During the middle decades of the 19th C Henry Moseley wrote a series of papers challenging the then emerging orthodoxies as to what provides the power necessary to move glaciers down alpine valleys. Based upon his own measurements of the shear strengths of ice he fairly convincingly demonstrated that the forces provided by gravity acting alone are incapable of providing the levels of power required to overcome the material strengths and enable the observed movements of glacial ice. His arguments would have been even more powerful in the context of continental ice sheets where the forces of gravity are generally considerably less than even the mildest of alpine glacial valleys. He argued, and some of the most influential scientists of the day agreed, that the missing energy was derived from fluctuations in the levels of the solar energy being absorbed by the glacial ice. Although his early papers suggested a fairly simplistic explanation as to how these fluctuations in solar energy, become manifest in terms of mechanical energy in the form of expansions and contractions, Moseley did not get the chance to elaborate on how he thought this model would work in glacial motion. He had, it is true, identified how this action could move a solid sheet of lead or even ice down an inclined slope. But the papers promised in his last contribution on the subject of glaciers, published in September 1871, did not appear before his death in January 1872. This is to be regretted, since the ideas he was exploring and which promised to help explain the power needed to propel glacial ice have since been seemingly neglected.
I am hopeful that the short accounts in the last few postings, outlining some of the exchanges that took place in the middle decades of the 19th C, along with some more recent reconsideration of the possible influences from alternations in thermal energy, might result in reconsideration of current models for the movement of glaciers. There seem to be some important issues that remain imperfectly understood. It seems clear to me, for example, that even if the forces of gravity are considered capable of explaining glacial motion then with the even greater energies potentially derived from alternations in the solar energy entering the glacial ice it should be even easier to explain these movements. At the very least the unfinished but productive debate of the mid. 19th C could be usefully reopened. It is possible that by doing so some of the paradox within current theories of glacial action may be more convincingly resolved. Rather than trying to explain all glacial motion in terms of either gravity or thermal action, it is to be hoped that both will come to be seen as providing in differing circumstances varying but important contributions to the power necessary to move glaciers. In these circumstances it is to be hoped that the important contributions from Canon Henry Moseley might be given the credit they would appear to deserve.
Tuesday 11 May 2010
some remaining glacial paradox
Some of the issues relating to the question of what constitutes the greater part of glacial motion, basal slip or shear distortion of the ice body, would seem to be as alive today as they were in the mid 19th C. Of the many glaciers classified as cold based the contribution to the total motion from base slip is evidently small – as it was in the glaciers observed by Tyndall and Forbes. It remains far from clear that the forces derived from gravity alone are sufficient to induce the shear distortions in the ice body. And if they are sufficient then when supplemented by the potentially very considerable forces derived from the conversion of solar radiation to mechanical energy they would be even more so. It is even less clear how the glacial ice subject to just gravity force could inflict the massive erosion damage to the bed and walls of the glacier whilst transporting huge quantities of debris and often massive boulders along its path. This must be especially so for continental glacial sheets and those that occurred in even greater extent during the periodic ice ages. Again, an additional source of primary power seems to be required.
It is furthermore difficult to reconcile current explanations of glacial motion with the clear evidence that the forces being exerted have a strong cyclical component. There are clearly periods when the motion is being pushed by massive compressive action, and other periods when the ice is being pulled by a dominantly tensile action. This pulsating characteristic of the motion of glaciers is accompanied by failure patterns that reflect this push–pull nature of the motion. It is also the reason why at certain times and at certain locations there will be a piling-up of the ice while at other periods at possibly different locations various forms of tensile tearing to form fissures and crevices will be more prevalent. The extruding of ice from a cirque over a rock shoulder or through a constricted portion of the valley is clearly associated with compression. The opening-up of transverse fissures at these same locations at different times of the annual cycle is symptomatic of tensile action. The differences in the ice properties that give rise to the regular ogives, or “Forbes bands”, would appear to reflect this cyclic form of motion. That the fractures caused by these cyclic forms of the motion, and indeed the motion itself, are more in evidence at the surface than at the base would support the view that the additional source of motivating energy is also in greater abundance near the surface.
There appear to be grounds for doubting whether current explanations are able to adequately account for the well known seasonal variations in glacial motion. While the explanation for the greater motion of glaciers during the spring to summer period might be partially explained by the greater abundance of surface melt water making its way to the base of the glacier, this cannot adequately account for the greater levels of shear deformation within the body of the ice that also occur during this period. This is especially true for cold based glaciers. Again, the seasonal variations in motion are much more in evidence over the top 10-20 m of the glacier. This is once more strongly suggestive of an additional energy source being in greater abundance near the surface of glaciers.
If a glacier is more appropriately thought of as a series of “more or less imperfectly welded separate portions, traversed by fissures” (15) it is far from clear how a model treating the ice as a continuous flowing, visco-plastic, fluid can fully capture the response. A similar argument was used to undermine Moseley’s implicit suggestion that the crawling lead sheet could help to explain glacial motion. In the same way that if some visco-plastic flow could occur within these more or less continuous blocks of ice so too could the thermal ratchet described by Moseley operate on these largely discrete blocks. As is shown in reference (17) the stresses derived from gravity on these lengths of more or less continuous ice would be relatively minor compared with those that might arise from what appear to be practical fluctuations in ice temperature.
References used here
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
It is furthermore difficult to reconcile current explanations of glacial motion with the clear evidence that the forces being exerted have a strong cyclical component. There are clearly periods when the motion is being pushed by massive compressive action, and other periods when the ice is being pulled by a dominantly tensile action. This pulsating characteristic of the motion of glaciers is accompanied by failure patterns that reflect this push–pull nature of the motion. It is also the reason why at certain times and at certain locations there will be a piling-up of the ice while at other periods at possibly different locations various forms of tensile tearing to form fissures and crevices will be more prevalent. The extruding of ice from a cirque over a rock shoulder or through a constricted portion of the valley is clearly associated with compression. The opening-up of transverse fissures at these same locations at different times of the annual cycle is symptomatic of tensile action. The differences in the ice properties that give rise to the regular ogives, or “Forbes bands”, would appear to reflect this cyclic form of motion. That the fractures caused by these cyclic forms of the motion, and indeed the motion itself, are more in evidence at the surface than at the base would support the view that the additional source of motivating energy is also in greater abundance near the surface.
There appear to be grounds for doubting whether current explanations are able to adequately account for the well known seasonal variations in glacial motion. While the explanation for the greater motion of glaciers during the spring to summer period might be partially explained by the greater abundance of surface melt water making its way to the base of the glacier, this cannot adequately account for the greater levels of shear deformation within the body of the ice that also occur during this period. This is especially true for cold based glaciers. Again, the seasonal variations in motion are much more in evidence over the top 10-20 m of the glacier. This is once more strongly suggestive of an additional energy source being in greater abundance near the surface of glaciers.
If a glacier is more appropriately thought of as a series of “more or less imperfectly welded separate portions, traversed by fissures” (15) it is far from clear how a model treating the ice as a continuous flowing, visco-plastic, fluid can fully capture the response. A similar argument was used to undermine Moseley’s implicit suggestion that the crawling lead sheet could help to explain glacial motion. In the same way that if some visco-plastic flow could occur within these more or less continuous blocks of ice so too could the thermal ratchet described by Moseley operate on these largely discrete blocks. As is shown in reference (17) the stresses derived from gravity on these lengths of more or less continuous ice would be relatively minor compared with those that might arise from what appear to be practical fluctuations in ice temperature.
References used here
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
"demolition" of Moseley's theory of glacial motion?
What initially drew my attention to Moseley’s work was a contemporary report by Doug Benn (11) of a short communication by Wallace (12) in 1871 to the Philosophical Magazine. Wallace was one of a fairly impressive range of critics advocating views that seem to have resulted in Moseley’s work on glacial motion now being less widely known and acknowledged than it would appear to deserve. After considerable criticism over the proceeding 2 years Wallace might have felt justified in his pronouncement that Moseley’s theory of contraction and expansion, then referred to as the “crawling theory”, had been “completely demolished”. The person said to have wielded the final blow of the demolition hammer, and this is what really caught my eye, was none other than James Croll (13). However, on careful reading of the contributions of Mathews (14), Ball (15), Wallace (12) and particularly Croll (13, 16) it is, in my view, very far from clear that an effective hatchet job had been delivered on the important contributions of Henry Moseley. A full account of all the deliberations leading up to the exchanges at the end of the 1860’s would require more space than is currently available. So here are just a few remarks relating to what appear to have been some of the most damaging of the criticisms together with Moseley’s and some of my own assessments of the validity of these criticisms.
Did Croll’s Comments Constitute a Demolition? Let me start from what appears to have been the last substantive comment on Moseley’s work. Wallace (12) claims that Croll (13, 16) demolished Moseley’s theory that the thermal energy causing expansion and contraction might be somehow responsible for providing the apparently missing force driving glacial motion. How he arrived at this conclusion is however baffling. To a very large extent Croll had concurred with Moseley’s conclusions that gravity acting alone could not conceivably be the sole agent causing the motion of glaciers. He also accepted that Moseley had demonstrated conclusively that a causal relationship exists between the incoming solar energy and the rate of motion experienced by glaciers. By arguing quite logically that the level of solar energy being transmitted could hardly be the result of glacial motions, Croll also concurred with Moseley that the motion of glaciers must therefore be the effect and the solar energy the cause in this relationship of dependence. The only substantive issue between Croll and Moseley would appear to be Croll’s insistence that the solar energy changed the material properties in a way that allowed the layers of ice within the body of the glacier to more easily slide one upon the other. In other words the heat increased the tendency for what we would now regard as visco-plastic flow. Croll’s arguments were ingenious but seemingly incorrect. He envisaged a process whereby the solar energy entering one molecule would be enough to break its bonds with its neighbouring molecules, allowing it to move relative to them, and in the process transfer the heat energy to these neighbouring molecules. These neighbouring molecules would in their turn do the same to their neighbours etc allowing a shear type failure to be propagated across the ice with such small mechanical force required that gravity alone would be enough. His notion of the molecules being able to move back and forth from the solid to liquid phase was founded upon the erroneous view that glacial ice remained fixed at freezing point (32oF). Like Ball, who argued that “no cause has been suggested that can tend sensibly to lower the temperature of the interior (of the glacier) below (32oF)” (15), Croll also seemed to believe there to be “nothing to lower the ice below freezing point; and as the sun’s rays do not raise the temperature of the ice above freezing point, the temperature must therefore remain unaltered” (13). In this he was quite wrong, as he was in his understanding that “heat entering the ice could not produce a mechanical pressure that would move the glacier; for heat produces contraction in volume not expansion” (13). This erroneous notion was seemingly based upon the observation that when subject to heat solid ice will occupy a smaller volume upon undergoing a phase change to form water.
