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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 18, issue 11 | Copyright
Nat. Hazards Earth Syst. Sci., 18, 2933-2949, 2018
https://doi.org/10.5194/nhess-18-2933-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 08 Nov 2018

Research article | 08 Nov 2018

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

Laura C. Dawkins and David B. Stephenson Laura C. Dawkins and David B. Stephenson
  • College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

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 14872 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.

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Short summary
Natural hazard losses are sensitive to the dependency between extreme values of the hazard variable at different spatial locations. It is therefore important to correctly identify and quantify dependency to accurately model the hazard and its resulting losses. Through application to a large data set of windstorm hazard footprints, this study demonstrates how extreme-value methods can be used to explore extremal dependency and hazard losses in very high dimensional natural hazard data sets.
Natural hazard losses are sensitive to the dependency between extreme values of the hazard...
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