Bayesian spatial modelling of climate extremes

This thesis is primarily concerned with determining effective and efficient methods to model spatial datasets of climate extremes. Climate extremes impact our technology, our infrastructure, the environment, and humans ourselves. Faced with the uncertainties and challenges of human-induced climate change, it is now more important than ever to understand the behaviour of climate extremes. Existing observations of extreme events are, by definition, rare, which makes any analysis and interpretation of this data more challenging than other analyses. Extrapolation beyond the observed extremes is necessary in order to plan for events worse than those already observed. This extrapolation needs a sound theoretical framework as mitigation and adaptation planning often involves practical and financial risks and implications. The framework applied should incorporate prior information, result in useful predictions of practical benefit, and be adaptable to model datasets across a dense spatial domain. It is these aims and objectives which guided and informed the research undertaken during the course of this thesis. The first study I undertook involved using dynamically downscaled climate model output from CMIP3 and CMIP5. From this, I analysed the temperature changes projected over Ireland for the mid-21st century under different future climate change scenarios. I found that annual mean temperatures were projected to rise by between 0.4C and 1.8C by the mid-century. On a seasonal basis, projected temperature changes differed by forcing scenario. Some scenarios saw future summers with the largest projected warming; others projected future winters to warm the most. An investigation into the projected change in temperature extremes found that in general there was greater projected changes in the number of cold nights and the number of hot days than for mean temperatures. In the next study undertaken, I applied extreme value theory (EVT) in a Bayesian spatial hierarchical framework in order to model extremes of significant wave heights off the west coast of Ireland for the period 1979-2012. I found that the highest extremes of significant wave height were to be expected off the west coast of Ireland roughly between 53N and 54.5N, with 100-year levels close to 17 m. A comparison of the Bayesian spatial model with a simpler maximum likelihood site-specific approach found that the former resulted in smoother surfaces of posterior parameters and return level maps, with less uncertainty while still showing a satisfactory fit to the data. In the final study undertaken, I extended the Bayesian spatial hierarchical framework using a dimension reduction technique called predictive processes. This extension was necessary in order to model a spatially dense dataset of extremes of daily maximum temperature anomalies over Dublin, Ireland, for the period 1981-2010. The results included a posterior median 100-year return level surface for anomalies of maximum temperature ranging from 8C to 10.7C across the domain, with an upperbound of 12.7C. Additional analysis involved placing more recent extremes (2011-2018) from synoptic stations across the domain in the context of the model results. Including this data in the analysis showed an increase in the frequency of extreme anomalies for this period, but not in their severity. The methods presented in this thesis can be readily adapted to any spatially-continuous dataset. One advantage to using a Bayesian framework is the incorporation of prior information, which leads to a reduction in the uncertainty of quantities such as return levels, and thus provides information on extremes which is more useful for practical applications. The main advantage of the predictive processes approach is the ability to fit a spatial model which would otherwise be too computationally expensive to fit, allowing me to achieve results which would not have been possible by fitting the full model to the dense dataset