Versatile Muskingum flood model with four variable parameters

Early researchers recognised that the long-established Muskingum hydrologic routing model's parameters vary with flood characteristics, but no methods were developed to account for this variation. Such methods would have made the model too complex to solve using prevailing technical knowledge. This paper presents a versatile non-linear Muskingum model with four variable parameters; each is represented by a two-step function of a dimensionless inflow variable, so the model thus has eight parameters. The model is general and produces a wide array of 15 special models with the number of parameters ranging from four to seven. The routing procedure is based on the modified Euler method. Three examples with different hydrograph types were used to evaluate model performance. Based on the application results, guidelines for model selection for different hydrograph types are presented. The recommended models have four to six parameters and substantially improve model performance for predicting flood flows compared with the traditional three-parameter model. This research continues to promote alternative thinking to improve model performance by modifying model structure, instead of the solution algorithm.