Statistical models for extreme weather events

Western Europe is typically prone to extreme weather events during the winter months, which typically take the form of windstorms or flooding. The storm Desmond brought strong winds and heavy rain to Ireland, northern England and Scotland in December 2015, resulting in an estimated $500 million worth of damage and extensive flooding, particularly in the region of Cumbria. Accurate modelling of such extreme weather events is necessary to ensure that the societal and infrastructural risk associated with these phenomena is minimised. In statistical modelling, extreme value analysis is typically used to model the rate and size of extreme weather events. Typically, practitioners can use the outputs of such an analysis to design flood defences to a standard such that there is only a small probability that defences are breached in a given year. These models can be applied at individual sites or adapted to address questions related to the spatial extent of an event, which is important for policy makers eager to reduce the economic and societal impacts associated with extreme weather. One aim of this thesis is to improve inference with regarding to existing extreme value methodology. First, we propose a reparameterisation of the likelihood corresponding to the Poisson process model for excesses above a high threshold, which improves mixing in a Bayesian framework and ensures more rapid convergence of the parameter chains in a Markov Chain Monte Carlo routine. The Poisson process model is often preferred for modelling extremes of non-stationary processes as the parameters are invariant to the choice of threshold; our approach may increase the possibility of this model being used more widely. Second, we propose an adjustment to the likelihood when implementing a spatial hierarchical model for extremes, which accounts for the dependence in the data when estimating model uncertainty. In both cases, the improvement in inference should increase confidence among practitioners of the outputs obtained from extreme value models. The main influence of extreme weather events in winter is from the passage of low-pressure extratropical cyclones from the North Atlantic. The second aim of this thesis is to quantify the risk associated with extreme wind speed events, which we call windstorms, arising from an extratropical cyclone system. First, we develop a model capturing the spatial variation of the track associated with the cyclone, from which we can simulate synthetic tracks with the same statistical characteristics of the observed record. Second, we describe an approach for modelling the spatial extent and severity of windstorms relative to the storm track, from which we can provide improved estimates of risk associated with windstorms at individual sites and jointly over a spatial domain. The methods described in this thesis can be used to address multiple questions related to windstorm risk, that is not available using current methodology