Co-occurring wintertime flooding and extreme wind over Europe, from daily to seasonal timescales

The risk posed by heavy rain and strong wind is now suspected to be exacerbated by the way they co-occur, yet this remains insufficiently understood to effectively plan and mitigate. This study systematically investigates the correlations between wintertime (Oct–Mar) extremes relating to wind and flooding at all timescales from daily to seasonal. Meteorological reanalysis and river flow datasets are used to explore the historical period, and climate projections at 12 km resolution are analysed to understand the possible effects of future climate change (2061–2080, RCP 8.5). A new flood severity index (FSI) is also developed to complement the existing storm severity index (SSI). Initially, Great Britain (GB) is taken as a comparatively simple yet informative study area, then analysis is extended to the full European domain. Aggregated across GB, wind gusts and precipitation correlate strongly ( 𝑟 𝑠 ∼ 0.6–0.8) at timescales from daily to seasonal, but peak around 10 days. A later peak is seen when considering correlations between wind gusts and river flows (40–60 days). This time is likely needed for catchments’ soils to saturate. A conceptual multi-temporal, multi-process model of GB wintertime flood-wind co-occurrence is proposed as a basis for future investigation. When historical analysis is extended across Europe we find the timescale of maximum correlation varies strongly between nations, likely as a result of different meteorological drivers. Impact focused correlation (FSI–SSI) is lower ( 𝑟 𝑠 ∼ 0.2) but increases notably with climate change at timescales of ∼ 40 days ( 𝑟 𝑠 ∼ 0.4). Tentatively, very severe episodes (i.e., both > 99th percentile) appear heavily influenced by climate change, increasing roughly threefold by 2061–2080 (p < 0.05). The return period of such an event is 16 years historically (compared to 56 years if the two hazards were independent), reduces to 5 years in future. Such metrics provide actionable information for insurers and other stakeholders.


Introduction
During winter, inland flooding and extreme wind are two of the hazards to most severely impact north-west Europe (Mitchell-Wallace et al., 2017).Although to climate scientists it might seem self-evident that these hazards are related, they are typically modelled independently in risk analyses.Evidence that they tend to systematically cooccur (Hillier et al., 2015;Martius et al., 2016;Owen et al., 2021b) is becoming increasingly robust (see Fig. 1 for examples) with the possibility that this significantly exacerbates joint risk.However, neither the interplay of hydro-meteorological mechanisms that give rise Fig. 1.A pictorial overview of methods applied to quantify compound wind extreme and flooding events across Europe within increasingly impact-focused datasets.We note most papers include multiple metrics, the most relevant results to our current work have been chosen.
19th January 2013 windstorm (Liberato, 2014) and storm Desmond in 2015 (Otto et al., 2018).A systematic relationship between flooding and extreme wind in NW Europe was first demonstrated by three papers (Matthews et al., 2014;Hillier et al., 2015;Martius et al., 2016), which also clearly illustrate the spectrum of contrasting, complementary approaches in use then and subsequently.
To identify the winter of 2013-2014 (Dec-Feb) as notably wet and stormy (Matthews et al., 2014) tracked extra-tropical cyclones (ETCs) in reanalysis products from 1871-2012 within the Iceland-UK domain.A seasonal 'storminess' metric (I) was developed and correlated with mean England-Wales precipitation using Pearson's r (r  ).Visually, r  is 0.7 ± 0.1 (p < 0.05).As part of defining Great Britain's (GB's) exposure to multi-hazard risks, Hillier et al. (2015) moved from meteorological measures (e.g., precipitation) to ascertain that co-occurrence extends to annual (Nov-Oct) impacts.Conclusions were based on evidence from a blend of insurance losses (1998-2013;ABI, Association of Bristish Insurers, 2014) and hydro-meteorological observations .Flooding and wind extremes over a threshold are found to occur ∼1.5 times more than expected, with joint 16-year return period losses higher by 20%-30% than if the hazards were independent.
In contrast, Martius et al. (2016) focus on near-surface wind and precipitation extremes, and short time-scales, mapping co-occurrence within a 72 h window for ERA-interim.Notably high percentages of co-occurring extremes are detected along the North-western coasts of Europe (e.g., Iberia, Norway), but are muted in other locations, and again ETCs are invoked as the explanatory process.Owen et al. (2021b) focus on short time windows to determine that co-occurrence in some places (e.g., GB, Norway) is typically within 1 h, and 70% of co-occurrences happen whilst an ETC is within 1110 km.
Recent work for GB from De Luca et al. ( 2017) uses peak river flow data for 260 basins in Great Britain (1975Britain ( -2014) ) to distinguish large multi-basin floods at a spatial scale that is comparable to ETCs (e.g., ∼1000 km).Analyses at 1-19 days and seasonal timescales, combined with a variety of meteorological indices were used to start to understand where 'memory' (Hillier et al., 2015) and time-lags in the hydro-meteorological system might arise.Seasonally, these multi-basin flood events correlate with numerous very severe gales (r  = 0.41, p < 0.05).In addition, Hillier et al. (2020) demonstrated an increase in joint seasonal impact on infrastructure (rail network) due to flood-wind dependence of 27.8%.
A key limitation to the previous studies is the limited ability to comment on truly rare events given the length of the reanalysis/observational record.To attempt to overcome this, the UNSEEN method (Thompson, 2017) has been used, involving multiple realisations of the last 20-30 years using seasonal hindcast models to create a synthetic 600 year record (Hillier and Dixon, 2020;Owen et al., 2021a).Seasonal impact-based measures for flood and wind have suggested that extremes can be captured well (e.g., Spearman's rank correlation (r  ) of up to 0.54 found in Hillier and Dixon, 2020).However, caution is needed over orography (Owen et al., 2021a;Ridder et al., 2021), and there is the possibility that higher-resolution simulations may even be better than reanalysis products such as ERA5 (Zscheischler et al., 2021).
In summary, there is an obvious limitation in the literature, which would benefit from a study that spans timescales from hourly (Owen et al., 2021b) to seasonal (Hillier and Dixon, 2020).A consistent application of techniques to a variety of data types (e.g., flow gauge, reanalysis, climate model ensembles) representing quantities along the progression from meteorological quantities to hazard and risk is also needed.Specifically, as a step towards better understanding the cooccurrence of flooding and extreme wind across North-Western Europe, this paper applies consistent methods to a variety of datasets and timescales to investigate the following research questions: 1. What are the key timescales of correlation for extreme precipitation and wind, and why? 2. Are these also the key timescales of interest in more impactbased metrics? 3. How are these results impacted by climate change?Great Britain (GB) is selected as an initial case study for these questions.It is a region exposed to winter storms destined for mainland Europe whilst being a relatively simple system, with rapid river response times (i.e., < 40 h;De Luca et al., 2017) and snow melt a limited influence.Following this, the results are extended to cover Europe.

