How Frequent Are Antarctic Sudden Stratospheric Warmings in Present and Future Climate?

Southern Hemisphere (SH) stratospheric sudden warmings (SSWs) result in smaller Antarctic ozone holes and are linked to extreme midlatitude weather on subseasonal to seasonal timescales. Therefore, it is of interest how often such events occur and whether we should expect more events in the future. Here, we use a pair of novel multimillennial simulations with a stratosphere‐resolving coupled ocean‐atmosphere climate model to show that the frequency of SSWs, such as observed 2002 and 2019, is about one in 22 years for 1990 conditions. In addition, we show that we should expect the frequency of SSWs, and that of more moderate vortex weakening events, to strongly decrease by the end of this century.

Due to the impacts on stratospheric ozone and surface weather on the subseasonal to seasonal timescale, it is important to determine how rare SSWs are in the SH, and whether we should expect more or less frequent SSWs under future climate change. However, given the shortness of the observational record, it is impossible to get an observational estimate of how often SSWs do occur on average. Recently, Wang et al. (2020) analyzed hindcasts of a seasonal forecasting system and found an average Antarctic SSW frequency of one every 25 years. However, the underlying model of this study had a strong mean westerly wind bias, raising some doubts on the validity of their results. Here, we revisit the question of how frequent Antarctic SSWs are in present climate, and also address possible changes under future climate change. This is accomplished by investigating two nearly 10,000-year-long simulations with a well-performing stratosphere-resolving coupled ocean-atmosphere model based on present-day (1990) and future (increased CO 2 ) conditions and by considering integrations from the sixth Climate Model Intercomparison Project (CMIP6).

Multimillennial Coupled GCM Simulations
We use a set of two 9,900-year-long simulations with the stratosphere-resolving version of the Geophysical Fluid Dynamics Laboratory's CM2.1 atmosphere-ocean coupled climate model (Delworth et al., 2006;Horan & Reichler, 2017), which has been used in particular for studies of stratosphere-troposphere coupling in the past (Horan & Reichler, 2017;Jucker & Reichler, 2018). The model has 48 vertical levels with approximately half of the levels situated in the stratosphere and a model top at 0.002 hPa. The horizontal resolution is ∼2° in latitude and 2.5° in longitude. The boundary conditions are set to perpetual 1990 conditions. More specifically, ozone in the year 1990 is comparable to both 2002 and the 2010s (Newman & Nash, 2019). The two simulations differ in their greenhouse gas forcing; CO 2 is set to 353 ppm in the "present-day" and 1,120 ppm in the "future" simulation, which is a quadrupling relative to preindustrial CO 2 concentration (and 3.2 times present-day concentration). This is the only difference between the two simulations. Atmospheric variables are stored on a daily frequency to allow for detailed dynamical analysis, including Eliassen-Palm fluxes.
In agreement with Horan and Reichler (2017), who have shown that this model compares well to reanalysis in the troposphere and northern hemisphere stratosphere, both the SH stratospheric zonal mean zonal wind and vertical component of the Eliassen-Palm flux from our present-day simulation show excellent agreement with those from ERA5 reanalysis (1979-2019) (Hersbach et al., 2020), for both mean and standard deviation (Figures 1a, 1c, and S1). We also note that the model intercomparison work by Reichler and Kim (2008) showed that CM2.1 had the best performance index among CMIP3 models, even though that version had only half the number of vertical levels compared to the version used here. Besides its performance in the atmosphere, which is of particular relevance here, the oceanic component has been validated extensively and also found to have a good representation of tropical (including ENSO, Wittenberg et al., 2006) as well as extratropical southern hemisphere ocean dynamics (Gnanadesikan et al., 2006).
Having multimillennial simulations with a model showing such small bias will allow us to robustly estimate SSW frequencies. In addition, having future projections will make it possible to address the question of whether or not we should expect another SSW to occur in the future, and we will show that increased greenhouse gas concentrations have a strong impact on SSW frequency.

