AbstractsMathematics

This thesis presents an approach for generating long synthetic sequences of single-site daily rainfall which can incorporate low-frequency features such as drought, while still accurately representing the day-to-day variations in rainfall. The approach is implemented in a two-stage process. The first stage is to generate the entire sequence of rainfall occurrence (i.e. whether each day is dry or wet). The second stage is to generate the rainfall amount on all wet days in the sequence. The models used in both stages are nonparametric (they make minimal general assumptions rather than specific assumptions about the distributional and dependence characteristics of the variables involved), and ensure an appropriate representation of the seasonal variations in rainfall. A key aspect in formulation of the models is selection of the predictor variables used to represent the historical features of the rainfall record. Methods for selection of the predictors are presented here. The approach is applied to daily rainfall from Sydney and Melbourne. The models that are developed use daily-level, seasonal-level, annual-level, and multi-year predictors for rainfall occurrence, and daily-level and annual-level predictors for rainfall amount. The resulting generated sequences provide a better representation of the variability associated with droughts and sustained wet periods than was previously possible. These sequences will be useful in catchment water management studies as a tool for exploring the potential response of catchments to possible future rainfall.