Mixed rectangular pulses models of rainfall

Abstract

In a recent paper ((3)) a fitting procedure for the Neyman-Scott rectangular pulses (NSRP) spatial-temporal model of rainfall was developed. In that paper, the NSRP third moment function was fitted to the equivalent sample value taken at one-hour time intervals. In this paper, the fitting and modelling procedure are extended to ensure a close fit is obtained to further sample properties over a range of time scales. The stochastic model is a ‘mixed’ model obtained as the superposition of two independent NSRP processes. The model is fitted to hourly data from Auckland, New Zealand, where a good fit to sample properties is obtained. It is found that a special case arises (the superposition of an NSRP process and a Poisson rectangular pulses process) for data over the summer period. A simulation study of extremes over a range of time scales supports the use of the model in hydrological applications.