A Fast-Slow Model of Banded Vegetation Pattern Formation in Drylands

TL;DR

This paper introduces a fast-slow switching model for banded vegetation pattern formation in drylands, capturing processes across multiple timescales to better understand ecohydrological dynamics and pattern characteristics.

Contribution

The paper presents a novel fast-slow reaction-advection-diffusion model that accurately represents processes at their natural timescales, reducing parameter fitting and improving ecological insights.

Findings

Model reproduces observed band spacing and colonization rates.

Soil moisture dynamics align with empirical time series data.

Framework enables investigation of rain event impacts on dryland patterns.

Abstract

From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple timescales. We propose a new fast-slow switching model in order to capture these processes on appropriate timescales within a conceptual modeling framework based on reaction-advection-diffusion equations. The fast system captures hydrological processes that occur on minute to hour timescales during and shortly after major rainstorms, assuming a fixed vegetation distribution. These include key feedbacks between vegetation biomass and downhill surface water transport, as well as between biomass and infiltration rate. The slow system acts between rain events, on a timescale of days to months, and evolves vegetation and soil moisture. Modeling processes at the appropriate timescales allows parameter values to be set by the actual processes they capture. This reduces the number of parameters that are chosen expressly to fit pattern characteristics, or to artificially slow down fast processes by the orders of magnitude required to align their timescales with the biomass dynamics. We explore the fast-slow switching model through numerical simulation on a one-dimensional hillslope, and find agreement with certain observations about the pattern formation phenomenon, including band spacing and upslope colonization rates. We also find that the predicted soil moisture dynamics are consistent with time series data that has been collected at a banded vegetation site. This fast-slow model framework introduces a tool for investigating the possible impact of changes to frequency and intensity of rain events in dryland ecosystems.