The Wave Geometry of Final Stratospheric Warming Events

Every spring, the stratospheric polar vortex transitions from its westerly wintertime state to its easterly summertime state due to seasonal changes in incoming solar radiation, an event known as the “final stratospheric warming" (FSW). While FSWs tend to be less abrupt than reversals of the boreal polar vortex in midwinter, known as sudden stratospheric warming (SSW) events, their timing and characteristics can be significantly modulated by atmospheric planetary-scale waves. Just like SSWs, FSWs have been found to have predictable surface impacts. While SSWs are commonly classified according to their 5 wave geometry, either by how the vortex evolves (whether the vortex displaces off the pole or splits into two vortices) or by the dominant wavenumber of the vortex just prior to the SSW (wave-1 versus wave-2), little is known about the wave geometry of FSW events. We here show that FSW events for both hemispheres in most cases exhibit a clear wave geometry. Most FSWs can be classified into wave-1 or wave-2 events, but wave-3 also plays a significant role in both hemispheres. Additionally, we find that in the Northern Hemisphere, wave-2 events are more likely to occur later in the spring, while in the Southern Hemisphere, 10 wave-1 or wave-2 events show no clear preference in timing. The FSW enhances total column ozone over the pole of both hemispheres during spring, but the spatial distribution of ozone anomalies can be influenced by the wave geometry and the timing of the event. We also describe the stratosphere’s downward influence on surface weather following wave-1 and wave-2 FSW events. Significant differences between the tropospheric response to wave-1 and wave-2 FSW events occur over North America and over the Southern Ocean, while no significant differences are found over the North Atlantic region, Europe, and 15

of days where the aspect ratio exceeds a value of 1. 80 (1.70) or where the centroid latitude is below a value of 71 (78) • S.
These thresholds are based on the 10th percentile of climatological FMA (SON) values in the ERA-interim record for the NH (SH). If the number of days exceeding the centroid latitude threshold is greater (smaller) than the number of days exceeding Table 1. Dates and classifications for all FSW events for the Northern and Southern Hemisphere according to ERA-interim data. Early (late) events are indicated in bold (cursive), referring to a date before (after) the median date of April 12 in the NH and November 19 in the SH.
Dates that fall within ± 2 days of the median date are not classified as early or late. U = unclassified (methods did not agree according to the criterion outlined in section 2). Superscripts indicate the JRA-55 classification if it was not in agreement with ERA-interim.
year NH FSW date wave @ 10hPa wave @ 50hPa SH FSW date wave @ 10hPa wave @ 50hPa 1979 the aspect ratio threshold, the event is classified as a wave-1 (wave-2) event. Here, we make the assumption that a "split" event can be classified as having primarily wave-2 structure (and "displacement" events as having wave-1 structure) but note that 130 some "split" midwinter SSWs are preceded predominantly by wave-1 activity, especially at long lead times (Labitzke, 1981;Bancalá et al., 2012). Another disadvantage of this method is that, as the sharp edge of the vortex (marked by a strong potential vorticity gradient) starts to weaken and dissipate in spring, the elliptical moments cannot be diagnosed, so this method is unable to classify FSW events as consistently as the other two methods.
For every event, each of these three methods indicates a preference for either wave-1 or wave-2, or it returns an "unclassified" 135 result. The final wave geometry classification used throughout the remainder of this study is then determined based on the agreement of at least two of the above methods. If no two methods agree, or if two methods yield a non-classification, the event as wave geometry for midwinter SSWs has been found to be sensitive to the reanalysis used (Gerber et al., 2021). In general, the classification of FSW events is consistent across the two reanalysis products, although a few discrepancies are noted in Tables 1 and 2. larger than the frequency of wave-2 midwinter SSWs (e.g., Barriopedro and Calvo (2014), who found 9 wave-2 events in the 150 1958-2010 period, using a 50 hPa geopotential height Fourier decomposition method).
Based on the classification at 50 hPa, in the NH, wave-2 events occur significantly later than wave-1 events (Fig. 1b), with 11 out of 16 wave-2 events from 1958-2019 occurring at least 2 days later than the median date of April 12. In the SH, no statistical difference between the date of wave-1 and wave-2 FSW events is observed from 1979-2018 (Fig. 1d). As noted previously, the SH final warming date tends to occur later during years of strong ozone depletion, as the late breakup is linked 155 via chemistry-climate feedbacks to stronger ozone loss that further cools and strengthens the vortex into late spring.
For illustration, Fig. 2a-h shows selected wave-1 and wave-2 cases of FSWs. Different years were selected for each level in order to showcase the presence of wave structures throughout the record during the satellite era. The wave-1 and wave-2 events show geopotential height structures that are strongly reminiscent of the structures observed during wave-1 and wave-2 midwinter SSW events, with the vortex shifted off the pole during wave-1 events and elongated or split into two smaller 160 vortices during wave-2 events. Although no event showed a dominant wave-3 pattern according to the above classifications, visual inspection and quantification of the wave-3 component using the Fourier decomposition method reveal a substantial role of wave-3 in some cases, which are highlighted in Fig. 2i-l.
Further evidence that wave-3 plays a more significant role in NH FSW events compared to midwinter SSW events is provided by comparing the ratio of wave-2 and wave-3 amplitudes to wave-1 amplitude averaged for the 15 days prior to SSW and FSW 165 events (Fig. 3). For both SSWs and FSWs, wave-2 and wave-3 amplitudes tend to be more comparable to wave-1 amplitudes in the troposphere (200 hPa); while in the lower stratosphere (50 hPa), wave-2 and 3 typically have smaller amplitudes than wave-1 (indicated by median ratios less than one), as expected from wave filtering (Charney and Drazin, 1961). However, prior to SSWs, wave-2 amplitudes are sometimes much larger than wave-1 amplitudes. The large spread, which is skewed toward more positive ratios of wave-2 relative to wave-1 prior to SSWs at all pressure levels, may be an indication of the role of non-linear 170 resonance just prior to these events (Esler and Matthewman, 2011;Domeisen et al., 2018;Albers and Birner, 2014). Wave-3 amplitudes are generally much smaller relative to wave-1 and wave-2 prior to SSWs. This is true for FSWs as well; however, the median ratios of both wave-2 and wave-3 relative to wave-1 for FSWs are higher than for SSWs at all levels (particularly at 50 hPa), suggesting that wave-2 and wave-3 are able to propagate higher as the westerly flow weakens in spring.

