Modelling the statistical dependence of rainfall event variables by a trivariate copula function

Abstract. In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by splitting the problem in two distinct items. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein a trivariate probability distribution of the rainfall event volume, the wet weather duration and the interevent time is proposed and verified by test statistics with regard to three long time series recorded in different Italian climates. The function was developed by applying a mixing technique to bivariate copulas, which were formerly obtained by analyzing the random variables in pairs. A unique probabilistic model seems to be suitable for representing the dependence structure, despite the sensitivity shown by the dependence parameters towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.