‘Local gradient’ and between-site variability of erosion rate on badlands in the Karoo, South Africa

Site-average values of local gradient, defined as the steepest slope angle measured at a point, are a powerful predictor of long-term rates of soil loss as measured by erosion pins on the non-channel floor portions of ten badland study sites in the Karoo area of South Africa. Local gradient may be easily measured using a smartphone clinometer. The successful use of local gradient here is in strong contrast to the previous failure of other site-specific attributes, including other measures of gradient and relief, to explain between-site variation in erosion rate on these study sites. Each measurement of local gradient may be thought of as a sample of the site’s microtopography. Microrelief is a strong determinant of the emergent patterns of inter-channel overland flow, and hence of the patterns of inter-channel erosion by flow. Local gradient changes most rapidly during the initial stages of channel incision. When channels are established, local gradient changes more slowly leading to almost-parallel retreat of channel sidewalls. A sensitivity analysis suggests that measurements of local gradient are not all equal with regard to prediction of long-term erosion rate. A greater share of predictive power is contributed by measurements made on very steep or vertical channel side wall areas, and a lesser share is contributed by measurements made on interfluves.