The role of North Atlantic-European weather regimes in the surface impact of sudden stratospheric warming events

Sudden stratospheric warming (SSW) events can significantly impact tropospheric weather for a period of several weeks, in particular over the North Atlantic and Europe. However, not all SSW events exhibit the same tropospheric response, if any, and it remains an open question what determines the existence, location, timing, and strength of the downward impact. We here explore the role of the state of the tropospheric flow in the North Atlantic region at the onset of SSW events for determining the subsequent surface impact. A refined definition of seven North Atlantic tropospheric weather regimes indicates 5 the Greenland blocking (GL) and Atlantic Trough (AT) regimes as the most frequent large-scale patterns following the weeks after an SSW. While GL is dominated by high pressure over Greenland, AT is dominated by a southeastward shifted storm track in the North Atlantic. We find that a blocking situation over western Europe and the North Sea (European Blocking) at the time of the SSW onset favours the GL response and the associated cold conditions over Europe. In contrast, an AT response and mild conditions are more likely if GL occurs already at SSW onset. For the remaining tropospheric flow regimes during 10 SSW onset, we find no clear response. The results indicate that the tropospheric impact of SSW events critically depends on the tropospheric state during the onset of the SSW, which could provide crucial guidance for subseasonal prediction.

Abstract. Sudden stratospheric warming (SSW) events can significantly impact tropospheric weather for a period of several weeks, in particular in the North Atlantic-European (NAE) region. While the stratospheric forcing often projects onto the North Atlantic Oscillation (NAO), the tropospheric response to SSW events, if any, is highly variable, and what determines the existence, location, timing, and strength of the downward impact remains an open question. We here explore how the variable tropospheric response to SSW events in the NAE region can be characterized in terms of a refined set of seven weather regimes and if the tropospheric flow in the North Atlantic region around the onset of SSW events is an indicator of the subsequent downward impact. The weather regime analysis reveals the Greenland blocking (GL) and Atlantic trough (AT) regimes as the most frequent large-scale patterns in the weeks following an SSW. While the GL regime is dominated by high pressure over Greenland, AT is dominated by a southeastward-shifted storm track in the North Atlantic. The flow evolution associated with GL and the associated cold conditions over Europe in the weeks following an SSW occur most frequently if a blocking situation over western Europe and the North Sea (European blocking) prevailed around the SSW onset. In contrast, an AT regime associated with mild conditions over Europe is more likely following the SSW event if GL occurs already around SSW onset. For the remaining tropospheric flow regimes during SSW onset we cannot identify a dominant flow evolution. Although it remains unclear what causes these relationships, the results suggest that specific tropospheric states in the days around the onset of the SSW are an indicator of the subsequent tropospheric flow evolution in the aftermath of an SSW, which could provide crucial guidance for subseasonal prediction.

Introduction
Sudden stratospheric warming (SSW) events can have a significant impact on the tropospheric large-scale circulation and hence on surface weather (Baldwin and Dunkerton, 2001). While a causal downward link from the stratosphere after SSW events has been confirmed in idealized experiments (e.g., Gerber et al., 2009), a robust quantification of the downward impact of SSWs in observational data remains challenging. First of all, the number of SSWs in the record of satellite-era reanalysis is small (26 events from 1979 to 2019), while the case-to-case variability in terms of their tropospheric impact is large. Second, the internal variability of the troposphere itself is high, such that it can mask a stratospheric influence. Predicting if, when, and where a downward impact from SSW events will occur is therefore not straightforward, yet a better prediction of the type and timing of a downward impact would significantly benefit a wide range of users.
