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Application of New Hybrid Optimization Technique for Parameter Estimation of New Improved Version of Muskingum Model

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Abstract

The Muskingum method is one of the most utilized lumped flood routing model in which calibration of its parameters provides an active area of research in water resources engineering. Although various techniques and versions of Muskingum model have been presented to estimate the parameters of different versions of Muskingum model, more rigorous approaches and models are still required to improve the computational precision of calibration process. In this study, a new hybrid technique was proposed for Muskingum parameter estimation which combines the Modified Honey Bee Mating Optimization (MHBMO) and Generalized Reduced Gradient (GRG) algorithms. According to the conducted literature-review on the improvement of Muskingum flood routing models, a new six-parameter Muskingum model was proposed. The hybrid technique was successfully applied for parameter estimation of this new version of Muskingum model for three case studies selected from literature. The obtained results were compared with those of other methods using several common performance evaluation criteria. The new hybrid method with the new proposed Muskingum model perform the best among all the considered approaches based on most of utilized criteria. The new Muskingum model significantly reduces the SSQ value for the double-peak case study. Finally, the achieved results demonstrate that not only the hybrid MHBMO-GRG algorithm overcomes the shortcomings of both phenomenon-mimicking and mathematical optimization techniques, but also the presented Muskingum model is appeared to be the most reliable version of Muskingum model comparing with other considered models in this research.

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References

  • Afzali S (2016) Variable-parameter Muskingum model. Iranian J Sci Technol, Trans Civil Eng 40(1):59–68

    Article  Google Scholar 

  • Afzali SH, Darabi A, Niazkar M (2016) Steel frame optimal design using MHBMO algorithm. Int J Steel Struct 16(2):455–465

    Article  Google Scholar 

  • Barati R (2011) Parameter estimation of nonlinear Muskingum models using Nelder-Mead Simplex algorithm. J Hydrol Eng 16(11):946–954

    Article  Google Scholar 

  • Barati R (2012) Discussion of parameter estimation of the nonlinear Muskingum model using Parameter-Setting-Free Harmony Search by Zong Woo Geem

  • Barati R (2013) Application of Excel Solver for parameter estimation of the nonlinear Muskingum models. KSCE J Civil Eng 17(5):1139–1148

    Article  Google Scholar 

  • Barati R (2014) Discussion of parameter estimation of the nonlinear Muskingum flood-routing model using a Hybrid Harmony Search algorithm by Halil Karahan, Gurhan Gurarslan, and Zong Woo Geem. J Hydrol Eng 19(4):842–845

    Article  Google Scholar 

  • Chow VT (1959) Open channel hydraulics. McGraw-Hill, New York

    Google Scholar 

  • Chu HJ, Chang LC (2009) Applying Particle Swarm Optimization to parameter estimation of the nonlinear Muskingum model. J Hydrol Eng 14(9):1024–1027

    Article  Google Scholar 

  • Das A (2004) Parameter estimation for Muskingum models. J Irrig Drain Eng 130(2):140–147

    Article  Google Scholar 

  • Easa SM (2013a) Improved nonlinear Muskingum model with variable exponent parameter. J Hydrol Eng 18(12):1790–1794

    Article  Google Scholar 

  • Easa SM (2013b) New and improved four-parameter non-linear Muskingum model. Proc ICE-Water Manag 167(5):288–298

    Google Scholar 

  • Easa SM (2014) Versatile Muskingum flood model with four variable parameters. Proc ICE-Water Manag 168(3):139–148

    Google Scholar 

  • Easa SM (2015) Evaluation of nonlinear Muskingum model with continuous and discontinuous exponent parameters. KSCE Journal of Civil Engineering pp 1–10, doi:10.1007/s12205-015-0154-1

  • Easa SM, Barati R, Shahheydari EJN, Barati T (2014) Discussion: New and improved four-parameter non-linear Muskingum model. Proc ICE-Water Manag 167(10):612–615

    Google Scholar 

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

  • Geem ZW (2006) Parameter estimation for the nonlinear Muskingum model using the BFGS technique. J Irrig Drain Eng 132(5):474–478

    Article  Google Scholar 

  • Geem ZW (2010) Parameter estimation of the nonlinear Muskingum model using Parameter-Setting-Free Harmony Search. J Hydrol Eng 16(8):684–688

    Article  Google Scholar 

  • Gill MA (1978) Flood routing by the Muskingum method. J Hydrol 36(3):353–363

    Article  Google Scholar 

  • Haddad OB, Hamedi F, Fallah-Mehdipour E, Orouji H, Mariño MA (2015a) Application of a hybrid optimization method in Muskingum parameter estimation. Journal of Irrigation and Drainage Engineering p 04015026

