River Flood Routing Using a Spatial Variable Exponent Parameter Nonlinear Muskingum Model and Sine Cosine Algorithm by Considering Lateral Flow

Abstract

Abstract Due to advancements in optimization technology, numerous variable-parameter Muskingum models have been proposed in recent decades, aimed at enhancing the effectiveness of the Muskingum model. This study proposes a novel approach to river flood routing that employs a spatial variable exponent parameter nonlinear Muskingum model with lateral flow considerations. The proposed nonlinear Muskingum model with a variable exponent parameter considers spatial variations, in contrast to earlier studies that concentrated on modifying exponent parameters in response to variable inflow levels. The Muskingum parameters of the proposed model were estimated using an improved Sine Cosine Algorithm (SCA), which was applied to fit six previously reported flood hydrographs. The proposed method aims to minimize the Sum of Square Errors (SSE) between observed and routed outflows. The study demonstrates that by incorporating lateral inflows into the Muskingum model for Wilson, Linsley, and Viessman and Lewis flood data, two sub-reaches produce significantly better results. Conversely, for fitting flood data exhibited by Wye and Dinavar flood data, the three sub-reaches Muskingum model yields superior results. In the case of Lawler flood data, it is suggested that the traditional nonlinear model could be adequate, and there may be no need to incorporate sub-reaches, as the Sum of Square Errors (SSE) remains unchanged. Overall, the study provides a promising approach to addressing river flood routing problems.