Abstract
Supplying plants with inorganic nutrients and water is a major function of roots (Nye and Tinker 1977; Nielsen 1983; Barber 1984; Jungk and Claassen 1989; Gahoonia and Nielsen 1991, 1992a,b). It is still a major challenge to agricultural research to quantitatively predict production of a crop as influenced by uptake of nutrients and water. Models can be of great assistance to understand how different factors and their interactions influence crop functioning. A model is per definition a simplification of part of reality. To quote Van Wijk (1963): “Generally it is necessary to introduce drastic simplifications in an agricultural problem to make it amenable to a mathematical analysis. Objections are sometimes raised that such simplifications restrict or even preclude the applicabilitychr.... However this need not be the case. The very purpose of the mathematical physical treatment is to isolate the essential characteristics of the problem and to abstract them from the less essential ones”.
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References
Abramowitz M, Stegun IA (1970) Handbook of mathematical functions. Dover Publications, New York
Altemüller HJ, Haag Th (1983) Mikroskopische Untersuchungen an Maiswurzeln im ungestörten Bodenverband. Kali-Briefe (Büntehof) 16 (6): 349–363
Amijee F, Barraclough PB, Tinker PB (1991) Modelling phosphorus uptake and utilisation by plants. In: Johansen C, Lee KK, Sahrawat KL (eds) Phosphorus nutrition of grain legumes in the semi-arid tropics, pp 63–77 ICRISAT, Pabanchever, Judia
Baldwin JP, Nye PH (1974) A model to calculate the uptake by a developing root system or root hair system of solutes with concentration variable diffusion coefficients. Plant Soil 40: 703–706
Baldwin JP, Nye PH, Tinker PB (1973) Uptake of solutes by multiple root systems from soil. III. A model for calculating the solute uptake by a randomly dispersed root system developing in a finite volume of soil. Plant Soil 38: 612–625
Barber SA (1962) A diffusion and mass flow concept of soil nutrient availability. Soil Sci 93: 39–48
Barber SA (1984) Soil nutrient bioavailability. A mechanistic approach. Wiley, New York
Barber SA, Cushman JH (1981) Nitrogen uptake model for agronomic crops. In: Iskandar IK (ed) Modelling wastewater renovation. John Wiley, New York, pp 382–410
Barley KP (1970) The configuration of the root system in relation to nutrient uptake. Adv Agron 22: 159–201
Bear J (1972) Dynamics of fluids in porous media. American Elsevier, New York, 764 pp
Bolt GH, Bruggenwert MGM (1979) Composition of the soil. In: Bolt GH, Bruggenwert MGM (eds) Soil chemistry A. Basic elements. Elsevier, Amsterdam, 1979, pp 1–11
Bouldin DR (1961) Mathematical description of diffusion processes in the soil-plant system. Soil Sci Soc Amer Proc 25: 476–480
Bouten W (1992) Monitoring and modelling forest hydrological processes in support of acidification research. Doct Thesis, University of Amsterdam, Amsterdam
Bray RH (1954) A nutrient mobility concept of soil plant relationships. Soil Sci 78: 9–22
Campbell GS (1985) Soil physics with BASIC. Elsevier, Amsterdam
Campbell GS (1991) Simulation of water uptake by plant roots. In: Hanks J, Ritchie JT (eds) Modeling plant and soil systems. Agronomy Monograph 31, American Society of Agronomy, Madison, Wisconsin, pp 273–285
Carlslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, Oxford, 510 pp
Claassen N (1989) Die Aufnahme vom Nährstoffen aus dem Boden durch die höhere Pflanze als Ergebnis von Verfügbarkeit and Aneignungsvermögen. Habilitationsschrift, Georg-August Universität, Göttingen, 327 pp
Claassen N, Barber SA (1976) Simulation model for nutrient uptake from soil by a growing plant root system. Agron J 68: 961–964
