| Summary: | The study of the initial-boundary value problem for a non-stationary one-dimensional heat conduction equation, which models the temperature distribution of permafrost soil and ice thickness, was carried out. A mathematical model is constructed taking into account solid-liquid phase transitions. To determine the parameters of the model, data from a meteorological station and reports on engineering and geological surveys were used, with the help of which the necessary physical and thermal characteristics of the computational area were obtained. The finite volume method was used to solve the problem numerically. For a steady-state periodic regime, dependences of average monthly temperatures on depth for each month are constructed, the depth of seasonal thawing and freezing, as well as the depth of zero amplitudes are found. The forecast of the temperature regime for 2100 is modeled according to the selected scenarios of the Representative Concentration Pathway (RCP) of global warming. The scenarios are based on the IPCC AR5 and SP databases, as well as taking into account the existing policy framework and the stated policy intentions of the IEA Stated Policies Scenario (STEPS). The modeling performed clearly confirmed the impact of global warming on the cryosphere of our planet.
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