River Flood Routing Using the Multi-Reach Linear Muskingum Approach and Marin Predators Algorithm

Flood routing is an essential and fundamental issue in water resources management and flood control engineering. The Muskingum model is one of the well-known and the most widely used hydrological flood routing approaches. In addition to reasonable accuracy, the linear Muskingum model is also simpler and has a lower cost than that of hydraulic and nonlinear Muskingum models. In this study, a multi-reach linear Muskingum method considering lateral flow is proposed to increase the accuracy and efficiency of the current version of the Muskingum model. To the aim, the river path is divided into a finite number of sub-intervals, and the Muskingum model is then separately applied to each sub-interval successively; in such a way that the input flood hydrograph for each sub-interval is indeed the same as the output flood hydrograph from Muskingum calculations in the previous sub-interval. Here, besides the parameters  and ,  as lateral flow coefficient and  as the number of sub-intervals are also considered as decision variables where the Marine Predators Algorithm (MPA) was used to determine their optimized values. The results showed that the multi-reach approach increased the accuracy of the sum of squared deviation (SSQ) by 70 and 73 percent for Wilson data and Wye river flood, respectively, indicating a higher accuracy for the multi-reach version Muskingum compared to that of single-reach.In addition, the multi-reach Muskingum approach was tested on three flood events of Karun river, in which the calculated statistical criteria, all, show a high accuracy for the proposed method and the MPA.