A New Efficient Method to Solve the Stream Power Law Model Taking Into Account Sediment Deposition

Abstract

The stream power law model has been widely used to represent erosion by rivers but does not take into account the role played by sediment in modulating erosion and deposition rates. Davy and Lague (2009, https://doi.org/10.1029/2008JF001146) provide an approach to address this issue, but it is computationally demanding because the local balance between erosion and deposition depends on sediment flux resulting from net upstream erosion. Here, we propose an efficient (i.e., O(N) and implicit) method to solve their equation. This means that, unlike other methods used to study the complete dynamics of fluvial systems (e.g., including the transition from detachment‐limited to transport‐limited behavior), our method is unconditionally stable even when large time steps are used. We demonstrate its applicability by performing a range of simulations based on a simple setup composed of an uplifting region adjacent to a stable foreland basin. As uplift and erosion progress, the mean elevations of the uplifting relief and the foreland increase, together with the average slope in the foreland. Sediments aggrade in the foreland and prograde to reach the base level where sediments are allowed to leave the system. We show how the topography of the uplifting relief and the stratigraphy of the foreland basin are controlled by the efficiency of river erosion and the efficiency of sediment transport by rivers. We observe the formation of a steady‐state geometry in the uplifting region, and a dynamic steady state (i.e., autocyclic aggradation and incision) in the foreland, with aggradation and incision thicknesses up to tens of meters.

Long‐Term Coupling and Feedback Between Tectonics and Surface Processes During Non‐Volcanic Rifted Margin Formation

“…The stream discharge Q w represents the total precipitation accumulated on the upstream part of the watershed, Q w =A•P, where P is the precipitation rate and A is upstream drainage area given by A ¼ Li 1:4 À Á 1 0:55 where L i is the length of the drainage area or the river in our case given in kilometers (Hack, 1957;Rigon et al, 1996;Willett, 2010). A sediment transport length function ξ(q) controls sediments deposition along the fluvial profile (Davy & Lague, 2009;Kooi & Beaumont, 1994;Yuan et al, 2019) where q is the stream discharge per unit of river width. The rate of fluvial deposition is controlled by…”

Influence of orographic precipitation on the topographic and erosional evolution of mountain ranges

“…Given that the erosion-deposition approach can take nonlocal sediment processes into account, it has been adopted in recent landscape evolution models (e.g. Davy & Lague, 2009;Langston & Tucker, 2018;Yuan, Braun, Guerit, Rouby, & Cordonnier, 2019;Guerit et al, 2019). There is no distinction between different grain sizes in CIDRE.…”

“…On the other hand, a small ζq means that the sediment flux is limited by the capacity to transport incoming sediment. This value determines the detachment-limited or transport-limited degree of the local sediment flux (Davy & Lague, 2009;Guerit et al, 2019). If ζq is very large, the river model reduces to the simple Stream Power Law model (e.g.…”

Times associated with source-to-sink propagation of environmental signals during landscape transience

“…3b2). The same approach can be used when channels are described as a continuum between transport-and detachmentlimited behaviors (Davy and Lague, 2009;Carretier et al, 2016;Yuan et al, 2019a). For transportlimited rivers, the river response time for a 1D fluvial system was suggested to scale with channel length and the diffusion coefficient and can be calculated following equation 1 (Howard, 1982;Paola et al, 1992;Allen et al, 2013).…”