The Equilibrium State of Water in the Systems

  • Klaus Reichardt
  • Luís Carlos Timm


The state of equilibrium of water in the Soil-Plant-Atmosphere System (SPAS) is essential for the understanding of the dynamic processes that occur in the system, which will be dealt in the chapters to come. We introduce thermodynamic concepts to the state of water in a universal form, with a physical understanding for agronomists, environmentalists, biologists and all scientists interested in deeply studying the SPAS as a whole. The concepts are first applied to the simplest equilibrium state, which is that of pure water in a glass, then progressively coming to more complex situations of agricultural crops in the field. It is shown why the general tendency of water is to move spontaneously from the soil to the plant, and from the plant to the atmosphere. For this, the concept of total potential of the water is explored and applied to the most different situations. Soil water retention, available water to plants, and several other concepts related to irrigation and soil management are discussed, all related to the understanding of the energy status of the water in the SPAS. Of great importance is also the presentation of the mostly used instruments for the quantification of water in different systems, and for the measurement of the status of energy of the water.


  1. Angelocci LR (2002) Água na planta e trocas gasosas/energéticas com a atmosfera: introdução ao tratamento biofísico. Angelocci LR, PiracicabaGoogle Scholar
  2. Bacchi OOS, Reichardt K, Calvache M (2002) Neutron and gamma probes: their use in agronomy. International Atomic Energy Agency, ViennaGoogle Scholar
  3. Bakker G, van Der Ploeg MJ, de Rroij GH, Hoogendam CW, Gooren HPA, Huiskes C, Koopal LK, Kruidhof H (2007) New polymer tensiometers: measuring matric pressures down to the wilting point. Vadose Zone J 6:196–202CrossRefGoogle Scholar
  4. Blake GR, Hartge KH (1986) Bulk density. In: Klute A (ed) Methods of soil analysis. American Society of Agronomy; Soil Science Society of America, Madison, pp 363–375Google Scholar
  5. Campbell GS, Gardner WH (1971) Psychrometric measurement of soil water potential: temperature and bulk density effect. Soil Sci Soc Am Proc 35:8–12CrossRefGoogle Scholar
  6. Carneiro C, De Jong E (1985) In situ determination of the slope of the calibration curve of a neutron probe using a volumetric technique. Soil Sci 139:250–254CrossRefGoogle Scholar
  7. Cássaro FAM, Tominaga TT, Bacchi OOS, Reichardt K, Oliveira JCM, Timm LC (2000) The use of a surface gamma-neutron gauge to explore compacted soil layers. Soil Sci 165:665–676CrossRefGoogle Scholar
  8. Cassel DK, Klute A (1986) Water potential: tensiometry. In: Klute A (ed) Methods of soil analysis. American Society of Agronomy; Soil Science Society of America, Madison, pp 563–596Google Scholar
  9. Colman EA, Hendrix TM (1949) Fiberglass electrical soil moisture instrument. Soil Sci 67:425–438CrossRefGoogle Scholar
  10. Crestana S, Mascarenhas S, Pazzi-Mucelli RS (1985) Static and dynamic three dimensional studies of water in soil using computed tomographic scanning. Soil Sci 140:326–332CrossRefGoogle Scholar
  11. Davidson JM, Nielsen DR, Biggar JW (1963) The measurement and description of water flow through Columbia Silt Loam and Hesperia Sandy Loam. Hilgardia 34:601–617CrossRefGoogle Scholar
  12. Dourado-Neto D, Nielsen DR, Hopmans JW, Reichardt K, Bacchi OOS (2000) Software to model soil water retention curves (SWRC, version 2.00). Sci Agric 57:191–192CrossRefGoogle Scholar
  13. Dourado-Neto D, Timm LC, Oliveira JCM, Reichardt K, Bacchi OOS, Tominaga TT, Cassaro FAM (1999) State-space approach for the analysis of soil water content and temperature in a sugarcane crop. Sci Agric 56:1215–1221CrossRefGoogle Scholar