Data and methods
In the following subsections the observed meteorological data (Section 2.1) and climate model data (Section 2.2) used to create meteorologically derived proxies for wind and flood risk are discussed.Following this National Rail impact data is described, which forms a damage relevant comparison to our derived estimates (Section 2.3).Table 1 summarises all the meteorological datasets used.Following this, assessment of the co-occurrence of wind and precipitation extremes is reviewed in terms of relevant statistical measures (Section 2.4) and the plausible metrics which range from essentially climatic to those which relate more directly to risk or impact (Section 2.5).
All metrics used in this study are calculated during extended winter (October-March) and nationally aggregated.When using the UK Climate Projections Data (UKCP), thresholds defined for historical data  are applied to both present and future climate to understand potential changes.

Observed meteorological data
To assess the co-occurrence of extreme wind and precipitation events over GB, multi-decadal records of meteorological data are required.Reanalysis data products are a useful tool to provide this kind of information.The primary historical data used in this paper is the ERA5 reanalysis (Hersbach et al., 2020).ERA5 is based on the European Centre for Medium Range Weather forecasting's Integrated Forecasting System (IFS) cycle Cy41r2, which was operational in 2016.
To complement the ERA5 data, daily total river discharges are taken from the Global Flood Awareness System (GLOFAS) (Harrigan et al., 2020).This dataset is simulated by forcing the LISFLOOD hydrological modelling chain with inputs from the ERA5 reanalysis; see Hirpa et al. (2018) for further details of the model framework setup and calibration.It is therefore compatible with other outputs from ERA5 used here.GLOFAS is, however, considered relatively coarse when modelling river flows.The quality of a reanalysis product compared to observed data could also be questioned.To complement the analysis using ERA5 and GLOFAS, daily river flow, precipitation and 10 m wind speed data from 671 catchments across GB, created as part of the CAMELS-GB dataset is also used (Coxon et al., 2020).The wind speed and precipitation data used in CAMELS-GB is taken from CHESS-MET (Robinson et al., 2016) which is a 1 km gridded product available over the UK; see Table 1 and Appendix A for further details.

Climate model data
Using observed meteorological data only allows for a small selection of possible extreme wind and precipitation events to be analysed.Climate model simulations present an opportunity to consider plausible, but as yet unrealised, alternatives.However, climate models need to be fully evaluated to ensure that they represent the essential processes that give rise to extreme winds and precipitation events.In this study the UK Climate Projections 2018 (UKCP18, from hereon referred to as UKCP) regional model simulations are chosen for analysis.The UKCP simulations have been used for a number of impact studies and have been shown to have a good representation of historical precipitation (Lowe et al., 2018;Cotterill et al., 2021;Tucker et al., 2022;Lane and Kay, 2021) and wind gusts (Manning et al., 2021) when compared to lower resolution climate model simulations and gridded observations.
The regional simulations provide hourly data over the same area as the commonly used EURO-CORDEX domain Jacob et al. (2014).Simulations run from 1980-2080 using the Representative Concentration Pathway (RCP) 8.5 climate change scenario, and the setup of the 12 member perturbed parameter ensemble is described in detail in Tucker et al. (2022).Hourly instantaneous wind gusts and total precipitation are taken from all 12 ensemble members for two periods,1981-2000 and 2061-2080.Matching river flows are derived by using the UKCP precipitation and temperature data (and derived potential evapotranspiration data) to drive the Grid-to-Grid (G2G) hydrological model (Kay, 2021).The resulting daily mean river flows have been output on a 1 km grid over GB, and have been summarised nationally on a daily time step, to construct impact-based metrics (as outlined in Hillier and Dixon, 2020).Further details of the UKCP-based river flows are given in Griffin et al. (2022b).

