Macro-roughness model of bedrock–alluvial river morphodynamics

Abstract

Abstract. The 1-D saltation-abrasion model of channel bedrock incision of Sklar and Dietrich (2004), in which the erosion rate is buffered by the surface area fraction of bedrock covered by alluvium, was a major advance over models that treat river erosion as a function of bed slope and drainage area. Their model is, however, limited because it calculates bed cover in terms of bedload sediment supply rather than local bedload transport. It implicitly assumes that as sediment supply from upstream changes, the transport rate adjusts instantaneously everywhere downstream to match. This assumption is not valid in general, and thus can give rise to unphysical consequences. Here we present a unified morphodynamic formulation of both channel incision and alluviation that specifically tracks the spatiotemporal variation in both bedload transport and alluvial thickness. It does so by relating the bedrock cover fraction to the ratio of alluvium thickness to bedrock macro-roughness, rather than to the ratio of bedload supply rate to capacity bedload transport. The new formulation (MRSAA) predicts waves of alluviation and rarification, in addition to bedrock erosion. Embedded in it are three physical processes: alluvial diffusion, fast downstream advection of alluvial disturbances, and slow upstream migration of incisional disturbances. Solutions of this formulation over a fixed bed are used to demonstrate the stripping of an initial alluvial cover, the emplacement of alluvial cover over an initially bare bed and the advection-diffusion of a sediment pulse over an alluvial bed. A solution for alluvial-incisional interaction in a channel with a basement undergoing net rock uplift shows how an impulsive increase in sediment supply can quickly and completely bury the bedrock under thick alluvium, thus blocking bedrock erosion. As the river responds to rock uplift or base level fall, the transition point separating an alluvial reach upstream from an alluvial-bedrock reach downstream migrates upstream in the form of a "hidden knickpoint". A tectonically more complex case of rock uplift subject to a localized zone of subsidence (graben) yields a steady-state solution that is not attainable with the original saltation-abrasion model. A solution for the case of bedrock-alluvial coevolution upstream of an alluviated river mouth illustrates how the bedrock surface can be progressively buried not far below the alluvium. Because the model tracks the spatiotemporal variation in both bedload transport and alluvial thickness, it is applicable to the study of the incisional response of a river subject to temporally varying sediment supply. It thus has the potential to capture the response of an alluvial-bedrock river to massive impulsive sediment inputs associated with landslides or debris flows.

The SPACE 1.0 model: a Landlab component for 2-D calculation of sediment transport, bedrock erosion, and landscape evolution

“…Their model tracks the thickness of a sediment layer compared to the macro-roughness of the bedrock surface such that alluvial thickness less than the macro-roughness length scale results in exposed bedrock. Their geometric approach is similar to that of Lague (2010), but the Zhang et al (2015) model incorporates both tools and cover effects due to its derivation from the saltation-abrasion model (Sklar and Dietrich, 2004). While Zhang et al (2015) note that their model could incorporate downstream variations in channel width, it does not do so in the form they presented.…”

“…Inoue et al (2014) used a modified 1-D Exner equation for sediment mass conservation incorporating both mobile bed load and an alluvial layer. Lague (2010) and Zhang et al (2015) followed a similar approach, further modifying the sediment mass conservation framework to include below-capacity sediment transport. Exner sediment transport in bedrock-alluvial systems was expanded to 2-D by Nelson and Seminara (2012) and Inoue et al (2016Inoue et al ( , 2017, though the specifics of calculating sediment flux differ between the model of Nelson and Seminara (2012) and the latter two.…”

“…The 2-D mixed bedrock-alluvial models proposed by Inoue et al (2016Inoue et al ( , 2017 could potentially be incorporated into existing landscape evolution model frameworks, but the feasibility of such an integration is unclear as the models have been tested over hourly to daily timescales, not geologic timescales. The models most suited to landscape evolution applications are those of Fowler et al (2007), Lague (2010), Inoue et al (2014), andZhang et al (2015). The Inoue et al (2014) model realistically incorporates hydraulic roughness of both bedrock and alluvium but is designed to handle a constant sediment supply rate, a constraint which is unlikely to be satisfied in landscape evolution modeling applications.…”

“…Inoue et al (2017) advanced the model of Inoue et al (2016) by incorporating a simple parameterization for bedrock bank erosion to investigate meander bend migration. Zhang et al (2015) presented a channel longitudinal profile model coupling local sediment transport dynamics with the saltation-abrasion incision rule of Sklar and Dietrich (2004). The model of Zhang et al (2015) can capture transience driven by changes in q s /q c , or downstream propagation of changes in sediment supply.…”

“…Zhang et al (2015) presented a channel longitudinal profile model coupling local sediment transport dynamics with the saltation-abrasion incision rule of Sklar and Dietrich (2004). The model of Zhang et al (2015) can capture transience driven by changes in q s /q c , or downstream propagation of changes in sediment supply. Their model tracks the thickness of a sediment layer compared to the macro-roughness of the bedrock surface such that alluvial thickness less than the macro-roughness length scale results in exposed bedrock.…”