Statistical modelling of environmental extremes - Auld, Graeme (The University of Edinburgh, 2022)
This thesis is concerned with the development of theory and statistical methodologies that may be used to analyse environmental extremes. As extreme environmental events are often associated with large economic costs and loss of human life, accurate statistical modelling of such events is crucial in order to be able to accurately estimate their frequency and intensity. A key feature of environmental time series is that they display serial correlation which must be modelled in order for valid inferences to be drawn. One line of research in this thesis is the development of flexible time series models that may be used to simulate the behaviour of an environmental process after entering an extreme state. This allows us to estimate quantities such as the mean duration of an extreme event. We illustrate our modelling approach and methodology by simulating the behaviour of daily maximum temperature in Orleans, France, over a three week period given that the temperature exceeds 35C at the start of the period. Much of extreme value theory for time series has been developed under the assumption of strict stationarity, a mathematically convenient but often unrealistic assumption for environmental data. Our second project extends some well known classical results for strictly stationary time series to a more general setting that allows for non-stationarity. We show that for weakly dependent time series with common marginal distributions, the distribution of the sample maximum at large thresholds is characterized by a parameter that plays an analogous role to the extremal index of a stationary time series, and may be estimated similarly. Our results are applied to the particular case where non-stationarity arises through periodicity in the dependence structure as may be expected in certain environmental time series. We also show how our results may be further generalized to allow for different marginal distributions. Another strand of research in this thesis concerns the detection and quantification of changes in the distribution of the annual maximum daily maximum temperature (TXx) in a large gridded data set of European daily temperature during the years 1950-2018. We model TXx throughout Europe using a generalized extreme value distribution, with the log of the atmospheric concentration of CO2 as a covariate. It is commonplace in the geoscientific literature for such models to be fit separately at each spatial location over the domain of interest. To reflect the fact that nearby locations are expected to be similarly affected by any climate change, we instead consider models that incorporate spatial dependence, and thus increase efficiency in parameter estimation compared to separate model fits. We find strong evidence for shifts towards hotter temperatures throughout Europe. Averaged across our spatial domain, the 100-year return temperature based on the 2018 climate is approximately 2C hotter than that based on the 1950 climate. Our final project concerns the evaluation of bias in climate model output and how such biases contribute to biases in hazard indices. Based on copula theory we develop a multivariate bias-assessment framework, which allows us to disentangle the biases in hazard indicators in terms of biases in the underlying univariate drivers and their statistical dependence. Based on this framework, we dissect biases in fire and heat stress hazards in a set of global climate models by considering two simplified hazard indicators: the wet-bulb globe temperature (WBGT) and the Chandler burning index (CBI).