Why Wallace considered Croll’s molecular explanation to provide a demolition of Moseley's views is therefore less than convincing. That he believed Croll to demolish Moseley’s views becomes even harder to understand when Wallace himself then goes on to point out the major fallacy in Croll's own explanation of the role solar energy might be playing in changing the material properties of the ice, the only real point of disagreement Croll had with Moseley. “If heat entering the glacier loosens the molecules in its passage and enables them to move insensibly into new positions, it is difficult to understand”, argues Wallace, “what causes the numerous longitudinal and transverse fissures of a glacier, the production of which is often attended by loud reports, and which indicate movement of masses, not molecules.” And Wallace quite correctly asks “how could molecular motion lead to that heavy grinding of the ice over its bed, which scores and wears down the hardest rocks, and whitens great rivers with its finely triturated mud?” If Wallace considers Croll’s explanation to be fallacious it is difficult to comprehend how he can then claim that it “demolishes (Moseley’s) theory”?
In any case Wallace’s ground for dismissing Croll’s explanation is a few paragraphs later itself contradicted by his support for the importance of the results from the ice beam bending tests conducted by Mathews and Osler (14). Mathews’s tests were supposed to show that the ice of the glacier moved in much the same way as an “imperfect fluid” – the term used for what we would now regard as viscous flow. Such a flow model advocated by Mathews and supported by many others such as Forbes (7), Ball (15) and Wallace (12), would itself be inconsistent with the violent tension tearing associated with the sudden rendering apart of ice masses to form fissures and crevices. If the small gravity forces are able to generate a viscous flow it remains difficult to really explain the very different orders of magnitude of force that would be needed to result in the “heavy grinding” action cited as making Croll’s theory untenable? But in any case it is far from clear that the results from the simple beam test reported by Mathews were really contrary to those used in support of the theory espoused by Moseley.
Did the Mathews Bending Tests Provide a Challenge? One of the central features of the arguments used by Moseley to support his thesis that gravity acting alone is not capable of explaining why glaciers move down gentle slopes, was the shearing capacity of ice. His experiments had shown that typical compacted ice samples failed in shear at stresses of around 75 lb/in2. These tests were conducted in air at temperatures well above freezing point. In a later communication (18) Moseley points out that the shear capacities at temperatures below zero are considerably higher. That the figure of 75 lb/in2 exceeded by a factor of 30 to 40 (in fact on the basis of the figures quoted this should have been 55 as used in his later contribution (18)) the average shear generated within a typical glacier by gravity acting alone, and hence exceeded by a factor of 30 to 40 the supposed shear stress required to cause the glacier to undergoing a shear flow failure, was a central part of the argument supporting Moseley's claim that glaciers would not move as a result of gravity alone. Mathews’s experiments on ice planks were supposed by many to disprove this central tenant of Moseley’s argument. But did they?
It is true that the shear stresses involved in Mathews’s tests were well below the levels of 75 lb/in2. And yet the beams tested displayed a tendency for major strains to develop, the greater parts of which were dependent on time. But to claim that this proves that ice undergoes visco-plastic, creep, straining at low shear stresses was even at the time somewhat perverse. The ice planks tested in bending under their own weight had span-to-depth ratios of between 30 and 40. At these levels of slenderness the components of vertical deformation resulting from shear action would be negligible; for such a slender beam almost the entire vertical deformation results from bending action and depends upon the magnitudes of the direct tension and compression stresses being generated on respectively the bottom and top fibres of the beam. Quick calculations suggest that these direct tensions and compressions would in Mathews’s experimental samples have been between 60 and 90 lb/in2; these would have been easily enough to cause tensile fracture of the ice and/or extensive creep deformation. And of course this is what Mathews observed. He makes it quite clear that on “the under surface of the plank near the point of flexure, (which is presumably the middle section of the beam) I noticed a number of very minute fissures extending a short distance into the ice”. He went on to claim that these fissures “were certainly not sufficient to account for the flexure of the plank”. On what basis he makes this claim is not clear. At direct flexural stress levels of these magnitudes it is remarkable that the beams did not suffer violent tensile fractures. That they did not would suggest strength levels for the ice at least as great as those found by Moseley. It seems highly improbable that these tests could in any way disprove the central tenant of Moseley’s theory in support of the impossibility of gravity alone propelling ice down typical alpine glaciers. The tests would certainly not support the inference that at very low shear stresses “a mass of ice may change its form under strains produced by the gravitation of its particles, without becoming fractured, and without returning to its original form when the strain ceases” (14). Moseley was aware of the shortcomings of the Mathews tests. As he remarked (18) “Mr Mathews’s experiment would … require to be greatly varied to bring it into analogy with the case of a glacier. If a glacier is supposed to descend by bending, the bending must be supposed to be in the plane of its surface or in the direction parallel to that plane, and not perpendicular to it, as it was in the case of the ice plank. To make his experiment apply to the case of the glacier, Mr Mathews should have placed his plank on the two bearers not flatwise, but edgewise. Indeed, looking at the proportion of the length to the width of a glacier, and considering that it is in the direction of its length that the bend must take place if it descends by bending, the plank ought rather to have been placed vertically on one of its ends”. He might have added that the length of the plank so orientated, in order to preserve the appropriate dimensional similitude, should have been the breadth of the Mathews’s test plank times the ratio of the glacier length to its width! On this basis the beam would no longer be acting in flexure. It would be deforming almost in pure shear, which, under the action of its small down-slope component, would be practically imperceptible. And this is of course the point Moseley was making.
Before leaving the subject of Mathews’s tests it is worth commenting upon another seemingly erroneous interpretation of them used to undermine the arguments of Moseley. Mathews observes that the deformed shapes of the ice beams were similar to the transverse shapes of the surface ice flow on glaciers (14). He conceded, almost in line with Moseley’s suggestion, the validity of an experiment in which the planks might be placed with their longer cross-section dimensions parallel to the flow of the glacier. While he recognised the need to allow for a greatly reduced gravitational component in this orientation he did not it seems make any allowance for the considerably increased flexural stiffness and strength that would result from this orientation. Even for the thicker of his two test beams the flexural stiffness would be more than 6 times as great as when oriented with the shorter side parallel to the loading. Making allowance for the reduction by approximately 12 in the down-slope gravity force that would be acting and it becomes clear that the shear stresses would be lower by a factor of 12 compared with those in his reported tests. But more significant given their role in the behaviour in Mathews’s tests, the flexural stresses would be reduced by a factor of nearly 30 and the flexural deformations by roughly 75. And this is with a beam having a span to depth ratio 12. For a glacier of width, say, 360 ft this would correspond with a strip between adjacent lateral crevices of just 30 ft. Over most sections of a glacier the spacings between substantial lateral fissures are observed to be very much greater than this, and even if they were so closely spaced the stresses and their accompanying deformations would be most unlikely to account for the observed flow of glacier ice.
Neglect of Failure Zone Localisation: Another common criticism levelled at Moseley’s idealised model of glacial motion was that he assumed the whole “bulk or weight of the glacier, or any portion of it to which the formula of the shearing force may be applied, (would involve) the whole mass shear(ing) at once by the action of gravity on the same mass” (12). Wallace argued that this “does not recognise the possibility of one portion of the glacier acting by its own weight to shear another and much smaller portion”. He opined that this must surely occur as a result of the “irregularity of the bed in which every glacier moves”. With evident logic he added that this would result in the ice “mass (being) everywhere in varying states of tension and compression”. This would mean that at “at any moment, therefore, the whole descending weight of a portion of the glacier containing perhaps thousands of cubic yards of ice, may act so as to cause the shearing of a few superficial feet where the tension is greatest.” Moseley had to some extent already countered (8) this argument with a simple example of a strip of glacial ice 1 in squared in cross-section and a mile in length being supported at its lower end on just three sides of the strip over a length of just 1 inch. He points out that the down-slope force of this 1 mile strip is 194.42 lb., when the slope is 4o 52’. If resisted by shear on just the 3 sides of the cubical inch this would exert a “resistance of 3x75 lbs., or 225 lbs. That resistance stops therefore the descent of this strip of ice, one mile long, having no other resistance than this opposed to its descent, by reason of its detachment from the rest. It is clear, then, that it could not have descended by its weight only when it adhered to the rest, and when its descent was opposed by the shear of its whole length”.
While this example is informative, it does not entirely address the issue raised by Wallace. When the ice is being resisted locally by some bedrock protrusion the force being delivered would need to take account of the depth of the glacier over the 1 mile length, assuming that is, a vertical crevice has formed downstream of the point at which the blockage has occurred. Under these circumstances it is conceivable, although unlikely, that the 1 mile section of unsupported ice could be delivering a force sufficient to produce the local fracture needed to unlock the movement. A point that none of the protagonists of the debates in the mid-18th C appear to have made is the following; although had he lived a little longer one suspects that Moseley would soon have done so. Imagine another experiment with a strip of ice 1 m in width but in a glacier having thickness t (m). The force to be resisted by a protruding obstruction on the glacier floor if it were required to resist the entire down-slope component of weight of a length of glacier equal to L (m), having the same slope as that considered by Moseley, would be 0.9 x t x L (kN). A closely related example was presented in Reference (4). If it is assumed that vertical sections of the glacier ice remain vertical during the deformation, then for just a 1oC increase in average temperature within a glacier having ice with a coefficient of thermal expansion 90 x 10-6 / oC and an elastic modulus of 10 x 10+6 kN/m2 would even over a short length of glacier exert a force of 900 x t kN on this same protrusion. That is, an unsupported length of glacier equal to 1000m would be required for gravity to deliver the same level of fracturing force onto a recalcitrant piece of protruding rock. It would seem to follow that if gravity acting alone is capable of causing failures in such circumstances then realistically small changes in average temperature, making due allowance for the thermal gradients through the thickness of the ice, would be even more likely to do so. Alternations in temperature could in such circumstances easily explain the occurrence of tensile cracking and compressive crushing action.
