Influence of the surface water reservoir to the thermal regime of frozen ground

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


2020. Vol. 6. № 1 (21)

Influence of the surface water reservoir to the thermal regime of frozen ground

For citation: Gorelik J. B., Zemerov I. V. 2020. “Influence of the surface water reservoir to the thermal regime of frozen ground”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 6, no. 1 (21), pp. 10-40. DOI: 10.21684/2411-7978-2020-6-1-10-40

About the authors:

Jacob B. Gorelik, Dr. Sci. (Geol.-Mineral.), Head of the Laboratory of Heat and Mass Transfer Events, Earth Cryosphere Institute, Tyumen Scientific Center of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID,

Ilya V. Zemerov, Postgraduate Student, Earth Cryosphere Institute, Tyumen Scientific Center of the Siberian Branch of the Russian Academy of Sciences;


Excessive flooding of the built-up territories in the areas of permafrost soils often occurs due to changes in natural factors (including climatic) or design deficiencies and can negatively affect frozen soils for a long time. Currently, there is no complete methodology for calculating this effect. The solution to this problem is closely related to clarifying the nature of the formation of temperature shift, which at the moment is not clear enough. The aim of the work is to create a methodology for predicting changes in soil temperature in the event of a shallow reservoir on its surface

In the first part of the article, the simplest theoretical model of the phenomenon of temperature shift is proposed, on the basis of which fairly convenient analytical expressions are obtained for the average annual temperature at the bottom of the active layer, depending on climatic factors and soil properties. The model most clearly demonstrates the nature of the occurrence of the phenomenon and can be used for simple assessments, as well as in the educational process. In particular, it is demonstrated that the magnitude of the shift is caused not only by the difference in the thermophysical characteristics of thawed and frozen soil, but also by the asymmetry of climatic parameters.

In the second part of the article, using the quasistationary methods, calculations of the predicted temperature of the soil when a reservoir of a given depth on its surface occurs. Unlike previously used methods, the predicted parameters of the soil are counted from its unperturbed state, which is determined by the authors previously proposed method, which allows us to evaluate the direction of the changes (towards cooling or warming). It is shown that the influence of a shallow (up to a meter deep) surface water body on the temperature of frozen soils substantially depends on the process of mixing water in the summer. For the first time, the direction of these processes has been established: with a high degree of mixing, the influence is always warming and grows with the depth of the reservoir; in the absence of mixing, the pond cools the base at shallow depths, and with an increase in depth above a certain value, an warming effect occurs, which, however, is much lower than in the presence of mixing. The practical applications of the results are considered.


  1. Are F. E. 1974. “Thermal regime of the small-depth lakes in the Eastern Siberia taiga zone (on the example of Central Yakutia)”. In: Lakes of the Siberian Permafrost, pp. 98-116. Novosibirsk: Nauka. [In Russian]

  2. Balobaev V. T. 1964. “Influence of the surface layer to thermal regime and to depth of seasonal thaw penetration of the frozen ground”. In: Thermal processes in the frozen ground, pp. 7-38. Moscow: Nauka. [In Russian]

  3. Balobaev V. T. 1991. Geothermy of frozen ground in the North Asia Lithosphere. 193 pp. Novosibirsk: Nauka. [In Russian]

  4. Barenblutt G. I. 1954. About some approximation methods in theory of one-dimensional unsteady liquid filtration at elastic regime. Izvestiya Akademii nauk SSSR, no. 9, pp. 35-49. [In Russian]

  5. Bosikov I. P., Sokolova V. A. 1974. “Textures of water sediments as a criteria of thermokarst lake’s water quantity”. In: Lakes of the Siberian Permafrost, pp. 33-39. Novosibirsk: Nauka. [In Russian]

  6. Vorontsov V. V., Kraev A. N., Igoshin M. E. 2014. “Stabilization of car road base critical deformations at permafrost”. The Russian Automobile and Highway Industry Journal, no. 6 (40), pp. 67-72. [In Russian]

  7. Gavrilova M. K., Popov P. P. 1974. “Microclimate of Central Yakutia lakes”. In: Lakes of the Siberian Permafrost, pp. 67-82. Novosibirsk: Nauka. [In Russian]

  8. Gavrilova M. K., Stepanov A. N. 1974. “Radiation balance of Central Yakutia lakes”. In: Lakes of the Siberian Permafrost, pp. 83-88. Novosibirsk: Nauka. [In Russian]

  9. Gavrilova M. K. 1974. “Thermal balance of Central Yakutia lakes”. In: Lakes of the Siberian Permafrost, pp. 88-98. Novosibirsk: Nauka. [In Russian]

  10. Gorelik J. B., Pazderin D. S. 2017. “Correctness of formulation and solution of thermotechnical problems of forecasting temperature field dynamics in the ground base of structures on permafrost”. Earth’s Cryosphere, vol. 21, no. 3, pp. 49-59. [In Russian]

