Parameter Estimation of the Nonlinear Muskingum Model Using Simulated Annealing

The Muskingum method is frequently used to route floods in Hydrology. However, application of the model is still difficult because of the parameter estimation’s. Recently, some of heuristic methods have been used in order to estimate the nonlinear Muskingum model. This paper presents a efficient heuristic algorithm, Simulated Annealing, which has been used to estimate the three parameters nonlinear Muskingum model. The results show the high accuracy of the algorithm in estimation of the parameters, so that it is obtained terms of the sum of the square of the deviations between the observed and routed outflows (SSQ), the sum of the absolute value of the deviations between the observed and routed outflows (SAD), deviations of peak of routed and actual flows (DPO), and deviations of peak time of routed and actual outflow (DPOT), 36/78, 23/44, 0/9 and 0, respectively. As Value of the SSQ has obtained equal its value Harmony Search method that is the best answer between the heuristic Optimization Algorithms that has been used so far. Finally, the performance of the new proposed method has been compared with other methods. The results showed that the height efficiency of the algorithm in parameter optimization of the nonlinear Muskingum model. SA algorithm in the second example the Karun River flood test and the results were compared with the GA method. The results showed that SA algorithms estimate is better than the GA method. As the error sum of squares (SSQ) before 4947/06, the total absolute error (SAD) against 412/8, Dubai actual peak was 1182 cubic meters per second and peak Routing 1191 was obtained by the difference of these two (DPO) times less a percentage error and the occurrence of different steps in Dubai when the real peak and has Routing (DPOT) zero respectively. Finally, this research capability in the blank verses optimal SA algorithm making Muskingum model parameters indicated therefore, to use SA algorithm in this area is recommended.