Dryland vegetation patterns

2025

1. Submitted

   A flow-kick model of dryland vegetation patterns: the impact of rainfall variability on resilience

   Punit Gandhi, Matthew Oline, and Mary Silber

   Mar 2025

   Abs arXiv Bib

   In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by harvesting additional stormwater from upslope low-infiltration bare zones. We are interested in the robustness of this pattern formation survival mechanism to changes in rainfall variability. For this, we use a flow-kick modeling framework that treats storms as instantaneous kicks to the soil water. The positive feedbacks in the storm-level hydrology, that act to concentrate water within the vegetation bands, are captured through the spatial profiles of the soil water kicks. Between storms, the soil water and vegetation, modeled by a two-component reaction-diffusion system, evolve together. We use a combination of linear stability analysis and numerical simulation to compare predictions of idealized periodic rainfall, with no variability, to predictions when there is randomness in the timing and magnitude of water input from storms. We show that including these random elements leads to a decrease in the parameter range over which patterns appear. This suggests that an increase in storm variability, even with the same mean annual rainfall, may negatively impact the resilience of these pattern-forming dryland ecosystems.

   @misc{gandhi2025flowkickmodeldrylandvegetation,
     title = {A flow-kick model of dryland vegetation patterns: the impact of rainfall variability on resilience},
     author = {Gandhi, Punit and Oline, Matthew and Silber, Mary},
     year = {2025},
     eprint = {2501.01569},
     archiveprefix = {arXiv},
     primaryclass = {nlin.PS},
     url = {https://arxiv.org/abs/2501.01569}
   }

2023

1. SIADS

   A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation

   Punit Gandhi, Lily Liu, and Mary Silber

   SIAM Journal on Applied Dynamical Systems, Mar 2023

   Abs DOI arXiv Bib

   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.

   @article{gandhi2023pulsed,
     author = {Gandhi, Punit and Liu, Lily and Silber, Mary},
     title = {A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation},
     journal = {SIAM Journal on Applied Dynamical Systems},
     volume = {22},
     number = {2},
     pages = {657-693},
     year = {2023},
     doi = {10.1137/22M1469572},
     url = {https://doi.org/10.1137/22M1469572},
     eprint = {https://doi.org/10.1137/22M1469572}
   }

2020

1. Physica D

   A fast–slow model of banded vegetation pattern formation in drylands

   Punit Gandhi, Sara Bonetti, Sarah Iams, Amilcare Porporato, and Mary Silber

   Physica D: Nonlinear Phenomena, Mar 2020

   Abs DOI arXiv Bib

   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.

   @article{gandhi2020fast,
     title = {A fast--slow model of banded vegetation pattern formation in drylands},
     author = {Gandhi, Punit and Bonetti, Sara and Iams, Sarah and Porporato, Amilcare and Silber, Mary},
     journal = {Physica D: Nonlinear Phenomena},
     volume = {410},
     pages = {132534},
     year = {2020},
     publisher = {Elsevier},
     keywords = {Pattern formation, Vegetation bands, Dryland ecohydrology, Reaction–advection–diffusion equations, fast–slow switching model},
     issn = {0167-2789},
     doi = {https://doi.org/10.1016/j.physd.2020.132534},
     url = {https://www.sciencedirect.com/science/article/pii/S0167278919307328}
   }

2019

1. Springer

   Vegetation Pattern Formation in Drylands

   Punit Gandhi, Sarah Iams, Sara Bonetti, and Mary Silber

   Mar 2019

   Abs DOI arXiv Bib

   This chapter aims to (1) provide background for conceptual mathematical models of spontaneous pattern formation, in the context of dryland vegetation patterns, and (2) review observational studies of the phenomenon. The chapter also highlights challenges and opportunities associated with the development of the models in light of increasing availability of remote sensing data. This includes both satellite imagery of the patterns and elevation data of the topography. The vast scales, in time and space, associated with the key processes further suggest avenues for improved mathematical modeling paradigms.

   @inbook{gandhi2019vegetation,
     author = {Gandhi, Punit and Iams, Sarah and Bonetti, Sara and Silber, Mary},
     editor = {D'Odorico, Paolo and Porporato, Amilcare and Wilkinson Runyan, Christiane},
     title = {Vegetation Pattern Formation in Drylands},
     booktitle = {Dryland Ecohydrology},
     year = {2019},
     publisher = {Springer International Publishing},
     address = {Cham},
     pages = {469--509},
     isbn = {978-3-030-23269-6},
     doi = {10.1007/978-3-030-23269-6_18},
     url = {https://doi.org/10.1007/978-3-030-23269-6_18}
   }

2018

1. R. Soc. Interface

   A topographic mechanism for arcing of dryland vegetation bands

   Punit Gandhi, Lucien Werner, Sarah Iams, Karna Gowda, and Mary Silber

   Royal Society Interface, Mar 2018

   Abs DOI arXiv Bib

   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 arc convex-downslope when growing on top of a ridge, and convex-upslope when growing in a valley. This behaviour 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 behaviour.

   @article{gandhi2018topographic,
     title = {A topographic mechanism for arcing of dryland vegetation bands},
     author = {Gandhi, Punit and Werner, Lucien and Iams, Sarah and Gowda, Karna and Silber, Mary},
     journal = {Royal Society Interface},
     volume = {15},
     number = {147},
     pages = {20180508},
     year = {2018},
     doi = {10.1098/rsif.2018.0508},
     url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsif.2018.0508},
     eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2018.0508}
   }