"Hydrological events are often characterized by the joint behavior of several correlated random variables (e.g. storm duration and intensity). As a consequence, the critical events should be defined in terms of two or more variables; that avoids the over- or underestimation of the hydrological risk, that might be produced by the univariate probability analysis.. In the multivariate analysis, the choice of an appropriate return period for structure design leads to infinite combinations of values (isoline of the return period), each of them could be used to evaluate the effects of different hydrological loads on the structure. This work presents a new methodology to identify a limited subset of design events from the set of the infinite combinations, on the basis of their probability of occurrence. This methodology uses the copula function to represent the joint probability distribution of the considered variables.. The use of copulas enables to model the correlation structure between the variables independently of their marginal distributions. It also allows to adopt marginal distributions not belonging to the same probability family or complex marginal distributions such as finite mixtures of distributions. Furthermore copulas yield analytical expressions for the isolines of the return periods.. This work takes into consideration the case of design events characterized by the joint behavior of two variables, even if the proposed approach can be easily generalized to the multivariate case.. The proposed methodology is illustrated and discussed through the case study of the Tiber River, where copulas have been used to model the joint behavior of the annual maximum peak flows and the corresponding volumes of the floods that exceeded the threshold of 1800 m3\/s at Ripetta (Rome) gauge. In this case the joint probability distribution of peak flows and volumes has been evaluated using all the information available, including: 1) the daily flow series available starting from 1782, and 2) the censored series of the peak flows of the exceptional floods that inundated the town of Rome starting from the XV century. The application of the proposed methodology allowed to select limited sets of flood events to be used in the design of flood control reservoirs on the Tiber River.. "
Volpi, E., Fiori, A., Mancini, C., Calenda, G. (2011). Identification of hydrological events using copulas. In IUGG XXV General Assembly, Melbourne, Australia, 2011..