A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation

A multivariate analysis on flood variables is needed to design some hydraulic structures like dams, as the complexity of the routing process in a reservoir requires a representation of the full hydrograph. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume, in order to know the probability of occurrence of a given inflow hydrograph. However, the risk of dam overtopping is given by the maximum water elevation reached during the routing process, which depends on the hydrograph variables, the reservoir volume and the spillway crest length. Consequently, an additional bivariate return period, the so-called routed return period, was defined in terms of risk of dam overtopping based on this maximum water elevation obtained after routing the inflow hydrographs. The theoretical return periods, which give the probability of occurrence of a hydrograph prior to accounting for the reservoir routing, were compared with the routed return period, as in both cases hydrographs with the same probability will draw a curve in the peak-volume space. The procedure was applied to the case study of the Santillana reservoir in Spain. Different reservoir volumes and spillway lengths were considered to investigate the influence of the dam and reservoir characteristics on the results. The methodology improves the estimation of the Design Flood Hydrograph and can be applied to assess the risk of dam overtopping.

Bivariate return period based on copulas for hydrologic dam design: comparison of theoretical and empirical approach

Hydrologic frequency analyses are usually focused on flood peaks. Multivariate analyses on flood variables have not been so exhaustively studied despite the fact that they are required to represent the full hydrograph, which is essential for designing some structures like dams. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume. An empirical bivariate return period was defined in terms of acceptable risk to the dam through the maximum water elevation reached during the routing process, in order to perform a risk assessment of dam overtopping. A Monte Carlo procedure was developed to compare the probability of occurrence of a flood with the return period linked to the risk of dam overtopping. The procedure is applied to the case study of the Santillana reservoir in Spain. A set of synthetic peak-volume pairs was generated by the fitted copula and synthetic hydrographs were routed through the reservoir. Different reservoir volumes and spillway lengths were considered. Hydrographs with the same risk were represented by a curve in the peak-volume space. These curves were compared to those linked to the probability of occurrence of a flood event, in order to improve the estimation of the Design Flood Hydrograph.