Parameter Optimization of the Nonlinear Muskingum Model Using Artificial Bee Colony (ABC) Algorithm

Flood routing, as a mathematical method for predicting the changing magnitude and celerity of a flood wave as it propagates down rivers, provides the substantive bases for conducting flood zonation, flood forecasting and design of river structures. The Muskingum technique is one of important and most frequently used techniques of flood routing. In the present research, accuracy of some methods for optimization of Muskingum parameters (K, x and m) including graphical technique, linear programming, genetic algorithm, ant colony algorithm and artificial bee colony algorithm has been evaluated by using statistics of 9 flood hydrographs contemporaneous detected in two hydrometric stations of Mola Sani and Ahwaz in a 63-km reach of Karun River called Mola Sani-Ahwaz. In order to evaluate the different techniques, statistical criteria of the root-mean-square error (RMSE), relative error (RE), mean absolute error (MBE), mean error deviation (MAE), Nash and Sutclife coefficient (NS), coefficient of determination (R2) and also visual comparison by plotting estimated and observed hydrographs were used. The results showed that artificial bee colony and genetic algorithms with RMSE of 79.85 m3/s were found to be superior to graphical technique with RMSE of 88.07 m3/s for estimation of Muskingum model parameters. Comparing peak flow of hydrographs indicate more accurate for graphical technique with mean absolute error (MAE) of 31.2 m3/s than genetic algorithm with MAE of 58.8 m3/s and artificial bee colony algorithm with MAE of 62.18 m3/s.