Banded Vegetation Patterns in Drylands: Modeling across timescales

Periodic spatial patterns of vegetation growth have been observed in dryland ecosystems. These patterns are thought to arise through self-organization in the water-limited environments that support them, and reaction-advection-diffusion models have suggested that the patterns are a precursor to ecosystem collapse as water becomes increasingly scarce. On gently sloped terrain, dryland vegetation patterns often appear as repeating bands of dense vegetation that are decameters wide and spaced on the order of hectometers apart, with bare soil in between. While observations indicate uphill migration of the bands on a century timescale, the water is input during rainstorms that last just a few hours. We explore the impact of assumptions about the fast hydrology associated with overland flow and infiltration during rainstorms on the slow dynamics of the patterns. We consider both temporally periodic and stochastic rain input within a conceptual fast-slow switching model that exploits the difference in timescales involved.