 
Summary: The Stochastic Theory of Fluvial Landsurfaces
Bjšorn Birnir
Department of Mathematics,
Jorge HernŽandez
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 transportlimited erosion,
using wellestablished 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
organizedcritical) systems, possessing both an initial transient state and a stationary state,
