Periodic model selection for rainfall using conditional maximum likelihood

Modelling accumulated rainfall at a given time scale has always been an important problem in hydrology for many applications. In many parts of the world rainfall is highly seasonal and parameter estimation of selected models is usually carried out by months or seasons at any particular location. A method is proposed by which the parameters of a point rainfall model, the Compound Poisson model are estimated by Maximum Likelihood to simulate monthly rainfall in Guarico state, located at the Central plains of Venezuela. Due to the marked seasonal pattern in the region, the parameters are modelled by using periodic functions. Two types of periodic functions: Fourier series and quadratic polynomial splines were used. A Conditional Maximum Likelihood Method is proposed by which the coefficients of each periodic function are estimated for each parameter. At each step of the Conditional Maximum Likelihood method, an information Criteria is used to select the number of Fourier harmonics or knot points to be used in the periodic representation of each model parameter. Results are presented for selected locations at the central plains of Venezuela. Regionalization of this method to simulate rainfall in locations without measurements records is also discussed.