The idea that moving sediment drives bedrock erosion is not new. It was proposed qualitatively in the nineteenth century and confirmed by laboratory flume experiments in recent decades. What has been missing, the authors argue, is a complete coupling between the fate of individual grains and the erosion they cause. Bedrock erosion produces new sediment, depends on grains being in motion, and is simultaneously prevented when grains come to rest and blanket the bed. A river’s ability to cut rock is therefore inseparable from the full life cycle of its sediment load — erosion, transport, deposition and re-entrainment — and previous models handled that entanglement only partially, often with ad hoc corrections.

The core of the new theory is a deceptively simple question: when a grain is deposited on the bed, does it get lifted back into the flow, or does it strike the bedrock and chip it away? The researchers formalise this choice with a partitioning coefficient that describes the proportion of time the river spends eroding its sediment cover rather than abrading bedrock. When the flow is strong enough to sweep away everything that settles, every deposited grain is lifted back up, and the energy that would otherwise go into the cover instead goes into the rock. When deposition outpaces re-erosion, sediment accumulates, the bedrock is shielded, and abrasion stops.

From this partitioning, the team derives a key dimensionless quantity they call the bedrock coefficient: the volumetric fraction of bedrock eroded by each sediment impact, expressed as the ratio between the energy delivered by a grain and the rock’s resistance to abrasion. Combined with a transport length — the characteristic distance over which a river adjusts its sediment load toward equilibrium between erosion and deposition — this coefficient governs how quickly sediment-starved reaches approach capacity. Notably, the bedrock transport length that emerges from the equations is typically far longer than the ordinary bedload transfer length, meaning abrasion-driven rivers adjust over much greater distances than purely alluvial ones.

One of the study’s most satisfying results is theoretical rather than numerical. The classic cover-effect formulation of Sklar and Dietrich, published in 2004, describes bedrock erosion as proportional to the shortfall between actual sediment load and transport capacity. That expression was derived empirically, from flume observations. Davy and colleagues show that their coupled equations reproduce exactly the same cover term — but now as a consequence of sediment mass balance rather than curve fitting. The old empirical rule, in other words, turns out to be a natural outcome of treating grains as objects that must be lifted before they can impact again.

The framework also extends into two dimensions, incorporating lateral erosion of channel walls and lateral deposition on the floodplain edges of the channel. When the researchers analysed a river fed by uniform sediment supply from hillslopes, they found something counterintuitive: the sediment load can settle at a value that exceeds the classical transport capacity. Capacity, in this picture, is not an intrinsic property of the flow alone but depends on how much material the surrounding landscape delivers. For the South Fork Eel River in California, a case study borrowed from earlier abrasion work, the effect of hillslope supply becomes significant only when hillslope erosion rates approach metres per year — but the mathematics makes clear that supply and capacity cannot be treated independently.

To bring the theory to life, the team implemented the equations in their numerical platform River.lab/eros, which tracks small packets of water and sediment — dubbed precipitons — as they travel downstream solving the shallow-water equations and exchanging sediment with the bed and banks at every step. The approach lets channel width emerge from the simulation rather than being imposed, and it resolves both vertical incision and lateral erosion and deposition. Because realistic abrasion rates are roughly a million times slower than sediment transport, the authors exploit the quasi-steady behaviour of the sediment system to scale simulation times with rock resistance.

The showcase application is the Rheinfall at Schaffhausen, Switzerland — a twenty-metre-high knickpoint on the Hochrhein that formed about 15,000 years ago and has barely moved since. Using a lidar-derived digital elevation model at six-metre resolution and an inflow of 370 cubic metres per second, the team ran simulations with varying sediment concentrations. When the bedrock was treated as easily erodible sediment, the knickpoint simply diffused away, its slope flattening in place without upstream migration. But when abrasion governed the erosion, something dramatic happened: narrow canyons, thirty to fifty metres wide, propagated upstream from the base of the waterfall, carrying the knickpoint’s shape with them almost intact.

The sediment supply proved to be the master variable. With no incoming sediment, the knickpoint eroded only briefly, consuming the pre-existing patches of sediment on the bed before grinding to a halt — a result that mirrors the real Rheinfall, whose outflow from Lake Constance is virtually sediment-free because the lake traps Alpine debris. At low to moderate concentrations, the knickpoint retreated upstream while keeping its height and steep slope of roughly ten percent. At higher concentrations, sediment deposition raised the base of the fall and flattened it. In every case, erosion first carved a narrow canyon — where reduced width amplifies shear stress and impact rates — and the river widened only after the knickpoint had passed, a two-stage evolution the authors attribute to any contrast between bedrock and sediment erodibility.

Quantitatively, knickpoint retreat rates scaled with sediment flux to the power of about 0.8, and decreased with rock resistance faster than inversely — a preliminary result the authors treat cautiously, since canyon geometry and grid resolution may confound the scaling. The broader message is harder to dispute: whether a waterfall retreats as a migrating cliff or dissolves as a diffusing bump depends on the delicate balance between grains being lifted and grains striking rock. By grounding that balance in explicit sediment dynamics, the new model gives landscape evolution studies a physically consistent way to read the erosion histories written in bedrock rivers — and explains why some of the world’s great waterfalls hold their ground while others march relentlessly upstream.

Subject of Research: Coupled modelling of sediment-driven bedrock incision and knickpoint retreat in rivers

Article Title: Lift or impact: modelling bedrock incision coupled with sediment dynamics

Article References: Davy, P., Schwanghart, W., Mey, J., Darcel, C., & Landgraf, A. (2026). Lift or impact: modelling bedrock incision coupled with sediment dynamics. Earth Surface Dynamics, 14(4), 635-651. https://doi.org/10.5194/esurf-14-635-2026

Image Credits: AI Generated

DOI: 10.5194/esurf-14-635-2026

Keywords: bedrock incision, sediment transport, abrasion, knickpoint, cover effect, landscape evolution, river erosion, transport capacity, Rheinfall, canyon formation, geomorphology, numerical modelling