Abstract
Variable-parameter Muskingum models emerge as a highly efficient approach among the prevalent hydrological flood routing methods, owing to their accuracy and robustness. This research introduces a novel partitioning framework aimed at refining outcomes from a nonlinear variable-parameter Muskingum model by introducing fuzzification to the adjacent sub-periods of the inflow hydrograph. The results prove the efficacy of the proposed method in enhancing the accuracy of routed outflow, aligning well with the inherent characteristics of a flooding event. Validation of the newly introduced fuzzified nonlinear variable-parameter Muskingum model was conducted using four distinct case studies from the literature, including Wilson's data, the flood events in Rivers Wye and Wyre, and Viessman and Lewis' data. The evaluation of the proposed framework's effectiveness utilized the Sum of Squared Deviations (SSQ) as the objective function of the model, along with six different supplemental metrics. The results demonstrated a meaningful increase in the accuracy of the nonlinear Muskingum model for the respective cases studied. The findings imply that the proposed partitioning framework is adaptable to the variable-parameter Muskingum models with an intensity-based partitioning technique, thereby advancing the results of this conventional flood routing method.
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References
Akbari R, Hessami-Kermani M-R (2023) A new method for dividing flood period in the variable-parameter Muskingum models. Hydrol Res 53:241–257. https://doi.org/10.2166/nh.2021.192
Akbari R, Hessami-Kermani M-R, Shojaee S (2020) Flood routing: improving outflow using a new nonlinear Muskingum model with four variable parameters coupled with PSO-GA algorithm. Water Resour Manag 34:3291–3316. https://doi.org/10.1007/s11269-020-02613-5
Al-Bedyry N, Mergan M, Rasheed M, Al-Khafaji Z, Al-Husseinawi FN (2023) The use of genetic expression programming to optimize the parameters of the Muskingum method comparison with numerical methods, Euphrates river a case study. Arch Civ Eng 2023:507–519. https://doi.org/10.24425/ace.2023.146094
Atashi V, Barati R, Lim YH (2023) Improved river flood routing with spatially variable exponent Muskingum model and sine cosine optimization algorithm. Environ Process 10(3):42. https://doi.org/10.1007/s40710-023-00658-3
Ayvaz MT, Gurarslan G (2017) A new partitioning approach for nonlinear Muskingum flood routing models with lateral flow contribution. J Hydrol 553:142–159. https://doi.org/10.1016/j.jhydrol.2017.07.050
Azadnia A, Zahraie B (2010) Optimization of nonlinear Muskingum method with variable parameters using multi-objective particle swarm optimization. EWRI Congress 2010: Challenges of Change, pp. 2278–2284. https://doi.org/10.1061/41114(371)233
Barati R (2013) Application of excel solver for parameter estimation of the nonlinear Muskingum models. KSCE J Civ Eng 17:1139–1148. https://doi.org/10.1007/s12205-013-0037-2
Chu HJ, Chang LC (2009) Applying particle swarm optimization to parameter estimation of the nonlinear Muskingum model. J Hydrol Eng 14:1024–1027. https://doi.org/10.1061/(ASCE)HE.19435584.0000070
De Jong KA (1975) An analysis of the behavior of a class of genetic adaptive systems. University of Michigan
Easa SM (2013) Improved nonlinear muskingum model with variable exponent parameter. J Hydrol Eng 18:1790–1794. https://doi.org/10.1061/(asce)he.1943-5584.0000702
Easa SM (2014a) Closure to “Improved Nonlinear Muskingum Model with Variable Exponent Parameter” by Said M. Essa. J Hydrol Eng. https://doi.org/10.1061/(asce)he.1943-5584.0001041
Easa SM (2014b) New and improved four-parameter nonlinear Muskingum model. Proc Inst Civ Eng Water Manag 167:288–298. https://doi.org/10.1680/wama.12.00113
Farzin S, Farzin S, Singh VP, Karami H, Farahani N, Ehteram M, Kisi O, Allawi MF, Mohd NS, El-Shafie A (2018) Flood routing in river reaches using a three-parameter Muskingum model coupled with an improved bat algorithm. Water J 10:1130. https://doi.org/10.3390/w10091130
Gill MA (1978) Flood routing by the Muskingum method. J Hydrol 36:353–363. https://doi.org/10.1016/0022-1694(78)90153-1
Holland JH (1973) Genetic algorithms and the optimal allocation of trials. SICOMP 2(2):88–105. https://doi.org/10.1137/0202009
Kang L, Zhou L, Zhang S (2017) Parameter estimation of two improved nonlinear Muskingum models considering the lateral flow using a hybrid algorithm. Water Resour Manag 31:4449–4467. https://doi.org/10.1007/s11269-017-1758-7
