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.

An effect of a snow cover on solar heating and melting of lake or sea ice

“…It is interesting that the maximum heating of snow occurs in the second half of the day and even at d snow 200 mm only the surface layer of snow 2-3 mm thick melts. This result is qualitatively different from the case of thick snow cover considered in (Dombrovsky et al, 2019;Dombrovsky and Kokhanovsky, 2022) due to heat sinking into the ice layer. Of course, this heat sink is more noticeable in case of a thin snow layer, but remains significant even at d snow 200 mm.…”

“…The resulting transport RTE looks like that for the hypothetic isotropic scattering but with the transport scattering coefficient (Dombrovsky, 2012;Dombrovsky, 2019). It should be recalled that the transport approximation has been successfully employed in diverse problems of radiative transfer in thermal engineering (Dombrovsky et al, 2017;Dombrovsky et al, 2020), biomedicine (Tuchin, 2007;Sandell and Zhu, 2011;Dombrovsky et al, 2012;Jacques, 2013;Eisel et al, 2018;Dombrovsky, 2022), and geophysics (Dombrovsky and Kokhanovsky, 2022;Dombrovsky and Kokhanovsky, 2023;Dombrovsky et al, 2019;.…”

“…The influence of uncertainty in the experimental values of the ice absorption index on the computational data for solar heating of snow and ice has been analyzed by Dombrovsky and Kokhanovsky (2022), Dombrovsky and Kokhanovsky (2023). It was shown that the discrepancy between the data of (Warren and Brandt, 2008;Picard et al, 2016) in the λ < 0.6 μm range does not significantly affect the results of calculations.…”

“…It is assumed that optical properties of ice do not change along the horizontal ice surface and the radiative transfer along the surface of an ice-covered lake may not be considered. The 1D model for the propagation of obliquely incident radiation in an ice layer containing gas bubbles has been described recently by Dombrovsky and Kokhanovsky (2022). It is assumed that there are no any bubbles in water, and scattering by a small amount of plankton is insignificant.…”

“…In addition, at low altitudes, unlike in high mountains, not only direct solar radiation but also diffuse radiation from the light-scattering atmosphere should be taken into account. In this problem, we use the same data as in the papers by Dombrovsky et al (2019) and Dombrovsky and Kokhanovsky (2022) for the summer solstice during the Arctic polar summer at latitude 70 o .…”