c2 = 1 + fl
where fl is the fraction of the snowpack which is wet. Further, we have
1 ∂ Ds
where Ps is the average load pressure within the snowpack, and ηc is a viscosity
coefficient, which has the form
ηc = η0 exp ( 0.08T + 28ρt )
where ρt is the total density of the solid and liquid phases of the snow, and η0 = 5E+08.
Also calculated with snow depth are ρi (the density of ice within the snowpack), ρt (the
density of ice plus irreducible water saturation plus mobile water saturation), φ (the total
pore volume as a fraction of total volume), φe (pore volume excluding pore volume filled
with immobile water when meeting irreducible saturation requirements, as a fraction of
total volume), and SWE (the snow water equivalent).
7.2.5 Effective Saturation Exponent
The general applicability of the relationship kw ∝ Senc is discussed in depth in Mualem
(1978). Since a way to determine nc from the available meteorological and lysimeter data
could not be found, FASST simply uses a constant nc, and its value is left up to the user,
(with a default of 3.3).
The refreezing algorithm uses a time-averaged value of temperature over the most recent
period in which the snowpack is predicted to be less than isothermal, and a depth-
averaged value of saturation, along with bulk-approximated thermal conductivity of
snow, to calculate the depth of penetration of the refreezing front. Since these values are
updated every time step, the depth of penetration produced should be accurate enough.
An analytical solution of the well-known Neumann type (Carslaw and Jaeger 1959) given
2k1 (T f - Ts ) t
where X is the depth of the freezing front, k1 is the thermal conductivity of the medium in
the refrozen state, Tf is the temperature of fusion, Ts is the surface (ambient air)
temperature, t is time, ρ is the density of the medium, and lf is the latent heat of fusion.
k1 is taken to be 0.0045 J/s cm⋅C, which is approximately the thermal conductivity of
snow of density 0.3 g/cm3. Tf is taken as 0 C, while Ts is taken as the average
temperature over the current period of freeze depth propagation. lf is taken as 333.05 J/g,