Application of a Hybrid Optimization Method in Muskingum Parameter Estimation

Abstract

Two new mathematical forms of the nonlinear Muskingum model called NL4 and NL5, involving four and five parameters, respectively, can be used in river flood routing. The accuracy of the estimation of the Muskingum model parameters is essential for flood routing. This paper proposes a novel hybrid algorithm, based on the shuffled frog leaping algorithm (SFLA) and Nelder-Mead simplex (NMS), for the estimation of parameters of two new nonlinear Muskingum models. The proposed methodology is applied by considering minimization of the sum of the square deviation (SSD) between observed and routed outflows in (1) experimental, (2) real, and (3) multimodal examples. Results show that the SSD is 0.91, 3.97, and 4.44% smaller (better) than pertinent values obtained by the genetic algorithmgeneralized reduced gradient (GA-GRG) method in experimental, real, and multimodal examples, respectively.

Flood Routing in River Reaches Using a Three-Parameter Muskingum Model Coupled with an Improved Bat Algorithm

“…Two case studies were considered as bench problems, which have been used by different researchers using many methods for flood routing (Wilson and Karahan floods), and one case study was related to a river in Myanmar that had an important flood. The Wilson flood is considered as an important case study and different researchers tested different algorithms on this case study [2,3,[28][29][30], and thus a comprehensive study can be considered for this case study. The Karahan flood is considered as one of the case studies that have been investigated by different researchers as a benchmark problem [28][29][30][31]35].…”

“…In fact, most of the previous researches ignore the lateral flow while using the simple Muskingum model. Therefore, if lateral flow exists and has high volume, the Muskingum model simulates the flood without consideration of lateral flow [23][24][25][26][27][28][29][30][31], and hence, the achieved accuracy is relatively low. In fact, simplification of the Muskingum equation was a reason to omit the effect of lateral flow for flood routing, whilst there is lateral flow in the reach when the flood happens in nature.…”

“…The river under study was divided into several smaller reaches, and for each reach, routing was done separately. In other words, for each reach, parameters X, K, β, and m were calculated separately, and the output hydrograph was obtained based on the input flood hydrograph and the assumed values of X, K, β, and m for the first reach [3,21,28,31]. This output hydrograph was considered as the input hydrograph for the second reach, and so on.…”

“…The sum of squared deviations (SSD): SSD index is used as the objective function in the present study. The index calculates the total of squared deviations between observed and real discharges [28,[42][43][44][45][46]:…”

“…Under the three-parameter Muskingum method, Geem [27] found the harmony algorithm (HA) to have higher convergence than PSO and GA. Under the four-parameter Muskingum method, the Frog Leaping Algorithm (FLA) was found to have a lower computational error, than PSO and GA [28]. Niknazar and Afzali [29] used an improved Honey Bee Algorithm (IHBA) to optimize three parameters of the Muskingum method, and found it to be superior to GA and PSO.…”