National rail impact data
In the context of natural hazards, meteorological data are proxies, studied as they are argued to relate to extremes that have the potential to cause impacts.As a reality check, it is also therefore useful to consider observed impacts.
Network Rail (NR), who are the owner and infrastructure provider of most of the rail network in GB, record delays to trains.NR's hazard-coded Weather Related Incident Impact Data (WRIID) contains ∼274,000 incidents (2006-2019) that have each been assigned to a hazard and impact location (the originating site of delays).It is at a resolution of typically ∼10 min and <5 km.72.5% of these costs occur in the winter half-year (Oct-Mar).Impact in WRIID is quantified financially (pounds sterling), derived from delay minutes, and additionally each incident is described qualitatively e.g., fallen tree on line.We make use of the number of incidents occurring due to extreme winds or flooding, and the costs associated with extreme winds or flooding in Section 3.1.
Whilst losses in the summer remain substantial, at this time floodwind correlation in the WRIID data is negligible.This demonstrates that the categorisation used is robust.This is because if flood and wind were being confused or mixed a false correlation would be present, and it is difficult to imagine why this artefact would vary by season.Thus, the WRIID data overcame a limitation common in insurance data (see Hillier et al., 2015 Appendix B).The WRIID data have been used previously for work on heat Ferranti et al. (2016) and Ferranti et al. (2018) and seasonal multi-hazard analysis (Hillier et al., 2020), but not yet for the sub-seasonal examination of flooding and extreme wind.Data is aggregated (summed) to GB level for analysis here.Appendix B gives future information on the categorisation of flood-wind damage in WRIID.

Defining co-occurring events
The studies described in Section 1 use a range of methods to define the presence compounding perils, shown schematically in Fig. 1.The choice of approach is dependent on the nature of the research question.The three most common methods are: • Pearson's correlation coefficient, r  (e.g., Matthews et al., 2014;De Luca et al., 2017;Hillier and Dixon, 2020).• The logistic regression model (e.g., Martius et al., 2016), which quantifies the odds-ratio (multiplicative factor) of predicting a precipitation extreme at a specific grid point given a wind extreme occurring.• Extremal dependency measures based on co-occurrence or otherwise of wind and precipitation extremes above a given percentile.This was proposed by Coles et al. (1999), illustratively used in Hillier et al. (2015), Martius et al. (2016) and Owen et al. (2021b), and includes the idea of an occurrence ratio (i.e., observed number of co-occurrences divided by the number expected due to chance).
This list is not exhaustive, with other methods used including the examination of residual tail dependence (Vignotto et al., 2021) and more impact-based assessments such as a change in Annual Exceedance probabilities (the probability of annual aggregate losses exceeding a threshold; Hillier et al., 2015;Hillier and Dixon, 2020;Bevacqua et al., 2021).
A key aim of this study is to assess the relationship between extremes relating to flooding and wind damage across multiple timescales, to unify results from previous studies.To achieve this, the Spearman's rank (r  ) correlation is calculated within non-overlapping windows of varied length throughout the chosen datasets.Window length ranges from one day, as in Martius et al. (2016) and Owen et al. (2021b), out to 180 days as in Hillier and Dixon (2020).Spearman's rank is the main statistic deployed as it is a non-parametric metric that is simple, familiar and thus amenable to easy communication to varied stakeholders, and there is no indication that correlation disappears when moving from the body of the distribution into the tail (see Appendix C).

Impact-based metric definitions
To understand the complex relationship between wind and flood damage, a set of GB-aggregates have been developed ranging in a progression from weather to impact.The first metrics used are GBaggregate total daily precipitation (P), maximum daily 10 m wind gusts (v) and total daily river flow (q).The daily data are then aggregated to the timescales used in the correlation analysis.P and q are aggregated through summation, whereas for v the mean of daily maxima is calculated over the period of interest.Population weightings for 2020 (Doxsey-Whitfield et al., 2015), when used, are applied to each grid cell of the meteorological data before aggregation.Population weightings here are used as a proxy for the location of assets at risk that would experience loss or damage from extreme weather.
The metrics used to most directly estimate impact in this study are the Storm Severity Index (SSI) and a new Flood Severity Index (FSI).The SSI was originally developed by Klawa and Ulbrich (2003a) and follows the form used in Pinto et al. (2012) and Priestley et al. (2018): Here v , is the daily maximum wind gust at longitude i and latitude j. pop , is the 2020 population density in a given location, taken from Doxsey-Whitfield et al. (2015).N  and N  show the total number of longitudes and latitudes calculations are performed over respectively.Throughout the paper the SSI and FSI metrics are calculated at daily resolution (t = 1 day) and subsequently aggregated to longer temporal periods for correlation analysis.Therefore, v 98 , always represents the gridded daily 98th percentile from October-March.
v 3 is a well-established proxy for damage (see Hillier and Dixon, 2020 for discussion), and v 98  is the local (i.e., per grid cell) 98th percentile, used as wind damage typically occurs over this threshold (Klawa and Ulbrich, 2003a;Priestley et al., 2018).Use of a daily 98th percentile allows for a comparison between datasets without the need for bias correction, which would be required were a fixed threshold used.It also facilitates an easy comparison with the CHESS-MET historical dataset (see Table 1) where only daily-mean 10 m wind speeds are available.The percentile threshold also accounts for local spatial variations in building construction on the assumption that buildings are generally constructed to be resistant to locally expected gust maxima.
The Flood Severity Index (FSI) is defined as: The form is developed from the SSI with parameters defined in the same way, except here the key hydro-meteorological variable is q, the daily total river flow.We note that FSI is always calculated at a daily timescale, using the 99.5th percentile of daily total river flows.A modified threshold is used for the damage and the cubic behaviour is removed to account for the differences in wind vs. flood damage.Population weightings are included as previously described for SSI to account for the increased amount of damage reported in large population centres.
Defining percentile thresholds for flood damage is difficult, as they are more diverse than those seen for wind damage (e.g., incorporating effects such as surface runoff, snow melt and landslides Williams, 1978;Martius et al., 2016).A complex trade-off emerged when designing the FSI metric between accurately selecting percentile exceedances associated with flood damage, and having enough years of data for statistically robust results (see Section 4.1 for further details).
Fig. 2 shows the relationship between FSI and the WRIID loss data from National Rail.This gives confidence that this metric is able to capture losses on an annual timescale, in the case of the number of floods the correlation is very high (0.74) with reductions seen when considering the costs associated with flooding (0.49).Further analysis (not shown) showed the ability of FSI to capture notable events, such as the February 2020 flooding associated with wind storms Dennis and Ciara.We note that, unsurprisingly, the metric struggles to capture very localised flooding events, such as the 2004 Boscastle flood.Appendix D gives an overview of the number of times recorded floods from the Chronology of British Hydrological Events (Black and Law, 2004) were found in the FSI dataset, giving further confidence that the metric can capture the most extreme events in the observed record.

