Design hyetograph analysis with 3-copula function

A design hyetograph is a synthetic rainfall temporal pattern associated with a return period, usually determined by means of statistical analysis of observed mean rainfall intensity through intensity-duration-frequency (IDF) curves. Since the univariate approach is simple to apply and data availability is scarce, only the mean intensity of a rainfall storm is usually analysed statistically. The other characteristics of a rainfall storm, such as peak (maximum intensity), total depth and duration, are found indirectly throughout the several phases of hydrological analysis by suitable work assumptions. The aim of this paper is to apply a multivariate approach in order to analyse jointly observed data of critical depth, peak and total depth. In particular, bivariate analysis of peak-total depth conditioned on critical depth is developed using a 3-copula function to define the trivariate joint distribution. Following the proposed procedure, once design return period and related critical depth are selected, it is possible to determine-in a probabilistic way-peak and total depth, without advancing a priori hypotheses on the design hyetograph pattern.