Bivariate modeling of flood peak and volume for assessing the hydrological safety of dams

The dam failure can be caused by multiple factors such as slope instability, presence of structural faults, or overflow. The latter is one of the most frequent causes and accounts for more than 40 % of them worldwide. Checking the hydrological safety of dams means assessing the ability of the dam, and thus of its outlets, to dispose of intense flood events without overflow. In Italy, the assessment of the hydrological safety of dams is a key and urgent issue in Italy. About the 8% of the large dams were built more than one century ago, and such a percentage is expected to increase up to 23% in a decade. Traditionally, such assessment is performed by means of the millennial quantile of flood peak. However, in literature, it has been shown that the determination of critical flood events should consider the statistical dependence between flood peak and flood volume. In the present work, we assess the hydrological safety of three Italian dams (namely, Ceppo Morelli, Mignano, and Molato) exploiting a bivariate approach, which stems from the method presented by De Michele et al., 2005. The statistical dependence between flood peak and volume is firstly estimated and modelled using copula models. Massive synthetic simulations are afterward performed to estimate the rate of overtopping of each dam, and consequently the return period. Results show that all the three dams result as hydrologically safe, even if Ceppo Morelli dam needs to be regularly monitored. Furthermore, for each dam, we also define a critical region, where the couples flood peak-flood volume may lead to overtopping. It is observed that the shape of such regions strictly depends both on flood peak and volume. Eventually, the routing effects of the three dams are compared, with respect to the return period and assuming three different dependence behaviors. It is proved that an overestimate of the dependence degree would result in an underestimate of the dam routing effect, and viceversa, leading to improper assessment of the risk.