Dryland ecosystems commonly exhibit periodic bands of vegetation, thought to form due to competition between individual plants for heterogeneously distributed water. In this paper, we develop a Fourier method for locally identifying the pattern wavenumber and orientation, and apply it to aerial images from a region of vegetation patterning near Fort Stockton, TX, USA. We find that the local pattern wavelength and orientation are typically coherent, but exhibit both rapid and gradual variation driven by changes in hillslope gradient and orientation, the potential for water accumulation, or soil type. Endogenous pattern dynamics, when simulated for spatially homogeneous topographic and vegetation conditions, predict pattern properties that are much less variable than the orientation and wavelength observed in natural systems. Our local pattern analysis, combined with ancillary datasets describing soil and topographic variation, highlights a largely unexplored correlation between soil depth, pattern coherence, vegetation cover and pattern wavelength. It also, surprisingly, suggests that downslope accumulation of water may play a role in changing vegetation pattern properties.
Keywords: Fourier analysis; arid ecosystems; pattern formation.