The tropospheric impact of SSW events is communicated by a range of mechanisms including synoptic-and planetaryscale waves (e.g., Song and Robinson, 2004;Domeisen et al., 2013;Hitchcock and Simpson, 2014;Smith and Scott, 2016). The subsequent tropospheric variability in the North Atlantic-European (NAE) region is often characterized in 374 D. I. V. Domeisen et al.: Weather regimes in the response to sudden stratospheric warmings terms of the bimodal North Atlantic Oscillation (NAO), commonly defined through a station-based index (Cropper et al., 2015;Domeisen et al., 2018), or by the first empirical orthogonal function (EOF) of geopotential height in the North Atlantic sector. Furthermore, multimodal weather regime classifications based on k-means clustering of the leading EOFs in the North Atlantic sector tend to denote two out of several weather regimes as the positive (NAO+) and negative (NAO−) phases of the NAO given the similarity of their spatial patterns to the bimodal NAO definition (Michelangeli et al., 1995;Cassou, 2008;Ferranti et al., 2015;Charlton-Perez et al., 2018). After SSW events the NAE region tends to exhibit more persistent states of the negative phase of the NAO (Domeisen, 2019), as well as more frequent transitions towards NAO− and fewer away from NAO− (Charlton-Perez et al., 2018). NAO− is associated with enhanced meridional air mass exchanges, in particular, more cold air outbreaks in northern Europe but fewer over the Nordic Seas (Kolstad et al., 2010;Kretschmer et al., 2018b;Papritz and Grams, 2018;Huang and Tian, 2019), as well as increased precipitation in southern Europe Ayarzagüena et al., 2018). The Pacific sector tends to be less strongly affected in the aftermath of SSW events (Greatbatch et al., 2012;Butler et al., 2017), though the occurrence of wave reflection in the stratosphere can be associated with Pacific blocking (Kodera et al., 2016) and cold spells over North America (Kretschmer et al., 2018a;Matthias and Kretschmer, 2020). Given the preferred occurrence and the increased persistence of certain surface signatures in the NAE region after SSW events as compared to climatology, medium-to long-range predictability over Europe has been suggested to increase after SSW events (Sigmond et al., 2013;Domeisen et al., 2015;Karpechko, 2015;Butler et al., 2016;Scaife et al., 2016;Jia et al., 2017;Beerli et al., 2017;Domeisen et al., 2020a). SSW events themselves are often not predictable beyond a few days to weeks, with high interevent variability (Taguchi, 2014(Taguchi, , 2016Domeisen et al., 2020b), although probabilistic predictability can be found for longer timescales .
The analysis of the high case-by-case variability in the tropospheric signature after an SSW event is further complicated by the fact that there exists a range of different metrics for characterizing the downward impact, with each definition yielding a different set and number of SSW events with apparent surface impacts. In particular, the occurrence and type of downward impact has been investigated with respect to the SSW geometry, i.e., split versus displacement events (Charlton and Polvani, 2007;Mitchell et al., 2013;Maycock and Hitchcock, 2015;Seviour et al., 2016;Lehtonen and Karpechko, 2016), though no statistically robust differences with respect to wave geometry emerge in the tropospheric response. In addition, it has been suggested that precursors to SSW events with a downward influence differ from SSWs without such a tropospheric impact in terms of strength and location (Nakagawa and Yamazaki, 2006;Domeisen, 2019;Zhang et al., 2019), in particular with respect to forcing over Eurasia (White et al., 2019;Tyrrell et al., 2019;Peings, 2019). Furthermore, the evolution of the stratosphere-troposphere system following the SSW (Kodera et al., 2016) and in particular the persistence of the lower stratospheric response after the SSW event (Hitchcock et al., 2013a;Karpechko et al., 2017;Runde et al., 2016;Polichtchouk et al., 2018) have been found to determine the existence and type of a downward response. These studies use indices for the downward effect that are based on exclusively stratospheric or a combination of stratospheric and tropospheric indicators. For comparison, in this study we will investigate purely tropospheric indicators of the downward impact of SSW events. Definitions of a downward impact using tropospheric indicators are generally based on largescale circulation indices such as the NAO (Charlton-Perez et al., 2018;Domeisen, 2019) or tropospheric jet location (Garfinkel et al., 2013;Afargan-Gerstman and Domeisen, 2020;Maycock et al., 2020).
Furthermore, remote forcing can affect both the stratosphere and the troposphere and thereby either mask or strengthen the downward response from the stratosphere. A range of tropical remote connections can impact the NAE region through both a tropospheric and a stratospheric pathway (Attard et al., 2019), such as the Quasi-Biennial Oscillation (QBO) (Gray et al., 2018;Andrews et al., 2019), the Madden-Julian Oscillation (MJO) (Garfinkel et al., 2014;Barnes et al., 2019), and El Niño-Southern Oscillation (ENSO) (Jiménez-Esteve and Domeisen et al., 2019), in addition to extratropical tropospheric forcing in the North Pacific (Honda and Nakamura, 2001;Sun and Tan, 2013;Drouard et al., 2013), Arctic sea ice (Sun et al., 2015), and snow cover in Eurasia (Cohen et al., 2014). It therefore has to be kept in mind that the stratosphere is only one possible forcing of the troposphere.
