A technique for the calculation of evaporation from the soil surface based on moisture profiles

  • S. V. Zasukhin
Systems Analysis and Operations Research


The problem of calculating the evaporation from the soil surface is formulated as an optimal control problem. The controlled process of the vertical water transfer in soil is described by a onedimensional nonlinear second-order parabolic partial differential equation. The objective function is the squared Euclidean distance between the calculated values of the soil moisture at various depths and certain prescribed values. To improve the efficiency of finding a numerical solution, the sensitivity of the soil moisture at various depths to the variations of evaporation is estimated by means of fast automatic differentiation. The analysis of these estimates made it possible to determine an effective thin subsurface soil layer in which the moisture is most sensitive to the variations of evaporation; it is in this soil layer where the objective function should be calculated.


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  1. 1.
    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
  2. 2.
    M. Shao and R. Horton, “Integral method for estimating soil hydraulic properties,” Soil Sci. Soc. Am. J. 62, 585–592 (1998).CrossRefGoogle Scholar
  3. 3.
    X. Han, M. Shao, and R. Horton, “Estimating van genuchten model parameters of undisturbed soils using an integral method,” Pedosphere 20, 55–62 (2010).CrossRefGoogle Scholar
  4. 4.
    W. Durner, E. Priesack, and H.-J. Vogel, “Determination of parameters for flexible hydraulic functions by inverse modeling,” in Proceedings of the International Workshop on Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media, Riverside, CA, October 22–24, 1997, Ed. by M. Th. van Genuchten, F. J. Leij, and L. Wu (Univ. California, Riverside, CA, 1999), pp. 817–829.Google Scholar
  5. 5.
    M. Th. van Genuchten, F. J. Leij, and S. R. Yates, The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils (US Salinity Lab, Riverside, CA, 1991).Google Scholar
  6. 6.
    M. G. Scaap, F. J. Leij, and M. Th. van Genuchten, “Rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer func-tions,” J. Hydrol. 251, 163–176 (2001).CrossRefGoogle Scholar
  7. 7.
    W. Durner and K. Lipsius, “Determining soil hydraulic properties,” in Encyclopedia of Hydrological Sciences, Ed. by M. G. Anderson and J. J. McDonnell (Wiley, Chichester, UK, 2005), pp. 1121–1144.Google Scholar
  8. 8.
    K. Zhang, “Parameter identification for root growth based on soil water po-tential measurements—an inverse modeling approach,” Proc. Environ. Sci. 19, 574–579 (2013).CrossRefGoogle Scholar
  9. 9.
    D. Yang, T. Zhang, K. Zhang, D. J. Greenwood, J. Hammond, and P. J. White, “An easily implemented agrohydrological procedure with dynamic root simulation for water transfer in the crop-soil system: validation and application,” J. Hydrol. 370, 177–190 (2009).CrossRefGoogle Scholar
  10. 10.
    X. Yang and X. You, “Estimating parameters of van Genuchten model for soil water retention curve by intelligent algorithms,” Appl. Math. Inf. Sci. 7, 1977–1983 (2013).CrossRefGoogle Scholar
  11. 11.
    I. A. Sharov, Exploitation of Hydromeliorative Systems (Sel’khozgiz, Moscow, 1959) [in Russian].Google Scholar
  12. 12.
    N. N. Ivanov, “Determination of evaporation quantities,” Izv. Vses. Geogr. Ob-va 86, 189–196 (1954).Google Scholar
  13. 13.
    G. K. L’gov, Irrigated Agriculture (Kolos, Moscow, 1979) [in Russian].Google Scholar
  14. 14.
    A. M. Alpat’ev, Hydrologic Cycle in Nature and their Conversion (Gidrometeoizdat, Leningrad, 1969) [in Russian].Google Scholar
  15. 15.
    A. Yu. Cheremisinov, V. N. Zherdev, and A. A. Cheremisinov, The Dynamics of Climate, Water Balances and Resources of the Central Chernozem Region (Voronezh. Gos. Agrarn. Univ., Voronezh, 2013) [in Russian].Google Scholar
  16. 16.
    A. R. Konstantinov, “Irrigation rationing: methods, their estimation, ways to refine,” Gidrotekh. Meliorats., No. 1, 19–28 (1986).Google Scholar
  17. 17.
    V. P. Singh, Hydrologic Systems, Vol. 2: Watershed Modeling (Prentice-Hall, Englewood Cliffs, NJ, 1989).Google Scholar
  18. 18.
    F. I. Morton, Evaporation and Climate: A Study in Cause and Effect (Inland Water Branch, Department of Energy, Mines and Resources, Ottawa, Canada, 1968).Google Scholar
  19. 19.
