Statistical model for daily precipitation

Daily records of precipitation measured in Modena (Po Plain in Italy) since March 1830, were analyzed in the framework of a stochastic bivariate model. The following stochastic variables were chosen: q, equivalent height of water precipitated during the wet day; d, number of dry days which precede the wet day. The two variables appear reasonably independent so that, in a wet day, the overall probability that the next wet day is labelled by q and d is given by the product of two independent probabilities. The probability that the next wet day occurs after d+1 days follows a Polya distribution. This distribution has two parameters which show a seasonal dependence. The probability distribution of the equivalent height of precipitated water, q follows a gamma distribution. This distribution has also two parameters which show a seasonal dependence.