Nonlinear Muskingum Model for Flood Routing in Irrigation Canals Using Storage Moving Average

Abstract

The Muskingum routing method involves the calculation of the storage volume in river reaches. The accurate calculation of the storage volume is difficult to achieve with the nonlinear Muskingum model (NMM). This paper couples the storage moving average (SMA) with NMM to produce a Muskingum storage moving average model (MUSSMAM), which has improved the accuracy of storage volume and output hydrograph calculation over the NMM. The parameters of the NMM and the weighting coefficients in the SMA are treated as dimensionless parameters in the combined MUSSMAM formulation. A hybrid method that merges the generalized reduced gradient (GRG) solver with an evolutionary (EV) solver is employed to obtain the best combination of parameter values of the MUSSMAM. The sum of the squared deviation (SSQ) between observed and routed inflows is the objective function optimized with the hybrid GRG-EV solver. The proposed MUSSMAM is tested with experimental, real, and multimodal hydrograph-routing problems. These results demonstrate that MUSSMAM reduces the SSQ by 2, 10, and 29 percent compared to the NMM in experimental, real, and multimodal problems, respectively.