River self-organisation inhibits discharge control on waterfall migration.

The action of rivers within valleys is fundamentally important in controlling landscape morphology, and how it responds to tectonic or climate change. The response of landscapes to external forcing usually results in sequential changes to river long profiles and the upstream migration of waterfalls. Currently, models of this response assume a relationship between waterfall retreat rate and drainage area at the location of the waterfall. Using an experimental study, we show that this assumption has limited application. Due to a self-regulatory response of channel geometry to higher discharge through increasing channel width, the bed shear stress at the lip of the experimental waterfall remains almost constant, so there was no observed change in the upstream retreat rate despite an order of magnitude increase in discharge. Crucially, however, the strength of the bedrock material exhibits a clear control on the magnitude of the mean retreat rate, highlighting the importance of lithology in setting the rate at which landscapes respond to external forcing. As a result existing numerical models of landscape evolution that simulate the retreat of waterfalls as a function of drainage area with a fixed erodibility constant should be re-evaluated to consider spatial heterogeneity in erodibility and channel self-organisation.