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

Abstract

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