Conversion of soil water retention and conductivity parameters from van Genuchten–Mualem to Groenevelt and Grant model
Marina Luciana Abreu de Melo
A * , Quirijn de Jong van Lier A and Robson André Armindo B
+ Author Affiliations
- Author Affiliations
A Soil Physics Laboratory, Center for Nuclear Energy in Agriculture, University of São Paulo, P.O. Box 96, Piracicaba, SP, Brazil.
B Department of Physics, Federal University of Lavras, 37200-000 Lavras, MG, Brazil.
Soil Research 59(8) 837-847 https://doi.org/10.1071/SR21051
Submitted: 22 February 2021 Accepted: 19 May 2021 Published: 4 October 2021
© 2021 The Author(s) (or their employer(s)). Published by CSIRO Publishing
Abstract
The van Genuchten–Mualem (VGM) model is used largely to represent the relative soil hydraulic conductivity and soil water retention functions [Kr(Θ) and Θ(h)]. Alternative equations proposed by Groenevelt and Grant (GRT) present advantages regarding mathematical versatility. Considering the VGM model cannot be analytically converted into the GRT model, this study empirically related parameters n and α (VGM) to parameters p and k (GRT). We used 90 value combinations of n and α and minimised the sum of squared differences between VGM and GRT models. Linear equations were fitted and validated using soil samples from the UNSODA database. A singular equation of p as a function of n was fitted, while a two-step procedure was required to correlate k and α. All fits resulted in very high precision (r ≥ 0.999) and accuracy (RMSD ≤ 0.025 m3 m−3) for the water retention function and very high precision (r ≥ 0.994) for the hydraulic conductivity function. The accuracy for the Kr(Θ) function was high (RMSD ≤ 0.50) for 34 of the 40 tested soils. The derived empirical equations can be used to convert the equation parameters for Θ(h) regardless of soil type, and for Kr(Θ) with some restrictions upon parameter combinations.
Keywords: hydraulic conductivity, incomplete beta function, incomplete gamma function, mathematical models, modelling, soil hydraulic properties, soil physics, soil water retention.
References
Armindo RA, de Jong van Lier Q, Turek ME, Huf dos Reis AM, de Melo MLA, Palma Ramos ME, Ono GM (2019) Performance of the Groenevelt and Grant model for fitting soil water retention data from Brazilian soils. Revista Brasileira de Ciencia do Solo 43, 1–12.| Performance of the Groenevelt and Grant model for fitting soil water retention data from Brazilian soils.Crossref | GoogleScholarGoogle Scholar |
Brooks RH, Corey AT (1964) Hydraulic properties of porous media and their relation to drainage design. Transactions of the ASAE 7, 0026–0028.
| Hydraulic properties of porous media and their relation to drainage design.Crossref | GoogleScholarGoogle Scholar |
Burdine NT (1953) Relative permeability calculations from pore size distribution data. Journal of Petroleum Technology 5, 71–78.
| Relative permeability calculations from pore size distribution data.Crossref | GoogleScholarGoogle Scholar |
Campbell GS (1974) A simple method for determining unsaturated conductivity from moisture retention data. Soil Science 117, 311–314.
| A simple method for determining unsaturated conductivity from moisture retention data.Crossref | GoogleScholarGoogle Scholar |
Childs EC, Collis-George N (1950) The permeability of porous materials. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences 201, 392–405.
| The permeability of porous materials.Crossref | GoogleScholarGoogle Scholar |
da Silva AC, Armindo RA, dos Santos Brito A, Schaap MG (2017) SPLINTEX: a physically-based pedotransfer function for modeling soil hydraulic functions. Soil and Tillage Research 174, 261–272.
| SPLINTEX: a physically-based pedotransfer function for modeling soil hydraulic functions.Crossref | GoogleScholarGoogle Scholar |
da Silva AJP, Pinheiro EAR, de Jong van Lier Q (2020) Determination of soil hydraulic properties and its implications for mechanistic simulations and irrigation management. Irrigation Science 38, 223–234.
