Extratropical cyclones are the most damaging natural hazard to affect western Europe. Serial clustering occurs when many intense cyclones affect one specific geographic region in a short period of time which can potentially lead to very large seasonal losses. Previous studies have shown that intense cyclones may be more likely to cluster than less intense cyclones. We revisit this topic using a high-resolution climate model with the aim to determine how important clustering is for windstorm-related losses.

The role of windstorm clustering is investigated using a quantifiable metric (storm severity index, SSI) that is based on near-surface meteorological variables (10 m wind speed) and is a good proxy for losses. The SSI is used to convert a wind footprint into losses for individual windstorms or seasons. 918 years of a present-day ensemble of coupled climate model simulations from the High-Resolution Global Environment Model (HiGEM) are compared to ERA-Interim reanalysis. HiGEM is able to successfully reproduce the wintertime North Atlantic/European circulation, and represent the large-scale circulation associated with the serial clustering of European windstorms. We use two measures to identify any changes in the contribution of clustering to the seasonal windstorm loss as a function of return period.

Above a return period of 3 years, the accumulated seasonal loss from HiGEM is up to 20 % larger than the accumulated seasonal loss from a set of random resamples of the HiGEM data. Seasonal losses are increased by 10 %–20 % relative to randomized seasonal losses at a return period of 200 years. The contribution of the single largest event in a season to the accumulated seasonal loss does not change with return period, generally ranging between 25 % and 50 %.

Given the realistic dynamical representation of cyclone clustering in HiGEM, and comparable statistics to ERA-Interim, we conclude that our estimation of clustering and its dependence on the return period will be useful for informing the development of risk models for European windstorms, particularly for longer return periods.

Extratropical cyclones are the dominant weather hazard that affects western
Europe. On average extratropical cyclones cause over USD 2 billion of losses to the
insurance industry per year in Europe

There have been several attempts to quantify losses associated with severe
extratropical cyclones in reanalysis data and with data from general
circulation models (GCMs)

North Atlantic winter cyclones have a tendency to occur in groups that affect
specific geographical regions within a given period of time. This process is
known as serial clustering

Despite previous studies assessing the return periods of European windstorm
losses

The main science questions that will be addressed in this study are as follows:

Is HiGEM able to capture the upper tropospheric large-scale dynamics associated with European cyclone clustering?

Does the SSI calculated using HiGEM output provide comparable results for individual windstorms and seasonal accumulations to those obtained from the ERA-Interim reanalysis?

Does windstorm clustering contribute more to losses in Europe for winter seasons with large accumulated losses?

The paper continues as follows. The data and methods used are described in Sect. 2. The results follow in Sect. 3, which starts with an evaluation of HiGEM, then an analysis of the SSI as a suitable metric for comparing windstorms in HiGEM and ERA-Interim. Finally the importance of clustering for seasons with large accumulated European windstorm losses is addressed. The conclusions are presented in Sect. 4.

The main data source for this work is simulations performed using HiGEM

For comparison, the reanalysis from the European Centre for Medium Range
Weather Forecasts (ECMWF) ERA-Interim dataset

To identify extratropical cyclones in both datasets we use the tracking
algorithm of

We follow the method of

The metric developed by

Losses due to wind occur on approximately 2 % of all days

Buildings are generally constructed in such a way that they can sustain gusts that are expected
locally. Hence, the 98th percentile is the local value (

Losses do not occur if the wind speed does not exceed the local threshold (

The value of

Winds exceeding the 98th percentile that do not occur over land are ignored as they will not contribute to losses (

Insured losses from windstorms are dependent on the location of insured property, which are proportional
to the local population density. The SSI is scaled by the 2015 global population density at the corresponding grid box (pop

The SSI is calculated at every land grid point and is used in two different forms for the main analysis in this study. Following insurance industry naming conventions, the first approach will be to calculate the maximum loss event in a year (herein referred to as the occurrence exceedance probability, OEP), and the second will calculate the total loss for an entire DJF season (herein referred to as the annual exceedance probability, AEP).

The OEP is calculated as the spatial sum of the maximum SSI within a 72 h
period (i.e. the maximum SSI calculated from the 6-hourly wind speeds in a
72 h period, per grid point). The 72 h time window is consistent with that
used by reinsurance companies for defining a particular event

The AEP is calculated in the same way as the OEP, except that instead of using the single 72 h maximum wind footprint, it sums all the individual 72 h maximum wind speed footprints in the 90-day winter period. In the calculation of the AEP all events are retained. The sensitivity to retaining all events is tested later.

There are several ways to assess the clustering of windstorms, which give different information and perspectives. Described below are the three methods which will be used in this study.

The first measure is the dispersion statistic (

Track density

Another measure for assessing the impact of the clustering of cyclones is to examine the ratio of the AEP to an AEP that is calculated when all the storms have been randomized in time (this will herein be referred to as AEP_random). The randomization reorders all of the 72 h SSI periods in the 918 DJF periods from HiGEM. Artificial DJF seasons are constructed by randomly sampling 30 72 h periods into a new order to remove any dynamical clustering between events that may be present in the HiGEM climate model. The AEP / AEP_random measure of clustering is particularly important for reinsurers as it provides information on how having dynamically consistent years (e.g. from the HiGEM model) provides different AEPs relative to a set of random (stochastic) model year.

