Fluvial erosion/transport equation of landscape evolution models revisited

TLDR: In this paper, a mesoscale erosion/deposition model is presented, which couples the dynamics of streamflow and topography through a sediment transport length function x(q), which is the average travel distance of a particle in the flow before being trapped on topography.

Abstract: We present a mesoscale erosion/deposition model, which differs from previous landscape evolution models equations by taking explicitly into account a mass balance equation for the streamflow. The geological and hydrological complexity is lumped into two basic fluxes (erosion and deposition) and two averaged parameters (unit width discharge q and stream slope s). The model couples the dynamics of streamflow and topography through a sediment transport length function x(q), which is the average travel distance of a particle in the flow before being trapped on topography. This property reflects a time lag between erosion and deposition, which allows the streamflow not to be instantaneously at capacity. The so-called x-q model may reduce either to transport-limited or to detachment-limited erosion modes depending on x. But it also may not. We show in particular how it does or does not for steady state topographies, long-term evolution, and high-frequency base level perturbations. Apart from the unit width discharge and the settling velocity, the x(q) function depends on a dimensionless number encompassing the way sediment is transported within the streamflow. Using models of concentration profile through the water column, we show the dependency of this dimensionless coefficient on the Rouse number. We discuss how consistent the x-q model framework is with bed load scaling expressions and Einstein's conception of sediment motion.