Evolution of the stratospheric polar vortex edge intensity and duration in the Southern hemisphere over the 1979 – 2020 period

. The intensity and position of the Southern Hemisphere stratospheric polar vortex edge is evaluated as a function of equivalent latitude over the 1979 – 2020 period on three isentropic levels (475 K, 550 K and 675 K) from ECMWF ERA-Interim reanalysis. The study also includes an analysis of the onset and breakup dates of the polar vortex, which are determined from wind thresholds (e.g. 15.2 m.s − 1 , 20 m.s − 1 and 25 m.s − 1 ) along the vortex edge. The vortex edge is stronger in late winter, over September - October - November with the period of strongest intensity occurring later at the lowermost level. A 5 lower variability of the edge position is observed during the same period. At the same period, we observe a lower variability of the edge position. Long-term increase of the vortex edge intensity and break-up date is observed over the 1979 – 1999 period, linked to the increase of the ozone hole. Long-term decrease of the vortex onset date related to the 25 m.s − 1 wind threshold is also observed at 475 K during this period. The solar cycle and to a lower extent the quasi-biennal oscillation (QBO) and El Niño Southern Oscillation (ENSO) modulate the inter-annual evolution of the strength of the vortex edge and 10 the vortex breakup dates. Stronger vortex edge and longer vortex duration is observed in solar minimum (minSC) years, with the QBO and ENSO further modulating the solar cycle inﬂuence, especially at 475 K and 550 K: during West QBO (wQBO) phases, the difference between vortex edge intensity for minSC and maxSC years is smaller than during East QBO (eQBO) phases. The polar vortex edge is stronger and lasts longer for maxSC/wQBO years than for maxSC/eQBO


Introduction
The stratospheric polar vortex is a seasonal low-pressure system characterized by a strong wind belt that isolates polar air from lower latitudes. It appears due to the seasonal cooling associated with the decrease of solar radiation above the pole (Randel and Newman, 1998). As the incident solar energy decreases, and the gradient of temperature between the pole and the tropics becomes stronger, the strength of the stratospheric westerly winds increases. When the winds reach a critical value, 20 a large-scale vortex is formed, which extends from the lowermost stratosphere to the stratopause. Depending on altitude, the maximum area encompassed by the polar vortex exceeds millions of square kilometers (NOAA, 2021). Above an altitude of about 14 km, the vortex edge region is stable and constitutes a powerful barrier, preventing mixing of cold polar air with warmer air masses from lower latitudes. Over Antarctica, the polar vortex is generally present from May until the end of November April until December with a large variability in the breakup dates resulting from the year-to-year variability 25 of dynamical processes in the stratosphere Rao and Garfinkel 2021). Conversely, the less stable Arctic polar vortex has more year-to-year variability (e.g. Andrews et al. 1987;Hu et al. 2014;Butler et al. 2019).
