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

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 ($CVa{R}_{\alpha }$ ), a modified form of value-at-risk ($Va{R}_{\alpha }$ ), that takes account of both the magnitude and probability of damage loss has been widely applied to water resources issues. However, quantification of $CVa{R}_{\alpha }$ under nonstationary conditions has not been addressed in the literature. This study proposes an approach that incorporates $CVa{R}_{\alpha }$ in quantifying the flood damage loss under nonstationary conditions, and then $CVa{R}_{\alpha }^n$ associated with flood risk over a specified time horizon is deduced. To illustrate the concept of $CVa{R}_{\alpha }$ , this study applies $CVa{R}_{\alpha }$ 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 $CVa{R}_{\alpha }$ 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 $CVa{R}_{\alpha }$ value as a constraint when studying the adaptive FLWL optimization problem.