Spatio‐temporal Scaling of Vegetation Growth and Soil Formation from Percolation Theory

Holtzman

Ghanbarian

2017

Water

Abstract:Optimal flow paths obtained from percolation theory provide a powerful tool that can be used to characterize properties associated with flow such as soil hydraulic conductivity, as well as other properties influenced by flow connectivity and topology. A recently proposed scaling theory for vegetation growth appeals to the tortuosity of optimal paths from percolation theory to define the spatio-temporal scaling of the root radial extent (or, equivalently, plant height). Root radial extent measures the maximum horizontal distance between a plant shoot and the root tips. We apply here the same scaling relationship to unsteady (horizontal) flow associated with plant transpiration. The pore-scale travel time is generated from the maximum flow rate under saturated conditions and a typical pore size. At the field-scale, the characteristic time is interpreted as the growing season duration, and the characteristic length is derived from the measured evapotranspiration in that period. We show that the two scaling results are equivalent, and they are each in accord with observed vegetation growth limits, as well as with actual limiting transpiration values. While the conceptual approach addresses transpiration, most accessed data are for evapotranspiration. The equivalence of the two scaling approaches suggests that, if horizontal flow is the dominant pathway in plant transpiration, horizontal unsteady flow follows the same scaling relationship as root growth. Then, we propose a corresponding scaling relationship to vertical infiltration, a hypothesis which is amenable to testing using infiltration results of Sharma and co-authors. This alternate treatment of unsteady vertical flow may be an effective alternative to the commonly applied method based on the diffusion of water over a continuum as governed by Richards' equation.

Section: Percolation Scaling Theory For Solute Transportmentioning

confidence: 65%

Section: Potential Relationship With Unsteady Flowmentioning

confidence: 71%

Section: Experimental Datamentioning

confidence: 99%

Section: Experimental Datamentioning

confidence: 99%

Section: Relevance Of Percolation Scaling To Vegetation Growth and Somentioning

confidence: 99%

See 3 more Smart Citations

A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

Holtzman

Ghanbarian

2017

Water

Percolation theory for solute transport in porous media: Geochemistry, geomorphology, and carbon cycling

Water Resources Research

Ghanbarian

2016

Understanding the time‐dependent scaling of chemical weathering has been a significant research goal for over a decade. A percolation theoretical treatment of nonreactive solute transport that was previously shown compatible with the scaling of chemical weathering rates is here shown to be compatible with soil formation rates, and with C and N sequestration rates in the soil as well. In this theoretical framework, the percolation backbone fractal dimensionality, which generates the long‐time tail of the solute arrival time distribution, also predicts the scaling of the reaction rates, while laboratory proportionality to the fluid flow velocity translates to an analogous relevance of the vertical infiltration rate in the field. The predicted proportionality of solute transport to net infiltration generates simultaneously the variability in soil formation rates across 4 orders of magnitude of precipitation and 12 orders of magnitude of time scales.

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Sahimi

2017

Reviews of Geophysics

141

We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.