Forecast of the soil temperature in permafrost in response of climate warming

A. A. Fedotov, V.V. Kaniber, P. V. Khrapov


The article studies the initial boundary value problem for a non-stationary one-dimensional heat equation that simulates the distribution of ground temperature in the region of Yakutsk. To determine the parameters of the mathematical model, data from the meteorological station and expertise of geotechnical surveys were used. Simulation of the soil temperature distribution was carried out until the moment of reaching the non-stationary periodic mode. For the numerical solution of the problem, the finite volume method (FVM) was used. The calculations were started on the January 1st of the first year of observation of the soil temperature. In order to analyze the temperature field, graphs of the temperature dependence on the depth were constructed for June and October of the 1st, 10th, 35th, 50th and 100th years. The study of the results showed that it takes about 50 years for the soil temperature to reach a non-stationary periodic mode at a depth of 30 m. Then the temperature distribution of each month were simulated and the depth of active-layer was found to be 5 m, as well as the depth of zero annual amplitudes equal to 17 m. Temperature ranges were set: for the surface from -18 to 16.5°C; for 5 m from -6 to 0.5°C and for 10 m from -3 to -2°C. The forecast of the soil temperature distribution for 2080 was modeled according to two scenarios of the Representative Concentration Pathway of global warming: moderate RCP2.6 and negative RCP8.5. The RCP2.6 Scenario showed the preservation of permafrost with an increase of active-layer by more than 2 times, as well as an increase of soil temperature by an average of 2.5°C. The results of calculations for the RCP8.5 scenario indicate the complete disappearance of permafrost at depths of 30 m and beyond, which will lead to soil destabilization in the considered area

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Anisimov, Oleg A., and Frederick E. Nelson. "Permafrost distribution in the Northern Hemisphere under scenarios of climatic change." Global and Planetary Change 14.1-2 (1996): 59-72.

Nelson F. E., Anisimov O. A., Shiklomanov N. I. Climate change and hazard zonation in the circum-Arctic permafrost regions //Natural Hazards. – 2002. – T. 26. – #. 3. – S. 203-225.

Parfenova E., Tchebakova N., Soja A. Assessing landscape potential for human sustainability and ‘attractiveness’ across Asian Russia in a warmer 21st century //Environmental Research Letters. – 2019. – T. 14. – #. 6. – S. 065004.

Boike, J., Grau, T., Heim, B., Günther, F., Langer, M., Muster, S., Gouttevin, I. and Lange, S. "Satellite-derived changes in the permafrost landscape of central Yakutia, 2000–2011: Wetting, drying, and fires." Global and Planetary Change 139 (2016): 116-127.


Fedotov A.A., Hrapov P.V., Tarasjuk Ju.V. Modelirovanie dinamiki temperaturnogo polja gruntov vokrug magistral'nyh gazoprovodov v kriolitozone. International Journal of Open Information Technologies. 2020. T. 8. # 2. S. 7-13.

RSN 67–87. Inzhenernye izyskanija dlja stroitel'stva. Sostavlenie prognoza izmenenij temperaturnogo rezhima vechnomerzlyh gruntov chislennymi metodami. M.: Gosstroj RSFSR, 1987. 40 s.

Meteorologicheskij centr v g. Jakutsk. Indeks WMO: 24959 //Vserossijskij nauchno-issledovatel'skij institut gidrometeorologicheskoj informacii (VNIIGMI-MCD). URL:

Balobaev V. T. Geotermija merzloj zony litosfery severa Azii. – Nauka. Sib. otd-nie, 1991.

Zakljuchenie jekspertizy inzhenernyh izyskanij ot 15.12.2016 g. URL:

SNiP 2.02.04-88 Stroitel'nye normy i pravila. Osnovanija i fundamenty na vechnomerzlyh gruntah. M.: Gosudarstvennyj stroitel'nyj komitet SSSR, 1990. 55 c.

Patankar S.V. Chislennoe reshenie zadach teploprovodnosti i konvektivnogo teploobmena pri techenii v kanalah. M.: Izdatel'stvo MJeI. 2003. 312 s. (Perevod s anglijskogo. Patankar S.V. Computation of conduction and duct flow heat transfer. Innova-tive Research, Inc. 1991.).

Krylov D.A., Sidnjaev N.I., Fedotov A.A. Matematicheskoe modelirovanie raspredelenija temperaturnyh polej // Matematicheskoe modelirovanie. 2013. T. 25. # 7. S. 3–27.

Biskaborn B. K. et al. Permafrost is warming at a global scale //Nature communications. – 2019. – T. 10. – #. 1. – S. 264.

"Representative Concentration Pathways (RCPs)". IPCC. URL:

Koven C. D., Riley W. J., Stern A. Analysis of permafrost thermal dynamics and response to climate change in the CMIP5 Earth System Models //Journal of Climate. – 2013. – T. 26. – #. 6. – S. 1877-1900.

Sidnjaev N.I., Mel'nikova Ju.S., Hrapov P.V., Glasko A.V. Vlijanie temperaturnogo rezhima kriolitozony na nadezhnost' osnovanij. Problemy mashinostroenija i nadezhnosti mashin. 2012. # 3. S. 81-88.

Krylov D.A., Fedotov A.A. Temperaturnyj rezhim vechnomerzlogo grunta pod zdaniem so svajnym fundamentom // Vestnik MGTU im. N.Je.Baumana. Ser. «Estestvennye nauki». 2013. # 3. S. 106–116.

Stendel M., Christensen J. H. Impact of global warming on permafrost conditions in a coupled GCM //Geophysical Research Letters. – 2002. – T. 29. – #. 13. – S. 10-1-10-4.

Zimov S. A., Schuur E. A. G., Chapin III F. S. Permafrost and the global carbon budget //Science(Washington). – 2006. – T. 312. – #. 5780. – S. 1612-1613.

Turetsky M. R. et al. Permafrost collapse is accelerating carbon release. – 2019.

Tchebakova N. M. et al. Agroclimatic potential across central Siberia in an altered twenty-first century //Environmental Research Letters. – 2011. – T. 6. – #. 4. – S. 045207.


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