Flood Events : Extreme Value Problems and Efficient Estimation of Loss

Barlow, Anna and Sherlock, Chris and Tawn, Jonathan (2021) Flood Events : Extreme Value Problems and Efficient Estimation of Loss. PhD thesis, Lancaster University.

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Abstract

Widespread flood events have heavy consequences on society and the environment. Gaining insight into the occurrence and impact of these rare flood events is thus of interest to many parties such as governments, environmental organisations and insurance companies. To assess flood risk, past events are studied and used to t statistical models from which plausible flood events are simulated over large areas and large periods of time. These simulated extreme events then drive other models, such as models of loss for insurance purposes, to provide insight into the possible impact of future flood events. This thesis addresses problems in the analysis of extreme river flows which cause flooding, and the inefficiency of simulation of yearly loss due to flooding. Firstly, many extreme value analyses are conducted in reaction to the occurrence of a large flooding event. This timing of the analysis introduces bias and poor coverage probabilities into the associated risk assessments subsequently leading to over-designed flood protection schemes. These problems are explored through studying stochastic stopping criteria and new likelihood-based inferences are proposed that mitigate against these difficulties. Simulated extreme events are used along with geographical knowledge and property information to simulate losses at each property for each flood event over many years. These simulations are then aggregated to obtain total yearly losses and to estimate return levels of yearly loss. The large number of simulations needed makes this process computationally expensive. A new method is proposed, using novel concentration inequalities, which reduces the number of years that need to be simulated. Finally, modelling extreme flood events is complicated due to temporal dependence and the spatial dependencies of river flows between multiple locations with the presence of time lags between locations. The theory of multivariate temporally dependent extremes is explored, with focus on measures of dependence, and areas of further research are highlighted.