Scaling of Richards' Equation for Infiltration and Drainage

Warrick, A. W.; Hussen, A. A.

doi:10.2136/sssaj1993.03615995005700010004x

Cited by 25 publications

(20 citation statements)

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“…Note that two curves hold the “shape similarity” when they are scalable into a unified curve using a linear transformation. An advantage of this method over similar work (e.g., Warrick and Hussen, 1993) is that it is not restricted to a specific hydraulic model—hence, all existing and future models can be used for these solutions. The main restrictions are that the method is limited to the aforementioned simple boundary and initial conditions maintained in a homogenous soil profile.…”

Section: Theorymentioning

confidence: 99%

“…Scaling is also used for obtaining invariant solutions to unsaturated soil‐water phenomena where a single solution of which, will suffice for a variety of soil hydraulic properties and initial conditions. During the past four decades, such methods have been frequently developed mainly for unsaturated water flow, for example, by Reichardt et al (1972), Simmons et al (1979), Warrick et al, (1985), Vogel et al, (1991), Kutilek et al, (1991), Warrick and Hussen (1993), Nachabe (1996), Wu and Pan (1997), Kozak and Ahuja (2005), Roth (2008), and Sadeghi et al, (2011, 2012a, 2012b).…”

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confidence: 99%

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Scaled Solutions to Coupled Soil‐Water Flow and Solute Transport during the Redistribution Process

Sadeghi

Jones

2012

Vadose Zone Journal

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A recently developed method for scaling Richards' equation during soil‐water redistribution was extended here to derive invariant solutions for solute transport for a range of soils and initial conditions. Any arbitrary model for hydraulic properties can be used in Richards' equation. A transport model including both terms of convection and diffusion/dispersion is considered where the soil–solute reactions described by a linear sorption isotherm are considered. To evaluate the proposed method, Hydrus‐1D simulations were used to solve the water flow and solute transport equations for various soil textures and initial conditions. The resulting soil water content and solute concentrations profiles were scaled using the proposed method. The scaled results were nearly invariant for loam to clay soil textures and for a variety of initial conditions. The invariance of the scaled results implies a robust approach to scaling water flow and solute transport during the redistribution process and readily produces approximate solutions of the highly nonlinear governing equations.

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Section: Theorymentioning

confidence: 99%

mentioning

confidence: 99%

Scaled Solutions to Coupled Soil‐Water Flow and Solute Transport during the Redistribution Process

Sadeghi

Jones

2012

Vadose Zone Journal

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“…Warrick and Hussen, 1993;Sadeghi et al, 2016); (ii) derivation of general solutions for soil water processes such as infiltration (Khatri and Smith, 2006;; solute transport (Sadeghi and Jones, 2012) and soil moisture redistribution (Warrick and Hussen, 1993); (iii) formulation of soil water relations with minimum possible variables (e.g. Warrick and Hussen, 1993;Sadeghi et al, 2016); (ii) derivation of general solutions for soil water processes such as infiltration (Khatri and Smith, 2006;; solute transport (Sadeghi and Jones, 2012) and soil moisture redistribution (Warrick and Hussen, 1993); (iii) formulation of soil water relations with minimum possible variables (e.g.…”

Section: Introductionmentioning

confidence: 99%

General Equation for Advance and Recession of Water in Border Irrigation

Chari

Davary

Ghahraman

et al. 2019

Irrigation and Drainage

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Advance and recession curves are of great importance for assessing the performance of border irrigation. In recent years, scaling techniques have helped to reduce the required measurements and to provide formulation of soil–water relations. The purpose of this study was to develop an invariant equation for calculating advance and recession curves in border irrigation using scaling techniques. The kinematic wave model and the Philip infiltration equation were used to simulate border irrigation. Scale factors were defined such that the kinematic wave equation remained independent of the initial and boundary conditions of the soil. Scaled advance and recession curves showed certain patterns, which led us to introduce a power and a binomial equation for advance and recession phases, respectively. The scaled equations were applied on 25 vegetated and non‐vegetated borders. Four performance indices were calculated for each border, including application efficiency (Ea), deep percolation ratio (DPR), tail water ratio (TWR) and water requirement efficiency (Er). Results showed that the maximum differences between measured and estimated values were 4% for Ea, 9% for DPR and 4% for Er. Considering the simplicity and soil‐condition independence of the proposed method, it can be concluded that scaled advance and recession curves could provide a reasonable estimate of border irrigation performance. © 2019 John Wiley & Sons, Ltd.

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“…Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of unsaturated water flow. Hence, these methods considerably reduce the calculations required for heterogeneous soils (Warrick and Hussen, 1993). So far, various methods for scaling RE have been proposed (Reichardt et al, 1972;Warrick and AmoozegarFard, 1979;Warrick et al, 1985;Vogel et al, 1991;Kutilek et al, 1991;Warrick and Hussen, 1993;Neuweiler and Cirpka, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…However, these methods are limited to specific hydrological processes and/or soil hydraulic models. For example, the method of Warrick and Hussen (1993), developed for infiltration and redistribution, applies only for the Brooks-Corey hydraulic functions.…”

Section: Introductionmentioning

confidence: 99%

Scaling to generalize a single solution of Richards' equation for soil water redistribution

Sadeghi

Ghahraman

Davary

et al. 2011

Sci. agric. (Piracicaba, Braz.)

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Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of water flow in unsaturated soils. In this study, a new method is developed to scale RE for the soil water redistribution process. Two similarity conditions are required: similarity in the shape of the soil water content profiles as well as of the water flux density curves. An advantage of this method is that it is not restricted to a specific soil hydraulic model -hence, all such models can be applied to RE. To evaluate the proposed method, various soil textures and initial conditions were considered. After the RE was solved numerically using the HYDRUS-1D model, the solutions were scaled. The scaled soil water content profiles were nearly invariant for medium-and fine-textured soils when the soil profile was not deeply wetted. The textural range of the soils in which the similarity conditions are held decreases as the initial conditions deal with a deeply wetted profile. Thus, the scaling performance was poor in such a condition. This limitation was more pronounced in the coarse-textured soils. Based on the scaling method, a procedure is suggested by which the solution of RE for a specific case can be used to approximate solutions for many other cases. Such a procedure reduces complicated numerical calculations and provides additional opportunities for solving the highly nonlinear RE as in the case of unsaturated water flow in soils.

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Scaling of Richards' Equation for Infiltration and Drainage

Cited by 25 publications

References 0 publications

Scaled Solutions to Coupled Soil‐Water Flow and Solute Transport during the Redistribution Process

Scaled Solutions to Coupled Soil‐Water Flow and Solute Transport during the Redistribution Process

General Equation for Advance and Recession of Water in Border Irrigation

Scaling to generalize a single solution of Richards' equation for soil water redistribution

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