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Muskingum Models’ Development and their Parameter Estimation: A State-of-the-art Review

Author

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  • Wen-chuan Wang

    (North China University of Water Resources and Electric Power)

  • Wei-can Tian

    (North China University of Water Resources and Electric Power)

  • Dong-mei Xu

    (North China University of Water Resources and Electric Power)

  • Kwok-wing Chau

    (The Hong Kong Polytechnic University)

  • Qiang Ma

    (China Institute of Water Resources and Hydropower Research)

  • Chang-jun Liu

    (China Institute of Water Resources and Hydropower Research)

Abstract

River flood routing is an important issue in current water resources management. As a popular hydrological flood routing method, Muskingum model has always been the dominant method of flood routing. This paper reviews the development of Muskingum model and the research status of its parameter estimation. The characteristics and relationships of different types of Muskingum models are compared, and it is found that the combination of mathematical techniques and evolutionary algorithms has shown good results in parameter estimation in recent years. In addition, this paper also gives a brief overview of six accuracy evaluation criteria and nine research case data sets commonly used in the literature. It also introduces some challenges of the Muskingum model and new trends in future research, which should interest researchers and engineers.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:waterr:v:37:y:2023:i:8:d:10.1007_s11269-023-03493-1
    DOI: 10.1007/s11269-023-03493-1
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    References listed on IDEAS

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    1. Omid Bozorg Haddad & Farzan Hamedi & Hosein Orouji & Maryam Pazoki & Hugo Loáiciga, 2015. "A Re-Parameterized and Improved Nonlinear Muskingum Model for Flood Routing," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3419-3440, July.
    2. Reyhaneh Akbari & Masoud-Reza Hessami-Kermani & Saeed Shojaee, 2020. "Flood Routing: Improving Outflow Using a New Non-linear Muskingum Model with Four Variable Parameters Coupled with PSO-GA Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(10), pages 3291-3316, August.
    3. Majid Niazkar & Seied Hosein Afzali, 2016. "Application of New Hybrid Optimization Technique for Parameter Estimation of New Improved Version of Muskingum Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(13), pages 4713-4730, October.
    4. Wanlong Yang & Jun Wang & Jueyi Sui & Fangxiu Zhang & Baosen Zhang, 2019. "A Modified Muskingum Flow Routing Model for Flood Wave Propagation during River Ice Thawing-Breakup Period," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(14), pages 4865-4878, November.
    5. Mike Spiliotis & Alvaro Sordo-Ward & Luis Garrote, 2021. "Estimation of Fuzzy Parameters in the Linear Muskingum Model with the Aid of Particle Swarm Optimization," Sustainability, MDPI, vol. 13(13), pages 1-26, June.
    6. 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.
    7. 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.
    8. Ling Kang & Song Zhang, 2016. "Application of the Elitist-Mutated PSO and an Improved GSA to Estimate Parameters of Linear and Nonlinear Muskingum Flood Routing Models," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-20, January.
    9. 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.
    10. Ting Wei & Songbai Song, 2022. "Comparison of Frequency Calculation Methods for Precipitation Series Containing Zero Values," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(2), pages 527-550, January.
    11. 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.
    12. Zhou Sheng & Aijia Ouyang & Li-Bin Liu & Gonglin Yuan, 2014. "A Novel Parameter Estimation Method for Muskingum Model Using New Newton-Type Trust Region Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, December.
    13. 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.
    14. 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.
    15. Hadi Norouzi & Jalal Bazargan, 2022. "Calculation of Water Depth during Flood in Rivers using Linear Muskingum Method and Particle Swarm Optimization (PSO) Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(11), pages 4343-4361, September.
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