Basal Slippage or Material Deformation: Moseley had in his critique of current theories based upon the forces of gravity been strongly influenced by the observations of Tyndall (10) on the Mer de Glace. These showed that just a small proportion of the movement was due to the shear failure between the base of the glacier and the underlying rock. In his analysis Moseley (8,9) made allowance for the shear distortions within the body of the ice which accounted for the major part of the flow. For this he was criticised by Wallace who pointed out that in these analyses he “has neglected … the capability of ice when in a state of deliquescence to slide along a surface of small inclination, as demonstrated by the well-known experiment of William Hopkins.” Ball (15) reinforced this point by suggesting that “observation abundantly proves that the resistance offered by the bed of great glaciers to the sliding of the lower surface is very much less than even the smallest amount of shear force derived from (Moseley’s) several discordant observations”. We now know, of course, that the proportion of the motion that can be attributed to basal sliding as opposed to the material shearing of the body of the ice depends critically upon the nature and particularly the temperature of the glacier bed. Even at the time when knowledge of what happens at glacier beds was much more limited, Moseley replied, very reasonably, that among the resistances gravity would have to overcome “I reckon those of the sides and bottom of the channel to be as great as though the ice were frozen to them; and considering what are the obstacles in the actual channel from projecting rocks, bends in its direction, and frequent contractions, the assumption of a resistance at least equal to that which would result in the imaginary form of the glacier from the ice being frozen to its bottom and sides, is not perhaps unreasonable.” He continues a little later by noting that “the differential motion is in point of fact, by far the greater part of the motion of the glacier - thirteen fourteenths of it on the Aar Glacier, according to Professor Forbes (19); so that the resistance to the differential motion, measured by its work, is by far the greatest resistance.” Moseley reports (p148-149 (18)) confirmation from his own experiments that under the appropriate conditions a block of ice may “descend on an inclined plane by its weight alone – and therefore not to be mechanically impossible that a glacier should descend by its weight alone, if it descended as the block of ice did in (Hopkin’s) experiment. But it does not. There is an essential difference; and precisely in this difference lies the impossibility of the glacier descending by its own weight alone.” Moseley then goes on to reiterate that “the block of ice descended bodily; its parts did not move one over the another or alongside one another, but with a common motion of descent; whereas not less than thirteen fourteenths of the motion of the Glacier of the Aar is, according to Professor Forbes, not in common motion, but that of its particles one beside another and one over another, which is called the differential motion, and to which is opposed the resistance to shearing, which is at the rate of not less than 75 lbs. per square inch.” On this point Moseley concludes that “Mr Hopkin’s experiment leaves therefore more than thirteen fourteenths of the power necessary to cause the glacier to descend unaccounted for.”
While recent boreholes have confirmed that in many glaciers there is meltwater present which would allow low friction basal slippage (11), it has to be admitted that these must in general be the exception rather than the rule. Much of the data on basal conditions has been gathered in those regions of the glaciers where access is relatively easy. It is these very regions where it is most likely that warm beds will result in loss of adhesion of the ice to the bed and water at pressure will allow low shear slippage to take place. That this is the exception is evidenced by the erosive powers of glaciers within which the bed shear resistance must be considerable to generate the massive forces required to fracture and drag along the bed the rocks fragments from small to massive dimensions.
Crawling Model Inconsistent with Observation: Another issue that was addressed in the criticisms of Moseley’s supposed crawling motion is that it is inconsistent with important observations on glacial motion. Ball (15) remarks that he has met no one “practically conversant with the phenomenon of glaciers who could be brought seriously to discuss the theory”. He proceeded to list the assumptions in Moseley’s model that were at variance “with the facts of nature”. Apart from those already mentioned above, he maintains that glaciers do not present a continuous mass like a sheet of metal. Glaciers are, he observes, “more or less imperfectly welded separate portions, traversed by fissures, and whose upper surface is cut by deep rents extending to a depth very much greater than that subject to the influence of external changes in temperature.” However, Moseley’s model would equally well apply to the separate and largely continuous sheets of glacial ice lying between adjacent rifts. With these rifts acting as very effective conduits for the ingress of surface melt and other water they provide a very plausible means whereby surface solar energy could be transmitted into the body of the glacial blocks. Upon freezing this water would give out its latent heat causing considerable changes in temperature to large volumes of internal ice. The expansions and contractions needed to mobilise Moseley’s thermal ratchet would then be operating on relatively short lengths of the glacier. Any very small uphill motions occurring in these short sections of essentially continuous ice above the stagnation point for each of these finite length blocks would be largely undetectable. In any case if they did occur they would help to close the fissures and crevices, making it more likely that during the next warming cycle the expansion would be constrained and therefore add to the downward forces tending to produce motion.
While Moseley had not addressed the issue of the discontinuous nature of the deformations of glacial ice, it is more than possible that suitably extended his theory could have provided a convincing explanation for this discontinuous behaviour. As observed above few of the other theories being put forward at the time could account for these discontinuities. It is clear that at some locations and at some times glacial ice shows evidence of tensile behaviour whereas at others it may display properties more consistent with the existence of high compressive stress. It also seems fairly clear that these changes from tension to compression dominated forms of deformation response show strong cyclical patterns. There are few obvious reasons why an essentially continuous form of flow within the ice, as envisaged by the gravity inspired, visco-plastic, models of the type favoured by Forbes (7), and many others both in the mid 19th C and today, should give rise to such clear cyclical patterns of response. On the other hand Moseley’s theory is predicated on such cyclical patterns of behaviour. Add to Moseley’s gravity induced ratchet, acting on each of these to some extent discrete lengths of ice, that of the material ratchet (4) and it becomes entirely conceivable that alternations in temperature could be playing a major role in not only accounting for these forms of discontinuous behaviour but also in the very movement of glaciers.
In his fairly forthright dismissal of Moseley’s “crawling theory”, Forbes (7) raises very real doubts about the extent to which heat can flow to and from the interior of the glacier. Moseley’s adoption of the daily variations in air temperature as being indicative of the changes in temperature within the body of the ice to support his calculated motions, Forbes find “perfectly untenable”. While agreeing that the percolation of surface melt water into the fissures could account for the increases in temperature, due to its release of latent heat upon congelation, Forbes perceptively asks “how is the cold of the night to operate in reducing the temperature of the mass of the ice from 300 to 600 or more feet in thickness through the enormous average depression of 9.5oF?” He goes on to suggest that “the water so efficient by its percolation in raising the temperature (if necessary) to 32o, being frozen, is now powerless. Cold can be conveyed downward, or to speak more correctly, heat can be transmitted upwards through the ice only by the slow process of conduction, and this on the supposition that depression of superficial temperature is all that the theory might require.” Forbes quotes some of the temperature observations of De Saussure’s Travels, and points out that on many summer days the temperatures do not fall below zero at any hour during the night. “It is in the summer that the glacier moves fastest” Forbes continues, and “it is with my observations of motions in July that Mr Moseley compares the results of his theory: it is of no avail to say there are periods of the year when congelation penetrates at night some inches or even it may be some feet into the ice, and when therefore the sensible heat of the glacier may be said to vary, though, if regard be had to its vast thickness, it must be on an average and in the most extreme circumstances to an absolutely inappreciable degree.” It seems clear that Moseley’s attempt to explain measured movements of glaciers by reliance upon daily temperature variations was seriously flawed. These flaws were more so when one considers the final paragraph of Forbes’s contribution (7).
Moseley had condemned an earlier attempt by Charpentier to account for “glacier motion in terms of the daily congelation of water which percolates it, and the expansion of its mass consequent thereon” (5) by appealing to Forbes’s observation that in summer there is very little congelation of the melt water more than a few inches from the surface. In apparent contradiction of his own views Moseley asks how this dearth of water the expansion of which is supposed to explain the motion of glaciers could account for the observation that “it is summer that the daily motion of the glacier is greatest.” In this condemnation of Charpentier’s theory Forbes opines that Mr Moseley “clearly passes sentence on his own, which could not come into action until the other had produced its effects” (7). However, it is far from clear that in this respect Forbes’s observations can be relied upon. It is now well recognised that during the heat of summer the volumes of surface melt water, and indeed other precipitation possibly at elevated temperatures, percolating into the body of the glacier reach their maximum. Apart from some comparatively rare glaciers most of this water does transfer its higher heat energy into the colder ice. In some the surplus melt water reaching the glacier base is believed to contribute to a higher than normal level of basal slip. In those where basal slip is not greatly increased it seems clear that these greater volumes of congeling water will induce expansion by both the change in state and the increased temperature of the extant ice. Both these effects could be providing major contribution to the forward motion of the ice.
References used in this blog:
(4) Croll, James G A “The Movement of Glaciers”, submitted but rejected by the J of Glaciology, 2004.
(5) Moseley, Henry. “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
(6) Moseley, Henry. “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
(7) Forbes, J. D. “Remarks on the Rev H Moseley’s Theory of the Descent of Glaciers”, Proc Roy Soc., vii, June 7, 1855, 411-417.
(8) Moseley, Henry. “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
(9) Moseley, Henry. “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
(10) Tyndall, “Surface Velocity Measurements of the Mer de Glace”, Phil. Trans. Royal Society, cxlix, part 1, 265-266.
(11) Benn, D. “The Theory of Glacial Motion”, http://www.edu/~smithch/wallace/S184.htm
(12) Wallace, A R. “The Theory of Glacial Motion”, Phil. Mag., February, 1871.
(13) Croll, James. “On the Physical Cause of the Motion of Glaciers”, discussion of Moseley’s papers references (5,8), Phil. Mag., March, 1869, 201-206.
(14) Mathews, W. “Mechanical Properties of Ice and their Relation to Glacier Motion”, Alpine Journal, Feb., 1870 and Nature, March 24, 1870, 534-535.
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(16) Croll, James. “On the Cause of the Motion of Glaciers”, Phil. Mag., September, 1870, 153-170.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
(18) Moseley, Henry. Reply to discussion of References (5,8). Phil. Mag., 42, no 278, August, 1871, 138-149.
(19) Forbes, Travels in the Alps of Savoy, .
Did Croll’s Comments Constitute a Demolition? Let me start from what appears to have been the last substantive comment on Moseley’s work. Wallace (12) claims that Croll (13, 16) demolished Moseley’s theory that the thermal energy causing expansion and contraction might be somehow responsible for providing the apparently missing force driving glacial motion. How he arrived at this conclusion is however baffling. To a very large extent Croll had concurred with Moseley’s conclusions that gravity acting alone could not conceivably be the sole agent causing the motion of glaciers. He also accepted that Moseley had demonstrated conclusively that a causal relationship exists between the incoming solar energy and the rate of motion experienced by glaciers. By arguing quite logically that the level of solar energy being transmitted could hardly be the result of glacial motions, Croll also concurred with Moseley that the motion of glaciers must therefore be the effect and the solar energy the cause in this relationship of dependence. The only substantive issue between Croll and Moseley would appear to be Croll’s insistence that the solar energy changed the material properties in a way that allowed the layers of ice within the body of the glacier to more easily slide one upon the other. In other words the heat increased the tendency for what we would now regard as visco-plastic flow. Croll’s arguments were ingenious but seemingly incorrect. He envisaged a process whereby the solar energy entering one molecule would be enough to break its bonds with its neighbouring molecules, allowing it to move relative to them, and in the process transfer the heat energy to these neighbouring molecules. These neighbouring molecules would in their turn do the same to their neighbours etc allowing a shear type failure to be propagated across the ice with such small mechanical force required that gravity alone would be enough. His notion of the molecules being able to move back and forth from the solid to liquid phase was founded upon the erroneous view that glacial ice remained fixed at freezing point (32oF). Like Ball, who argued that “no cause has been suggested that can tend sensibly to lower the temperature of the interior (of the glacier) below (32oF)” (15), Croll also seemed to believe there to be “nothing to lower the ice below freezing point; and as the sun’s rays do not raise the temperature of the ice above freezing point, the temperature must therefore remain unaltered” (13). In this he was quite wrong, as he was in his understanding that “heat entering the ice could not produce a mechanical pressure that would move the glacier; for heat produces contraction in volume not expansion” (13). This erroneous notion was seemingly based upon the observation that when subject to heat solid ice will occupy a smaller volume upon undergoing a phase change to form water.
