stratosphere in most winters. Scherhag [1] recorded the first of such warming, which takes place when the temperature rises suddenly at 10 hPa pressure level poleward of 60° N/S latitude in a matter of a few weeks [2]. The meridional temperature gradient is reversed, and the direction and speed of the zonal winds are changed during the major SSW period [3,4]. The observed temperature increase is in the range of 30-40 K at 60°-90° N/S latitude, and it is followed by a reversal of westerlies during major warming (MW), but only a weakening of the westerlies during minor warming (mW) [5,6]. Despite the WMO criterion for SSW, there are still debates on certain conditions chosen such as the latitude and duration of wind reversal [7][8][9]. The polar vortex dynamics and positions are altered by SSW-related changes in the westerlies, which finally culminate in either the displacement or breaking of the vortex [10][11][12].
The wave mean flow interactions between the climatological westerlies and the planetary waves is the actuating mechanism of SSWs. The westerlies of the polar vortex are forced by quasi-stationary waves (Rossby waves), resulting in a slowing of the winds and thus, the adiabatic warming there [13]. The vortex regains its shape and location depending on the type of wave forcings (e.g. wave number 1, 2 or 3). The classification of MW events to the split and displacement types differ based on the criterion such as the central dates and datasets used. For instance, the MW in 2009/10 (central date 9 February 2010) is identified as a displacement event in the study of Kuttippurath and Nikulin [7], but a vortex split event in other studies [14,15]. They followed the criteria that closely resembled Charlton and Polvani [12] (CP07). The CP07 criterion classifies the events depending on the absolute vorticity of polar vortex. Unlike this, in the years following, the events were also classified based on the type of wave forcing causing the event. The vortex split events are often found associated with wave 2 forcing and displacement events are related to wave 1 forcing [16]. However, in a few winters, the split events were not forced by wave 2, but by wave 1 (e.g. 2018/19). Recently, another method of classifying the events was also devised by Choi et al. [17], where the MW occurrences are categorised as split and displacement events based on the nature of vortex and wave forcing (1 or 2) before and after the central dates.
SSWs are more common in the Northern Hemisphere (NH) than in the Southern Hemisphere (SH) due to strong planetary wave forcing in NH [18]. The two main elements that encourage this disparity are the difference in land and sea temperatures, as well as the topographical variations in these regions. The El Nino Southern Oscillation (ENSO), Quasi-Biennial Oscillation (QBO), sea ice concentration (SIC) and sea surface temperature (SST) anomalies also influence the wave forcing [19][20][21][22][23][24]. Climate change has a different effect on SSW events in NH than it does in SH. In a changing climate context, the SSW events tend to become more common in NH although no clear evidence has surfaced yet [25,26]. An inherent consequence of SSW is noticeable in the surface climate for a few weeks or months [23,27]. Aside from the effects on the surface temperature and precipitation, similar effects can be observed in the upper atmosphere such as in the mesosphere and ionosphere [28].
The occurrence of SSW has been increasing since its earliest documentation in January 1952. This rate of increase in frequency differs in different studies based on the criterion chosen for the classification of warming. The most used metric to classify the SSW into MW and mW is CP07, where the warming is considered to be major when the wind reverses at 10 hPa at the 60° N/S latitude from November to April, and must reverse for at least 10 days continuously before late April. However, the number of MWs can differ based on datasets. The assessment of reanalysis datasets for the period 1958-2002 conducted by CP07 shows that the SSW occurs in the order of six events per decade. Studies have also shown that SSW occurred once every two winters from the late 1950s to 1990 [14,29]. Conversely, a single minor warming episode (1989/1990) was observed during the period 1989/90-1997/98 [30]. The warmings became more common beyond this period i.e., 1998/99-2008/09 [7]. Several winters were marked by the presence of multiple SSWs such as in 1998/99, 2001/02, 2007/08 and 2009/10 [31][32][33][34]. The study of Kuttippurath and Nikulin [7] revealed that the frequency of SSW in 1998/99-2009/10 (∼ 1.1 MWs/winter) increased by nearly twice that recorded in 1957/58-1997/98 (∼ 0.6 MWs/winter). Statistical characteristics of SSWs using model simulations and reanalysis showed that there is a high frequency of SSWs before the 1990s with an average of 5-6 events in a decade [35]. Similar model results of the SSW frequency are also presented in the study of Liu et al. [36]. All three studies show that the majority of these warmings occur in the month of January, followed by February.
