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 8 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.