The role of subsurface water dynamics in vegetative pattern formation in a level arid region

The transport of subsurface water within a homogeneous porous unsaturated vadose zone is considered to be governed by Richards’ conservation of mass equation with vegetation growing on its upper horizontal arid boundary surface and its horizontal lower surface being impermeable. It is assumed that Richards’ equation and its lower boundary satisfy a linear and semi-infinite limit, respectively, while an existing vegetation-groundwater system is adopted on its upper one, groundwater being identified with subsurface water content on the upper boundary. A rhombic planform nonlinear stability analysis is applied to this system to investigate the formation of stationary two-dimensional vegetative patterns consisting of periodic arrays of spots (leopard bush), gaps (pearled bush), or bicontinuous mazes (labyrinthine tiger bush) observed to occur on arid flat environments. The results of that analysis can be represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. Then, a morphological sequence of bare ground and stable vegetative states is produced upon traversing an experimentally-determined root suction characteristic curve based on soil type as a function of rainfall rate through that parameter space. Finally, this predicted sequence along a rainfall gradient is used to motivate an aridity classification scheme and compared with both theoretical results from similar systems and observational evidence relevant to the occurrence of leopard, pearled, or labyrinthine tiger bush vegetative patterns.