Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes

Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction–diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of biomass and soil water, qualitatively capture the emergence of various types of vegetation patterns in arid environments, they are phenomenological and have a limited predictive power. We ameliorate these limitations by deriving the vertically averaged Richards’ equation to describe flow (as opposed to “diffusion”) of water in partially saturated soils. This establishes conditions under which this nonlinear equation reduces to its weakly nonlinear reaction–diffusion counterpart used in the previous models, thus relating their unphysical parameters (e.g., diffusion coefficient) to the measurable soil properties (e.g., hydraulic conductivity) used to parameterize the Richards equation. Our model is valid for both flat and sloping landscapes and can handle arbitrary topography and boundary conditions. The result is a model that relates the environmental conditions (e.g., precipitation rate, runoff and soil properties) to formation of multiple patterns observed in nature (such as stripes, labyrinth and spots). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of Mathematical Biology Springer Journals

Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes

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Publisher
Springer US
Copyright
Copyright © 2017 by Society for Mathematical Biology
Subject
Mathematics; Mathematical and Computational Biology; Life Sciences, general; Cell Biology
ISSN
0092-8240
eISSN
1522-9602
D.O.I.
10.1007/s11538-017-0348-4
Publisher site
See Article on Publisher Site

Abstract

Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction–diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of biomass and soil water, qualitatively capture the emergence of various types of vegetation patterns in arid environments, they are phenomenological and have a limited predictive power. We ameliorate these limitations by deriving the vertically averaged Richards’ equation to describe flow (as opposed to “diffusion”) of water in partially saturated soils. This establishes conditions under which this nonlinear equation reduces to its weakly nonlinear reaction–diffusion counterpart used in the previous models, thus relating their unphysical parameters (e.g., diffusion coefficient) to the measurable soil properties (e.g., hydraulic conductivity) used to parameterize the Richards equation. Our model is valid for both flat and sloping landscapes and can handle arbitrary topography and boundary conditions. The result is a model that relates the environmental conditions (e.g., precipitation rate, runoff and soil properties) to formation of multiple patterns observed in nature (such as stripes, labyrinth and spots).

Journal

Bulletin of Mathematical BiologySpringer Journals

Published: Oct 19, 2017

References

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