Here, we analyse the SSWs occurred during the period 2010/11-2020/21. We perform a comprehensive analysis of all minor and major warmings that have happened in the past decade. Four major warmings were recorded in the winters of 2012/13, 2017/18, 2018/19 and 2020/21 [37][38][39][40][41][42]. The impact of SSW on the Arctic ozone and the frequency of SSWs over the course of time are evaluated. The first section of the study examines the temporal evolution of meteorological parameters. The polar vortex dynamics is an inevitable component in the analysis of SSWs, and thus the Potential Vorticity (PV) maps are examined afterwards. The dynamical evolution of the fluxes is described in the last part of the first section and is crucial to understanding the wave components of dynamical forcing. The last part concludes with an examination of the relationship between ozone concentration and SSW timings (Table 1).

Data and methods
The Charlton and Polvani (CPO7) [12] criterion is applied to classify the winters as major warming and minor warming. When the temperature rises rapidly (20-30 K) North and South of 60° N/S and is accompanied by a reversal of zonal winds at 10 hPa, the event is a MW. Warming is referred to as a mW when the reversal of zonal winds does not accompany the increase in temperature. We use the Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) data to investigate the changes in temperature and zonal winds [43]. These reanalysis datasets have a resolution of 0.5° × 0.625° and a temporal resolution of three hours at 42 pressure levels. The classification of events based on the nature of polar vortex position and movements is similar to that of Cohen and Jones [14]. The breaking of a polar vortex during spring, and thus, the change in the direction of the zonal winds, characterise the final warming [44]. The final warming dates are analysed in our study based on the date of final reversal of the westerly at 10 hPa in the 65° N latitude, as done by Black and Daniel [45]. As a result, once the westerlies shift to easterlies due to the final warming, they will prevail until the next autumn.
Apart from this, the dynamical evolution of the winters is analysed using the Eliassen Palm (EP) flux divergence, heat flux, momentum flux and the amplitudes of wave forcings. The EP flux analysis assists in the estimation of tropospheric wave forcing. Detailed descriptions of this are found in Andrews et al. [4]. The divergence of EP flux is calculated using the method devised by Jucker [46]. Different methods of scaling the flux vectors are also described in other studies [47]. The EP flux considered in our study combines the vertical and meridional components. The dynamics of the vortex is examined to identify the years of vortex split and displacement using the PV maps [48]. The vortex edge is estimated by the Nash et al. [49] criteria. These maps are overlaid using the geopotential heights taken from the MERRA 2 data.
The relationship between the concentration of ozone and the presence of MW in the winters is evaluated using the total column ozone (TCO) obtained from the TOMS (Total Ozone Mapping Spectrometer), OMI (Ozone Monitoring Instrument) and OMPS (Ozone Mapping and Profiler Suite) satellite instruments. The trend in TCO is evaluated for the past four decades and correlation of the TCO with temperature, wind, Area of the Polar Stratospheric Clouds (A psc ) and the geopotential height (GPH) is estimated using the linear regression method. The mean PSC area (A psc ) at 460 K computed from the MERRA-2 dataset is taken from the NASA ozone watch website. The statistical significance of the relationship between the parameters and TCO is evaluated using the two-tailed t-test.

Warmings during the winters 2010/11-2020/21
The evolution of zonally averaged temperature for the winters of 2010/11-2020/21 at 60° N and 90° N is presented in Fig. 1. Individual years are shown in different colours and the third panel of Fig. 1 shows the seasonal development of mean zonal winds at 60° N. The significance of examination at 90° N is to analyse the amplification effect of the change in temperature due to SSW in the polar region. Climatology of the temperature and zonal winds is also presented in Fig. 1, to better understand the inter-annual variability. The estimates of zonal wind speed at 60° N reveal that the winters 2012/13, 2017/18, 2018/19 and 2020/21 were characterised by the reversal of wind. The most severe and prolonged warming was in 2012/13. The temperature at 60° N began to increase by late December (202 K) (20-24 December) and it reached the peak of warming in early January (234 K, 10-11 January). Therefore, a rise of about 30 K was observed in that winter [38]. However, the next MW was observed after 4 years, in 2017/18 and temperature rise of about 24-26 K (60° N) was found in the winter (214-238 K, early February to mid-February). Model predictions of Rao et al. [44] and Karpechko et al. [50] also estimated similar dates of onset for the MW in that winter. The warming in 2018/19 and 2020/21 began in mid-December and continued until early January. Unlike the previous warmings, the rise in temperature at 60° N for both winters was moderate in the range of 20 K (210-230 K). Contrary to this, the temperature rise almost doubled at 90° N for both 2020/21 (38 K) and 2018/19 (40 K) MWs, and the intensity of warming at 90° N was lower for 2012/13 and 2017/18.