Why Wallace considered Croll’s molecular explanation to provide a demolition of Moseley's views is therefore less than convincing. That he believed Croll to demolish Moseley’s views becomes even harder to understand when Wallace himself then goes on to point out the major fallacy in Croll's own explanation of the role solar energy might be playing in changing the material properties of the ice, the only real point of disagreement Croll had with Moseley. “If heat entering the glacier loosens the molecules in its passage and enables them to move insensibly into new positions, it is difficult to understand”, argues Wallace, “what causes the numerous longitudinal and transverse fissures of a glacier, the production of which is often attended by loud reports, and which indicate movement of masses, not molecules.” And Wallace quite correctly asks “how could molecular motion lead to that heavy grinding of the ice over its bed, which scores and wears down the hardest rocks, and whitens great rivers with its finely triturated mud?” If Wallace considers Croll’s explanation to be fallacious it is difficult to comprehend how he can then claim that it “demolishes (Moseley’s) theory”?
In any case Wallace’s ground for dismissing Croll’s explanation is a few paragraphs later itself contradicted by his support for the importance of the results from the ice beam bending tests conducted by Mathews and Osler (14). Mathews’s tests were supposed to show that the ice of the glacier moved in much the same way as an “imperfect fluid” – the term used for what we would now regard as viscous flow. Such a flow model advocated by Mathews and supported by many others such as Forbes (7), Ball (15) and Wallace (12), would itself be inconsistent with the violent tension tearing associated with the sudden rendering apart of ice masses to form fissures and crevices. If the small gravity forces are able to generate a viscous flow it remains difficult to really explain the very different orders of magnitude of force that would be needed to result in the “heavy grinding” action cited as making Croll’s theory untenable? But in any case it is far from clear that the results from the simple beam test reported by Mathews were really contrary to those used in support of the theory espoused by Moseley.
Did the Mathews Bending Tests Provide a Challenge? One of the central features of the arguments used by Moseley to support his thesis that gravity acting alone is not capable of explaining why glaciers move down gentle slopes, was the shearing capacity of ice. His experiments had shown that typical compacted ice samples failed in shear at stresses of around 75 lb/in2. These tests were conducted in air at temperatures well above freezing point. In a later communication (18) Moseley points out that the shear capacities at temperatures below zero are considerably higher. That the figure of 75 lb/in2 exceeded by a factor of 30 to 40 (in fact on the basis of the figures quoted this should have been 55 as used in his later contribution (18)) the average shear generated within a typical glacier by gravity acting alone, and hence exceeded by a factor of 30 to 40 the supposed shear stress required to cause the glacier to undergoing a shear flow failure, was a central part of the argument supporting Moseley's claim that glaciers would not move as a result of gravity alone. Mathews’s experiments on ice planks were supposed by many to disprove this central tenant of Moseley’s argument. But did they?
It is true that the shear stresses involved in Mathews’s tests were well below the levels of 75 lb/in2. And yet the beams tested displayed a tendency for major strains to develop, the greater parts of which were dependent on time. But to claim that this proves that ice undergoes visco-plastic, creep, straining at low shear stresses was even at the time somewhat perverse. The ice planks tested in bending under their own weight had span-to-depth ratios of between 30 and 40. At these levels of slenderness the components of vertical deformation resulting from shear action would be negligible; for such a slender beam almost the entire vertical deformation results from bending action and depends upon the magnitudes of the direct tension and compression stresses being generated on respectively the bottom and top fibres of the beam. Quick calculations suggest that these direct tensions and compressions would in Mathews’s experimental samples have been between 60 and 90 lb/in2; these would have been easily enough to cause tensile fracture of the ice and/or extensive creep deformation. And of course this is what Mathews observed. He makes it quite clear that on “the under surface of the plank near the point of flexure, (which is presumably the middle section of the beam) I noticed a number of very minute fissures extending a short distance into the ice”. He went on to claim that these fissures “were certainly not sufficient to account for the flexure of the plank”. On what basis he makes this claim is not clear. At direct flexural stress levels of these magnitudes it is remarkable that the beams did not suffer violent tensile fractures. That they did not would suggest strength levels for the ice at least as great as those found by Moseley. It seems highly improbable that these tests could in any way disprove the central tenant of Moseley’s theory in support of the impossibility of gravity alone propelling ice down typical alpine glaciers. The tests would certainly not support the inference that at very low shear stresses “a mass of ice may change its form under strains produced by the gravitation of its particles, without becoming fractured, and without returning to its original form when the strain ceases” (14). Moseley was aware of the shortcomings of the Mathews tests. As he remarked (18) “Mr Mathews’s experiment would … require to be greatly varied to bring it into analogy with the case of a glacier. If a glacier is supposed to descend by bending, the bending must be supposed to be in the plane of its surface or in the direction parallel to that plane, and not perpendicular to it, as it was in the case of the ice plank. To make his experiment apply to the case of the glacier, Mr Mathews should have placed his plank on the two bearers not flatwise, but edgewise. Indeed, looking at the proportion of the length to the width of a glacier, and considering that it is in the direction of its length that the bend must take place if it descends by bending, the plank ought rather to have been placed vertically on one of its ends”. He might have added that the length of the plank so orientated, in order to preserve the appropriate dimensional similitude, should have been the breadth of the Mathews’s test plank times the ratio of the glacier length to its width! On this basis the beam would no longer be acting in flexure. It would be deforming almost in pure shear, which, under the action of its small down-slope component, would be practically imperceptible. And this is of course the point Moseley was making.
Before leaving the subject of Mathews’s tests it is worth commenting upon another seemingly erroneous interpretation of them used to undermine the arguments of Moseley. Mathews observes that the deformed shapes of the ice beams were similar to the transverse shapes of the surface ice flow on glaciers (14). He conceded, almost in line with Moseley’s suggestion, the validity of an experiment in which the planks might be placed with their longer cross-section dimensions parallel to the flow of the glacier. While he recognised the need to allow for a greatly reduced gravitational component in this orientation he did not it seems make any allowance for the considerably increased flexural stiffness and strength that would result from this orientation. Even for the thicker of his two test beams the flexural stiffness would be more than 6 times as great as when oriented with the shorter side parallel to the loading. Making allowance for the reduction by approximately 12 in the down-slope gravity force that would be acting and it becomes clear that the shear stresses would be lower by a factor of 12 compared with those in his reported tests. But more significant given their role in the behaviour in Mathews’s tests, the flexural stresses would be reduced by a factor of nearly 30 and the flexural deformations by roughly 75. And this is with a beam having a span to depth ratio 12. For a glacier of width, say, 360 ft this would correspond with a strip between adjacent lateral crevices of just 30 ft. Over most sections of a glacier the spacings between substantial lateral fissures are observed to be very much greater than this, and even if they were so closely spaced the stresses and their accompanying deformations would be most unlikely to account for the observed flow of glacier ice.
Neglect of Failure Zone Localisation: Another common criticism levelled at Moseley’s idealised model of glacial motion was that he assumed the whole “bulk or weight of the glacier, or any portion of it to which the formula of the shearing force may be applied, (would involve) the whole mass shear(ing) at once by the action of gravity on the same mass” (12). Wallace argued that this “does not recognise the possibility of one portion of the glacier acting by its own weight to shear another and much smaller portion”. He opined that this must surely occur as a result of the “irregularity of the bed in which every glacier moves”. With evident logic he added that this would result in the ice “mass (being) everywhere in varying states of tension and compression”. This would mean that at “at any moment, therefore, the whole descending weight of a portion of the glacier containing perhaps thousands of cubic yards of ice, may act so as to cause the shearing of a few superficial feet where the tension is greatest.” Moseley had to some extent already countered (8) this argument with a simple example of a strip of glacial ice 1 in squared in cross-section and a mile in length being supported at its lower end on just three sides of the strip over a length of just 1 inch. He points out that the down-slope force of this 1 mile strip is 194.42 lb., when the slope is 4o 52’. If resisted by shear on just the 3 sides of the cubical inch this would exert a “resistance of 3x75 lbs., or 225 lbs. That resistance stops therefore the descent of this strip of ice, one mile long, having no other resistance than this opposed to its descent, by reason of its detachment from the rest. It is clear, then, that it could not have descended by its weight only when it adhered to the rest, and when its descent was opposed by the shear of its whole length”.
While this example is informative, it does not entirely address the issue raised by Wallace. When the ice is being resisted locally by some bedrock protrusion the force being delivered would need to take account of the depth of the glacier over the 1 mile length, assuming that is, a vertical crevice has formed downstream of the point at which the blockage has occurred. Under these circumstances it is conceivable, although unlikely, that the 1 mile section of unsupported ice could be delivering a force sufficient to produce the local fracture needed to unlock the movement. A point that none of the protagonists of the debates in the mid-18th C appear to have made is the following; although had he lived a little longer one suspects that Moseley would soon have done so. Imagine another experiment with a strip of ice 1 m in width but in a glacier having thickness t (m). The force to be resisted by a protruding obstruction on the glacier floor if it were required to resist the entire down-slope component of weight of a length of glacier equal to L (m), having the same slope as that considered by Moseley, would be 0.9 x t x L (kN). A closely related example was presented in Reference (4). If it is assumed that vertical sections of the glacier ice remain vertical during the deformation, then for just a 1oC increase in average temperature within a glacier having ice with a coefficient of thermal expansion 90 x 10-6 / oC and an elastic modulus of 10 x 10+6 kN/m2 would even over a short length of glacier exert a force of 900 x t kN on this same protrusion. That is, an unsupported length of glacier equal to 1000m would be required for gravity to deliver the same level of fracturing force onto a recalcitrant piece of protruding rock. It would seem to follow that if gravity acting alone is capable of causing failures in such circumstances then realistically small changes in average temperature, making due allowance for the thermal gradients through the thickness of the ice, would be even more likely to do so. Alternations in temperature could in such circumstances easily explain the occurrence of tensile cracking and compressive crushing action.
