  Patterns of vegetation are a characteristic feature of many semi-arid
regions. The limiting resource in these ecosystems is water, which is added to
the system through short and intense rainfall events that cause a pulse of
biological processes such as plant growth and seed dispersal. We propose an
impulsive model based on the Klausmeier reaction-advection-diffusion system,
analytically investigate the effects of rainfall intermittency on the onset of
patterns, and augment our results by numerical simulations of model extensions.
Our investigation focuses on the parameter region in which a transition between
uniform and patterned vegetation occurs. Results show that decay-type processes
associated with a low frequency of precipitation pulses inhibit the onset of
patterns and that under intermittent rainfall regimes, a spatially uniform
solution is sustained at lower total precipitation volumes than under
continuous rainfall, if plant species are unable to efficiently use low soil
moisture levels. Unlike in the classical setting of a reaction-diffusion model,
patterns are not caused by a diffusion-driven instability but by a combination
of sufficiently long periods of droughts between precipitation pulses and water
diffusion. Our results further indicate that the introduction of pulse-type
seed dispersal weakens the effects of changes to width and shape of the plant
dispersal kernel on the onset of patterns.
