The topographic index (TI) plays a key role in TOPMODEL which is a conceptual rainfall-runoff model of small river basins. The TI, depending in each point of the catchment upon local stream slope and upslope contributing drainage area, is usually computed from a regular raster digital elevation model (DEM). Many studies have shown that the TI distribution is largely affected by the DEM resolution; for example, the mean of TI increases when the DEM resolution decreases, i.e. with coarser cell sizes and this shift leads to larger calibrated transmissivities and saturated hydraulic conductivities. We propose a simple explanation to the shift by using the fractal characteristics of river basins; the probability distribution of contribution area shows a good agreement with a power law form, and the plot of mean slope versus contribution area also has a power law scaling. Combining these two relations together, we obtain a new formula between the shift of the TI distribution and the DEM resolution. We also examine how the TI distribution deviates from the power law.