    H. H. G. Savenije, “Determination of evaporation from a catchment water balance at a monthly time scale,” Hydrol. Earth Syst. Sci. 1, 93–100 (1997).CrossRefGoogle Scholar
  20. 20.
    V. S. Mezentsev and I. V. Karnatsevich, Moisture Conditions of the West Siberian Plain (Gidrometeoizdat, Leningrad, 1969) [in Russian].Google Scholar
  21. 21.
    H. L. Penman, “Natural evaporation from open water, bare soil and grass,” Proc. R. Soc. London 193, 120–145 (1948).CrossRefGoogle Scholar
  22. 22.
    J. Monteith, “Evaporation and the environment,” in Proceedings of the 19th Symposium of the Society of Experimental Biology (Cambridge Univ. Press, Cambridge, UK, 1965), pp. 205–234.Google Scholar
  23. 23.
    C. H. B. Priestley and R. J. Taylor, “On the assessment of surface heat flux and evaporation using large-scale parameters,” Mon. Weather Rev. 100, 81–92 (1972).CrossRefGoogle Scholar
  24. 24.
    M. E. Jensen, R. D. Burman, and R. G. Allen, Evapotranspiration and Irrigation Water Requirements, ASCE Manuals and Reports on Engineering Practice No. 70 (Am. Soc. Civil Engrs., New York, 1990).Google Scholar
  25. 25.
    J. Doorenbos and A. H. Kassam, “Yield response to water,” FAO Irrigation and Drainage Paper No. 33 (FAO, Rome, 1979).Google Scholar
  26. 26.
    R. G. Allen, W. O. Pruitt, J. A. Businger, L. J. Fritschen, M. E. Jensen, and F. H. Quinn, “Evaporation and transpiration,” in Hydrology Handbook, ASCE Manual and Reports on Engineering Practice (ASCE, New York, 1996), pp. 125–252.Google Scholar
  27. 27.
    G. Katata, N. Haruyasu, U. Hiromasa, N. Agam, and P. R. Berliner, “Development of a land surface model including evaporation and adsorption processes in the soil for the land-air exchange in arid regions,” J. Hydrometeorol. 8, 1307–1324 (2007).CrossRefGoogle Scholar
  28. 28.
    J. D. Kalma, T. R. McVicar, and M. F. McCabe, “Estimating land surface evaporation: a review of methods using remotely sensed surface temperature data,” Surv. Geophys. 29, 421–469 (2008).CrossRefGoogle Scholar
  29. 29.
    A. N. Gel’fan, E. L. Muzylev, A. B. Uspenskii, Z. P. Startseva, S. A. Uspenskii, and P. Yu. Romanov, “A remote sensing based land surface model: development and application for assessing intra-annual variability of water and heat balances of a vast region,” Sovrem. Probl. Distants. Zondir. Zemli Kosmosa 9 (5), 183–191 (2012).Google Scholar
  30. 30.
    B. Martens, D. Miralles, H. Lievens, D. Fernandez-Prieto, and N. Verhoest, “Improving terrestrial evaporation estimates over continental australia through assimilation of SMOS soil moisture,” in Advances in the Validation and Application of Remotely Sensed Soil Moisture, Int._J. Appl. Earth Observ. Geoinform., Vol. 48 (Spec. Iss.), 146–162 (2016).CrossRefGoogle Scholar
  31. 31.
    D. G. Miralles, T. R. H. Holmes, R. A. M. de Jeu, J. H. Gash, A. G. C. A. Meesters, and A. J. Dolman, “Global land-surface evaporation estimated from satellite-based observations,” Hydrol. Earth Syst. Sci. 15, 453–469 (2011).CrossRefGoogle Scholar
  32. 32.
    K. R. Aida-Zade and Yu. G. Evtushenko, “Fast automatic differentiation on computers,” Mat. Model. 1, 121–139 (1989).MathSciNetMATHGoogle Scholar
  33. 33.
    A. Griewank, “On automatic differentiation,” in Mathematical Programming: Recent Developments and Applications, Ed. by M. Iri and K. Tanabe (Kluwer Academic, Tokyo, 1989), pp. 83–108.Google Scholar
  34. 34.
    Automatic Differentiation of Algorithms. Theory, Implementation and Application, Ed. by A. Griewank and G. F. Corliss (SIAM, Philadelphia, 1991).Google Scholar
  35. 35.
    Yu. Evtushenko, “Automatic differentiation viewed from optimal control theory,” in Automatic Differentiation of Algorithms. Theory, Implementation and Application, Ed. by A. Griewank and G. F. Corliss (SIAM, Philadelphia, 1991), pp. 25–30.Google Scholar
  36. 36.
    Yu. Evtushenko, “Computation of exact gradients in distributed dynamic systems,” Optim. Methods Software 9, 45–75 (1998).MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    A. Griewank, Evaluating Derivatives (SIAM, Philadelphia, 2000).MATHGoogle Scholar
  38. 38.
    A. M. Shutko, Microwave (SHF) Radiometry of Water Surface and Ground (Nauka, Moscow, 1986) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Dorodnicyn Computing Center, Federal Research Center Computer Science and ControlRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia

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