Extreme value analysis of non-stationary processes : a study of extreme rainfall under changing climate

Abstract

The aim of this study has been to gain a greater understanding of the accuracy and levels of uncertainty associated with extreme rainfall event estimates, whilst considering both stationary and non-stationary processes (climate change). This study started with the analysis and comparison of two extreme event fitting/estimation techniques: Linear Moments (L-Moments) and Maximum Likelihood Estimation (MLE) for the estimation of Generalized Extreme Value (GEV) distribution parameters. This thesis has found that MLE provides a number of advantages over L-Moments, especially when working with long or pooled data sets. These advantages include:  The generation of confidence limits;  Homogeneity testing; and,  Trend detection / simulation. However, the results of the analysis show that it is advisable to use L-Moments for single site analysis when the available data is less than 40 years in length. In this situation, L-Moments were found to produce less uncertainty. Hosking and Wallis (1988) defined a method for the generation of synthetic data sets; this work has been reproduced and built upon as part of this thesis. Using this method it has been possible to gain insight on:  Inter-site-dependence versus spatial separation (distance, km);  The effects of inter-site-dependence on pooling groups;  Regional correlation descriptors (level of dependence in a region);  Synthetic data generation for regions with varying levels of dependence;  Network Maximum (Netmax) Growth Curves; and,  The effective number of sites in a defined region/pooling group. This has been carried out using the „R‟ statistical software/programming environment. Dales and Reed (1989), proposed the use of Netmax data (the largest value for one year across the network or pooling group) to increase the accuracy at the tail of an extreme event distribution by theoretically extending the curve. This hypothesis suggests that the separation between these two curves (the regional growth curve and the Netmax growth curve) is constant; allowing the Netmax curve to be translated and overlain on the regional growth curve. This study has found that the separation varies iv with return period, implying that spatial correlation reduces (events become more independent) with increased rarity (or return period). However, these findings suggest complications with the use of Netmax data for the purpose of extending the regional growth curve. In addition to the work detailed above, a method of trend detection in annual maximum rainfall has been demonstrated using synthetic data. Synthetic data has been used to enable control over the data, with this greater certainty and understanding in the results are achieved. The same analysis was repeated on observed annual maxima for 1, 5 and 10 day durations, revealing evidence of trends, with stronger signals at higher durations. The trend was detected in the Location parameter, which relates to the mean. When using Synthetic data to understand the sensitivity of this test, it was found that the Location parameter required the weakest trend to be detected. In summary this thesis has used synthetic data to gain a better understanding of: 1. Distribution fitting techniques; 2. Single site analysis; 3. Regional Analysis; 4. Spatial dependence; and, 5. Trend Detection. All of the software that has been written as a result of this thesis to demonstrate the topics discussed, is included in Appendix 5, with explanations on the method of use. Should additional information be required, please contact Professor C. Kilsby at Newcastle University, who will forward on your enquiry.