Non-stationary environmental extremes

Zanini, Elena and Eastoe, Emma and Jonathan, Philip and Randell, David and Tawn, Jonathan (2018) Non-stationary environmental extremes. PhD thesis, Lancaster University.

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Abstract

Our physical environment gives rise to extreme events (river floods, heatwaves, atmospheric pollution, hurricanes, earthquakes) that have the potential to endanger lives and cause large economic loss. Understanding the characteristics of extreme ocean environments in particular, and their interactions with marine and coastal structures, is critical to the safety of all who inhabit coastal regions, or depend on the ocean for their livelihoods. Extreme value analysis presents a useful framework to quantifying the extreme ocean environment from samples of observations. Reliable extreme value models for the ocean environment must accommodate known sources of systematic variation in ocean storm severity due to covariates such as wave direction and season. This motivates the two main areas of research addressed in this thesis. The first area considers the introduction of covariates in the generalised Pareto and non-homogeneous Poisson point process models for extremes. The relative performance of non-stationary forms of these models is investigated in terms of ease of implementation, parameter estimation and predictive performance on both simulated and hindcast samples. Both approaches have their merits. The key finding is the importance of employing a model formulation that captures the covariate-response relationship appropriately. The second area of research is the development and evaluation of approaches to estimate the covariate-response relationship. Covariate effects in extreme ocean storms are often intricate, requiring a flexible framework to estimate the variation of extreme value model parameters as a function of covariates. Parameterisations need to be sufficiently complex to be physically realistic, but sufficiently parsimonious to be practically useful. Semi- and non-parametric models are ideal candidates. A covariate parameterisation often needs to accommodate rapid change or specific covariate interactions in one part of the covariates domain, but smoother variation in other parts. The covariate parameterisation needs to be sufficiently flexible and reliable to facilitate the study of extreme ocean environments from different ocean basins with fundamentally different physical characteristics. Model sophistication usually comes at the expense of computational stability and efficiency. Modelling procedures are required which are capable of incorporating multiple covariates (suche as direction, season, location, water depth), ensuring appropriate smoothness of model parameter variation with covariates, to maximise predictive performance whilst avoiding overfitting. Extreme value models within which model parameter variation with respect to covariates is described using penalised splines, Bayesian adaptive regression splines, radial basis functions and covariate domain partitioning are considered for 1-D and 2-D covariates. The performance of each is evaluated using simulated and hindcast samples. Spline-based models perform relatively well, in terms of predictive performance and computational stability, across a range of applications. Radial basis functions and covariate domain partitioning formulations appear to provide a promising parsimonious alternative when covariates interact strongly.