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KSCE Journal of Civil Engineering

, Volume 17, Issue 5, pp 1139–1148 | Cite as

Application of excel solver for parameter estimation of the nonlinear Muskingum models

  • Reza BaratiEmail author
Article

Abstract

The Muskingum model continues to be a popular procedure for river flood routing. An important aspect in nonlinear Muskingum models is the calibration of the model parameters. The current study presents the application of commonly available spreadsheet software, Microsoft Excel 2010, for the purpose of estimating the parameters of nonlinear Muskingum routing models. Main advantage of this approach is that it can calibrate the parameters using two different ways without knowing the exact details of optimization techniques. These procedures consist of (1) Generalized Reduced Gradient (GRG) solver and (2) evolutionary solver. The first one needs the initial values assumption for the parameter estimation while the latter requires the determination of the algorithm parameters. The results of the simulation of an example that is a benchmark problem for parameter estimation of the nonlinear Muskingum models indicate that Excel solver is a promising way to reduce problems of the parameter estimation of the nonlinear Muskingum routing models. Furthermore, the results indicate that the efficiency of Excel solver for the parameter estimation of the models can be increased, if both GRG and evolutionary solvers are used together.

Keywords

flood routing hydrologic model spreadsheets parameter estimation 

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References

  1. Akbari, G. H. and Barati, R. (2012). “Comprehensive analysis of flooding in unmanaged catchments.” Proceedings of the Institution of Civil Engineers-Water Management, p. 165.Google Scholar
  2. Akbari, G., H. Nezhad, A. H., and Barati, R. (2012). “Developing a model for analysis of uncertainties in prediction of floods.” Journal of Advanced Research, Vol. 3, No. 1, pp. 73–79.CrossRefGoogle Scholar
  3. Al-Humoud, J. M. and Esen, I. I. (2006). “Approximate methods for the estimation of Muskingum flood routing parameters.” Water Resources Management, Vol. 20, No. 6, pp. 979–990.CrossRefGoogle Scholar
  4. ASCE Task Committee on Definition of Criteria for Evaluation of Watershed Models of the Watershed Management Committee, Irrigation and Drainage Division. (1993). “Criteria for evaluation of watershed models.” Journal of Irrigation and Drainage Engineering, ASCE, Vol. 119, No. 3, pp. 429–442.CrossRefGoogle Scholar
  5. Barati, R. (2011). “Discussion of Parameter estimation for nonlinear Muskingum model based on immune clonal selection algorithm.” Journal of Hydrologic Engineering, ASCE, Vol. 16, No. 4, pp. 391–393.CrossRefGoogle Scholar
  6. Bhattacharjya, R. K. (2011). “Solving groundwater flow inverse problem using spreadsheet solver.” Journal of Hydrologic Engineering, ASCE, Vol. 16, No. 5, pp. 472–477.CrossRefGoogle Scholar
  7. Choudhury, P. (2007). “Multiple inows muskingum routing model” Journal of Hydrologic Engineering, ASCE, Vol. 12, No. 5, pp. 473–481.CrossRefGoogle Scholar
  8. Choudhury, P., Shrivastava, R. K., and Narulkar, S. M. (2002). “Flood routing in river networks using equivalent muskingum inow.” Journal of Hydrologic Engineering, ASCE, Vol. 7, No. 6, pp. 413–419.CrossRefGoogle Scholar
  9. Chow, V. T. (1959). “Open channel hydraulics.” McGraw-Hill, New York, p. 680.Google Scholar
  10. Chu, H. J. (2009). “The Muskingum flood routing model using a neurofuzzy approach.” KSCE Journal of Civil Engineering, KSCE, Vol. 13, No. 5, pp. 371–376.CrossRefGoogle Scholar
  11. Chu, H. J. and Chang, L. C. (2009). “Applying particle swarm optimization to parameter estimation of the nonlinear Muskingum model.” Journal of Hydrologic Engineering, ASCE, Vol. 14, No. 9, pp. 1024–1027.CrossRefGoogle Scholar
  12. Das, A. (2004). “Parameter estimation for muskingum models.” Journal of Irrigation and Drainage Engineering, ASCE, Vol. 130, No. 2, pp. 140–147.CrossRefGoogle Scholar
  13. Das, A. (2007). “Chance-constrained optimization-based parameter estimation for Muskingum models.” Journal of Irrigation and Drainage Engineering, ASCE, Vol. 133, No. 5, pp. 487–494.CrossRefGoogle Scholar
  14. Fontane, D. (2001). “Multi-objective simulation and optimization of reservoir operation using Excel.” Proceeding of the Second Federal Interagency Hydrologic Modeling Conference, Las Vegas, NV, USA.Google Scholar
  15. Geem, Z. W. (2006). “Parameter estimation for the nonlinear Muskingum model using the BFGS technique.” Journal of Irrigation and Drainage Engineering, ASCE, Vol. 132, No. 5, pp. 474–478.CrossRefGoogle Scholar
  16. Gill, M. A. (1978). “Flood routing by Muskingum method.” Journal of hydrology, Vol. 36, No. 3–4, pp. 353–363.CrossRefGoogle Scholar