Given the large variability of the tropospheric flow evolution following SSW events and the influence of additional remote factors mentioned above, the prediction of the SSW response in the troposphere remains difficult for an individual event, despite the general shift towards NAO negative conditions in a statistical sense. The goal of this study is to investigate if tropospheric flow regimes in the NAE region can help us understand the variability of the SSW response in the observational record. More specifically, we here address the question of whether the tropospheric flow evolution in the NAE region after an SSW is statistically different from that without an SSW using seven weather regimes in the NAE region. Weather regimes are quasi-stationary, recurrent, and persistent patterns of the large-scale extratropical circulation (e.g., Michelangeli et al., 1995). While many studies showed that there are preferred transitions between different regimes, internal tropospheric variability is high and a regime onset often occurs on short timescales (e.g., Vautard, 1990;Michel and Rivière, 2011). Therefore predictability due to regimes arises from regime persistence on timescales of several days rather than typical regime sequences over several weeks. However, recent work revealed important shifts of regime occurrence and transition probabilities between regimes on subseasonal timescales of several weeks depending on the external forcing such as the stratospheric polar vortex state (Charlton-Perez et al., 2018;Papritz and Grams, 2018;. This motivates the study at hand aiming at investigating if the variability in the tropospheric flow evolution following SSW events can be characterized in terms of the weather regime around the SSW onset.
2 Data and methods

Data and classifications
ERA-Interim reanalysis (Dee et al., 2011) from 1979 to 2019 is the data basis for this study. The SSW events are defined based on daily mean data at the native ERA-Interim horizontal grid resolution. The SSW central dates are defined as the first day of easterly zonal mean zonal winds at 10 hPa and 60 • N between the 1 December and 31 March. Events have to be preceded by at least 20 consecutive days of daily mean westerly winds. If an event fulfills the criterion for both a SSW and a final warming event, it is excluded from the analysis. Final warming events are defined as the first day of the year when the zonal mean zonal winds at 10 hPa and 60 • N reverse and do not return to westerly for more than 10 consecutive days. These SSW central dates agree with Table 2 in Butler et al. (2017), which provides central dates up to 2013, and are defined using the same criterion thereafter. The central dates for the more recent SSW events are 12 February 2018 and 2 January 2019 (see Table 1). Following Karpechko et al. (2017) the event on 24 March 2010 has been excluded to avoid an overlap with the aftermath of the SSW event on 9 February 2010. This yields 25 SSW events for the period 1979-2019.
The tropospheric flow over the NAE region is described in terms of seven year-round weather regimes defined in Grams et al. (2017) based on 6-hourly data for the period 1979-2019 using 1.0 • horizontal resolution (Appendix Fig. A1). As for the canonical seasonal definition using four regimes (e.g., Michelangeli et al., 1995;Michel and Rivière, 2011;Ferranti et al., 2015;Charlton-Perez et al., 2018), the mean patterns of the seven regimes are based on a k-means clustering in the phase space spanned by the leading seven EOFs (explaining 76 % of the variance) of 10 d low-pass-filtered 500 hPa geopotential height anomalies. In addition, we employ a normalized projection (weather regime index I WR ) following Michel and Rivière (2011) for each of the seven regimes to define objective and persistent weather regime life cycles and for a filtering of time steps without a clear regime structure ("no regime" category). In essence, an active life cycle requires an I WR above a certain threshold for at least 5 consecutive days (minimum persistence of an active regime life cycle) and a continuous increase/decrease during the onset/decay phases (see methods of Grams et al., 2017, for details). As different life cycles can be active simultaneously, in particular during the onset and decay phases, individual days are attributed to a specific regime life cycle only if I WR is also the maximum of all I WR . The life cycle definition allows for a continuous extension of the weather regime attribution to more recent data without repeating the EOF analysis and clustering (here done for the years 2016-2019).
We use this weather regime classification to stratify SSW events according to the large-scale tropospheric flow conditions in the North Atlantic around their onset (see Table 1). To do so, we select for each SSW the dominant weather regime that is active during at least one 6-hourly time step in a time window ±5 d around the onset day (at 00:00 UTC) of the SSW. We consider a weather regime to be dominant if the mean I WR in the time window ±5 d around the onset reaches a maximum compared to other active regime life cycles. Manual inspection of the 25 considered SSW events confirms the unambiguity of this approach. An identified weather regime is required to be dominant for a minimum of 3 d in the considered 10 d period around the SSW central date.
Three of the seven regimes are dominated by a cyclonic 500 hPa geopotential height anomaly ("cyclonic regimes"; see A potential modulation of the frequency of occurrence of the seven regimes can be understood in terms of the link between the respective regimes and the NAO (Beerli and Grams, 2019, their Figs. 2 and 6). While ZO and ScTr project onto NAO+, GL strongly projects onto NAO−. EuBL and AT do not project strongly onto either NAO phase.

