A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation

Abstract

We develop a model for investigating the impact of rainstorm variability on the formation of banded vegetation patterns in dryland ecosystems. Water input, during rare rainstorms, is modeled as an instantaneous kick to the soil water. The redistribution, from surface water to soil moisture, accounts for the impact of vegetation on infiltration rate and downslope overland flow speed. These two positive feedbacks between water and biomass distributions act on the fast timescales of rain storms. During dry periods, a classic reaction-diffusion framework is used for the slow processes associated with soil water and biomass. This pulsed precipitation model predicts that the preferred spacing of the vegetation bands is determined by the characteristic distance that a storm pulse of water travels overland before infiltrating into the soil. In this way, the vegetation pattern is determined by the fast ecohydrological processes and may be attuned with its dryland precipitation pattern. We demonstrate how this modeling framework, suited for stochastic rain inputs, can be used to investigate possible collapse of a dryland pattern-forming ecosystem under different precipitation patterns with identical low annual mean. Model simulations suggest, for instance, that shorter rainy seasons and greater variability in storm depth may both hasten ecosystem collapse.