A value of AEP / AEP_random larger than 1 suggests that the dynamically consistent clustering and the severity of cyclones in HiGEM result in a larger AEP, relative to that expected from a randomly sampled set of events. Similarly, a value less than 1 suggests that the consistent grouping of cyclones gives a lower AEP than would be expected at that particular return period.

The final measure used to assess clustering is the ratio of the OEP to the AEP. If the total loss in a season were characterized by just one single 72 h cyclone event then, by definition, the AEP and OEP would be identical. However, if the OEP were much smaller than the AEP then this would suggest there are many cyclone events contributing to the AEP. The OEP / AEP ratio therefore quantifies the dominance of a single loss event in a season. The OEP / AEP ratio is calculated using the OEP and AEP in the same season.

It should be noted that all the above measures provide different interpretations of the occurrence of clustering. The dispersion statistic is a measure of how grouped storms are in time relative to a Poisson distribution. This can be physically interpreted as measuring the seriality of clustering. The ratio of AEP to AEP_random provides information on the dynamically consistent grouping of cyclones affects the accumulated seasonal losses (e.g. that produced from a climate model) compared to a completely random series of cyclones. The OEP to AEP ratio gives information on the dominance of the largest loss event in the overall seasonal losses. One of the additional objectives of this study is to ascertain how consistent the different measures of clustering are for seasonal losses.

Dynamical composites of clustered days at

A majority of the results in this paper will be expressed in terms of return period. The return period provides a period of time in which an event of a certain magnitude is expected to occur. Return periods have been allocated in a way such that the maximum AEP year is assigned a return period of the length of the dataset divided by its rank (for the maximum event the rank is 1). Therefore the maximum AEP year from ERA-Interim has a return period of 36 years, and the highest AEP year in HiGEM has a return period of 918 years, as they both occur once in their total time period respectively. The second largest events then have return periods of 18 and 459 years for ERA-Interim and HiGEM respectively. This continues until the lowest ranked year, which has a return period of 1 year. For a majority of our analysis we rank the OEP in the order of descending AEP. This ensures we maintain a temporal connection between the OEP and AEP at all return periods and means that the largest OEP may not necessarily occur in the highest AEP year. Some analysis is performed on independently ordered AEP and OEP, which removes the connection between maximum events and the years in which they occur.

The return periods of the most extreme events are estimated using a
generalized Pareto distribution (GPD) that is fitted to the AEP and OEP data
above a specified threshold (“peak over threshold” method). The GPD is fit
using the maximum likelihood method, following

HiGEM has a good representation of the large-scale tropospheric circulation

98th percentile of 10 m wind speed (ms

The dispersion of cyclones in the North Atlantic for ERA-Interim and HiGEM is
shown in Fig.

It was shown in

All of the composites of clustered days (Fig.

HiGEM has been found to have a good representation of North Atlantic extratropical cyclones and cyclone clustering, as well as the large-scale circulation driving this behaviour. This demonstrates the suitability of using HiGEM to investigate clustered windstorm-related losses.

The SSI is widely used for quantifying losses related to windstorms. We now
compare the SSI for both HiGEM and ERA-Interim. The characteristic of the SSI
is that it is calculated above a set threshold, the 98th percentile of the
local distribution of 10 m wind speed (

DJF average of 6-hourly SSI for ERA-Interim

To address the lower European wind speeds, a simple bias correction is applied
to the 10 m wind speeds in HiGEM. This is done by correcting the 10 m
wind speeds by the spatially averaged offset in the

Spatial maps of the DJF average SSI are shown in Fig.

Figure

In Fig.

Also shown in Fig.

Return periods of AEP for ERA-Interim (red line). The light grey lines are the 10 000 bootstrap samples of the HiGEM_bc AEP. The black dashed lines are the associated 95 % confidence intervals of the HiGEM_bc AEP and the black solid line is the median.

Return periods of the AEP (red points) and OEP (blue points) for HiGEM_bc. The OEP and AEP are sorted according to AEP magnitude. The solid red line is the GPD fit applied to the AEP using a 90th percentile threshold. The dashed red lines are the associated 95 % confidence intervals. The black line represents the mean of 10 000 non-replacement random samples of the HiGEM_bc AEP data. The surrounding shaded grey region represents the 95 % confidence interval of these 10 000 samples. The GPD fit and confidence intervals are only plotted above the GPD threshold.

The ratio of the model AEP to the 10 000 random samples of the AEP for increasing return period. Black dots are the raw data points. The dark grey region below the 10-year return period indicates the 95 % confidence interval of the raw AEP / AEP_random. Above the 10-year return period the dark grey shaded region bounded by the black dashed lines is the 95 % confidence interval using the fitted AEP (red line in Fig. 6) in the calculation and the black solid line is the median of the spread. Confidence intervals from the GPD fits are only shown above the GPD threshold.