Statistical testing
Since SSW events only occur roughly every second winter , the subsequent stratification according to tropospheric flow conditions requires careful statistical testing to extract significant results that are distinct from sampling uncertainty. The overarching questions we address in this study are whether after SSWs the tropospheric flow evolution is different from situations without an SSW and to what extent this depends on the tropospheric state at the time of the SSW. To investigate these questions, we consider subsamples of all SSWs. In all cases the relevant null hypothesis is that the flow evolution after SSWs is indistinguishable from that occurring in the absence of an SSW. The testing procedure, thus, comprises the following two steps: 1. First, we assess the robustness of the samples by performing a Monte Carlo resampling. For that purpose, we resample the original samples 100 times with repetitions. The number of random samples is chosen according to the maximum number of possible combinations with repetitions of the smallest subset of SSW events that will be considered in this study (N = 5 events corresponding to 126 independent combinations). This yields confidence intervals, estimating the uncertainty inherent in each sample. Due to the small sample size, these confidence intervals are relatively large.
2. Second, we compute 1000 random samples of the same size as the original sample but for random periods with the same weather regime at the central date but no SSW occurring within ±60 d, yielding estimates of the distributions in the absence of SSWs. Prescribing the same weather regime at the central date for the random samples filters out signals which might result from regime persistence or preferred regime transitions independent of external forcings. Testing for significance is done by comparing the confidence intervals and distributions obtained from the random samples for overlap.
Applying this method to anomalies of geopotential height and 2 m temperature, we consider anomalies as robust if the width of the confidence interval is smaller than the amplitude of the anomaly. In addition, the sample mean is significant at, e.g., the 10 % level, if the confidence intervals overlap by less than 10 % with the Monte Carlo distribution. A similar procedure is applied to test significance of lagged weather regime occurrence. Anomalies of geopotential height are defined with respect to the climatological (1979-2019) 21 d running mean. In order to remove the background warming, which is particularly pronounced at high latitudes, we consider detrended anomalies of 2 m temperature. For that purpose, we use as the climatology a centered 9-year mean instead of the entire study period. Note that at the beginning and end of the study period the first and last 9 years are used, respectively.

Weather regimes during SSW events
As a first step, we evaluate the sequence of weather regimes from 60 d before to 60 d after an SSW for all 26 SSW cases during 1979-2019 (Fig. 1, Table 1). Note that Fig. 1 shows the dominant persistent regime, so that alternating regimes in a time window shorter than the persistence criterion of 5 d indicate simultaneously active regime life cycles (see Sect. 2.1 for details). This figure suggests a preferred occurrence of AT (purple) and GL (blue) during the weeks after an SSW compared to the weeks before. This is further emphasized by the 5 d running mean of the anomalous frequency of weather regimes around SSW events, which provides a more complete overview over the modulation of regime frequencies after SSWs (Fig. 2). We show the 5 d running mean frequency anomaly to account for the 5 d minimum duration of an active regime life cycle. Different from the testing procedure outlined in Sect. 2.2, we here consider the distribution of lagged 5 d mean frequencies by selecting for each day in the original sample a random day ±15 d around the original day of year but from a different winter. In addition, the random day must exhibit the same weather regime as the original day to replicate potential regime dependence. We then compute the mean lagged weather regime frequency for each random sample as for the original sample and test for significance at the 10 % level (bold). For reference, we show the absolute frequencies of weather regimes in Fig. A2.
GL and EuBL are the most prominent regimes around the onset of SSW events with a 5 d mean frequency of around 19 % and 21 %, respectively (Fig. A2a). The frequency of EuBL is significantly enhanced from 5 d prior until the onset of the SSW (Fig. 2a), in agreement with Woollings et al. (2010) and Nishii et al. (2011). The cyclonic regimes ZO and ScTr, as well as the blocked regimes AR and ScBL, tend to be suppressed at the time of SSW events. This is consistent with the strong projection of the ZO and ScTr regimes onto NAO+, which also tends to be suppressed after SSW events (Charlton-Perez et al., 2018). On the other hand, AR (yellow, significant peak around lag −20 to −10) and the related ScTr (orange, significant around lag −10) regimes are more frequent in the period 1-3 weeks before the SSW onset. The prominence of AR around 15 d before the onset of an SSW event agrees with the suggested precursor role of blocking over the Atlantic before SSW events (Martius et al., 2009). Furthermore, blocking over the Ural region in Eurasia has been suggested as a precursor to SSW events (Kolstad and Charlton-Perez, 2011;Peings, 2019;White et al., 2019). The Ural blocking precursor projects onto the EuBL and especially the ScBL regimes, which are also found to show significant positive anomalies of occurrence within the 3 weeks before SSW events (Fig. 2a). It is well known that precursors in the North Pacific also tend to be prevalent before SSW events, e.g., Garfinkel et al. (2012) and Lehtonen and Karpechko (2016), though these are not possible to identify with the present analysis, which is focused on the NAE region. After the SSW onset, AT frequencies are significantly enhanced, peaking at around 20 % after 7 d (Fig. A2a), corresponding to a frequency anomaly of around 12 % for the same lag (Fig. 2a). Thereafter, GL (lag 12 to 40 d) and AT (lag 17-35 d) are the most likely weather regimes with enhanced frequency anomalies of up to 15 % (Fig. 2a), while in absolute terms frequencies for both are around 20 %-25 % and neither of the two clearly dominates (Fig. A2a). This dominant occurrence of both GL and AT after SSW events obscures the potential tropospheric impact of an SSW in a composite, as AT and GL trigger contrasting large-scale weather conditions (mild and windy for AT, cold and calm for GL) for large parts of Europe .