  14. Durigon A, de Jong van Lier Q (2011) Determinação das propriedades hidráulicas do solo utilizando tensiômetros de polímeros em experimentos de evaporação. Rev Bras Cienc Solo 35:1271–1276CrossRefGoogle Scholar
  15. Durigon A, Gooren HPA, de Jong van Lier Q, Metselaar K (2011) Measuring hydraulic conductivity to wilting point using polymer tensiometers in an evaporation experiment. Vadose Zone J 10:741–746CrossRefGoogle Scholar
  16. Ehlers W, Goss M (2016) Water dynamics in plant production, 2nd edn. CABI, CroydonCrossRefGoogle Scholar
  17. Ferraz ESB (1983) Gamma-ray attenuation to measure soil water content and/or bulk densities of porous media. In: IAEA Symposium, Aix-en-Provence, France, pp 449–460Google Scholar
  18. Gardner WH, Calissendorff C (1967) Gamma-ray and neutron attenuation measurement of soil bulk density and water content. In: IAEA and FAO Symposium. Isotope and radiation techniques in soil physics and irrigation studies, Istanbul, pp 101–113Google Scholar
  19. Gardner WH, Campbell GS, Calissendorff C (1972) Systematic and random errors in dual gamma energy soil bulk density and water content measurements. Soil Sci Soc Am Proc 36:393–398CrossRefGoogle Scholar
  20. Gardner WR, Kirkham D (1952) Determination of soil moisture by neutron scattering. Soil Sci 73:391–401CrossRefGoogle Scholar
  21. Greacen EL (1982) Soil water assessment by the neutron method. CSIRO, AdelaideGoogle Scholar
  22. Haines WB (1930) Studies of the physical properties of soils: V. The hysteresis effects in capillary properties and the modes of moisture distribution associated. J Agric Sci 20:97–116CrossRefGoogle Scholar
  23. Hakansson I (1990) A method for characterizing the state of compactness of the plough layer. Soil Tillage Res 16:105–120CrossRefGoogle Scholar
  24. Hakansson I, Lipiec J (2000) A review of the usefulness of relative bulk density values in studies of soil structure and compaction. Soil Tillage Res 53:71–85CrossRefGoogle Scholar
  25. Hu W, Shao MA, Wang QJ, Reichardt K (2008) Soil water content variability of the surface layer of a loess plateau hillside in China. Sci Agric 65:277–289CrossRefGoogle Scholar
  26. IAEA (1976) Tracer manual on crops and soils. International Atomic Energy Agency, ViennaGoogle Scholar
  27. Jensen PA, Somer E (1967) Scintillation techniques in soil-moisture and density measurements. In: IAEA and FAO Symposium. Isotope and radiation techniques in soil physics and irrigation studies, Istanbul, pp 31–48Google Scholar
  28. Kirda C, Reichardt K (1992) Comparison of neutron moisture gauges with non-nuclear methods to measure field soil water status. Sci Agric 49:111–121 (special number)CrossRefGoogle Scholar
  29. Kirkham MB (2014) Principles of soil and plant water relations, 2nd edn. Academic, OxfordGoogle Scholar
  30. Kramer PJ, Boyer PJ (1995) Water relations of plants and soils. Academic, New YorkGoogle Scholar
  31. Libardi PL (2012) Dinâmica da água no solo, 2nd edn. EDUSP, São PauloGoogle Scholar
  32. Macedo A, Vaz CMP, Naime JM, Jorge LAC, Crestana S, Cruvinel PE, Pereira JCD, Guimarães MF, Ralisch R (2000) Soil management impact and wood science – recent contributions of Embrapa Agricultural Instrumentation Center using CT imaging. In: Cruvinel PE, Colnago LA (eds) Advances in agricultural tomography. Embrapa Agricultural Instrumentation, São Carlos, pp 44–54Google Scholar
  33. Miller EE, Miller RD (1956) Physical theory of capillary flow phenomena. J Appl Phys 27:324–332CrossRefGoogle Scholar
  34. Miller EE, Miller RD (1955a) Theory of capillary flow: I. Practical implications. Soil Sci Soc Am Proc 19:267–271CrossRefGoogle Scholar
  35. Miller EE, Miller RD (1955b) Theory of capillary flow: II. Experimental information. Soil Sci Soc Am Proc 19:271–275CrossRefGoogle Scholar
  36. Moraes SO (1991) Heterogeneidade hidráulica de uma Terra Roxa Estruturada. PhD Thesis, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo, Piracicaba, São Paulo, BrazilGoogle Scholar
