A point rainfall model based on a three-state continuous Markov occurrence process

Abstract

A four-parameter three-state Markov process model for rainfall occurrence at a point is described. The model gives rise to rainfall events which consist of clusters of showers in a similar fashion to existing Poisson cluster process models, but has a more direct physical interpretation since showers do not overlap in time. Parameters may be estimated by maximum likelihood from observed runs of wet and dry hours. Runs of dry hours follow a mixed geometric distribution which is verified using hourly occurrence data for Spokane in mid-winter. The sequential occurrence structure permits a two-parameter autocorrelated exponential (shot noise) intensity process to be associated with the occurrence process which in turn permits the model to match rainfall intensity and occurrence statistics for Denver in mid-summer better than an existing five-parameter rectangular pulse Poisson cluster process model. The occurrence model can be directly related to a simpler two-state model for applications at coarser time scales. Daily statistics for the corresponding two-state model are shown to be consistent with daily statistics for the three-state model. The occurrence model can also be extended to include additional weather states of hydrological significance, such as periods of nonprecipitating cloud.