A spatial model for soil-atmosphere interaction: Model construction and linear stability analysis

A simple model is developed to investigate the role of spatial dynamics in the soil-atmosphere system. The model is constructed by considering the mas s and energy balance equations for soil and atmosphere, closed with a two-d imensional, corrected quasigeostrophic approximation for large-scale atmosp heric motions: and a suitable model for rainfall occurrence. The main resul t presented concerns the linear stability analyses of the homogenous equili brium solutions for dry and wet climates. In the first case (desert) the sy stem is stable and no spatial perturbation internal to the system can produ ce spatial heterogeneities. In the second case (wet climate) the dynamics c an produce spatial instabilities of several scales, resulting in likely pat terns of wet and dry zones. A key role in triggering this instability is pl ayed by the sensible heat flux to the atmosphere, which in turn is linked t o soil moisture.