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. Natural hazards, such as European windstorms, have widespreadeffects that result in insured losses at multiple locations throughout acontinent. Multivariate extreme-value statistical models for suchenvironmental phenomena must therefore accommodate very high dimensionalspatial data, as well as correctly representing dependence in the extremes toensure accurate estimation of these losses. Ideally one would employ aflexible model, able to characterise all forms of extremal dependence.However, such models are restricted to a few dozen dimensions, hence an apriori diagnostic approach must be used to identify the dominant form ofextremal dependence. Here, we present various approaches for exploring the dominant extremaldependence class in very high dimensional spatial hazard fields: taildependency measures, copula fits, and conceptual loss distributions. Theseapproaches are illustrated by application to a data set of high-dimensionalhistorical European windstorm footprints (6103 spatial maps of 3-day maximumgust speeds at 14 872 locations). We find there is little evidence ofasymptotic extremal dependency in windstorm footprints. Furthermore,empirical extremal properties and conceptual losses are shown to be wellreproduced using Gaussian copulas but not by extremally dependent models suchas Gumbel copulas. It is conjectured that the lack of asymptotic dependenceis a generic property of turbulent flows. These results open up thepossibility of using geostatistical Gaussian process models for fastsimulation of windstorm hazard fields.

Quantification of extremal dependence in spatial natural hazard footprints: independence of windstorm gust speeds and its impact on aggregate losses