Upscaling local-scale transport processes in large-scale relief dynamics

Abstract

The objective of this paper is to discuss the form and parameters of the macroscopic continent-scale erosion law. The law comes from a spatial integration of local transport processes on the resulting topography. It thus depends on the relief/drainage organization that results from the development of geomorphic instabilities such as differential incisions.Assuming local transport processes to depend on local slope and water discharge, we have calculated topographic evolution to derive the characteristic time scales of erosion dynamics. We especially focused on the case of a declining plateau which presents two main phases: a first phase when the drainage pattern establishes, and a declining phase when topography decreases almost exponentially in the absence of tectonic input. The latter phase is characterized by a time scale which depends on the system size, on the organization of the drainage network, and on the parameters of the transport process. We show that the macroscopic erosion law has the characteristics of an abnormal diffusion whose basic time-length exponent a is determined by the parameters of the fluvial process. This result sheds new light on the observed negative correlation between current denudation rates and drainage areas in world-wide fluvial watersheds.