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This report discusses the one-dimensional freezing of dry snow/ wet snow systems for the condition first examined by Stefan: the problem of heat conduction with phase change. There are two systems of internal freezing: one is a closed system of temperature rise in a dry snow layer sandwiched between upper and lower wet snow layers; the other an open system of freezing of a thin wet layer provoked mainly by an upper dry snow layer facing the atmosphere at its surface. The latter negatively concerns the release of some avalanches, because the weak layers of surface avalanches in districts where the melt-freeze metamorphism prevails (as in the Horuriku district of Japan) may be the thin wet granular snow layers.
Numerical results are given for different conditions of internal freezing. A comparison with field observations reveals the fundamental aspect of this phenomenon and the possibility of avalanche release.