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

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.