Resumen
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