Basal Slippage or Material Deformation: Moseley had in his critique of current theories based upon the forces of gravity been strongly influenced by the observations of Tyndall (10) on the Mer de Glace. These showed that just a small proportion of the movement was due to the shear failure between the base of the glacier and the underlying rock. In his analysis Moseley (8,9) made allowance for the shear distortions within the body of the ice which accounted for the major part of the flow. For this he was criticised by Wallace who pointed out that in these analyses he “has neglected … the capability of ice when in a state of deliquescence to slide along a surface of small inclination, as demonstrated by the well-known experiment of William Hopkins.” Ball (15) reinforced this point by suggesting that “observation abundantly proves that the resistance offered by the bed of great glaciers to the sliding of the lower surface is very much less than even the smallest amount of shear force derived from (Moseley’s) several discordant observations”. We now know, of course, that the proportion of the motion that can be attributed to basal sliding as opposed to the material shearing of the body of the ice depends critically upon the nature and particularly the temperature of the glacier bed. Even at the time when knowledge of what happens at glacier beds was much more limited, Moseley replied, very reasonably, that among the resistances gravity would have to overcome “I reckon those of the sides and bottom of the channel to be as great as though the ice were frozen to them; and considering what are the obstacles in the actual channel from projecting rocks, bends in its direction, and frequent contractions, the assumption of a resistance at least equal to that which would result in the imaginary form of the glacier from the ice being frozen to its bottom and sides, is not perhaps unreasonable.” He continues a little later by noting that “the differential motion is in point of fact, by far the greater part of the motion of the glacier - thirteen fourteenths of it on the Aar Glacier, according to Professor Forbes (19); so that the resistance to the differential motion, measured by its work, is by far the greatest resistance.” Moseley reports (p148-149 (18)) confirmation from his own experiments that under the appropriate conditions a block of ice may “descend on an inclined plane by its weight alone – and therefore not to be mechanically impossible that a glacier should descend by its weight alone, if it descended as the block of ice did in (Hopkin’s) experiment. But it does not. There is an essential difference; and precisely in this difference lies the impossibility of the glacier descending by its own weight alone.” Moseley then goes on to reiterate that “the block of ice descended bodily; its parts did not move one over the another or alongside one another, but with a common motion of descent; whereas not less than thirteen fourteenths of the motion of the Glacier of the Aar is, according to Professor Forbes, not in common motion, but that of its particles one beside another and one over another, which is called the differential motion, and to which is opposed the resistance to shearing, which is at the rate of not less than 75 lbs. per square inch.” On this point Moseley concludes that “Mr Hopkin’s experiment leaves therefore more than thirteen fourteenths of the power necessary to cause the glacier to descend unaccounted for.”
While recent boreholes have confirmed that in many glaciers there is meltwater present which would allow low friction basal slippage (11), it has to be admitted that these must in general be the exception rather than the rule. Much of the data on basal conditions has been gathered in those regions of the glaciers where access is relatively easy. It is these very regions where it is most likely that warm beds will result in loss of adhesion of the ice to the bed and water at pressure will allow low shear slippage to take place. That this is the exception is evidenced by the erosive powers of glaciers within which the bed shear resistance must be considerable to generate the massive forces required to fracture and drag along the bed the rocks fragments from small to massive dimensions.
Crawling Model Inconsistent with Observation: Another issue that was addressed in the criticisms of Moseley’s supposed crawling motion is that it is inconsistent with important observations on glacial motion. Ball (15) remarks that he has met no one “practically conversant with the phenomenon of glaciers who could be brought seriously to discuss the theory”. He proceeded to list the assumptions in Moseley’s model that were at variance “with the facts of nature”. Apart from those already mentioned above, he maintains that glaciers do not present a continuous mass like a sheet of metal. Glaciers are, he observes, “more or less imperfectly welded separate portions, traversed by fissures, and whose upper surface is cut by deep rents extending to a depth very much greater than that subject to the influence of external changes in temperature.” However, Moseley’s model would equally well apply to the separate and largely continuous sheets of glacial ice lying between adjacent rifts. With these rifts acting as very effective conduits for the ingress of surface melt and other water they provide a very plausible means whereby surface solar energy could be transmitted into the body of the glacial blocks. Upon freezing this water would give out its latent heat causing considerable changes in temperature to large volumes of internal ice. The expansions and contractions needed to mobilise Moseley’s thermal ratchet would then be operating on relatively short lengths of the glacier. Any very small uphill motions occurring in these short sections of essentially continuous ice above the stagnation point for each of these finite length blocks would be largely undetectable. In any case if they did occur they would help to close the fissures and crevices, making it more likely that during the next warming cycle the expansion would be constrained and therefore add to the downward forces tending to produce motion.
While Moseley had not addressed the issue of the discontinuous nature of the deformations of glacial ice, it is more than possible that suitably extended his theory could have provided a convincing explanation for this discontinuous behaviour. As observed above few of the other theories being put forward at the time could account for these discontinuities. It is clear that at some locations and at some times glacial ice shows evidence of tensile behaviour whereas at others it may display properties more consistent with the existence of high compressive stress. It also seems fairly clear that these changes from tension to compression dominated forms of deformation response show strong cyclical patterns. There are few obvious reasons why an essentially continuous form of flow within the ice, as envisaged by the gravity inspired, visco-plastic, models of the type favoured by Forbes (7), and many others both in the mid 19th C and today, should give rise to such clear cyclical patterns of response. On the other hand Moseley’s theory is predicated on such cyclical patterns of behaviour. Add to Moseley’s gravity induced ratchet, acting on each of these to some extent discrete lengths of ice, that of the material ratchet (4) and it becomes entirely conceivable that alternations in temperature could be playing a major role in not only accounting for these forms of discontinuous behaviour but also in the very movement of glaciers.
In his fairly forthright dismissal of Moseley’s “crawling theory”, Forbes (7) raises very real doubts about the extent to which heat can flow to and from the interior of the glacier. Moseley’s adoption of the daily variations in air temperature as being indicative of the changes in temperature within the body of the ice to support his calculated motions, Forbes find “perfectly untenable”. While agreeing that the percolation of surface melt water into the fissures could account for the increases in temperature, due to its release of latent heat upon congelation, Forbes perceptively asks “how is the cold of the night to operate in reducing the temperature of the mass of the ice from 300 to 600 or more feet in thickness through the enormous average depression of 9.5oF?” He goes on to suggest that “the water so efficient by its percolation in raising the temperature (if necessary) to 32o, being frozen, is now powerless. Cold can be conveyed downward, or to speak more correctly, heat can be transmitted upwards through the ice only by the slow process of conduction, and this on the supposition that depression of superficial temperature is all that the theory might require.” Forbes quotes some of the temperature observations of De Saussure’s Travels, and points out that on many summer days the temperatures do not fall below zero at any hour during the night. “It is in the summer that the glacier moves fastest” Forbes continues, and “it is with my observations of motions in July that Mr Moseley compares the results of his theory: it is of no avail to say there are periods of the year when congelation penetrates at night some inches or even it may be some feet into the ice, and when therefore the sensible heat of the glacier may be said to vary, though, if regard be had to its vast thickness, it must be on an average and in the most extreme circumstances to an absolutely inappreciable degree.” It seems clear that Moseley’s attempt to explain measured movements of glaciers by reliance upon daily temperature variations was seriously flawed. These flaws were more so when one considers the final paragraph of Forbes’s contribution (7).
Moseley had condemned an earlier attempt by Charpentier to account for “glacier motion in terms of the daily congelation of water which percolates it, and the expansion of its mass consequent thereon” (5) by appealing to Forbes’s observation that in summer there is very little congelation of the melt water more than a few inches from the surface. In apparent contradiction of his own views Moseley asks how this dearth of water the expansion of which is supposed to explain the motion of glaciers could account for the observation that “it is summer that the daily motion of the glacier is greatest.” In this condemnation of Charpentier’s theory Forbes opines that Mr Moseley “clearly passes sentence on his own, which could not come into action until the other had produced its effects” (7). However, it is far from clear that in this respect Forbes’s observations can be relied upon. It is now well recognised that during the heat of summer the volumes of surface melt water, and indeed other precipitation possibly at elevated temperatures, percolating into the body of the glacier reach their maximum. Apart from some comparatively rare glaciers most of this water does transfer its higher heat energy into the colder ice. In some the surplus melt water reaching the glacier base is believed to contribute to a higher than normal level of basal slip. In those where basal slip is not greatly increased it seems clear that these greater volumes of congeling water will induce expansion by both the change in state and the increased temperature of the extant ice. Both these effects could be providing major contribution to the forward motion of the ice.
References used in this blog:
(4) Croll, James G A “The Movement of Glaciers”, submitted but rejected by the J of Glaciology, 2004.
(5) Moseley, Henry. “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
(6) Moseley, Henry. “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
(7) Forbes, J. D. “Remarks on the Rev H Moseley’s Theory of the Descent of Glaciers”, Proc Roy Soc., vii, June 7, 1855, 411-417.
(8) Moseley, Henry. “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
(9) Moseley, Henry. “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
(10) Tyndall, “Surface Velocity Measurements of the Mer de Glace”, Phil. Trans. Royal Society, cxlix, part 1, 265-266.
(11) Benn, D. “The Theory of Glacial Motion”, http://www.edu/~smithch/wallace/S184.htm
(12) Wallace, A R. “The Theory of Glacial Motion”, Phil. Mag., February, 1871.
(13) Croll, James. “On the Physical Cause of the Motion of Glaciers”, discussion of Moseley’s papers references (5,8), Phil. Mag., March, 1869, 201-206.
(14) Mathews, W. “Mechanical Properties of Ice and their Relation to Glacier Motion”, Alpine Journal, Feb., 1870 and Nature, March 24, 1870, 534-535.
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(16) Croll, James. “On the Cause of the Motion of Glaciers”, Phil. Mag., September, 1870, 153-170.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
(18) Moseley, Henry. Reply to discussion of References (5,8). Phil. Mag., 42, no 278, August, 1871, 138-149.
(19) Forbes, Travels in the Alps of Savoy, .
Henry Moseley's crawling theory for glacial movement
In his initial explanation for the observed motions of a solid sheet subject to the combined influences of small down-slope gravity forces and the alternations of temperature, Moseley was to open up the possibility of a similar action at work in the motion of glaciers. The occurrence and causes of glacial motion were exercising many minds in the middle decades of the 19th C. Indeed, the possibility that such a thermal ratchet could be at work in the motion of glaciers may well have encouraged Moseley to again dust off his observations made more than a decade earlier (5) and explain them in the context of the theoretical model outlined in Reference (6). In his writing on glaciers however, he was careful to avoid his earlier suggestion that the precise thermal ratchet model of Reference (5) could somehow provide a complete explanation of the motion of glaciers. This may well have been the result of some fairly strident critical remarks from Forbes (7) whose views Moseley clearly respected and whose careful and detailed field observations Moseley had so heavily relied upon. His initial contribution to the later debate on glacial movement was, perhaps confusingly, entitled “on the mechanical possibility of descent of glaciers by their weight only” (8). This paper was read before the Royal Society on the 7th January, 1869. When the analytical component of this paper was also published, later that same year, its title, more accurately reflecting the papers conclusions, had become “on the mechanical impossibility of descent of glaciers by their weight only” (9).
The substance of this pair of publications was to show that gravity acting on its own could not be providing a motivating force sufficient to overcome the various resistances opposing the motion. His theoretical model envisaged a highly idealised form of glacial channel. The glacier was taken to be straight over its entire length, with a uniform rectangular cross-section that provided a constant resistance to the shearing action of the ice. It was further assumed that the ice was subjected to a uniform gravitational force throughout its length, which, under all these circumstances would result in a rate of movement that was also constant over its length. The angle of incline was taken to be constant at 4o 52’ to reproduce the conditions at the location called Tacul on the Mer de Glace, where Tyndall (10) had not long before recorded the characteristics of the glacial motions. Moseley fully appreciated the limitations of his model in respect of more realistic glacial circumstances. However, he reasoned with what appears to have been sound logic that his idealisations would if anything overestimate the powers of gravity acting on the ice to cause motion. Even so, Moseley calculated the shear stress required to provide the resistance to the gravitational motion was just a little more than 1.3 lb/in2 compared with typical shear strength of ice found, in experiments he performed, to be 75 lb/in2. These and other very simple illustrative calculations led Moseley to conclude that “it results from this investigation that the weight of the glacier is insufficient to account for its descent; that it is necessary to conceive, in addition to its weight, the operation of some other and much greater force”.
