A Novel Parameter Estimation Method for Muskingum Model Using New Newton-Type Trust Region Algorithm

Parameters estimation of Muskingum model is very significative in both exploitation and utilization of water resources and hydrological forecasting. The optimal results of parameters directly affect the accuracy of flood forecasting. This paper considers the parameters estimation problem of Muskingum model from the following two aspects. Firstly, based on the general trapezoid formulas, a class of new discretization methods including a parameter θ to approximate Muskingum model is presented. The accuracy of these methods is second-order, when θ≠1/3. Particularly, if we choose θ=1/3, the accuracy of the presented method can be improved to third-order. Secondly, according to the Newton-type trust region algorithm, a new Newton-type trust region algorithm is given to obtain the parameters of Muskingum model. This method can avoid high dependence on the initial parameters. The average absolute errors (AAE) and the average relative errors (ARE) of the proposed algorithm of parameters estimation for Muskingum model are 8.208122 and 2.462438%, respectively, where θ=1/3. It is shown from these results that the presented algorithm has higher forecasting accuracy and wider practicability than other methods