It forms in November and lasts until the end of February or early April, depending on the year. The stratospheric polar vortex have been the subject of studies linked to the ozone layer depletion of the ozone layer, which started in the late 1970 (Farman et al., 1985;Solomon 1999). Ozone loss occurs in both hemispheres. This loss is variable in the northern hemisphere as 5 many studies have shown (Solomon 1999;Goutail et al. 2005;Pommereau et al. 2018;WMO 2018;Grooß and Müller 2020). In the Southern Hemisphere, the ozone hole, defined as an area with total ozone values less than 220 DU, has become a recurring seasonal phenomenon. Ozone destruction begins in late winter, close to the edge region of the polar vortex, as solar radiation increases over the Pole. The destruction of ozone inside the southern vortex accelerates from late August until late September or early October, reaching an almost complete destruction of ozone in the lower stratosphere. The depletion of the 10 ozone layer is caused by anthropogenic emission of ozone depleting substances (ODS -mainly chlorofluorocarbons and halons and their industrial substitutes), which enhances ozone destruction cycles by halogen compounds. This depletion is largest in the polar vortex due to the activation of chlorine species through heterogeneous reactions that take place at the surface of polar stratospheric clouds (PSCs) which form in the cold polar vortex (Solomon, 1999). The increase in solar radiation over the Pole at the end of winter triggers rapid chemical cycles which quickly destroy ozone, leading to the appearance of the well-known 15 ozone hole over Antarctica (e.g. WMO, 2018). PSCs are found to be much more abundant in the Antarctic polar vortex as compared to the Arctic polar vortex due to the increased stability of the southern polar vortex. As a result of the asymmetry in polar vortex intensity, the southern vortex experiences much colder temperatures in winter, which results in stronger ozone depletion over a large area (the so-called ozone hole). By the end of spring, stratospheric temperatures increases, the polar vortex breaks up and ozone depleted air masses dilute into the Southern Hemisphere. From one year to the next, the severity 20 of the ozone hole will thus depends on the strength of the polar vortex, its minimum temperatures and duration. The future recovery of the ozone layer and disappearance of the ozone hole depends on the polar vortex evolution of the polar vortex under the influence of both the decrease of ODS abundance in the stratosphere and the increase of greenhouse gases (GHG) as both phenomena impact radiative, dynamical and chemical processes in the stratosphere. Many studies document this phenomenon (e.g. WMO 2018 and references therein). The polar vortex also has an impact on the climate surface in 25 both hemispheres. Indeed, studies have shown an effect of the stratospheric polar vortex displacements on cold spells in the northern hemisphere, in North America (Tripathi et al., 2015). In the southern hemisphere, others have shown that a weak vortex can have an influence on the surface climate in Australia. Lim et al. (2019) have highlighted that selected years of lower vortex intensity results in higher temperatures and less precipitation over eastern Australia. The dramatic weakening of the Antarctic vortex in 2019 had a large impact on meteorological conditions over the country 30 that resulted in the strong Australian fires of the turn of the year 2019/2020.
The inner vortex is characterized by high absolute values of potential vorticity (PV). As this parameter is conserved on isentropic surfaces during weeks, the mapping of PV maps on such surfaces is one of the primary diagnostic tools for the analysis of dynamical processes analyses in the stratosphere and inside the polar vortex. McIntyre and Palmer (1983) first represented daily PV global maps of isentropic surfaces, demonstrating a material separation in the stratosphere between the 35 main vortex, characterized by high absolute PV values, the surf zone, characterized by a weak absolute PV values, and a zone of strong meridional PV gradient in between: the so-called vortex boundary or vortex edge, which is an area of low mixing representing a dynamical barrier to air masses exchanges. Numerous studies on the vortex boundary definition have been performed. Nash et al. (1996) defined the vortex edge as the location of the maximum PV gradient as a function of equivalent latitude (EL), weighted by the wind module mean speed. This is the method used in this study. The equivalent latitude is a 5 parameter defined from the PV maximum within the vortex, e.g. Butchart and Remsberg (1986). EL defines the latitude limit of the polar area which exceeds a certain PV value (maximum PV is then given at EL = 90 degrees, e.g. Butchart and Remsberg (1986)). A