A point process model for rainfall: further developments

A stochastic model for rainfall at a single site is studied in which storms arrive in a Poisson process, each storm consisting of a cluster of a random number of rain cells, each cell having random duration and depth. A model studied in an earlier paper is extended to provide a better fit to empirical experience, the extension being based on the attachment of a single random variable to each storm to achieve in particular some correlation between the durations of the cells within a single storm. The properties of the new model are developed, its fitting to two sets of empirical data is described and the examination of adequacy of fit is studied in some detail via properties not used in the fitting procedure. Finally a theoretical study is made of short-term prediction from the model.