Summary: The Stochastic Theory of Fluvial Landsurfaces
Bj¨orn Birnir

Department of Mathematics,
Jorge Hern´andez
Department of Statistics
and Applied Probability
and
Terence R. Smith
Department of Geography
University of California
Santa Barbara, CA 93106, USA
Abstract
A stochastic theory of fluvial landsurfaces is developed for transport-limited erosion,
using well-established models for the water and sediment fluxes. The mathematical mod-
els and analysis is developed showing that some aspects of landsurface evolution can be
described by Markovian stochastic processes. The landsurfaces are described by non-
deterministic stochastic processes, characterized by a statistical quantity the variogram,
that exhibits characteristic scalings. Thus the landsurfaces are shown to be SOC (Self-
organized-critical) systems, possessing both an initial transient state and a stationary state,

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics