A major control on bedrock incision is the interaction between alluvial cover and erosive mobile grains. The extent of alluvial cover is typically predicted as a function of relative sediment flux (sediment supply rate over bed load transport capacity, q bs /q bc ), yet little is known about how the bed roughness affects the alluvial cover. We performed field experiments with various flow discharges, sediment supply rates, grain sizes, and bed surface topographies. We then developed physically based models for estimating the threshold of sediment movement and the extent of alluvial cover, so as to include the effect of roughness change. The results for the threshold of sediment movement and the extent of alluvial cover obtained from our models show reasonable agreement with the results of the field experiments. We explored the sensitivity of the models to variations in sediment supply and bedrock relative roughness (bedrock hydraulic roughness height over grain size, k sb /d). The results suggest the following: (1) a larger relative roughness yields a greater dimensionless critical shear stress required for initial sediment motion; (2) at a given sediment supply rate, the extent of alluvial cover is larger when the relative roughness is larger; (3) when the sediment supply rate and the relative roughness are small, throughput bed load moves over (and can abrade) a purely bedrock channel with no alluvial cover; and (4) the critical value of sediment supply rate below which throughput bed load transport occurs increases with decreasing relative roughness. The experimental results and analysis provide a framework for treating the (a) incisional morphodynamics of purely bedrock rivers by throughput bed load with no alluvial cover, (b) incisional/alluvial morphodynamics of mixed bedrock-alluvial rivers, and (c) purely alluvial morphodynamics, as well as the transition between these states.

An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

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 ubiquitous presence of river drainage basins in the terrestrial environment suggests that distributed overland flow generated by rainfall tends to spontaneously organize itself into dendritic systems of discrete channels. Several recent numerical models describe the evolution of complete drainage basins from the initial condition of rainfall on a flat, tilted plateau, the surface of which has been provided with random elevation perturbations. These analyses model overland flow via the assumption of a perfect balance between gravitational and frictional terms, i.e. in terms of normal flow.Linear stability analysis applied to the normal flow model has been shown, however, to fail to select a wavelength corresponding to a finite distance of separation between incipient basins. This suggests that the normal flow model may not be a sufficient basis for studying drainage basin development, especially at the finest scales of morphologic significance.Here the concept of a threshold condition for bed erosion is combined with an analysis of the full equations of shallow overland flow in order to study wavelength selection. Classical linear stability analysis is shown to be inadequate to analyse the problem at the level of inception. An alternative linear analysis of bed perturbations based on the threshold condition is developed, and shown to lead to the selection of finite wavelength of the correct order of magnitude.The analysis here is driven from the upstream direction in that bed erosion is first caused only when sufficient flow has gathered from upstream due to rainfall. A downstream-driven theory of incipient channelization that is not necessarily dependent upon rainfall is presented in Izumi (1993), and is presently in preparation for publication.

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Abstract. The 1-D saltation-abrasion model of channel bedrock incision of Sklar and Dietrich, 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 unphysical consequences. Here we present a unified morphodynamic formulation of both channel incision and alluviation which specifically tracks the spatiotemporal variation of both bedload transport and alluvial thickness. It does so by relating the cover fraction not to a ratio of bedload supply rate to capacity bedload transport, but rather to the ratio of alluvium thickness to a macro-roughness characterizing the bedrock surface. The new formulation 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, so 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 solution for the case of a zone of rock subsidence (graben) bounded upstream and downstream by zones of rock uplift (horsts) yields a steady-state solution that is unattainable 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 progressive buried not far below the alluvium. Because the model tracks the spatiotemporal variation of 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.