Scaling of the Richards Equation Under Invariant Flux Boundary Conditions

Kutílek, Miroslav; Zayani, K.; Haverkamp, R.; Parlance, J.-Y.; Vachaud, G.

doi:10.1029/91wr01550

Cited by 17 publications

(6 citation statements)

References 8 publications

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“…We expect the numerous uniquely scaled solutions of Buckingham-Darcy and Richards' equations now only theoretically available (e.g. Kutilek et al 1991;Warrick & Hussen 1993;Nachabe 1996) to be extended to specific landscape and field regions categorized by mapping units described by information containing scale factors for their soil water properties.…”

Section: Future Researchmentioning

confidence: 99%

Selected research opportunities in soil physics

Nielsen

Kutílek

Wendroth

et al. 1997

Sci. agric. (Piracicaba, Braz.)

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Section: Future Researchmentioning

confidence: 99%

Selected research opportunities in soil physics

Nielsen

Kutílek

Wendroth

et al. 1997

Sci. agric. (Piracicaba, Braz.)

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“…This way, a single solution is valid for a similar class of soils with similar definite conditions. Another technique is based on postulation of RE in a form invariant to the boundary condition (Kutilek et al, 1991). Recently the scaling technique was developed, which makes it possible to generalize a single solution of RE to many dissimilar soils and conditions (Sadeghi et al, 2012a(Sadeghi et al, , 2021b.…”

Section: Introductionmentioning

confidence: 99%

Scaling analysis of Richards equation for horizontal infiltration and its approximate solution

Zi-Qing

2021

Soil Science Soc of Amer J

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Richards equation (RE) of Brooks-Corey soil is invariant under some scaling transformations and can be reduced to ordinary differential equations (ODEs) with scale symmetry analysis. From the reduced ODE, it is convenient to get the solution of RE (mostly numerically). The admissible scaling transformations of RE can transform a given solution to other solutions, by which the explicit relations between wetting front (or its velocity) and boundary moisture and between cumulative infiltration and boundary moisture for horizontal infiltration are deduced. For horizontal infiltration into dry soil with constant boundary moisture, the contour of water distribution curve can be represented by a shape factor R, which can be regarded as a constant for a given soil. Based on the reduced ODE and the parameter R, an explicit approximate solution for horizontal soil water infiltration is proposed, which just relies on R.The shape factor R is related to Brooks-Corey power exponent n and independent of the boundary moisture. With the obtained R-n relations, the relative deviation of the approximate solution can be less than 0.001. The approximate solution keeps high precision in any time range of the infiltration process.

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“…In addition to describing soil variability, scaling has facilitated a parallel avenue helping to formulate unsaturated flow and transport in similar soils in a universal, scale‐invariant or soil‐independent manner [ Reichardt et al ., ; Warrick and Amoozegar‐Fard , ; Sharma et al ., ; Youngs and Price , ; Warrick et al ., ; Sposito and Jury , ; Kutilek et al ., ; Warrick and Hussen , ; Nachabe , ; Wu and Pan , ; Shukla et al ., ; Rasoulzadeh and Sepaskhah , ; Kozak and Ahuja , ; Roth , ; Sadeghi et al ., ; Sadeghi and Jones , ]. Referring to macro Miller, Nielsen, and Warrick‐type similitude, Sposito [] examined invariance of the Richards' equation with Lie group analysis leading to power‐law or exponential soil hydraulic functions [ Warrick , , p. 46].…”

Section: Introductionmentioning

confidence: 99%

A critical evaluation of the Miller and Miller similar media theory for application to natural soils

Sadeghi

Ghahraman

Warrick

et al. 2016

Water Resources Research

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The Miller-Miller similar media theory is widely applied to characterize the spatial variability of soil hydraulic properties. For a group of soils, a distinct scaling factor is commonly assigned to each individual soil to coalesce the soil water characteristic and hydraulic conductivity functions to single curves. It is generally assumed that the Miller-Miller theory is valid as long as soils are ''similar'' either with regard to their microscopic pore space geometry or the closely related macroscopic soil hydraulic functions. In this paper, it is illustrated that similarity is not the sole required condition for validity of the Miller-Miller theory. In addition, the interrelation between the soil water characteristic and the hydraulic conductivity functions considered for scaling need to be comparable. The interrelation is dependent not only on the pore space geometry, but also on solid-liquid interactions. Hence similar interrelation cannot be concluded from similarity of microscopic pore space geometry. A dimensionless parameter termed the ''joint scaling factor'' was defined and applied to evaluate the soundness of the interrelation condition for 26 soils from the UNSODA database that were grouped into six classes of similar soils. Obtained results clearly reveal the crucial importance of the interrelation condition for the Miller-Miller scaling theory, which has been hidden behind the ''similarity'' requirement, and contradict the general belief that Miller-Miller scaling is valid as long as soils are ''similar.''

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Scaling of the Richards Equation Under Invariant Flux Boundary Conditions

Cited by 17 publications

References 8 publications

Selected research opportunities in soil physics

Selected research opportunities in soil physics

Scaling analysis of Richards equation for horizontal infiltration and its approximate solution

A critical evaluation of the Miller and Miller similar media theory for application to natural soils

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