Comparison of Overland Flow Hydrograph Models

Abstract

The diffusion equation is a simplification of the two‐dimensional continuity and momentum equations. This simpler dynamic model of two‐dimensional hydraulics affords the hydrologist a means to quickly estimate floodflow effects for overland flow. A numerical model using the diffusion approach (DHM) is applied to a set of idealized catchments in order to develop synthetic unit hydrograph S‐graph equivalents. The model is based on an explicit, integrated finite‐difference scheme, and the catchment is represented by topographic elevation and geometric data. Synthetic unit hydrographs (S‐graphs) developed from use of the DHM are used to advance interesting relationships between the unit hydrograph lag factor and the constant effective rainfall intensity used to generate the S‐graphs. Sensitivity of the synthetic S‐graphs to variations in idealized catchment size, slope, shape, friction parameters, and effective rainfall intensity are examined. Comparisons between linear and nonlinear unit hydrograph models, and a diffusion (DHM) and kinematic wave simplification of DHM are made for various time distributions of effective rainfall. Use of the standard SCS unit hydrograph is shown to provide a reasonable approximation of two‐dimensional overland flow as predicted by a DHM or kinematic routing technique.