Modelling of Nonlinear Muskingum Method Using Control System Concept

Flood routing is a mathematical procedure to predict the change in magnitude, speed and shape of a flood wave, when it propagates down a river or through a reservoir, as a function of time. The Muskingum model continues to be a popular method for flood routing for river reach. The linear form of the Muskingum model has been widely applied to river flood routing. However, a nonlinear relationship between storage and discharge exists in actual river systems, making the use of the linear model inappropriate. In this study, a model for representing Muskingum nonlinear method is developed by using control system concept. The continuity and storage equations are used together for such a development. The nonlinear model is represented in an implicit manner by using Simulink library in MATLAB. The resulting outflow hydrograph is compared with the result obtained using conventional method. It is found that the methodology can represent the nonlinear Muskingum method very well. The advantage of this representation is that it can be easily manageable and manoeuvrable, especially where there are large number of stream links and lateral inflows. In addition, it will be amenable for the parameter estimation in an easy way, though not attempted in this study.