Spatiotemporal Scaling of Vegetation Growth and Soil Formation: Explicit Predictions

Abstract

In a previous study, vegetation linear extent and soil depth as functions of time were proposed to follow percolation-based scaling laws of power-law form. Although the power-law exponents are specified by theory, the fundamental length, x 0 , and time, t 0 , scales must be generated from physical arguments. In principle, these length and time scales can vary widely with climate, soil, and plant variables. In the previous study, approximate values, microns and seconds, were proposed for x 0 and t 0 , based on typical soil flow rates, x 0 /t 0 , under saturated conditions, and the concept of a single pore having a diameter measured in microns. But the focus here is on development of predictive relationships for soil depth and vegetation linear extent as functions of time and, thus, on guidance for choosing specific values for x 0 and t 0 . In the present study, it is argued that the relevant flow rate for soil formation is net (deep) infiltration, whereas for vegetation extent, the relevant flux must equate to transpiration. In vegetation, linear extent refers (approximately) equivalently to plant height, or root radial extent. Here root radial extent is taken as half the diameter of the projected root system. Since the root radial extent and the root biomass are by definition related through the root fractal dimensionality, the proposed relevance of transpiration to root radial extent implies a specific relationship between transpiration and root productivity, a measure of the root biomass added in a year. When above-ground and below-ground biomass are closely related, one can infer a proportionality of net primary productivity to root biomass changes. The general concepts are tested on large data-bases for the temporal evolution of plant heights and soil depths, as well as the productivity as a function of evapotranspiration and soil calcic and gypsic horizon depths.

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

“…Progress has recently been made in this direction (Yu & Hunt, ), and the problem has been addressed more quantitatively, correcting two errors in existing calculations (Salehikhoo et al, ). More clearly even than the relevance to chemical weathering should be the relevance of solute transport to the formation of calcic and gypsic horizons. The relevance of percolation scaling of solute transport to the formation of such horizons in arid and semiarid regions was recently confirmed (Hunt, ; Hunt & Ghanbarian, ). The strong dependence of solute transport on length and timescales suggests the possibility that other phenomena, such as vegetation growth rates, may be also affected by the “edaphic” constraints of the soil. Evidence is accumulating that the exponent that characterizes 2‐D optimal paths describes the spatiotemporal scaling of vegetation growth, and that the variability across species, climates, and substrates can be attributed to variation in transpiration rates (Hunt, , ).…”

“…The relevance of percolation scaling of solute transport to the formation of such horizons in arid and semiarid regions was recently confirmed (Hunt, ; Hunt & Ghanbarian, ). The strong dependence of solute transport on length and timescales suggests the possibility that other phenomena, such as vegetation growth rates, may be also affected by the “edaphic” constraints of the soil. Evidence is accumulating that the exponent that characterizes 2‐D optimal paths describes the spatiotemporal scaling of vegetation growth, and that the variability across species, climates, and substrates can be attributed to variation in transpiration rates (Hunt, , ). The scaling hypotheses in vegetation growth and soil formation that were described earlier assume that the water that plants use—transpiration—drives vegetation growth, while the water that is not taken up by plants, or evaporated off the soil, or runs off the surface, but percolates through to the bottom of the soil layer, contributes to chemical weathering and soil formation.…”

“…If the soil production function turns out to have a direct relationship with vertical flow rates, the results described here for soil production should be relevant to landscape evolution models. Progress has also been made in this direction (Hunt, ; Hunt & Ghanbarian, ; Yu et al, ). The appropriate generalization appears to be precipitation less the sum of evapotranspiration and runoff, all divided by the porosity. The possibility that, in the presence of erosion, soils can reach steady state conditions should be investigated.…”

Prediction of Soil Formation as a Function of Age Using the Percolation Theory Approach

“…The theory of solute transport limited weathering ("percolation theory"; Hunt and Ghanbarian, 2016;Hunt, 2017;Yu et al, 2017) that explains the observed overall dependence of chemical weathering rates and soil formation on (1) time (or soil depth), (2) climate, i.e., the dominant influence on flow rates, (3) substrate heterogeneity scale, (4) erosion rates (thus relief), is based on a percolation theoretical treatment of solute transport. The erosion rate depends on the relief, or topography, and the time is expressed explicitly, thus accounting for all five of Dokuchaev's original soil forming factors.…”

“…The solute velocity is obtained from a known scaling relationship between transit time and system length (Lee et al, 1999), plus the identification of the fundamental length and time scales (Hunt, 2017). The Damköhler number, Da I , which is the ratio (Salehikhoo et al, 2013) of a solute advection time to a reaction time under well-mixed conditions (Yu and Hunt, 2017a), measures the importance of solute transport relative to reaction kinetics on chemical weathering rates.…”