Predicting the Topographic Limits to a Gully Network Using a Digital Terrain Model and Process Thresholds

A digital terrain model is used with process thresholds to predict the extent of a stable gully network in a 5 km 2 catchment of the southeastern highlands of Australia. The model, developed by Dietnch et al . 1992, 1993, predicts the topographic controls on channel networks and interprets these in terms of a critical shear stress for channel incision (τ c ) applied by saturation overland flow. We adapt the model slightly to compare the shear stress applied by Hortonian overland flow to that applied by saturation overland flow. The limits to gully erosion in the catchment are controlled strongly by a topographic threshold that has an inverse relationship between upslope catchment area and local gradient. The topographic threshold for channel incision is reproduced using a simple model of Hortonian overland flow and a τ c appropriate for incision into a degraded grass surface (τ c = 245 dyn/cm 2 ). This is consistent with historical evidence for the timing of gully erosion. The study confirms a strong topographic control on the extent of the channel network in a catchment significantly different from the western North America catchments where the topographic threshold was first demonstrated. Despite its simplicity, the model for incision by overland flow appears capable of distinguishing the hydrological processes responsible for channel incision when these are reflected in the relationship between channel network and landscape morphology. The model requires relatively simple inputs, suggesting it may be useful for mapping gully erosion hazard in actively eroding catchments.