Improved Nonlinear Muskingum Model with Variable Exponent Parameter

The nonlinear Muskingum model has three parameters (storage parameter, weighting parameter, and exponent parameter) that are assumed in model estimation to be constant. The exponent parameter, which has no physical meaning, represents the average nonlinear behavior of the flood during the entire routing period. To address the variations of nonlinearity during the routing period, this paper considers a variable exponent parameter that varies with the inflow level. The boundaries of the inflow levels are considered to be dimensionless parameters. The problem is formulated as a mathematical optimization model that minimizes the sum of the squared (SSQ) or absolute deviations between the observed and estimated outflows. An efficient spreadsheet-based software is implemented. The proposed model was applied by using three examples involving single peak, multipeak, and nonsmooth hydrographs. The results show that the range of the optimal exponent parameters is small, yet the improvement in the fit of the nonlinear Muskingum model is substantial; the SSQ reduction reaches 35%, compared with the case of a constant exponent parameter. The proposed model should be of interest to researchers and engineers working in the area of flood management.