An investigation of Australian rainfall using extreme value theory
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2018 Dr. Kate Saunders
In this thesis, we use extreme value theory to fit statistical models to observations of Australian daily rainfall extremes. We build upon the existing literature by challenging the basic assumptions of these models when applied in a climate setting. The types of applications we consider range from univariate extreme value theory, to spatial extremes with dependence, and finally to an investigation of extremal dependence. The combined application content provides an in-depth investigation into our understanding of Australian rainfall extremes and the risks posed by these extreme events. We consider how large scale climate drivers, such as El Niño Southern Oscillation (ENSO), can influence the distribution of rainfall extremes. Using observations of daily rainfall from station data, we quantify the magnitude and spatial influence of ENSO on the distribution of seasonal maximum daily rainfall. We contrast these results obtained from an at-station analysis, with those from a simple spatial model, ultimately producing maps of the region of ENSO influence. We then consider an application where we use max-stable processes to model rainfall extremes in continuous space with dependence. We fit a max-stable process to the annual maximum daily rainfall in South East Queensland and simulate the extreme precipitation field. We quantify the severity of an historical flash flood in this region, showing that the probability of this event was significantly higher given the phase of ENSO. Finally, we examine variation in the dependence behaviour of daily rainfall extremes. For Australia, a single dependence structure for spatial models of rainfall extremes is unrealistic. This is due to the country size, variations in climate and complexity of topography. In order help account for these variations, we present a regionalisation of Australia. In this regionalisation, locations are grouped according to similar dependence of rainfall extremes. The overarching goal of this thesis is to improve our understanding of the risks posed by extreme rainfall events in Australia. We achieve this by utilising spatial, statistical models. However, we acknowledge that using extreme value theory for modelling real world applications in practice has challenges. We highlight these practical considerations in our applications, so that other researchers may be aware of the advantages of this kind of modelling, as well as some of its practical limitations.
Keywordsextreme value theory; Australian rainfall extremes; max-stable processes; El Niño Southern Oscillation
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