  11. Gorelik J. B. 2010. “On the calculation methods of the engineering construction displacements caused by freezing layer frost heave process”. Earth’s Cryosphere, vol. 14, no. 1, pp. 50-62. [In Russian]

  12. Gorelik J. B. 2011. “Generalized theoretical model for calculate ice accumulation and deformations of freezing grounds”. Earth’s Cryosphere, vol. 15, no. 4, pp. 46-51. [In Russian]

  13. Gorelik J. B. 2011. “Physical and mechanical aspects of phase transitions in frozen and freezing grounds”. Paper presented at 4th Conference of Russian Geocryologists (7-9 June, Moscow), pp. 42-49. Moscow: Moscow State University. [In Russian]

  14. Grebenets V. I., Isakov B. A. 2016. “Deformations of car roads and railways at the Norilsk — Talnach part and methods of its preventions”. Earth’s Cryosphere, vol. 20, no. 2, pp. 69-77. [In Russian]

  15. Demin A. I. 1966. “Thermal regime of bed sediments for small depth of Arctic sea”. In: Seasonal thawing and freezing of soils in the North-East of the USSR, pp. 40-46. Moscow: Nauka. [In Russian]

  16. Dostovalov B. N., Kudriyvtsev V. A. 1967. General geocryology. Moscow: Moscow State University. 403 pp. [In Russian]

  17. Didishko P. I. 2017. “Deformations of railway bed and its preventions in conditions of permafrost”. Earth’s Cryosphere, vol. 21, no. 4, pp. 43-57. [In Russian]

  18. Carslaw H. S., Jaeger J. C. 1964. Conduction of heat in solids. Moscow: Nauka, 487 pp. [In Russian]

  19. Kondratiev C. V. 2016. “Deformations of car road bed ‘Amur’ at the part Chita — Khabarovsk with high icy permafrost”. Cand. Sci. (Geol.-Mineral.) diss. abstract. Irkutsk. 22 pp. [In Russian]

  20. Lykov A. V. 1954. Transferal phenomena in capillary-porous media. Moscow; Leningrad: Gostechizdat. 296 pp. [In Russian]

  21. Muhin N. I. 1974. “Particularity of formation and evolution of thermokarst lakes at lowland of Yana — Indigirka region”. Lakes of the permafrost zone of Siberia, Novosibirsk: Nauka, pp. 18-26. [In Russian]

  22. Kudriyvtsev V. A. (ed.). 1978. General geocryology. Moscow: Moscow State University. 464 pp. [In Russian]

  23. Kudriyvtsev V. A. (ed.). 1974. Bases of prognoses for permafrost at engineering and geological investigations. Moscow: Moscow State University. 432 pp. [In Russian]

  24. Pavlov A. V. 2008. Monitoring of permafrost. Novosibirsk: GEO, 230 pp. [In Russian]

  25. Porchaev V. G. 1970. Thermal interaction of buildings with permafrost. Moscow: Nauka. 208 pp. [In Russian]

  26. Tychonov A. N., Samarsky A. A. 1972. Methods of mathematical physics. Moscow: Nauka. 736 pp. [In Russian]

  27. Fayko L. I. 1986. Applications of ice and icy phenomena at business. Krasnoyarsk: Krasnoyarsk State University. 157 pp. [In Russian]

  28. Feldman G. M. 1973. Calculation methods of permafrost temperature regime. Moscow: Nauka. 254 pp. [In Russian]

  29. Feldman G. M. 1988. Water flow in unfrozen and freezing grounds. Novosibirsk: Nauka. 258 pp. [In Russian]

  30. Feldman G. M. 1977. Prognoses of temperature regime for grounds and evolution of cryogenic processes. Novosibirsk: Nauka. 102 pp. [In Russian]

  31. Feldman G. M. 1984. Thermokarst and permafrost. Novosibirsk: Nauka. 262 pp. [In Russian]

  32. Shavlov A. V. 1996. Ice at structure transitions. Novosibirsk: Nauka. 188 pp. [In Russian]

  33. Shur Y. L. 1988. Upper layer of frozen ground and thermokarst. Novosibirsk: Nauka. 213 pp. [In Russian]

  34. Shur Y. L. 1977. Thermokarst. Moscow: Nedra. 80 pp. [In Russian]

  35. Gorelik J. B. 2012. “Physical and Mechanical Processes in Cryogenic Formations Associated with Temperature Change”. Proceedings of the 10th International Conference on Permafrost, vol. 2, pp. 111-115. Salekhard.

  36. Gorelik J. B. 2008. “The Mechanism of Ice Formation in Connection with Deformation of Freezing Layer”. Proceedings of the 9th International Conference on Permafrost. pp. 535-540. Fairbanks, Alaska.