Self-organization and scaling relationships of evolving river networks

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

The power spectra S of linear transects of Earth's topography is often observed to be a power law function of wave number k with exponent close to -2: S(k) ∝ k-2. In addition, river networks are fractal trees that satisfy several power law relationships between their morphologic components. A model equation for the evolution of Earth's topography by transport-limited erosional processes which produces fractal topography and fractal river networks is presented, and its solutions are compared in detail to real topography. The model is the diffusion equation for sediment transport on hillslopes and channels with the diffusivity constant on hillslopes and proportional to the three-halves power of discharge in channels. The dependence of diffusivity on discharge is consistent with sediment rating curves. We study the model in two ways. In the first analysis the diffusivity is parameterized as a function of elevation, and a Taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which includes the spatially variable diffusivity to first order in the elevation. The solution to this equation is a self-affine or fractal surface with linear transects that have power spectra S(k) ∝ k-1.8, independent of the age of the topography, consistent with observations of real topography. The hypsometry produced by the model equation is skewed such that lowlands make up a larger fraction of the total area than highlands as observed in real topography. In the second analysis we include river networks explicitly in a numerical simulation by calculating the discharge at every point. We characterize the morphology of real river basins with five independent scaling relations between six morphometric variables. Scaling exponents are calculated for seven river networks from a variety of tectonic environments using high-quality digital elevation models. River networks formed in the model match the observed scaling laws and satisfy Tokunaga side-branching statistics.

Original languageEnglish (US)
Article number1998JB900110
Pages (from-to)7359-7375
Number of pages17
JournalJournal of Geophysical Research: Space Physics
Volume104
Issue numberB4
StatePublished - Apr 10 1999
Externally publishedYes

Fingerprint

self organization
rivers
Topography
topography
Rivers
scaling
Fractals
diffusivity
river
fractals
Power spectrum
hillslope
power spectra
power law
transect
Earth (planet)
hypsometry
exponents
Landforms
landforms

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Atmospheric Science
  • Astronomy and Astrophysics
  • Oceanography

Cite this

Self-organization and scaling relationships of evolving river networks. / Pelletier, Jon.

In: Journal of Geophysical Research: Space Physics, Vol. 104, No. B4, 1998JB900110, 10.04.1999, p. 7359-7375.

Research output: Contribution to journalArticle

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