GB historical correlation analysis: progression from hydro-meteorology to impacts
Fig. 3a shows the Spearman's rank correlation between GB-average hydro-meteorology and impact variables at various timescales throughout October to March,1979-2021 using ERA5 weather variables and GLOFAS river flows.All grid boxes are equally weighted.(So the impact of population from the SSI and FSI equations is removed.)Equal weightings are examined first as population weightings may not be representative for all users (e.g., rail networks, telecommunications, power lines and crops).To calculate the Spearman's rank correlation over timescales greater than 1 day (the resolution of the underlying variables) the following rules are followed: • The maximum daily 10 m wind gust is calculated over the required time period.• Daily river flows and precipitation are summed over the required time period.• The daily SSI and FSI are accumulated over the required time period.
Non-overlapping periods are used for analysis, so for example at the 180 day timescale, a maximum or sum for October-March data is calculated for each of the winters from 1980-2021, giving 41 data points.
The correlation between 10 m wind gusts and total precipitation is around 0.7 at all timescales, broadly agreeing with past studies that looked at various temporal scales from daily to seasonal (Matthews et al., 2014;Hillier and Dixon, 2020;Owen et al., 2021b).A peak correlation of ∼0.8 is seen with a 10 day window.Timescales on Fig. 3 are of key interest to the insurance sector.The first is 5 days.This is typically the period during which claims are attributed to a single windstorm including associated flooding.The second is 21 days.This is typically the period in which damage is accrued for an event classed as a flood.
For wind gusts and total river flow (gold line in Fig. 3a) correlation is lower (∼0.4) at daily timescales, similar to De Luca et al. (2017).After this it rises to a comparable level (∼0.65) at timescales of 40-60 days.This delay is likely associated with the wetting up of catchments over time (see Section 4.2).Therefore, while precipitation has been used as a proxy for flood damage in a number of previous short-term studies on compound wind-flood events (e.g., Martius et al., 2016;Owen et al., 2021b,a;Ridder et al., 2022;Li et al., 2022), these results highlight a potential to exaggerate the correlation between flooding and wind damage at lead times of less than ∼40 days.
The final set of lines on Fig. 3a show the correlation between SSI and FSI, which are indices more directly related to impactful extremes.Here correlation is ∼0.4,albeit with some indication of lower values at daily timescales and higher ones across seasons.This correlation is generally lower than reported in the literature, but differs from most studies in that it emphasises the correlation between the most extreme events across GB.
Including population weightings (Fig. 3b) causes a mild reduction (∼0.1) in correlation for all cases.Correlation between wind gusts and total precipitation drops to ∼0.6 at daily to weekly timescales, as more heavily populated regions have a weaker correlation than those over large orography (see Hillier and Dixon, 2020).Broadly, correlations in recorded losses due to wind and flood damage from National Rail (Fig. 3c) agree with those from GB-average total river flows vs mean maximum wind gusts, providing an additional justification for arguing that the proxies selected propagate into real-world impacts.
The choice of historical data product may influence the results.So, to robustly ascertain the correlations' presence, the analysis was repeated using observed river flow data from CAMELS-GB  and a 1 km reanalysis product CHESS-MET.A similar pattern of reducing correlations with increasingly impact-based metrics was found, Particularly when sub-setting to only use the 134 largest river catchments (i.e., the top 20%; see Appendix A).

GB historical extreme SSI and FSI
With only a 42 year observed period available, the ability to capture events extreme in both FSI and SSI is limited.It is possible however to investigate, separately for each metric, where and when events with the most extreme values of the metric occur.Fig. 4 shows for ERA5 and GLOFAS, the spatial distribution of occurrences of the top 1% and top 0.1% of SSI and FSI events.Here an event is limited to a daily value of each metric (note that no population weightings are applied here) although similar results are seen for 3-day accumulations.
Of the top 1% of SSI events (Fig. 4a) ∼70% of them affect grid cells across central and northern England, tapering to 30% over northern Scotland.The top 0.1% of SSI events support this idea (Fig. 4b).Nearly all (7 out of 8 events) occur over Northern England and Wales, implying a large footprint.Thus, the most extreme SSI events impact a large spatial region, most of GB.Fig. 4c shows that the most extreme SSI events are most likely in January and February, with the majority of the top 1% of events happening in December-February.
Conversely, only 30% of the top 1% of FSI events happen in the same location (Fig. 4d), implying they are much more localised.There is more spatial co-occurrence over the top 0.1% of FSI events, implying they are larger in area and are most common over the East coast   Table 1.events in November than seen for SSI.Understanding the spatial variability of these extremes is important for understanding an insurer's portfolio of risk across multiple perils.
There are only two incidents when an extreme (top 1%) SSI event co-occurs with an extreme FSI event (i.e., a 1 in 20 year return period).These are the 7th February 1990 and 13th December 2000.The event on 7th February 1990 was associated with storm Judith, the second storm in a sequence of seven events, which ran from 25th January to 1st March 1990.Judith followed the notable storm Daria (Klawa and Ulbrich, 2003a).The 13th December 2000 was a time when 17 severe flood warnings were in operation across Southern England and a number of ferries were stranded in the English channel, again associated with stormy conditions (see http://www.met.reading.ac.uk/ brugge/diary2000.html).It is interesting to note neither of these were wind storms associated with substantial losses, although this may be an artifact due to the temporal proximity to storm Daria (Klawa and Ulbrich, 2003a;Roberts et al., 2014).This analysis supports the idea that the largest wind events are not necessarily very wet (Hillier and Dixon, 2020) adding insight for flooding, and for the most extreme compound events across GB.This will be a topic of future investigation.