We now subdivide the 25 SSW events with respect to the weather regime that dominates during the 10 d around the SSW onset: GL (five cases), EuBL (seven cases), and the cyclonic regimes (ZO, ScTr, AT; eight cases). The remaining five cases either have no clear regime signature (no regime, two events) or are associated with AR (three events) at their onset. Because of the small sample size, we do not consider these cases here. For the GL subset (Figs. 2b, A2b), all other regimes are subsequently suppressed except for AT and EuBL. The frequency of GL itself drops immediately after the SSW, reaching values below 10 % around a lag of 20 d (Fig. A2b) -far below its climatological mean frequency. AT, and to a lesser degree also EuBL, become significantly more frequent immediately after the SSW until about a lag of 10 d, reaching absolute frequencies of 35 % and 20 %, respectively (Fig. A2b). After a period with no clear regime assignment, AT becomes the dominant regime starting at lag 18 d with anomalous frequencies above 40 % (Fig. 2b), peaking above 50 % absolute frequency about 23 d after the SSW and remaining significantly enhanced until a lag of 33 d (Fig. A2b). From lag 25 d until lag 40 d, EuBL becomes significantly enhanced, peaking at 40 % absolute frequency around lag 30 d.
For the EuBL subset (Figs. 2c, A2c), the subsequent regime frequencies are quite different to GL around the on- set of an SSW. First, the frequency of AR is significantly enhanced directly after the SSW, with peaks at 30 % absolute frequency at lag 10 d. This is then followed by a period of preferred occurrence of GL (lag 15 to 25 d) and AT (lag 21 to 32 d) with an absolute frequency reaching up to 45 % and 35 %, respectively. The dominance of GL from lag 33 to 45 d (above 45 % peak frequency) is particularly striking.
Cyclonic regimes around the time of the SSW (Fig. 2d, A2d) exhibit a less prominent regime frequency modulation after an SSW compared to the EuBL and GL subsets. Still, GL (lag 5-35 d), AR (lag 24-31 d), and AT (lag 25-37 d) are significantly enhanced, but absolute frequencies remain around 20 %-30 %. Note that this corresponds to significantly increased frequencies of 10 %-20 % for these regimes in the considered time windows. However, most often no single regime dominates after an SSW event with a cyclonic regime at lag 0, hinting at cases with no downward response after the SSW event. Of the eight SSWs with cyclonic weather regimes at lag 0, Karpechko et al. (2017) investigated seven and classified five out of the seven SSW events as lacking a tropospheric impact. For EuBL and GL around the onset of the SSW, seven out of seven and one out of five, respectively, are classified as having a tropospheric impact. The reasons for this will be discussed in the next section.
Despite the large tropospheric variability in the aftermath of SSW events, the investigation of lagged regime frequencies reveals that (1) the AT and GL regimes are more likely to follow an SSW (as compared to other weather regimes) and (2) that this subsequent modulation is sensitive to the tropospheric flow regime around the onset of the SSW. The dominance of EuBL and GL at the time of the SSW onset hints at a significantly more likely GL response (after EuBL at lag 0) vs. AT (after GL at lag 0) after an SSW, respectively. Thus the stratospheric impact on the evolution of the tropospheric flow in the NAE region and hence the associated surface weather may be connected to the presence of a particular tropospheric regime around the onset of the SSW.

Temporal evolution of the downward impact
We focus in the following on the modulation of stratospheretroposphere coupling for the previously discussed sets of SSWs. For that purpose, we evaluate the temporal evolution of standardized geopotential height anomalies averaged over the NAE sector (60-90 • N, 80 • W-40 • E) by compositing a given set of SSW events. Using the full hemisphere, that is, the full longitude range instead of the here used longitude sector over the North Atlantic, yields the same qualitative results due to the strong imprint of the anomalies induced by the SSW in the NAE sector (Fig. A3).
