The in(a/tan/β) 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 distribution of variable source areas within a catchment. One such index has been applied widely using the distribution function catchment model, TOPMODEL, of Beven and Kirkby (1979). Validation of the spatial predictions of TOPMODEL may be affected by the algorithm used to calculate the model's topographic index. A number of digital terrain analysis (DTA) methods are therefore described for use in calculating the TOPMODEL 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 resolutions. It is shown that an interaction between hillslope contributing area accumulation and the analytical definition of the channel network has a major influence on calculated ln(a/tan beta) index patterns. A number of DTA tests were performed to explore this interaction. The tests suggested that an 'optimum' channel. initiation threshold (CIT) may be identified for positioning river headwaters in a raster digital terrain model (DTM). This threshold was found to be dependent on DTM grid resolution. Grid resolution is also suggested to have implications for the validation of spatial model predictions, implying that 'optimum' TOPMODEL parameter sets may be unique to the grid scale used in their derivation. Combining existing DTA procedures with an identified CIT, a procedure is described to vary the directional diffusion of contributing area accumulation with distance from the channel network.

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