Table 3. Maximum frost depth, its earliest occurrence, and
time of complete thaw.
Earliest
Maximum
occurrence of
Complete
frost
max. frost
thaw of
penetration
penetration
system
(cm)
(day)
(day)
BCWarmest
10% mc no inclusion
13.18
84.88
102.80
sand inclusion
13.23
84.92
102.80
17% mc no inclusion
14.50
85.96
102.80
sand inclusion
14.64
86.12
103.10
sandy soil inclusion
14.58
86.00
103.20
25% mc no inclusion
14.94
86.75
105.00
inclusion
15.53
86.25
104.80
BCWarm
10% mc no inclusion
36.06
141.50
183.20
sand inclusion
35.34
140.90
181.20
17% mc no inclusion
39.24
142.20
184.50
sand inclusion
33.39/33.85
115.70/140.80
180.00
sandy soil inclusion
33.03/33.20
115.60/140.60
180.20
25% mc no inclusion
40.14
142.80
185.50
inclusion
31.90/31.84
115.30/140.50
181.00
BCCold
10% mc no inclusion
58.95
139.10
183.40
sand inclusion
57.83
139.00
181.00
17% mc no inclusion
61.17
139.20
184.60
sand inclusion
54.43
138.90
183.20
sandy soil inclusion
53.54
138.80
182.60
25% mc no inclusion
60.89
139.30
186.00
sand inclusion
49.97
138.80
184.10
mc: moisture content.
sensor cable will freeze during the winter. De-
volume of soil freezing can be considered in
pending on the soil's moisture content, a 7- to 9-
terms of the soil's diffusivity, which also increas-
cm-thick layer of unfrozen soil overlying the sen-
es with moisture content. These two effects, high-
sor cable will persist. Although the frost penetra-
er conductivity and higher diffusivity of released
tion is only slightly greater when a sand inclu-
latent heat in the moist soil when frozen, combine
sion is present, the thickness of the unfrozen soil
to offset the high latent heat and heat capacity of
layer is much less, only ∼0 to 2 cm, because the
the moist soil, which are impediments to the ad-
remaining depth is occupied by the relatively
vance of the freezing front. The net result is deep-
dry, less lossy sand. For this type of winter con-
er frost penetration the more moist the soil is.
dition, the presence of the sand inclusion should
Frost penetration in 10% or 17% moisture con-
result in better sensor system performance. The
tent silty soil under BC-Warmest conditions is lit-
advantage of having the sand inclusion present
tle different (less than 0.25 cm deeper) when a
is essentially unrelated to its effect on heat flow.
sand inclusion is present (Fig. 11a, b; Table 3). In
these soils the freezing front does not reach the
2. BC-Warm
top of the sand inclusion. Frost penetration in the
Simulations with this boundary condition are
25% moisture content silty soil does extend to the
representative of frost penetration in soil that be-
top of the inclusion (Fig. 11c). A rapid advance of
comes snow-covered during the winter. The
the freezing front, from 15 cm to 15.5 cm, follows
maximum frost depth is slightly dependent on
due to the lower latent heat and heat capacity of
the wetness of the soil; it is 36, 39 and 40 cm for
the dryer sand. The sand remains frozen for only
soil moisture contents of 10, 17 and 25%, respec-
a short time, ~4 days, because the boundary con-
tively, and no sand inclusion (Fig. 12, Table 3).
dition is already moderating, i.e., the soil surface
By the time (∼100 to 106 days, depending on
has begun warming.
moisture content of the soil) that the freezing
The BC-Warmest simulations show that when
front has reached a depth of 30 cm, the soil sur-
no inclusion is present, not all the soil above a
12
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