GB UKCP correlation analysis: historical and future
Fig. 5 shows an equivalent correlation analysis to Fig. 3a but for the UKCP 12 km ensemble.The historical correlations (Fig. 5a) between climate variables are similar to observations, albeit with reduced aleatory uncertainty (i.e., error bars) due to the larger sample size.The correlations between SSI and FSI are lower than those seen in the ERA5 data by ∼0.1, particularly at short timescales.These results suggest that UKCP captures some of the processes responsible for the observed correlation between extreme flood and wind events.
When comparing the historical and future periods in UKCP there is a small but discernible increase in the correlation between total river flow and instantaneous wind gusts (Fig. 5b).Increased correlation is also seen between SSI and FSI at short timescales out to ∼1 month.Unpacking this further shows that in the future period a moderate decrease in days with an SSI occurring (−2% p < 0.05), and a similarly sized increase in days with an FSI (+ 3% p < 0.05).
Table 2 presents results when focusing on the most extreme FSI and SSI days.The return period of exceeding the 95th percentile of SSI and FSI concurrently goes from 0.7 years at present, to 0.4 years in a future climate.In the historical period the co-occurrence of daily SSI and FSI jointly exceeding the 99th percentile has a return period of 13 years, which is reduced to only 4 years in the future period.This is evidence for an increasing probability of co-occurring extremes in the future, even if extreme SSI days may be a little less frequent.

Correlations across Europe
Although GB has been the focus of this paper notable differences are seen when the larger spatial domain of Europe is considered.Spearman's rank correlation between total river flows and 10 m wind gusts is selected to illustrate the results as it is most similar to the National Rail flood-wind correlations in Fig. 3c.Fig. 6 shows results for 37 European countries at daily, weekly, monthly and seasonal timescales.Different countries correlations peak at different timescales, presumably due to the contrasting driving processes.For example, on daily timescales, highest correlations are seen over GB and Ireland, likely due to their relatively isolated river networks.However, on seasonal timescales highest correlation is seen over Spain and Portugal with correlations exceeding 0.9.
Many previous studies used precipitation as a proxy for flooding, which we have shown is not always appropriate, at least for GB on timescales of <2 months.Specifically, Fig. 6 provides a means of advancing on previous interpretations as timescales are indicative of particular driving hydro-meteorological processes.Selected timescales and features of the maps are discussed in Section 4.4.
The key point to note is that the GB results, although useful, are not indicative of the full European response and a bespoke analysis is needed to capture the relationship between flood and wind damage in each country.

Discussion
Spearman's Rank correlation (r  ) has been used to robustly show the correlation between wintertime extremes associated with wind damage and flooding.In GB, r  for historical times is 0.6-0.8,present within various proxies for hazard, reanalysis datasets, hydrological models, and impacts on rail infrastructure.To understand better how this may be used to estimate multi-sector impacts, a Flood Severity Index (FSI) to pair with the established storm Index (SSI) has been proposed and is further discussed in Section 4.1.The relative contributions of varied drivers of the co-occurrence of flooding and extreme winds can be assessed and assimilated into a conceptual model (Section 4.2).Furthermore, an extrapolation can be made into the future (Section 4.3) and the correlation analysis broadened across Europe (Section 4.4).

Flood Severity Index
When developing the FSI, a key decision point was the river flow exceedance threshold used to distinguish flooding.Critical thresholds for flooding depend on the duration of the event, the local precipitation Table 2 Summary statistics for the co-occurrence of extreme SSI and FSI events that exceed the stated percentiles for historic (1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000) and future (2061-2080) climate in UKCP.The first two columns are the number and return period (RP) of events expected if the FSI and SSI were independent.The Ratio is the number of simulated events divided by the number expected if the two variables were independent.All results are significant (p < 0.01, using a binomial distribution.climatology and the impact of flood defences (Tian et al., 2019).Flood protection, in particular, is ubiquitous along European rivers and is typically designed to prevent damage by events with a return period of up to 1 in 100 years, and possibly higher in particular locations (Buijs et al., 2007).However, such low frequency events are rare by definition and an FSI metric constructed only from historical daily river flows with 1% annual probability (i.e., 99.99998th percentile at a daily time scale) would have a few, if any non-zero data points.The short observational record (in our case ∼40 years of ERA5 data) also creates a challenge for estimating very extreme behaviours, and the uncertainty on estimating these high percentile thresholds is very large.Instead, for an effective FSI measure we select events that, whilst rare in the observational record, are sufficiently frequent to give a meaningful sample size and have a correlation that seems to reflect that of more extreme events that actually result in flood damage.This choice is a compromise.We select the 99.5th percentile in each grid box.We assume that larger and more widespread exceedance of this threshold will give a stronger indication of potential flood damage.
As a consequence of these arguments, and testing against historic occurrences (Section 3.2 and Appendix D), we believe that the novel FSI metric is useful.It reflects events with potential to cause impact, is readily computable from climate model data, and can be the basis of statistics (e.g., Table 2) in a form that may be useable by stakeholders across a range of sectors.

