The study uses ERA5 reanalysis data based on the Integrated Forecasting System (IFS) Cycle 41r2 (Hersbach et al., 2020). Data are extracted for the entire calendar year from 1980–2020 and 40 complete winters (December–February) are analysed labelled by the year of January–February (i.e. 1981–2020). The variables used in the analysis are 850 hPa relative vorticity (variable “vo”), mean sea level pressure (variable “msl”), maximum 10 m wind gust since previous preprocessing (variable “10fg”), total precipitation (variable “pr”), and significant height of combined wind waves and swell (variable “swh”, hereafter significant wave height). ERA5 is provided at a 0.25×0.25 degree resolution (0.5×0.5 degrees for “swh” variable) and used at 1 hourly temporal frequency.

Winter average near-surface wind speeds in Europe in ERA5 have been shown to agree better with observation towers than several other reanalysis datasets (Ramon et al., 2019). As is standard for climate models, wind gusts are post-processed in ERA5 following the approach described in ECMWF IFS Documentation (2016). Comparison with meteorological station data in Sweden indicates strong wind gusts (≳ 15 m s⁻¹) are generally underestimated in ERA5 (Minola et al., 2020). This is consistent with Chen et al. (2024) who evaluated ERA5 against weather station observations in North America and showed that in winter spatially-averaged near-surface wind speeds within ETCs are well represented (r∼ 0.9), but wind speeds associated with the most intense ETCs and local extremes within ETCs are generally underestimated. Lodise et al. (2024; their Fig. 7) also compared Northern hemisphere ETC wind speeds in ERA5 with radar altimeter measurements and found ERA5 has a low bias by ∼ 5 % in the region of strongest 10 m wind speeds in the eastern hemisphere of cyclones relative to the translational direction. For significant wave height, Bessonova et al. (2025) and Fanti et al. (2023) compared ERA5 to global buoy measurements and found an underestimation in ERA5 which was most pronounced for larger wave height measurements. Lodise et al. (2024) also found that in ERA5 significant wave heights within Northern hemisphere ETC footprints are biased low by ∼ 5 % compared with radar altimeter data. For daily precipitation, ERA5 shows the smallest biases in the winter extratropics compared to other global regions and seasons (Lavers et al., 2022) and captures observed variability across Europe with significant skill compared with E-OBS observations (Bandhauer et al., 2022). However, ERA5 underestimates the magnitude of extreme daily precipitation but it can generally capture the location and timing of precipitation extremes (Lavers et al., 2022). Therefore, based on studies that have evaluated ERA5, we conclude that the extreme European ETC hazards derived in this study are likely to be conservative estimates.

The TRACK algorithm is used to identify and track ETCs (Hodges, 1994, 1995, 1999). TRACK identifies ETCs based on maxima in the hourly 850 hPa relative vorticity field. Prior to tracking, the vorticity field is spectrally truncated to T42 resolution and filtered to remove wavenumbers less than 5, which ensures the analysis focuses on synoptic scale disturbances. Following identification of cyclonic maxima, identification points are refined using a B-spline interpolation and steepest ascent maximization. ETCs are then grouped into tracks using a nearest neighbour approach. These are then refined by the minimization of a cost function for track smoothness subject to adaptive constraints. As we are only interested in well-developed and long-lived ETCs, tracks must persist for at least 48 h and travel at least 1000 km from their origin. Due to the focus of this study being on Europe and the North Atlantic, only tracks that are present in the region 30–75° N, 100° W–40° E are retained in the analysis. For each track in the study region, we identify the atmospheric and oceanic state that is attributable to the presence of the ETC based on a distance criterion. At each hourly step in the lifecycle, the hazard “footprint” around the ETC is extracted using a radial distance of either 5 or 10° from the cyclone centre. A 5° radius is used for the wind gust and significant wave height variables and a 10° radius for precipitation. This is due to the maximum winds of an ETC mainly being within 5° of the cyclone centre (Priestley and Catto, 2022), but a larger area of influence on precipitation due to the scale of fronts (Kodama et al., 2019). The analysis focuses on the boreal winter season from December–February (DJF) when the North Atlantic storm track is most active, so the ETC tracks are filtered to retain DJF storms.

