A model for seasonal variation of rainfall at Adelaide and Turen

Abstract

A rigorous statistical methodology is given to estimate the coefficients of annually periodic functions representing the parameters of a continuous time rainfall model. The methodology is applied to the Rectangular Pulses Poisson model (RPPM) which simulates rainfall occurrences and rainfall amounts in continuous time. Two types of periodic functions, Fourier series and periodic quadratic polynomial splines, are used to represent the seasonal variation of the rainfall model parameters at two locations, Adelaide (Australia) and Turen (Venezuela). The coefficients of the periodic functions representing each model parameter are estimated by minimising a weighted residual sum of squares between observed and theoretical statistics of daily data. The numbers of coefficients of the periodic functions are selected by applying successive approximate likelihood ratio tests, by which the number of required coefficients is increased until no further improvement is gained with respect to a previous fit. Comparisons between the goodness of fit and numbers of selected coefficients show marginally superior performance of the periodic quadratic polynomial splines in comparison with Fourier Series for this particular rainfall model. The methodology is intended to provide an efficient procedure to parameterize the seasonal variability of rainfall data with the smallest number of coefficients, by reducing the original number of degrees of freedom used in the estimation procedure. The coefficients of the periodic functions are amenable to spatial interpolation and interpolated values can be used to simulate rainfall at any point of a particular region, for more detailed climatic impact assessment analyses.