Simulating flood event sets using extremal principal components

Abstract: Hazard event sets, a collection of synthetic extreme events over a given period, are important for catastrophe modelling. This paper addresses the issue of generating event sets of extreme river flow for northern England and southern Scotland, a region which has been particularly affected by severe flooding over the past 20 years. We start by analysing historical extreme river flow across 45 gauges, located within the study region, using methods from extreme value analysis, including the concept of extremal principal components. Our analysis reveals interesting connections between the extremal dependence structure and the region's topography/climate. We then introduce a framework which is based on modelling the distribution of the extremal principal components in order to generate synthetic events of extreme river flow. The generative framework is dimension-reducing in that it distinctly handles the principal components based on their contribution to describing the nature of extreme river flow across the study region. We also detail a data-driven approach to select the optimal dimension. Synthetic flood events are subsequently generated efficiently by sampling from the fitted distribution. Our approach for generating hazard event sets can be easily implemented by practitioners and our results indicate good agreement between the observed and simulated extreme river flow dynamics. For the considered application, we also find that our approach outperforms existing statistical approaches for generating hazard event sets.