An investigation of Australian rainfall using extreme value theory

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 maxstable 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. Declaration This is to certify that: i. the thesis comprises only my original work towards the PhD except where indicated in the Preface, ii. due acknowledgment has been made in the text to all other material used iii. the thesis is fewer than 100 000 words in length, exclusive of tables, maps, bibliographies and appendices. Signed Kate Saunders Preface This thesis is based solely on the research I carried out during my PhD canditature at the School of Mathematics and Statistics, at the University of Melbourne. This research has been supported by the Australian Research Council through the Laureate Fellowship FL130100039, by the Commonwealth Scientific and Industrial Research Organisation through top up funding, and the Australian Centre of Excellence in Mathematical and Statistical Frontiers. As part of the financial support I have received, I have had the opportunity to travel and to present my research, both at domestic and at international conferences. These opportunities to share my research and network have been invaluable. I would like to acknowledge the support I received to present at the 13th International Meeting on Statistical Climatology in Canmore in 2016. At this conference, I presented an early version of the work in Chapter 6. It was here that Anthony Davison made some helpful suggestions as to how I might model the non-linearity of my response surface. This work was published in Weather and Climate Extremes (Saunders et al., 2017). I was responsible for the core ideas in this paper and was the primary author, with contribution to the paper content of 90%. I would also like to acknowledge the support I received to visit the National Centre for Atmospheric Research (NCAR) in Boulder, Colorado in 2016. It was during this visit, that I was fortunate to spend time with Phillipe Naveau while he was there on sabbatical and I began the research that ultimately became Chapter 7. I hope to publish this work shortly. Acknowledgments To my three supervisors: Thank you for your kindness and patience throughout this process. Your combined experience and guidance have been key to making this journey a successful one. Peter, thank you for always being in my corner. Your unwavering belief in my ability has helped me to grow in confidence. The PhD is as much a personal journey as it is a professional one, and I have had the luxury of taking risks knowing that you were supporting me. David, thank you for helping me to bridge the interdisciplinary gap. You are the reason I went to the 13th International Meeting on Statistical Climatology and visited the National Center for Atmospheric research, both of which I consider to be turning points in the PhD. Alec, I’m extremely grateful for time I got to spend with you at CSIRO. Thank you for being my extreme value theory sounding board and for helping me to understand my research as part of the broader discipline. x ‘It takes a village . ’ I feel blessed to have had such a fantastic network of people who have supported me throughout this process. Unfortunately, I can’t mention you all here, but below are a few special acknowledgments. Ellen and Tim, I feel very lucky to have shared an o ce with you both. Your friendship has made this journey all the more enjoyable. Ellen, thank you for being my confidant. Tim, thank you for having a laugh and putting up with all my rot. To my colleagues at the Climate College, your generosity and support has been overwhelming. Special thanks to Lisa, Mandy, Tash and Alister for both keeping me on track and abetting my procrastination. Claire, I’m grateful to have shared so much of this journey with you, both here at University and at CSIRO. Gala, thank you for your honesty and strengthening my voice when it was needed. Carolyn and Fletcher, and Bretta, you each created a small person while I created this thesis. Thank you for helping me maintain perspective. Jackson, you sparked my passion for data visualisation, thank you for your R advice and generosity. Daryl, thank you for taking the time to proofread my thesis. I strongly believe you have made me a better writer, hopefully my reviewers think so too. To Mum, Dad, and Mackenzie: thank you for your love and support. It has been tumultuous at times throughout this process, and you have gotten me through. I don’t say it enough, but I love you. I’m sorry I can be a ratbag at times.