Upscaling surface flow equations depending upon data availability at different scales

Abstract

St. Venant equations, which are used to model sheet flows, are point-scale, depth-averaged equations, requiring data on model parameters at a very fine scale. When data are available at the scale of a hillslope transect, the point equations need to be upscaled to conserve the mass and momentum at that scale, Hillslope-scale upscaled model must be developed if data are available at that scale. The performance of the three models applied to simulate flows from non-rilled surfaces revealed that the hillslope-scale upscaled model performs as good as the point-scale model though it uses far less data. The transectionally-upscaled model slightly underestimates the observed data.