New nonlinear variable-parameter Muskingum models

The Muskingum model has been widely utilized for flood routing by water resources engineers for decades. Since the relation between channel storage and weighted summation of inflow and outflow seems to be nonlinear, a constant exponent parameter is used to account for this nonlinearity. On the other hand, the nonlinear Muskingum models with constant parameters cannot address variation of Muskingum parameters during flood period. In this paper, fourteen new Muskingum models with variable parameters are proposed. In these models, the routing period is divided into two or three sub-periods and the proposed versions of the Muskingum models can possess parameters with different values in these sub-periods. This capability enhances the Muskingum flood routing approach to better capture the reach characteristics and subsequently improve the routing results. The flood routing results for the selected data set demonstrate that three variable-parameter model reduces the SSQ value more than 89% comparing with the best three constant-parameter Muskingum model in the literature. Additionally, it was concluded that considering x-parameter as a variable parameter during a flood period affects the parameter estimation more than imposing the K- and m-parameters to be variable.