The ETC hazard variables examined are the maximum daily precipitation, or equivalently the wettest winter day due to an ETC, the winter total precipitation due to ETCs, the maximum 3 s 10 m wind gust, and the maximum significant wave height. The first measure relates to the likelihood of flooding, particularly pluvial flooding in urban areas or fluvial flooding in catchments with high antecedent soil moisture (e.g., Ivancic and Shaw, 2015); it is similar to the commonly used R×1day metric which represents the wettest calendar day in the year and is widely used in the climate extremes literature (e.g., Seneviratne et al., 2021). The second hazard represents the cumulative winter precipitation due to ETCs which is also related to flood hazards due to the relationship with antecedent soil moisture (e.g., Bennett et al., 2018). The third hazard relates to the likelihood of wind damage; and the fourth relates to the likelihood of coastal flooding and damage to coastal infrastructure from wave overtopping. The hazard footprints resulting from the tracking (Sect. 2.1) are post-processed to extract the maximum value at each gridpoint the ETC intersects over its lifecycle, or in the case of precipitation the maximum daily accumulation and the total accumulation over the ETC lifecycle. An example of the hazard footprints identified from this method for Storm Ciara in February 2020 is shown in Fig. 1.

For each winter season, the hazard footprints from all tracked ETCs are overlaid and the maximum value at each gridpoint is then selected for the winter. The resulting field therefore represents the most extreme ETC hazard (maximum 3 s 10 m wind gust, maximum hourly significant wave height, or daily precipitation) experienced at each gridpoint in a given winter except for winter total precipitation where the precipitation totals for all ETCs in the season are summed; these are used in the regression analysis. The choice of extracting the most extreme hazards within the season provides an upper limit on the most hazardous conditions that might be expected based on a relationship with the seasonal modes of variability; this extends previous work that has taken a seasonally aggregate view (e.g., Degenhardt et al., 2023) and emphasises short-term extreme hazards which may be useful to stress test the resilience of infrastructure and buildings. Note, the extremes are therefore not spatially contiguous and the values at neighbouring gridpoints may come from different ETCs within a given season.

For part of the analysis, we also calculate a storm damage index (SDI) (Karremann et al., 2014), which is the population weighted meteorological storm severity index (SSI) (Klawa and Ulbrich, 2003). The SSI is calculated as 1SSIi,j=vi,jmaxvi,j98-13, where i and j are the gridbox coordinates, vmax is the maximum wind speed value associated with the ETC, v98 is the 98th percentile of the winter wind speed distribution over December 1980–February 2020. Negative values of SSI are set to zero to ensure cyclonic wind speeds below the 98th percentile threshold do not contribute to the loss metrics.

Since the losses associated with windstorms will be strongly related to the exposure of people and buildings, the SSI can be scaled by the population estimate at each grid box to estimate a storm damage index (SDI) 2SDIi,j=SSIi,j×populationi,j, where gridded population data for 2015 are taken from the Gridded Population of the World fourth version (GPWv4; Center For International Earth Science Information Network-CIESIN-Columbia University, 2017). For comparison with earlier studies, the SDI is summed over all storms within a given season to give a seasonal SDI value (e.g., Degenhardt et al., 2023).

The NAO and EAP (also known as the Atlantic Ridge) modes of variability are calculated as the first two empirical orthogonal functions (EOF1 and EOF2) of DJF mean sea level pressure in the Euro-Atlantic sector (90° W–40° E, 20–80° N) and the associated principal component timeseries (PC1 and PC2). These are hereafter referred to as PC1 and PC2, respectively.

The ETC hazards are assessed quantitatively for land and sea subregions within the domain 25° W–40° E; 35–75° N. Land regions are defined following the 0.5 Mm² regions of Stone (2019), which represent approximately equal areas regions along political/economic boundaries. The regional seas are defined following the European Environment Agency regions defined by the EU (https://sdi.eea.europa.eu/data/51035cd2-3dea-4b39-94c7-e53946603c2a, last access: 28 March 2026) which categorise four main European seas: Mediterranean, Baltic, Black Seas and North East Atlantic Ocean, all of which except the Baltic Sea are further divided into subregions. There are 16 land regions and 15 regional sea regions analysed in the study. The hazards are first averaged over the regions before being analysed for their covariance with the NAO and EAP.

We perform least squares linear and multiple linear regression of the winter maximum ETC hazards at each gridpoint against the winter mean PC1 and PC2 timeseries within the Euro-Atlantic domain 25° W–40° E, 35–75° N. To assess the suitability of the statistical model to describe the data, we examine the R2, linearity, metric homoscedasticity, normality of residuals and the independence using the Durbin Watson (DW) statistic to test for autocorrelation in the residuals. The DW statistic ranges from 0 to 4, with a value of 2 indicating zero autocorrelation in the residuals. For linearity, homoscedasticity and normality we assess p-values using a 95 % confidence level, such that p<0.05 denotes the required condition is not met and the regression model performance is unsatisfactory, while p>0.05 denotes the condition is met.

