Estimation of Nonlinear Muskingum Parameters in Flood Routing Using Graphical Method

Articles in Press

Document Type : Research Paper

Authors

1 Shahrekord University

2 Gorgan University of Agricultural Sciences and Natural Resources

10.22059/jwim.2025.395793.1233

Abstract

Flood Routing is one of the fundamental topics in water resources system management and flood control engineering. The Muskingum model is among the most well-known and widely used hydrological routing methods. In the nonlinear Muskingum method, three parameters must be estimated: the storage coefficient (K), the weighting factor for inflow and outflow (χ), and the exponent of the storage term (m). In contrast, the linear Muskingum method only involves the first two parameters (K and χ), making it simpler with one less variable. This research focuses on presenting a simple graphical method for estimating the parameters of the nonlinear Muskingum model. To assess the accuracy and reliability of the proposed graphical method, results were compared with those obtained from Excel's SOLVER tool, which is considered a more precise technique. The graphical method was applied to three flood events. The results showed that the parameters derived using the proposed method were very close to those estimated using SOLVER. Notably, across all flood events, both the performance criteria and hydrographs indicated that the graphical method for the nonlinear Muskingum model outperformed its linear counterpart in terms of accuracy. Furthermore, comparisons between observed peak discharge and the estimated peak discharge revealed that, in all cases, the nonlinear Muskingum model provided values closer to the actual recorded data than the linear model. For instance, the Nash-Sutcliffe Efficiency (NSE) values obtained for the Wilson, Wye, and Karun flood events were as follows: Wilson Flood: 0.19 (linear graphical), 0.35 (nonlinear graphical), 0.96 (SOLVER); Wye Flood: 0.86 (linear graphical), 0.95 (nonlinear Graphical), 0.97 (Solver); Karun Flood: 0.62 (linear graphical), 0.98 (nonlinear graphical), 0.99 (SOLVER).

Keywords

Main Subjects

Water and Irrigation Management

Articles in Press, Accepted Manuscript
Available Online from 18 August 2025

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