Performance improvement of the linear muskingum flood routing model using optimization algorithms and data assimilation approaches

The Muskingum model is one of the most widely used hydrological methods in flood routing, and calibrating its parameters is an ongoing research challenge. We optimized Muskingum model parameters to accurately simulate hourly output hydrographs of three flood-prone rivers in the Karun watershed, Iran. We evaluated model performance using the correlation coefficient (CC), the ratio of the root-mean-square error to the standard deviation of measured data (PSR), Nash–Sutcliffe efficiency (NSE), and index of agreement ( d ). The results show that the gray wolf optimization (GWO) algorithm, with CC = 0.99455, PSR = 0.155, NSE = 0.9757, and d = 0.9945, performed better in simulating the flood in the first study area. The Kalman filter (KF) improved these measures by + 0.00516, − 0.1246, + 0.02328, and + 0.00527, respectively. Our findings for the second flood show that the gravitational search algorithm (GSA), with CC = 0.9941, PSR = 0.1669, NSE = 0.9721, and d = 0.9921, performed better than all other algorithms. The Kalman filter enhanced each of the measures by + 0.00178, − 0.0175, + 0.0055 and + 0.0021, respectively. The gravitational search algorithm also performed best in the third flood, with CC = 0.9786, PSR = 0.2604, NSE = 0.9321, and d = 0.9848, and with improvements in accuracy using the Kalman filter of + 0.01081, − 0.0971, + 0.394, and + 0.0078, respectively. We recommend the use of GWO-KF for flood routing studies with flood events of high volumes and hydrograph base times, and use of GSA-KF for studies with flood events of high volumes and hydrograph base times.