Some previous studies have investigated the signals of North Atlantic modes of variability in seasonal European SDI and ETC frequency based measures (e.g., Degenhardt et al., 2023). We also tested our analysis on these variables but found issues with the performance of linear regression at the grid point scale. By construction, SDI = 0 when vmax<v98 (see Eq. 1). This non-linear behaviour means a linear regression is likely to perform poorly if applied over all time points. Typical performance of linear regression for SDI against PC1 and PC2 is shown in Fig. 2 for a gridpoint near Birmingham (52.5° N, 1.875° W). Figure S1 in the Supplement shows the full statistical metrics for the linear regression performance for SDI across our study region. While statistically significant regression coefficients against PC1 and PC2 are obtained in some regions (Fig. S1a), the analysis of the regression performance reveals the homoskedasticity and normality criteria are poorly met within those regions (Fig. S1c), meaning there is too much variance and non-normal behaviour in the error term and the model is not well defined. Previous studies have generally presented R2 values for similar regression analyses but not further measures of model performance; while reasonable R2 values can in principle be achieved (Fig. S1b), the linear model is not suitable for this data.

ETC frequency related measures, such as total count or number of ETCs exceeding a specified wind gust threshold, are discrete variables where linear regression can perform poorly. Fewer issues were found with the performance of linear regression for seasonal ETC count (Fig. S2), though some European regions show residuals that do not satisfy the criteria of normality or zero autocorrelation in the residuals. Therefore, we encourage caution in applying simple statistical analyses like linear regression to data which may not satisfy the requirements for a linear model. For these reasons we do not include frequency or SDI based ETC hazard metrics in this study.

Figure 3 shows the climatological winter signals derived from the cyclone footprints and PC1 and PC2 regression maps for the four ETC hazard types: (a) winter total precipitation accumulation, (b) maximum daily precipitation accumulation, (c) winter maximum 10 m wind gust and (d) winter maximum significant wave height. The PC1 and PC2 regression slopes are shown as percentage anomalies from the climatology, with equivalent absolute anomalies shown in Fig. S3. The accompanying R2 values for the regressions are shown in Fig. 4 and the evaluation of the regression performance is shown in Fig. S4, which shows the linear regression performs much better for these variables than those discussed in Sect. 2.6.

The relationship between PC1 and winter total precipitation in Europe due to ETCs is similar to that found for precipitation not conditioned on ETCs (e.g., McKenna and Maycock, 2022), with wetting over the UK and Scandinavia and drying over the Iberian peninsula (Fig. 3aii); this is consistent with previous work showing the majority of winter European precipitation falls within ETCs (Hawcroft et al., 2012). For PC2, the signal comprises an increase in winter precipitation over the UK, western France and the Iberian peninsula with drying over Scandinavia (Fig. 3aiii). In contrast to the coherent signals in winter total precipitation from ETCs with PC1, there is a much weaker relationship with the winter maximum daily precipitation from ETCs, though where a significant relationship is seen, the canonical NAO north/south Europe wet/dry dipole pattern is evident (Fig. 3bii). In contrast, a positive PC2 anomaly corresponds with a significant increase in winter maximum daily precipitation over Portugal and parts of western UK (Fig. 3biii). Scaife et al. (2008) showed a relationship between 5-day precipitation extremes and the NAO, with more events above the 90th percentile and less events below the 10th percentile over the UK and northern Europe during NAO positive. The relative lack of significant relationships with PC1/PC2 could be a result of the relatively noisy data, since at each gridpoint we are taking the wettest day in the winter associated with any ETC and regressing this against the seasonal NAO/EAP.

In contrast, there is a strong signal of winter maximum 10 m wind gust in both PC1 and PC2, with large regions with anomalies of 10 %–15 % above climatology (Fig. 3c). For positive PC1, the UK, Scandinavia, Netherlands and Northern Germany show increased maximum wind gusts, while Portugal and Northern Spain show a decrease (Fig. 3cii). For positive PC2, southern and south-west England and Wales show an increase wind gust along with Portugal and Spain, while parts of Scandinavia and eastern Mediterranean show a reduction (Fig. 3ciii).

The patterns of anomalous significant wave height largely mirror those of wind gusts, reflecting their known co-relationship (e.g., Dobrynin et al., 2019), with positive height anomalies of 10 %–15 % around the UK and Scandinavian coasts for PC1 (Fig. 3dii). For PC2, there are comparable anomalies around Southern Ireland and south-west England, as well as anomalies of 5 %–10 % around the French, Portuguese and Spanish coastlines (Fig. 3diii).