PV field sorted by EL will then make the polar vortex concentric around the pole. This is the method used in this study. Nakamura (1996) has developed the effective diffusivity diagnostic, which is applied on tracers to identify transport barriers and regions of mixing regions. Hauchecorne et al. (2002) used this method to quantify the transport 10 of polar vortex air to mid-latitudes, as well as to evaluate the polar vortex barrier intensity. The method of elliptical diagnostics of a contour used by Waugh (1997), consists in fitting an ellipse to the contour of a parameter. It subsequently determines several variables of this ellipse, for example latitude and longitude of the center, the equivalent latitude, or its orientation. It is possible to calculate the elliptical diagnostics of a contour of conservative tracers such as PV or long-lived chemical species around the polar vortex edge region . The vortex forms in autumn, intensifies throughout the winter 15 and disappears in spring/summer. Its overall strength is variable from one year to the next. Different studies have analyzed the inter-annual variability of the polar vortex induced by forcings such as the solar flux (SF), Quasi-Biennial Oscillation (QBO) and El Niño Southern Oscillation (ENSO), particularly in the Northern Hemisphere. QBO is a quasi-periodic oscillation of the equatorial zonal wind between easterlies and westerlies. Holton and Tan (1980) made a composite study of zonal wind in the Northern Hemisphere at 50 hPa from 1962 to 1977 based on the different QBO phases. They showed that the vortex is less 20 disturbed during the West phase of the QBO (wQBO) at 50 hPa than during the East phase (eQBO). Labitzke and Van Loon (1988) evaluated the temperature and strength of the Arctic polar vortex according to the solar cycle and the QBO. They found that the vortex is warm and weak during solar maxima/eQBO phases, and cold and strong during solar minima/wQBO phases at 50 hPa. Camp and Tung (2007) supports this finding that the state of the northern hemisphere polar stratosphere is less perturbed during solar cycle minimum and westerly QBO phases. Then, Baldwin and Dunkerton (1998) showed 25 over a period of 18 years, that the Antarctic polar vortex at 10 hPa is slightly colder during wQBO. ENSO is an irregular oscillation in winds and sea surface temperatures over the tropical eastern Pacific Ocean, affecting the climate of the tropics and subtropics. It influences also other climatic parameters such as precipitations worldwide and ozone levels in the lower stratosphere (WMO, 2018). Domeisen et al. (2019) have indicated that the El Niño events are associated with a warming and weakening of the polar vortex in the polar stratosphere in both hemispheres, and Li et al. (2016) have shown that 30 early breakup of the southern polar vortex occurs during El Niño events. In contrast, Rao and Ren (2020) did not find a significant impact of the canonical ENSO index on the Southern Hemisphere polar vortex in both observations and modeling studies. With indices of Niño-3 and Niño-4 regions, Hurwitz et al. (2011) have shown that during "warm pool event" (positive SST in Niño-4 regions) the heat flux is higher and the Antarctic vortex breaks up earlier. Several methods have been suggested in order to determine the onset and breakup dates of the polar vortex. They are based on a 35 minimum area computed from equivalent latitudes (Manney et al. 1994;Zhou et al. 2000) or wind mean speed thresholds along the edge (e.g. Nash et al. 1996). Manney et al. (1994) and Zhou et al. (2000) consider that the vortex breaks down and disappears when its size falls below 1% of the Earth's surface, or when its edge position is larger than 78.5 • EL. More recently, Millan et al. (2020) compared the polar vortex evolution with different reanalyses, including ERA-Interim. Results showed that all reanalyses where in agreement with the reanalysis ensemble mean (REM), which shows that we can be confident with 5 the ERA-Interim reanalyses for our study. The latter is used in WMO (2018) to calculate the dates at which the Arctic and Antarctic polar vortex breaks each spring.
The objective of this paper is to analyze the long-term evolution of the intensity, position and duration of the Southern polar vortex edge as a function of equivalent latitude over several decades (1979 -2020). ERA-Interim reanalyses and operational data from the European Centre for Medium-Range Weather Forecast (ECMWF) are used for the study, which includes an 10 evaluation of the onset and breakup dates of the polar vortex over the period. At an inter-annual scale, the signature of the 11-year solar cycle, QBO and ENSO, is evaluated on the vortex edge evolution. This is the first study of the variability of the Antarctic stratospheric polar vortex edge and persistence over a long period (42 years).
