Stochastic modelling of daily rainfall: the impact of adjoining wet days on the distribution of rainfall amounts

Daily rainfall data for each month of the year have been classified according to the number of adjoining wet days (0, 1 or 2). The data sets used were long-term records for 14 stations in Australia, 6 in South Africa, and 24 in North America, and medium-term (≈20 years) records for 22 island stations in the Western Pacific. For all regions, a nonparametric test showed a low probability that the data in the different classes were from the same distribution, at least for some months of the year. Stochastic models, which treat the classes separately, generally resulted in a better fit than currently used models which group the data together. The magnitude of the ratios of the class means to the overall mean daily rainfall shows that serious errors may result from models which do not take account of these differences, either explicitly by separate modelling of the classes, or implicitly by a multi-state transition probability matrix for rainfall amounts. This work was supported by author-developed software for the statistical analysis of historical rainfall data, parameter estimation by maximum likelihood for a range of models, comparison of model fitting by the Akaike Information Criterion, and daily rainfall simulation.