Performance Evaluation of Different Numerical Schemes for Muskingum Flood Routing (Case study: Karoon River, Iran)

The Muskingum model, widely used in flood routing, is the first order differential equation. The accuracy of the routing storage equation of the model depends on correct parameter estimation and a numerical method employed for its solution. In the present study, different explicit numerical methods are used for solving the equation. These methods include Euler, modified Euler, Runge-Kutta 4th order and Runge-Kutta-Fehlberg. For optimal parameter estimation, Shuffled Complex Evolution (SCE) algorithm is adopted. The performance of different numerical schemes are studied by appropriate evaluation criteria. The methods are tested against three historical and well-known flood data from literature and a field data from Karoon River, Iran as a natural river. Results indicated a good performance of the SCE algorithm and the Runge-Kutta 4th order method in the flood hydrograph numerical simulations. Regarding the sum of squared deviations and for the flood data of Karoon River, the Runge-Kutta 4th order method yielded 18% better results than traditional Euler method in the field condition of a natural river. Similar results can be observed for the first case study, where the Runge-Kutta 4th order method yielded 178% better results than traditional Euler method. However, for second and third case studies the results of all considered numerical methods nearly are in a same level of accuracy. Therefore, it can be said that an appropriate numerical scheme for a hydrological flood routing problem can be adopted by considering the relationship between storage volume and weighted flow.