A combined Pòlya process and mixture distribution approach to rainfall modelling

Abstract. A new probabilistic interpretation of at site rainfall sequences is introduced for the development of a stochastic model of rain.
The model, is divided into two sub models; the first one describing the total number of rainfall spells within a window of time is described by a Pòlya process in order to reproduce better the variable probability of occurrence of rainfall during storm events (due to the presence of different numbers of rainfall cells); the second sub model, conditional on the first one, describes the total quantity of rainfall in the time window, given a number of rainfall spells.
The probabilistic rainfall model, which has shown interesting properties in reproducing the probability distribution of observed data at time scales ranging from one hour to twenty-four hours, may be the basis for a number of applications which include the development of a conditional stochastic generator of rain, within the frame of real-time flood forecasting, and the derivation of a probabilistic distribution of rainfall extremes at the various time scales.