Dam Spillways Adequacy Evaluation through Bivariate Flood Frequency Analysis and Hydrological Continuous Simulation

Abstract

A large number of dams, built in Italy in the last century, were sized using limited and in some cases sparse hydrological data. As a result, the design flood values were affected by this drawback to which it has to be added a poor knowledge of flood formation processes and statistical techniques used for that. In recent years, sophisticated statistical methods have been developed for the analysis of hydrological variables, and nowadays much more data are available. Therefore, these two aspects can be brought to critically review the hydrological safety of old dams. Considering the dependence between flood peak and flood volume, this study proposes a procedure based on a bivariate statistical approach to evaluate dam spillway adequacy. In particular, the one-parameter Archimedean copula, which has been found particularly useful in hydrology, was selected. Due to the limited number of data available for this study, a continuous hydrological simulation approach was also adopted in order to extend the available data with long synthetic discharge time series. This approach makes use of methodologies for stochastic generation of rainfall and temperature along with a continuous hydrological model for discharge estimation. The Montedoglio dam, a reservoir on the Upper Tiber River in Central Italy subtending an area of 267 km 2 , was considered as case study. Starting from the synthetic and observed time series of discharge flood peak and flood volume available for this dam, the copula method was employed to determine the joint frequency distribution. From the two copulas (synthetic and observed), 1000 pairs of flood peak and volume were randomly extracted thus simulating the dam behaviour during its life time (i.e. 1000 years). These pairs were then transformed into discharge hydrographs, estimated considering the geomorphologic characteristics of the catchment. A third set of discharge hydrographs, directly derived from the synthetic time series, was also used for the analysis. Successively, the hydrological safety of the dam was evaluated by the reservoir routing of the three sets of discharge hydrographs, checking if the authorized maximum storage water level was exceeded. The results obtained with the three methods are quite similar allowing to assess the spillway adequacy for the investigated dam.