| Determination of soil hydraulic properties and its implications for mechanistic simulations and irrigation management.Crossref | GoogleScholarGoogle Scholar |
de Jong van Lier Q (2014) Revisiting the S-index for soil physical quality and its use in Brazil. Revista Brasileira de Ciencia do Solo 38, 1–10.
| Revisiting the S-index for soil physical quality and its use in Brazil.Crossref | GoogleScholarGoogle Scholar |
de Jong van Lier Q, Pinheiro EAR (2018) An alert regarding a common misinterpretation of the van Genuchten α parameter. Revista Brasileira de Ciência do Solo 42, e0170343
| An alert regarding a common misinterpretation of the van Genuchten α parameter.Crossref | GoogleScholarGoogle Scholar |
de Jong van Lier Q, van Dam JC, Metselaar K, de Jong R, Duijnisveld WHM (2008) Macroscopic root water uptake distribution using a matric flux potential approach. Vadose Zone Journal 7, 1065–1078.
| Macroscopic root water uptake distribution using a matric flux potential approach.Crossref | GoogleScholarGoogle Scholar |
de Jong van Lier Q, Dourado Neto D, Metselaar K (2009) Modeling of transpiration reduction in van Genuchten–Mualem type soils. Water Resources Research 45, W02422
| Modeling of transpiration reduction in van Genuchten–Mualem type soils.Crossref | GoogleScholarGoogle Scholar |
de Jong van Lier Q, Pinheiro EAR, Inforsato L (2019) Hydrostatic equilibrium between soil samples and pressure plates used in soil water retention determination: consequences of a questionable assumption. Revista Brasileira de Ciência do Solo 43, e0190014
| Hydrostatic equilibrium between soil samples and pressure plates used in soil water retention determination: consequences of a questionable assumption.Crossref | GoogleScholarGoogle Scholar |
Dexter AR (2004) Soil physical quality: Part I. Theory, effects of soil texture, density, and organic matter, and effects on root growth. Geoderma 120, 201–214.
| Soil physical quality: Part I. Theory, effects of soil texture, density, and organic matter, and effects on root growth.Crossref | GoogleScholarGoogle Scholar |
Durner W (1994) Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resources Research 30, 211–223.
| Hydraulic conductivity estimation for soils with heterogeneous pore structure.Crossref | GoogleScholarGoogle Scholar |
Durner W, Schultze B, Zurmuh T (1999) State-of-the-art in inverse modeling of inflow/outflow experiments. In ‘Proceedings of the international workshop on characterization and measurement of the hydraulic properties of unsaturated porous media, Riverside, CA, USA, 22–24 October 1997’. (University of California: Riverside, CA, USA)
Grant CD, Groenevelt PH (2015) Weighting the differential water capacity to account for declining hydraulic conductivity in a drying coarse-textured soil. Soil Research 53, 386
| Weighting the differential water capacity to account for declining hydraulic conductivity in a drying coarse-textured soil.Crossref | GoogleScholarGoogle Scholar |
Grant CD, Groenevelt PH, Robinson NI (2010) Application of the Groenevelt–Grant soil water retention model to predict the hydraulic conductivity. Soil Research 48, 447–458.
| Application of the Groenevelt–Grant soil water retention model to predict the hydraulic conductivity.Crossref | GoogleScholarGoogle Scholar |
Groenevelt PH, Bolt GH (1972) Water retention in soil. Soil Science 113, 238–245.
| Water retention in soil.Crossref | GoogleScholarGoogle Scholar |
Groenevelt PH, Grant CD (2004) A new model for the soil-water retention curve that solves the problem of residual water contents. European Journal of Soil Science 55, 479–485.
| A new model for the soil-water retention curve that solves the problem of residual water contents.Crossref | GoogleScholarGoogle Scholar |
Groenevelt PH, Grant CD, Semetsa S (2001) A new procedure to determine soil water availability. Australian Journal of Soil Research 39, 577–598.
