  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. 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. By analyzing the impact of an additional 0,5 degrees Celsius 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.
