Extreme value modelling for protecting and maintaining critical infrastructure from natural hazards

D'Arcy, Eleanor and Tawn, Jonathan (2024) Extreme value modelling for protecting and maintaining critical infrastructure from natural hazards. PhD thesis, Lancaster University.

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Abstract

Safeguarding critical infrastructure is paramount as we face escalating natural hazards. This thesis uses extreme value modelling to enhance our understanding and estimation of extreme sea levels (ESLs) and river flows. We focus on the intrinsic complexities of non-stationarity and dependence inherent in such phenomena and propose novel statistical methodologies to address these challenges. Coastal and fluvial flooding are some of the most widespread natural disasters today. Estimates of ESLs and river flows can be useful for guiding design criteria of flood defences. We illustrate how falsely assuming stationarity and independence affects estimation. We find that current methods over- or under-estimate extreme events, depending on the location of interest, which, if used for defence design, could lead to a waste of resources or put communities at risk, respectively. We develop a novel methodology for ESLs that accounts for non-stationarity in skew surges and peak tides, the dependence between these components and their temporal dependence. We discuss how to simulate skew surge time series that replicate their seasonality, temporal dependence and extreme values; these are useful for coastal erosion maintenance planning and predicting surge barrier closure rates. Lastly, we present a novel model for temporal dependence in extreme river flows based on a maxautoregressive moving average process. We derive new extremal dependence features and show how this process can capture the unique features of river flow extremes. Additional methods are discussed relevant to the Extreme Value Analysis conference data challenges. Ultimately, this thesis contributes to advancing extreme value modelling techniques tailored specifically to protecting and maintaining critical infrastructure against natural hazards. By enhancing our ability to prepare for extreme events, our findings can inform policy-making and infrastructure planning to foster greater resilience in the face of escalating natural hazards.