A downscaling method of topographic index distribution for matching the scales of model application and parameter identification

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Higher resolution topographic information contained in the topographic index of TOPMODEL is lost when digital elevation models (DEMs) with a coarse grid resolution are used; thus, the topographic index is scale dependent, demonstrating identified model parameter values to be dependent on DEM resolution. This makes it difficult to use model parameter values identified through a different resolution of TOPMODEL. The inconsistency is the result of the difference between the scale at which the model parameters are identified and the scale at which the model is applied. To overcome this problem, scale laws that govern the relationship between the resolution of digital elevation data and geomorphometric parameters of the topographic index were analysed and a method to downscale the topographic index distribution developed to account for the difference in scales between model application and parameter identification. The method to downscale the topographic index is composed of two ideas: one involves introducing a resolution factor to account for the scale effect in upslope catchment area per unit contour length in the topographic index; the other utilizes a fractal method through steepest slope scaling to account for the scale effect on slopes. This method successfully derived a topographic index distribution of a fine-resolution DEM by using only a coarse-resolution DEM. The method has been applied successfully to the Kamishiiba catchment (210 km2) in Japan and has demonstrated that the downscaled topographic index distribution derived using a 1000 m grid DEM is very similar to the topographic index distribution derived via fine-target-resolution DEMs. The method is then coupled with a TOPMODEL simulation to match the scales of model application and parameter identification. It is shown that the simulated runoff from the downscaled TOPMODEL applied at 1000 m resolution of the Kamishiiba catchment, with the same set of effective parameter values derived from 50 m resolution DEM, matched the simulated runoff in the 50 m DEM resolution TOPMODEL. It was also shown that TOPMODEL coupled with the downscaling method of the topographic index accurately simulated runoff for different rainfall events in the catchment without recalibration.

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