Cushman JH (1979) An analytical solution to solute transport near root surfaces for low initial concentration: I. Equations development. Soil Sci Soc Am J 43: 1087–1090
Cushman JH (1980) Completion of the list of analytical solutions for nutrient transport to roots. 1. Exact linear models. Water Resour Res 16: 891–896
Dainty J (1976) Water relations of plant cells. In: Lüttge U, Pitman MG (eds) Transport in plants. II.A Cells. Encyclopaedia of Plant Physiology. New Series, vol 2. Springer, Berlin Heidelberg New York, pp 12–35
Darrah PR (1993) The rhizosphere and plant nutrition: a quantitative approach. In: Barrow NJ (ed) Plant nutrition from genetic engineering to field practice. Kluwer, Dordrecht, the Netherlands, pp 3–23
De Jager A (1985) Response of plants to localised nutrient supply. PhD Thesis, University of Utrecht, Utrecht, 137 pp
De Willigen P (1981) Mathematical analysis of diffusion and mass flow of solutes to a root assuming constant uptake. Inst Bodemvruchtbaarheid, Rapport 6–81, 56 pp
De Willigen P (1990) Calculation of uptake of nutrients and water by a root system. Nota 210, Institute for Soil Fertility, Haren, the Netherlands
De Willigen P, van Noordwijk M (1978) Calculations on phosphate uptake by a crop in relation to rooting density and P-status of the soil (In Dutch). Inst Bodemvruchtbaarheid Rapport 19–78, 63 pp
De Willigen P, van Noordwijk M (1987) Roots, plant production and nutrient use efficiency, PhD Thesis, Wageningen Agricultural University, Wageningen
De Willigen P, van Noordwijk M (1994a) Mass flow and diffusion of nutrients to a root with constant or zero-sink uptake. I. 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. II. Zero-sink uptake. Soil Sci 157: 171–175
De Willigen P, van Noordwijk M (1995) Model for interactions between water and nutrient uptake. In: Kabat P, Marshall B, van den Broek BJ, Vos J, van Keulen H (eds) Modelling and parametrization of the soil-plant-atmosphere system, a comparison of potato growth models. Wageningen Press, Wageningen, pp 135–153
De Willigen P, Dijksterhuis G, Chardon W (1998) Dynamique et disponibilité du Phosphore dans les sols. In: Breman H, Sissiko K (eds) L’intensification agricole au Sahel. Karthala, Paris. pp 266–284
Doussan C, Vercambre G, Pagès L (1998a) Modelling of the hydraulic architecture of root systems: an integrated approach of water absorption–model description. Ann Bot 81: 213–223
Doussan C, Vercambre G, Pagès L (1998b) Modelling of the hydraulic architecture of root systems: an integrated approach of water absorption–distribution of axial and radial conductances in maize. Ann Bot 81: 225–232
Dunham RJ, Nye PH (1973) The influence of soil water content on the uptake of ions by roots. Soil water content gradients near a plane of onion roots. J Appl Ecol 10: 585–598
Dunham RJ, Nye PH (1974) The influence of soil water content on the uptake of ions by roots. Chloride uptake and concentration gradients in soil. J Appl Ecol 11: 581–596
Feddes RA, Kowalik PJ, Zaradny H (1978) Simulation of field water use and crop yield. Simulation monographs, PUDOC, Wageningen, 189 pp
Fiiter AH (1987) An architectural approach to the comparative ecology of plant root systems. New Phytol. (Suppl.) 106: 61–77
Gahoonia TS, Nielsen NE (1991) A method to study rhizosphere processes in thin soil layers of different proximity to roots. Plant Soil 135: 143–146
Gahoonia TS, Nielsen NE (1992a) Control of pH at soil root interface. Plant Soil 140: 49–54 Gahoonia TS, Nielsen NE (1992b) The effect of root-induced pH change on the depletion of inorganic and organic phosphate. Plant Soil 143: 185–191
Gahoonia TS, Raza S, Nielsen NE (1994) Phosphorus depletion in the rhizosphere as influenced by soil moisture. Plant Soil 159: 213–218
