Eurasian Soil Science

, Volume 50, Issue 4, pp 445–455 | Cite as

An improved Mualem–Van Genuchten method and its verification using data on Beit Netofa clay

  • V. V. Terleev
  • W. Mirschel
  • V. L. Badenko
  • I. Yu. Guseva
Soil Physics


An improved Mualem–Van Genuchten method for estimating soil hydraulic conductivity in the vadose zone from data on filtration coefficient and water-retention capacity of soil is proposed. The approach offered by Kosugi for a functional description of hydraulic conductivity of soil is applied. To calculate the values of hydraulic conductivity by Mualem’s formula, the function of differential water capacity of soil with interpreted parameters has been used instead of the function of integral water capacity of soil, which describes the water-retention capacity of soil. Approximations to functions of soil water-retention capacity and hydraulic conductivity are offered here. On the basis of some concepts on the specificity of the curve that describes soil water-retention capacity, a technique for identification of these parameters is developed. The experimental data from two parts of capillary pressure range, on which the water-retention capacity of soil is measured, are used in the technique. The first part corresponds to the zone of mainly film moisture, where the sorption component of the capillary-sorption forces retaining the water in the soil predominates. The second part includes (a) the zone of the mainly capillary-suspended moisture, where the capillary component of the capillary-sorption forces predominates, and (b) the zone of the capillary-backed moisture. The improved method for estimating relative values of hydraulic conductivity of soil has been verified with the use of measured data for the Beit Netofa Сlay soil. The advantages of this method include (a) the ability to identify parameters of the soil hydrophysical functions using relatively available soil indices and (b) the higher accuracy of calculating the soil hydraulic conductivity in comparison with the original version of the method.


