Abstract
Uptake of water by plant roots can be considered at two different Darcian scales, referred to as the mesoscopic and macroscopic scales. At the mesoscopic scale, uptake of water is represented by a flux at the soil–root interface, while at the macroscopic scale it is represented by a sink term in the volumetric mass balance. At the mesoscopic scale, uptake of water by individual plant roots can be described by a diffusion equation, describing the flow of water from soil to plant root, and appropriate initial and boundary conditions. The model involves at least two characteristic lengths describing the root–soil geometry and two characteristic times, one describing the capillary flow of water from soil to plant roots and another the ratio of supply of water in the soil and uptake by plant roots. Generally, at a certain critical time, uptake will switch from demand-driven to supply-dependent. In this paper, the solutions of some of the resulting mesoscopic linear and nonlinear problems are reviewed. The resulting expressions for the evolution of the average water content can be used as a basis for upscaling from the mesoscopic to the macroscopic scale. It will be seen that demand-driven and supply-dependent uptake also emerge at the macroscopic scale. Information about root systems needed to operationalize macroscopic models will be reviewed briefly.
Article PDF
Similar content being viewed by others
References
Aronson D.G., Peletier L.A. (1981) Large time behaviour of solutions of the porous medium equation in bounded domains. J. Differ. Equ. 39, 378–412
Arora V.K., Boer G.J.: A representation of variable root distribution in dynamic vegetation models. Earth Interact. 7, Paper No. 6, 1-19 (2003)
Carslaw H.S., Jaeger J.C. (1959) Conduction of Heat in Solids, 2nd edn. Oxford University Press, London
Cowan I.R. (1965) Transport of water in the soil–plant-atmosphere system. J. Appl. Ecol. 2, 221–239
Dalton F.N., Raats P.A.C., Gardner W.R. (1975) Simultaneous uptake of water and solutes by plant roots. Agronomy J. 67, 334–339
Denmead O.T., Shaw R.H. (1962) Availability of soil water to plants as affected by soil moisture content and meteorological conditions. Agron. J. 54, 385–390
De Willigen, P., Van Noordwijk, M.: Roots, plant production and nutrient use efficiency. PhD Thesis, Wageningen Agricultural University (1987)
De Willigen P., Van Noordwijk M. (1994a) Mass flow and diffusion of nutrients to a root with constant or zero-sink uptake 1. Constant uptake. Soil Sci. 157, 162–170
De Willigen P., Van Noordwijk M. (1994b) Mass flow and diffusion of nutrients to a root with constant or zero-sink uptake 2. Zero-sink uptake. Soil Sci. 157, 171-175
De Willigen P., Nielsen N.E., Claassen N., Castrignan A.M. (2000) Modelling water and nutrient uptake. In: Smit A.L., Bengough G., Engels C., van Noordwijk M., Pellerin S., van de Geijn S. (eds) Root Methods: A Handbook. Springer, Berlin
Feddes, R.A.: Water, heat and crop growth. PhD Thesis, Wageningen Agricultural University (1971)
Feddes R.A., Kowalik P.J., Zaradny H. (1978) Simulation of Field Water Use and Crop Yield. Simulation Monograph, Pudoc, Wageningen
Feddes R.A., Hoff H., Bruen M., Dawson T., de Rosnay P., Dirmeyer P., Jackson R.B., Kabat P., Kleidon A., Lilly A., Pitman A.J. (2001) Modeling root water uptake in hydrological and climate models. Bull. Am. Meteorol. Soc. 82, 2797–2809
Feddes R.A., Raats P.A.C. (2004) Parameterizing the soil–water-plant root system. In: Feddes R.A., De Rooij G.H., Van Dam J.C. (eds) Wageningen UR Frontis Series, vol. 6, Unsaturated-zone Modeling, Progress, Challenges and Applications. Kluwer, Dordrecht, pp. 95-141
Fiscus E.L. (1975) The interaction between osmotic and pressure-induced water flow in plant roots. Plant Physiol. 55, 917–922
Gale M.R., Grigal D.F. (1987) Vertical root distributions of northern tree species in relation to successional status. Can. J. Forestry Res. 17, 829–834
Gardner W.R. (1960) Dynamic aspects of water availability to plants. Soil Sci. 89, 63–73
Gardner W.R. (1991) Modeling water uptake by roots. Irrigat. Sci. 12, 109–114
Gerwitz A., Page E.R. (1974) An empirical mathematical model to describe plant root systems. J. Appl. Ecol. 11, 773–781
Gilding B.H. (1991) Qualitative mathematical analysis of the Richards equation. Transport Porous Media 5, 561–566
Heinen, M.: Dynamics of water and nutrients in closed, recirculating cropping systems in glasshouse horticulture: with special attention to lettuce grown in irrigated sand beds. PhD Thesis, Wageningen Agricultural University (1997)