Moseley was aware of the many contemporaneous reports that glaciers generally experienced the greater part of their forward motion through material distortion rather than basal sliding. This had been recorded during Tyndall’s observations on the Mer de Glace (10). He incorporated into his simple theoretical model allowance for differential strain rates across the width and through the depth of the glacial ice. He reasoned that the relatively small component of motion attributable to base and wall sliding meant that the shear resistance between the ice and the glacial valley was generally higher than that of the ice itself. And he further concluded that the force needed, additional to the weight, “must also be such as would produce those internal molecular displacements and those strains which are observed actually to take place in glacier ice, and must therefore be present to every part of the glacier as its weight is, but more than 30 times as great". The figure of 30 to 40 times as great as the force resulting from the weight alone keeps reappearing in the subsequent discussion and yet the limited numerical examples provided would suggest that the figure should have been more like 50 to 60.
That Moseley considered heat from solar radiation might provide the missing source of energy was made very clear in reference (6). He calculates the force additional to its weight would over 24 hours be required to do extra work of 7706513 ft.lbs (it is curious that even at a time when the arithmetic must have been tedious, a seemingly spurious 7 significant figures are so often used!). This is said to be equivalent to 61.76 ft.lbs of work for every square inch of glacial surface, which is “equivalent to 0.0635 heat-units, or to the heat necessary to raise 0.0635 lbs. of water by one degree Fahrenheit. This amount of heat passing into the mass of the glacier per square inch per day, and reconverted into mechanical work there, would be sufficient, together with its weight, to bring the glacier down.” Moseley does not elaborate upon the form that he considers this conversion to mechanical energy might take, but given the prior publications (5,6) it might be inferred that he had in mind the mechanical effects of expansion and contraction. We will probably never know, since the further paper promised (at pp139 and 145) in Moseley’s response (18) to the subsequent criticisms of his papers (5,6,8,9) was never it seems produced. Moseley died in January, 1872, just a few months after his last and very lucid response (18) to the many criticisms that his work was to attract.
So what were these criticisms and how did Moseley respond? These questions I will take up in my next posting.
References used in this blog:
(5) Moseley, Henry. “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
(6) Moseley, Henry. “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
(7) Forbes, J. D. “Remarks on the Rev H Moseley’s Theory of the Descent of Glaciers”, Proc Roy Soc., vii, June 7, 1855, 411-417.
(8) Moseley, Henry. “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
(9) Moseley, Henry. “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
(10) Tyndall, “Surface Velocity Measurements of the Mer de Glace”, Phil. Trans. Royal Society, cxlix, part 1, 265-266.
(11) Benn, D. “The Theory of Glacial Motion”, http://www.edu/~smithch/wallace/S184.htm
(12) Wallace, A R. “The Theory of Glacial Motion”, Phil. Mag., February, 1871.
(13) Croll, James. “On the Physical Cause of the Motion of Glaciers”, discussion of Moseley’s papers references (5,8), Phil. Mag., March, 1869, 201-206.
(14) Mathews, W. “Mechanical Properties of Ice and their Relation to Glacier Motion”, Alpine Journal, Feb., 1870 and Nature, March 24, 1870, 534-535.
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(16) Croll, James. “On the Cause of the Motion of Glaciers”, Phil. Mag., September, 1870, 153-170.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
(18) Moseley, Henry. Reply to discussion of References (5,8). Phil. Mag., 42, no 278, August, 1871, 138-149.
The substance of this pair of publications was to show that gravity acting on its own could not be providing a motivating force sufficient to overcome the various resistances opposing the motion. His theoretical model envisaged a highly idealised form of glacial channel. The glacier was taken to be straight over its entire length, with a uniform rectangular cross-section that provided a constant resistance to the shearing action of the ice. It was further assumed that the ice was subjected to a uniform gravitational force throughout its length, which, under all these circumstances would result in a rate of movement that was also constant over its length. The angle of incline was taken to be constant at 4o 52’ to reproduce the conditions at the location called Tacul on the Mer de Glace, where Tyndall (10) had not long before recorded the characteristics of the glacial motions. Moseley fully appreciated the limitations of his model in respect of more realistic glacial circumstances. However, he reasoned with what appears to have been sound logic that his idealisations would if anything overestimate the powers of gravity acting on the ice to cause motion. Even so, Moseley calculated the shear stress required to provide the resistance to the gravitational motion was just a little more than 1.3 lb/in2 compared with typical shear strength of ice found, in experiments he performed, to be 75 lb/in2. These and other very simple illustrative calculations led Moseley to conclude that “it results from this investigation that the weight of the glacier is insufficient to account for its descent; that it is necessary to conceive, in addition to its weight, the operation of some other and much greater force”.
Moseley was aware of the many contemporaneous reports that glaciers generally experienced the greater part of their forward motion through material distortion rather than basal sliding. This had been recorded during Tyndall’s observations on the Mer de Glace (10). He incorporated into his simple theoretical model allowance for differential strain rates across the width and through the depth of the glacial ice. He reasoned that the relatively small component of motion attributable to base and wall sliding meant that the shear resistance between the ice and the glacial valley was generally higher than that of the ice itself. And he further concluded that the force needed, additional to the weight, “must also be such as would produce those internal molecular displacements and those strains which are observed actually to take place in glacier ice, and must therefore be present to every part of the glacier as its weight is, but more than 30 times as great". The figure of 30 to 40 times as great as the force resulting from the weight alone keeps reappearing in the subsequent discussion and yet the limited numerical examples provided would suggest that the figure should have been more like 50 to 60.
That Moseley considered heat from solar radiation might provide the missing source of energy was made very clear in reference (6). He calculates the force additional to its weight would over 24 hours be required to do extra work of 7706513 ft.lbs (it is curious that even at a time when the arithmetic must have been tedious, a seemingly spurious 7 significant figures are so often used!). This is said to be equivalent to 61.76 ft.lbs of work for every square inch of glacial surface, which is “equivalent to 0.0635 heat-units, or to the heat necessary to raise 0.0635 lbs. of water by one degree Fahrenheit. This amount of heat passing into the mass of the glacier per square inch per day, and reconverted into mechanical work there, would be sufficient, together with its weight, to bring the glacier down.” Moseley does not elaborate upon the form that he considers this conversion to mechanical energy might take, but given the prior publications (5,6) it might be inferred that he had in mind the mechanical effects of expansion and contraction. We will probably never know, since the further paper promised (at pp139 and 145) in Moseley’s response (18) to the subsequent criticisms of his papers (5,6,8,9) was never it seems produced. Moseley died in January, 1872, just a few months after his last and very lucid response (18) to the many criticisms that his work was to attract.
So what were these criticisms and how did Moseley respond? These questions I will take up in my next posting.
References used in this blog:
(5) Moseley, Henry. “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
(6) Moseley, Henry. “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
(7) Forbes, J. D. “Remarks on the Rev H Moseley’s Theory of the Descent of Glaciers”, Proc Roy Soc., vii, June 7, 1855, 411-417.
(8) Moseley, Henry. “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
(9) Moseley, Henry. “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
(10) Tyndall, “Surface Velocity Measurements of the Mer de Glace”, Phil. Trans. Royal Society, cxlix, part 1, 265-266.
(11) Benn, D. “The Theory of Glacial Motion”, http://www.edu/~smithch/wallace/S184.htm
(12) Wallace, A R. “The Theory of Glacial Motion”, Phil. Mag., February, 1871.
(13) Croll, James. “On the Physical Cause of the Motion of Glaciers”, discussion of Moseley’s papers references (5,8), Phil. Mag., March, 1869, 201-206.
(14) Mathews, W. “Mechanical Properties of Ice and their Relation to Glacier Motion”, Alpine Journal, Feb., 1870 and Nature, March 24, 1870, 534-535.
(15) Ball, J. “On the Cause of the Descent of Glaciers”, Phil. Mag., July, 1870, 1-10.
(16) Croll, James. “On the Cause of the Motion of Glaciers”, Phil. Mag., September, 1870, 153-170.
(17) Croll, James G A. “Comparisons of the Stresses in Glaciers when subject to Gravity and Thermal Loading”, to be submitted to J of Glaciology, 2005.
(18) Moseley, Henry. Reply to discussion of References (5,8). Phil. Mag., 42, no 278, August, 1871, 138-149.
Wednesday 5 May 2010
more on why don't pingos disappear in winter?
As I mentioned in my brief reply to Inessentially Speaking (see posting "why pingos don't disappear in winter" April 26, 2010) I had included in a research grant application to the UK’s Engineering and Physical Science Research Council a proposal to include some new field measurements using remotely monitored GPS records to track the timing of the growth of pingos throughout the year. For reasons of extreme weather during anything other than a few summer months such readings had not previously been possible.
My thinking was that at least during the early growth period, when the thickness of permafrost and ice beneath the pingo was relatively low, the time lag between the mid-summer maximum surface temperatures and the through-thickness maximum average temperature would probably be relatively small. This would mean maximum compressive energy would reach its maximum fairly soon after the mid summer surface maximum temperatures. This would imply a rapid build-up of compressive strain energy in the permafrost over the period April through to roughly the July - August period (at least in the Northern Hemisphere). It would be this rapid build-up of compressive strain energy that would be causing any incremental increase in the thermal upheaval buckle deformation. This is depicted in Figure 1 below, which suggests that maximum incremental uplift would be reached at around July - August.
Equally, once the compressive strain energy had all but expended itself in producing the thermal uplift the subsequent cooling over the August to January period would fairly quickly be expected to produce high tensile strain energy much of which would be released through thermal cracking. While it is suggested the upward growth of the underlying ice lens would prevent the summer growth in uplift from being entirely lost during the winter months, it is likely that some slight settling back would occur. This is suggested in the attached sketch. Over a period of virile growth it might be anticipated that if thermal upheaval were the cause of pingo growth, or at least a major contributory cause, then a year on year pattern of growth something like that shown would be observed.
In contrast, any spike in the pore water pressure would occur when the cold wave reaches the underside of the permafrost. Allowing for thermal lag this would mean maximum growth occurring nearer to mid winter.
It is a pity we were unable to carry-out such measurements. But perhaps by now someone else has?
