Errors of kinematic-wave and diffusion-wave approximations for steady-state overland flows

Steady-state flows occur in a variety of geophysical processes. Their mathematical treatment is usually based on either the dynamic-wave equations or their approximations—kinematic wave and diffusion wave. Errors of these approximations were derived for steady-state cases of overland flow under the zero depth-gradient at the downstream boundary condition. Although both the diffusion-wave and the kinematic-wave approximations were found to be in good agreement with the dynamic wave representation for a range of flow conditions, their error greatly depended on the parameter KF02 where K is the kinematic-wave number and F0 is the Froude number. In general, the diffusion-wave approximation was superior to the kinematic wave approximation.