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In this section we investigate the stratospheric dynamical characteristics of the final warming events. Figure 4 shows a composite of zonal mean zonal wind around the time of the FSW using the date of the FSW at 10 hPa and the wave classification When comparing the rate of wind deceleration with respect to wave geometry, wave-2 events in the SH (red lines in Fig. 4c,d) exhibit a stronger deceleration as compared to wave-1 events. The average deceleration between lags of -30 to -11 days before the FSW event and days 11 to 30 after the event is 35.0 m/s (40.5 m/s) for wave-1 (wave-2) at 10 hPa and 29.8 m/s (34.2 m/s) 185 at 50hPa (Fig. 4c,d). For the NH, this difference is less distinct. In the NH the average deceleration over the same period is 23.5 m/s (20.8 m/s) for wave-1 (wave-2) events at 10 hPa, and 12.8 m/s (12.3 m/s) for wave-1 (wave-2) events at 50 hPa. The deceleration associated with wave-2 is greater than for wave-1 events only for the ± 10 days around the FSW event (Fig. 4a,b).
Note the larger variability for wave-2 events due to the smaller sample size. Within the month after the event occurs at 10 hPa, no significant difference in wind speed can be found between wave-1 and wave-2 events at 10 or 50 hPa for either hemisphere.   is important to note that detecting the FSW at 10 hPa or 50 hPa based on the wind reversal to easterlies yields a much more significant shift in the timing of the SH as compared to the NH (Newman, 1986).

Implications for ozone distribution during spring onset 200
To investigate the influence of final warming wave geometry on total column ozone, we use the Bodeker Scientific Filled Total Column Ozone (TCO) Database (Version 3.4) (Bodeker et al., 2020). This dataset combines measurements from multiple satellite-based instruments, and fills missing data with a machine-learning based method to create a temporally and spatially gap-free database of total column ozone from 31 Oct 1978 to 31 Dec 2016. We also compared these results to the same analysis using ERA-interim ozone at the 500K isentrope (lower stratosphere) and the results were very similar (not shown).

