Analysis and prediction of changes in the temperature of the pure freshwater ice column in the Antarctic and the Arctic

Anatoliy Fedotov, Vladimir Kaniber, Pavel Khrapov


This paper investigates the initial boundary value problem for a non-stationary one-dimensional heat equation that simulates the temperature distribution in freshwater ice near the Earth's poles. The mathematical model has been constructed taking into account solid-liquid phase transitions. Data from meteorological stations were used to determine the model parameters, with the help of which the necessary physical and thermophysical characteristics of the computational domain were obtained. For the numerical solution of the problem, the finite volume method (FVM) was used. In order to analyze changes in the temperature field of ice and determine the time required to reach a non-stationary periodic regime, graphs of temperature versus depth were plotted for January at two stations. The study of the results showed that it takes about 50 years of modeling with constant initial data for the temperature of an ice layer up to 20 m deep to reach the periodic regime. For the obtained periodic regime, the temperature versus depth dependences for each month were plotted, and the depth of the active layer, as well as the depth of zero annual amplitudes were found for each meteorological station. A forecast of the ice temperature regime for 2100 was modeled for three Representative Concentration Pathway (RCP) scenarios of global warming: moderate RCP2.6, corresponding to the current emissions of RCP7 and adopted at the Paris Agreement in 2015 RCP1.9. The scenarios are based on the IPCC AR5 and SSP databases, as well as on the existing policy frameworks and declared political intentions of The IEA Stated Policies Scenario (STEPS). The plotted graphs clearly demonstrated that even a moderate RCP2.6 scenario (warming by 2°С) can lead to a serious reduction in the ice cover area, while the RCP7 scenario will lead to even more unsatisfactory consequences. In turn, the scenario of limiting climate warming to 1,5 ° С from pre-industrial levels (RCP1.9) would significantly slow down ice thawing. By analyzing the impact of an additional 0,5°C of warming on other areas, a reduction in the full range of risks to humanity and the planet as a whole becomes evident with the proper efforts of the global community. Thus, the conducted modeling has confirmed the need to reduce the rate of global warming.

Full Text:



Hoegh-Guldberg O. et al. Impacts of 1.5 C global warming on natural and human systems //Global warming of 1.5 C. An IPCC Special Report. – 2018.

Khrapov P. V., Kaniber V. V. Comparative analysis of climate change in the Antarctic and Arctic //International Journal of Open Information Technologies. – 2019. – Т. 7. – №. 8. – P. 32-43.

RSN 67–87. Engineering surveys for construction. Making a forecast of changes in the temperature regime of permafrost by numerical methods. Moscow: Gosstroy RSFSR, 1987.40 p.

"Weather and Climate – The Climate of Amundsen–Scott". Weather and Climate (Погода и климат) (in Russian). Retrieved April 20, 2021.


"Weather and Climate – The Climate of Esperanza Base". Weather and Climate (Погода и климат) (in Russian). Retrieved April 20, 2021.



Popov S. V. et al. The structure of the upper part of the glacier in the area of the planned runway of Mirny station, East Antarctica (based on materials from 2014/15) // Cryosphere of the Earth. - 2017. - T. 21. - No. 1. - P. 73-84.

van den Broeke M. Depth and density of the Antarctic firn layer //Arctic, Antarctic, and Alpine Research. – 2008. – Т. 40. – №. 2. – P. 432-438.

"Weather and Climate-The Climate of Kap Morris Jesup". Weather and Climate (Погода и климат) (in Russian). Retrieved April 20, 2021.


Farrell S. L. et al. A first assessment of IceBridge snow and ice thickness data over Arctic sea ice //IEEE Transactions on Geoscience and Remote Sensing. – 2011. – Т. 50. – №. 6. – P. 2098-2111.

All-Russia Research Institute of Hydrometeorological Information - World Data Center (ARIHMI-WDC), Roshydromet URL: Retrieved April 20, 2021

"Weather and Climate-The Climate of Hayes Island" (in Russian). Weather and Climate (Погода и климат) (in Russian). Retrieved April 20, 2021.


Lavrent'ev I. I. et al. The thickness of the snow cover on the East Grönfjord glacier (Spitsbergen) according to radar measurements and standard snow surveys // Ice and Snow. - 2018. - T. 58. - No. 1. - P. 5-20.

