Spatial interpolation of the parameters of a rainfall model from ground-based data

A methodology is presented by which the variability of daily rainfall in space and time is summarized by a set of parameters of a stochastic point rainfall model. The spatial variability of the parameters of the Rectangular Pulses Poisson Model (RPPM) was investigated across a region of South-East Queensland, Australia. Daily data from 102 stations were used to calibrate the model parameters at each point. A suitable periodic function was fitted to the model parameters, which were assumed seasonal with a period of 1year. A number of significant coefficients of the periodic functions representing the broad seasonal behaviour across the region were selected for each model parameter. The coefficients of the periodic functions were interpolated to consider simultaneously seasonal changes within the year and variability between locations. Spatial interpolation of these coefficients was carried out by using thin plate smoothing splines as a function of position and also by considering the dependence of the interpolated surfaces on elevation. By incorporating the dependencies on elevation, the interpolated values showed a more complex pattern, which were in good agreement with the rainfall characteristics of the location and its interaction with the terrain. The reliability of the interpolated surfaces in representing the rainfall characteristics across the region was demonstrated with an independent set of locations which were not used in the fitting procedure. This shows the capability of the method in providing realistic stochastically generated rainfall at any point of the region without historical information. It is anticipated that this methodology could be applied to the remaining parameters of a stochastic weather generator whose parameters could be calibrated from a sparse ground-based network with incomplete records. Applications of this analysis within the framework of the IGBP core project Biospheric Aspects of the Hydrological Cycle (BAHC) are also discussed.