The paper is organized as follows. Section 2 presents the ECMWF dataset and the data sources of the forcings (SF, QBO, and ENSO) used for the analysis of inter-annual variability of the polar vortex edge. Section 3 describes the methods used in 15 the study, such as the MIMOSA (Modélisation Isentrope du transport Méso-échelle de l'Ozone Stratosphérique par Advection) model (Hauchecorne et al., 2002), which is used to construct the PV maps as a function of potential temperature and equivalent latitude. The methods used for the vortex edge characterization and for determining the onset and breakup dates of the polar vortex are also discussed in this section. Section 4 presents the statistical analysis of the annual evolution of the vortex edge over the studied period as well as its inter-annual evolution, related to the SF, QBO and ENSO forcings, while results on 20 the inter-annual evolution of the vortex onset and breakup dates are given in Section 5. Further discussion of the results and perspective of the study are presented in Section 6. where in agreement with the reanalysis ensemble mean (REM), which shows that we can be confident with the ERA-Interim reanalyses for our study. They are characterized by a resolution of 1.125 • latitude x 1.125 • longitude. ERA-Interim temperature, geopotential and wind data are the inputs for the MIMOSA model, which computes PV and EL fields on different 30 isentropic surfaces with a resolution of 0.3 • latitude x 0.3 • longitude, using a polar projection centered on the South. ERA-Interim temperature, geopotential and wind data with a resolution of 1.125 • latitude x 1.125 • longitude are inputs to the MIMOSA model, which is a three-dimensional high-resolution PV advection model (Hauchecorne et al., 2002). From MIMOSA high resolution PV fields it is possible to follow the evolution of polar air masses and filamentation processes of the polar vortex. Sampled every 6 hours, ERA-Interim reanalyses are interpolated on selected isentropic surfaces.
The model computes PV and EL fields on the isentropic surfaces with a resolution of 0.3 • latitude x 0.3 • longitude, using a polar projection centered on the South from 90 • S to 10 • N. The advection method is applied to this orthographic grid.
After some time, the MIMOSA grid is distorted by the horizontal gradients of the wind fields. A re-interpolation of the 5 PV fields on the original grid every 6 hours is then performed. Finally, in order to take into account diabatic processes, a relaxation of the MIMOSA advected PV (APV) towards the ECMWF PV is made every 12 hours with a 10 day time constant. The MIMOSA model is a three-dimensional high-resolution PV advection model (Hauchecorne et al., 2002) which This model has been used to analyze, among other studies, the permeability of the southern polar vortex to volcanic aerosols from Cerro Hudson and Mount Pinatubo eruptions in 1991 , and to predict the extension in the lower mid-10 latitude stratosphere of polar and subtropical air masses (Heese et al., 2001). or to evaluate average total ozone evolution within the Antarctic vortex with PV fields simulated by the model, used to determine the vortex position in Pazmino et al. (2018). In Pazmino et al. (2018), PV fields simulated by the model are used to evaluate average total ozone evolution within the Antarctic vortex. For this study, PV fields are computed at 675 K, 550 K and 475 K isentropic levels. 15 Forcings considered for the analyses of the inter-annual variability of the vortex edge are described in Table 1. For the solar flux, we are mainly interested in the variability induced by the 11-year solar cycle. The F10.7 solar flux data record related to this cycle covers six solar cycles, including those covering our study period, the last four. It correlates well with the 11year sunspot cycle (Mishra et al., 2005, Tiwari andKumar, 2018) and has been used frequently as a proxy for solar activity (e.g. Solomon, 1999;Gray, 2003;Pazmino et al., 2018). It is defined in solar flux units (1 sfu = 10 -22 W.m -2 .Hz -1 ). For our study, we averaged the 10.7 cm solar flux and other proxies over the May -November period, which corresponds to the time period when the Southern polar vortex is well formed. , in order to analyse its impact on the vortex edge. Data were obtained for the 21 st to the 24 th solar cycles 21 to 24 (1976 to 2020). Years characterized by minimum and maximum solar intensity were selected from the difference of maximum and minimum intensity of each cycle (a methodology also considered in Rao et al. 2019). The minimum (maximum) intensity threshold was defined as the lower (upper) third of this difference, so that 25 the minimum and maximum thresholds are different for each cycle. The selection results in 15 maximum solar (maxSC) years and 20 minimum solar (minSC) years over the whole studied study period. In order to investigate the influence of QBO on the polar vortex, we used Singapore monthly mean zonal wind at the 50 hPa level, and averaged this parameter each year during the same period as for the solar cycle. QBO is sorted by negative phase for East QBO (eQBO) with 19 years and positive phase for West QBO (wQBO) with 23 years. In the case of El Niño Southern Oscillation, the Multivariate ENSO Index (MEI) 30 version 2 was used in this study. It correspond to the combination of empirical orthogonal function (EOF) of sea level pressure (SLP), sea surface temperature (SST), zonal and meridional components of surface wind and outgoing longwave radiation in the tropical Pacific basin. Data are for bi-monthly periods to take into account the seasonality of ENSO (see data availability [4]). Referring to the NOAA description of the MEI.v2 index (see data availability [4]): "The EOF are calculated for 12 overlapping bi-monthly "seasons" in order to take into account ENSO's seasonality, and reduce effects of higher frequency intra-seasonal variability". As for SC and QBO, we averaged these data during the May -November period.