Compositing all SSW events (Fig. 3a) yields the classical dripping paint plot of Baldwin and Dunkerton (2001, their Fig. 2). Qualitative differences compared to the figure from Baldwin and Dunkerton (2001) are due to the different variable (geopotential height in our study vs. northern annular mode, NAM) and the number of events (25 in our study vs. 18) for a different time period (1979-2019 in our study vs. 1958-1999). When compositing all SSW events, the down-ward impact between 10 and 60 d after the SSW onset is robust at the 25 % but not the 10 % level (see Fig. A4a). Together with the relatively weak amplitude of the anomalies, this reflects the large case-to-case variability in the tropospheric impact of SSWs. Despite the low robustness, the anomaly around a lag of 15 d is unlikely to be obtained from a random sampling as evident from the less than 10 % overlap between the confidence and random distributions (Fig. 3a). This suggests that in the aftermath of an SSW (lag 15-25 d), indeed positive geopotential height anomalies over the NAE sector are significantly more likely than in the absence of an SSW.
SSW events that occur during GL (Fig. 3b) are associated with an immediate, strongly positive anomaly in the troposphere. Consistent with Fig. A2b, when GL is present around the onset of the SSW, GL or AR are often already present before the SSW event, which is likely the cause of the positive tropospheric geopotential height anomalies several days prior to the event. Notably, there are no significant and robust (Figs. 3b and A4b) anomalies after 10 d of the onset of the SSW except for a weak negative geopotential height anomaly after 20 d (significant at the 25 % level), indicating a cyclonic flow regime in the NAE region. This is consistent with the significantly enhanced likelihood for the occurrence of the AT regime at this lag (Fig. A2b). Note that both the immediate positive geopotential height anomalies and the weak tropospheric anomalies in the aftermath of the event are not the result of cancellations in the composites but are rather typical across cases. In fact, four out of the here identified five GL events have been classified by Karpechko et al. (2017) as having no downward impact.
For EuBL around the onset of the SSW event, a robust (10 % level) positive tropospheric anomaly can be observed at the time of the SSW (Fig. A4c). This anomaly is not significant (Fig. 3c), reflecting that it is not different from generic anomalies during EuBL. However, robust, significant, and strongly positive geopotential height anomalies are present in the troposphere at lags of 15-20 and 30-55 d after the SSW event. This is consistent with the classification of all of the here defined seven EuBL events as having a tropospheric impact in Karpechko et al. (2017). These positive anomalies are consistent with the finding that first AR and then GL are much more likely in the aftermath of an SSW with EuBL around lag 0 (compare to Fig. A2c). Furthermore, comparing to the panel for all SSW events (Fig. 3a) indicates that the EuBL cases dominate the perceived downward response in the canonical response for SSW events.
During cyclonic regimes around the onset of the SSW, there is no substantial tropospheric anomaly in the NAE region at the time of the SSW, but a positive albeit weak anomaly can be observed around days 15-20 after the SSW event (Fig. 3d). This anomaly is not robust at the 25 % level, but it is significantly different from a random sample at the 25 % level (Fig. A4d). Several SSWs with a cyclonic regime around the onset are followed by GL at a longer lag ( Fig. A2d), thus likely causing these anomalies. Still, the GL absolute frequencies remain below 30 % (Fig. A2). These findings and the small amplitude of the anomalies suggest that the variability in the tropospheric flow evolution after SSWs is large after a cyclonic regime at lag 0, which is also confirmed by the inspection of individual cases (not shown).
The question arises of whether other factors might contribute to the differing tropospheric evolution in the aftermath of the SSW event. In particular, a differing amplitude and persistence of the lower stratospheric anomaly can be observed in Fig. 3 between the different composites. Events with EuBL around the onset and a strong downward impact tend to have a longer stratospheric persistence, but an equally long persistence can be observed for cyclonic regimes around the onset of the SSW, with little downward impact. The five SSW events associated with GL have a shorter-lived lower stratospheric response. As events with a persistent lower stratospheric response are often associated with socalled polar jet oscillation (PJO) events (Kuroda and Kodera, 2004;Hitchcock et al., 2013b), a comparison with Table 1 in Karpechko et al. (2017) reveals that two out of five SSW events with a GL regime (and, respectively, four out of seven EuBL events) around the onset are associated with a PJO event. While this is not a clear result, it indicates that the shorter (longer) persistence in the lower stratosphere for the SSWs associated with GL (EuBL) may add support to the persistence of the tropospheric response for several of the events, but the statistics are too small to provide a clear result. Similarly, four out of seven EuBL events are split events (rather than displacements), while two out of five GL events are split events, according to the classification in Karpechko et al. (2017).

Impact on surface weather
Since each weather regime is associated with characteristic surface weather, the modulation of regime successions in the aftermath of an SSW by the tropospheric state at the time of an SSW might contribute to the marked variability in the surface impact. Hence, we here consider spatial composites of anomalies of 2 m temperature (T2m') and 500 hPa geopotential height (Z500') for the three groups of SSW events discussed in the previous sections (Fig. 4a-c) and for all SSW events (Fig. 4d) for days 0 to 25 after the SSW (Fig. A5 for days 25-50).
