Dryland Vegetation Pattern Formation: Modeling Possible Annihilation Under Changing Rainfall Patterns

A beautiful example of spontaneous pattern formation appears in the distribution of vegetation in some dry-land environments. Examples from Africa, Australia and the Americas reveal that vegetation, at a community scale, can respond to aridity stress by forming into stripe-like bands, that alternate with striking regularity with bands of bare soil. These bands form on gentle slopes that lead to overland water flow during the rare storms, and are transverse to the grade. The bands harvest the water from the upslope bare regions. A typical length scale for such patterns is 100 m; they are readily surveyed by modern satellites. Ecologists have proposed that characteristics of the vegetation patterns may provide early warning signs of eco-system collapse. We develop a mathematical model that allows us to investigate the possible collapse of banded vegetation under changes in the precipitation patterns, including not only changes to mean annual precipitation, but also possible changes in seasonality, storm frequency and storm depth, which are parameters of our stochastic rainfall model. We also propose that the spacing of the vegetation bands is set by the properties of the overland water transport and its infiltration rate into the soil, both of which depend on the amount of biomass on the surface. Our modeling framework parsimoniously exploits the disparity of timescales between the rain events, typically hours, to the biomass growth over decades. It emphasizes the possible importance of storm properties for the patterns to form and remain robust.