Apart from the major warmings, minor warmings were also observed during the period of study. A temperature difference of 20 K was noticed at 90° N in 2010/11 and 2019/20 from late January to early February. However, the  Figure 2 shows the vertical development of the zonally averaged temperature (coloured contours [left]) from 60° N to 90° N along with the evolution of the westerlies and easterlies (coloured contours [right]) (zonally averaged over 60°-90° N). As discussed in much of the previous studies, following a MW event, the high-temperature regions descent to lower altitudes and is also accompanied by the descent of the easterlies. The extent of descent to the lowermost altitudes depends on the severity of warming and they remain in the same altitude for a short period (a week or more). During the 2012/13 winter, the easterlies appeared in late January and extended to altitudes as low as 75 hPa, as depicted in Fig. 2. The higher temperature contours of 240-250 K are found near the upper stratosphere (1-10 hPa). The lowermost descent of easterlies is observed during the MW of 2017/18. The high-temperature contours were found at altitudes lower than 10 hPa and the easterlies were present at altitudes lower than 75 hPa. Similar descent is also found in 2020/21, but is not as strong as the MW in 2017/18. The descent of easterlies

Potential vorticity analysis
A majority of SSW episodes conclude with either a split or displacement of the polar vortex. These changes in the vortex are significant because they assist to determine the severity of warmings, which can affect regional weather, and can aid in the diagnosis of wave forcings. These can be studied effectively using the PV maps. We have computed the Ertel's potential vorticity (EPV, 1 EPV = 10 -3 PVU) ( The geopotential height contours are superimposed on the PV maps. Geopotential height values are higher over warmer regions and vice versa. These contours closely follow the shape of polar vortex. Figure 3 shows the temporal evolution of polar vortex at 10 hPa. The early stages of the formation of vortex are observed for all MW winters. The vortex is observed to be circular and concentric in the beginning of warming in 2012/13 and 2017/18. However, the vortex is distorted to a coma-shaped and elongated for the 2018/19 and 2020/21 winters, respectively. In the lower altitudes or at 70 hPa the distinct concentric shapes of vortices are hardly identifiable (Fig. 4).
The vortex was stable in early December 2012 and was fully formed by the end of December as observed from Fig. 3. The MW in 2012/13 begun in late December and reached the peak stage during early January. Thus, as the westerlies changed to easterlies, the vortex became unstable and started to elongate (6 January 2013). Furthermore, on 8 January 2013, the vortex split and migrated to the mid-latitudes. A part of the vortex moved to Central North America and the other lobe displaced to Russia [37]. This split in the vortex and displacement to the nearby regions are also visible at 10 hPa. In 2017/18, a fully developed vortex is observed in December and as the warming begins, the vortex became less stable and split into two lobes on 12 February 2018 [41,57]. The split is very evident at 10 hPa (Fig. 3), but less identifiable at 70 hPa (Fig. 4). The split became more explicit at both latitudes in the days following as the easterlies extended to lower altitudes, as illustrated in Fig. 2. The breaking of vortex in early (4) January of 2019 owing to MW that commenced in mid-December led to the shift of vortex to the eastern North America and Russia. The evolution of geopotential height with warming is also presented in the study of Lee and Butler [55].