Gardner WR (1960) Dynamic aspects of water availability to plants. Soil Sci 89: 63–73 Geelhoed J (1998) Phosphateavailability in the soil-root ysytem: integration of oxide surface chemistry, transport and uptake. PhD Thesis, Wageningen Agricultural University, 177 pp
Geelhoed JS, Findenegg GR, van Riemsdijk WH (1997) Availability to plants of phosphate adsorbed on goethite: experiment and simulation. Eur J Soil Sci 48: 473–481
Green PJ, Sibson R (1977) Computing Dirichlet tessellations in the plane. Comput J 21: 168173
Greenwood DJ, Neeteson JJ, Draycott A (1985) Response of potatoes to N fertiliser. Plant Soil 85: 163–183
Hansen S, Jensen HE, Nielsen NE, Svendsen H (1990) DAISY: A Soil Plant System Model. Danish simulation model for transformation and transport of energy and matter in the soil plant athmosphere system. The national Agency for Environmental Protection, Copenhagen, 369 pp
Hansen S, Jensen HE, Nielsen NE, Svendsen H (1991) Simulation of nitrogen dynamics and biomass production in winter wheat using the Danish simulation model DAISY. Fert Res 27: 245–261
Herckelrath WM, Miller EE, Gardner WR (1977) Water uptake by plants. II The root contact model. Soil Sci Soc Am Proc 41: 1039–1043
Hillel D, Talpaz H, Van Keulen H (1976) A macroscopic-scale model of water uptake by a nonuniform root system and of water and salt movement in the soil profile. Soil Sci 121: 242–255
Hoffland E (1991) Mobilisation of rock phosphate by rape. PhD Thesis, Wageningen Agricultural University, Wageningen
Hoffland E, Bloemhof HS, Leffelaar PA, Findenegg GR, Nelemans JA (1990) Simulation of nutrient uptake by a growing root system considering increasing root density and interroot competition. Plant Soil 124: 149–155
Jones CA, Kinity JR (eds) (1986) CERES-maize: a Simulation model of maize growth and development. Texas A&M University Press, College Station, 194 pp
Jones JW, Ritchie JT (1991) Crop growth models. In: Hoffman GJ, Howell TA, Solomon KH (ed) Management of farm irrigation systems. ASAE, St. Joseph, MI. pp 63–89
Jungk A, Claassen N (1989) Availability in soil and acquisition by plants as the basis for phosphorus and potassium supply to plants. Z Pflanzenernaehr Bodenkd 152: 151–157
Knight J, Philip JR (1974) Exact Solutions in non linear diffusion. J Eng math 8: 219–227
Lafolie F, Bruckler L, Tardieu F (1991) Modelling root water potential and soil-root water transport: I. Model presentation. Soil Sci Soc Am J 55: 1203–1211
Mayus M (1998) Millet growth in windbreak-shielded fields in the Sahel, experiment and model. PhD Thesis, Wageningen Agricultural University, Wageningen
Molz FJ (1981) Models of water transport in the soil-plant system: a review. Water Resour Res 17: 1245–1260
Nielsen NE (1983) Plant parameters controlling the efficiency of nutrient uptake from soil. In: United Nations Economic Commission for Europe (ed) efficient use of fertilisers in agriculture. Developments in Plant and Soil Sciences, vol 10. Martinus Nijhoff, Dordrecht, the Netherlands, pp 199–217
Nimah A, Hanks RJ (1973) Model for estimating soil water, plant, and atmospheric interrelations. I Description and sensitivity. Soil Sci Soc Amer Proc 37: 522–527
Nye PH (1966) The effect of the nutrient intensity and buffering power of a soil, and the absorbing power, size and root hairs of a root, on nutrient absorption by diffusion. Plant Soil 25: 81–105
Nye PH (1992a) Towards the quantitative control of crop production and quality. I. The role of computer models in soil and plant research. J Plant Nutr 15 (6&7): 1131–1150
Nye PH (1992b) Towards the quantitative control of crop production and quality. II. The scientific basis for guiding fertiliser and management practice, particularly in poorer countries. J Plant Nutr 15 (6&7): 1151–1173
