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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation

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  • Dariusz Gąsiorowski

    (Gdańsk University of Technology)

  • Romuald Szymkiewicz

    (Gdańsk University of Technology)

Abstract

Two nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It is shown that the difference between the results provided by both versions of the nonlinear Muskingum equation depends on the longitudinal bed slope of a channel. For an increasing slope, when a propagating wave becomes more kinematic, the value of the exponent considered as the free parameter tends to its value resulting from the kinematic wave theory. Consequently, when the character of an open channel flow tends to a kinematic one, the dimensionally inconsistent version of the nonlinear Muskingum equation becomes a consistent one. The results of the numerical analysis suggest that apart from the parameters involved in the Muskingum equation, usually considered as free, the parameters of the numerical method of the solution (the number of reservoirs and the time step) should be considered also as free parameters. This conclusion results from the fundamental property of the Muskingum equation, relating to the numerical roots of the wave attenuation process. All numerical examples and tests relate to the solutions of the system of Saint Venant equations, considered as the benchmark.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:waterr:v:34:y:2020:i:10:d:10.1007_s11269-020-02599-0
    DOI: 10.1007/s11269-020-02599-0
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    References listed on IDEAS

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    1. Omid Bozorg-Haddad & Mehri Abdi-Dehkordi & Farzan Hamedi & Maryam Pazoki & Hugo A. Loáiciga, 2019. "Generalized Storage Equations for Flood Routing with Nonlinear Muskingum Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2677-2691, June.
    2. Ling Kang & Liwei Zhou & Song Zhang, 2017. "Parameter Estimation of Two Improved Nonlinear Muskingum Models Considering the Lateral Flow Using a Hybrid Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4449-4467, November.
    3. Xiaohui Yuan & Xiaotao Wu & Hao Tian & Yanbin Yuan & Rana Muhammad Adnan, 2016. "Parameter Identification of Nonlinear Muskingum Model with Backtracking Search Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(8), pages 2767-2783, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Chengpeng Lu & Keyan Ji & Wanjie Wang & Yong Zhang & Tema Koketso Ealotswe & Wei Qin & Jiayun Lu & Bo Liu & Longcang Shu, 2021. "Estimation of the Interaction Between Groundwater and Surface Water Based on Flow Routing Using an Improved Nonlinear Muskingum-Cunge Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(8), pages 2649-2666, June.

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