Eliassen Palm flux divergence and wave forcings
A significant component influencing the variability of polar vortex and its position is the intensity of wave forcings from the lower latitudes [20,58]. Therefore, the estimation of flux divergence and wave forcings are inevitable elements in the assessments of SSWs. The heat flux, momentum flux, amplitudes of the geopotential waves and the EP flux divergences are examined by considering their temporal progression at 60° N and 10 hPa, and are depicted in Fig. 5. The EP flux divergence is important also from the perspective of zonal winds. That is, negative values of EP flux divergence imply that the westerlies are decelerated (convergence) or that the westerlies could revert to easterlies. Conversely, positive values of EP flux divergence suggest strong westward winds or acceleration of the westerlies. Therefore, the EP flux divergence is significant to study the dynamics of polar vortex. The first panel of Fig. 5 shows the heat flux for the years 2010/11-2020/21. The heat flux increases up to the order 500-550 Kms −1 during the period of warming in 2012/13 and are the highest among the winters [59]. The corresponding momentum flux also increases to reach the peak value of 400 ms −1 in late December and early January. The heat flux (400-500 Kms −1 ) and momentum flux (300-400 ms −1 ) magnitudes in 2017/18 and 2018/19 are very similar, but are slightly lower in 2020/21 (300-400 Kms −1 and 200-300 ms −1 , respectively). An interesting feature noticed is the high heat flux at 10 hPa and the highest momentum flux just before the peak warming period in all years, as also noted by Kuttippurath and Nikulin [7]. The estimates of mean zonal (45°-75° N) eddy heat flux at 100 hPa by Lu et al. [42] reveal an intensification of these fluxes right before the MW in 2020/21. A similar analysis is also present in the study of Lee and Butler [55] for the 2018/19 winter, where enhanced heat flux was found in late December prior to the MW in January 2019. Consistent patterns of higher heat flux forcings during the period of mWs are also shown in Fig. 5. Strahan et al. [60] also observed reduced (enhanced) wave forcing as analysed from the eddy heat flux at 100 hPa in the cold (warm) winters during the period 2005-2015.
The third and fourth panels of Fig. 5 are important as they expose the component of wave forcing responsible for the warming. The amplitudes of wavenumber 1 and 2 are analysed since they correspond to the mid-latitude planetary Rossby waves. The amplitude of planetary waves reduces as the zonal wavenumber increases. The 2012/13 winter was forced by high amplitudes of wave 1 (1200-1300 gpm) in December 2012, which was followed by a moderate wave 2 forcing (700-800 gpm) in early January. Therefore, the weakening of vortex began due to the influence of wave 1 and the vortex split was initiated by wave 2 [37,61,62]. The situation in 2017/18 winter was also similar, as wave 1 reached its highest amplitude (1500 gpm) prior to the warming and was followed by an increase in the magnitude of wave 2 (1300-1400 gpm) [44]. However, in 2018/19 and 2020/21, the forcing of wave 1 was more prominent (1500-1600 gpm). The wave 1 amplitude during the warming in 2020/21 is the highest in the past 40 years [56]. Among the external factors that influence the variability of polar vortex as discussed before in the first part of this study are the effects of ocean-atmosphere coupled processes (e.g. ENSO) and other tropospheric phenomena (e.g. QBO). A detailed description of the external forcing on the SSW winters is presented in the study of Baldwin et al. [63]. It has been observed from previous studies that the MW

Major warmings and ozone
Apart from the impact of MWs on the meridional temperature gradient, zonal winds and surface conditions, the effect on polar stratosphere composition is also quite significant and has been studied in much of the previous literature [7,63,66,67]. The warming causes a displacement of vortex and is also capable of changing the formation and amount of PSCs (Polar Stratospheric Clouds) responsible for ozone depletion. Henceforth, the MWs indirectly affect the amount of ozone loss in warm winters. Figure 6 compares the amount of polar cap ozone for a period of 12 years (2010-2021). The total column ozone (TCO) is obtained from satellite data and is averaged north of 63° N for January and February. The panels below in Fig. 6 show the interannual variability of the area of PSC (A psc ), zonal mean temperature (60°-90° N), zonal mean wind (60°-90° N), and the geopotential height (60°-90° N).