  • Haddad OB, Hamedi F, Orouji H, Pazoki M, Loáiciga HA (2015b) A re-parameterized and improved nonlinear Muskingum model for flood routing. Water Resour Manag 29(9):3419–3440

    Article  Google Scholar 

  • Hamedi F, Haddad O, Orouji H (2015) Discussion of application of Excel Solver for parameter estimation of the nonlinear Muskingum models by Reza Barati. KSCE J Civil Eng 1(19):340–342

    Article  Google Scholar 

  • Hirpurkar P, Ghare AD (2014) Parameter estimation for the nonlinear forms of the Muskingum model. J Hydrol Eng 20(8):04014,085

    Article  Google Scholar 

  • Hosseini SM (2009) Application of spreadsheets in developing flexible multiple-reach and multiple-branch methods of Muskingum flood routing. Comput Appl Eng Educ 17(4):448–454

    Article  Google Scholar 

  • Karahan H (2014) Discussion of improved nonlinear Muskingum model with variable exponent parameter by Said M. Easa. J Hydrol Eng 19(10):07014,007

    Article  Google Scholar 

  • 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(3):352–360

    Article  Google Scholar 

  • Karahan H, Gurarslan G, Geem ZW (2015) A new nonlinear Muskingum flood routing model incorporating lateral flow. Eng Optim 47(6):737–749

    Article  Google Scholar 

  • Kim JH, Geem ZW, Kim ES (2001) Parameter estimation of the nonlinear Muskingum model using Harmony Search. JAWRA J Amer Water Resour Assoc 37(5):1131–1138

    Article  Google Scholar 

  • Latt ZZ (2015) Application of feedforward artificial neural network in Muskingum flood routing: a black-box forecasting approach for a natural river system. Water Resour Manag 29(14):4995–5014

    Article  Google Scholar 

  • Luo J, Xie J (2010) Parameter estimation for nonlinear Muskingum model based on Immune Clonal Selection Algorithm. J Hydrol Eng 15(10):844–851

    Article  Google Scholar 

  • 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

  • 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(7):2143–2160

    Article  Google Scholar 

  • Mohan S (1997) Parameter estimation of nonlinear Muskingum models using Genetic Algorithm. J Hydraul Eng 123(2):137–142

    Article  Google Scholar 

  • Niazkar M, Afzali SH (2015a) Assessment of Modified Honey Bee Mating Optimization for parameter estimation of nonlinear Muskingum models. J Hydrol Eng 20(4):04014,055

    Article  Google Scholar 

  • Niazkar M, Afzali SH (2015b) Optimum design of lined channel sections. Water Resour Manag 29(6):1921–1932

    Article  Google Scholar 

  • Niazkar M, Afzali SH (2016) Streamline performance of Excel in stepwise implementation of numerical solutions. Comput Appl Eng Educ 24(4):555–566

    Article  Google Scholar 

  • O’Donnel T (1985) A direct three-parameter Muskingum procedure incorporating lateral inflow. Hydrol Sci J 30(4):479–496

    Article  Google Scholar 

  • Tung YK (1985) River flood routing by nonlinear Muskingum method. J Hydraul Eng 111(12):1447–1460

    Article  Google Scholar 

  • Vatankhah AR (2014) Discussion of parameter estimation of the nonlinear Muskingum flood-routing model using a hybrid Harmony Search algorithm by Halil Karahan, Gurhan Gurarslan, and Zong Woo Geem. J Hydrol Eng 19(4):839–842

    Article  Google Scholar 

  • Viessman W, Lewis GL (2003) Introduction to Hydrology, 5th edn. Prentice Hall India (P) Limited

  • Wilson EM (1974) Engineering hydrology. Macmillan Education LTD, Hampshire, United Kingdom

  • Xu DM, Qiu L, Chen SY (2011) Estimation of nonlinear Muskingum model parameter using Differential Evolution. J Hydrol Eng 17(2):348–353

    Article  Google Scholar 

  • Yoon J, Padmanabhan G (1993) Parameter estimation of linear and nonlinear Muskingum models. J Water Resour Plan Manag 119(5):600–610

    Article  Google Scholar 

  • 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(8):2767–2783

    Article  Google Scholar 

Download references

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Correspondence to Seied Hosein Afzali.

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Niazkar, M., Afzali, S.H. Application of New Hybrid Optimization Technique for Parameter Estimation of New Improved Version of Muskingum Model. Water Resour Manage 30, 4713–4730 (2016). https://doi.org/10.1007/s11269-016-1449-9

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  • DOI: https://doi.org/10.1007/s11269-016-1449-9

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