Abstract
By the methods of the thermodynamics of nonequilibrium processes and continuum mechanics we obtain a system of equations for quantitative description of the processes of heat-moisture transfer in soils; we state boundary conditions on the earth-atmosphere interface. We formulate the direct and inverse problems of heat-moisture transfer for the directed toward the application of the data of terrestrial and remote measurements. We conduct numerical studies for model problems.
Similar content being viewed by others
Literature cited
E. N. Bortnik and B. V. Gera, “Determination of the effective thermophysical characteristics of the earth's surface,” in:Proc. 12th Conf. Young Scholars Inst. Appl. Probl. Mech. Math, [in Russian], Akad. Nauk Ukr. SSR, L'vov (1988), pp. 12–16.
Ya. I. Burak, B. P. Galapats, and E. Ya. Chaplya, “Deformation of electrically conducting bodies taking account of heterodiffusion of charged admixture particles,”Fiz.-Khim. Mekh. Mater., No. 5, 8–14 (1980).
V. L. Bysov, I. A. Koltunov, A. M. Pletnev, and T. D. Lysenko, “Determination of the thermophysical parameters of formations of the earth's surface from the data of remote radiometric sensing,” Preprint: Akad. Nauk Ukr. SSR, Fiz.-Tekh. Inst. Nizk. Temp., No. 13, Khar'kov (1985).
B. V. Gera, “The inverse problem of determining the characteristics of averaged heat sources in a half-space,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 3, 75–79 (1988).
J. T. Khyuton, ed.Global Climate [in Russian], Gidrometeoizdat, Leningrad (1985).
E. S. Sergeev, ed.Soil Science [in Russian], Moscow University Press (1983).
R. D. Jackson, “Estimation of evapotranspiration on the local and regional scales,”Tr. Inst. Inzh. Elektrotekh. Radioelektr.,73, No. 6, 137–151 (1985).
I. D'yarmati,Nonequilibrium Thermodynamics [Russian translation], Mir, Moscow (1974).
I. A. Koltunov, Ya. Noiman, and A. M. Pletnev, “The problem of determining the thermophysical pa-rameters of formations of the earth's surface from data of radiometric sensing in different formulations,” Preprint: Akad. Nauk Ukr. SSR, Fiz.-Tekh. Inst. Nizk. Temp., Khar'kov (1986)
K. Ya. Kondrat'ev, “The influence of processes on a land surface on climatic change and the international project of satellite climatology of the land surface: (Survey),”Issled. Zemli iz Kosmosa, No. 6, 106–115 (1985)
L. Z. Kriksunov and G. A. Padalko,Thermovisors: A Handbook [in Russian], Tekhnika, Kiev (1987).
A. V. Lykov, “Mass-Thermal Transfer in Capillary-Porous Media,” in:Heat and Mass Transfer in Capillary-Porous Bodies [in Russian], Nauka i Tekhnika, Minsk (1965), pp. 3–27.
V. I. Lyal'ko,Heat-Mass Transfer in the Lithosphere [in Russian], Naukova Dumka, Kiev (1985).
V. I. Lyal'ko, M. M. Mitnik, L. D. Vul'fson, and Z. M. Shportyuk,Geothermic Prospecting for Useful Minerals [in Russian], Naukova Dumka, Kiev (1979).
V. I. Lyal'ko, O. N. Sibirtseva, and Z. M. Shportyuk, “Interpretation of geothermic anomalies using the solution of inverse problems,” Preprint: Akad. Nauk Ukr. SSR, Inst. Geol. Nauk, No. 27 (1981).
A. Myunster,Chemical Thermodynamics [Russian translation], Mir, Moscow (1971).
Directive to Hydrometeoroloigic Stations and Posts [in Russian], Gidrometeoizdat, Leningrad (1961).
S. A. Nerpin and A. R. Chudnovs'kii,Energy and Mass Transfer in a Plant-Soil-Air System [in Russian], Gidrometeoizadat, Leningrad (1975).
Ya. S. Podstrigach, “The diffusion theory of deformation of an isotropic continuous medium,”Vopr. Mekh. Real. Tverd. Tela, No. 4, 71–99 (1964).
Ya. S. Podstrigach, A. B. Karasev, B. V. Gera, P. A. Zhuk, and E. Ya. Chaplya, “Models of heatmoisture transfer in soil and problems of identification of their parameters from terrestrial measurements and remote sensing in the infrared range,” Preprint: Akad. Nauk Ukr. SSR, Inst. Prikl. Probl. Mekh. Mat., No. 19–88, L'vov (1988).
Ya. S. Podstrigach and P. R. Shvets,Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).
I. S. Kaurichev, ed.Practical Soil Science [in Russian], Kolos, Moscow (1980).
E. A. Reutov and A. M. Shutko, “Estimating the temperature profile of soil from the data of remote ultraviolet and infrared measurements,”Issled. Zemli iz Kosmosa, No. 4, 78–85 (1987).
R. Sleicher,The Water Regime of Plants [Russian translation], Mir, Moscow (1970).
A. I. Tikhonov and V. Ya. Arsenin,Methods of Solving Ill-posed Problems [in Russian], Nauka, Moscow (1986)
B. V. Shilin,Thermal Aerial Photography in the Study of Natural Formations [in Russian], Gidrometeoizdat, Leningrad (1980).
S. R. J. Axelsson, “Thermal modeling for the interpretation of IR-data,” in:Proc. 17 Int. Symp. Remote Sens. Envir., Vol. 2, Ann Arbor (1983), pp. 498–518.
P. J. Camillo, R. J. Curney, and T. J. Schmugge, “A soil and atmospheric boundary layer model for evapotranspiration and soil moisture studies,”Water Resources Research,19, No. 2, 371–380 (1983).
R. J. Curney and P. J. Camillo, “Modeling daily evapotranspiration using remotely sensed data,”J. Hydrology,69, 305–324 (1987).
A. El Badia and M. Courdesses, “Identification of spatially varying parameters in distributed parameter systems,” in:11th IMACS World Cong. Comput., Oslo, Vol. 4 (1986), pp. 263–267.
D. Ho, “A soil thermal model for remote sensing,” IEEE Trans. Geos. and Remote Sens.GE-25, No. 2, 221–229 (1987).
R. J. Curney and D. K. Hall, “Satellite-driver surface energy balance estimates in the Alaskan sub-Arctic,”J. Climate and Appl. Meteorology,22, 115–125 (1983).
J. C. Price, “Estimation of regional scale evapotranspiration through analysis of satellite thermal-infrared data,”IEEE Trans. Geos. and Remote Sens.,GE-20, No. 3, 286–305 (1982).
M. Raffy and F. Becker, “An inverse problem occurring in remote sensing in the thermal infrared bands and its solution,”J. Geophys. Res.,90, No. D3, 5809–5819 (1985).
Additional information
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 8–20.
Rights and permissions
About this article
Cite this article
Pidstrigach, Y.S., Karas'ov, O.B., Gera, B.V. et al. Mathematical modeling of heat-moisture transfer in soil and the problem of interpretation of data of remote sensing of the Earth's surface. J Math Sci 67, 2818–2829 (1993). https://doi.org/10.1007/BF01095853
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01095853