Calculation of Water Depth during Flood in Rivers using Linear Muskingum Method and Particle Swarm Optimization (PSO) Algorithm

To estimate the damage caused by flooding rivers, it is critical to analyze unsteady flow and determine downstream water depth. Hydraulic methods for examining unsteady river flow require cross-sectional specifications of the river at a close distance with optimal accuracy. Obtaining these specifications is often time-consuming and expensive. In contrast, hydrologic routing methods, such as the linear Muskingum method, are more beneficial for the analysis of unsteady flow. In flood routing, the linear Muskingum method has only been utilized to calculate the outflow hydrograph (downstream). However, in practical problems regarding flood analysis, such as economic analysis, damage assessment, and flood management and engineering, downstream water depth is needed. By employing kinematic wave relations, the linear Muskingum method, and the Particle Swarm Optimization (PSO) algorithm, the present study estimates water depth, with respect to time, of a downstream section of the Karun River, between the Mollasani (upstream) and Ahwaz (downstream) hydrometric stations. The proposed approach is simpler and less expensive and more accurate than hydraulic methods. The current work estimated the values of the Mean Relative Error (MRE) to the total flood and the Mean Relative Error (MRE) to the peak section of input depth along with the absolute value of the peak deviations of the observed and routed depth (DPO) as 1.29, 0.24, and 1.16 percent, respectively.