Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy

We use the principle of maximum entropy to propose a parsimonious model for generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients and hence provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for modelling and simulation of seasonal rainfall at the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described.