calculated, a weighted average of the two is taken as the average crystal volume within
the pack.
7.2.2 Permeability
The most exhaustive search published to date for the permeability of snow as a function
of grain size and snow density probably comes from the work of Shimizu (1970), in
which he considered previous models of snow permeability produced by Bader (1954),
Bender (1957), and Kuroiwa (1968), as well as a range of his own tests, and came to the
conclusion
kw0 = 0.077d 2 exp ( -7.8ρs )
(7.37)
where d is the snow grain diameter (cm) and ρs is the specific gravity (g/cm3). In our
model, d is computed as
3
d = 23
(7.38)
Vav
4π
where Vav is the average crystal volume computed above. ρs is taken as the density of
frozen water within the snowpack, either as computed in the snow depth prediction
routine, or as a constant 0.3 g/cm3 if snow depth is not being computed.
7.2.3 Irreducible Water Saturation
In the FASST snow module, the irreducible water saturation of snow is computed as a
fraction of total volume. Kattlemann (1986) reported that Sulahrie (1972) found a value
as high as 40% in some cases, while most authors have reported measurements in the
range of 0% to 10%.
7.2.4 Snow Depth
Snow depth prediction equations are based on the form used by Jordan (1991a), which in
turn come from Anderson (1973). Both SNTHERM.89 (Jordan 1991a) and Anderson's
earlier model break the snow into layers based on age, density, and crystal structure,
while here the simplicity of a uniform bulk snowpack is maintained. The model predicts
the rate of densification, then adjusts the snowdepth accordingly. The equations used are
as follows
1 ∂ Ds
= -2.778 10-6 c1c2 exp [-0.04T ]
(7.39)
Ds ∂ t metamorphism
where Ds is the depth of snow, t is time (s), T is temperature (C), and
ρi ≤ 0.12
c1 = 1
(7.40)
c1 = exp ⎡-46 ( ρi - 0.15)⎤
ρi ≥ 0.12
⎣
⎦
where ρi is the density of water in the frozen state within the snowpack (g/cm3) and
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