Rainfall modelling using Poisson-cluster processes: a review of developments

Over a decade ago, point rainfall models based upon Poisson cluster processes were developed by Rodriguez-Iturbe, Cox and Isham. Two types of point process models were envisaged: the Bartlett-Lewis and the Neyman-Scott rectangular pulse models. Recent developments are reviewed here, including a number of empirical studies. The parameter estimation problem is addressed far both types of Poisson-cluster based models. The multiplicity of parameters which can be obtained for a given data set using the method of moments is illustrated and two approaches to finding a best set of parameters are presented. The use of a proper fitting method will allow for the problems encountered in regionalisation to be adequately dealt with. Applications of the point process model to flood design are discussed and finally, results for a model with dependent cell depth and duration are given. Taking into account the spatial features of rainfall, three multi-site models are presented and compared. They are all governed by a master Poisson process of storm origins and have a number of cell origins associated with each storm origin. The three models differ as to the type of dependence structure between the cell characteristics at different sites. Analytical properties are presented for these models and their ability to represent the spatial structure of a set of raingauge data in the South-West of England is examined. Continuous spatial-temporal models are currently being developed and results are presented for a model in which storm centres arrive in a homogeneous Poisson process in space-time, and cells follow them in time according to a Bartlett-Lewis type cluster. Examples of simulations using this model are shown and compared with radar data from the South-West of England. The paper concludes with a summary of the main areas in which further research is required.