Considerable information on the permafrost is available from oil wells in the Prudhoe Bay, Alaska, area

(Lachenbruch et al. 1982). Using the actual permafrost data, we note that the property ratios for ε = 0.379

(Tables A1 and A2) are very close to measured and estimated values (Lachenbruch et al. 1982). Some tem-

perature possibilities for Prudhoe are listed in Table 3. Figures 16a and b can be used to estimate the per-

mafrost formation time, depending upon the temperature chosen.

At Prudhoe Bay, Alaska, the permafrost has the following present conditions:

ε = 0.379

α1 = 58.89 m2/yr

measured *k*21 = 0.5795

measured present permafrost thickness, *X*p = 599.3 m.

Then, the equilibrium permafrost thickness is

∆*T*1

= 602.8 m.

The calculated equilibrium thickness is essentially the same as the measured value. How long would it take

to reach this depth if the surface temperature had been *T*s = 10.99C for an indefinite period? The nature

of the solution is such that the final equilibrium values will be reached only after very long times. From

Figure 18 we find the time to reach 90% of equilibrium (542.0 m) is

2

* G*

*t *= 241.2

τ = α1

∆*T*1

thus *t *= 500,740 years. This time is obviously quite long and suggests that the present climate of Prudhoe

Bay is probably considerably warmer than it has been on average over the past glacial cycles. Such warm-

ing over the past 15,000 years is widely accepted.

Prudhoe Bay, with the Brigham and Miller (1983) paleotemperature scenario, has the following: *T*s =

13.69C for 225,000 years before warming to 11C in the last 15,000 years. For this case *X*e = 763.5 m.

For *t *= 225,000 years, τ = 67.3. From Figure 16, with *S*T = 0.1827, we read σ = 1.412. Thus, in 225,000

years the permafrost will grow to *X *= 626.5 m. This value will then slowly decay to the new equilibrium of

602.8 m over 15,000 years. This requires a melt rate of 1.58 mm/yr. This value is well within the estimated

average thaw rate of 2.5 mm/year for this case (see Appendix D). Note that a lower surface temperature

will greatly accelerate growth since the new equilibrium depth will be greater than before. Hence, a much

larger fraction of the growth will be during the early, rapid growth stage.

Figure 22 shows the permafrost thickness at Prudhoe Bay after six glacial cycles with some typical fea-

tures of permafrost growth demonstrated. First, the initial permafrost growth is quite rapid, reaching a

thickness of 570 m after 120,000 years, with the paleotemperature model of Figure 7a. The thickness then

slowly approaches an equilibrium value of 739 m but it will surpass the present thickness of 600 m after

about 185,000 years. Thus, a paleotemperature model as cold as that of Figure 7b will yield permafrost that

is too thick. Also shown is the finite difference prediction of Osterkamp and Gosink (1991), using Figure 6

(which has the same mean temperature as Fig. 7a) and starting with 600 m of permafrost, that indicates

much faster permafrost growth and thicker permafrost. Their quasi-steady model neglects sensible heat, as-

18