Conditional Value-at-Risk for Nonstationary Streamflow and Its Application for Derivation of the Adaptive Reservoir Flood Limited Water Level

Abstract

The existing risk-based approaches for quantifying expected flood damage loss may not be suitable in the changing environment when streamflow becomes nonstationary. Conditional value-at-risk (CVaRα), a modified form of value-at-risk (VaRα), that takes account of both the magnitude and probability of damage loss has been widely applied to water resources issues. However, quantification of CVaRα under nonstationary conditions has not been addressed in the literature. This study proposes an approach that incorporates CVaRα in quantifying the flood damage loss under nonstationary conditions, and then CVaRαn associated with flood risk over a specified time horizon is deduced. To illustrate the concept of CVaRα, this study applies CVaRα into the adaptive flood limited water level (FLWL) optimization. With China’s Three Gorges Reservoir (TGR) as a case study, the results indicate that (1) the CVaRα not only can represent the possible flood damage loss over a time horizon in the future, but also can reflect the flood risk probability by choosing a suitable confidence level; and (2) it is reliable to take account of the CVaRα value as a constraint when studying the adaptive FLWL optimization problem.