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.

While most of the world's large rivers are heavily engineered, channel response to engineering measures on decadal to century and several 100 km scales is scarcely documented. We investigate the response of the Lower Rhine River (Germany‐Netherlands) to engineering measures, in terms of channel slope and bed surface grain size. Field data show domain‐wide incision, primarily associated with extensive channel narrowing. Remarkably, the channel slope has increased in the upstream end, which is uncommon under degradational conditions. We attribute the observed response to two competing mechanisms: bedrock at the upstream boundary increases the channel slope over the upstream part of the alluvial reach to compensate for the reduction of net annual sediment mobility, and extensive channel narrowing reduces the equilibrium slope. Another striking feature is the advance and flattening of the gravel‐sand transition, suggesting its gradual fading due to an increasingly reduced slope difference between the gravel and sand reaches.