  37. Nobel PS (1983) Biophysical, plant physiology and ecology. W.H. Freeman & Company, New YorkGoogle Scholar
  38. Oertli JJ (1984) Water relations in cell walls and cells in the intact plants. Z Pflanz Bod 47:187–197CrossRefGoogle Scholar
  39. Paltineanu IC, Starr JL (1997) Real-time soil water dynamics using multisensor capacitance probes: laboratory calibrations. Soil Sci Soc Am J 61:1576–1585CrossRefGoogle Scholar
  40. Philip JR (1964) Similarity hypothesis for capillary hysteresis in porous materials. J Geophys Res 69:1553–1562CrossRefGoogle Scholar
  41. Pires LF, Borges JAR, Bacchi OOS, Reichardt K (2010) Twenty-five years of computed tomography in soil physics: a literature review of the Brazilian contribution. Soil Tillage Res 110:197–210CrossRefGoogle Scholar
  42. Pires LF, Macedo JR, Souza MD, Bacchi OOS, Reichardt K (2002) Gamma-ray computed tomography to characterize soil surface sealing. Appl Radiat Isot 57:375–380CrossRefGoogle Scholar
  43. Poulovassilis A (1962) Hypothesis of pore water, an application of the concept of independent domains. Soil Sci 93:460–463CrossRefGoogle Scholar
  44. Rawlins SL (1966) Theory for thermocouple psychrometers used to measure water potential in soil and plant samples. Agric Met 3:293–310CrossRefGoogle Scholar
  45. Reichardt K (1965) Uso das radiações gama na determinação da umidade e da densidade do solo. PhD Thesis, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo, Piracicaba, São Paulo, BrazilGoogle Scholar
  46. Reichardt K (1987) A água em sistemas agrícolas. Manole, Barueri, BrazilGoogle Scholar
  47. Reichardt K, Portezan-Filho O, Bacchi OOS, Oliveira JCM, Dourado-Neto D, Pilotto JE, Calvache M (1997) Neutron probe calibration correction by temporal stability parameters of soil water content probability distribution. Sci Agric 54:17–21 (special number)CrossRefGoogle Scholar
  48. Rock PA (1969) Chemical thermodynamics: principles and applications. The Macmillan Company, TorontoGoogle Scholar
  49. Schindler U (1980) Ein schnellverfahren zur messung der wasserleitfähigkeit im teilgesättigten boden an stechzylinderproben. Arch Acker-u Pflanzenbau u Bod 24:1–7Google Scholar
  50. SENTEK (2001) Calibration of Sentek soil moisture sensors. Sentek Pty Ltd, Stepney, AustraliaGoogle Scholar
  51. Serrarens D, Macintyre JL, Hopmans JW, Bassoi LH (2000) Soil moisture calibration of TDR multi-level probes. Sci Agric 57:349–354CrossRefGoogle Scholar
  52. Silva AP, Bruand A, Tormena CA, da Silva EM, Santos GG, Giarola NFB, Guimarães RML, Marchão RL, Klein VA (2014) Indicators of soil physical quality: from simplicity to complexity. In: Teixeira WG, Ceddia MB, Ottoni MV, Donnagema GK (eds) Application of soil physics in environmental analysis: measuring, modelling and data integration. Springer, New York, pp 201–221Google Scholar
  53. Silva AP, Tormena CA, Dias Junior MS, Imhoff S, Klein VA (2010) Indicadores da qualidade do solo. In: De Jong van Lier Q (ed) Física do solo. Sociedade Brasileira de Ciência do Solo, Viçosa, pp 241–282Google Scholar
  54. Stolf R (1992) Teoria e teste experimental de fórmulas de transformação dos dados de penetrômetro de impacto em resistência do solo. Rev Bras Cienc Solo 15:229–235Google Scholar
  55. Stolf R, Cassel DK, King LD, Reichardt K (1998) Measuring mechanical impedance in clayey gravelly soils. Braz J Soil Sci 22:189–196Google Scholar
  56. Stolf R, Thurler AM, Bacchi OOS, Reichardt K (2011) Method to estimate soil macroporosity and microporosity based on sand content and bulk density. Braz J Soil Sci 35:447–459Google Scholar
  57. Taiz L, Zeiger E, Moller IM, Murphy A (2018) Fundamentals of plant physiology. Oxford University Press, OxfordGoogle Scholar
  58. Taylor SA, Ashcroft GL (1972) Physical edaphology: the physics of irrigated and non-irrigated soils. W.H. Freeman & Company, New YorkGoogle Scholar
