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

Channel routing is important in flood forecasting and watershed modeling. The general constant-parameter Muskingum-Cunge (CPMC) method is second-order accurate and easy to implement. With specific discretizations such that the temporal and spatial intervals maintain a unique relationship, the CPMC method can be third-order accurate. In this paper, we derive the average lateral inflow term in the second- and third-order accuracy CPMC method, and demonstrate that For spatially and temporally variable lateral inflow, the effect of lateral inflow on simulated discharge varies with spatial and temporal discretizations, the value and spatial and temporal variations of lateral inflow, wave celerity, and diffusion coefficient. Comparison of the CPMC solution with the analytical solution shows that both the second- and third-order accuracy schemes are more accurate than the simplified method by which spatial derivatives of lateral inflow are ignored. For small time steps, the third-order accuracy CPMC method results in higher accuracy than the second-order scheme even when the third-order accuracy criterion is not fully met. For large time steps, the temporal and spatial discretization of the third- and second-order scheme becomes the same, but the third-order scheme yields higher accuracy than the second-order scheme because of the third-order accurate estimation of the lateral inflow term.