Development of Nonlinear Muskingum Model and its Compare with HEC-RAS Model for Flood Routing in Rivers

Document Type : Research Article



Flood routing in rivers is a mathematical procedure to determine flow hydrograph at a point in a river. One of routing methods is based on solution of Saint-Venant equations for unsteady flows. Because this method is very complex and need to more information of river, other methods with simple calculations and reasonably accurate results have been extended and give generally satisfactory results for hydrologist researchers and need to lower information of river. Muskingum model is one of these methods that accuracy in evaluation of its parameters effects on predicting flood hydrograph, especially peak rate of flow. As far as genetic algorithm is an appropriate solution to determine optimized nonlinear Muskingum coefficients, in this study we used this method to determine optimized coefficients in MATLAB and for a wide range of hydrographs getting from HEC-RAS software. Then the nonlinear Muskingum coefficients were presented as functions of river characteristics and inflow hydrograph. The model has been developed using the functions and solving of differential continuty equation with Rung-Kutta order 4. To determine the accuracy of the model, measured hydrographs of 5 floods in a reach, were compared to hydrographs computed by the model and HEC-RAS software and the results were analyzed using RMSE factor and correlation coefficient. Results indicate that there was no significant diference between the model and HEC-RAS .


  1. قبادیان، رسول (1387). «مدل ریاضی روندیابی هیدرولیکی سیلاب در رودخانۀ قره­سو با استفاده از حل عددی معادلات جریان غیرماندگار». هفتمین کنفرانس هیدرولیک ایران، ایران، تهران، آبان ماه.
  2. مرادی، حمیدرضا؛ وفاخواه، مهدی؛ اکبری باویل، علی (1386). «مقایسۀ روندیابی سیل با دو روش ماسکینگام و ماسکینگام-کانژ در بخشی از رودخانۀ لیقوان». مجله علوم و فنون کشاورزی و منابع طبیعی، شمارۀ 42 :342-335.
    1. Soentoro, Edya (1991). Comparison of Flood Routing Methods, Master of Applied Science. Department of Civil Engineering, University of British Columbia, pp.106.
    2. Patricia, C.; Raimundo, S. (2005). “Solution of Saint-Venant Equation to Study Flood in Rivers through Numerical Methods”. 25th Annual American Geophysical Union Hydrology Days, USA, Colorado, March.
    3. Maidment, David R. (1992). Hand Book of Hydrology. New York, McGraw-Hill, pp. 1424.
    4. Chow, Ven Te; Maidment, David R.; Mays, Larry W. (1998). Applied Hydrology. New York, McGraw-Hill, pp. 572.
    5. Knebl, M.R.; Yang, Z.L.; Hutchison, K.; Maidment, D.R. (2005). “Regional Scale Flood Modeling Using NEXRAD Rainfall, GIS, and HEC-HMS/RAS: A Case Study for the San Antonio River Basin Summer 2002 Storm Event”. Journal of Environmental Management, 75, 325-336.
    6. Sholtes, Joel (2009). Hydraulic Analysis of Stream Restoration on Flood Wave Propagation. Master of Applied Science, Department of Physical Geography, University of North Carolina.
    7. Ponce, V.M.; Lugo, A. (2001). “Modeling Looped Rating in Muskingum-Cunge Routing”. Journal of Hydrologic Engineering (ASCE), 6(2), 119-124.

10. and Flood Routing”. In Proceedings of the Conference of the North Atlantic Division, U. S. Engineer Department, USA, New London, June.

11. Gill, M.A. (1978). “Flood Routing by Muskingum Method”. Journal of Hydrology, 36, 353-363.

12. Yoon, J.; Padmanabhan, G. (1993). “Parameter Estimation of Linear and Nonlinear Muskingum Models”. Journal of Water Resources Planning and Management, 119(5), 600-610.

13. Wilson, Eric Montgomery (1990). Engineering Hydrology. Washington, Scholium Intl, pp. 348.

14. Samani, H.M.V.; Shamsipour, G.A. (2004). “Hydrologic Flood Routing in Branched River Systems via Nonlinear Optimization”. Journal of Hydraulic Research, 42(1), 55-59.

15. Alhumoud, J.M.; Esen, I.M. (2006). “Approximate Methods for the Estimation of Muskingum Flood Routing Parameters”. Water Resources Management, 20(6), 979-990.

16. Karahan, H. (2012). “Predicting Muskingum Flood Routing Parameters Using Spreadsheets”. Computational Applications in Engineering Education, 20(2), 280-286.

17. Tung, Y.K. (1984). “River Flood Routing by Nonlinear Muskingum Method”. Journal of Hydraulics Division, 111(12), 1447-1460.

18. Mohan, S. (1997). “Parameter Estimation of Nonlinear Muskingum Models Using Genetic Algorithm”. Journal of Hydraulic Engineering (ASCE), 123(2), 137-142.

19. Cunge, J.A. (1969). “On the Subject of a Flood Propagation Computation Method (Muskingum Method)”. Journal of Hydraulic Research, 7(2), 205-230.

20. Goldberg, David E. (1989). Genetic Algorithm in Search, Optimization and Machine Learning. Boston, Addison Wesley, pp. 438.

Volume 1, Issue 2 - Serial Number 2
October 2014
Pages 111-122
  • Receive Date: 06 June 2014
  • Revise Date: 03 January 2015
  • Accept Date: 17 September 2014
  • First Publish Date: 23 September 2014
  • Publish Date: 23 September 2014