Forcings of interannual variability
Then mean ENSO over the period is sorted to distinguish La Niña, characterized by a negative MEI (cold ENSO), and El Niño, characterized by a positive MEI (warm ENSO). The studied period is characterized by 21 wENSO and 21 cENSO years.

Vortex edge characterization
As mentioned in the introduction, the vortex edge is characterized by a strong PV gradient. To represent the vortex edge position, the method described in Nash et al. (1996) is used, which consists in determining the position of the edge from the where W correspond to the wind module is the wind mean speed. 15 Several methods have been used in order to determine the onset and breakup dates of the polar vortex in the Northern hemisphere (NH), as mentioned previously. Manney et al. (1994)  This defines the duration of the polar vortex. Subsequently, using wind fields in addition to the PV gradient as a function of EL, Nash et al. (1996) considered that the vortex is well formed at 450 K when the wind module wind mean speed along the vortex edge is equal to or greater than 15.2 m.s −1 . They also used the 3.2 m.s −1 standard deviation interval to provide a range of dates during which the vortex forms and breaks. Then  analyzed the breakup date of the Arctic and Antarctic polar vortex using NCEP data for the 1958-1999 period. They showed a tendency of extension of the breakup date   Figure 2 represents the statistical evolution of the vortex edge position in EL as described in Figure 1 for the PV gradient.

Onset and Breakup determination Determination of polar vortex onset and breakup dates
For this parameter, medians and percentiles curves show a similar behavior for the various levels from May to late September for all levels. The maximum polar vortex edge position is reached between mid-July and late August at 675 K, between mid-July and mid-August at 550 K and between mid-August and September at 475 K, with respective median average values  Hoppel et al. 2003). The 2019 winter impacts the minimum curve during the last 2 weeks of September at 675 K and is 5 located between the minimum curve and the 20th percentiles from September until the beginning of November for each levels.
During this year, a minor SSW occurred at the end of August, which displaced and weakened the polar vortex.
The stratospheric polar vortex abruptly weakened and warmed on August 25th (Lim et al., 2021). MERRA2 analyses showed a rapid 50 K increase of polar temperature at 10 hPa between September 5 and September 11 (Yamazaki et al., 2020). Minimum values of winds at 10 hPa and 60 • S were found on September 18 . This event induced 10 the smallest Antarctic ozone hole on record. Although it appeared earlier than usual in August, the ozone hole reached an area of 15 million km 2 by September 1, but decreased to an area of 8 million km 2 by September 17 (Lim et al., 2021).    There is less variability and fewer differences between maxSC and minSC years during the period of maximum intensity of the edge (see section 4.1). The difference between the medians was assessed by a Mann-Whitney and differences are 5 significant from 9 to 18 September at 675 K, from 18 July to 11 August and from 27 August to 7 September at 550K, and from 15 to 20 June at 475 K. are largest during the July -August period at 550 K with a mean p-value of 0.03.

Quasi-Biennial Oscillation
We have then studied the modulation of the SC influence on the vortex edge by the QBO. Figure 5 represents the composite analysis of the polar vortex edge intensity throughout the winter for the 1979 -2020 period at 550 K and 475 K, with maxSC and minSC years sorted with respect to the phase of the QBO: eQBO and wQBO are in the left and right panels respectively.
