Resumen
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°?) 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 ° ? 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.