Transport-limited fluvial erosion - Simple formulation and efficient numerical treatment

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.