The Diffusion wave equations are obtained from the unsteady flow continuity equation and momentum equation by neglecting the local inertia and convective acceleration terms in the momentum equation [Sjosberg, 1981]:
The bottom slope is incorporated into the gradient of H.
An advantage of the diffusion wave equation is the absence of wave characteristics and hence no distinction must be made between subcritical and supercritical flows. The solution will be continuous because a hydraulic jump cannot develop.
The kinematic wave assumption is even simpler than the diffusion wave approximation since the pressure term is also ignored in the solution. The kinematic solution is bed slope equals friction slope, or So = Sf.
EXTRAN uses the Kinematic Wave equation for special flow situations.