  17. Grabow G. L. and McCornick P. G. (2007). “Planning for water allocation and water quality using a spreadsheet-based model.” Journal of Water Resources Planning and Management, ASCE, Vol. 133, No. 6, pp. 560–564.CrossRefGoogle Scholar
  18. Huddleston, D. H., Alarcon, V. J., and Chen, W. (2004). “Water distribution network analysis using Excel.” Journal of Hydraulic Engineering, ASCE, Vol. 130, No. 10, pp. 1033–1035.CrossRefGoogle Scholar
  19. Kim, J. H., Geem, Z. W., and Kim, E. S. (2001). “Parameter estimation of the nonlinear Muskingum model using harmony search.” Journal of the American Water Resources Association, Vol. 37, No. 5, pp. 1131–1138.CrossRefGoogle Scholar
  20. Lasdon, L. S. and Smith, S. (1992). “Solving sparse nonlinear programs using GRG.” ORSA Journal on Computing, Vol. 4, No. 1, pp. 2–15.MathSciNetzbMATHCrossRefGoogle Scholar
  21. Lasdon, L. S., Waren, A. D., Jain, A., and Ratner, M. (1978). “Design and testing of a generalized reduced gradient code for nonlinear programming.” ACM Transactions on Mathematical Software, Vol. 4, No. 1, pp. 34–50.zbMATHCrossRefGoogle Scholar
  22. Lee, J. S. (2003). “Uncertainties in the predicted number of life loss due to the dam breach floods.” KSCE Journal of Civil Engineering, KSCE, Vol. 7, No. 1, pp. 81–91.CrossRefGoogle Scholar
  23. Lee, J. S. and Noh, J. W. (2003). “The impacts of uncertainty in the predicted dam breach floods on economic damage estimation” KSCE Journal of Civil Engineering, KSCE, Vol. 7, No. 3, pp. 343–350.CrossRefGoogle Scholar
  24. Luo, J. and Xie, J. (2010). “Parameter estimation for nonlinear Muskingum model based on immune clonal selection algorithm.” Journal of Hydrologic Engineering, ASCE, Vol. 15, No. 10, pp. 844–851.CrossRefGoogle Scholar
  25. McCuen, R. H., Knight, Z., and Cutter, A. G. (2006). “Evaluation of the Nash-Sutcliffe efficiency index.” Journal of Hydrologic Engineering, ASCE, Vol. 11, No. 6, pp. 597–602.CrossRefGoogle Scholar
  26. Mohan, S. (1997). “Parameter estimation of nonlinear Muskingum models using genetic algorithm.” Journal of Hydraulic Engineering, ASCE, Vol. 123, No. 2, pp. 137–142.CrossRefGoogle Scholar
  27. Murtagh, B. A. and Saunders, M. A. (1978). “Large-scale linearly constrained optimization.” Mathematical Programming, Vol. 14, No. 1, pp. 41–72.MathSciNetzbMATHCrossRefGoogle Scholar
  28. Papamichail, D. and Georgiou, P. (1994). “Parameter estimation of linear and nonlinear Muskingum models for river flood routing.” Transactions on Ecology and the Environment, 7, WIT Press, http://www.Witpress.com, ISSN pp. 1743–3541.Google Scholar
  29. Premium Solver Platform, User Guide. (2010). Frontline Systems, Inc., Notes downloaded from the site http://www.solver.com.Google Scholar
  30. Toprak, Z. F. (2009) “Flow discharge modeling in open canals using a new fuzzy modeling technique (SMRGT).” CLEAN-Soil, Air, Water, Vol. 37, No. 9, pp. 742–752.CrossRefGoogle Scholar
  31. Toprak, Z. F. and Cigizoglu, H. K. (2008) “Predicting longitudinal dispersion coefficient in natural streams by artificial intelligence methods.” Hydrological Processes, Vol. 22, No. 20, pp. 4106–4129.CrossRefGoogle Scholar
  32. Toprak, Z. F., Eris, E., Agiralioglu, N., Cigizoglu, H. K., Yilmaz, L., Aksoy, H., Coskun, G., Andic, G., and Alganci, U. (2009) “Modeling monthly mean flow in a poorly gauged basin by fuzzy logic.” CLEAN-Soil, Air, Water, Vol. 37, No. 7, pp. 555–564.CrossRefGoogle Scholar
  33. Toprak, Z. F. and Savci, M. E. (2007). “Longitudinal dispersion coefficient modeling in natural channels using fuzzy logic.” CLEAN-Soil, Air, Water, Vol. 35, No. 6, pp. 626–637.CrossRefGoogle Scholar
  34. Tung, Y. K. (1985). “River flood routing by nonlinear Muskingum method.” Journal of Hydraulic Engineering, ASCE, Vol. 111, No. 12, pp. 1447–1460.CrossRefGoogle Scholar
  35. Wilson, E. M. (1974). Engineering hydrology, MacMillan, Hampshire, UK.Google Scholar
  36. Wong, T. S. W. and Zhou, M. C. (2004). “Determination of critical and normal depths using excel.” Proceedings of World Water and Environmental Resources Congress, Saltlake City Utah, USA.Google Scholar
  37. Yidana, S. M. and Ophori, D. (2008). “Groundwater resources management in the Afram plains area, Ghana.” KSEC Journal of Civil Engineering, KSCE, Vol. 12, No. 5, pp. 349–357.CrossRefGoogle Scholar
  38. Yoon, J. W., and Padmanabhan, G. (1993). “Parameter estimation of linear and nonlinear Muskingum models.” Journal of Water Resources Planning and Management, ASCE, Vol. 119, No. 5, pp. 600–610.CrossRefGoogle Scholar

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Young Researchers Club and Elites, Mashhad BranchIslamic Azad UniversityMashhadIran

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