A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments

Shannon Dixon; Nancy Huntly; Priscilla E. Greenwood; Luis F. Gordillo; Shannon Dixon; Nancy Huntly; Priscilla E. Greenwood; Luis F. Gordillo

doi:10.3934/mbe.2018052

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1155-1164. doi: 10.3934/mbe.2018052

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A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments

1.
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
2.
Ecology Center, Utah State University, Logan, UT 84322, USA
3.
Mathematics Department, University of British Columbia, Vancouver, BC, Canada

Received: 16 June 2017 Accepted: 16 March 2018 Published: 01 October 2018
MSC : Primary: 92B05; Secondary: 60K30

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming part of these regions into deserts in some cases. Although it is documented that a decreasing tendency in precipitation might induce earlier disappearance of vegetation, quantifying the relationship between decrease of precipitation and vegetation endurance remains a challenging task due to the inherent complexities involved in distinct scenarios. In this paper we present a model for precipitation-vegetation dynamics in semi-arid landscapes that can be used to explore numerically the impact of decreasing precipitation trends on appearance of desertification events. The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.
- Desertification,
- water-vegetation model,
- precipitation,
- semi-arid environments,
- drylands
Citation: Shannon Dixon, Nancy Huntly, Priscilla E. Greenwood, Luis F. Gordillo. A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1155-1164. doi: 10.3934/mbe.2018052

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Abstract

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming part of these regions into deserts in some cases. Although it is documented that a decreasing tendency in precipitation might induce earlier disappearance of vegetation, quantifying the relationship between decrease of precipitation and vegetation endurance remains a challenging task due to the inherent complexities involved in distinct scenarios. In this paper we present a model for precipitation-vegetation dynamics in semi-arid landscapes that can be used to explore numerically the impact of decreasing precipitation trends on appearance of desertification events. The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.

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