Mathematical Modeling of Glacier Melting in the Arctic with Regard to Climate Warming

• Main Authors: Anatoliy Fedotov, Vladimir Kaniber, Pavel Khrapov
• Format: Article in Journal/Newspaper
• Language: Russian
• Published: The Fund for Promotion of Internet media, IT education, human development «League Internet Media» 2021
• Subjects: arctic; ice; glacier; pole; global warming; ablation; melting; thawing; forecast; prediction; temperature regime; non-stationary periodic regime; modeling; thaw depth; active layer; depth of zero annual amplitudes; heat equation; finite volume method; Electronic computers. Computer science; QA75.5-76.95; Arctic; Global warming; Ice cap
• Online Access: https://doi.org/10.25559/SITITO.17.202104.1007-1021; https://doaj.org/article/ce3d594000bd41eababeb2afb7d41a4d

The paper studies the initial boundary-edge problem for the non-stationary one-dimensional thermal conductivity equation, which models the temperature distribution in the glacier. 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 calculation area were obtained. The finite volume method was used for numerical solution of the problem. The non-stationary periodic regime was investigated, temperature-depth dependences were plotted for each month and the depth of the active layer and the depth of zero annul amplitudes for two glaciers: the Vavilov Ice Cap and the Austre Gronfjordbreen were found. Glacier temperature regime forecast for the year 2100 are modelled for three global warming scenarios: a moderate RCP2.6, the RCP7 corresponding to current emissions and the RCP1.9 adopted at the Paris Agreement in 2015. The scenarios are based on the IPCC AR5 and SSP databases, and on the existing policy framework and stated policy intentions The IEA Stated Policies Scenario (STEPS). The plotted graphs clearly show that even the moderate RCP2.6 scenario (2°C warming) can lead to noticeable glacier thawing, while the RCP7 scenario would lead to unprecedented consequences. In turn, a scenario limiting climate warming to 1.5°C from pre-industrial levels (RCP1.9) would markedly slow glacial thawing. Having analysed the irreversible degradation of the ice cover at a warming of an additional 0.5°C, and considering the adverse effects of this warming on many areas, the need to contain the rate of temperature increase is clear. The simulations have clearly confirmed the impact of global warming on our planet's cryosphere.