During SSWs dominated by GL around their onset, initially strongly positive T2m' values prevail over Greenland and the Canadian Archipelago, whereas western Russia and Scandinavia are anomalously cold, consistent with the anomalous ridge over Greenland and the low geopotential height anomalies over Scandinavia (Fig. 4a). With the subsequent progression of weather regimes -typically towards the cyclonic AT regime or EuBL -mild conditions are established throughout central Europe from a lag of 20 d onwards. indicates that the confidence intervals and the random distributions overlap by less than 25 % (10 %). Figure A3 shows a version of this figure for the full longitude range. This is in stark contrast to the negative NAO phase and the associated cold conditions that are commonly expected as the canonical response to SSWs over Europe Kolstad et al., 2010;Domeisen et al., 2020a).
For SSWs that are dominated by EuBL around their onset, cold anomalies prevail over northern Europe, albeit also extending over large parts of central Europe (Fig. 4b). They peak at −4 to −6 K around lags beyond 20 d, which corresponds well with the occurrence of the GL regime. Note that negative T2m' values in the composite for all SSWs are much weaker (see Fig. 4d). The associated retrogression of initial positive Z500' over the eastern North Atlantic to Greenland along with a strengthening of negative Z500' over the southeastern North Atlantic around lag 15-25 d is striking. Furthermore, GL is associated with warm anomalies over Greenland and eastern Canada.
Finally, as expected by the varied regime succession for the SSWs with cyclonic regimes at their onset, composite T2m and Z500 anomalies are weaker for these events (Fig. 4c). Thus, the canonical response of surface temperature (i.e., the composite for all SSWs, Fig. 4d) is the result of averaging over -in important regions opposing -temperature anomalies for SSWs with GL, EuBL, or a cyclonic regime around the onset.

Summary and discussion
This study aimed to shed light on the large case-to-case variability of the tropospheric response to SSW events and their associated surface impacts, as well as the dependence on the tropospheric weather regime around the onset of the SSW. To that end, we have exploited in a statistical framework the observational record of the satellite era (1979-2019) as represented in the ERA-Interim reanalysis. Our conclusions are as follows: 1. In the aftermath of an SSW event, the tropospheric flow in the NAE region exhibits an evolution that is unlikely to occur in the absence of an SSW. Specifically, positive geopotential height anomalies related to Greenland blocking are statistically more likely to occur after the onset of the SSW than in the absence of an SSW. This is consistent with the expected (canonical) negative NAO response of the troposphere to SSWs (e.g., Charlton-Perez et al., 2018).
2. The significant and robust positive geopotential height anomalies found in the period 10-60 d after SSWs are predominantly the result of SSWs with European blocking dominating around their onset. This is manifested for this subset of events in a transition from EuBL to GL that then dominates at lags of 15-20 and 30-55 d after the SSW onset, which is statistically significantly different from the natural progression from EuBL to GL. These events all correspond to SSWs that have in the literature been classified as having a tropospheric response (e.g., Karpechko et al., 2017). For other tropospheric regimes at SSW onset the tropospheric response is weaker and less robust and significant.
3. For Greenland blocking at the SSW onset, a weak preference for cyclonic flow regimes around 20-30 d after the SSW is apparent, with an opposite surface response in the aftermath of the SSW as compared to SSW onsets dominated by EuBL. These events almost exclusively correspond to SSWs that have in the literature been classified as having no tropospheric response.
4. SSWs that occur during cyclonic weather regimes exhibit a considerably weaker and less significant response as compared to SSW events associated with EuBL, with a modestly enhanced likelihood for GL.
Depending on the tropospheric weather regime around the SSW onset, different surface signatures result. Specifically, the signature in 2 m temperature resembling the expected canonical NAO− state, e.g., cold conditions prevailing over 382 D. I. V. Domeisen et al.: Weather regimes in the response to sudden stratospheric warmings much of northern Europe, occurs for the EuBL cases. In contrast, mild temperatures in large parts of Europe are found for SSWs with GL around their onset. It is important to distinguish these cases, since although EuBL and GL frequently (that is, for roughly 50 % of all SSWs) occur around the onset of SSW events, they lead to a different subsequent evolution and different associated surface temperatures. In particular, the most common SSW events exhibit a transition from EuBL (GL) around SSW onset to GL (AT) around 3-4 weeks after the SSW, respectively, along with their contrasting large-scale weather impacts . Note that these differences cannot be identified by using a set limited to four weather regimes. These findings indicate that the presence of either a EuBL or GL regime at SSW onset will allow us to disentangle the difference in surface weather and hence to determine if and when a downward impact of the SSW is expected. This is highly relevant for subseasonal forecasting.
