An analytical two-stage risk analysis model in the real-time reservoir operation

•An analytical model is built considering flood risk beyond the forecast horizon.•The effective forecast horizon is captured to balance forecast accuracy and length.•Larger forecast uncertainties may not lead to greater flood risks. Flood risk analysis is vital for real-time reservoir operation. The reservoir operation horizon (OH) is generally longer than the streamflow forecast horizon (FH), while the gap between the FH and the OH was seldom considered in analytical flood risk models. This study develops an analytical two-stage risk model covering the period within the FH (the first stage) and from the FH to the OH (the second stage). In the first stage, the errors in forecasted streamflow and reservoir water level-storage relationships are considered using the multinormal distribution within the FH. In the second stage, design flood hydrographs are used to estimate the flood risk by conducting reservoir routing. Finally, the total flood risk is calculated by using the copula method to combine the flood risks from the first and second stages. Results for a case study using China’s Three Gorges Reservoir indicate that an effective FH can be identified to minimize flood risk, and balance between the forecast accuracy and length of the horizon. The length of the effective FH is not fixed and depends on reservoir inflow. Moreover, larger errors will not always lead to greater flood risks. The proposed method provides useful information on flood risk for real-time reservoir operation.