800
Osterkamp and
Prudhoe Bay, Alaska
Gosink (1991)
Permafrost Growth
600
Ts (C)
Glacial
Cycle
I, II
G
11.00
I
11.00
Present
III, IV
G
13.76
13.76 Glac.
Permafrost
400
T =
s
I
10.00
10.00 IG
Thickness
V
G
9.00
T = 11.00
s
I
8.00
VI
G
13.76
I
11.00
200
I
II
III
IV
V
VI
0
7 10 5
0
1
2
3
4
5
6
Time (yr)
Figure 22. Growth of permafrost at Prudoe Bay, Alaska; effect of paleotemperature scenarios.
sumes fixed geothermal heat flow to the freezing inter-
Table 4. Effect of previous cooling on perma-
face, and starts with permafrost depth far less than equi-
frost growth time.* X = 541.0 m.
librium. All of these approximations overestimate the
Time
freeze rate. The second curve of Figure 22 shows the sig-
Case
(years)
Comment
G
nificant effects if the paleotemperature model is modified
No pre-cool
0.0286
486,100
uses eq 10
by only a small amount. The predicted permafrost thick-
Pre-cool
0.0220
78,900
uses eq 10
ness will reach present values after about 640,000 years
Pre-cool
0.0286
105,400
uses eq B15
eq 27, U = 1 mm/yr
Syngenetic
0.0286
172,500
and will tend to oscillate about this value.
* Soil properties for Prudhoe Bay, ∆T1 = 10.0C.
Example 3
Consider the effect of previous cooling at
Table 5. Formation time of deep permafrost.*
Prudhoe Bay. If the equivalent geothermal gra-
Xe = 1813 m.
dient is G = 0.0220C, then the time to reach
Time
541 m is 78,940 years. The results of three pos-
Case
(years)
Comment
G
sibilities are shown in Table 4. Note the very
No pre-cool
0.0286
4,190,600
uses eq 10
large effect of previous cooling or cyclic ther-
Pre-cool
0.0220
488,900
uses eq 10
mal modulation.
Pre-cool
0.0286
358,900
uses eq B15
eq 27, U = 1mm/yr
Syngenetic
0.0286
784,100
Neumann (φ = 0)
0.0
64,800
absolute minimum time
Deep permafrost
* Soil properties for Prudhoe Bay, ∆T1 = 29.3C.
Example 1
Consider the case of very thick permafrost,
on the order of 1600 m. Let the properties be those of Prudhoe Bay but ε = 0.4, ∆T1 = 29.27C, G = 0.0286,
α1 = 57.99 m2/yr, then Xe =1813 m. The value of the surface temperature chosen is on the order of 12C
less than present winter temperatures experienced in parts of Canada, Russia and Greenland, although it is
doubtful that such temperatures could have persisted for 1 million years. The value used illustrates the long
time needed to form deep permafrost by conduction alone. We will find the time required to form 90% of
the permafrost or 1632 m. The calculations are as before, with ST = 0.4 (see Fig. 15 for the case without
previous cooling). The results are given in Table 5. The formation time is very long, even with previous
cooling. This example used Prudhoe Bay properties and geothermal gradient, which could be significantly
different at a site in Siberia with deep permafrost.
Example 2
Consider the question of the maximum permafrost thickness that is probable. This will occur if the fro-
zen thermal conductivity is large, the geothermal heat flow and latent heat are low, and the surface temper-
ature is minimal (within the constraints discussed earlier). Let ε = 0.2, Ts = 23.5C, qg = 0.042 W/m2, and
assume coarse-grained soil with kg = 5.86 W/m K. The results of the calculation are shown in Table 6.
19
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