Solar-heating rates and temperature profiles in Antarctic snow and ice

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Abstract
Observations of temperature maxima at about 10 cm depth in cold Antarctic snow during summer have previously been explained by proposing that solar heating is distributed with depth whereas thermal infrared cooling is localized at the surface (the “solid-state greenhouse”). An increase in temperature from the surface to 10 cm depth (ΔΤ ≈ 4 K) found by Rusin (1961) on the Antarctic Plateau was successfully reproduced by Schlatter (1972) in a combined radiative-transfer and heat-transfer model. However, when we improve the model’s spectral resolution, solving for solar radiative fluxes separately in 118 wavelength bands instead of just one “average” wavelength, ΔΤ shrinks to 0.2 Κ and moves toward the surface, indicating that the solid-state greenhouse is largely an artifact of inadequate spectral resolution. The agreement between Schlatter’s broad-band model and Rusin’s measurement suggests that the measurement is inaccurate, perhaps due to solar heating of the buried thermistors. Similar broad-band models which have been applied to the icy surface of Jupiter’s satellite Europa are also shown to overestimate the solid-state greenhouse by a factor of about 6.The reason that the solid-state greenhouse effect is insignificant in the case of Antarctic snow is that the wavelengths which do penetrate deeply into snow (visible light) are essentially not absorbed and are scattered back to the surface, whereas the wavelengths that are absorbed by snow (near-infrared) are absorbed in the top few millimeters. The conditions needed to obtain a significant solid-state greenhouse are examined. The phenomenon becomes important if the scattering coefficient is small (as in blue ice) or if the thermal conductivity is low (as in low-density snow, such as near-surface depth hoar).