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

Abstract

AbstractThe kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from 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 KF02 > 5, where K is the kinematic‐wave number and F0 is the Froude number. Therefore, the regions (KF02, 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 the downstream end, for KF02 ≥ 20 with F0 ≤ 1; 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 KF02 > 35 with F0 ≤ 1. 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 KF02 ≥ 15 with F0 ≤ 1; 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 KF02 ≥ 30 with F0 ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF02 > 10 with F0 ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF02 > 15 with F0 ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF02 > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF02 > 12·5 with F0 ≤ 1. The lower limits of the regions, defined on KF02, 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 influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd.