Tracking the Uncertainty Propagation Process Between Hydrological Forecasting and Reservoir Real-Time Optimal Operation

The inherent uncertainty in hydrological forecasting poses a challenge for reservoir real-time optimal operation. In this paper, a stochastic framework is proposed to track the uncertainty propagation process between hydrological forecasting and reservoir operation. The framework simulates the comprehensive uncertainty of hydrological forecasts in the form of ensemble forecasts and scenario trees. Based on the derived analytic relationship between the performance metric Nash-Sutcliffe efficiency coefficient (NSE) and forecast uncertainty probability distribution, we use three methods (two are commonly used classical methods and one is the Gaussian copula method) simultaneously to generate inflow forecast ensembles. Compared with the two classical methods, the Gaussian copula method additionally takes into account the temporal correlation of reservoir inflows. Then, the neural gas method is employed to transform the generated ensembles into a scenario tree, which is further used as an input for reservoir stochastic optimization. To improve the adaptability to uncertainties in inflow forecasts, we establish a stochastic optimization model that optimizes the expectation of objective values over all scenarios. Meanwhile, we propose a parallel differential evolution (DE) algorithm based on parallel computing techniques for solving the stochastic optimization model efficiently. Risk assessment is performed to capture the uncertainty and corresponding risk associated with the reservoir optimal decision. The proposed framework is demonstrated in a flood control reservoir system in China. Furthermore, we conduct several numerical experiments to explore the effect of forecast uncertainty level and temporal correlation on reservoir real-time optimal operation. The results indicate that the temporal correlation of inflows must be considered in inflow stochastic simulation and reservoir stochastic optimization, otherwise the operational risk is likely to be overestimated or underestimated, thus leading to operation failures. Based on the risk simulation surface, reservoir operators can examine the robustness of operational decisions and thus make more reliable final decisions.