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.
Cowperthwait, P.S.P. (2003), Mixed rectangular pulses models of rainfall, Research Letters in the Information and Mathematical Sciences, 5, 61-70