Abstract
In existing studies, external factors, such as hydrologic, hydraulic, and decision-making uncertainties, have been widely recognized as major risk source in reservoir flood routing. There are few researches focused on the intrinsic uncertainties which rooted in the reservoir flood routing modeling, for instance, the sensitivity of the water level to the initial condition in the passage of flood routing. The governing equation of the reservoir flooding routing is a first-order Ordinary Differential Equation, which can be simplified as a water balance equation. A deterministic mathematical model can be set up by combining the governing equation with the flood operating rules and the water level-storage relationship functions of reservoirs. As far as the deterministic model is concerned, nonlinear behaviors and their characteristics in different stages of flood routing were discussed for the reservoir with multistage operating rule by simulations in this paper. The results showed that the state variables (i.e., water level and discharge rate) of the system are not sensitive to initial small perturbations in the free overflow stage. However, in the confined outflow stage, which usually appears in segmented flood operating rules designed for multi-purpose flood control, a small initial disturbance can grow gradually over time with the evolution of the system, as a result, a large deviation of the water level and discharge rate of the reservoir could developed at the end of the simulation. Additionally, some case studies were conducted in this paper to demonstrate this nonlinear response of flood routing to the initial disturbance. Although the nonlinear behaviors in reservoir flood routing are still subject to further study, once again, it proves that uncertainties appear there indeed in a deterministic system according to this research. The results of this paper indicate that the nonlinear responses and the corresponding uncertainties rooted in it may have to be considered deliberately in different stages of flood routing, because this could has potential impacts not only on reservoir flood control but also on the reliability of the risk assessment.
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ACKNOWLEDGMENTS
The authors acknowledge the financial support granted by the Fundamental Research Funds for the Central Universities, CHD (nos. 300102299206, 300102269201), and the key research and development project of Shaanxi Province(no. 2019SF-237), China.
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Zhao Liu, Yu, Y., Wang, L. et al. Discussion on Nonlinear Behaviors in Reservoir Flood Routing Modeling and Derived Uncertainties. Water Resour 47, 855–864 (2020). https://doi.org/10.1134/S0097807820050231
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DOI: https://doi.org/10.1134/S0097807820050231