A MODEL FOR SEASONAL-VARIATION OF RAINFALL AT ADELAIDE AND TUREN

A rigorous statistical methodology is given to estimate the coefficien ts of annually periodic functions representing the parameters of a con tinuous time rainfall model. The methodology is applied to the Rectang ular Pulses Poisson model (RPPM) which simulates rainfall occurrences and rainfall amounts in continuous time. Two types of periodic functio ns, 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 coef ficients of the periodic functions representing each model parameter a re estimated by minimising a weighted residual sum of squares between observed and theoretical statistics of daily data. The numbers of coef ficients of the periodic functions are selected by applying successive approximate likelihood ratio tests, by which the number of required c oefficients is increased until no further improvement is gained with r espect 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 Fourie r Series for this particular rainfall model. The methodology is intend ed to provide an efficient procedure to parameterize the seasonal vari ability of rainfall data with the smallest possible number of coeffici ents, by reducing the original number of degrees of freedom used in th e 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 de tailed climatic impact assessment analyses.