Nye PH (1992c) Towards the quantitative control of crop production and quality. III. Some recent developments in research into the root-soil interface. J Plant Nutr 15 (6&7): 1175–1192
Nye PH, Marriott FHC (1969) A theoretical study of the distribution of substances around roots resulting from simultaneous diffusion and mass flow. Plant Soil 30: 459–472
Nye PH, Tinker PB (1977) Solute movement in the soil-root system. Sudies in Ecology vol 4. Blackwell Scientific Publications, Oxford, 342 pp
Olsen SR, Kemper WD (1968) Movement of nutrients to plant roots. Adv Agron 20: 91–151 Pagès L, Jordan MO, Picard D (1989) Simulation of the three-dimensional architecture of the maize root system. Plant Soil 119: 147–154
Passioura JB (1980) The transport of water from soil to shoot in wheat seedlings. J Exp Bot 31: 333–345
Prummel J (1957) The significance of the thickness of the arable layer for the evaluation of soil analysis data. (In Dutch). Landbouwkd Tijdschr 69: 703–712
Raats PAC (1970) Steady infiltration from line sources and furrows. Soil Sci Am Proc 34: 709–714
Rappoldt C (1992) Diffusion in aggregated soil. PhD Thesis, Wageningen Agricultural University, 162 pp
Rengel Z (1999) Mineral nutrition of crops. Food Products Press, New York, 399 pp
Rijtema PE, Kroes JG (1991) Some results of nitrogen simulations with the model ANIMO. In: Groot JJR, de Willigen P, Verberne ELJ (eds) Nitrogen turnover in the soil-crop system. Kluwer, Dordrecht, pp 189–199
Sharp RE, Davies WJ (1985) Root growth and water uptake by maize plants in drying soil. J Exp Bot 36: 1441–1456
Stroosnijder L (1976) Infiltratie en herverdeling van water in grond. PUDOC, Wageningen, 213 pp
Turner NC (1974) Stomatal behaviour and water status of maize, sorghum and tobacco under field conditions. II At low water potential. Plant Physiol 53: 360–365
Van den Broek BJ (1992) Predicting times of irrigation with a simulation model. M Sc Thesis, University of Alberta, Alberta, 122 pp
Van den Honert TH (1948) Water transport in plants as a catenary process. Discuss Faraday Soc 3: 146–153
Van der Paauw F (1971) An effective water extraction method for the determination of plant-available soil phosphorus. Plant Soil 34: 467–481
Van Keulen H, Seligman NG (1987) Simulation of water use, nitrogen nutrition and growth of a spring wheat crop. PUDOC, Wageningen, Simulation Monographs, 310 pp
Van Keulen H, Seligman NH, Goudriaan J (1975) Availability of anions in the growth medium to roots of an actively growing plant. Neth J Agric Sci 23: 131–138
Van Noordwijk M, Lusiana B (1990) WaNu1CAS 1. 1. Background of a model of water nutrient and light capture in agroforestry systems. Working Document, International Centre for Research in Agroforestry (ICRAF), Bogor, Indonesia
Van Noordwijk M, de Willigen P, Ehlert PAI, Chardon WJ (1990) A simple model of P uptake as a possible basis for P fertiliser recommendations. Neth J Agric Sci 38: 317–322
Van Wijk WR (1963) Physiscs of plant environment. North-Holland publ. Co., Amsterdam, 382 pp.
Wösten JHM (1987) Beschrijving van de waterretentie-en doorlatendheidskarakteristieken uit de Staringreeks met analytische functies. Stiboka rapport 2019, Stiboka Wageningen, 53 pp
Youngs EG, Gardner WR (1963) A problem of diffusion in the infinite hollow cylinder. Soil Sci Soc Am Proc 27: 475–476
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de Willigen, P., Nielsen, N.E., Claassen, N., Castrignanò, A.M. (2000). Modelling Water and Nutrient Uptake. In: Smit, A.L., Bengough, A.G., Engels, C., van Noordwijk, M., Pellerin, S., van de Geijn, S.C. (eds) Root Methods. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04188-8_15
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