  59. Timm LC, Pires LF, Roveratti R, Arthur RCJ, Reichardt K, Oliveira JCM, Bacchi OOS (2006) Field spatial and temporal patterns of soil water content and bulk density changes. Sci Agric 63:55–64CrossRefGoogle Scholar
  60. Tominaga TT, Cássaro FAM, Bacchi OOS, Reichardt K, Oliveira JCM, Timm LC (2002) Variability of soil water content and bulk density in a sugarcane field. Aust J Soil Res 40:605–614Google Scholar
  61. Topp GC (1969) Soil water hysteresis measure in a sandy loam and compared with the hysteresis domain model. Soil Sci Soc Am Proc 33:645–651CrossRefGoogle Scholar
  62. Topp GC, Davis JL (1985) Measurement of soil water content using time domain reflectometry (TDR): a field evaluation. Soil Sci Soc Am J 49:19–24CrossRefGoogle Scholar
  63. Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16:574–582CrossRefGoogle Scholar
  64. Topp GC, Davis JL, Annan AP (1982) Electromagnetic determination of soil water content using TDR. I. Applications to wetting fronts and steeps gradients. Soil Sci Soc Am J 46:672–678CrossRefGoogle Scholar
  65. Topp GC, Miller EE (1966) Hysteresis moisture characteristics and hydraulic conductivities for glass-bead media. Soil Sci Soc Am Proc 30:156–162CrossRefGoogle Scholar
  66. Tschapek M (1984) Criteria for determining the hydrophilicity-hydrophobicity of soil. J Plant Nutr Soil Sci 147:137–149Google Scholar
  67. Van Bavel CHM, Underwood N, Swanson RW (1956) Soil moisture measurement by neutron moderation. Soil Sci 82:29–41CrossRefGoogle Scholar
  68. Van Genuchten MT (1980) A closed-form equation for predicting the conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRefGoogle Scholar
  69. Vaz CMP, Crestana S, Mascarenhas S, Cruvinel PE, Reichardt K, Stolf R (1989) Using a computed tomography miniscaner for studying tillage induced soil compaction. Soil Technol 2:313–321CrossRefGoogle Scholar
  70. Vaz CMP, Hopmans JW (2001) Simultaneous measurement of soil penetration resistance and water content with a combined penetrometer-TDR moisture probe. Soil Sci Soc Am J 65:4–12CrossRefGoogle Scholar
  71. Vaz CMP, Tuller M, Lasso PRO, Crestana S (2014) New perspectives for the application of high-resolution benchtop X-ray MicroCT for quantifying void, solid and liquid phases in soils. In: Teixeira WG, Ceddia MB, Ottoni MV, Donnagema GK (eds) Application of soil physics in environmental analysis: measuring, modelling and data integration. Springer, New York, pp 261–281Google Scholar
  72. Villa Nova NA, Oliveira AS, Reichardt K (1992) Performance and test of a direct reading ‘air-pocket’ tensiometer. Soil Technol 5:283–287CrossRefGoogle Scholar
  73. Villa Nova NA, Reichardt K, Libardi PL, Moraes SO (1989) Direct reading “air-pocket” tensiometer. Soil Technol 2:403–407CrossRefGoogle Scholar
  74. Villagra MM, Matsumoto OM, Bacchi OOS, Moraes SO, Libardi PL, Reichardt K (1988) Tensiometria e variabilidade espacial em Terra Roxa Estruturada. Rev Bras Cienc Solo 12:205–210Google Scholar
  75. Wiebe HH, Campbell CS, Gardner WH, Rawlins SL, Cary JW, Brown W (1971) Measurement of plant and soil water status. Utah Agricultural State, LoganGoogle Scholar
  76. Wind GP (1966) Capillary conductivity data estimated by a simple method. In: International Association for Scientific Hydrology. Wageningen Symposium, Water in the unsaturated zone, Wageningen, pp 181–191Google Scholar
  77. Zemansky MW, Dittman RH (1997) Heat and thermodynamics: an intermediate textbook, 7th edn. McGraw-Hill, New YorkGoogle Scholar
  78. Zimmermann U, Stendle E (1978) Physical aspects of water relations of plant cells. Adv Bot Res 6:45–117CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Klaus Reichardt
    • 1
  • Luís Carlos Timm
    • 2
  1. 1.Centro de Energia Nuclear na Agricultura and Escola Superior de Agricultura “Luiz de Queiróz”University of Sao PauloPiracicabaBrazil
  2. 2.Rural Engineering Department, Faculty of AgronomyFederal University of PelotasCapão do LeãoBrazil

Personalised recommendations