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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 634852, 7 pages
Research Article

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

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Electrical and Information Engineering, Hunan Institute of Traffic Engineering, Hengyang, Hunan 421001, China
3School of Information Science and Engineering, Hunan City University, Yiyang, Hunan 413000, China
4Department of Mathematics and Computer Science, Chizhou College, Chizhou, Anhui 247000, China

Received 28 August 2014; Accepted 4 December 2014; Published 21 December 2014

Academic Editor: Valder Steffen Jr.

Copyright © 2014 Zhou Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 to approximate Muskingum model is presented. The accuracy of these methods is second-order, when . Particularly, if we choose , 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 . It is shown from these results that the presented algorithm has higher forecasting accuracy and wider practicability than other methods.