A Mechanistic Model of Waterfall Plunge Pool Erosion into Bedrock

Abstract

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.

Statistical modelling of co-seismic knickpoint formation and river response to fault slip

“…Baynes et al, 2015), rock strength (e.g. Stock and Montgomery, 1999;Hayakawa and Matsukura, 2003;Baynes et al, 2018), fracture density and orientation (Antón et al, 2015;Brocard et al, 2016) and the spacing and height of the waterfalls (Scheingross and Lamb, 2017). Preservation of knickpoint shape during retreat is poorly understood as very little data exist on the temporal evolution of their shape.…”

“…Even if most simulations of this paper are done with a simple kinematic model using a constant knickpoint velocity, we now consider a model with a knickpoint velocity that depends on knickpoint height with V R = r(1 + h/ h 0 ) q , where d is a constant, set to the previously used constant knickpoint retreat rate of 0.1 m year −1 , h the knickpoint height, h 0 = 1 m a reference knickpoint height and r = 0.1 an exponent representing the sensitivity of knickpoint velocity to knickpoint height. This model is motivated by mechanical arguments suggesting a dependency of knickpoint velocity to their height (Scheingross and Lamb, 2017). We allow a quicker knickpoint of height h i that encounters slower knickpoints of height h j to merge, forming in turn a single knickpoint of height h i + h j and of greater speed than the former knickpoints.…”

“…If the migration of knickpoints or slope patches is classically modelled using the stream power incision model (Rosenbloom and Anderson, 1994;Whittaker and Boulton, 2012;Royden and Perron, 2013), this approach was recently questioned by experimental (Baynes et al, 2018) and field (Brocard et al, 2016) results, suggesting no obvious dependency of the migration rate on river discharge. Mechanistic models of waterfall erosion and retreat offer another more accurate but more complex approach (Scheingross and Lamb, 2017).…”

“…with a slope above average local slope) and waterfalls (i.e. with a slope close to infinity) appears as a fundamental ingredient of their survival, retreat rate and river incision (Hayakawa and Matsukura, 2003;Baynes et al, 2015;Scheingross and Lamb, 2017). Similar issues arise for hillslope dynamics impacted by fault scarp development (Arrowsmith et al, 1996) and possibly for faults in glaciated landscapes.…”

A fundamental equation for describing the rate of bedrock erosion by sediment‐laden fluid flows in fluvial, coastal, and aeolian environments

“…Geomorphic changes strongly associated with fluvial abrasion (Wohl, 1998;Whipple et al, 2013) may be represented by various features such as the lowering of bedrock channel floors (Seidl et al, 1994;Hancock et al, 1998;Johnson et al, 2010;Inoue et al, 2014), the widening of bedrock channels (Finnegan et al, 2007;Turowski et al, 2008;Fuller et al, 2016), the development of potholes (Springer et al, 2005(Springer et al, , 2006Johnson and Whipple, 2007;Pelletier et al, 2015), the growth of plunge pools (Lamb et al, 2007;Scheingross and Lamb, 2017), knickpoint retreat (Haviv et al, 2010;Valla et al, 2010), and the formation of hanging valleys (Crosby et al, 2007). Following Howard and Kerby (1983) who postulated that the bedrock incision rate can be approximated by the bottom shear stress of streams, many models to describe the erosion rate, collectively called the stream-power model (Whipple, 2004), have been proposed for the study of bedrock river evolution (overviews by Sklar and Dietrich, 2006;Whipple et al, 2013).…”