My thinking was that at least during the early growth period, when the thickness of permafrost and ice beneath the pingo was relatively low, the time lag between the mid-summer maximum surface temperatures and the through-thickness maximum average temperature would probably be relatively small. This would mean maximum compressive energy would reach its maximum fairly soon after the mid summer surface maximum temperatures. This would imply a rapid build-up of compressive strain energy in the permafrost over the period April through to roughly the July - August period (at least in the Northern Hemisphere). It would be this rapid build-up of compressive strain energy that would be causing any incremental increase in the thermal upheaval buckle deformation. This is depicted in Figure 1 below, which suggests that maximum incremental uplift would be reached at around July - August.
Equally, once the compressive strain energy had all but expended itself in producing the thermal uplift the subsequent cooling over the August to January period would fairly quickly be expected to produce high tensile strain energy much of which would be released through thermal cracking. While it is suggested the upward growth of the underlying ice lens would prevent the summer growth in uplift from being entirely lost during the winter months, it is likely that some slight settling back would occur. This is suggested in the attached sketch. Over a period of virile growth it might be anticipated that if thermal upheaval were the cause of pingo growth, or at least a major contributory cause, then a year on year pattern of growth something like that shown would be observed.In contrast, any spike in the pore water pressure would occur when the cold wave reaches the underside of the permafrost. Allowing for thermal lag this would mean maximum growth occurring nearer to mid winter.
It is a pity we were unable to carry-out such measurements. But perhaps by now someone else has?
Tuesday 4 May 2010
not the first to question glacial motion theories
It was after producing a short note (Croll, 2004) arguing that a thermal ratchet process described in the most recent postings, might help explain at least some forms of glacial ice movement that I became aware of a similar model having been proposed by Henry Moseley as early as 1855 (Moseley, 1855). Curious as to why his intriguing theory seems to have been almost entirely lost from the literature on glacial flow I was compelled to look back at the fascinating debate that occurred on this issue in the years following Moseley’s publication dealing with glaciers. For me the results of this search have been both encouraging, in that I have distinguished company sharing the view that thermal effects may be important in the movement of glaciers, and genealogically quirky. It is though, for the former reason that I thought others might be interested in a summary of the issues that this debate highlighted. Some of these issues, as I will explain, appear to have been misunderstood at the time and a number would seem to be still not satisfactorily resolved today.
MOSELEY AND THE THERMAL MOVEMENT OF LEAD SHEETS:
Henry Moseley would today be regarded as something of a child prodigy. At the age of 17 years, as a pupil at the naval school in Portsmouth, he had his first scientific paper published in the Philosophical Magazine, attempting to measure the depth of the cavities being observed on the surface of the moon. After a distinguished undergraduate career at Cambridge, and having been ordained in 1827, Moseley worked as a curate at West Monkton in Somerset. As was common this did not prevent him from continuing his studies of mathematics and mechanics, and he produced his first book on hydrostatics in 1830. His reputation saw him appointed as the first professor of natural and experimental philosophy and astronomy at the newly established King’s College London. In that capacity he made a number of important contributions to development of practical science and engineering. In 1853 he was with royal patronage appointed to a residential canonry at Bristol Cathedral. While his mind was undoubtedly on other matters he continued his passion for mechanics. He was for example attracted to the phenomenon whereby the lead sheeting on the southern facing roof of the choir chapel at Bristol Cathedral was over time found to move down the slope and end up in the guttering, whereas that on the northern slope suffered no such fate. In 1855 he prepared the article listed below reporting the fact of the descent of a solid body on an inclined plane when subjected to alternations in temperature. Very probably stimulated by the contemporaneous discussions as to the causes of the motions of glacial ice, he attempted to show that the simple formula derived for the movement of a lead sheet might also account for the observed movement of alpine glaciers. It was these rather simple calculations purporting to show that alternations in temperature could also explain the motion of glacial ice that sparked off a controversy that was to run intermittently for the next 15 years. Before addressing Moseley’s contentious application of his theoretical model to glaciers it might be helpful to briefly outline his arguments relating to the motion of a solid sheet.
Figure 1 reproduces Moseley’s diagrams used in his 1855 paper to derive a formula for the descent of a mass due to alternations in temperature. These refer to a “uniform bar AB placed on an inclined plane” which, when “subject to extension from increase of temperature, a portion XB will descend, and the rest XA will ascend; the point X being where they separate being determined by the condition that the force requisite to push XA up the plane is equal to that required to push XB down it.” By invoking simple considerations of equilibrium with the down-slope component of the weight of the sheet, Moseley shows that the point B will have descended by amount u+, given by
eqn (1) see Figures
In this expression I have used a notation similar to that adopted in a recent independent derivation (see eqn (1) of the posting "thermal ratchet models of glacial motion", which is somewhat different from that employed by Moseley; α represent the coefficient of linear expansion of the solid, T the increase in temperature, l the length of the bar AB, θ the inclination of the rod to the horizontal and θ* the limiting inclination of the rod before kinematic friction will result in sliding under gravity alone. To allow direct comparison with eqn (1) of which relates to a sheet of unit width, it might be observed that
eqn (2) see Figures.
where q is the kinematic friction force per unit area between the rod and the slope, γ is the unit weight of the solid rod, and t is the thickness of the sheet.
Moseley goes on to observe that on the basis of Figure 2, also reproduced from Moseley (1855), “when contraction takes place the converse of the above will be true. The separating point X will be such, that the force requisite to pull XB up the plane is equal to that required to pull AX down it. BX is obviously equal to AX in the other.” Hence, by the time the bar has returned to its former temperature, “the point B (Figure. 2) will by this contraction be made to descend through the space”,u- , where
eqn (3) see Figures
On this basis the total descent of “B by elongation and contraction is therefore determined by the equation
eqn (4) see Figures
This process, referred to at the time of its derivation as the “crawling theory” (to distinguish this form of motion from that I believe to be of perhaps even greater importance in many glaciers, I had adopted the terminology “gravity ratchet” (Croll, 2004)), was followed up in early 1869 by a paper, a summary of which was read before the Royal Society in January 1869 (Moseley, 1869a), that described a somewhat more elaborate theoretical model for the motions of a solid body on an inclined plane subject to fluctuations in temperature. In this fairly lengthy, but today difficult to follow discussion, Moseley again established how the combined influences of the gravitational forces acting on the inclined mass of a solid body, together with the effects of shear breaking expansion and contraction forces caused by changes in temperature, are able to account for the downward, incremental, motions of a solid sheet such as the lead on the Cathedral roof. Neither temperature nor gravity acting alone would it was argued be sufficient to cause these motions. Each was found necessary but not sufficient to induce the downward motion. In this important but largely forgotten contribution Moseley reports a simple experiment he undertook in his back garden between 16th February and 28th June, 1858. Since it would appear that this experiment has not been repeated*, and because it was to form the backdrop to the later arguments concerning the motions of glacial ice, the following is a brief description of what he did and what he found.
On a 9 foot plank of specially prepared wood (to be specific Deal) of width 5 inch, he placed an equally long sheet of lead having a thickness of 1/8th inch. To prevent it falling off, the lead sheet was carefully turned over each of the longitudinal edges in a way that would not impede its downward movement by causing it to stick to the plank. The plank with the lead sheet was fixed at an inclination of 18o 32’ to the southern facing wall of Canon Moseley’s house. It was arranged to allow convenient recording, to 1/100th of an inch, of the positions of the bottom edge of the lead “every morning between 7 and 8 o’clock, and every evening between 6 and 7 o’clock”. As confirmation of his explanation for the observations on the movement of the lead sheeting on the Cathedral roof, he found “on the days when the thermometer in the sun varied its height rapidly and much (as on bright days with cold winds, or when clouds were driven over the sun) that the descent was greatest. So remarkably indeed was this the case, that every cloud which shut off the sun for a time from the lead, and every cold gust of wind that blew upon it in the sunshine, seemed to bring it a step down. On the contrary, when the sky was open and clear, and the heat advanced and receded uniformly, the descent was less … It was least of all on days when there was continuous rain. During the night it was often imperceptible.” And as Moseley remarked any night time movement was most probably the result of the sunshine in the spring to summer months experienced before his early morning readings or after those in the evening. The detailed results tabulated (Moseley, 1869b) for the month of May are indeed convincing with regard these overall conclusions. That alternations in temperature acting on a solid having a down-slope gravitational force less than that required to overcome the frictional resistance (the slope required for friction between the lead and the wood to allow gravity alone to cause motion was 22o 30’) seems clear. It is surprising therefore that this experiment does not appear to have been repeated* and the fact of its occurrence largely overlooked in most of the subsequent discussion of the flow of glacial ice.
* This is no longer the case. Over the academic year 2007-08 a pair of UCL undergraduate students repeated the experiments taking quantitative readings of the downward motions of the lead sheet when subject to precisely controlled levels of thermal fluctuations. Their results are reported in Kaimakamis and Patel (2007)
References mentioned in blog:
Croll, James G. A. (2004) “The Movement of Glaciers”, submitted to the J of Glaciology, 2004.
Kaimakamis, A, and Patel, K (2007) Pulsatile motions of solid bodies due to thermo-mechanical action, thesis presented in partial fulfillment of MEng Degree, Dept. of Civil Engng., University College London.
Moseley, Henry. (1855) “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
Moseley, Henry. (1869a) “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
Moseley, Henry. (1869b) “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
Moseley, Henry. (1869c) “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
MOSELEY AND THE THERMAL MOVEMENT OF LEAD SHEETS:
Henry Moseley would today be regarded as something of a child prodigy. At the age of 17 years, as a pupil at the naval school in Portsmouth, he had his first scientific paper published in the Philosophical Magazine, attempting to measure the depth of the cavities being observed on the surface of the moon. After a distinguished undergraduate career at Cambridge, and having been ordained in 1827, Moseley worked as a curate at West Monkton in Somerset. As was common this did not prevent him from continuing his studies of mathematics and mechanics, and he produced his first book on hydrostatics in 1830. His reputation saw him appointed as the first professor of natural and experimental philosophy and astronomy at the newly established King’s College London. In that capacity he made a number of important contributions to development of practical science and engineering. In 1853 he was with royal patronage appointed to a residential canonry at Bristol Cathedral. While his mind was undoubtedly on other matters he continued his passion for mechanics. He was for example attracted to the phenomenon whereby the lead sheeting on the southern facing roof of the choir chapel at Bristol Cathedral was over time found to move down the slope and end up in the guttering, whereas that on the northern slope suffered no such fate. In 1855 he prepared the article listed below reporting the fact of the descent of a solid body on an inclined plane when subjected to alternations in temperature. Very probably stimulated by the contemporaneous discussions as to the causes of the motions of glacial ice, he attempted to show that the simple formula derived for the movement of a lead sheet might also account for the observed movement of alpine glaciers. It was these rather simple calculations purporting to show that alternations in temperature could also explain the motion of glacial ice that sparked off a controversy that was to run intermittently for the next 15 years. Before addressing Moseley’s contentious application of his theoretical model to glaciers it might be helpful to briefly outline his arguments relating to the motion of a solid sheet.
