Seasonal rainfall totals of Australian stations can be modelled with distributions from the Tweedie family

Abstract

ABSTRACTTheoretical probability distributions of seasonal rainfall totals have potential applications in fitting models and generating synthetic data. One of the major challenges in fitting distributions for seasonal rainfall from countries like Australia is that the data differ significantly for various seasons across stations. The wet stations may possess strictly positive rainfall amounts only, whereas dry stations may observe seasons with no rainfall. Furthermore the data ranges from approximately symmetric to highly skewed. We explore fitting distributions from the Tweedie family of distributions to model seasonal rainfall. The Tweedie family of distributions includes continuous‐symmetric (normal), continuous‐skewed (gamma) and mixture‐type (Poisson–gamma, P–G) distributions. This study analysed seasonal rainfall totals from 989 Australian stations with data for about 100 years. For various seasons, within the Tweedie family the P–G distributions were optimal for about 50% of stations, the gamma distributions were near‐optimal for approximately 40% and the normal distributions were near‐optimal elsewhere. Most of the stations where the gamma distributions are near‐optimal are concentrated on the Australian coastline. The quantile–quantile (QQ) plots indicate that the models fit well to the seasonal rainfall totals of selected stations. Almost everywhere, various statistics of observed seasonal rainfall are within the empirical 95% confidence intervals of the respective statistics of simulated data using the Tweedie models. The model performs better in modelling extremely high rainfall events (95th percentiles) than the extremely low (5th percentiles) rainfall events. In addition, the P–G distribution within the Tweedie family models the probability of no rainfall and, for about 97% of stations, the observed probability of no rainfall is within the 95% confidence interval of the simulated probability of no rainfall. The ability of the Tweedie models to simulate the extreme rainfall amounts and the probability of no rainfall can be useful in drought monitoring and in water resources planning and management.