Accuracy of kinematic wave and diffusion wave for spatialvarying rainfall excess over a plane
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The 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 K F 20 > 5, where K is the kinematic-wave number and F 0 is the Froude number. Therefore, the regions (K F 20 , F 0 ) 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 K F 20 20 with F 0 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 K F 20 > 35 with F 0 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 K F 20 15 with F 0 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 K F 20 30 with F 0 1. For zero-depth gradient at the downstream end, the accuracy field of the kinematic-wave was found to be greater and characterized for K F 20 > 10 with F 0 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for K F 20 > 15 with F 0 1. The diffusive-wave solution was found accurate in the region defined for K F 20 > 7.5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for K F 20 12.5 with F 0 1. The lower limits of the regions, defined on K F 20 , can be considered generally valid for both approximations, but for F 0 < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright 2000 John wiley & Sons, Ltd.