Timescales, and a conceptual model of GB co-occurrence
Reported correlations of extremes relating to flooding and wind damage in GB vary with timescale.Proposals to understand these observations in terms of physical processes (Hillier et al., 2015;De Luca et al., 2020;Hillier and Dixon, 2020;Owen et al., 2021b) have yet to be reconciled by integrating them into a conceptual model incorporating the main hydro-meteorological processes over GB.
A conceptual model of these driving processes is shown in Fig. 7. Timescale, progression from meteorological variables to impact, and physical processes are interwoven into an initial and necessarily simplified view that we hope will form the basis for debate.
Previous studies analysing individual storms (Fink et al., 2009;Liberato, 2014;Raveh-Rubin, 2015;Matthews et al., 2018;Otto et al., 2018) and systematic flood-wind correlation (Matthews et al., 2014;Hillier et al., 2015;Martius et al., 2016) were all based on an empirical presumption that extra-tropical cyclones (ETCs) are the dominant driver of wintertime hazard and risk.Such distinct, large scale weather phenomena, sets a key time-scale of ∼1-3 days for co-occurrence.Across datasets, this analysis robustly confirms (Figs. 3 and 5) that there is strong co-occurrence (r  ∼ 0.7) for precipitation and wind gusts in this time frame.So, in line with abundant evidence that some storms can be both wet and windy, a large part, but not all, of this is attributed here to individual atmospheric events (Fig. 7, darkest grey box).The model also highlights that dependency appears to remain strong in the tail of the distribution at this timescale (Table 2,Fig. C.10a,d), something that is not required even if the bulk of events correlate.
There are a number of curiosities, however, to challenge this simple view.Hillier and Dixon (2020), demonstrate that storms impacting north-west GB either tend to be very wet or very windy, not extreme in both.They postulate that this is because storms with the most damaging winds are likely to still be actively interacting with the jet stream, but those with the most extreme rain are probably not.This explains the low daily correlation observed in ERA-interim (Martius et al., 2016), and their results showing 80%-90% of the impact of a link between wind and rain extremes across a season comes from longer timescales than this in GB.In a mirror of this finding, at sub-storm timescales a peak in correlation is found at 1-2 h, descending to a 24-72 h window even as 70% of co-occurrences happen when an ETC is within 1000 km (Owen et al., 2021b).This pattern is confirmed and set in context by this paper's findings, with much lower on the correlations between precipitation and wind gusts at daily than weekly timescales (Fig. 3).
On weekly timescales (i.e., 4-15 days), historical data (Fig. 3) robustly demonstrate that co-occurrence for weather related variables (i.e.P, v 3 ) increases to peak at ∼10 days.This increase on a timescale greater than a storm's residency over GB implies it is typically not just individual storms causing the correlation, strengthening support for this specific idea (Hillier et al., 2015;De Luca et al., 2017).More generally, these observations strongly support the postulate that persistence or 'memory' in the hydro-meteorological system is a critical part of the story (Hillier et al., 2015).The origin of the memory must be atmospheric, hydrological, or both, simply because these are the two sets of processes at work in GB.Three main possibilities have been suggested: • Persistence in synoptic conditions such as jet stream position, the presence of atmospheric rivers (Lavers et al., 2011;Dacre and Pinto, 2020) or recurrent rossby wave packets (Ali et al., 2021) lasting from 3 days up to a few weeks, driving a multi-storm hazard (Priestley et al., 2018).• Persistent large-scale flow patterns, such as the North Atlantic Oscillation (Feser et al., 2015;Hillier et al., 2015;Dacre and Pinto, 2020) • Soil saturation in catchments (Kendon and McCarthy, 2015;Hillier et al., 2015;De Luca et al., 2017;Berghuijs et al., 2019) It is well-established that ETCs can cluster, with several arriving across 1-2 weeks (Mailier et al., 2006;Vitolo et al., 2009), with a recent example over GB experienced in February 2022 (i.e., Dudley -wind North GB, Eunice -wind in South GB, Franklin -flooding in north GB).A key observation is that peak flows tend to occur 0-13 days after very severe gales, interpreted as indicating that flooding occurs in the last of a few storms due to soil becoming saturated (De Luca et al., 2017).Use of hydrological modelling in this paper that includes soil wetness, water absorption, run-off and river flow (i.e., GLOFAS, G2G) greatly strengthens this hypothesis as it shows correlation rising from 0.4 (t = 1 day) to 0.6 by monthly timescales (∼0-60 days).Thus, catchment saturation is a key part of the model, although, we note that there will be variability between catchments.
On longer timescales, up to seasonal (180 days), compound risk appears to be elevated by persistent underlying environmental conditions (Hillier et al., 2015;De Luca et al., 2017;Hillier and Dixon, 2020), but understanding of processes gets significantly more speculative.In terms of atmospheric climate modes, positive North Atlantic Oscillation (NAO) has been proposed as it is a well-established as a condition favouring storminess in GB (Hillier and Dixon, 2020) although whether the cause is the long term average itself or a tendency to support more frequent and persistent episodes of high NAO conditions (i.e., >1.0) is not clear at present.It has also been postulated that persistence might be induced by teleconnections to the western Pacific warm pool (Huntingford et al., 2014;Hillier et al., 2015).Empirically, some role for long-term soil wetness is suggested since frequent very severe gales and the largest multi-basin floods coincide with enduringly wet conditions as recorded in standardised precipitation indices (De Luca et al., 2017).
A challenge remains to work out the details.Outstanding questions exist about all the time-scales upon which processes driving co-occurrence act, including: • What causes individual storms lasting 1-2 days to produce flooding and extreme wind, as opposed to both or neither?• What large-scale drivers lead to storm clusters capable of driving co-occurrence over sub-seasonal timescales?• How exactly do catchment properties induce memory up to monthly timescales?• Are the processes that govern the correlation at (3-6 month) timescales the same as those present at sub-seasonal timescales?

