Modelling spatial extreme events with environmental applications

Jonathan Tawn,Rob Shooter,Ross Towe,Rob Lamb

doi:10.1016/j.spasta.2018.04.007

Abstract

Spatial extreme value analysis has been an area of rapid growth in the last decade. The focus has been on modelling the spatial componentwise maxima by max-stable processes. Here, we will explain the limitations of these modelling approaches and show how spatial models can be developed that overcome these deficiencies by exploiting the flexible conditional multivariate extremes models of Heffernan and Tawn (2004). We illustrate the benefits of these new spatial models through applications to North Sea wave analysis and to widespread UK river flood risk analysis.

Highlights

In many environmental applications data are collected from a number of spatial locations, for example numerous locations across an ocean basin or locations across a river network
The statistical analysis includes extensions to the Heffernan and Tawn methodology as stated in Section 3.1 such as the handling of missing values as well as efficient simulation techniques for high dimensional data sets and methods to model the rate of the number of extreme events per year (Keef et al, 2013)
In order to assess the validity of the statistical models, comparisons such as those shown in Figure 8 were made

Summary

Introduction

In many environmental applications data are collected from a number of spatial locations, for example numerous locations across an ocean basin or locations across a river network. Interest has been in the extremal behaviour at individual sites. Our interest lies in developing a framework in which it is possible to estimate probabilities of joint events over space. For wave heights we may want to know the probability of no offshore structure being damaged in a storm, and for river levels the probability that the total damages from a flood exceed £1 billion. Probabilities of the occurrence of extreme spatial events are of particular interest to the reinsurance industry for deriving aggregate financial loss distributions, and to governments in terms of risk assessment and emergency planning.

Objectives

Methods

Results