Estimation of Muskingum parameter by meta-heuristic algorithms

Abstract

The Muskingum model is a hydrologic flood routing method in which the accuracy of the parameter estimation affects the routed hydrograph, especially in both the value and time of the flood peak. Meta-heuristic algorithms are good candidates to determine optimal/near-optimal parameters in the Muskingum model. In this paper, two metaheuristic algorithms -the simulated annealing (SA) algorithm and the shuffled frog leaping algorithm (SFLA) -are applied and compared in two benchmark and real case studies, considering the sum of the squared deviation (SSQ) between observed and routed outflows and the sum of the absolute value of deviation (SAD) between observed and routed outflow as the objective functions, and deviation of value and occurrence time of the routed flood peak (DPO and DPOT) as the important parameters on the routed flood hydrograph. Results show that the SFLA improves (decreases) the SSQ and SAD by 0 . 03% and 0 . 39% in the benchmark problem, and by 3 . 59% and 2 . 03% in the real case study, respectively, compared to reported results using various optimisation algorithms. In addition, the SFLA improves (decreases) the DPO of the routed hydrograph in the benchmark problem by 56 . 67% compared to the best (minimum) result using the Tung method.

Discussion: Estimation of Muskingum parameter by meta-heuristic algorithms

“…However, not only one-dimensional (1D) and 2D distributed flood routing models (Akbari and Barati, 2012;Xia et al, 2012) and lumped flood routing models (Barati, 2011) can be used to route the hydrograph of the downstream section, but semi-distributed models such as Muskingum-Cunge procedures (Barati et al, 2013;Perumal and Sahoo, 2007) can also be used. Orouji et al (2012) used the data of Karoon River as a real case study. However, the use of a non-linear model for this dataset is questionable.…”

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Orouji et al (2012) utilised simulated annealing (SA) and shuffled frog leaping algorithm (SFLA) algorithms to calibrate the parameters of the non-linear Muskingum model. The study is both appropriate and interesting, especially for the application of SFLA, but the discusser would like to draw attention to two points -flood routing model classification and storage equation selection.

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“…The study is both appropriate and interesting, especially for the application of SFLA, but the discusser would like to draw attention to two points -flood routing model classification and storage equation selection. Orouji et al (2012) indicated that there are two general procedures to route the hydrograph of flooding along river reaches -hydraulic (i.e. distributed) and hydrologic (i.e.…”

Editorial

“…Recent papers include those by Geem (2011), Xu et al (2012, Karahan et al (2013), Orouji et al (2013) and Easa (2013). In this issue of the journal, Easa (2014) reports on the development of a new four-parameter model.…”

Editorial

“…By contrast, Orouji et al (2013) describe the application of two meta-heuristic algorithms; namely simulated annealing (SA) and the shuffled frog leaping algorithm (SFLA) to calibrate the parameters of the nonlinear Muskingum flood routing model. The authors compare SA and SFLA to other approaches that have been used elsewhere (see Karahan et al, 2013).…”