Distributed Muskingum model with a Whale Optimization Algorithm for river flood routing

Abstract This research introduces a novel nonlinear Muskingum model for river flood routing, aiming to enhance accuracy in modeling. It integrates lateral inflows using the Whale Optimization Algorithm (WOA) and employs a distributed Muskingum model, dividing river reaches into smaller intervals for precise calculations. The primary goal is to minimize the Sum of Square Errors (SSE) between the observed and modeled outflows. Our methodology is applied to six distinct flood hydrographs, revealing its versatility and efficacy. For Lawler's and Dinavar's flood data, the single-reach Muskingum model outperforms multi-reach versions, demonstrating its effectiveness in handling lateral inflows. For Lawler's data, the single-reach model (NR = 1) yields optimal parameters of K = 0.392, x = 0.027, m = 1.511, and β = 0.010, delivering superior results. Conversely, when fitting flood data from Wilson, Wye, Linsley, and Viessman and Lewis, the multi-reach Muskingum model exhibits better overall performance. Remarkably, the model excels with the Viessman and Lewis flood data, especially with two reaches (NR = 2), achieving a 21.6% SSE improvement while employing the same parameter set. This research represents a significant advancement in flood modeling, offering heightened accuracy and adaptability in river flood routing.