Effects of catchment discretization on topographic index distributions

Digital elevation models (DEMs) are widely used in topographically-based hydrology models. Most researchers dealing with DEMs have worked exclusively with either grid or contour based techniques. Intercomparisons of these techniques are empirical in nature, few in number and limited to a small number of catchments. We examine the relative effects of these techniques on the distribution of the topographic index (TI) for nine idealised hillslope types and eight natural catchments (4.4–83 km 2) in southeast Australia. In particular we investigate the underlying causes for the frequently observed increase in the TI with grid size. A simple analytical model for a parallel-planar hillslope indicates that median TI is asymptotic with respect to the number of grid cells and a linear function of grid size. We demonstrate that the latter result holds for hillslopes with more complex geometry. Using a multiple flow direction algorithm, we find that hillslope geometry and flow partitioning affect the spatial pattern of the TI and the rate of change ( M) of median TI with grid size. This makes it impractical to recommend general guidelines for the value of the directional parameter in flow partitioning algorithms. For the natural catchments we show that median TI is also a linear function of grid size and that there is some evidence for a linear relationship between M and the inverse of the median topographic slope. Throughout the investigation we find that contour DEMs are less sensitive to changes in resolution than grid DEMs.