What chance of a sudden stratospheric warming in the southern hemisphere?

Sudden stratospheric warmings (SSWs) are amongst the most dramatic events in the Earth’s atmosphere and they drive extreme surface weather conditions. They have been recently linked to the hot and dry weather conditions that favour wildfires over Australia. However, the chance of a southern hemisphere event is unknown because it has only been observed once. Legitimate estimation of the frequency of SSW events requires a large sample of realistic model simulations. Here we show that the chance of an event is close to 4% per year, implying that an event will occur, on average, every 25 yr, using a state-of-the-art model that simulates SSWs accurately. It is thus not surprising that there was a near miss in the September prior to the Australian wildfire of 2019, given the 40 yr of comprehensive satellite records and just one observed Antarctic event. According to this new estimate, it would also not be surprising to see a second SSW event in the coming years in the southern hemisphere. Such a stratospheric warming event might bring further extreme surface weather conditions and natural hazards, as it may raise the risk of increased rainfall in the latitudinal band of 35–50°S. Meanwhile, the associated hot and dry weather conditions over austral subtropical continents might increase the risk of wildfires over these regions.


Introduction
Sudden stratospheric warmings (SSWs) are amongst the most dramatic examples of fluid dynamical variability in the climate system. They involve the complete reversal of the zonally averaged westerly winds and a rise of order 50 K in winter polar stratospheric temperature. SSW events have been detected in the northern hemisphere for as long as we have been making stratospheric observations (Scherhag 1952), but only a single southern hemisphere event is recorded in current observations and this occurred over a decade ago, in September 2002 Krüger et al (2005, Manney et al 2005. The striking inter-hemispheric asymmetry in SSW occurrence can be explained by differing climatological features caused by topography and landsea contrast in the two hemispheres (Waugh and Polvani 2010). The northern hemisphere stratosphere exhibits only moderate strength westerlies in its winter polar night jet, reaching around 40 m s −1 , and large stationary wave amplitudes are found near the tropopause for the longest waves (wave 1, 2 and 3), which peak in amplitude at around 60 • N Kubitz 1996, Scaife et al 2000). In contrast, the southern hemisphere westerlies are, on average, double the strength of those in the north. Wave amplitudes are generally below the amplitude threshold needed to induce a breakdown of the polar vortex, a reversal to zonal mean easterlies at 10 hPa and 60 • S, and hence an SSW (Holton andMass 1976, Yoden 1987). Instead, either a steady regime or a regime with small amplitude high-frequency vacillations on a timescale of ∼10 d, apparently driven by shear instability, occurs in most southern hemisphere winters .
Despite this, there were occasional reports of SSW events in the southern hemisphere in long climate simulations before 2002 . Similarly, ensembles of seasonal forecasts have also been noted to occasionally exhibit SSW events in the southern hemisphere (Seviour et al 2014). Idealized models are also able to simulate an occasional SSW under southern hemisphere-like conditions (Kushner and Polvani 2005). This is all consistent with the rare occurrence of SSW events in the southern hemisphere and with the idea that on rare occasions, accumulated wave activity fluxes from the troposphere (Matsuno 1971, Andrews andMcintyre 1976) might exceed the level needed to generate an SSW event in the southern hemisphere.
Given the small sample of just one observed event, the surface impacts of SSW events in the southern hemisphere are not well documented. Nevertheless, it appears that the surface effects that follow an SSW event in the southern hemisphere are dynamically similar to the more frequent and much better documented impacts in the northern hemisphere (Baldwin and Dunkerton 1999, Kidston et al 2015, Lim et al 2019. The southern hemisphere jet stream weakens and the storm track shifts equatorward for weeks or even months after the stratospheric wind weakens substantially or reverses, corresponding to a negative shift of the southern annular mode (Hartmann andLo 1998, Lim et al 2019). This leads to anomalous surface weather, with cooling and increased rainfall in Tasmania, southern New Zealand, and southern parts of South America and anomalously warm and dry conditions over large remaining parts of Australia (Gillett et al 2006) that can significantly increase risks of wildfire in this region (Lim et al 2019).
Here we use large ensembles of model simulations from the Met Office Seasonal Prediction System, GloSea5 (Maclachlan et al 2015), to estimate the chance of an SSW in the current climate. GloSea5 accurately reproduces the observed northern hemisphere SSW frequency (Scaife et al 2016) and exhibits state-of-the-art skill in predicting the North Atlantic oscillation and southern annular mode over monthly to seasonal time scales , Seviour et al 2014. These ensemble simulations are all subject to current levels of external forcing from greenhouse gases but also contain large internal variability manifested as atmospheric and oceanic sensitivity to initial conditions. They therefore correspond to multiple realisations of the current climate that are statistically consistent with the single realisation that is the observed record. We also show the expected impacts of SSW events on the surface weather in the southern hemisphere using this much larger sample of events than the single observed 2002 event.

