Resumen
The article studies the initial boundary value problem for a non-stationary one-dimensional heat equation that simulates the distribution of soil temperature in the area of Norilsk. The mathematical model is based on solid-liquid phase transitions. To determine the model parameters, data from the meteorological station and reports on engineering and geological surveys were used to obtain the necessary physical and thermophysical characteristics of the calculated area. For the numerical solution of the problem, the finite volume method (FVM) was used. The calculation was started on January 1 of the first year of observation of the soil temperature distribution. Simulation of the soil temperature distribution was carried out until the moment of reaching the non-stationary periodic mode. In order to analyze the temperature field, graphs of the temperature dependence on the depth for January and July of the 7 selected years of observation were constructed. 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 20 m. For a steady-state periodic mode, temperature dependences on the depth for each month are constructed and the depth of the active layer (0.5 m) and the depth of zero amplitudes (12 m) are found. The forecast of the ground temperature distribution for 2080 was modeled for two scenarios of Representative Concentration Pathway (RCP) of global warming: moderate RCP2.6 and negative RCP8.5. The RCP2.6 scenario showed an increase in the depth of thawing (freezing) by 0.1 m and a decrease in the depth of zero amplitudes by 1 m, as well as an increase of soil temperature at all depths by an average of 2°C. The results of calculations for the RCP8.5 scenario showed an increase in the depth of the active layer by 0.5 m (2 times compared to the present time) and a decrease in the depth of zero amplitudes by 4 m, the soil temperature increased by 5.7°C on average. In connection with the fuel spill that occurred in May 2020 from a storage tank in Norilsk due to subsidence of the foundation mainstays, the soil temperature distribution was modeled in 1980. The results showed an increase in the depth of the active layer since 1980 by 0.1 m, which could cause subsidence of the foundation piles of the storage tank. Further, a comparison of the long-term average monthly temperatures by decades was made, in which it was found that 2010-2020 has the largest number of the highest values of average monthly temperatures. This study further confirms the degradation of permafrost