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Parameter Estimation of Two Improved Nonlinear Muskingum Models Considering the Lateral Flow Using a Hybrid Algorithm

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Abstract

The Muskingum model was one of the most popular methods for flood routing in water resources engineering, many researchers had presented various versions of Muskingum model so as to enhance the precision of the Muskingum model in their papers. Similarly, two new nonlinear Muskingum models were presented in this paper. One considered the lateral flow, and the other considered the lateral flow and a variable exponent parameter, simultaneously. Minimizing the sum of the squared (SSQ) deviations between the observed and routed outflows was considered as the objective, and then three benchmark examples and a real example in Iran were applied to verify performances of two proposed models. A hybrid algorithm, which combined the improved real-coded adaptive genetic algorithm and the Nelder-Mead simplex algorithm, was utilized for parameter estimation of two proposed models. Comparisons of the optimal results for four examples by different models showed that two proposed models can produce more accurate fit to observed outflows, and the proposed model, which simultaneously considered a variable exponent parameter and the lateral flow, reduced the SSQ obviously.

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References

  1. Barati R (2011) Parameter estimation of nonlinear Muskingum models using Nelder-Mead simplex algorithm. J Hydrol Eng 16:946–954. doi:10.1061/(ASCE)HE.1943-5584.0000379

  2. Barati R (2012) Discussion of "parameter estimation of the nonlinear Muskingum model using parameter-setting-free harmony search" by Zong woo Geem. J Hydrol Eng 17:1414–1416. doi:10.1061/(ASCE)HE.1943-5584.0000500

  3. Barati R (2013) Application of excel solver for parameter estimation of the nonlinear Muskingum models. KSCE J Civ Eng 17:1139–1148. doi:10.1007/s12205-013-0037-2

  4. Bozorg Haddad O, Hamedi F, Fallah-Mehdipour E, Orouji H, Mariño MA (2015a) Application of a hybrid optimization method in Muskingum parameter estimation. J Irrig Drain Eng 141:04015026. doi:10.1061/(ASCE)IR.1943-4774.0000929

  5. Bozorg Haddad O, Hamedi F, Orouji H, Pazoki M, Loáiciga HA (2015b) A re-parameterized and improved nonlinear Muskingum model for flood routing. Water Resour Manag 29:3419–3440. doi:10.1007/s11269-015-1008-9

  6. Chen J, Yang X (2007) Optimal parameter estimation for Muskingum model based on gray-encoded accelerating genetic algorithm. Commun Nonlinear Sci Numer Simul 12:849–858. doi:10.1016/j.cnsns.2005.06.005

  7. Chow VT (1959) Open Channel hydraulics. McGraw-Hill, New York

  8. Easa SM (2013) Improved Nonlinear Muskingum Model with Variable Exponent Parameter 18. doi:10.1061/(ASCE)HE.1943-5584.0000702

  9. Easa SM (2014a) Closure to "improved nonlinear Muskingum model with variable exponent parameter" by said M. Easa. J Hydrol Eng 19:07014008. doi:10.1061/(ASCE)HE.1943-5584.0001041

  10. Easa SM (2014b) New and improved four-parameter non-linear Muskingum model. Proceedings of the Institution of Civil Engineers - Water Management 167:288–298. doi:10.1680/wama.12.00113

  11. Gavilan G, Houck MH (1985) Optimal Muskingum river routing. In: Computer applications in water resources, ASCE, 1985. New York, pp 1294–1302

  12. Geem ZW (2011) Parameter estimation of the nonlinear Muskingum model using parameter-setting-free harmony search. J Hydrol Eng 16:684–688. doi:10.1061/(ASCE)HE.1943-5584.0000352

  13. Geem ZW (2014) Issues in optimal parameter estimation for the nonlinear Muskingum flood routing model. Eng Optim 46:328–339. doi:10.1080/0305215X.2013.768242

  14. Gill MA (1978) Flood routing by the Muskingum method. J Hydrol 36:353–363. doi:10.1016/0022-1694(78)90153-1

  15. Hamedi F, Haddad OB, Orouji H (2015) Discussion of “application of excel solver for parameter estimation of the nonlinear Muskingum models” by Reza Barati. KSCE J Civ Eng 19:340–342. doi:10.1007/s12205-014-0566-3

