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

The objective of this paper is to discuss the form and parameters of the ma croscopic continent-scale erosion law. The law comes from a spatial integra tion of local transport processes on the resulting topography. It thus depe nds on the relief/drainage organization that results from the development o f geomorphic instabilities such as differential incisions. Assuming local transport processes to depend on local slope and water disch arge, we have calculated topographic evolution to derive the characteristic time scales of erosion dynamics. We especially focused on the case of a de clining plateau which presents two main phases : a first phase when the dra inage 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 orga nization of the drainage network, and on the parameters of the transport pr ocess. We show that the macroscopic erosion law has the characteristics of an abnormal diffusion whose basic time-length exponent a is determined by t he parameters of the fluvial process. This result sheds new light on the ob served negative correlation between current denudation rates and drainage a reas in world-wide fluvial watersheds. (C) 2000 Elsevier Science Ltd. All r ights reserved.