Only results for the lower levels are shown, as the differences are less clear at 675 K. In each panel, the dark (light) grey area 5 indicates the 20 th and 80 th percentiles of maxSC (minSC) years with the median in red (blue). Note that during the studied period there is are only 5 years for maxSC/eQBO versus 10 years for minSC/eQBO, and 10 years for both maxSC/wQBO and minSC/wQBO. These results are synthetized in Table 2. (see Table 2).
At 550 K, both QBO phases are characterized by a stronger vortex edge during minSC years but the differences between minSC and maxSC medians are largest during eQBO years. Largest variability of vortex edge intensity for minSC years (with

El Niño Southern Oscillation
We have also studied the combined modulation of the polar vortex edge by both the SC and ENSO. Figure 6 displays similar composites as in Figure 5 but selecting warm (wENSO) and cold (cENSO) ENSO phases (see section 2).
At both 550 K and 475 K, the largest difference between minSC and maxSC median vortex edge intensity is observed for cENSO years, with minSC years still characterized by the largest intensity. MaxSC year's vortex duration is also larger 5 during cENSO than wENSO years. At both levels, the difference between maxSC and minSC vortex edge intensity is small and insignificant during wENSO years, while cENSO are generally characterized by stronger vortex edge for both minSC and maxSC years. The polar vortex breaks earlier during the warm phase of ENSO, and especially during the maxSC years with a breakup in November. These results are in agreement with the literature (Li et al. 2016;Domeisen et al. 2019).

Inter-annual evolution of the Polar Vortex edge
As seen in section 4.1, the maximum median intensity is reached from September to late October at 675K, from September to early November at 550K, and early November at 475K during the September -November period depending on the isentropoc level. In order to study the interannual evolution of the maximum intensity and position of the vortex edge during these periods, we identified the day when the maximum was reached at each level and averaged the parameters over ±15 days 5 around this date. Figure 7 represents the inter-annual evolution of the polar vortex edge maximum intensity at each isentropic level over the 1979 -2020 period, averaged over September 15 -October 15, October and October 15 -November 15 at 675 K, 550 K and 475 K, respectively. Red circles (blue squares) indicate maxSC (minSC) years. Symbols-free years are years with 10.7 cm SF values in between minSC or maxSC years.
At 550 K and 475 K, an increase of the vortex edge intensity from the beginning of the period up to the end of the 1990s is visible while this increase is not observed at 675 K. It is about 121% and 136% at 550 K and 475 K respectively between 1980 and 1996, and about 61% and 86% between 1980 and 2000 at the same levels. This increase can be attributed to the increased 5 intensification of the ozone hole during the 1980s and 1990s as mentioned in other studies (Bodeker et al., 2002). From 2000, the intensity remains at a high level due to the continuing appearance of the ozone hole. Superimposed is the medium-term variability linked to the SC and inter-annual variability linked to the QBO and ENSO. In agreement with results in section 4.1 and 4.2, peaks observed around 1986, 1996, 2005 and 2016 are the signature of the 11-year solar cycle corresponding to minSC years. We note however that some maxSC years show high vortex edge intensity values, as e.g. 2014 at both 550 K and 475 K 10 levels. This year is in west QBO phase, which confirms the previous conclusion that vortex edge intensity of maxSC years is stronger during wQBO phases. However, it is a in a warm ENSO phase, while it was shown that the maxSC when the median vortex edge intensity was is lower during wENSO than during cENSO under maxSC conditions. It should be noted that the latest solar cycle (cycle number 24) was less intense than the previous ones (Jiang et al., 2015) and    due to the major warming and the vortex split, which occurred during that year. It was shown that the major warming in 2002, the first one observed over Antarctica, was mainly due to increased planetary waves activities in the southern stratosphere (Hoppel et al., 2003). Aside for With the exception of this year, the maximum edge position fluctuates between -65.7 • EL and -55.3 • EL, at all levels combined. At 550 K and 475 K levels, the edge position decreases from 1981 to 1994, with values varying from -56.6 • EL and -58.6 • EL to -63.4 • EL and -63.7 • EL respectively at both levels (average decrease of 7 • EL to 5 • EL in 14 years). It can be noted that these years correspond to the period when the intensity of the vortex edge increases. At 675

Onset and breakup of the Polar Vortex
The evolution of onset dates of the polar vortex throughout the winter from 1979 to 2020 at the 675 K, 550 K and 475 K isentropic levels is displayed in Figure 9. It represents the day of the year when the polar vortex is well formed, e.g. when the horizontal wind speed at the vortex edge is above the threshold values of 15.2 m.s −1 , 20 m.s −1 and 25 m.s −1 as suggested by Akiyoshi et al. (2009). In each panel, the blue, dark grey and light grey curves represent onset dates for the 15.2 m.s −1 , 20 m.s −1 and 25 m.s −1 thresholds respectively.
