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Show - 9 - Referring to Yosida1s microscopic air temperature gradient, GQ, it is seen that the microscopic vapor pressure gradient between two adjacent ice particles in the snow cover may be determined if G0 is known and the vapor pressure in contact with each particle is assumed to be the saturation vapor pressure over ice at the appropriate temperatures. From the character of the saturation vapor pressure « urve for ice, it is immediately apparent that the magnitude of this vapor pressure gradient will be dependent on the absolute temperature as well as on GQ. The wide variation in this vapor pressure gradient for a given temperature gradient which can be expected over the range of temperatures found in natural snow covers is illustrated in Figure 1, Empirical observations in the field confirm this dependency. Rate of depth hoar formation is commonly found to be highest at the bottom of a shallow winter snow cover, where the temperature is highest, and diminishes toward the surface. The decrease in air density accompanying decrease in the ambient air pressure reduces the relative contribution of the air to heat transfer in snow and allows freer diffusion of water vapor. This effect becomes significant at high altitudes, and presumably contributes to the empirically observed fact that depth hoar formation is more common at high altitudes, ( A severe temperature environment and shallow snow cover can also be responsible for this fact.) In order to obtain conveniently the magnitude of this altitude dependency, reference is made to Bowen's ( 12) analysis of relative heat transfer by diffusion of air and water vapor, which showed that Q7" - u ^ b V7TF) 760 where Q, = sensible heat transfer |
