Zur Theorie des Wärmehaushaltes strahlungsdurchlässiger Medien

In view of the fact that large areas of the earth's surface are temporarily or permanently covered by a medium pervious to radiation, i.e. water, snow or ice, attention is directed to that special feature of the heat economy of these media having to do with radiation balance and heat transfer. Primarily, the purpose of the theory is to find an explanation for the observed distribution of temperature within these media. A first attempt to solve this problem was previously made by the author (REUTER 1948 a) in a study of the heat economy of snow cover. The essential basis of the present as well as the earlier treatment lies in the assumption that snow, ice and water, while pervious to insolation, are nevertheless impervious to outgoing radiation. The present paper treats only the simple case of constant incoming penetrating radiation and at the same time a constant effective outgoing radiation from the surface of the medium. One of the principal results is that the temperature maximum produced during the heating process does not appear at the surface, but rather at some depth below. Although the case of water is not treated in this report, the results obtained for ice may be applied, with slight modification, to the case of calm pure water in view of the use of the same coefficients of absorption for both water and ice.