Analysis of Erosion Thresholds, Channel Networks, and Landscape Morphology Using a Digital Terrain Model

To investigate the linkage between erosion process and channel network extent, we develop two simple erosion threshold theories driven by a steady state runoff model that are used in the digital terrain model TOPOG to predict the pattern of channelization. TOPOG divides the land surface into elements defined by topographic contours and flow lines, which can be classified as divergent, convergent and planar elements. The calibration parameter for the runoff model is determined using empirical evidence that the divergent elements which comprise the ridges in our study area do not experience saturation overland flow, where as the convergent elements in the valleys do during significant runoff events. A threshold theory for shallow landsliding predicts a pattern of instability consistent with the distribution of landslide scars in our $$1.2 km^{2}$$ study site and confirms the interpretation, based on field observations, that indicate the steeper channel heads to be at least partially controlled by slope instability. Most sites of predicted and observed slope instability do not, however, support a channel head, hence landslide instability alone is not sufficient for channelization. In contrast, most elements predicted to be eroded by saturation overland flow coincide with the observed location of the channel network. In addition, areas of predicted downslope decrease in relative sediment transport capacity were found to correspond to locations where channels became discontinuous. The topographic threshold given by the saturation overland flow erosion theory varies with the third power of critical boundary shear stress, suggesting that critical shear stress, although difficult to quantify with much precision in the field, is a dominant control on the extent of the channel network where saturation overland flow is significant. Current extent of the channel network in our field site, for example, may best be explained as resulting from grazing-induced reduction in surface resistance.