Figure 12. Thermal state at end of melting (a) and
Figure 11. Bottom thaw of permafrost.
long-term equilibrium (b).
+ δ. The maximum thaw rate occurs if all of the geothermal heat flow goes into melting, but this is physi-
cally impossible.
Given sufficient time, the entire permafrost volume melts and the soil temperature is as shown in Figure
12--curve a. A layer of soil of thickness Xo + δo will be thermally modulated. The temperature gradient for
depths greater than Xo+ δo is G, the geothermal gradient. Also shown in Figure 12 is the dashed line (curve
b) denoting the equilibrium temperature distribution with the same geothermal gradient but no cooling.
This state would be reached if the surface remained at Tf for a long time after thaw was completed. Clearly,
the sensible heat that must be removed in the modulated case (curve a) will be less than that for the original
freeze discussed earlier (curve b). This means that cooled soil (after cyclic melting or warming) will freeze
much faster with the same mean surface temperature. This temperature modulation will only be significant
for zones of relatively shallow permafrost, for which appreciable thaw can take place during the intergla-
cials of about 15,000 years. The equations and solution are discussed in Appendix B.
Syngenetic growth of permafrost
Syngenetic growth of permafrost oc-
curs when material is deposited at the
surface while freezing is in progress.
This is inherently a much more efficient
freeze process and the growth of frozen
layers can be greatly accelerated. Figure
13 shows a sketch of the process with the
surface deposit laid down such that the
surface, held at a constant temperature
Ts, is moving at a constant velocity U.
The total frozen zone at any time is equal
to the material frozen at the interface
X(t), plus the depositional layer Ut. The
syngenetic system will be inherently un-
stable with no equilibrium solution. If
the frozen zone should equal the hetero-
genetic steady-state value (U = 0), the
motion of the upper surface will cause
Figure 13. Geometry and coordinate system for freeze of a
semi-infinite medium with moving upper surface.
melting at the base of the permafrost.
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