Future correlation
In agreement with past studies focused on historical precipitation and wind gusts (Martius et al., 2016;Owen et al., 2021b), there is broad similarity between correlation patterns for UKCP for 1981-2000 andhistoric observations (compare Figs. 3 and5).Broadly, correlation in the future UKCP (2061-2080) at first appears similar, yet there is a development of enhanced co-occurrence for the more extreme short-timescale joint events ( Table 2, Fig. 5b).
If true, an increase in jointly occurring very severe extremes of roughly threefold by 2061-2080 (p < 0.05), with commensurate decrease in return period from 13 to 4 years is dramatic.We note that UKCP regional simulations are based on one possible global climate model projection, for which multiple ensemble members are run under one high emissions scenario.Other global climate model projections also need to be investigated to determine how robust these initial results are.
As to the origin of the increased co-occurrence, we postulate that flooding driven by extreme precipitation is the limiting factor for a compound event.This originates in the temporal observation that large multi-basin floods (De Luca et al., 2017) tend to occur 0-13 days after a storm.This is consistent with the role of catchment saturation identified in this study and in Ledingham et al. (2019) for annual maximum rainfall vs. flood runoff.It is commonly a pre-condition for flooding, which extreme winds do not have, making flooding the limiting factor for co-occurrence.A similar argument applies spatially, based on this study's observation that the largest FSI events (top 0.1%) are more localised than SSI ones (Fig. 4), and are thus limiting.In addition the UKCP results show that with respect to the historical period  there is moderate decrease in SSI days in 2061-2080 (−2%) and a similarly sized increase in days with an FSI (+ 3%), and it is easier to imagine the quantity that is increasing driving an increased level of co-occurrence.A similar result is seen by Yaddanapudi et al. (2022) in coastal regions when analysing wind and flood responses to climate change in CMIP6 simulations.More widely, support for this postulate comes from studies demonstrating a warmer and therefore wetter atmosphere (Lowe et al., 2018) and a likely increase in extreme precipitation associated with this (Chan et al., 2014;Kendon et al., 2020;Fowler et al., 2021) and increased high river flows (Kay et al., 2021;Griffin et al., 2022b).Future work could address the role of changing soil moisture in the occurrence of these compound events (incorporating results from Kay et al., 2022;Griffin et al., 2022b).Opportunities to link these results with present and futures changes in the spatial structure of the flood damage (e.g., taking account of existing flood defences and the local exposure of people and property) to provide more direct risk-based severity insights across multiple hazards also exist.All these aspects continue to evolve and are likely to be of most direct relevance to stakeholders.

Extending across Europe
Previous studies have shown maps of flood-wind relationships across Europe at daily (Martius et al., 2016;Owen et al., 2021b) or seasonal (Hillier and Dixon, 2020) timescale.Fig. 6 presents a more complete picture.The patterns in Fig. 6 allow an initial interpretation to be offered.On daily timescales, highest wind-river flow correlations are seen over GB and Ireland, likely due to their relatively isolated and therefore rapidly responding river networks.
At weekly and monthly timescales the countries in central and northern Europe which are commonly impacted by extra-tropical cyclones see highest correlations, with lower correlations over southern and eastern Europe.Indeed, high monthly correlations are seen in countries which experience significant storm clustering (Roberts et al., 2014;Priestley et al., 2018).The fact that Western Europe experiences stronger correlations on all timescales supports the analysis of Berghuijs et al. (2019) which shows the dominant driver of flooding over Western Europe being soil moisture processes, rather than extreme precipitation or snowmelt.
On seasonal timescales, highest correlation is seen over Spain and Portugal, which suggests the drivers causing extreme river flows are very similar to those causing extreme winds (see also Hénin et al., 2021).Generally low correlations are seen over Sweden and Finland at all timescales.Part of this is likely due to these countries being in the lee of mountains sheltered from passing cyclones in a correlation shadow (Hillier and Dixon, 2020).However, temperature and snow melt are known to strongly influence river flows here (Arheimer and Lindström, 2015;Berghuijs et al., 2019) which will reduce correlation as they are not directly related to storms and their extreme winds, and simple climate phenomena like the NAO may not be appropriate for describing processes in these regions (Kingston et al., 2009).Correlations are also lower than GB values for countries which have much larger river catchment areas (e.g., Germany).The explanation might be physical, or to do with our methods focus on country-level data.An approach based on event footprints may be needed in future work to capture behaviour in neighbouring countries.
It is important to note that different stakeholders are sensitive to correlations in different ways on a variety of time-frames (e.g., an event emergency response in <24 h, or event duration of up to 5 days defined in a reinsurance contract, or planning decisions relating to annual budgets or limits in a regulator's guidance).

