Bivariate flood frequency analysis for the hydrological safety of dams

A large number of dams, built in Italy in the last century, have been dimensioned using hydrological data sample limited in length of time series. Therefore, the design flood was affected from the scarcity of data and a poor knowledge of the flood formation processes. Nowadays, besides the data availability, sophisticated statistical methods addressed for extreme events have been developed and can be fundamental to review the hydrological safety of old dams. Based on the previous contents, in this paper a bivariate statistical approach, describing the dependence structure between flood peak and flood volume, is proposed. The analysis is carried out through the application of a one-parameter Archimedean copula, particularly useful in the practical hydrology. Since the Archimedean copula represents a family of functions, a procedure based on the goodness-of-fit statistics for selecting the best one has been carried out. The chosen copula function provided an estimate of variables flood peak and volume for a given joint return period. The bivariate probability distribution has been expressed in terms of marginal probability distributions of the two considered variables, that can have different form. Pairs of flood peak and volume with a fixed joint return period have been selected and a hypothetical shape of the flood hydrograph has been surmised. The proposed method has been applied to the Calcione dam, a small reservoir located in Central Italy, in order to re-assess its hydrological safety by comparing the copula method results with those obtained from a hydrological lumped conceptual model.