A methodology for calculating the spatial distribution of the area-slope equation and the hypsometric integral within a catchment

The area-slope relationship and the hypsometric curve are well known catchment descriptors. The main shortcoming of traditional area-slope and hypsometry extraction methods is their limited ability to represent heterogeneity within the catchment. Here we present a new methodology for explicit calculation of the spatial distribution, at a pixel scale within a catchment, of the area-slope parameters and the hypsometric integral. This method allows us to create a quantitative representation of the area-slope equation and the hypsometric integral which can potentially be used in a variety of geomorphologic applications. The results show that the spatial distribution of both the area-slope equation and the hypsometric integral are noisy at the pixel scale. In order to reduce the noise three averaging techniques were examined. Subcatchment-scale averaging was found to be the best at identifying the spatial distribution of the area-slope equation and hypsometric integral. At the subcatchment scale the spatial distribution of the area-slope equation and the hypsometric integral approximated the spatial distribution of soil morphological and geological units of the Goulburn River catchment in eastern Australia. The spatially distributed area-slope results were tested using manually extracted subcatchment average area-slope values and found to be well correlated. The spatially distributed hypsometric integral was also well correlated with landform concavity and convergence. The subcatchment-scale averaging of the spatially distributed area-slope equation and hypsometric integral is shown to be a promising tool for producing spatially distributed data. The techniques are demonstrated on a catchment that has marked spatial variation in soils and geology. The results show that the spatially explicit maps can potentially identify the spatial extent of these soil types and geological features and agrees well with existing soil maps.