OCR Text |
Show - 3 - VAPOR TRANSFER IN SNOW The flux of water vapor through a unit area normal to the z axis ( where z is measured in the direction of the gradient of temperature) ignoring thermal diffusion, can be expressed as cr- - D # § <•> where p is the vapor pressure and D is the apparent diffusion coefficient. The influence of snow structure on D will be discussed later. Assuming that the change in D with distance z is small, the rate of accumulation of vapor within a region can be written as - § T = Df£ - r ( 2) where r is the rate at which vapor is deposited in the solid form. Because of the rapid formation and condensation of vapor, p may be taken as the equilibrium vapor pressure with very little error. This quantity, ignoring the small effects due to high surface area volume ratios, may be taken as a function of temperature only, p = p^ ' , and may be approximated by p= se ( 3) where L, the latent heat of vaporization, and the constant s are assumed to be independent of temperature. The temperature may be expressed as a function of coordinate z by means of the temperature profile T = T( z). Since the temperature profile is a slowly varying function of time, dp/ fit maY be set equal to zero and S p I& 2T may be written as cI p/ di. 2' * Equation ( 2) can consequently be written as |