A clustered spatial-temporal model of rainfall

Abstract

A spatial–temporal model of rainfall is studied in which storms arrive in a Poisson process in time, each storm giving rise to a random number of elliptical rain cells. Each rain cell moves with a random velocity for a random time before terminating. Rain is deposited by the cell at a random intensity which is constant over the area of the cell and over its lifetime. The main properties of this model are studied analytically where possible. Further properties and the aggregation of model properties over space for direct comparison with rainfall radar data require the numerical evaluation of integrals.