Sensitivity of dryland vegetation patterns to storm characteristics

Abstract

Ecohydrological phenomena are o ften multiscale in nature, with behavioTur that emerges from the interaction of tightly coupled systems having characteristic timescales that differ by orders of magnitude. Models address these differences using timescale separation methods, where each system is held in psuedo‐steady state while the other evolves. When the computational demands of solving the ‘fast’ system are large, this strategy can become numerically intractable. Here, we use emulation modelling to accelerate the simulation of a computationally intensive ‘fast’ system: overland flow. We focus on dryland ecosystems in which storms generate overland flow, on timescales of 101 − 2 s. In these ecosystems, overland flow delivers crucial water inputs to vegetation, which grows and disperses ‘slowly’, on timescales of 107 − 9 s. Emulation allows for a physically realistic treatment of flow, advancing on phenomenological descriptions used in previous studies. Resolving the within‐storm processes reveals novel dynamics, including new transition pathways from patchy vegetation to desertification, that are specifically controlled by storm processes.

A Pulsed-Precipitation Model of Dryland Vegetation Pattern Formation

“…of the type reported in [27]. An interesting point of comparison can already be made between our wavenumber selection results and those presented in a recent paper by Crompton and Thompson [28]. Their study uses a different approach to determining the soil moisture distribution following a storm event.…”

“…Our pulsed-precipitation model paves the way exploration of stochastic rainfall patterns by allowing computational over the original fast-slow model, thus making large numbers of trials feasible. We note that computational speed has also been addressed by applying machine learning techniques to predict the soil water distribution following rain in a more detailed hydrological model [28]. Although stochasticity and seasonality of rainfall were not considered in that paper, they did include storm duration, along with storm depth, as training parameters, and observed similar qualitative trends of increased band spacing with increased storm depth.…”

“…The choice of periodic boundary conditions does not allow for exploration of the impact of surface water run off. Both effects have been considered in [32,28] using very different approaches to model surface hydrology. Our focus in this work has been on the influence of hydrological processes across timescales and the biomass model used here is based directly on previous conceptual models [23,12].…”

Hydrologic Connectivity and Patch‐To‐Hillslope Scale Relations in Dryland Ecosystems

“…Applications also include mathematical models characterizing pattern formation in drylands (e.g., HilleRisLambers et al., 2001; Rietkerk et al., 2002, and others), which typically replace stochastic rainfall events by a constant annual rate; however, this idealized representation is known to influence the predicted pattern morphology (Crompton & Thompson, 2021; Gandhi et al., 2020; Siteur et al., 2014). If C = 0 is assumed—optimized rainfall capture by the vegetation, and equivalent to the periodic boundary conditions typically prescribed in these models—the study approach could be used to parameterize and constrain the distance that surface water travels before it infiltrates into the soil (Gandhi et al., 2020), and thereby insert realistic storms and runoff run‐on processes into mathematical models describing dryland vegetation patterns.…”