THE LN(A TAN-BETA) INDEX - HOW TO CALCULATE IT AND HOW TO USE IT WITHIN THE TOPMODEL FRAMEWORK/

Topographic indices may be used to attempt to approximate the likely d istribution of variable source areas within a catchment. One such inde x has been applied widely using the distribution function catchment mo del, TOPMODEL, of Beven and Kirkby (1979). Validation of the spatial p redictions of TOPMODEL may be affected by the algorithm used to calcul ate the model's topographic index. A number of digital terrain analysi s (DTA) methods are therefore described for use in calculating the TOP MODEL topographic index, ln(a/tan beta) (a = upslope contributing area per unit contour; tan beta = local slope angle). The spatial pattern and statistical distribution of the index is shown to be substantially different for different calculation procedures and differing pixel re solutions. It is shown that an interaction between hillslope contribut ing area accumulation and the analytical definition of the channel net work has a major influence on calculated ln(a/tan beta) index patterns . A number of DTA tests were performed to explore this interaction. Th e tests suggested that an 'optimum' channel. initiation threshold (CIT ) may be identified for positioning river headwaters in a raster digit al terrain model (DTM). This threshold was found to be dependent on DT M grid resolution. Grid resolution is also suggested to have implicati ons for the validation of spatial model predictions, implying that 'op timum' TOPMODEL parameter sets may be unique to the grid scale used in their derivation. Combining existing DTA procedures with an identifie d CIT, a procedure is described to vary the directional diffusion of c ontributing area accumulation with distance from the channel network.