Upscaling sediment-flux-dependent fluvial bedrock incision to long timescales

Abstract

<p><span>Fluvial bedrock incision is driven by the impact of moving bedload particles. Mechanistic, sediment-flux-dependent incision models have been proposed, but the stream power incision model (SPIM) is frequently used to model landscape evolution over large spatial and temporal scales. This disconnect between the mechanistic understanding of fluvial bedrock incision on the process scale, and the way it is modelled on long time scales presents one of the current challenges in quantitative geomorphology. Here, a mechanistic model of fluvial bedrock incision that is rooted in current process understanding is explicitly upscaled to long time scales by integrating over the distribution of discharge. The model predicts a channel long profile form equivalent to the one yielded by the SPIM, but explicitly resolves the effects of channel width, cross-sectional shape, bedrock erodibility and discharge variability. The channel long profile chiefly depends on the mechanics of bedload transport, rather than bedrock incision. In addition to the imposed boundary conditions specifying the upstream supply of water and sediment, and the incision rate, the model includes four free parameters, describing the at-a-station hydraulic geometry of channel width, the dependence of bedload transport capacity on channel width, the threshold discharge of bedload motion, and reach-scale cover dynamics. For certain parameter combinations, no solutions exist. However, by adjusting the free parameters, one or several solutions can usually be found. The controls on and the feedbacks between the free parameters have so far been little studied, but may exert important controls on bedrock channel morphology and dynamics. </span></p>

Influence of Rarely Mobile Boulders on Channel Width and Slope: Theory and Field Application

“…Here, τ * = ρ HS/( ρ s − ρ ) D is the Shields number, H is flow depth (m), τ c * is the critical Shields stress for the onset of bedload motion, D (m) is bedload grain size, g (9.81 ms −2 ) is the gravitational acceleration, and γ is a nondimensional constant larger than one (e.g., Wong & Parker, 2006). Assuming a steady flow, using continuity and a flow resistance equation, neglecting the threshold of motion term, and generalizing for width‐dependence, Equation 17 can be expressed (e.g., Turowski, 2021) as a water discharge‐based equation for sediment transport (Rickenmann, 2001), taking the form of $$$\frac{\,{Q}_{\mathrm{s}}}{{W}^{q}}={K}_{\text{BL}}{Q}^{m}{S}^{n}$$$ …”

“…However, given the unsteady nature of bedload transport and along‐stream variations in channel width (Cook et al., 2020), the parameter q may differ from zero. Analytically derived end‐member approximations were discussed in Turowski (2021), yielding q values of zero, 0.1, or 2.5.…”

“…Still, the degree to which the slope adjusts to each of these components remains unclear (Johnson et al., 2009). While channel slope is commonly considered to be the consequence of bedrock erosion and reshaping of the longitudinal profile (e.g., Royden & Perron, 2013), recent studies suggested that equilibrium of bedrock channels could be attained by a modification of the slope of sediment overlying the bedrock (Phillips & Jerolmack, 2016; Turowski, 2020, 2021). As in alluvial channels, rearrangement of the bed to form a new sediment‐bed slope can be achieved via selective sediment deposition and entrainment during floods (Mackin, 1948; Schneider, Rickenmann, Turowski, & Kirchner, 2015; Schumm & Parker, 1973; Turowski & Hodge, 2017).…”

The influence of bedrock river morphology and alluvial cover on gravel entrainment. Part 2: Modelling critical shear stress

“…How τ c changes with increasing cover has implications for predicting the relationship between sediment flux and sediment cover, which is important for modelling channel incision and landscape evolution (Lague, 2010; Sklar & Dietrich, 2004; Turowski, 2021). If sediment cover increases τ c , in turn making sediment grains less mobile, then this positive feedback can produce rapid deposition of sediment cover, known as runaway alluviation (Chatanantavet & Parker, 2008; Demeter et al, 2005; Finnegan et al, 2007).…”

From Process to Centuries: Upscaling Field‐Calibrated Models of Fluvial Bedrock Erosion

“…Such events could cause orders of magnitude higher erosion rates than typical annual floods, as long as the bedrock bed remains exposed. Upscaling bedload tool‐ and cover‐dependent predictions ( SAws or RSA model) is appropriate to assess river erosivity exceeding centennial scales (Turowski, 2021). In addition, these models can be inverted to estimate long‐term bedload supply from measured incision rates.…”