Estimation of Muskingum parameter by meta-heuristic algorithms

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 meta-heuristic 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.