  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.
