Bivariate return period for design hyetograph and relationship with T-year design flood peak

This study focuses on the return period evaluation for design hyetographs, which is usually estimated by adopting a univariate statistical approach. Joint Return Period (JRP) and copula-based multivariate analysis are used in this work to better define T-year synthetic rainfall patterns which can be used as input for design flood peak estimation by means of hydrological simulation involving rainfall-runoff(RR) models. Specifically, a T-year Design Hyetograph (DH) is assumed to be characterized by its peak H, at the chosen time resolution δt, and by the total rainfall height W, cumulated on its critical duration dCrit, which has been a priori fixed. As stated in technical literature, the choice of the expression for JRP depends on which event is deemed as critical for the investigated system; the most important cases are: (i) all the variables must exceed a certain magnitude to achieve critical conditions; or (ii) at least one variable must be greater than a threshold; or (iii) critical conditions are induced by all the events with a joint Cumulative Density Function (CDF) overcoming an assigned probability threshold. Once the expression for JRP was chosen, the relationship among multivariate T-year design hyetographs and T-year design flood peak was investigated for a basin located in Calabria region (southern Italy). Specifically, for the selected case study, a summary diagram was obtained as final result, which allows the main characteristics of T-year DHs to be estimated, considering both the univariate and the copula based multivariate analysis, and the associated T-year design flood peaks obtained through the simulation with a RR model