(7.41)

where *f*l is the fraction of the snowpack which is wet. Further, we have

1 ∂ Ds

=- s

(7.42)

ηc

where *P*s is the average load pressure within the snowpack, and ηc is a viscosity

coefficient, which has the form

ηc = η0 exp ( 0.08*T *+ 28ρt )

(7.43)

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).

The general applicability of the relationship *k*w ∝ *S*enc is discussed in depth in Mualem

(1978). Since a way to determine *n*c from the available meteorological and lysimeter data

could not be found, FASST simply uses a constant *n*c, 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

by

2*k*1 (T f - *T*s ) t

(7.44)

ρl f

the refrozen state, *T*f is the temperature of fusion, *T*s is the surface (ambient air)

temperature, *t *is time, ρ is the density of the medium, and *l*f is the latent heat of fusion.

snow of density 0.3 *g/cm*3. *T*f is taken as 0 *C*, while *T*s is taken as the average

temperature over the current period of freeze depth propagation. *l*f is taken as 333.05 *J/g*,

65