Interactions between model predictions, parameters and DTM scales for topmodel

The scale-dependence of the popular rainfall-runoff model, TOPMODEL, is assessed for a small headwater catchment in the Nepal Middle Hills. Digital terrain analysis is used to calculate the frequency distributions of slope, tan beta, upslope contributing area, a, and the combined hydrological wetness index ln(a/tan beta) for a range of digital elevation model (DEM) grid sizes between 20 and 500 m. The resulting distributions of the topographic index are strongly sensitive to grid size, in which changing estimates of the upslope contributing area are identified as the first-order control. Sensitivity analysis reveals that model predictions are consequently grid-size dependent, although this effect can be modulated by recalibrating the saturated hydraulic conductivity parameter of the model as grid size changes. An analytical link between this parameter and the shape of the probability distribution of the index is tested and found to be reliable over a wide range of scales. A significant change in the model response to scale is identified between grid sizes of 100 and 200 m. This change in grid size is also marked by rapid deterioration of the topographic information contained in the DEM, measured in terms of the statistical entropy. It is suggested that this break in the scaling relationship corresponds to typical hillslope lengths in the dissected terrain, and this scale thus marks a fundamental natural threshold for DEM-based applications. (C) 1998 Elsevier Science Ltd. All rights reserved.