differential water capacity water-retention capacity hydraulic conductivity of soil physical and statistical interpretation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. D. Voronin, Fundamentals of Soil Physics (Moscow State Univ., Moscow, 1986) [in Russian].Google Scholar
  2. 2.
    A. M. Globus, Experimental Hydrophysics of Soils (Gidrometeoizdat, Leningrad, 1969) [in Russian].Google Scholar
  3. 3.
    A. M. Globus, Soil-Hydrophysical Support of Agroecological Mathematical Models (Gidrometeoizdat, Leningrad, 1987) [in Russian].Google Scholar
  4. 4.
    B. N. Michurin, Doctoral Dissertation in Agriculture (Moscow, 1967).Google Scholar
  5. 5.
    S. V. Nerpin and A. F. Chudnovskii, Soil Physics (Nauka, Moscow, 1967) [in Russian].Google Scholar
  6. 6.
    I. I. Sudnitsyn, New Assessment Methods of Hydrophysical Properties of Soils and Water Supply of Forest (Nauka, Moscow, 1966) [in Russian].Google Scholar
  7. 7.
    N. N. Semenova, V. V. Terleev, G. I. Suhoruchenko, E. E. Orlova, and N. E. Orlova, “On One Method for the Numerical Solution of a System of Parabolic Equations,” Vestnik of St.-Petersb. Univ., Ser. 1: Mathematics. 49 (2), 138–146 (2016). doi 10.3103/ S1063454116020138CrossRefGoogle Scholar
  8. 8.
    V. V. Terleev, V. L. Badenko, A. G. Topaj, W. Mirschel, and I. Yu. Guseva, “Advantages of the improved Mualem–Van Genuchten approach on the example of clay soil,” Agrofizika, No. 4 (16), 27–34 (2014).Google Scholar
  9. 9.
    V. V. Terleev, M. A. Narbut, A. G. Topaj, and W. Mirschel, “Modeling the hydrophysical properties of the soil as a capillary-porous medium and modification of the Mualem–Van Genuchten approach: theory,” Agrofizika, No. 2 (14), 35–44 (2014).Google Scholar
  10. 10.
    V. V. Terleev, A. G. Topaj, W. Mirschel, and P. D. Gurin, “Modelling the water-retention curve on the base of the concept of capillary hysteresis and lognormal pore-size distribution of soil: theory,” Agrofizika, No. 1, 9–19 (2014).Google Scholar
  11. 11.
    V. V. Terleev, A. G. Topaj, W. Mirschel, and P. D. Gurin, “Modelling the main drainage and moistening branches of hysteretic loop inherent for the soil water-retention capacity,” Agrofizika, No. 1, 22–29 (2013).Google Scholar
  12. 12.
    V. V. Terleev, W. Mirschel, V. L. Badenko, I. Yu. Guseva, and P. D. Gurin, “Physical-statistical interpretation of the parameters of the soil water retention function,” Agrofizika, No. 4, 1–8 (2012).Google Scholar
  13. 13.
    E. V. Shein, A Course on Soil Physics (Moscow State Univ., Moscow, 2005) [in Russian].Google Scholar
  14. 14.
    E. V. Shein, “Physically based mathematical models in soil science: history, current state, problems, and outlook (analytical review),” Eurasian Soil Sci. 48, 712–718 (2015). doi 10.1134/S1064229315070091CrossRefGoogle Scholar
  15. 15.
    L. R. Ahuja and D. Swartzendruber, “An improved form of soil-water diffusivity function,” Soil Sci. Soc. Am. Proc. 36, 9–14 (1972).CrossRefGoogle Scholar
  16. 16.
    V. Badenko, V. Terleev, N. Arefiev, Ju. Volkova, and O. Nikonova, “Agro-ecosystem model AGROTOOL coupled with GIS for simulation of the spatial variability of the soil hydrophysical properties,” The 2015 AASRI International Conference on Industrial Electronics and Applications (IEA 2015) (London, 2015), pp. 452–455.Google Scholar
  17. 17.
    V. Badenko, V. Terleev, and A. Topaj, “AGROTOOL software as an intellectual core of decision support systems in computer aided agriculture,” Appl. Mech. Mater. 635–637, 1688–1691 (2014). doi 10.4028/www. Scholar
  18. 18.
    W. Brutsaert, “A concise parameterization of the hydraulic conductivity of unsaturated soils,” Adv. Water Resour. 23, 811–815 (2000).CrossRefGoogle Scholar
  19. 19.
    W. Brutsaert, “Probability laws for pore-size distribution,” Soil Sci. 101, 85–92 (1966).CrossRefGoogle Scholar
  20. 20.
    R. Haverkamp, M. Vauclin, J. Touma, P. J. Wierenga, and G. Vachaud, “A comparison of numerical simulation model for one-dimensional infiltration,” Soil Sci. Soc. Am. J. 41, 285–294 (1977).CrossRefGoogle Scholar
  21. 21.
    K. Kosugi, “General model for unsaturated hydraulic conductivity for soil with lognormal pore-size distribution,” Soil Sci. Soc. Am. J. 63, 270–277 (1999).CrossRefGoogle Scholar
  22. 22.
    K. Kosugi, “Lognormal distribution model for unsaturated soil hydraulic properties,” Water Resour. Res. 32, 2697–2703 (1996).CrossRefGoogle Scholar
  23. 23.
    K. Kosugi, “Three-parameter lognormal distribution model for soil water retention,” Water Resour. Res. 30, 891–901 (1994).CrossRefGoogle Scholar
  24. 24.
    K. Kosugi and J. W. Hopmans, “Scaling water retention curves for soils with lognormal pore-size distribution,” Soil Sci. Soc. Am. J. 62, 1496–1505 (1998).CrossRefGoogle Scholar
