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)

sumes fixed geothermal heat flow to the freezing inter-

face, and starts with permafrost depth far less than equi-

librium. All of these approximations overestimate the

freeze rate. The second curve of Figure 22 shows the sig-

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, ∆*T*1 = 10.0C.

Consider the effect of previous cooling at

Prudhoe Bay. If the equivalent geothermal gra-

dient is *G *= 0.0220C, then the time to reach

541 m is 78,940 years. The results of three pos-

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

* Soil properties for Prudhoe Bay, ∆*T*1 = 29.3C.

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, ∆*T*1 = 29.27C, *G *= 0.0286,

α1 = 57.99 m2/yr, then *X*e =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 *S*T = 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.

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, *T*s = 23.5C, *q*g = 0.042 W/m2, and

assume coarse-grained soil with *k*g = 5.86 W/m K. The results of the calculation are shown in Table 6.

19

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