As espected, Due to the stronger radiative processes in the upper stratosphere, the temperature contrast between the polar region and mid-latitudes is stronger and the polar vortex forms more rapidly with a faster wind. Thus the vortex Similarly, as in Figure 9, Figure 10 shows the day when the polar vortex breaks up in Spring due to the final vortex warming, at 475 K, 550 K and 675 K isentropic levels. As mentioned in Nash et al. (1996), when the vortex is weakening between early and late Spring, the winds at the vortex edge also weaken, leading to the final vortex breakup. The vortex breakup is thus considered to occur given when the horizontal wind mean speed along the vortex edge falls below the 15.2 m.s −1 , 20 m.s −1 or 25 m.s −1 threshold values.

5
The vortex forms earlier at the highest levels and it also breaks earlier: the average breakup dates for the different threshold values are on days 340, 334 and 325 at 475 K, 550 K and 675 K, respectively. Rao and Garfinkel (2021) found that the average southern hemisphere stratospheric final warming at 50 hPa occurs around 2 December with JRA-55 reanalyses, which is consistent with our results at 475 K (on December 5 ). We notice some early breakup of the polar vortex: for example, in 1988 (the vortex broke up 13 days before the mean breakup date at 675 K, 20 days at 550 K and 21 days at 475 K). 10 In 2002, the breakup occurred 18, 9 and 8 days before the mean breakup date at 475 K, 550 K and 675 K, respectively. Some late breakups are observed during the last two decades particularly at 15.2 m.s −1 . The year 1999 is clearly noticeable at 475 K and 550 K with respectively 21 and 27 days respectively, after the mean breakup date for this threshold value. The years 2007,2008,2010 and 2015 also stand out for the three levels: around 14 days, 15 days and 14 days after the mean breakup date at 475 K, 550 K and 675 K, respectively. Finally, the year 2020 is noticeable for its exceptionally late breakup date, with 15 a breakup date occurring 20, 21 and 29 days after the mean threshold dates at 475 K, 550 K, and 675 K, respectively.
The latter value at 675 K sets a record over the whole studied period for the 675 K level.
The Figure This figure shows that the difference between the breakup dates for the various threshold values is much smaller than for the onset dates. The average difference between breakup dates for 15.2 m.s −1 and 25 m.s −1 is equal to 11.5, 8.9 and 8.2 days at 475 K, 550 K and 675 K, respectively, compared to ±32.9, ±21 and ±17.2 days, respectively, for the onset 20 dates. The smaller differences can be explained by the important role played by of dynamical processes in the vortex breakup while the vortex formation is mainly controlled by radiative processes that are less variable from one year to the next. A larger inter-annual variability is also observed for the breakup dates at the various levels and threshold values. Similarly, as for the onset dates, we calculated the standard deviation over the period after averaging the different curves of the different threshold mean and removing the long-term trend by a 3-degree polynomial. The standard deviation is equal to 10.6, 10.2 and 10.4 days 5 at 475 K, 550 K and 675 K, respectively, compared to 8.2, 4.8 and 3.7 days for onset dates.
