Geoscience Reference
In-Depth Information
Figure 2.30 Frost penetration into a soil: frozen soil and soil moisture above the
freezing front, liquid soil moisture below the freezing front.
b) Because the snow deck thickness may vary from place to place, even within one
ield, the 2 cm used under (a) is rather uncertain. Therefore, estimate the temperature
difference over the snow deck also for layer thicknesses of 1 and 3 cm.
Soil Freezing
Another situation in which solid water and phase changes play a role is the freezing
of a soil. If the temperature in the soil is cooled to below the freezing point of water,
the soil moisture that is present will freeze. Owing to this phase change latent heat of
freezing is released, which will warm the soil again. Freezing takes place at the inter-
face between frozen soil and nonfrozen soil, the freezing front (see Figure 2.30 ). To
cool the soil further, this released latent heat needs to be removed. It can be removed
only upward, as the sink of energy is located at the surface. Thus, the downward
movement of the freezing front is limited by the ability of the soil to remove the
released latent heat.
Let us assume a linear temperature proile above the freezing front (i.e., a constant
T z
z
soil heat lux with depth, see Eq. ( 2.29 )): Tz t
(,)
=+ −
0
d
(
TT
)
, where T 0 is the
d
f
0
f
temperature at the soil surface, T f is the temperature at the freezing front (0 ºC) and z f
is the depth of the freezing front, which is a function of time. The rate at which latent
heat is released when the soil moisture freezes ( Q released ) depends on the soil moisture
content θ and the rate at which the freezing front moves downward:
d
d
z
t
Q
= θρ
L
f
(2.47)
released
w
f
where L f is the latent heat of fusion and ρ w is the density of liquid water. The amount
of heat that can be removed upward is 5 :
T
T
=
T
z
f
0
Q
=
λ
λ
(2.48)
removed
s
s
z
d
f
=−
T
z
5 Regarding the sign, note that in general the heat transport is Q
λ
, which would be negative (upward) in this
s
case. Hence Q removed = ‒ Q .
d
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