Heinen, M., De Willigen, P.: FUSSIM2: A two-dimensional simulation model for water flow, solute transport, and root uptake of water and nutrients in partly unsaturated porous media. In: Quantitative Approaches in Systems Analysis, vol. 20. DLO Research Institute for Agrobiology and Soil Fertility, Wageningen (1998)
Heinen, M., De Willigen, P.: FUSSIM2: New features and updated user’s guide. Alterra Report, vol. 363. Alterra, Wageningen (2001)
Herkelrath W.N., Miller E.E., Gardner W.R. (1977a) Water uptake by plants I Divided root systems. Soil Sci. Soc. Am. J. 41, 1033–1037
Herkelrath W.N., Miller E.E., Gardner W.R. (1977b) Water uptake by plants II The root contact model. Soil Sci. Soc. Am. J. 41, 1033–1037
Huxley J.S. Problems of Relative Growth, 2nd edn. Republication of 1932 1st edition published by Methuen, London, with a new introduction by the author and a supplementary essay by E.C.R. Reeve and the author. Dover, New York (1972)
Jackson, R.B.: The importance of root distributions for hydrology, biogeochemistry, and ecosystem functioning. In: Tenhunen J.D., Kabat P. (eds.) Integrating Hydrology, Ecosystem Dynamics, and Biogeochemistry in Complex Landscapes, Report of the Dahlem Workshop, Berlin, January 18–23, 1998, Wiley, Chichester, UK (1999)
Jackson R.B., Canadell J., Ehleringer J.R., Mooney H.A., Sala O.E., Schulze E.D. (1996) A global analysis of root distributions for terrestrial biomes. Oecologia 108, 389–411
Jackson R.B., Mooney H.A., Schulze E.D. (1997) A global budget for fine root biomass, surface area, and nutrient contents. Proc. Natl. Acad. Sci. USA 94, 7362–7366
Jacobsen B.F. (1974) Water and phosphate transport to plant roots. Acta Agricult. Scand. 24, 55–60
Jensen, C.R., Hensen, I.E., Hansen, S.: A root contact model and potential differences to water flow in the soil plant system. In: Sinha S.K., Sane P.V., Bhargava S.C., Agrawal P.V. (eds.) Proceedings of the International Congress of Plant Physiology. New Delhi, India, February 15–20, 1988, vol. 2, pp. 825-831. Society for Plant Physiology and Biochemistry, New Delhi (1990)
Jensen C.R., Svendsen H., Andersen M.N., Lösch R. (1993) Use of the root contact concept, an empirical leaf conductance model and pressure–volume curves in simulating crop water relations. Plant Soil 149, 1–26
Kirchhoff G. (1894) Vorlesungen über der Theorie der Wärme. Barth, Leipzig
Miller E.E., Miller R.D. (1956) Physical theory of capillary flow phenomena. Physics 27, 324–332
Passioura J.B., Cowan I.R. (1968) On solving the non-linear diffusion equation for the radial flow of water to roots. Agricult. Metorol. 5, 129–134
Philip, J.R.: The physical principles of soil water movement during the irrigation cycle. In: Proc. Intern. Congr. Irrigation and Drainage, 3rd, San Francisco, vol. 8, pp. 125–153. (1957)
Plilip J.R. (1991) Effects of root and subirrigation depth on evaporation and percolation losses. Soil Sci. Soc. Am. J. 55, 1520–1523
Plilip J.R. (1997) Effect of root water extraction on wetted regions from continuous irrigation sources. Irrigat. Sci. 17, 127–135
Raats P.A.C. (1970) Steady infiltration from line sources and furrows. Soil Sci. Soc. Am. Proc. 34, 709–714
Raats P.A.C. (1974a) Steady flows of water and salts in uniform soil profiles with plant roots. Soil Sci. Soc. Am. Proc. 38, 717–722
Raats P.A.C. (1974b) Steady infiltration into crusted soils. 10th Int. Congress Soil Sci. (Moscow) Trans. 1, 75–80
Raats, P.A.C.: The distribution of the uptake of water by plants: inference from hydraulic and salinity data. In: Seminaires sur l’irrigation localisée. 1. Mouvement de l’eau et des sels en function des charactéristiques des sols soumis à l’irrigation localisée, Proc. AGRIMED Seminar on the Movement of Water and Salts as a Function of the Properties of the Soil under Localized Irrigation, held 6-9 November 1979 at Bologna, Italy, pp.35–46. Institut d’Agronomie de l’Université de Bologne, Bologna, Italy, (1982)
Raats, P.A.C.: Applications of the theory of mixtures in soil science. In: Truesdell C. (ed.) Rational Thermodynamics, with an Appendix by C.-C. Wang, 2nd edn, corrected and enlarged, to which are adjoined appendices by 23 authors. Chapt Appendix 5D, pp. 326–343. Springer Verlag, New York (1984)
Raats, P.A.C.: Characteristic lengths and times associated with processes in the root zone. In: Hillel D., Elrick D.E. (eds.) Scaling in Soil Physics: Principles and Applications, pp. 59-72. Soil Science Society of America, Madison, Wisconsin, USA (1990a)
Raats, P.A.C.: On the roles of characteristic lengths and times in soil physical processes. In: Proc. 14th Int. Congr. Soil Sci., held 12–18 August 1990, at Kyoto, Japan, vol. 1, pp. 202–207 (1990b)