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TCO anomalies are calculated based on the 1979-2016 daily climatology. Here we composite TCO anomalies based on FSW dates at the 10 hPa level but using classifications at 50 hPa, near where ozone levels peak in the polar stratosphere.  percentile for the wave-1 (wave-2) classification. some qualitative differences between wave-1 and wave-2 TCO anomalies in the NH, the significance levels suggest that the differences between wave-1 and wave-2 events are few.
In the SH, TCO anomalies associated with wave-1 events mirror wave-1 events in the NH, with a displaced region of negative TCO anomalies over the Antarctic peninsula prior to the FSW, and positive TCO anomalies over the polar cap and negative 11 https://doi.org/10.5194/wcd-2020-63 Preprint. Discussion started: 5 January 2021 c Author(s) 2021. CC BY 4.0 License. the Drake passage/Amundsen Sea are significantly different from wave-1 events. However, after the FSW, wave-2 events are also followed by enhanced TCO over the polar cap.
Though the wave geometry does indicate qualitative influences on the spatial structure of TCO anomalies, we find a more substantial role of the timing of the FSW on the TCO anomalies, particularly in the SH (Fig. 5i-p). In the NH, where wave-1 225 events tend to occur earlier and wave-2 events tend to occur later (Fig. 1b), the TCO anomalies for early and late events are qualitatively similar to the wave-1 and wave-2 composites (Fig. 5a,b,e,f), except that the positive TCO anomalies over North America prior to, and over the polar cap after, early FSWs are larger and statistically different from the anomalies during late FSWs. In the SH, however, early FSWs show positive TCO anomalies both prior to and after the event, while late FSWs show negative TCO anomalies both prior to and after the event (though for both early and late cases, the TCO anomaly is more 230 positive after the event than before). These differences reflect a key point, which is that late events in the SH tend to occur in years with strong ozone depletion that further strengthen the vortex winds and allow the vortex to persist longer. Moreover, because the SH vortex in the lower stratosphere persists for several weeks after the FSW occurs at 10 hPa (Fig. 4), there appears to be less mixing of polar vortex and mid-latitude ozone in the 15 days after the FSW, compared to the NH (Newman, 1986).
As found in previous studies, the FSW is clearly important in the evolution of springtime TCO in both hemispheres, with 235 the event leading to more positive TCO anomalies over the polar cap no matter the classification. We further show that both the wave geometry and timing of the event can play a role in the springtime TCO anomalies, which may have implications for ecosystems and human health due to increased ultraviolet (UV) radiation exposure (Barnes et al., 2019). For example, prior to wave-1 (and early NH) FSWs there are more widespread negative TCO anomalies that are shifted further off the pole towards more populated areas (Fig. 5a,c,i). Late events in the NH induce much weaker changes in the TCO anomalies, whereas late 240 events in the SH are associated with persistent negative polar cap TCO anomalies that reflect chemistry-climate feedbacks due to large ozone depletion events.

Surface impacts
We next investigate potential differences in the surface impact between wave-1 and wave-2 FSW events, using the classification at 50 hPa. The surface structures using the classification at 10 hPa (not shown) do not differ qualitatively from the surface 245 impacts based on the 50 hPa classification. Figure 6 shows the composite response for wave-1 and wave-2 FSWs for linearly detrended 500hPa geopotential height anomalies for 60 days after the FSW event. The detrending was applied to account for possible trends in the storm tracks but does not qualitatively change the results. The average over all NH FSW events (Fig. 6a) shows a negative NAO structure with a high pressure anomaly over Greenland and a low pressure anomaly over Europe and the adjacent North Atlantic region. A negative geopotential height anomaly is observed in the North Pacific off the coast of 250 western Canada. When dividing the response between wave-1 and wave-2 (Fig. 6c,e), the negative NAO response persists for both types of events, but the response over North America is opposite between wave-1 and wave-2 events, with a positive (negative) anomaly over Canada for wave-1 (wave-2) events and the opposite response over the southern U.S. These differences between wave-1 and wave-2 events over North America are significant. Other areas of significant differences between wave-1