| 17 Feb 2026
Lift or impact: modeling bedrock incision coupled with sediment dynamics
Abstract. We analyze how the process of bedrock incision by the impact of sediment grains can be described and coupled with sediment dynamics. We first point out that the key parameter is a bedrock dimensionless coefficient that describes the ratio between the volumes of impacting sediments and bedrock erosion. We then write the coupled equations by introducing a partitioning coefficient between sediment and bedrock erosions. It describes the time spent doing one or the other erosion process – or the proportion of depositing grains that impact bedrock. In a 1D along-stream system, the resulting equations lead to a similar description of the cover effect proposed by Sklar and Dietrich (2004), giving a rationale to their expression. In a second step, we extend the concept to lateral erosion or deposition fluxes. We develop analytical solutions for a river fed by uniform lateral sediment fluxes from hillslope and show why the sediment load can exceed the transport capacity. We then implement the equations in the numerical code River.lab/eros, where water depth and velocity, as well as erosion and deposition fluxes, are solved with the method of precipitons. As an example, we simulate the evolution of the Rheinfall at Schaffhausen, Switzerland, a prominent knickpoint along the Hochrhein. In contrast with sediment processes, where the knickpoint slope decreases by diffusion without upstream displacements, bedrock abrasion allows knickpoint to move upstream while retaining almost the same shape. This is consistent with detachment-limited behavior as emphasized in the theoretical part of the paper. The knickpoint shape (foot elevation and height) and retreat rates are highly dependent on the sediment load in river. Bedrock erosion first happens in a narrow canyon that propagates upstream, and then the river widens after the knickpoint passed by.
In this study, the authors propose a numerical analysis model for analyzing elevation changes in mixed bedrock-aluvial channels using a different formulation than previous studies. I feel that their formulation is challenging and novel. However, it is unclear what new capabilities have been achieved as a result. Furthermore, there are several unclear points in the modeling. Below I list a few major comments for the review along with some line-by-line comments.
Major comments:
1. A two-dimensional model considering bedrock erosion (including lateral erosion) and alluvial deposition (including bar formation) has been proposed by Inoue, Parker and Stark (2017, ESPL), Inoue et al. (2021, JGR), and Cho and Nelson (2025). The novelty needs to be further clarified. It is insufficient to simply state that the fundamental equations are new; the authors need to clearly define their novelty in terms of the phenomena they can address.
2. I find the explanations for transport length, saltation length, deposition rate and impact velocity problematic (Lines 85-87). Transport length is often defined as the distance a sediment travels from the moment it starts moving until it stops. This is different from the distance of a single jump (i.e., saltation length or hop length). Also, d (deposition rate) in Equation 2 is the volume of deposited particles divided by the transport length multiplied by the river width, which is clearly a different definition from the particle collision velocity. If you claim these are similar, you must clearly state the previous research that supports that relationship.
3. Please provide sufficient explanation regarding particle size, roughness, and the amount of sediment supplied from the upstream end in in the calculation conditions (Section 4.2). Regarding roughness in particular, you describes the importance of roughness on alluvial cover in Introduction, but there is no mention of how roughness is treated in your model or numerical calculations.
4. Providing longitudinal and transverse profiles of the alluvial layer thickness on the bedrock "hs" would help to more easily understand the cover effects.
Line-by-line comments
Eq. 2: Add an explanation for ξ to the text following the equation. L71 is too far away.
Eq. 5: Add an explanation of α to the text following the equation.
L67: D-->Ds
L68: Include references that support the idea that A* is between 0.04 and 0.1. For MPM, qs = 8(τ*-τ*c)^1.5sqrt(RgDs^3), and the value of A* depends on τ*c and particle size.
Eq. 7: x*-->x. Otherwise, the dimensions of the left and right sides do not match.
L84: Please add explanations for ρs, wsi, and kv.
L91: Does this mean that the alluvial cover ratio pc = 0? or pc <1?
Eq.10: Since α is used in equation 5, please use a different symbol.
Eq. 12: Substituting equation 12 into the second equation of equation 11, the right-hand side becomes 0. This is strange, as it means that the alluvial layer thickness does not change over time.
L125: Do not write a statement regarding conflicts of interest in Figure 1.
Eq 20: If ξb is the transport length and ξ is the saltation length, then equation (2) should use ξb.
L176: Recently, Inoue et al. (2025, GRL) experimentally demonstrated that bedrock lateral erosion due to particle impacts increases with increasing lateral slope. Please refer to their work. Their experiments also showed that secondary flow suppresses lateral erosion. Please describe how the effects of secondary flow are considered in this model.
L262: In the appendix, please provide the basic equations for two-dimensional flow, the method for calculating shear stress, and the methods for calculating sediment transport in the x (streamwise) and y (lateral) directions. Also, indicate whether there is any double counting of the bed elevation change due to sediment transport in the y direction and the lateral erosion shown in Figure 2.
L296: Provide information regarding the grain size of the bed material. Also, describe how the sediment inflow from the upstream end was determined.
Fig. 4: Add legends to the two top figures of the color map. One has one, but the text is too small to read. For the bottom figure, indicate the dimension on the vertical axis.
Fig. 5: The legend in the color map is too small to read.
Fig. 11: Add legend to the color maps.