SSW Definitions
We follow the most common definition of SSW as the reversal of u 1060 , the zonal mean zonal wind at 60°S and 10 hPa ("SSW-reversal", Charlton & Polvani, 2007). However, in observations, only the September 2002 event is an SSW-reversal event, while the 2019 event is widely considered an SSW but did not show wind reversal at 60°S and 10 hPa. Therefore, we have performed our analysis with an additional definition, allowing for a more general determination of SSW frequency and future change.
We found that the simplest method to define SSWs in the SH which detects both 2002 and 2019 as the only events during the satellite era is that the zonal mean zonal wind anomaly with respect to the day of the year at 60°S and 10 hPa passes below −40 m/s. The onset date is then defined as the day when the zonal mean zonal wind anomaly crosses −20 m/s for the last time before crossing −40 m/s. These "SSW-weak" events follow the common features of stratosphere-troposphere coupling in the SH in their significant surface impact on monthly timescales ( Figure S3).
For both definitions, two events have to be separated by at least 20 days, and the onset date has to be at least 20 days before the vortex breakdown, which is defined as the last day of the year when u 1060 becomes negative.
Finally, we follow Lim et al. (2018) who showed that weaker events can also have an impact at the surface, and we will also report results from their detection method based on the yearly time series of the first principal component of deseasonalized monthly mean zonal mean zonal wind between 55°S and 65°S. The corresponding empirical orthogonal function is two-dimensional but in month of the year-pressure space (instead of the conventional longitude-latitude space) and is centered around the vortex breakdown in spring (the "L18" method). This method does not provide onset dates, as there is only one value per year, and L18 is closely related to variations in the date of the vortex breakdown (positive for earlier breakdown; the correlation coefficient between the first Principal Component and the vortex breakdown date is r = 0.79 in ERA5 data, not shown). Following Lim et al. (2019), we apply a threshold of 0.8 standard deviations, which detects many more events than the other two definitions.

Occurrence of SSWs in the Southern Hemisphere
The present-day 9,900-year simulation produces 458 SSW-weak and 159 SSW-reversal events, corresponding to an average frequency of about one SSW-weak every 22 years and one SSW-reversal every 59 years. This compares well with the single SSW-reversal and only two SSW-weak events in the 42-year-long satellite observation record and the 63-year long nonsatellite observational record since 1957 (Naujokat & Roscoe et al., 2005), as well as Wang et al. (2020). In addition to yearly occurrence, we also analyze the seasonal occurrence of SSWs and find that the SSW-weak criterion detects events during the entire winter, with a peak occurrence in late August-September ( Figure 2d) and a mean occurrence of August 27 (note that early events in June and July have a similar impact to later events, not shown). The 2002 SSW occurred in late September, a time of the year when we estimate the mean return time of SSW-weak events to be 113 years, and the 2019 SSW occurred in early September, when the mean return time is estimated to be 102 years (Figure 2a). Irrespective of time of the year, our present-day simulations indicate that we should expect between 0 and 6 SSW-reversals and between 0 and 12 SSW-weak events per century, with most likely numbers of 0-2 SSW-reversal and 3-6 SSW-weak events per century (25th and 75th percentiles, Figures 2b and 2e). As indicated before, L18 events are much more abundant, with an occurrence of 7-36 events per century and a mean return time of one in 5 years (Figure 2h).
To get an estimate of when the next SSW might occur, we perform a return-time analysis, where we produce a histogram of the number of SSWs which occur within a given time interval (Figures 2c, 2f, and 2i). If SSWs are independent and random events, we can compare the observed return time distribution to a theoretical distribution (Text S6). The return time histogram follows closely the theoretical distribution for all methods, suggesting that in the SH, SSWs are independent and random, with a mean return time of about 59 years for SSW-reversal and 22 years for SSW-weak, or an annual probability of occurrence of 1.6% for SSW-reversal JUCKER ET AL.  Table 1). All of these probabilities are consistent with the observational record of one SSW-reversal and two SSW-weak events during the satellite era. Finally, neglecting any changes in climate from further greenhouse gas forcing since 1990, we estimate from the present-day simulation that the probability of at least one SSW by the end of the century (next 80 years) would be 74% for SSW-reversals and 98% for SSW-weak events. Of course, this is only hypothetical as greenhouse gas concentrations have already risen since 1990 and are projected to further increase in the future.

