Evaluation of nonlinear Muskingum model with continuous and discontinuous exponent parameters

The nonlinear Muskingum model is traditionally calibrated using a constant exponent parameter. A recent study has proposed a discontinuous function of the exponent parameter that has substantially improved model performance. This paper evaluates model performance using continuous and discontinuous parameters, expressed as a function of dimensionless inflow variable. The parameters were represented by discontinuous (two-step) function and continuous (three-coefficient) function, resulting in five-parameter nonlinear Muskingum model (5P-NLMM) for each scheme. Two continuous functions (logarithmic and exponential) were evaluated using two flood routing procedures: the Modified Euler's (ME) routing procedure and the FourthOrder Runge-Kutta (FORK) routing procedure. The continuous functions and routing procedures were integrated into the Muskingum model. The five parameters of the model were determined using optimization based on minimizing the deviations from observed outflows. The model was applied to three examples with different hydrograph types. The continuous parameter (with ME or FORK) substantially outperformed the discontinuous parameter for smooth and nonsmooth hydrographs, and vice versa for multipeak hydrograph. Guidelines for model selection for different types of hydrographs are presented.