Using disorder metrics to distinguish discharge-driven from drainage area-driven incision and quantify deviations in channel steepness

The rate of channel incision in bedrock rivers is often described using a power law relationship that scales erosion with drainage area. However, erosion in landscapes that experience strong rainfall gradients may be better described by discharge instead of drainage area. In this study, we test if these two end member scenarios result in identifiable topographic signatures in both idealized numerical simulations and in natural landscapes. We find that in simulations using homogeneous lithology, we can differentiate a posteriori between drainage area and discharge-driven incision scenarios by quantifying the relative disorder of channel profiles, as measured by how well tributary profiles mimic both the main stem channel and each other. The more heterogeneous the landscape becomes, the harder it proves to identify the disorder signatures of the end member incision rules. We then apply these indicators to natural landscapes, and find, among eight test areas, no clear topographic signal that allows us to conclude a discharge or area-driven incision rule is more appropriate. We then quantify the distortion in the channel steepness index induced by changing the incision rule. Distortion in the channel steepness index can also be driven by changes to the assumed reference concavity index, and we find that distortions in the normalized channel steepness index, frequently used as a proxy for erosion rates, is more sensitive to changes in the concavity index than to changes in the assumed incision rule. This makes it a priority to optimize the concavity index even under an unknown incision mechanism.