Accuracy of kinematic wave and diffusion wave for spatial-varying rainfall excess over a plane

The kinematic-wave and diffusive-wave approximations were investigated for
unsteady overland flow due to spatially varying rainfall excess. Three
types of boundary conditions were adopted: zero flow at the upstream end,
and critical flow and zero depth-gradient at the downstream end. Errors
were derived by comparing the dimensionless profiles of the flow depth
over the plane with those computed from the dynamic-wave solution. It was
found that the mean errors for both the approximations were independent of
the type of rainfall excess distribution for , where K is the kinematic-
wave number and F0 is the Froude number. Therefore, the regions ( F0)
where the kinematic-wave and diffusive-wave solutions would be fairly
accurate and for any distribution of spatially varying rainfall, were
characterized. The kinematic-wave approximation was reasonably accurate,
with a mean error of less than 5% and for the critical depth at downstream
end, for with F0¡Ü1; if the rainfall excess was concentrated in a
portion of the plane, the field where the kinematic-wave solution was
found accurate, it was more limited and characterized for with F0¡Ü1.
The diffusive-wave solution was in good agreement with the dynamic-wave
solution with a mean error of less than 5%, in the flow depth, for with
F0¡Ü1; for rainfall excess concentrated in a portion of the plane, the
accuracy of the diffusion wave solution was in a region more restricted
and defined for with F0¡Ü1. For zero-depth gradient at downstream end,
the accuracy field of the kinematic-wave was found more large and
characterized for with F0¡Ü1; for rainfall excess concentrated in a
portion of the plane, the region was smaller and defined for with F0¡Ü1.
The diffusive-wave solution was found accurate in the region defined
for , whereas for rainfall excess concentrated in a portion of the plane,
the field of accuracy was for with F0¡Ü1. The lower limits of the
regions, defined on , can be considered generally valid for both
approximations, but for F0<1 smaller lower limits were also characterized.
Finally, the accuracy of these approximations was significantly influenced
by the downstream boundary condition.