Enhanced Greenhouse Gas Forcing
To estimate the impact of enhanced greenhouse gas forcing on the occurrence of SSWs in the SH, we conducted a second 9,900-year-long simulation using increased CO 2 corresponding to the end of the century (1,120 ppm, instead of 353 ppm, henceforth called "future"). The occurrence of SSWs in this simulation decreases drastically. The number of SSW-reversals reduces from 159 SSWs for present-day to only 11 in the future simulation, while SSW-weak events decrease from 458 to only 32 ( Figure 2). This translates into a return time of one SSW-reversal every 883 and one SSW-weak every 309 years, and a maximum of 1 SSW-reversal and 2 SSW-weak events per century. Note how the most probable outcome by far for any given 100year period is 0 SSWs (median is 0 for both SSW-reversal and SSW-weak; Figures 2b and 2e, orange). From the theoretical fit, the probability of occurrence of at least one SSW-weak event in 80 years is now about 23% (2.8% for at least two SSWs; Table 1). The analysis also suggests that SSW-reversals become very rare (probability of 8.7% within 80 years). SSWs not only become much rarer, but are also occurring later in the year, with a mean date of 3 October for SSW-weak, that is, more than 1 month later than in the present-day simulation. For all definitions, there is a strong tendency for fewer SSWs in the future, including L18, which reduce to 0-11 events per century. Thus, while the 2019 event is consistent with the occurrence rate in our present-day simulation, it is inconsistent with the rate seen in our future simulation. Given the trend in SSW frequency, and that we are already one-third of the way toward the year 2080 (when the greenhouse gas concentrations are projected to reach the levels of our future simulation), we conclude that this latest event should not be attributed to increased CO 2 forcing, and might indeed be the last observed event this century.
The decrease in SSW frequency in the future is accompanied by a strengthening of the SH polar vortex (Figure 1b), which can be linked to stronger radiative cooling under increased greenhouse gas concentrations (Santer et al., 2013;Thompson et al., 2012). In addition, our simulations suggest a decrease in wave forcing, more so during spring than other times of the year (Figure 1d). Together with an earlier study, which found JUCKER ET AL. Yearly probability is the probability of an event occurring during any given year (1/mean return time), probability of exact observation is computed for 2 SSW-weak and 1 SSW-reversal in 41 years. Time periods give the interval after which an SSW is more probable than not (probability of one or more events > 50%). The labels "present" and "future" refer to the relevant CM2.1 simulations, and we use an 80-year period to compare to the time span 2021-2100 in the future simulation, but noting that this has CO 2 concentrations that are more representative of the end of the 21st century. Note that the observation percentages in the present simulation add to 101 instead of 100 due to rounding errors. SSW, sudden stratospheric warming.

Table 1
Results From the Theoretical Fitting of the Return Times (Figures 2c and 2f) a direct link between the SSW-reversal frequency and polar vortex strength (Jucker et al., 2014), our results suggest that the projected strengthening of the polar vortex along with a decrease in wave forcing are responsible for a substantial decrease in the probability of occurrence of SSWs.