Bekhovykh L.A., Makarychev S.V., Shorina I.V., Fundamentals of Hydrophysics. - 2008.

CNaR 2.02.04-88 Construction norms and rules. Foundations and foundations on permafrost soils. Updated edition (SP 25.13330.2012). Moscow: State Construction Committee of the USSR, 1990.114 p.

Shumsky P. A. Fundamentals of structural ice science: Petrography of fresh ice as a method of glaciological research. - Publishing house of the Academy of Sciences of the USSR, 1955.

Nazintsev Yu. L., Panov VV Phase composition and thermophysical characteristics of sea ice. - 2013.

Vargaftik NB Handbook of thermophysical properties of gases and liquids. - Ripol Classic, 1963.

Mikheev MA Mikheeva IM Basics of heat transfer. M // Energy. - 1977 .-- P. 343.

Samarskiy A.A., Vabishchevich P.N. Computational heat transfer. M .: Book House "Librokom", 2014. 784 p.

Patankar S.V. Computation of conduction and duct flow heat transfer. Innova-tive Research, Inc. 1991.

Krylov D.A., Sidnyaev N.I., Fedotov A.A. Mathematical modeling of the distribution of temperature fields // Mathematical modeling. 2013. Vol. 25, No. 7, pp. 3–27.

Biskaborn B. K. et al. Permafrost is warming at a global scale //Nature communications. 2019. Т. 10. №. 1. P. 264.

Brandt R. E., Warren S. G. Temperature measurements and heat transfer in near-surface snow at the South Pole //Journal of Glaciology. – 1997. – Т. 43. – №. 144. – P. 339-351.

Fedotov A. A., Kaniber V. V., Khrapov P. V. Forecast of the soil temperature in permafrost in response of climate warming //International Journal of Open Information Technologies. – 2020. – Т. 8. – №. 6. – P. 53-61.

"Explainer: How 'Shared Socioeconomic Pathways' explore future climate change". Carbon Brief. 2018-04-19. Retrieved 2021-04-20.

IPCC, 2014: Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151 p URL: Box 2.2

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

Fedotov A. A., Kaniber V. V., Khrapov P. V. Analysis and forecasting of changes in the soil temperature distribution in the area of the city of Norilsk //International Journal of Open Information Technologies. – 2020. – Т. 8. – №. 10. – P. 51-65.

Hausfather, Zeke; Peters, Glen (29 January 2020). "Emissions – the 'business as usual' story is misleading". Nature. 577 (7792): 618–20. doi:10.1038/d41586-020-00177-3. PMID 31996825

Schwalm, Christopher R.; Glendon, Spencer; Duffy, Philip B. (2020-08-18). "RCP8.5 tracks cumulative CO2 emissions". Proceedings of the National Academy of Sciences. 117 (33): 19656–19657. doi:10.1073/pnas.2007117117. ISSN 0027-8424. PMID 32747549.

Intergovernmental Panel on Climate Change (IPCC) Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC, 2014)

Working Group III of the Intergovernmental Panel on Climate Change (IPCC WGIII). AR5 scenario database version 1.0.2 (IIASA, 2014) (available at:

K. Riahi, D. P. Van Vuuren, E. Kriegler, et al. The shared socioeconomic pathways and their energy, land use, and greenhouse gas emissions implications: an overview. Global Environmental Change 42, 153-168 (2017).

International Institute for Applied Systems Analysis (IIASA). SSP database (shared socioeconomic pathways)—version 2.0 (IIASA, 2018) (available at:

International Energy Agency (IEA). World Energy Outlook 2020 (IEA, 2020) URL:

Stocker T. F. et al. Technical summary //Climate change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. – Cambridge University Press, 2013. – P. 33-115.

Pielke JR., Roger (April 10, 2021). "Most plausible 2005-2040 emissions scenarios project less than 2.5 degrees C or warming by 2100". doi:10.31235/ Retrieved 2021-04-26

Allen M. et al. Technical Summary: Global warming of 1.5° C. An IPCC Special Report on the impacts of global warming of 1.5° C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty. – 2019.


  • There are currently no refbacks.

Abava  Absolutech Convergent 2020

ISSN: 2307-8162