First, the growth of the underlying ice lens will prevent the permafrost sheet from fully settling back into its previous position. During the spring to summer uplift any cavities formed beneath the permafrost will at the high pore water pressures have water extruded into them. In the following autumn to winter drop in temperature this water lens would freeze to form the annual layer of what eventually becomes a stratified ice lens beneath the pingo.
Second, the differential properties of ice in compression and tension will ensure that during the following cooling season much of the thermal energy will almost immediately go into producing tensile strain in the permafrost sheet. During the compressive buckling a major part of the internal strain energy will have been expended in the lifting of the permafrost sheet. With the permafrost being able to sustain high compressive stress there will have been considerable visco-plastic relief of the compressive energy during the warming uplift. Together with flexural cracking these high rates of energy relief will mean that when the temperatures start to tumble in early autumn the permafrost will almost immediately want to develop membrane tensile stress associated with the now restrained contraction of the permafrost ice. As suggested in Figure 1(d) the seasonal drop in temperature would tend to relieve the buckled layer of the compressive stress which will have in any case dropped by any lengthening that accompanies the development of the upward buckle – the so called dilation effect noted by Mackay (1998). Being weak in tension the ice will develop fissures and cracks whose aggregate widths will be in proportion to the drop in temperature. It is possible that these tensile strains could produce radial crack patterns at the crown of the dome and polygonal but basically circumferential cracks around the base periphery. In much the same way as in the development of ice-wedge-polygons, these cracks will attract moisture and other precipitation which will be converted to ice. This has the effect of re-establishing the continuity of the permafrost sheet so that at the commencement of the next warming cycle the restraint to the outward expansion will once again start to develop the high compressive stresses needed to further propagate the upward growth of the pingo.
Each of these factors will mean that a proportion of the most recent upward deformation will have become locked-in, presenting an increased level of imperfection for the following seasonal, compression, growing cycle.
Whether another incremental buckle would occur during the subsequent warming period would depend upon a number of factors. The dome shape locked-in from the previous cycle will now present an increased amplitude of initial imperfection . This will, as indicated in previous blogs, decrease the temperature required to trigger another increment of uplift buckling. On the other hand there will have been some increase in the permafrost thickness around the periphery of the dome and as a result of the increased thickness of the ice lens beneath the pingo. This will have the effect of requiring an increased temperature to initiate another increment of uplift. All these factors, together with any increase in the effective weight of the permafrost sheet, arising from the pore water pressures becoming a declining fraction of the increasing overburden weight, could significantly influence the rates of seasonal upward growth. It must also be recalled that the material of the pingo will be developing considerable visco-plastic, creep, behaviour that will increasingly as deformation progresses be accompanied by fracture cracking. These factors are likely to have a major impact upon the temperatures required to propagate the uplift buckling and the nature of the associated buckling modes. Field evidence from the excellent records of Mackay’s more than 50 years of detailed observation and measurement, Mackay (1998), would indicate that the propagation during the early cycles can be quite rapid. This suggests that the effects of the increased effective imperfection dominate over any increases in thickness. During this initial, virile, growth period the mechanism discussed in Figure 1(c) to (d) might be repeated at reasonably regular annual cycles, accounting for the rapid early growth rates.
Over my professional life I have had a little experience of working in the Arctic, and have been following with interest your new ideas on the origins of pingos. I do wonder if there is not a very simple way to determine which of the two hypotheses for the development of pingos is likely to be the more relevant.
ReplyDeleteIf as you suggest it is the greatly increased thermal compression energy that is driving their growth then surely it might be anticipated that the growth would occur over the early spring to late summer period when the averaged increase in temperatures through the permafrost thickness is at its greatest (ie May through to August or even a little later)? I presume this might not necessarily be when surface temperature is at its greatest since the time lag for the thermal wave to propagate into the permafrost might mean the maximum thermal energy occurs a little after the maximum surface temperatures.
In contrast, if it is the growth of the ice volume at the underside of the permafrost that is creating the cryostatic pressures, as a result of the greater contained volume when ground water turns to ice, then the growth spurt might be anticipated to occur when the cold wave reaches the underside of the permafrost. Allowing for thermal lag would this not be expected to occur a little after the minimum surface temperatures are reached in mid winter (ie around February to May depending upon the thickness of the permafrost)?
If continuous measurements of upward growth showed the maximum rates of uplift around May to August then the odds are for a thermal explanation. If on the other hand the growth rates are at their greatest around February to April then the likelihood is that pressure might be the cause. Surely someone somewhere has taken measurements of the growth rates throughout the year?
Many thanks for these perceptive comments Inessentially Speaking (would be most interested in the etymology of your blog name!). You have raised issues that have long intrigued me and ones that I have for some time been trying to do something about. They intrigue me since it seems such an obvious thing to have measured to support whatever theory is being proposed, and especially now that all sorts of remote sensing methods could be used to remove the need to spend winters in what I am sure must be pretty unwelcoming environments. Indeed, an unsuccessful research grant application to the UK’s Engineering and Physical Science Research Council proposed as one of the field measurements the incorporation of remotely monitored continuous GPS measurement of targets strategically placed over the surface of a suitable pingo. I agree with you the timing of the growth during the year would be a powerful indicator of the relative claims for either the ground water pressure or the thermal upheaval buckling hypotheses. I have not been able to work out how to incorporate images into comments so will answer your query in somewhat greater depth in a blog later today. But thanks for raising this issue.
ReplyDeleteSince you mention Professor Mackay's 1998 classic paper on pingos could I raise an issue that at first sight seems to be in conflict with your hypothesised thermally induced origin of pingos. He refers to one pingo, dubbed "pulsating pingo" which suffered quite large changes in deformation as a result of having drilled into the underlying talik. If these small adjustments to the ground water pressure produce such large changes in surface elevation doesn't this negate your little theory?
ReplyDeleteWhile on the subject I also seem to remember Professor Mackay producing a little demonstration model that allowed school children to build their own pingos in their family refrigerators. Presumably these little experiments did not involve the sort of temperature changes needed to produce a thermal uplift buckle. Doesn’t this also lend support to the view that your hypothesised model cannot be correct?
Surely if your theory is to be taken seriously you would need to explain these two seemingly conflicting pieces of evidence?