Self-organized formation of banded vegetation patterns in semi-arid regions: A model

We propose a grid model for the vegetation in bands, with special emphasis on those comprising the tiger bush in the Sahel. The model is mechanistic and involves three basic effects, the coupling of which leads to a redistribution of rainfall water. First, plants stimulate water infiltration and soil moisture. Second, there is a cutoff value for the soil moisture, below which vegetation cannot subsist. Third, soil infiltration capacity under the canopy is more easily exceeded in locations with larger annual rainfall, thus implying a larger transfer of overland water inside vegetated areas. The presence of a slope is modeled by making the overland flow unidirectional. The combination of these three effects conveys a partition of the landscape into runoff-dominated and infiltration-dominated areas, the ratio of which is a decreasing function of annual rainfall. On the other hand, the infiltration-dominated sector collects a larger share of available water in near arid conditions than it does when rainfall is more abundant. The result is a pattern of thin, but highly productive bands under low rainfall. With increasing precipitation, bands widen but become less productive. Specific zoning of a band along a transect emerges from simulations, which are carried out under both constant and varying precipitation. The issue of the upslope migration of bands is also examined. The results are in accordance with the conclusions by Valentin and d’Herbès [Valentin, C., d’Herbès, J.M., 1999. Niger tiger bush as a natural harvesting system. Catena, 37, 231–256] on measurements taken along a precipitation gradient in Niger.