Comparison to NH
The occurrence of SSWs in the NH is very different from the SH, not just because of the much higher SSW frequency at present, but also in terms of future projections of both polar vortex strength and SSW frequency. As discussed in detail by Horan and Reichler (2017), our model climatology and variability in the NH compares well to reanalysis products (Figure 3), and it produces about five SSWs per decade in the NH, in accordance with observations (Jucker & Reichler, 2018). Therefore, we perform the same analysis for the NH and briefly report our findings here.
The return time distribution shows that at intervals shorter than 4 years, NH SSWs are not independent and random (Figure 3e), probably reflecting the influence of slowly evolving large scale climate modes, such as the El Niño Southern Oscillation or the quasibiennial oscillation, on the occurrence of SSWs (Anstey & Shepherd, 2014;Holton & Tan, 1980;Taguchi & Hartmann, 2006). The NH polar vortex is also weaker and more influenced by upward propagating planetary waves from the troposphere, resulting in a more variable polar vortex than in the SH (Figure 3, top). Our simulations suggest a slightly weaker polar vortex and more SSWs in the future NH (Figure 3, bottom; SSW-reversal only). However, we have less confidence in this result because strong dynamical coupling between the troposphere and the stratosphere in the NH complicates future projections, and also because several past studies were unable to reach a consensus on possible future changes of SSW occurrence rates over the NH (Ayarzagüena et al., 2018(Ayarzagüena et al., , 2020Manzini et al., 2014;Wu et al., 2019). There is also no consensus about the future strength of the polar vortex (Simpson et al., 2018), which is in agreement with our conclusion that the polar vortex strength is important for the frequency of SSWs.

CMIP6
To check the robustness of our single model simulations, we repeat our analysis with CMIP6 data (see supplementary Text S4 for details). We find that these models show a positive polar vortex strength bias ( Figure 4) and generally struggle to produce the observed frequency of SSWs, with a range of 0.3-2.4 SSWweak events on average in 80 years for piControl (Table S1). The low SSW frequency in CMIP6 was also briefly noted in the recent work (Ayarzagüena et al., 2020). However, the statistical analysis again suggests a decrease in SSWs in the future, with three models producing one single and two models producing no SSWweak event in SSP585 between 2021 and 2100 (Table S1b). Similar to our CM2.1 simulations, the CMIP6 models consistently project a strengthening of the SH polar vortex (Figure 4), suggesting that our main conclusion that SSWs will become much rarer in the future is robust.
Our enhanced CO 2 CM2.1 simulation only considers future increases in CO 2 . Changes in other radiatively active gases, in particular the expected recovery of the ozone hole by 2080 (Dhomse et al., 2018), are not included. However, our 1,120 ppm CO 2 concentration is equal to the CO 2 concentration at the end of the century following the SSP585 scenario, which in addition to CO 2 also increases other greenhouse gases such as methane and nitrous oxide (O'Neill et al., 2016;Meinshausen & Nicholls, 2020). Consequently, u 1060 of our future simulation compares well to the end of the 21st century in CMIP6 SSP585 model data (Figure 4b). This is consistent with previous findings that over the long term, the greenhouse effect from increasing CO 2 concentrations dominates the effect of the ozone hole recovery (Barnes & Polvani, 2013). The similarities in u 1060 and CO 2 concentrations between our CM2.1 simulations and CMIP6 models give us confidence that our enhanced CO 2 simulation is relevant for end-of-century projections.

Conclusions
The 2002 and 2019 SSWs both resulted in exceptionally small ozone holes, as have not been observed since the 1980s. They were also followed by extended periods of negative southern annular mode at the surface, and 2019 in particular was linked to the catastrophic fire season in South Eastern Australia. While possibly predictable on the seasonal time scale, it has been difficult to determine how often SSWs should be expected in the SH, due to a relatively short observational record on one hand and large model biases in the SH stratosphere in most comprehensive climate models on the other hand. Using a pair of exceptionally long and low bias climate model runs, we found that while SSWs in the SH have significant impacts on stratospheric ozone and surface weather, such events are rare and will become even rarer as CO 2 concentrations increase. In our simulation based on 1990 conditions, the mean return time for events similar to the 2002 and 2019 SSWs is about 22 years, with a 57% chance of at least two and a 30% chance of three or more SSW-weak events happening within the time period spanned by the satellite record. Thus, it is no surprise that two events have been observed, and there would be a fair chance of another SSW (of either flavor) in the near future, if CO 2 levels were kept constant. However, we show that one should not make predictions of future JUCKER ET AL.  occurrence from past data; given that the world follows a high emissions pathway, our projections suggest that events similar to 2002 and 2019 will become extremely rare, with a mean return time of one in 309 years (or 0.3% each year) by the end of the century.