Errors of kinematic-wave and diffusion-wave approximations for time-independent flows

Time-independent (or steady-state) cases of planar (overland) flow were treated. Errors of the kinematic-wave and diffusion-wave approximations were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth-gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with error in the range of 1–2% for values ofKF ₀ ² (7.5). Even for small values ofKF ₂ ⁰ (e.g.,KF ₂ ⁰ =0.75), the errors were typically in the range of 11–15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to vary from 7 to 13% in the regions 0.05x0.95 forKF ₀ ² =0.75 and was greater than 30% forKF ₀ ² =0.75.