 
Summary: THE SCALING OF FLUVIAL LANDSCAPES
Björn Birnir # Terence R. Smith + \Lambda George E. Merchant +
# Department of Mathematics, University of California at Santa Barbara, California 93106, USA
and University of Iceland, Science Institute, 3 Dunhaga, 107 Reykjavík
+ Department of Geography, University of California at Santa Barbara, California 93106, USA
\Lambda Department of Computer Science, University of California at Santa Barbara, California 93106,
USA
ABSTRACT
The analysis of a family of physicallybased landscape models leads to the analysis of two
stochastic processes that seem to determine the shape and structure of river basins. The par
tial differential equation determine the scaling invariances of the landscape through these
processes. The models bridge the gap between the stochastic and deterministic approach
to landscape evolution because they produce noise by sediment divergences seeded by in
stabilities in the water flow. The first process is a channelization process corresponding
to Brownian motion of the initial slopes. It is driven by white noise and characterized by
the spatial roughness coefficient of 0:5. The second process, driven by colored noise, is a
maturation process where the landscape moves closer to a mature landscape determined by
separable solutions. This process is characterized by the spatial roughness coefficient of
0:75 and is analogous to an interface driven through random media with quenched noise.
The values of the two scaling exponents, which are interpreted as reflecting universal, but
