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, 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 results indicate good agreement between the observed and simulated extreme river flow dynamics and, therefore, illustrate the usefulness of our approach to practitioners. For the considered application, we also find that our approach outperforms existing statistical approaches for generating hazard event sets.
Parts of this research were conducted while Christian Rohrbeck was beneficiary of an AXA Research Fund postdoctoral fellowship grant. Daniel Cooley’s work was partially supported by the U.S. National Science Foundation grant DMS-1811657.
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper. The river flow data were obtained through the National River Flow Archive.
"Simulating flood event sets using extremal principal components." Ann. Appl. Stat. 17 (2) 1333 - 1352, June 2023. https://doi.org/10.1214/22-AOAS1672