| OCR Text |
Show - 9 - THE RATE OF DEPTH HOAR FORMATION Here we shall apply the relations deduced in the foregoing section to calculating the rate at which depth hoar crystals of a given size might be expected to form in a given temperature regime. Apparently depth hoar crystals grow from one side of existing snow crystals or grains ( See Yosida, op. cit.) in a direction opposite to the vapor pressure gradient, while these same grains lose material by sublimation on the other side. We define depth hoar formation as complete hoar crystals deposited from water vapor. Size of these crystals may thereafter continue to increase. The source of material for these crystals is the vapor flux through the snow, J, previously evaluated. In order to relate J to the gross temperature gradient, equation ( 10) is substituted in equation ( 11): Using the expression for p from equation ( 3), we obtain J--- Dw^= 2£- Ver^ r_ ( 15) For a given temperature gradient, J increases very rapidly with temperature because of the exponential term. The term 1/ T2 preceding the exponential is nearly cancelled by the dependence of Dw on T^' 2, and the two together have no significant role in establishing temperature dependence. The exponential term ( and the vapor pressure) is reduced approximately by a factor of two for each 8 C drop in temperature. Thus the rate of formation of depth hoar should be much larger in the lower parts of the snow cover where the temperature is close to 0° C. ( See previous discussion of this in Report C- 1.) |
