A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

Hunt, A. G.; Holtzman, Ran; Ghanbarian, Behzad

doi:10.3390/w9020104

Cited by 11 publications

(9 citation statements)

References 51 publications

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“…However, in [80] it was shown that the length and time scales of the mean growing season transpiration, T g , and growing season length, t g , can be used in the scaling relationship for RRE = T g (t/t g ) 1/1.21 . More importantly, since the yearly increase in RRE turns out to equal the transpiration [80], the root volume, which increases as the RRE to the mass fractal dimension, Guidance for the choice of d f was taken from percolation theory and general knowledge about the architecture of roots and the soil (see Figure 2 for details). It has often been noted that the bulk of root mass is found in the top 2 m of soil [72], or the top 1 m [73].…”

Section: Concepts From Percolation Theorymentioning

confidence: 99%

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

Hunt

Faybishenko

Ghanbarian

et al. 2020

IJERPH

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The fate of water and water-soluble toxic wastes in the subsurface is of high importance for many scientific and practical applications. Although solute transport is proportional to water flow rates, theoretical and experimental studies show that heavy-tailed (power-law) solute transport distribution can cause chemical transport retardation, prolonging clean-up time-scales greatly. However, no consensus exists as to the physical basis of such transport laws. In percolation theory, the scaling behavior of such transport rarely relates to specific medium characteristics, but strongly to the dimensionality of the connectivity of the flow paths (for example, two- or three-dimensional, as in fractured-porous media or heterogeneous sediments), as well as to the saturation characteristics (i.e., wetting, drying, and entrapped air). In accordance with the proposed relevance of percolation models of solute transport to environmental clean-up, these predictions also prove relevant to transport-limited chemical weathering and soil formation, where the heavy-tailed distributions slow chemical weathering over time. The predictions of percolation theory have been tested in laboratory and field experiments on reactive solute transport, chemical weathering, and soil formation and found accurate. Recently, this theoretical framework has also been applied to the water partitioning at the Earth’s surface between evapotranspiration, ET, and run-off, Q, known as the water balance. A well-known phenomenological model by Budyko addressed the relationship between the ratio of the actual evapotranspiration (ET) and precipitation, ET/P, versus the aridity index, ET0/P, with P being the precipitation and ET0 being the potential evapotranspiration. Existing work was able to predict the global fractions of P represented by Q and ET through an optimization of plant productivity, in which downward water fluxes affect soil depth, and upward fluxes plant growth. In the present work, based likewise on the concepts of percolation theory, we extend Budyko’s model, and address the partitioning of run-off Q into its surface and subsurface components, as well as the contribution of interception to ET. Using various published data sources on the magnitudes of interception and information regarding the partitioning of Q, we address the variability in ET resulting from these processes. The global success of this prediction demonstrated here provides additional support for the universal applicability of percolation theory for solute transport as well as guidance in predicting the component of subsurface run-off, important for predicting natural flow rates through contaminated aquifers.

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Section: Concepts From Percolation Theorymentioning

confidence: 99%

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

Hunt

Faybishenko

Ghanbarian

et al. 2020

IJERPH

Self Cite

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“…Thus the height prediction generated by using the maximum flow velocity of 1 μm s −1 and a length scale of 10 μm is coincident with the height prediction using T g = 1650 mm and t g = 180 d, where 1650 mm is the largest transpiration value recorded in a world biome survey (Box et al, 1989) and 180 d is a characteristic growing season. More importantly, perhaps, the lower limit pore‐scale fluid flow velocity proposed here with the same length scale of 10 μm generates the lower limit plant height curve (Hunt et al, 2017) with the smallest transpiration observed, in the Namibian desert (Seeley, 1978), of 20 mm. Note that Eq.…”

Section: Theorymentioning

confidence: 66%

“…Hunt et al (2017), who addresses the upscaling of transpiration, showed that Eq. [1] for plant growth could be equally represented as

H = T_{normalg} {(\frac{t}{t_{normalg}})}^{1 / 1.217}

where H is the plant height (or RRE), T g is the transpiration in a growing season, and t g is the length of the growing season.…”

Section: Theorymentioning

confidence: 99%

Spatiotemporal Scaling of Vegetation Growth and Soil Formation: Explicit Predictions

Hunt

2017

Vadose Zone Journal

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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.

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“…This two-term formulation enjoys a rigorous mathematicalphysical underpinning. This includes recent work of Hunt et al (2017), who used percolation theory to interpret S and 𝑐𝐾 s . The use of 𝑑 = 2 expansion terms, however, has an important side effect.…”

Section: Core Ideasmentioning

confidence: 99%

Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

Jaiswal

Gao

Rahmati

et al. 2022

Vadose Zone Journal

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Many different equations have been proposed to describe quantitatively onedimensional soil water infiltration. The unknown coefficients of these equations characterize soil hydraulic properties and may be estimated from a n record, { t𝑖 , Ĩ𝑖 } 𝑛 𝑖=1 , of cumulative infiltration measurements using curve fitting techniques. The two-term infiltration equation, 𝐼(𝑡) = 𝑆 √ 𝑡 + 𝑐𝐾 s 𝑡, of Philip has been widely used to describe measured infiltration data. This function enjoys a solid mathematical-physical underpinning and admits a closed-form solution for the soil sorptivity, S [L T −1/2 ], and multiple, 𝑐 [−], of the saturated hydraulic conductivity, 𝐾 s [L T −1 ]. However, Philip's two-term equation has a limited time validity, 𝑡 valid [T], and thus cumulative infiltration data, Ĩ( t), beyond 𝑡 = 𝑡 valid will corrupt the estimates of S and 𝐾 s . This paper introduces a novel method for estimating S, c, 𝐾 s , and 𝑡 valid of Philip's twoterm infiltration equation. This method, coined parasite inversion, use as vehicle Parlange's three-parameter infiltration equation. As prerequisite to our method, wepresent as secondary contribution an exact, robust and efficient numerical solution of Parlange's infiltration equation. This solution admits Bayesian parameter estimation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and yields as byproduct the marginal distribution of Parlange's β parameter. We evaluate our method for 12 USDA soil types using synthetic infiltration data simulated with HYDRUS-1D. An excellent match is observed between the inferred values of S and 𝐾 s and their "true" values known beforehand. Furthermore, our estimates of c and 𝑡 valid correlate well with soil texture, corroborate linearity of the 𝑐(β) relationship for 0 ≤ 𝑡 ≤ 𝑡 valid , and fall within reported ranges. A cumulative vertical infiltration of about 2.5 cm may serve as guideline for the time-validity of Philip's two-term infiltration equation.

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A Percolation‐Based Approach to Scaling Infiltration and Evapotranspiration

Cited by 11 publications

References 51 publications

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

Predicting Water Cycle Characteristics from Percolation Theory and Observational Data

Spatiotemporal Scaling of Vegetation Growth and Soil Formation: Explicit Predictions

Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

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