Copula-Based Modeling of Flood Control Reservoirs

Copulas are shown in this paper to provide an effective strategy to describe the statistical dependence between peak flow discharge and flood volume featuring hydrographs forcing a flood control reservoir. A 52 year time series of flow discharges observed in the Panaro River (Northern Italian Apennines) is used to fit an event-based bivariate distribution and to support time-continuous modeling of a flood control reservoir, located online along the river system. With regard to reservoir performances, a method aimed at estimating the bivariate return period is analytically developed, by exploiting the derived distribution theory and a simplified routing scheme. In this approach, the return period is that of the peak flow discharge released downstream from the reservoir. Therefore, in order to verify the reliability of the proposed method, a nonparametric version of its frequency distribution is assessed by means of continuous simulation statistics. Copula derived and nonparametric distributions of the downstream peak flow discharge are found to be in satisfactory agreement. Finally, a comparison of bivariate return period estimates carried out by using alternative approaches is illustrated.