Data and method
We use an ensemble of initialized simulations produced by the GloSea5 seasonal forecasting system (Maclachlan et al 2015). This is based on the Global Coupled 2 configuration of the Hadley Centre Global Environment Model version 3 (HadGEM3-GC2; Williams et al 2015). The grid spacing in the atmosphere is 0.83 • in longitude and 0.55 • in latitude, with 85 vertical levels up to a height of 85 km, and the global ocean resolution is 0.25 • with 75 vertical levels.
Fourteen-member historical ensemble forecasts (hindcasts), running out to 216 d, are initialized on four dates per month for the 23 yr 1993-2015. We collate hindcasts from eight initialization dates from mid-May to mid-July each year, to form a final ensemble of 14 × 8 = 112 members per year, covering the period from August to mid-December each year (i.e. 2576 members in total). We use the daily mean, zonal mean, zonal wind at 10 hPa and 60 • S ([U]) to characterize the stratospheric circulation. We also use the monthly-mean 1.5 m air temperature, precipitation, and air pressure at mean sea level (MSLP ) to analyse surface impacts. We compare our hindcast results against data from the ERA -Interim reanalysis (Dee et al 2011) for the same period.
The fidelity of the climate model is assessed using the UNprecedented Simulated Extremes using ENsembles (UNSEEN) subsampling approach , Kent et al 2017. A single model ensemble member is randomly selected (with replacement) for each year to generate a subsample of equal size to the observations . This process is repeated to generate a dataset of 10 000 random subsamples. The mean, standard deviation, skewness, and kurtosis are calculated for each subsample. The model is deemed to pass the fidelity test if the corresponding ERA-Interim value falls within the 2.5-97.5 percentile range across all 10 000 subsamples derived for each statistic (figure S1 (available online at stacks.iop.org/ERL/15/104038/mmedia)).
Across August, September, and October the model exhibits a mean westerly bias in [U] but is indistinguishable from ERA-Interim in terms of the standard deviation, skewness, and kurtosis (see figure S1 for October tests). The fidelity in the model variability sets the ground for estimating the SSW occurrence. The mean bias increases from 5 m s −1 in August up to approximately 15 m s −1 in October (table S1). To account for this seasonality, the mean westerly bias is removed from the climate model dataset using a 10 d Gaussian filter on the observational climatology, in line with seasonal forecasting applications (Maclachlan et al 2015). Tests indicate that the results are insensitive to this smoothing (not shown). The existence of a westerly mean bias in the stratosphere indicates that the model has relatively weak upward wave activity from the troposphere, which is common among current chemistry-climate models (Waugh and Polvani 2010). The zero zonal wind is more dynamically meaningful for wave breaking of stationary waves than that of transient waves (Waugh and Polvani 2010) and quasi-stationary planetary waves forced in the troposphere were found to play an important role in the observed 2002 event Krüger et al (2005). Although a westerly bias may lead to underestimation of the SSW frequency, the bias-correction may help reduce the underestimation (Kim et al 2017). The bias-corrected winds are thus used throughout the analysis, as the model variability is comparable to the observed.
A major SSW of the southern hemisphere stratospheric polar vortex is defined as occurring when [U] becomes easterly (i.e. negative). The first day on which this occurs is defined as the 'central date' of the warming. We also require that [U] must become westerly (positive) again before the final warming occurs, generally during November/December (see figure 1( Seviour et al 2014), and that this is at least 20 d after the central warming date. This definition is consistent with that commonly used for northern hemisphere SSWs (Butler et al 2018). There are 96 SSW events among all the 2576 members of the GloSea5 hindcasts.
The chance of SSW occurrence is estimated using a ranking method from a pool of samples selected by bootstrapping . Each time 60% of the simulated years (i.e. 2576 × 60% = 1546 yr) are randomly selected and a subsample consists of the minimum value of zonal-mean zonal wind (i.e. the minimum polar vortex strength) for each selected year. The minimum zonal winds are ranked in each subsample, and this selection and ranking process is repeated 10 000 times to create a sample pool. Each rank thus consists of 10 000 samples of the minimum vortex strength, which are used to estimate the average chance of SSW occurrence and its 2.5%-97.5% range. Figure 1 shows the daily evolution of the stratospheric polar vortex for June to December, for the observed 1993-2015 climatology and the 2002 case when an SSW was observed in the southern hemisphere. Model simulations are also shown for the ten ensemble members simulating the strongest SSW events, out of a total of 96 ensemble members simulating SSWs, where the strength is defined by the most easterly value of [U] obtained after the SSW central date. The ten ensemble member time series are qualitatively consistent with the observed 2002 time series, with the vortex being weaker than climatology throughout September, October, and November. Most SSWs occur in October in the model compared to the single observed warming in late September 2002 Krüger et al (2005).

