A space-time Neyman-Scott model of rainfall: Empirical analysis of extremes

Abstract

A spatial-temporal model of rainfall, based on a Neyman-Scott stochastic point process, is fitted to hourly data taken from nine sites in the Arno Basin, Italy. The stochastic model is an extension of the temporal Neyman-Scott rectangular pulses model into two-dimensional space and introduces a further parameter into the model. In the model, storms arrive in a Poisson process, where each storm consists of discs representing rain cells, with centers distributed over an area according to a spatial Poisson process. The cells have a random radius, lifetime, and intensity, with the intensity remaining constant over the area of the disc and cell lifetime. A fitting procedure is proposed which couples the results obtained in two preceding papers: the second-order properties of the spatial-temporal model and the third moment function of the single site model [Cowpertwait, 1995, 1998]. The model is validated by comparing extreme historical hourly data and equivalent data simulated using the fitted spatial-temporal model. These comparisons are made using a regional frequency analysis, based on L moments, and log-log plots of the upper distribution tail. The results indicate that the model is able to preserve regional extremes and support the use of the model in hydrological applications.