Dealing with uncertainty in the probability of overtopping of a flood mitigation dam

摘要

In recent years, copula multivariate functions were used to model, probabilistically, the most important variables of flood events: discharge peak, flood volume and duration. However, in most of the cases, the sampling uncertainty, from which small-sized samples suffer, is neglected. In this paper, considering a real reservoir controlled by a dam as a case study, we apply a structure-based approach to estimate the probability of reaching specific reservoir levels, taking into account the key components of an event (flood peak, volume, hydrograph shape) and of the reservoir (rating curve, volume-water depth relation). Additionally, we improve information about the peaks from historical data and reports through a Bayesian framework, allowing the incorporation of supplementary knowledge from different sources and its associated error. As it is seen here, the extra information can result in a very different inferred parameter set and consequently this is reflected as a strong variability of the reservoir level, associated with a given return period. Most importantly, the sampling uncertainty is accounted for in both cases (single-site and multi-site with historical information scenarios), and Monte Carlo confidence intervals for the maximum water level are calculated. It is shown that water levels of specific return periods in a lot of cases overlap, thus making risk assessment, without providing confidence intervals, deceiving.