While these findings are limited by the small sample size of SSW events available in the observational record, the rigorous statistical testing for significance and robustness performed here suggests that the large case-to-case variability in the tropospheric response to SSWs can be described in terms of NAE weather regimes and may depend on the regime around the onset of the SSW for many of the observed SSWs. Our findings confirm that while the stratosphere does not represent the sole forcing of the tropospheric state, for many SSW events it is able to affect the tropospheric flow by suppressing some weather regimes and by favoring others, as found in Charlton-Perez et al. (2018). We here in addition show that the susceptibility of the troposphere to the stratospheric forcing depends on the tropospheric state around the time of the SSW. Other factors that can modulate the tropospheric response to SSW events are the persistence of the temperature anomaly in the lower stratosphere (Hitchcock et al., 2013a;Karpechko et al., 2017;Runde et al., 2016;Polichtchouk et al., 2018), as well as upstream effects in the North Pacific (Afargan-Gerstman and Domeisen, 2020;Jiménez-Esteve and Domeisen, 2018). An analysis of differences in the lower stratospheric persistence for the weather regimes considered here did not yield conclusive results, which warrants further studies. Note that it was not possible in our analysis to fully exclude differences in the stratospheric forcing between SSW events due to the small sample size. In particular, differences in stratospheric behavior, such as vortex geometry or the persistence of the temperature signal in the lower stratosphere, may influence the type and persistence of the downward response. We expect a negligible influence from the vortex geometry, as the differences in the surface signals between split and displacement events tend to be small (Charlton and Polvani, 2007;Mitchell et al., 2013;Maycock and Hitchcock, 2015;Seviour et al., 2016;Lehtonen and Karpechko, 2016) and are also affected by the small sample size. While the persistence of the lower stratospheric response likely affects the persistence and type of the tropospheric signal (Hitchcock et al., 2013a;Karpechko et al., 2017;Runde et al., 2016;Polichtchouk et al., 2018), we did not find a clear correspondence between persistent stratospheric events and tropospheric weather regime evolution. In particular, roughly half of SSW events associated with either EuBL (4 out of 7) or GL (2 out of 5) are associated with a persistent lower stratospheric response (note the small sample size). Hence, we could not find a clear equivalence between tropospheric weather regimes and lower stratospheric persistence.
Our goal is to emphasize that the troposphere has a role to play in the downward response of SSW events. The respective contributions of the stratosphere, the state of the troposphere over the North Atlantic, and upstream precursors will subsequently have to be disentangled in a modeling study. In particular, a model study to quantify the respective contributions to the tropospheric impact of different remote factors in comparison to the role of local North Atlantic variability might shed further light onto the complex role of stratosphere-troposphere coupling for surface weather. However, it is currently not sufficiently known to what extent complex prediction models are able to represent the diversity of tropospheric responses to stratospheric forcing, as this has not been sufficiently tested in models beyond the canonical response and selected case studies. From a preliminary analysis of subseasonal prediction models we anticipate large biases and a complex role of the representation of stratosphere-troposphere coupling in prediction models that will be difficult to disentangle. Hence, while state-of-the-art subseasonal prediction systems are often unable to forecast at the time of occurrence of the SSW event if a surface response is to be expected, our findings suggests that the presence or absence -and in fact the timing -of a surface impact following SSW events might in some cases be predictable based on the dominant weather regime around the onset of the SSW event. This could significantly improve the subseasonal prediction of tropospheric winter weather following SSW events over Europe.   by the weather regime that is dominant around the onset of the SSW as indicated by the titles of the panels. Robustness is assessed using confidence intervals by resampling the SSW events 100 times with repetition. If the magnitude of the anomaly exceeds the interquartile or the 10th-90th percentile ranges, the anomaly is highlighted by stippling or hatching, respectively. See Sect. 2.2 for details.   Domeisen et al.: Weather regimes in the response to sudden stratospheric warmings Data availability. The ERA-Interim reanalysis data (Dee et al., 2011) are available from ECMWF at https://apps.ecmwf.int/ datasets/data/interim-full-daily/ (last access: 7 August 2020).
Author contributions. The authors together initiated and designed the study, and all authors contributed to data analysis, discussion of results, and writing.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. Data analysis and visualization were performed using the NCAR Command Language (UCAR/NCAR/CISL/VETS, 2014). The authors thank the editor Pedram Hassanzadeh and the three anonymous reviewers for their reviews of the manuscript.
Financial support. Support was provided by the Swiss National Science Foundation through project PP00P2_170523 to Daniela I. V. Domeisen. The contribution of Christian M. Grams was supported by the Helmholtz Association as part of the Young Investigator Group "SPREADOUT" (grant no. VH-NG-1243).
Review statement. This paper was edited by Pedram Hassanzadeh and reviewed by three anonymous referees.