The Dynamics of Channel Slope, Width, and Sediment in Actively Eroding Bedrock River Systems

Abstract

The evolution of rivers in eroding landscapes plays a key role in determining landscape relief and modulating climate‐tectonic interactions. A common approach to quantifying river system evolution uses a one‐dimensional, detachment‐limited stream power equation. One potential drawback of this model is that it does not incorporate the effects of changes in channel width or the role of sediment transport dynamics. Here I present a new method for modeling the influence of channel width on river dynamics to explore how variable width and sediment transport impact river profile evolution. With this approach, vertical river erosion can operate based on any number of river erosion models, such as a simple shear stress model (e.g., detachment limited), sediment cover‐shear stress hybrid models, or mechanistic saltation‐abrasion models. I explore the sensitivity of these three models to increases in rock‐uplift rate (i.e., 2, 3, 5, 10, and 20× increase). Generally, the results show that incorporating channel width adjustment or sediment transport dynamics lowers the sensitivity of a river profile to rock‐uplift rate. For the sediment transport‐dependent models, the degree of sensitivity depends on whether the system is limited by bedrock exposure or erosion potential (i.e., detachment potential). The approach produces transient responses that reveal distinct patterns of width and slope, which may provide valuable insight into the limiting physical mechanisms of bedrock erosion in a region. The implications of the work are broad and include the potential to distinguish underlying erosion controls from field observations of width and slope as well as understanding climate‐tectonic interactions.

Pace and Process of Active Folding and Fluvial Incision Across the Kantishna Hills Anticline, Central Alaska

“…We weigh key field observations against model‐derived insights on sediment flux‐dependent bedrock incision (e.g., Whipple & Tucker, ; Yanites, ). First, the highest bedrock incision rates (~1.4 m/kyr since ~22 ka) occur across the fold crest, where channel narrowing (approximately threefold) and steepening (<twofold) enhance transport and erosive capacity by producing an approximately fivefold increase in unit stream power (Figures a–e).…”

“…The rapid sediment production yields broad alluvial channel reaches upstream and downstream of Eagle Gorge (Figures c and d). Within the gorge across the fold, however, the alluvial cover is thin and discontinuous; extensive bedrock exposure along the channel banks provides conditions favorable for bedrock incision (Figure S1c; e.g., Whipple & Tucker, ; Yanites, ). Taken together, the observed adjustments to channel width, slope, transport capacity, and sediment cover across the fold closely match patterns of channel response to changes in rock uplift predicted by models that allow these factors to co‐evolve (Yanites, ).…”

“…Despite the utility of fluvial archives of active tectonic deformation, debate continues over the fundamental processes behind these geomorphic records. For example, river profile analysis holds promise for the estimation of rock uplift rates directly from digital topography (e.g., Goren et al, ), but most extant approaches utilize a stream power incision model that neglects the possibly significant roles of dynamic channel width adjustment and sediment flux (Yanites, , and references therein). Moreover, while researchers commonly infer uplift rates from the incision of dated fluvial strath terraces, mechanisms of terrace formation may vary (e.g., climatic forcing versus autogenic effects; Schanz et al, ) with key implications for interpreting tectonic rates (e.g., Finnegan et al, ).…”

Spatially Variable Increase in Rock Uplift in the Northern U.S. Cordillera Recorded in the Distribution of River Knickpoints and Incision Depths

“…, |δz/δx| is channel slope, and m and n are exponents that depend on erosion physics and the scaling of both channel width and discharge with drainage area (Whipple & Tucker, 1999). As a 1-D approximation, this relationship implicitly assumes power law dependences of both (Lewis et al, 2012 discharge and channel width on drainage area (Whipple & Tucker, 1999); these dependences are widely observed (Montgomery & Gran, 2001;Wohl & David, 2008), although the dynamic adjustment of channel width remains an outstanding issue (Finnegan et al, 2005;Lague, 2014;Turowski et al, 2009;Whittaker et al, 2007;Whittaker & Boulton, 2012;Yanites, 2018;Yanites et al, 2010).…”

“…Bedrock river profiles are often described by the stream power model (Howard, ; Howard & Kerby, ; Whipple & Tucker, ): where z is elevation [ L ], t is time [ T ], x is distance upstream [ L ], U is rock‐uplift rate [ L / T ], K is bedrock erodibility [ L 1 − 2 m / T ], A is drainage area [ L 2 ], | δz / δx | is channel slope, and m and n are exponents that depend on erosion physics and the scaling of both channel width and discharge with drainage area (Whipple & Tucker, ). As a 1‐D approximation, this relationship implicitly assumes power law dependences of both discharge and channel width on drainage area (Whipple & Tucker, ); these dependences are widely observed (Montgomery & Gran, ; Wohl & David, ), although the dynamic adjustment of channel width remains an outstanding issue (Finnegan et al, ; Lague, ; Turowski et al, ; Whittaker et al, ; Whittaker & Boulton, ; Yanites, ; Yanites et al, ).…”