Banded patterns consisting of alternating bare soil and dense vegetation have
been observed in water-limited ecosystems across the globe, often appearing
along gently sloped terrain with the stripes aligned transverse to the
elevation gradient. In many cases these vegetation bands are arced, with field
observations suggesting a link between the orientation of arcing relative to
the grade and the curvature of the underlying terrain. We modify the water
transport in the Klausmeier model of water-biomass interactions, originally
posed on a uniform hillslope, to qualitatively capture the influence of terrain
curvature on the vegetation patterns. Numerical simulations of this modified
model indicate that the vegetation bands change arcing-direction from
convex-downslope when growing on top of a ridge to convex-upslope when growing
in a valley. This behavior is consistent with observations from remote sensing
data that we present here. Model simulations show further that whether bands
grow on ridges, valleys, or both depends on the precipitation level. A survey
of three banded vegetation sites, each with a different aridity level,
indicates qualitatively similar behavior.Comment: 26 pages, 13 figures, 2 table