Raats, P.A.C.: A superclass of soils. In: Van Genuchten M.Th., Leij F.J., Lund L.J. (eds.) Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, Proceedings of an International Workshop, held 11–13 Oct. 1989 at Riverside, Calif., USA, Univ. of Calif., Riverside, pp. 49–51 (1992)
Raats, P.A.C.: Spatial and material description of some processes in rigid and non-rigid saturated and unsaturated soils. In: Thimus J.-F., Abousleiman Y., Cheng, A.H.-D., Coussy O., Detournay E. (eds.) Poromechanics - A tribute to Maurice A. Biot, Proceedings of the Biot Conference on Poromechanics, held September 14–16, 1998 at Louvain-la-Neuve, pp. 135–140. Belgium, Balkema, Rotterdam, The Netherlands (1998)
Raats P.A.C. (2001) Developments in soil–water physics since the mid 1960s. Geoderma 100, 355–387
Raats, P.A.C., Smiles, D.E., Warrick, A.W.: Contributions to environmental mechanics: Introduction. In: Raats P.A.C., Smiles D.E., Warrick A.W. (eds.) Geophysical Monograph 129, Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere, pp. 1–28. American Geophysical Union, Washington, DC (2002)
Rappoldt C. (1990) The application of diffusion models to an aggregated soil. Soil Sci. 150, 645–661
Rappoldt, C.: Diffusion in aggregated soil. PhD Thesis, Wageningen Agricultural University (1992)
Rappoldt C., Verhagen J.H.G. (1999) Equivalent cylinder systems representing the soil matrix in diffusion-reaction models for an aggregated soil. Transport Porous Media 37, 1–24
Richards L.A. (1931) Capillary conduction of liquids through porous mediums. Physics 1, 318–333
Tanner C.B. (1967) Measurement of evapotranspiration. Agronomy 11, 534–574
Taylor H.M., Klepper B. (1975) Water uptake by cotton root systems: an examination of assumptions in the single root model. Soil Sci. 120, 57–67
Truesdell, C., Toupin, R.A.: The classical field theories. In: Encyclopedia of Physics, Vol. III/1, pp. 226–794 (1960)
Van Genuchten, M.Th.: A numerical model for water and solute movement in and below the root zone. Research Report no. 121, USDA-ARS, US Salinity Laboratory, Riverside CA, USA (1987)
Van Genuchten, M.Th., Leij, F.J., Lund, L.J. (eds.): Indirect methods for Estimating the Hydraulic Properties of Unsaturated Soils, Proceedings of an International Workshop, organized by the U.S. Salinity Laboratory, USDA-ARS, and the Department of Soil and Environmental Sciences of the University of California, both at Riverside, CA, USA, and held 11–13 Oct. 1989 at Riverside, CA, USA, Univ. of California, Riverside, CA, USA (1992)
Van Genuchten, M.Th., Leij, F.J., Wu, L. (eds.): Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media. Proceedings of an International Workshop organized by the U.S. Salinity Laboratory, USDA-ARS, and the Department of Environmental Sciences of the University of California, both at Riverside, CA, USA, and held 22–24 October, 1997 at Riverside, CA, USA, Univ. of California, Riverside, CA, USA, 2 Vols. (1999)
Van Noordwijk, M.: Functional interpretation of root densities in the field for nutrient and water uptake. In: Wurzelökologie und ihre Nutzanwendung – Root Ecology and its Practical Application, Int. Symp. Gumpenstein, 1982, Bundesanstalt Gumpenstein, Irdning, Bundesanstalt für alpenländische Landwirtschaft, pp. 207–226, Irdning, Austria, (1983)
Van Noordwijk, M.: Methods for quantification of root distribution pattern and root dynamics in the field. Methodology in Soil-K Research, Proc. 20th Colloq. Intern. Potash Inst., Bern, pp. 263–281 (1987)
Van Noordwijk, M., Brouwer, G.: Review of quantitative root length data in agriculture. In: McMichael B.L., Persson H. (eds.) Developments in Agricultural and Managed-Forest Ecology no 24, Plant Roots and their Environment, pp. 515–525. Elsevier, Amsterdam (1991)
Veen B.W., Van Noordwijk M., De Willigen P., Boone F.R., Kooistra M.J. (1992) Root–soil contact of maize, as measured by a thin-section technique, III Effects on shoot growth, nitrate and water uptake efficiency. Plant Soil 139, 131–138
Whitaker S. (1986) Flow in porous media II: the governing equations for immiscible, two-phase flow. Transport Porous Media 1, 105–125
Zeng X. (2001) Global vegetation root distribution for land modeling. J. Hydrometeorol. 2, 525–530
Zeng X., Dai Y.-J., Dickinson R.E., Shaikh M. (1998) The role of root distribution for climate simulation over land. Geophys. Res. Lett. 25, 4533–4536
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Raats, P.A.C. Uptake of water from soils by plant roots. Transp Porous Med 68, 5–28 (2007). https://doi.org/10.1007/s11242-006-9055-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-006-9055-6