A theory of stochastic fluvial landscape evolution
File(s)
Published version
Author(s)
Roberts, GG
Wani, O
Type
Journal Article
Abstract
Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker–Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity.
Date Issued
2024-02-01
Date Acceptance
2024-01-09
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2024, 480 (2283)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
480
Issue
2283
Copyright Statement
2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Subjects
advection
EQUATION
fluvial
landscape evolution
Markov process
Multidisciplinary Sciences
probability
RIVER INCISION MODEL
Science & Technology
Science & Technology - Other Topics
stochastic
Publication Status
Published
Article Number
ARTN 20230456
Date Publish Online
2024-02-07