Unsteady overland flow on flat surfaces induced by spatial permeability contrasts

Lateral redistribution of surface water in patchy arid ecosystems has been hypothesized to contribute to the maintenance of vegetation patches through the provision of a water subsidy from bare sites to vegetated sites. Such runon-runoff processes occur during Hortonian runoff events on topographically sloping ground. Surface flow redistribution may also occur on topographically flat ground if the presence of the vegetation patch creates a contrast in infiltration rate, leading to a free-surface gradient in ponded water. The precise dynamics and the eco-hydrologic role of this process has resisted complete theoretical treatment to date. Here the overland flow equations are modified to account for the presence of vegetation situated over a flat surface. The resulting model is solved numerically to determine whether this mechanism could influence the spatial partitioning of water in patchy arid ecosystems. Assumptions made about infiltration processes and overland flow in existing eco-hydrologic models of patchy and patterned arid ecosystems are evaluated in comparison to the solution of the ‘full’ coupled Saint-Venant equations with various infiltration models. The results indicate that the optimization of vegetation spatial patch scales with respect to water redistribution may be determined by the size of the infiltration redistribution length L over which the presence of an infiltration contrast perturbs baseline infiltration behavior.