  25. 25.
    K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math. 2, 164–168 (1944).CrossRefGoogle Scholar
  26. 26.
    D. W. Marquardt, “An algorithm for least-square estimation on non-linear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).CrossRefGoogle Scholar
  27. 27.
    S. Medvedev, A. Topaj, V. Badenko, and V. Terleev, “Medium-term analysis of agroecosystem sustainability under different land use practices by means of dynamic crop simulation,” IFIP Adv. Inf. Commun. Technol. 448, 252–261 (2015).CrossRefGoogle Scholar
  28. 28.
    Y. Mualem, A Catalogue of the Hydraulic Properties of Unsaturated Soils: Research Project 442 (Israel Institute of Technology, Haifa, Israel, 1976).Google Scholar
  29. 29.
    Y. Mualem, “A new model for predicting hydraulic conductivity of unsaturated porous media,” Water Resour. Res. 12, 513–522 (1976).CrossRefGoogle Scholar
  30. 30.
    R. A. Poluektov, S. M. Fintushal, I. V. Oparina, D. V. Shatskikh, V. V. Terleev, and E. T. Zakharova, “AGROTOOL—a system for crop simulation,” Arch. Agron. Soil Sci. 48 (6), 609–635 (2002). doi 10.1080/ 0365034021000041597CrossRefGoogle Scholar
  31. 31.
    R. A. Poluektov, I. V. Oparina, and V. V. Terleev, “Three methods for calculating soil water dynamics,” Russ. Meteorol. Hydrol., No. 11, 61–67 (2003).Google Scholar
  32. 32.
    R. A. Poluektov and V. V. Terleev, “Crop simulation model of the second and the third productivity levels,” in Modeling Water and Nutrient Dynamics in Soil-Crop Systems (Springer-Verlag, Dordrecht, 2007), pp. 75–89. doi 10.1007/978-1-4020-4479-3_7CrossRefGoogle Scholar
  33. 33.
    R. A. Poluektov and V. V. Terleev, “Modeling of the water retention capacity and differential moisture capacity of soil,” Russ. Meteorol. Hydrol., No. 11, 70–75 (2002).Google Scholar
  34. 34.
    R. A. Poluektov and V. V. Terleev, “Modeling the moisture retention capacity of soil with agricultural and hydrological characteristics,” Russ. Meteorol. Hydrol., No. 12, 73–77 (2005).Google Scholar
  35. 35.
    E. Rawitz, PhD Thesis (Hebrew Univ., Rehovot, 1965).Google Scholar
  36. 36.
    L. A. Richards, “Capillary conduction of liquids through porous mediums,” J. Appl. Phys. 1 (5), 318–333 (1931).Google Scholar
  37. 37.
    V. Terleev, V. Badenko, I. Guseva, and W. Mirschel, “Enhanced Mualem–Van Genuchten approach for estimating relative soil hydraulic conductivity,” Appl. Mech. Mater. 725–726, 355–360 (2015).CrossRefGoogle Scholar
  38. 38.
    V. V. Terleev, W. Mirschel, U. Schindler, and K.-O. Wenkel, “Estimation of soil water retention curve using some agrophysical characteristics and Voronin’s empirical dependence,” J. Int. Agrophys. 24 (4), 381–387 (2010).Google Scholar
  39. 39.
    V. Terleev, A. Nikonorov, V. Badenko, I. Guseva, Yu. Volkova, O. Skvortsova, S. Pavlov, and W. Mirschel, “Modeling of hydrophysical properties of the soil as capillary-porous media and improvement of Mualem–Van Genuchten method as a part of foundation arrangement research,” Adv. Civil Eng. 2016, art. ID 8176728, 1–7 (2016). doi 10.1155/2016/8176728Google Scholar
  40. 40.
    V. Terleev, E. Petrovskaia, N. Sokolova, A. Dashkina, I. Guseva, V. Badenko, Yu. Volkova, O. Skvortsova, O. Nikonova, S. Pavlov, A. Nikonorov, V. Garmanov, and W. Mirschel, “Mathematical modeling of hydrophysical properties of soils in engineering and reclamation surveys,” Proceedings of International Scientific Conference Week of Science in St. Petersburg–Civil Engineering (SPbWOSCE–2015) (Curran Associates, Red Hook, 2016), Vol. 53, pp. 1–6. doi 10.1051/matecconf/2016530101310.1051/matecconf/20165301013Google Scholar
  41. 41.
    V. V. Terleev, A. G. Topaj, and W. Mirschel, “The improved estimation for the effective supply of productive moisture considering the hysteresis of soil waterretention capacity,” Russ. Meteorol. Hydrol. 40 (4), 278–285 (2015). doi 10.3103/S106837391504007XCrossRefGoogle Scholar
  42. 42.
    M. Th. van Genuchten, “A closed form equation for predicting the hydraulic conductivity of unsaturated soils,” Soil Sci. Soc. Am. J. 44, 892–898 (1980).CrossRefGoogle Scholar
  43. 43.
    H. Vereecken, M. Weynants, M. Javaux, Y. Pachepsky, M. G. Schaap, and M. Th. van Genuchten, “Using pedotransfer functions to estimate the van Genuchten–Mualem soil hydraulic properties: a review,” Vadose Zone J. 9, 795–820 (2010).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • V. V. Terleev
    • 1
  • W. Mirschel
    • 2
  • V. L. Badenko
    • 1
  • I. Yu. Guseva
    • 1
  1. 1.Peter the Great St. Petersburg Polytechnic UniversitySaint-PetersburgRussia
  2. 2.Leibniz Centre of Agricultural Landscape Research (ZALF)MuenchebergGermany

Personalised recommendations