Improved Nonlinear Muskingum Model with Variable Exponent Parameter
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VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 18, Issue 12
Abstract
The nonlinear Muskingum model has three parameters (storage parameter, weighting parameter, and exponent parameter) that are assumed in model estimation to be constant. The exponent parameter, which has no physical meaning, represents the average nonlinear behavior of the flood during the entire routing period. To address the variations of nonlinearity during the routing period, this paper considers a variable exponent parameter that varies with the inflow level. The boundaries of the inflow levels are considered to be dimensionless parameters. The problem is formulated as a mathematical optimization model that minimizes the sum of the squared (SSQ) or absolute deviations between the observed and estimated outflows. An efficient spreadsheet-based software is implemented. The proposed model was applied by using three examples involving single peak, multipeak, and nonsmooth hydrographs. The results show that the range of the optimal exponent parameters is small, yet the improvement in the fit of the nonlinear Muskingum model is substantial; the SSQ reduction reaches 35%, compared with the case of a constant exponent parameter. The proposed model should be of interest to researchers and engineers working in the area of flood management.
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Acknowledgments
The author is grateful to anonymous reviewers for their thorough and most helpful comments.
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Published In
Journal of Hydrologic Engineering
Volume 18 • Issue 12 • December 2013
Pages: 1790 - 1794
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Mar 19, 2012
Accepted: Aug 7, 2012
Published online: Aug 18, 2012
Discussion open until: Jan 18, 2013
Published in print: Dec 1, 2013
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