Vegetation–soil water interaction within a dynamical ecosystem model of grassland in semi-arid areas

A dynamical ecosystem model with three variables, living biomass, wilted biomass and available soil wetness, is developed to examine the vegetation–soil water interaction in semi-arid areas. The governing equations are based on the mass conservation law. The physical and biophysical processes are formulated with the parameters estimated from observational data. Both numerical results and qualitative analysis of the model as well as observational data indicate that the maintenance of a grassland requires a minimum precipitation (or equivalently, a minimum moisture index), and the grassland and desert ecosystem can coexist when precipitation is within a range above this threshold. Sensitivity studies show that these numerical results are robust with respect to model parameters and the transformation functions. It is also found that the wilted vegetation plays a very important role in shaping the transition between grassland and desert. By using the theories of an attractor basin and multiple equilibrium states, the conditions for grassland maintenance and the strategy of grazing are also analysed.