A minimal model of soil water–vegetation interactions forced by stochastic rainfall in water-limited ecosystems

A minimal model of soil water–vegetation interaction in dryland ecosystems is developed as a vehicle to show how stochastic differential equations can be applied to this problem. In contrast to previous works, which assume a constant rainfall, the system is forced using stochastic rainfall, and the stationary probability distributions of the soil water content and the vegetation density are derived analytically. Thence, a sensitivity analysis of the stationary probability distributions on rainfall and model parameters has been carried out. This analysis points out the influence of the rainfall process, soil and vegetation properties on the stationary probability distributions of soil water and vegetation. The approach can potentially be extended to address more complex models.