Karahan H (2014) Discussion of “Improved Nonlinear Muskingum Model with Variable Exponent Parameter” by Said M. Easa. J Hydrol Eng. https://doi.org/10.1061/(asce)he.1943-5584.0001045
Karahan H, Gurarslan G, Geem ZW (2013) Parameter estimation of the nonlinear Muskingum flood routing model using a hybrid harmony search algorithm. J Hydrol Eng 18:352–360. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000608
Karahan H, Gurarslan G, Geem ZW (2015) A new nonlinear Muskingum flood routing model incorporating lateral flow. Eng Optimiz 47:737–749. https://doi.org/10.1080/0305215X.2014.918115
Kim JH, Geem ZW, Kim ES (2001) Parameter estimation of the nonlinear Muskingum model using harmony search. JAWRA 37(5):1131–1138. https://doi.org/10.1111/j.1752-1688.2001.tb03627.x
Lee EH (2021) Development of a New 8-Parameter Muskingum flood routing model with modified inflows. Water J 13:3170. https://doi.org/10.3390/w13223170
McCarthy GT (1938) The unit hydrograph and flood routing. Proc of NAC US Army Corps Eng 1938:608–609
Mirzazadeh P, Akbari GH, Ghodsi M (2022) Investigating Muskingum-Cunge Method Application of Different Schemes in Flood Routing. JHE 6(11):42–48. https://doi.org/10.22111/JHE.2023.45568.1092
Mohan S (1997) Parameter estimation of nonlinear Muskingum models using genetic algorithm. Hydraul Eng 123:137–142. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(137)
Moradi E, Yaghoubi B, Shabanlou S (2023) A new technique for flood routing by nonlinear Muskingum model and artificial gorilla troops algorithm. Appl Water Sci 13(2):49. https://doi.org/10.1007/s13201-022-01844-8
Mohaideen Abdul Kadhar K, Natarajan N, Vasudevan M, Gurusamy S (2022) Parameter evaluation of a nonlinear Muskingum model using a constrained self-adaptive differential evolution algorithm. Water Pract Technol 17(11):2396–2407. https://doi.org/10.2166/wpt.2022.137
NERC (1975) Natural Environment Research Council, Flood studies report (Vol. 3). Wallingford, UK
Niazkar M, Afzali SH (2016) Application of new hybrid optimization technique for parameter estimation of new improved version of Muskingum model. Water Resour Manag 30:4713–4730. https://doi.org/10.1007/s11269-016-1449-9
Norouzi H, Bazargan J (2021) Effects of uncertainty in determining the parameters of the linear Muskingum method using the particle swarm optimization (PSO) algorithm. J Water Clim Chang 12:2055–2067. https://doi.org/10.2166/wcc.2021.227
O’Donnell T (1985) A direct three-parameter Muskingum procedure incorporating lateral inflow. Hydrol Sci J 30:479–496. https://doi.org/10.1080/02626668509491013
Okkan U, Kirdemir U (2020) Locally tuned hybridized particle swarm optimization for the calibration of the nonlinear Muskingum flood routing model. J Water Clim Chang 11:343–358. https://doi.org/10.2166/wcc.2020.015
Spiliotis M, Sordo-Ward A, Garrote L (2021) Estimation of fuzzy parameters in the linear Muskingum model with the aid of particle swarm optimization. Sustain 13(13):7152. https://doi.org/10.3390/su13137152
Perumal M, Tayfur G, Rao CM, Gurarslan G (2017) Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods. J Hydrol 546:437–449. https://doi.org/10.1016/j.jhydrol.2017.01.025
Viessman W, Lewis GL (2002) Introduction to hydrology. New Jersey, USA
Wang WC, Tian WC, Xu DM, Chau KW, Ma Q, Liu CJ (2023) Muskingum models’ development and their parameter estimation: a state-of-the-art review. Water Resour Manag 25:1–22. https://doi.org/10.1007/s11269-023-03493-1
Wilson, EM (1974) Engineering Hydrology. Hampshire, UK
Zhang S, Kang L, Zhou L, Guo X (2017) A new modified nonlinear Muskingum model and its parameter estimation using the adaptive genetic algorithm. Hydrol Res 48:17–27. https://doi.org/10.2166/nh.2016.185
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All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by Amirfarhad Aletaha, Masoud-Reza Hesami-Kermani, and Reyhaneh Akbari. Amirfarhad Aletaha: Writing—original draft. Masoud-Reza Hessami-Kermani: Writing—original draft, Project administration. Reyhane Akbari: Project supervision.
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Aletaha, A., Hessami-Kermani, MR. & Akbari, R. Enhancing Flood Routing Accuracy: A Fuzzified Approach to Nonlinear Variable-Parameter Muskingum Model. Water Resour Manage (2024). https://doi.org/10.1007/s11269-024-03846-4
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DOI: https://doi.org/10.1007/s11269-024-03846-4