Uncertainty Analysis of Bivariate Design Flood Estimation and its Impacts on Reservoir Routing

Abstract

The bivariate hydrological quantile estimation may inevitably induce large sampling uncertainty due to short sample size. It is crucial to quantify such uncertainty and its impacts on reservoir routing. In this study, a copula-based parametric bootstrapping uncertainty (C-PBU) method is proposed to characterize the bivariate quantile estimation uncertainty and the impact of such uncertainty on the highest reservoir water level is also investigated. The Geheyan reservoir in China is selected as a case study. Four evaluation indexes, i.e. area of confidence region, mean horizontal deviation, mean vertical deviation and average Euclidean distance, are adopted to quantify the quantile estimation uncertainty. The results indicate that the uncertainty of quantile estimation and the highest reservoir water level increases with larger return period. The 90% confidence interval (CI) of highest reservoir water level reaches 1.56 m and 2.52 m under 20-year and 50-year JRP respectively for the sample size of 100. It is also indicated that the peak over threshold (POT) sampling method contribute to uncertainty reduction comparing with the annual maximum (AM) method. This study could provide not only the point estimator of design floods and corresponding design water level, but also the rich uncertainty information (e.g. 90% confidence interval) for the references of reservoir flood risk assessment, scheduling and management.