Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology

Abstract

[1] The sediment load of a bedrock river plays an important role in the fluvial incision process by providing tools for abrasion (the tools effect) and by covering and thereby protecting the bed (the cover effect). We derive a new formulation for the cover effect, in which the fraction of exposed bed area falls exponentially with increasing sediment flux or decreasing transport capacity, and explore its consequences for the model of bedrock abrasion by saltating bed load. Erosion rates predicted by the model are higher than those predicted by earlier models. In a closed system, the maximum erosion rate is predicted to occur when sediment supply is equal to transport capacity for a flat bed. By optimizing the channel geometry to minimize the potential energy of the stream and using representative values for both discharge and grain size, we derive equations for the geometry of a bedrock river and explore how predictions for width, slope, and bed cover vary as functions of drainage area, rock uplift rate, and rock strength. The equations predict a dependence of channel width on drainage area similar to the relations using a simple shear stress incision law. The slope-area relationship is predicted to be concave up in a log-log regime, with a curvature dependent on uplift rate. However, this curvature does not deviate sufficiently from a straight line to allow discrimination between models using empirical data. Dependence of channel width and slope on rock uplift rate can be separated into two domains: for low uplift rates, channel geometry is largely insensitive to uplift rate due to a threshold effect. At high uplift rates, there is a power law dependence. Bed cover is predicted to increase progressively downstream and to increase with increasing uplift rate. In our model, the width-to-depth ratio is a function of both tectonic and climatic forcing. This indicates that the scaling between channel width and bed slope is neither a unique indicator of tectonic forcing at steady state nor a signature of transience or steady state. We conclude that sediment effects need to be taken into account when modeling bedrock channel morphology.Citation: Turowski, J. M., D. Lague, and N. Hovius (2007), Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology,

The influence of sediment thickness on energy delivery to the bed by bedload impacts

“…Despite its importance for the understanding of bedrock channel morphology (Finnegan, Sklar, & Fuller, 2007;Turowski, Lague, & Hovius, 2007), channel-hillslope coupling (Hovius & Stark, 2006), the formation of erosional bedforms (Wilson, Hovius, & Turowski, 2013) and the evolution of whole mountain belts (Egholm, Knudsen, & Sandiford, 2013), the erosion of bedrock by fluvial processes is poorly understood. In general, processes driving bedrock erosion within a channel can be classified into four groups (Hancock, Anderson, & Whipple, 1998;Turowski, 2012, Chapter 29;Whipple, Hancock, & Anderson, 2000;Wilson et al, 2013).…”

“…Note that under the assumptions stated above, the exponential cover model arises for both the static and the dynamic cover effect (cf. Turowski, 2009;Turowski et al, 2007). Both the linear (Equation (1)) and the exponential (Equation (2)) cover models are steady state equations, that is, they cannot capture the transient adjustment of sediment cover to changing conditions of water flow and sediment supply.…”

“…The cover effect is often quantified as the fraction of uncovered area of the total bed, F e , and is typically modelled as a function of the ratio of sediment supply Q s to transport capacity Q t (Chatanantavet & Parker, 2008;Sklar & Dietrich, 2004;Turowski, 2009;Turowski et al, 2007). The most widely used cover function is the linear-decline model (Sklar & Dietrich, 1998, 2004, where…”

“…In contrast, as more sediment is supplied, it will cover the bed and protect it from impacts, and erosion rates decrease. This is known as the cover effect, which can be divided into a static cover effect, where shielding of the bed is due to stationary sediment, and a dynamic cover effect, where mobile particles interact and reduce the number of bed impacts (Turowski et al, 2007). There is now evidence for the importance of both the tools and the cover effect in a variety of field settings and over a range of spatial and temporal scales Beer, Turowski, Fritschi, & Rieke-Zapp, 2015;Cook, Turowski, & Hovius, 2013;Cowie et al, 2008;Hobley, Sinclair, Mudd, & Cowie, 2011;Jansen et al, 2011;Johnson, Whipple, Sklar, & Hanks, 2009;Turowski, Hovius, Hsieh, Lague & Chen, 2008;Turowski, Hovius, Wilson, & Horng, 2008;Wilson et al, 2013;Yanites et al, 2011).…”

“…Turowski et al (2007) derived the exponential cover model, which arises when uniformly sized sediment particles are randomly distributed onto a flat bed under uniform flow conditions (see also Turowski, 2009).…”