In regions where the regression coefficients are statistically significant, the combined PC1 and PC2 regressions explain up to around 50 % of the interannual variance of the winter maximum wind gust (Fig. 4c) and significant wave height (Fig. 4d), and locally up to around 70 % for winter total precipitation due to ETCs (Fig. 4a) but less for winter maximum daily precipitation over land areas (Fig. 4b).

Figure 5 shows percent anomalies in winter total precipitation (Pr), winter maximum wind gust (G) and significant wave height (Ht) due to ETCs associated with a +1σ anomaly of PC1 and PC2 aggregated to regional scales over land and ocean areas. At regional scales, the proportionately largest signals for PC1 (Fig. 5a) are in precipitation including increases of 8.9 % in West Russia, 17.5 % in North-West Russia, 15.9 % in Finland and Baltic Seas, 12.0 % in Sweden and 16.2 % in the UK, Denmark and Norway. There are also significant increases in wind gusts in these regions with a smaller relative magnitude of <10 %. There are significant anti-correlations between the hazards and PC1 in southern Europe including a decrease of 34.4 % in the Iberian Peninsula, 10.2 % in France, 13.5 % in Italy and 14.7 % in Romania, Bulgaria and Greece; however, there are no significant anomalies in maximum wind gust in these regions except for the Iberian Peninsula (-7.7 %). As expected, over ocean regions the anomalous wind gusts and significant wave height have similar magnitudes typically 5 %–10 % over exposed seas in the western part of the domain (Celtic Seas, Macaronesia, Iceland Sea, Greater North Sea, Norwegian Sea and the Baltic Sea.

For PC2 (Fig. 5b), the significant precipitation and wind gust signals are generally weaker over continental Europe, except for the Iberian peninsula (Pr = 26.4 %, G = 10.5 %), France (Pr = 13.0 %) and Sweden (G = -6.0 %). There are significant collocated wind gust and significant wave height anomalies with PC2 over western and northern seas: Macaronesia, Bay of Biscay and Iberian Sea, Norwegian Sea and Barents Sea.

Compound events where multiple hazards coincide in space and time are often particularly impactful (e.g., Owen et al., 2021). The results in Figs. 3 and 5 show areas of considerable overlap between the individual ETC hazards. To determine all the locations where either PC1 or PC2 modify one ETC hazard, we overlay the coloured areas for the winter total precipitation, wind gust and significant height hazard regression maps from Fig. 3 and plot the geographical coverage distinguishing regions affected by a single hazard type, regions unaffected by any hazard and regions affected by >1 hazard (Fig. 6a, c). An equivalent analysis for multivariate hazards where there are coincident signals in multiple variables for either PC1 or PC2 is performed; these are shown for permutations of two hazard types and all three hazards in Fig. 6b, d. Note given these are statistical relationships, we are not establishing whether the extremes occur from the same ETC and are therefore coincident in time; rather, this reflects whether regions could experience enhanced exposure to multivariate hazards within a winter season, depending on the relative phases of PC1 and PC2.

PC1 alters the exposure to only cumulative winter precipitation in Spain, southern France and northern Norway, Sweden and Finland (Fig. 6a). PC1 alters the intensity of only peak wind gusts in eastern England, the Netherlands, northern Germany, central Norway and Sweden and Baltic countries. PC1 does not affect hazard exposure in France, Switzerland, Germany and most countries in central and eastern Europe. For compound hazards, PC1 mainly associates with altered exposure to paired winter precipitation and wind gust hazards in Ireland and the western UK, western Norway, southern Sweden, Finland and western Russia (Fig. 6b). Compound wind gust and significant wave height hazards occur in the Irish Sea, the Channel, North Sea and Baltic Sea. The areas with compound exposure to all three hazards for PC1 are in the Atlantic Ocean, Norwegian Sea and parts of the Iberian Sea.

For PC2, there is no discernible change in exposure to any single hazard across most of central and eastern Europe (Fig. 6c). Central and northern England, Scotland, Ireland, northern and western France and western Norway show only altered exposure to winter precipitation amount for PC2. For compound hazards, PC2 alters exposure to winter precipitation and peak wind gust for Portugal and western Spain (Fig. 6d). PC2 alters exposure to wind gusts and significant wave height in the eastern Mediterranean and around the coast of Norway. The coasts around southern Ireland, Wales, south-west England, northern France and Portugal show altered exposure to all three hazards for PC2 which operate in the same sign (i.e. wetter, windier and higher significant wave height for positive PC2).

