A Mechanistic Model of Waterfall Plunge Pool Erosion into Bedrock

Landscapes often respond to changes in climate and tectonics through the formation and upstream propagation of knickzones composed of waterfalls. Little work has been done on the mechanics of waterfall erosion, and instead most landscape-scale models neglect waterfalls or use rules for river erosion, such as stream power, that may not be applicable to waterfalls. Here we develop a physically based model to predict waterfall plunge pool erosion into rock by abrasion from particle impacts and test the model against flume experiments. Both the model and experiments show that evolving plunge pools have initially high vertical erosion rates due to energetic particle impacts, and erosion slows and eventually ceases as pools deepen and deposition protects the pool floor from further erosion. Lateral erosion can continue after deposition on the pool floor, but it occurs at slow rates that become negligible as pools widen. Our work points to the importance of vertical drilling of successive plunge pools to drive upstream knickzone propagation in homogenous rock, rather than the classic mechanism of headwall undercutting. For a series of vertically drilling waterfalls, we find that upstream knickzone propagation is faster under higher combined water and sediment fluxes and for knickzones composed of many waterfalls that are closely spaced. Our model differs significantly from stream-power-based erosion rules in that steeper knickzones can retreat faster or more slowly depending on the number and spacing of waterfalls within a knickzone, which has implications for interpreting climatic and tectonic history through analysis of river longitudinal profiles.