Determination of the Nonlinear Muskingum Model Coefficients Using Genetic Algorithm and Numerical Solution of the Continuity Equation

Abstract

The optimization method is an appropriate choice for determining optimal parameters in the Muskingum model, in order to increase the speed of computations; coefficients of this model have been computed optimally with assistance of the genetic algorithm. These coefficients were computed from the linear Muskingum and Muskingum-Cunge models using required data and the available relations. In order to evaluate efficiency of the procedure of optimizing coefficients of the nonlinear Muskingum model via the genetic algorithm method compared with the other two methods used for determining these coefficients, outflow hydrographs were computed using the optimal coefficients and solving the continuity equations according to the Runge-Kutta method order 4 and was compared with the two flood routing methods from the Muskingum and Muskingum-Cunge models as well.

To study the precision of these three methods, square root of sum of squares of difference of discharges computed from each of the three methods and observational discharges obtained from the HEC-RAS RMSE software was used as the objective function and achieved results indicate more proximity of the computed hydrographs from the optimization coefficients in the Runge-Kutta order 4 to the outflow hydrographs obtained to the HEC-RAS software compared with the two Muskingum and Muskingum-Cunge models.