Many winters show anomalous North Atlantic atmospheric circulation that partly projects onto both PC1 and PC2, so it is possible that at some locations the exposure to ETC hazards will be modulated by both modes of variability. To determine these regions for each hazard type, we follow a similar process to Sect. 3.3 where the coloured areas from the regression maps in the middle and right columns of Fig. 3 are overlaid along each row. Where the two fields coincide shows the locations where the exposure to the hazard type will be affected by both PC1 and PC2. The resultant locations are shown in Fig. 7 for the winter total precipitation, wind gust and significant wave height. Figure 7 reveals virtually no regions of compound PC1 and PC2 winter total precipitation hazard over land, but coherent coastal regions where PC1 and PC2 affect variability for both wind gusts and significant wave height. These regions are surrounding Portugal, southern England, Wales, southern Ireland and southern Scandinavia. As before, over ocean points the patterns for the two variables are similar given that significant wave height is strongly driven by near-surface wind. The overlapping patterns for these variables indicates the absolute change in exposure to ETC hazards in a given winter will be affected by the relative amplitudes of both PC1 and PC2.

To further illustrate this, Fig. 8 shows absolute values of the expected ETC hazards for unitary combinations of the standardised PC1 and PC2 indices (i.e. +1σ PC1 and +1σ PC2; +1σ PC1 and -1σ PC2, etc., as shown by red dots in middle panel Fig. 8). These are constructed by superposing the PC1 and PC2 signals onto the winter climatology over all years. The scatterplot in the centre of Fig. 8 shows the combinations of PC1/PC2 indices in ERA5 for all winters from 1981–2020. Some combinations have been observed infrequently (PC1 < 0 and PC2 < 0), which shows it is rarely the case that negative NAO occurs with Atlantic ridging, but all four combinations of indices used to present the hazards lie within the distribution of observed PC1/PC2 indices and are therefore plausible examples. The hazard maps include solid contours denoting specific thresholds for wind gusts, based on the Beaufort scale for severe gale (25 m s⁻¹), violent storm (29 m s⁻¹) and hurricane strength (33 m s⁻¹) gusts, and for significant wave height based on the Douglas Sea Scale, for very high (9 m) and phenomenal (14 m) heights.

For the combination PC1- and PC2+, the winter maximum wind gust reaches violent storm intensity along the west coast of Ireland and the Bay of Biscay and severe gale intensity along the Iberian Peninsula and Norwegian coast (Fig. 8a). The maximum significant wave height reaches “very high” along the west coast of Ireland and precipitation is 10 %–30 % above normal in southern Ireland, England and Iberia, with drier conditions in Scandinavia (Fig. 8a).

In comparison, for the combination of PC1+ and PC2+ the winter maximum wind gust reaches hurricane intensity along the west coast Ireland, in Wales, south-west England and Scotland, with severe gale intensity in south-east England (Fig. 8b). Maximum wind gust reaches violent storm intensity along the Norway, Sweden and Finland coastlines (Fig. 8b). The area where winter maximum significant wave height reaches very high levels is expanded compared to PC1- and PC2+, reaching south-west England and extending into the Norwegian Sea. Precipitation is 10 %–30 % above normal in northern Scotland and the Iberian Peninsula (Fig. 8b).

For PC1+ combined with PC2-, the area where winter maximum wind gust reaches hurricane intensity extends further east towards the Norwegian coast, with violent storm intensity near south-west England and Wales (Fig. 8c). In contrast, in southern Europe winter maximum wind gust is alleviated reaching less than severe gale force in the Iberian Peninsula and severe gale force in the Bay of Biscay, Sweden and southern Finland. The region exposed to very high maximum significant wave height reaches the west of Ireland, Scotland, southern Iceland and the northern Norway coast (Fig. 8c). Precipitation shows drier than normal conditions in southern Ireland, England and Iberia, with above average precipitation in Scandinavia (Fig. 8c).

Lastly for PC1- combined with PC2-, winter maximum wind gust reaches severe gale intensity in the Bay of Biscay, with below severe gale level in southern England and Wales (Fig. 8d). Along the west coast of Ireland, northern Scotland and the Norwegian coast the maximum wind gust reaches violent storm intensity. The region exposed to very high significant wave height is more restricted to the west of Ireland. Maximum daily precipitation is 10 %–30 % below normal in northern Scotland and Iberia (Fig. 8d).

These examples illustrate the importance of the signals of extreme ETC hazards associated with PC1 and PC2 variability for the exposure of different parts of Europe to the risk of severe weather events.