Evaluation and Improvement of Routing Procedure for Nonlinear Muskingum Models

Abstract

Due to the existence of the nonlinear relationship between storage and discharge in Muskingum model, the model parameters and outflow cannot be directly determined. The traditional routing procedure has been widely applied in model calibration and flood routing. However, most previous studies only focused on the accuracy of parameter estimation which adopt the traditional routing procedure, ignored the correctness and effectiveness of routing procedure itself. In this study, three routing schemes of traditional routing procedure are evaluated by simulation experiment and the results demonstrate that the routing scheme 1 is the best, and scheme 3 is followed, the worst one is scheme 2. But the scheme 1 and 3 yield parameters estimates and the corresponding outflow hydrographs may violate the routing equations in terms of residuals. The scheme 2 is legitimate; however, the accuracy is not high enough. As an alternative, a new routing procedure based on iterative method is proposed for parameter estimation and flood routing of the nonlinear Muskingum models. The proposed routing procedure is applied to model calibration and flood routing for three examples involving single-peak, multi-peak, and non-smooth hydrographs. The results indicate that the proposed routing procedure can not only satisfy the routing equations for all time stages in the routing process, but also be superior to scheme 2. Therefore, it can be confidently applied to parameter estimation and flood routing for the nonlinear Muskingum models.