Conclusions
Rank correlation has been consistently calculated for a spectrum of time-windows and variety of data types, to better understand how a variety of hydro-meteorological processes contribute to the co-occurrence Spearman's rank correlation between various metrics, at various timescales from 1 to 180 days and aggregated across GB with precipitation and wind speeds taken from CHESS-MET and river flows taken from CAMELS-GB.Equal weighting is given to all grid boxes (as in Fig. 3).Shaded areas show two standard deviations of 2000 bootstrapped samples (95% confidence) of the correlations.Details of datasets used are given in Table 1.

Appendix B. WRIID data quality
In other loss datasets, mis-categorisation of some losses is a recognised issue.For instance, in the Association of British Insurers (ABI) General Insurance Statistics, some pluvial inundation (surface water flooding) is known by practitioners to be sometimes reported as wind damage because it is associated with stormy weather; see Hillier et al. (2015) for further details.This reporting artefact makes it difficult tov reliably establish a correlation between flooding and extreme wind.Such an artefact does not appear to be present in the WRIID dataset (see Fig. B.9).In winter significant correlation is seen between flood and wind damage (r  ∼ 0.5, p < 0.05), but in summer there is no demonstrable relationship (Fig. B.9).It is difficult to imagine a reporting artefact which might exist in winter and yet be avoided in summer.So, this gives confidence that the winter-time relationships shown in Fig. 3c are real and not explored further here.

Appendix C. Suitability of Spearman's Rank correlation
By using ranks, Spearman's Rank (r  ) minimises the influence of the heavy-tailed marginal distributions typical of extremes, and also reduces sensitivity to the exact form of the metrics selected (e.g., whether wind speeds are cubed or not).Namely, it allows for comparison of results in the presence of non-linear relationships such as between meteorological variables and damage metrics.Whilst, r  is simple, familiar and thus amenable for easy communication to varied stakeholders, two variables  1 and  2 might be dependent and yet uncorrelated in the extremes (i.e., asymptotically independent, e.g., Heffernan and Tawn, 2004).Introduced by Coles et al. (1999), extremal correlation () and residual tail dependence ( χ) are used to understand asymptotic behaviour; see Vignotto et al. (2021) for a fuller mathematical description. presents the probability of one variable being extreme given that the other one is extreme, whereas χ presents the strength of the relationship in the tails of the distribution.The point of presenting both of these statistics is that two variables can be dependent at the same time as being asymptotically independent ( χ < 1).It is common to present  and χ as estimates for different percentile thresholds, and then visually inspect their behaviour as the thresholds become more extreme.
For meteorological variables, precipitation and wind gusts in ERA5, χ is not converging towards 1, so the variables are asymptotically independent, yet neither is χ obvious or rapidly nearing zero, so dependency remains present a notable depth into the distributions tail.This result holds for timescales from daily to monthly ( As there is no indication that correlation disappears moving from the body into the tail of the data, r  is retained as the main statistic deployed.These statistics have been computed using R's taildep() function from the extRemes package (Gilleland and Katz, 2016).Aggregated at Bloomfield H.C. et al.

Fig. 2 .
Fig. 2. Relationship between annual-aggregated wintertime FSI and GB National Rail flood data for years 2006-2018.(a) Number of floods.(b) Cost of flooding.

Fig. 3 .
Fig. 3. Spearman's rank correlation between various metrics, at timescales from 1 to 180 days and aggregated across GB.ERA5 reanalysis and GLOFAS (a) with equal weighting given to all grid boxes and (b) with population weightings applied.(c) Correlation between number of events occurring due to extreme wind and flooding on the GB rail network (green) and correlation between costs due to extreme wind and flooding (grey).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .
Fig. 5. GB-aggregate Spearman's rank correlation between various metrics (climate progressing to impact), at various timescales from 1 to 180 days from the UKCP regional simulations (a) for the present climate period 1981-2000 where dashed lines show ERA5 correlations from Fig. 3.We note SSI and FSI are population weighted.(b) for the future climate period 2061-2080.Dotted lines show the historical correlations from panel (a) for ease of comparison.Solid lines in both panels show the ensemble-mean correlation, shaded areas show two standard deviations of 2000 bootstrapped samples of the Spearman's rank correlation.Further details of datasets used are given inTable 1.

Fig. 7 .
Fig. 7. Conceptual model of extremes related to UK wintertime flooding and wind damage.Key dimensions considered are time-scale (increasing left to right, purple text), proximity of the metric used to impact (green text), and the interplay of atmospheric and hydrological processes (graphics, black text).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig
Fig. A.8.Spearman's rank correlation between various metrics, at various timescales from 1 to 180 days and aggregated across GB with precipitation and wind speeds taken from CHESS-MET and river flows taken from CAMELS-GB.Equal weighting is given to all grid boxes (as in Fig.3).Shaded areas show two standard deviations of 2000 bootstrapped samples (95% confidence) of the correlations.Details of datasets used are given in Table1.

Fig. B. 9 .
Fig. B.9. Spearman's rank correlation between Rail losses due to wind and flood for (a) Number of events (b) Costs incurred.Computation on monthly (dots) and seasonal (∼90-day, dashes) timescales, with black indicating p < 0.05 despite only data from 2006-2018.
Fig. C.10a-c).Similar is true for the relationship between distributions of ERA5 wind gusts and GLOFAS river flows (Fig. C.10d-f).This pattern continues across the spectrum from weather to impact, including for monthly Network Rail losses (not shown).

Fig
Fig. D.11.Verification of GLOFAS FSI metric when compared to the flood chronology from Black and Law (2004).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1
Details of hydro-meteorological datasets used within this study. ).