An increasing trend of the breakup dates between 1979 and 1999 is seen at all levels, which is more pronounced at 475  We have analyzed the seasonal evolution of the stratospheric polar vortex edge intensity and position in equivalent latitude in the Southern hemisphere at three isentropic levels, using ECMWF ERA-Interim data over the 1979 -2020 period. The inter-annual evolution of the maximum vortex edge intensity and position, as well as the onset and breakup dates at these three isentropic levels were evaluated. The vortex edge intensity corresponds to the gradient of the potential vorticity weighted by the 5 wind module as a function of equivalent latitude (Nash et al., 1996). The studied parameters display long-term and short-term variations over the period that were analyzed using well known proxies of atmospheric variability in the stratosphere such as the solar cycle, the QBO and ENSO. Among the main results of our study, the influence of increasing ozone hole during the 1980s and 1990s on the studied parameters was clearly noticeable, confirming the results of Bodeker et al. (2002). This influence is mostly pronounced on the maximum intensity of the vortex edge, with an increase of 0.38 PV units/ • EL per year 10 at 550 K and 0.30 PV units/ • EL per year at 475 K between 1980 and 1996. It is also visible on the The vortex breakup dates with show an increasing trend of respectively 1.75 days.yr −1 , 1.5 days.yr −1 and 0.75 days.yr −1 at 475 K, 550 K and 675 K levels, for the average threshold values respectively over the 1979 -1999 period. We also find a decreasing trend over the same period for the onset dates but in this case only at 475 K and for the 25 m.s −1 threshold value only (1.5 days.yr −1 between 1980 and 1999). A We see a decreasing trend in the breakup dates after 2010 but this decrease was halted by the very long 15 vortex duration in 2020, which set a record at the 675 K level, and also by the late breakup in 2021.
The solar cycle and to a lower extent the QBO and ENSO modulate the inter-annual evolution of the maximum intensity of the vortex edge and the breakup dates. Stronger vortex edge intensity is observed in years of solar minimum. QBO and ENSO further modulate the solar cycle influence on the vortex edge, especially at 475 K and 550 K. During wQBO phases, the difference between vortex edge intensity for minSC and maxSC years is smaller than during eQBO phases. The polar vortex 20 edge is stronger and lasts longer for maxSC/wQBO than for maxSC/eQBO. Regarding ENSO, which has a lower impact than the QBO, the vortex edge intensity is somewhat stronger during cENSO phases for both minSC and maxSC. During this phase, the difference between minSC and maxSC medians is larger.
These results are mainly in agreement with the literature. Baldwin and Dunkerton (1998) found that the strongest influence of the QBO on the southern polar vortex occurs in late spring (November) when the final warming happens. From temperature composites at 10 hPa, they found that the vortex is slightly colder during the western phase of the QBO throughout the winter. Later, Haigh and Roscoe (2009) found that the southern stratospheric polar vortex breaks down later for combined maxSC/wQBO and minSC/eQBO years. The last two years of the study (2019 and 2020) stand out in our anal-5 ysis. In 2019, the vortex maximum area was particularly small, especially at 475 K and 675 K and the vortex broke up quite early. The breakup date at 475 K and 550 K for the 15.2 m.s −1 threshold is the lowest on record (on day 323 at 475 K and 319 at 550 K). In 2020, the vortex area was not particularly large and the vortex edge not particularly strong but its duration set a record at 675 K. This very long-lasting vortex was also characterized by a strong ozone destruction (https://public.wmo.int/en/media/news/2020-antarctic-ozone-hole-large-and-deep and https://public.wmo.int/en/media/news/record-break 10 (Stone et al., 2021). It will be interesting to see how the southern polar vortex evolves in the coming years.
A major perspective of our study is to extend the period analysis, using ERA5 reanalyses which are covering a longer period (from 1950) and with a higher resolution (https://www.ecmwf.int) (31 km grid for ERA5 versus 79 km for ERA-Interim).
The same parameters for the more widely studied Arctic polar vortex are currently being studied for comparison between the two hemispheres. Other factors, which particularly influence the northern hemisphere, such as the Arctic Oscillation/Northern 15 Annular Mode, will be included in the future study. Author contributions. A. Lecouffe made the study and provided the results. All authors discussed the results and contributed to the final paper.
Competing interests. The authors declare that they have no conflict of interest.