Abstract
Abstract. Most of the recent studies modeling fluvial erosion in the context of tectonic geomorphology focus on the detachment-limited regime. One reason for this simplification is the simple relationship of the constitutive law used here – often called stream-power law – to empirical results on longitudinal river profiles. Another no less important reason lies in the numerical effort that is much higher for transport-limited models than for detachment-limited models. This study proposes a formulation of transport-limited erosion where the relationship to empirical results on river profiles is almost as simple as it is for the stream-power law. As a central point, a direct solver for the fully implicit scheme is presented. This solver requires no iteration for the linear version of the model, allows for arbitrarily large time increments, and is almost as efficient as the established implicit solver for detachment-limited erosion. The numerical scheme can also be applied to linear hybrid models that cover the range between the two end-members of detachment-limited and transport-limited erosion.
Highlights
Rivers play a major if not dominant part in large-scale landform evolution
If horizontal displacement of the crust is not taken into account, models describing the evolution of a topography H (x1, x2, t) are typically written in the form
While the numerical error of the implicit scheme is even smaller than for the detachment-limited model (Fig. 6), it must be taken into account that all models in this field compute flow directions and changes in topography in separate steps
Summary
Rivers play a major if not dominant part in large-scale landform evolution. If horizontal displacement of the crust is not taken into account, models describing the evolution of a topography H (x1, x2, t) are typically written in the form. Transport-limited models directly define the sediment flux per unit width q instead of the erosion rate E at each point as a function of local properties such as catchment size and channel slope. Kooi and Beaumont (1994) proposed an approach that increases stability and allows for a physical interpretation, often called an undercapacity model or – in a more general context – linear decline model (Whipple and Tucker, 2002) It defines an equilibrium flux per unit width qe from local properties (channel slope, catchment size, etc.) and assumes that the erosion rate is.
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