Flood routing using the Muskingum model based on data clustering approaches and the Bald Eagle Search Optimization algorithm

The Muskingum model is one of the most frequently used flood routing models. In any reach of a river with hydrometric stations at its beginning and end, model parameters can be determined based on floods measured at the inlet and outlet of this reach. Therefore, if another flood enters this reach, the outflow flood can also be predicted using the data of this flood and the Muskingum model parameters without cost. In this research, the type-1 non-linear Muskingum model (NLMM1), the flood data clustering method based on the k-means model, and the combination of NLMM1 with k-means (K-NLMM1) are used. This approach is utilized for four flood data sets, including the Wilson flood, the Wye River flood, the Lewis-Viessman flood and the Sutculer flood. Two optimization problems are defined in this paper. The first problem is to determine the center of clusters and the second one is to specify the parameters of NLMM1 and K-NLMM1. The bald eagle search (BES) optimization algorithm is used to solve such problems. The objective function for determining the Muskingum model parameters is considered to be minimizing the sum of squares of the difference between the observed outflow hydrograph and the routed hydrograph (SSQ). For the first to fourth case studies, the SSQ of the NLMM1 model is computed to be 245.6, 54,185.6, 74,307.2 and 557.3 (m3/s)2, respectively. Also, the values of SSQ for the K6-NLMM1 superior model in the first to fourth case studies are computed to be 3.1, 1185.7, 40,427, and 115.3 (m3/s)2, respectively. Thus, by clustering the data, the SSQ value decreases in the range of 46–99%.