Article,
Scaling, Universality, and Geomorphology
Annual Review of Earth and Planetary Sciences, 28 (1): 571-610 (2000)
DOI: 10.1146/annurev.earth.28.1.571
Abstract
Theories of scaling apply wherever similarity exists across many
scales. This similarity may be found in geometry and in dynamical processes. Uni-
versality arises when the qualitative character of a system is sufficient to quantitatively
predict its essential features, such as the exponents that characterize scaling laws.
Within geomorphology, two areas where the concepts of scaling and universality have
found application are the geometry of river networks and the statistical structure of
topography. We begin this review with a pedagogical presentation of scaling and
universality. We then describe recent progress made in applying these ideas to net-
works and topography. This overview leads to a synthesis that attempts a classification
of surface and network properties based on generic mechanisms and geometric con-
straints. We also briefly review how scaling and universality have been applied to
related problems in sedimentology—specifically, the origin of stromatolites and the
relation of the statistical properties of submarine-canyon topography to the size dis-
tribution of turbidite deposits. Throughout the review, our intention is to elucidate not
only the problems that can be solved using these concepts, but also those that cannot.
