A 3-copula function application for design hyetograph analysis

A design hyetograph is a synthetic rainfall temporal pattern associated with a return period. Usually it is determined by means of statistical analysis of observed rainfall mean intensity through intensity–duration– frequency (IDF) curves. The other characteristics of a rainfall event, such as the peak, total depth and duration, are found indirectly throughout several phases of hydrological analysis, and trigger suitable work assumptions. The aim of this paper is to apply a multivariate approach in order to analyse jointly observed data of rainfall critical depth, maximum intensity and total depth. In particular, bivariate analysis intensity-total depth conditioning to critical depth is developed using a 3-copula function to define the trivariate joint distribution function. Following the proposed procedure, once a design return period and related critical depth are selected, it is possible to determine, in a probabilistic way, the intensity and total depth, without advancing a priori hypotheses on the design hyetograph pattern. In a case study, the results obtained with the proposed procedure are compared with those deduced from standard design hyetographs usually applied in practical hydrological applications.