The parameters are analysed for January and December-March periods. It is observed that the highest correlation between the variables such as the zonal mean temperature, wind and the geopotential height is observed . The corresponding zonal mean temperatures are also higher during these years. The TCO amount is highly correlated positively with the mean temperature in January and is statistically significant. Therefore, TCO is directly proportional to the mean temperature in January. However, this correlation reduces substantially and is slightly negative (− 0.03) when the mean temperatures between December and March are considered. Similarly, it is observed that TCO shows a high positive correlation (0.73) with the geopotential height and its value during the MW years is higher than that of the cold winters. The zonal mean wind and the area of PSCs show inverse relationship with TCO, with the correlation of − 0.67 and − 0.89, respectively. The calculated P-value and t-value also confirm the statistical significance of these estimates. Similarly, the relatively lower temperature and higher zonal wind speed promoted unprecedented ozone depletion or lower TCO in 2010/11 and 2019/20 [51,68]. Pommereau et al. [69] reveal that the highest percent of ozone loss during the period 1991-2017 was in the 2010/11 winter, although the winter 2019/20 was not included in their study. The corresponding A psc was also the highest for the 2010/11 and 2019/20 winters. The TCO amount for the SSW years is higher than that of other years.
The highest TCO in the MW winters is observed in 2018/19, which is a direct influence of the extremely small PSC area and high temperatures. The speed of zonal winds is low and the geopotential height is moderate in that winter. In 2012/13 and 2018/19, the PSC area is marginally reduced due to the strong warming during the period and thus, the TCO amount is highest among the 12 years. The zonal wind speed is lowest in January 2021; implying a weak polar vortex due to the warming. Although 2017/18 had a MW, the TCO is lower than that of other MW winters because of the relatively stronger polar vortex and higher A psc (in January) during the period. Since, most MWs occurred in January and February; the amount of ozone is also found to be increased consistently during the period. Therefore, the timing of maximum TCO varies directly with the occurrence of a MW. The ozone trend analysed for the past four decades (1979-2020) reveals that the TCO is decreasing at − 0.08 DU/year for the period January-March, but increasing at 0.30 DU/year in January-February, although these values are not statistically significant. It is probable that the increasing trend during the January-February period is influenced by the presence of frequent SSWs.

Conclusions
We have characterised the SSWs for the past 11 winters (2010/11-2020/21) in the Arctic. The occurrence of major warming was identified in 4 winters; namely 2012/13, 2017/18, 2018/19 and 2020/21. These events have a subsequent influence on the surface weather and there are ample shreds of evidence that imply the same [57,61,70]. The cold air outbreak following the major warming of 2017/18 was titled as the 'Beast from the East' due to the extreme cold winters that resulted after the warming in the Arctic [71]. Therefore, it is important to conduct a comprehensive study of these events together with the mW events to improve the predictability of these events in the coming years. We found that, among the MW winters, the most severe warming was manifested in 2012/13. This severity is identified by the steep temperature rise (30 K) and the longest persistence of easterly winds in that winter. The easterlies extended to altitudes as low as 75 hPa. The examination of the relationship between total column ozone and the occurrence of SSWs since 2000 revealed that the amount of ozone is directly proportional to the presence of warmings. A high negative correlation is noticed between TCO and the area of the PSCs. The highest TCO was observed in the MW of 2018/19 (420 DU) in agreement with the smallest PSC area (< 2 million km 2 ) in that winter. Despite the development of mWs in other winters, 2010/11, 2015/16 and 2019/20 were unusually cold for much of the early winter and henceforth, was responsible for significantly higher PSC area (6-8 million km 2 ) and smaller TCO (340-350 DU). Nevertheless, the ozone loss further was restricted by the mW events that occurred in the latter part of those winters. Therefore, our study also helps to analyse the connection between ozone and the SSWs. Funding This study received no funding.

Data availability
The data utilised in this study is open to the public. On request, the analysed data can be shared. The MERRA-2 data are on: https:// gmao. gsfc. nasa. gov/ reana lysis/ MERRA-2/, the CAMS data are on: https:// atmos phere. coper nicus. eu/ data. The total ozone column data obtained from the TOMS, OMI and OMPS satellite dataset from the NASA ozone watch site: https:// ozone watch. gsfc. nasa. gov/. The NCEP data are available on https:// psl. noaa. gov/ data/ gridd ed/ data. ncep. reana lysis. html.

Conflicts of interest
The authors declare no conflict of interest associated with this study.
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