| A new procedure to determine soil water availability.Crossref | GoogleScholarGoogle Scholar |
Hoffmann-Riem H (1999) General model for the hydraulic conductivity of unsaturated soils. In ‘Proceedings of international workshop on characterization and measurements of hydraulic properties of unsaturated porous media, Riverside, CA, USA, 22–24 October 1997’. pp. 31–42. (University of California: Riverside, CA, USA)
Inforsato L, de Jong van Lier Q, Pinheiro EAR (2020) An extension of water retention and conductivity functions to dryness. Soil Science Society of America Journal 84, 45–52.
| An extension of water retention and conductivity functions to dryness.Crossref | GoogleScholarGoogle Scholar |
Kosugi K (1996) Lognormal distribution model for unsaturated soil hydraulic properties. Water Resources Research 32, 2697–2703.
| Lognormal distribution model for unsaturated soil hydraulic properties.Crossref | GoogleScholarGoogle Scholar |
Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12, 513–522.
| A new model for predicting the hydraulic conductivity of unsaturated porous media.Crossref | GoogleScholarGoogle Scholar |
Nemes A, Schaap M, Leij Feike J, Wösten J, Henk M (2015) ‘UNSODA 2.0: unsaturated soil hydraulic database. Database and program for indirect methods of estimating unsaturated hydraulic properties’. (U.S. Salinity Laboratory, ARS, USDA: Washington, DC, USA).
Peters A, Iden SC, Durner W (2015) Revisiting the simplified evaporation method: identification of hydraulic functions considering vapor, film and corner flow. Journal of Hydrology 527, 531–542.
| Revisiting the simplified evaporation method: identification of hydraulic functions considering vapor, film and corner flow.Crossref | GoogleScholarGoogle Scholar |
Pinheiro EAR, de Jong van Lier Q, Inforsato L, Šimůnek J (2019) Measuring full-range soil hydraulic properties for the prediction of crop water availability using gamma-ray attenuation and inverse modeling. Agricultural Water Management 216, 294–305.
| Measuring full-range soil hydraulic properties for the prediction of crop water availability using gamma-ray attenuation and inverse modeling.Crossref | GoogleScholarGoogle Scholar |
Ross PJ, Williams J, Bristow KL (1991) Equation for extending water-retention curves to dryness. Soil Science Society of America Journal 55, 923–927.
| Equation for extending water-retention curves to dryness.Crossref | GoogleScholarGoogle Scholar |
Rudiyanto R, Minasny B, Shah RM, Setiawan BI, van Genuchten MT (2020) Simple functions for describing soil water retention and the unsaturated hydraulic conductivity from saturation to complete dryness. Journal of Hydrology 588, 125041
| Simple functions for describing soil water retention and the unsaturated hydraulic conductivity from saturation to complete dryness.Crossref | GoogleScholarGoogle Scholar |
Systat Software (2002) TableCurve 2D, version 5.01. (Systat Software: San Jose, CA)
van Genuchten MT (1980) Closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898.
| Closed-form equation for predicting the hydraulic conductivity of unsaturated soils.Crossref | GoogleScholarGoogle Scholar |
van Genuchten MT, Leij FJ, Yates SR (1991) ‘The RETC code for quantifying the hydraulic functions of unsaturated soils’. (U.S. Salinity Laboratory, ARS, USDA: Riverside, CA, USA)
Wang Y, Ma J, Guan H (2016) A mathematically continuous model for describing the hydraulic properties of unsaturated porous media over the entire range of matric suctions. Journal of Hydrology 541, 873–888.
| A mathematically continuous model for describing the hydraulic properties of unsaturated porous media over the entire range of matric suctions.Crossref | GoogleScholarGoogle Scholar |
Wang Y, Jin M, Deng Z (2018) Alternative model for predicting soil hydraulic conductivity over the complete moisture range. Water Resources Research 54, 6860–6876.
| Alternative model for predicting soil hydraulic conductivity over the complete moisture range.Crossref | GoogleScholarGoogle Scholar |
Zhang ZF (2011) Soil water retention and relative permeability for conditions from oven-dry to full saturation. Vadose Zone Journal 10, 1299–1308.
| Soil water retention and relative permeability for conditions from oven-dry to full saturation.Crossref | GoogleScholarGoogle Scholar |
