Algorithm for Delineating and Extracting Hillslopes and Hillslope Width Functions from Gridded Elevation Data

The subdivision of catchments into appropriate topography-based hydrologic units is an essential step in rainfall-runoff modeling, with the hillslope serving as a common fundamental unit for this purpose. Hillslope-based modeling approaches can utilize, for instance, the hillslope width function as a one-dimensional representation of three-dimensional landscapes by introducing profile curvatures and plan shapes. In this work, an algorithm was developed to delineate and extract hillslopes and hillslope width functions based on a new approach to calculate average profile curvatures and plan shapes from digital terrain data. The proposed method uses fuzzy logic rules and provides a quick and reliable assessment of hillslope characteristics, classifying hillslopes according to nine elementary landscapes (the so-called Dikau shapes). The algorithm was first tested on two contrasting (flat and steep) catchments in Quebec, Canada. The hillslope width functions obtained with the proposed method were able to preserve the modeled hillslope surface areas within approximately 1% while preserving monotonicity. The algorithm was then applied to the Plynlimon catchments in the United Kingdom for comparison with a previously published scheme. Despite fundamental differences in slope metrics calculations, the proposed method produced qualitatively similar large-scale features.