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

Abstract

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.

From Atmospheric Dynamics to Insurance Losses: An Interdisciplinary Workshop on European Storms

“…Using statistical modeling, David Stephenson (University of Exeter) discussed various approaches to quantify the dominant extremal dependence class for realistic windstorm footprints and found little evidence of asymptotic extremal dependency. When fitting the data with statistical distributions, the Gaussian copula appears to perform well, which allows the statistical simulation of windstorm footprints (Dawkins and Stephenson 2018). This approach opens the possibility of using geostatistical models for fast simulation of windstorm hazard maps, which can complement dynamical modeling approaches.…”

The Advanced Meteorology Explorer: a novel stochastic, gridded daily rainfall generator

“…Meta-elliptical copulas are able to capture extremal dependence between variables; however, they require the specification of one asymptotic dependence structure for all pairs of 15/61 variables. There is a growing literature in the area of flexible pairwise dependence models for extremal dependence (Wadsworth and Tawn, 2012;Huser and Wadsworth, 2019), though these models are non-trivial to apply and computationally challenging to fit to higher dimensional data (Dawkins and Stephenson, 2018). Their application is therefore found to be beyond the scope of this study.…”

“…The Gaussian copula assumes asymptotic independence between random variables, meaning that the largest values of the variables are represented as rarely occurring together (Coles et al, 1999). The alternative, asymptotic dependence, may also occur in environmental data (Dawkins and Stephenson, 2018), meaning that the largest values of the variables tend to occur at the same time. For additional flexibility in the AME framework, different forms of dependence structure (asymptotic independence and dependence) between pairs of sites is captured.…”

About the return period of a catastrophe

“…In the copula-based research by Bonazi et al (2012) and Dawkins and Stephenson (2018), the local extremes of European winter storms are sampled by a pre-defined list of significant events. Such sampling is not foreseen in extreme value statistics (Coles, 2010).…”