Figure

To test the sensitivity of Figs.

We have performed a non-replacement randomization of the 72 h periods that
make up the HiGEM_bc AEP with 10 000 samples, and this randomization ensures
that each random sample contains the exact same data as the original
918 years. This randomization allows us to assess how the intensity of losses
and the associated number of cyclones acts to influence the AEP in HiGEM_bc,
compared to a time series in which windstorms are occurring randomly. The mean of
these random samples is shown by the black line in Fig.

The ratio of AEP to AEP_random is shown in Figure

The difference can be interpreted physically by considering two recent DJF
periods in the UK. Firstly, the winter of 2009/2010 was characterized by a
strongly negative North Atlantic Oscillation and an absence of
extratropical cyclones influencing the UK for this period

In Fig.

A different view of clustering can be gained by examining how a single event
can affect the accumulated seasonal losses through the ratio of the OEP to
AEP. A high value implies that the single largest event is causing most of
the losses in a season, and a lower value implies a contribution to the
overall seasonal losses from many cyclones in that particular season. The
results from ERA-Interim and HiGEM are compared in Fig.

Figure

As with the ratio of AEP / AEP_random in Fig.

The aim of this study is to investigate the importance of serial clustering
on seasonal timescales for high return period loss events caused by European
windstorms. This is achieved using a GCM that is able to adequately capture
the large-scale dynamics controlling cyclone clustering. This work has been
performed using HiGEM, a high-resolution fully coupled climate model. The
performance of HiGEM has been evaluated using the ERA-Interim reanalysis.
Losses from European windstorms have been estimated using a version of the
SSI (storm severity index) applied to European land grid points. The main
conclusions of this work are as follows:

HiGEM can successfully reproduce the large-scale dynamics associated with clustering of European cyclones that are seen in ERA-Interim. The biases in DJF storm track activity in HiGEM are small, with the tilt and intensity of the North Atlantic storm track being well represented. The pattern of dispersion in the North Atlantic is also consistent with ERA-Interim, with cyclones clustering more near the exit of the storm track, and an underdispersive and regular nature in the entrance region. The large-scale circulation associated with clustering is also similar in HiGEM and ERA-Interim. Both show how clustering in different locations of western Europe is associated with a strong and extended upper level jet that is flanked on one or both sides by anomalous RWB. Hence, extratropical cyclone clustering in HiGEM is occurring for the right dynamical reasons.

SSI is used as a proxy to assess losses occurring from intense European windstorms. The SSI is applied to land points only and for an area than encompasses all of western and most of central Europe. It is found that HiGEM systematically underestimates 10 m wind speed over European land regions. A simple bias correction (uniform increase by 18.75 %) leads to a structure of the DJF SSI average that is consistent between the bias-corrected HiGEM (HiGEM_bc) and ERA-Interim. The return periods of AEP and OEP are found to be consistent between HiGEM_bc and ERA-Interim for return periods less that 36 years. Therefore, HiGEM_bc appears to be a suitable model for assessing long return period losses from European windstorms.

Compared to a random season of cyclones, the AEP from HiGEM_bc is larger at return periods greater than 3 years. The dynamically consistent representation of cyclone severity and clustering in HiGEM_bc results in values of AEP that are approximately 10 %–20 % larger than AEP_random at a return period of 200 years. Therefore, not having a dynamically consistent representation of cyclone clustering appears to result in an underestimation of losses above a 3-year return period.

The relative portion of the AEP that comes from the OEP is very variable across all return periods and there is no strong relationship between the two values. The contribution of the OEP to the AEP is found to be approximately 25 %–50 % in HiGEM_bc. Therefore, the relative influence of the largest loss event in a season does not change with return period.

In this study we have shown that having a dynamically consistent
representation of cyclone clustering and storm intensity causes the AEP to be
approximately 10 %–20 % higher (for return periods greater than 3 years) than that expected from a random selection of cyclones. Despite
the near constant values of AEP / AEP_random above a 3-year return period, the
absolute magnitude of the AEP relative to AEP_random is increasing with
return period. This absolute increase suggests an increase in cyclone
severity for higher return period loss seasons for cyclones of all
magnitudes. This result has implications for loss modelling in the insurance
industry and demonstrates that if a model does not adequately represent the
clustering behaviour of cyclones then losses will be underestimated for
larger return periods. Furthermore, as the wintertime average loss from
windstorms in Europe is over USD 2 billion

It has been shown in several studies

The ERA-Interim reanalysis data are available publicly from
the ECMWF upon request (

Matthew D. K. Priestley is funded by NERC via the SCENARIO DTP (NE/L002566/1)
and co-sponsored by Aon Benfield. Joaquim G. Pinto thanks the AXA Research
Fund for support. Len C. Shaffrey is funded by the ERA4CS WINDSURFER project
and the National Centre for Atmospheric Science. We thank ECMWF for their
ERA-Interim Reanalysis data (