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Channel routing is important in flood forecasting and watershed modeling. Thegeneral constant-parameter Muskingum-Cunge (CPMC) method is second-orderaccurate and easy to implement. With specific discretizations such that thetemporal and spatial intervals maintain a unique relationship, the CPMC methodcan be third-order accurate. In this paper, we derive the average lateralinflow term in the second- and third-order accuracy CPMC method, anddemonstrate that For spatially and temporally variable lateral inflow, theeffect of lateral inflow on simulated discharge varies with spatial andtemporal discretizations, the value and spatial and temporal variations oflateral inflow, wave celerity, and diffusion coefficient. Comparison of theCPMC solution with the analytical solution shows that both the second- andthird-order accuracy schemes are more accurate than the simplified method bywhich spatial derivatives of lateral inflow are ignored. For small time steps,the third-order accuracy CPMC method results in higher accuracy than thesecond-order scheme even when the third-order accuracy criterion is not fullymet. For large time steps, the temporal and spatial discretization of thethird- and second-order scheme becomes the same, but the third-order schemeyields higher accuracy than the second-order scheme because of the third-orderaccurate estimation of the lateral inflow term.

Accuracy of the Muskingum-Cunge method for constant-parameter diffusion-wave channel routing with lateral inflow