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Inverse Flood Routing Using Simplified Flow Equations

Author

Listed:
  • Dariusz Gąsiorowski

    (Gdansk University of Technology)

  • Romuald Szymkiewicz

    (Institute of Hydro-Engineering of the Polish Academy of Sciences)

Abstract

The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve the hydrograph at the upstream end, an inverse solution of the afore mentioned equations with backward integration in the x direction is carried out. The numerical solution of the kinematic wave equation and the Muskingum equation bases on the finite difference scheme. It is shown that both these equations are able to provide satisfying results because of their exceptional properties related to numerical diffusion. In the paper, an alternative approach to solve the inverse routing using the diffusive wave model is also presented. To this end, it is described by a convolution which involves the instantaneous unit hydrograph (IUH) corresponding to the linear diffusive wave equation. Consequently, instead of a solution of partial or ordinary differential equations, the integral equation with Laguerre polynomials, used for the expansion of the upstream hydrograph, is solved. It was shown that the convolution approach is more reliable comparing to the inverse solution of the simplified models in the form of differential equations.

Suggested Citation

  • Dariusz Gąsiorowski & Romuald Szymkiewicz, 2022. "Inverse Flood Routing Using Simplified Flow Equations," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(11), pages 4115-4135, September.
    • Handle: RePEc:spr:waterr:v:36:y:2022:i:11:d:10.1007_s11269-022-03244-8
    DOI: 10.1007/s11269-022-03244-8
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    References listed on IDEAS

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    1. G. Zucco & G. Tayfur & T. Moramarco, 2015. "Reverse Flood Routing in Natural Channels using Genetic Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4241-4267, September.
    2. Dariusz Gąsiorowski & Romuald Szymkiewicz, 2020. "Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(10), pages 3147-3164, August.
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    Cited by:

    1. Wen-chuan Wang & Wei-can Tian & Dong-mei Xu & Kwok-wing Chau & Qiang Ma & Chang-jun Liu, 2023. "Muskingum Models’ Development and their Parameter Estimation: A State-of-the-art Review," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(8), pages 3129-3150, June.

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