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The Stochastic Theory of Fluvial Landsurfaces

  • Author(s): Birnir, Bjorn
  • Hernandez, Jorge
  • Smith, Terence R
  • et al.
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 models and analysis is developed showing that landsurface evolution is described by Markovian stochastic processes. The landsurfaces are described by non-deterministic stochastic processes, characterized by a statistical quantity, the variogram, that exibits characteristic scalings. Thus the landsurfaces are shown to be SOC (Self-organized-critical) systems, or systems of color, possessing both an initial transient state and a stationary state. The theory reproduces established numerical results and measurements from DEMs (digital elevation models).

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