  16. Kang L, Zhang S (2016) Application of the elitist-mutated PSO and an improved GSA to estimate parameters of linear and nonlinear Muskingum flood routing models. PLoS One 11:e0147338. doi:10.1371/journal.pone.0147338

  17. 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. doi:10.1061/(ASCE)HE.1943-5584.0000608

  18. Karahan H, Gurarslan G, Geem ZW (2015) A new nonlinear Muskingum flood routing model incorporating lateral flow. Eng Optim 47:737–749. doi:10.1080/0305215X.2014.918115

  19. Kim JH, Geem ZW, Kim ES (2001) Parameter estimation of the nonlinear Muskingum model using harmony search. J Am Water Resour Assoc 37:1131–1138. doi:10.1111/j.1752-1688.2001.tb03627.x

  20. McCarthy GT (1938) The unit hydrograph and flood routing. In: Proceeding of the Conference of North Atlantic Division, U.S. Army Corps of Engineer District, Wahsington, DC

  21. Moghaddam A, Behmanesh J, Farsijani A (2016) Parameters estimation for the new four-parameter nonlinear Muskingum model using the particle swarm optimization. Water Resour Manag 30:2143–2160. doi:10.1007/s11269-016-1278-x

  22. Mohan S (1997) Parameter estimation of nonlinear Muskingum models using genetic algorithm. J Hydraul Eng 123:137–142. doi:10.1061/(ASCE)0733-9429(1997)123:2(137)

  23. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313. doi:10.1093/comjnl/7.4.308

  24. NERC (1975) Flood studies report, vol 3. Institute of Hydrology, Wallingford

  25. Niazkar M, Afzali SH (2014) Assessment of modified honey bee mating optimization for parameter estimation of nonlinear Muskingum models. J Hydrol Eng 20:04014055. doi:10.1061/(ASCE)HE.1943-5584.0001028

  26. Niazkar M, Afzali SH (2016) Application of New Hybrid Optimization Technique for Parameter Estimation of New Improved Version of Muskingum Model. Water Resour Manag :1–18. doi:10.1007/s11269-016-1449-9

  27. O'Donnell T (1985) A direct three-parameter Muskingum procedure incorporating lateral inflow. Hydrol Sci J 30:479–496. doi:10.1080/02626668509491013

  28. Orouji H, Bozorg Haddad O, Fallah-Mehdipour E, Mariño MA (2013) Estimation of Muskingum parameter by meta-heuristic algorithms. Proc Inst Civ Eng Water Manage 166:315–324. doi:10.1680/wama.11.00068

  29. Ouyang A, Li K, Truong TK, Sallam A, Sha EH-M (2014) Hybrid particle swarm optimization for parameter estimation of Muskingum model. Neural Comput & Applic 25:1785–1799. doi:10.1007/s00521-014-1669-y

  30. Viessman W, Lewis GL (2003) Introduction to hydrology. Prentice Hall India (P) Limited, New Jersey

  31. Wilson EM (1974) Engineering Hydrology. Macmillan Book Company, London

  32. Yang Z, Kang L (2010) Application and comparison of several intelligent algorithms on Muskingum Routing Model. In: 2010 2nd IEEE International Conference on Information and Financial Engineering (ICIFE), Chongqing, China. IEEE, pp 910–914. doi:10.1109/ICIFE.2010.5609501

  33. Yuan X, Wu X, Tian H, Yuan Y, Adnan RM (2016) Parameter identification of nonlinear Muskingum model with backtracking search algorithm. Water Resour Manag 30:2767–2783. doi:10.1007/s11269-016-1321-y

  34. Zhang S, Kang L, Zhou L, Guo X (2016) A new modified nonlinear Muskingum model and its parameter estimation using the adaptive genetic algorithm. Hydrol Res. doi:10.2166/nh.2016.185

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Acknowledgements

This study was financially supported by the National Key Research and Development Plan (Grant No. 2016YFC0402202) and the Hubei Support Plan of Science and Technology (Grant No. 2015BCA291).

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Correspondence to Liwei Zhou.

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Kang, L., Zhou, L. & Zhang, S. Parameter Estimation of Two Improved Nonlinear Muskingum Models Considering the Lateral Flow Using a Hybrid Algorithm. Water Resour Manage 31, 4449–4467 (2017). https://doi.org/10.1007/s11269-017-1758-7

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Keywords

  • Flood routing
  • Hydrologic method
  • Nonlinear Muskingum model
  • Variable exponent
  • Lateral flow