Muskingum Models’ Development and their Parameter Estimation: A State-of-the-art Review

River flood routing is an important issue in current water resources management. As a popular hydrological flood routing method, Muskingum model has always been the dominant method of flood routing. This paper reviews the development of Muskingum model and the research status of its parameter estimation. The characteristics and relationships of different types of Muskingum models are compared, and it is found that the combination of mathematical techniques and evolutionary algorithms has shown good results in parameter estimation in recent years. In addition, this paper also gives a brief overview of six accuracy evaluation criteria and nine research case data sets commonly used in the literature. It also introduces some challenges of the Muskingum model and new trends in future research, which should interest researchers and engineers.