Results
The 2002 September SSW event was followed by pronounced southern hemisphere surface climate anomalies in the following month (figure 2), in many respects similar to a typical northern hemisphere SSW event. The overall surface anomaly fields show contrasts between high and middle latitudes, albeit with additional fine structure. The MSLP indicated an extreme negative phase of the southern annular mode in October 2002 ( figure 2(a)). Correspondingly, the precipitation is anomalously high over 35-50 • S and anomalously low poleward and equatorward of this band (figure 2(b); see also figure S2). In this particular case, Australia, Brazil, and South Africa were drier than normal, whereas northern Argentina, southern Chile, and parts of New Zealand and Tasmania became extremely wet. Most of the Antarctic continent and central South America experienced a warmer than average spring (figure 2(c)).
As there is only a single observed SSW in the southern hemisphere, it is not possible to distinguish the effects of the event from other internal climate variability that could mask or enhance the effect of the SSW. We therefore compare the observed case with a composite of our ten strongest simulated SSW events. These tend to occur in October and thus the November surface anomaly composites for these events are shown in figures 2(d) and (e). The ten events consist of three vortex split events, similar to the observed 2002 SSW, and seven displacement events. Unlike northern hemisphere cases which tend

Summary and discussion
We estimate that the southern hemisphere is subject to rare, naturally occurring SSWs in about 4% of years on average over time (figure 3), corresponding to an event every 2-3 decades, with a total of 96 events identified out of 2576 realizations. The chance of occurrence decreases with strength (figure 3), indicating strong SSW events are less likely to occur than weak events. The observed SSW easterly strength in 2002 (about 22 m s −1 ) is stronger than any of the simulated events, which may be associated with the mean westerly bias in the model as noted in section 2. The surface impacts resemble the event of 2002 although there are some notable differences, likely due to coincidental but unrelated variability in the particular case of 2002. In September 2019 there was also a very disturbed polar vortex in the Antarctic stratosphere. Although a near miss in terms of reaching the zerowind threshold at 10 hPa, this event is likely to have contributed to the extensive and influential 2019 Australia wildfire, based on evidence from past events (Lim et al 2019). Thus, information on the frequency of SSW occurrence in the southern hemisphere will help society to better prepare and plan for the future climate and the associated societal impacts of these extreme events. Finally, we note the significant progress in modelling and forecasting that makes our analysis possible. Since the event in 2002, long-range forecast systems have been extended to include explicit representation of the stratosphere (Butler et al 2016) and this has now become accepted as an important additional source of prediction skill (Sigmond et al 2014, Scaife et al 2016, Lim et al 2019. While the wind variability in our model simulations is statistically similar to the observed variability in southern hemisphere stratospheric winds (figure S1), the SSW events tend to be weaker in amplitude than the 2002 event probably due to the westerly bias in the model climatology and so further work on gravity wave parameterizations (Ratnam et al 2004, Geller et al 2013 and interactive ozone schemes may benefit future simulations and predictions of southern hemisphere sudden stratospheric warmings.

Acknowledgments
We thank the European Centre for Medium-Range Weather Forecasts for providing ERA-Interim data. L W is supported by Grants 41875047 and 91837206 from National Natural Science Foundation of China (NSFC) and Grant JIH2308132 from Fudan University. This work was supported by the Met Office Hadley Centre Climate Programme funded by BEIS and Defra.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.