Re-scaling the topographic index to improve the representation of physical processes in catchment models

The assignment of hydrological model parameters from physically measurable catchment attributes remains an unsolved problem. Several authors have shown that for the hydrological model, TOPMODEL, there is a relationship between the scale of the digital elevation model (DEM) and the saturated hydraulic conductivity parameter used to calculate water table position and baseflow. For models that use DEM data from pixels measured in tens of metres, the value of the corresponding saturated hydraulic conductivities for satisfactory flow reproduction are often much larger than measured values and this causes most surface flow to be generated by the saturation excess mechanism. This is undesirable in environments where infiltration-excess runoff can also occur. This paper presents a way to objectively compensate for the distorting effect of DEM-scale on the value of the saturated hydraulic conductivity so that its measured value can be used in TOPMODEL simulations. The method described links the distribution of topographic index, ln(a/tan β), to a spatial variability measure (SVM) based on the Shannon and Weaver information content equation for a digital signal. By maximising the SVM, an optimum adjustment to the mean of the distribution of topographic index can be made so that the distribution represents what would have been calculated had a DEM been available at the spatial resolution at which the saturated hydraulic conductivity was measured. The method is applied to a TOPMODEL of the Mahurangi basin in New Zealand, and it is shown that physically reasonable simulations are achieved with the adjusted distribution of topographic index.