A New Method for the Determination of Flow Directions and Upslope Areas in Grid Digital Elevation Models

A new procedure for the representation of flow directions and calculation of upslope areas using rectangular grid digital elevation models is presented. The procedure is based on representing flow direction as a single angle taken as the steepest downwards slope on the eight triangular facets centered at each grid point. Upslope area is then calculated by proportioning flow between two downslope pixels according to how close this flow direction is to the direct angle to the downslope pixel. This procedure offers improvements over prior procedures that have restricted flow to eight possible directions (introducing grid bias) or proportioned flow according to slope (introducing unrealistic dispersion). The new procedure is more robust than prior procedures based on fitting local planes while retaining a simple grid based structure. Detailed algorithms are presented and results are demonstrated through test examples and application to digital elevation data sets. Introduction Flow directions based on digital elevation models (DEMs) are needed in hydrology to determine the paths of water, sediment and contaminant movement. Two important distributed quantities that depend on flow directions are the upslope area and specific catchment area. Upslope area, A, is defined as the total catchment area above a point or short length of contour (Moore et al., 1991). The specific catchment area, a, is defined as the upslope area per unit width of contour, L, (a = A/L) (Moore et al., 1991) and is a distributed quantity that has important hydrological, geomorphological and geological significance (Costa-Cabral and Burges, 1994). The specific catchment area contributing to flow at any particular location is useful for determining relative saturation and generation of runoff from saturation excess in models such as Topmodel (Beven and