Deep Heating of a Snowpack by Solar Radiation

Abstract

The observed gradual change in the Earth’s climate most noticeably affects the snow cover and ice sheets in the polar regions, especially during the long polar summer, when solar radiation leads to considerable increase in temperature and partial melting at some distance from the snow or ice surface. This effect, which in the polar regions is more pronounced in the snow cover, deserves serious attention as an important geophysical problem. In this article, for the first time, a theoretical analysis is made of the conditions under which the absorption of directional radiation penetrating a weakly absorbing scattering medium has a maximum at some distance from the illuminated surface. It is shown that the maximum absorption of radiation inside an optically thick medium exists only at illumination angles less than 60° from the normal. An analytical solution was obtained that gives both the magnitude of this maximum absorption and its depth below the illuminated surface. Calculations of solar radiation transfer and heat propagation in the snow layer are also performed. Various experimental data on the ice absorption index in the visible range are taken into account when determining the optical properties of snow. To calculate the transient temperature profile in the snow layer, the heat conduction equation with volumetric absorption of radiation is solved. The boundary conditions take into account the variation of solar irradiation, convective heat transfer, and radiative cooling of snow in the infrared transparency window of the cloudless atmosphere. The calculations show that the radiative cooling should be taken into account even during the polar summer.