A physical explanation of an observed link area‐slope relationship

An observed log‐log linear relationship between channel slope and contributing area is explained by the erosional physics that lead to catchment form. It is postulated that tectonic uplift is in balance with the fluvial erosion down wasting that dominates catchment erosion, and it is shown that this relationship results in the observed log‐log linear relationship at dynamic equilibrium. In addition, it has been observed that there are deviations from this log‐log linear relationship near the catchment divide, with observed slopes being lower than those predicted from the relationship. This is explained by noting that for small areas, fluvial erosion effects are dominated by soil creep and rain splash, modeled by diffusive physics. The area at which this deviation from log‐log linearity occurs is that point on the hillslope at which diffusive physics, like soil creep and rain splash, begin to dominate fluvial erosion. These predictions are confirmed by numerical simulations using a catchment evolution model.