Figure 1 reproduces Moseley’s diagrams used in his 1855 paper to derive a formula for the descent of a mass due to alternations in temperature. These refer to a “uniform bar AB placed on an inclined plane” which, when “subject to extension from increase of temperature, a portion XB will descend, and the rest XA will ascend; the point X being where they separate being determined by the condition that the force requisite to push XA up the plane is equal to that required to push XB down it.” By invoking simple considerations of equilibrium with the down-slope component of the weight of the sheet, Moseley shows that the point B will have descended by amount u+, given by
eqn (1) see Figures
In this expression I have used a notation similar to that adopted in a recent independent derivation (see eqn (1) of the posting "thermal ratchet models of glacial motion", which is somewhat different from that employed by Moseley; α represent the coefficient of linear expansion of the solid, T the increase in temperature, l the length of the bar AB, θ the inclination of the rod to the horizontal and θ* the limiting inclination of the rod before kinematic friction will result in sliding under gravity alone. To allow direct comparison with eqn (1) of which relates to a sheet of unit width, it might be observed that
eqn (2) see Figures.
Moseley goes on to observe that on the basis of Figure 2, also reproduced from Moseley (1855), “when contraction takes place the converse of the above will be true. The separating point X will be such, that the force requisite to pull XB up the plane is equal to that required to pull AX down it. BX is obviously equal to AX in the other.” Hence, by the time the bar has returned to its former temperature, “the point B (Figure. 2) will by this contraction be made to descend through the space”,u- , where
eqn (3) see Figures
On this basis the total descent of “B by elongation and contraction is therefore determined by the equation
eqn (4) see Figures
This process, referred to at the time of its derivation as the “crawling theory” (to distinguish this form of motion from that I believe to be of perhaps even greater importance in many glaciers, I had adopted the terminology “gravity ratchet” (Croll, 2004)), was followed up in early 1869 by a paper, a summary of which was read before the Royal Society in January 1869 (Moseley, 1869a), that described a somewhat more elaborate theoretical model for the motions of a solid body on an inclined plane subject to fluctuations in temperature. In this fairly lengthy, but today difficult to follow discussion, Moseley again established how the combined influences of the gravitational forces acting on the inclined mass of a solid body, together with the effects of shear breaking expansion and contraction forces caused by changes in temperature, are able to account for the downward, incremental, motions of a solid sheet such as the lead on the Cathedral roof. Neither temperature nor gravity acting alone would it was argued be sufficient to cause these motions. Each was found necessary but not sufficient to induce the downward motion. In this important but largely forgotten contribution Moseley reports a simple experiment he undertook in his back garden between 16th February and 28th June, 1858. Since it would appear that this experiment has not been repeated*, and because it was to form the backdrop to the later arguments concerning the motions of glacial ice, the following is a brief description of what he did and what he found.
On a 9 foot plank of specially prepared wood (to be specific Deal) of width 5 inch, he placed an equally long sheet of lead having a thickness of 1/8th inch. To prevent it falling off, the lead sheet was carefully turned over each of the longitudinal edges in a way that would not impede its downward movement by causing it to stick to the plank. The plank with the lead sheet was fixed at an inclination of 18o 32’ to the southern facing wall of Canon Moseley’s house. It was arranged to allow convenient recording, to 1/100th of an inch, of the positions of the bottom edge of the lead “every morning between 7 and 8 o’clock, and every evening between 6 and 7 o’clock”. As confirmation of his explanation for the observations on the movement of the lead sheeting on the Cathedral roof, he found “on the days when the thermometer in the sun varied its height rapidly and much (as on bright days with cold winds, or when clouds were driven over the sun) that the descent was greatest. So remarkably indeed was this the case, that every cloud which shut off the sun for a time from the lead, and every cold gust of wind that blew upon it in the sunshine, seemed to bring it a step down. On the contrary, when the sky was open and clear, and the heat advanced and receded uniformly, the descent was less … It was least of all on days when there was continuous rain. During the night it was often imperceptible.” And as Moseley remarked any night time movement was most probably the result of the sunshine in the spring to summer months experienced before his early morning readings or after those in the evening. The detailed results tabulated (Moseley, 1869b) for the month of May are indeed convincing with regard these overall conclusions. That alternations in temperature acting on a solid having a down-slope gravitational force less than that required to overcome the frictional resistance (the slope required for friction between the lead and the wood to allow gravity alone to cause motion was 22o 30’) seems clear. It is surprising therefore that this experiment does not appear to have been repeated* and the fact of its occurrence largely overlooked in most of the subsequent discussion of the flow of glacial ice.
* This is no longer the case. Over the academic year 2007-08 a pair of UCL undergraduate students repeated the experiments taking quantitative readings of the downward motions of the lead sheet when subject to precisely controlled levels of thermal fluctuations. Their results are reported in Kaimakamis and Patel (2007)
References mentioned in blog:
Croll, James G. A. (2004) “The Movement of Glaciers”, submitted to the J of Glaciology, 2004.
Kaimakamis, A, and Patel, K (2007) Pulsatile motions of solid bodies due to thermo-mechanical action, thesis presented in partial fulfillment of MEng Degree, Dept. of Civil Engng., University College London.
Moseley, Henry. (1855) “On the Descent of Glaciers”, Proc Roy Soc, 7, 1855, 333-342.
Moseley, Henry. (1869a) “On the Mechanical Possibility of the Descent of Glaciers by their Weight only”. Received, Oct. 1868, read before Royal Society, 7 Jan., 1869, reported Phil. Mag., 37, 229-235. Proc. Roy. Soc., xvii, Jan., 1869, pp202-207.
Moseley, Henry. (1869b) “On the Descent of a Solid Body on an Inclined Plane when subjected to alternations of Temperature”, Phil Mag, S.4, 38, August 1869, 99-118.
Moseley, Henry. (1869c) “On the Mechanical Impossibility of the Descent of Glaciers by their Weight only”, Phil Mag., 37, no 208, May, 1869, 363-370.
some more realistic considerations of glacial motion
While the mechanisms described in the previous postings are suggested to provide an important underlying energy source likely to help power the motion of certain forms of glaciers, they are highly idealised. Real glaciers will exhibit behaviour of considerably greater complexity, which will almost certainly include the following.
Thermal Gradients: Solar energy reaching the surface of the glacial ice will not result in uniform changes in temperature through the thickness. Ice is a poor conductor of heat and the snow covering often cuts-down the radiant energy reaching the lower sections of ice. However, it is well known that ice sheets display significant seasonal temperature variations (see for example Burgess et al, 2001) that can penetrate well into the body of the glacier. Inevitably the temperature fluctuations will show considerable attenuation with depth, giving rise to thermal variations like those shown in Figure 1(a). For this reason there is likely to be considerably greater thermally driven ratchet actions occurring over the upper layers of the glacial ice as compared with the ice at lower levels. This will be manifest by the increased fracturing, in the form of cracking and crevasses, experienced in the upper layers and of course greater than average annual forward motion.
Surface melt water is known to play an important part in the motion of glaciers. This is sometimes explained in terms of the water reaching the lower levels and acting as a form of lubricant to the frictional resistance at the rock interface. Why this explanation is less than convincing for all glacial motions is that if a lowering of the boundary shear failure stress were to always occur it would be extremely difficult to reconcile this with the extremely high shear forces that are clearly being generated at these boundaries That high shear forces are present is evidenced by the huge forces that are obviously needed to grind-away at the rock valleys and gouge out massive chunks of rock to form the glacial base and walls. Melt water could however, be having another very important action. The high volumes generated are probably an important component in the closing-up of the tension cracks and fissures. The latent heat stored in this runoff water will be considerable. When it is turned back into ice within the body of the fissured glacial ice it will release this latent heat energy into the lower regions of the underlying glacier. This form of latent heat flow from the surface into the body of the glacier could help to explain how the thermal expansion effects are more uniformly distributed through the thickness of the glacier. Increased forward motion experienced during periods of high rates of surface water melt might be expected to result from this most effective form of heat transfer. Such an alternative explanation would overcome one of the serious problems associated with the current models that ascribe this increased summer flow rate to just the effects of a form of bed fluidisation process.
Elastic-visco-plastic Distortions: The greater thermal activity in the upper layers of the glacier, together with the nature of the stress distributions through its thickness, as suggested in Figure 1(c), will increase the levels of shear with depth. Both elastic and visco-plastic creep shear straining will also increase with depth explaining why the rates of “flow” display typical vertical profiles like that shown in Figure 1(b). Relatively constant flow might be anticipated over the upper layers where the shear stresses will be low. Flow gradients will increase with depth. These gradients will be associated with the increasing shear strains occurring at depths approaching the lower layers. The high shear strains will accompany the build-up of shear stresses to levels required to fracture the rock and cause frictional failure at the ice-rock boundaries.
High edge shear stresses required to induce slip failures against the glacial valley walls will likewise result in shear stress gradients across the width of the glacier as suggested in Figure 2(b). Just as for the vertical variations in ice motion a shear strain, flow related, profile like that shown in Figure 2(a) would be expected.
Discontinuous Boundary Shear: While the basic ratchet motions were established in relation to idealised, uniform, kinematic bed friction failure, the same model would apply for ice-rock interfaces that display discontinuous failure properties. An extreme case could be that shown in Figure 3(a). Imagine that the section B is firmly bonded to a massive protruding rock, either on the glacial wall or bed. As the temperature is increased the compression force developed by the now restrained expansion relative to the fixed section A, will also build-up. Eventually a temperature might reach a level when the rock is fractured and gouged out from its surrounding rock face. This fracture will be associated with the sudden release of a huge amount of thermally induced strain energy, with a rapid (surge) motion of the glacial ice likely to follow. Similar discontinuous forms of forward behaviour could be experienced over the entire length of the glacier. The effects will be essentially similar to that described above for the smooth frictional behaviour. During the subsequent cooling period the tensions resulting from the restrained contraction will be most unlikely to cause a reversal of the bed friction motion for the simple reason that the ice is likely to fracture in tension well before it reaches the levels required to induce bed shear failure.
Burgess, M and Smith, S. (2001) Climate change indicators – permafrost. WG1, IPCC Third Assessment Report, Climate Change 2001: The Scientific Basis, Chapter 2.2.5.3 Permafrost. See also: http://sts.gsc.nrcan.gc.ca/permafrost.
Thermal Gradients: Solar energy reaching the surface of the glacial ice will not result in uniform changes in temperature through the thickness. Ice is a poor conductor of heat and the snow covering often cuts-down the radiant energy reaching the lower sections of ice. However, it is well known that ice sheets display significant seasonal temperature variations (see for example Burgess et al, 2001) that can penetrate well into the body of the glacier. Inevitably the temperature fluctuations will show considerable attenuation with depth, giving rise to thermal variations like those shown in Figure 1(a). For this reason there is likely to be considerably greater thermally driven ratchet actions occurring over the upper layers of the glacial ice as compared with the ice at lower levels. This will be manifest by the increased fracturing, in the form of cracking and crevasses, experienced in the upper layers and of course greater than average annual forward motion.
Surface melt water is known to play an important part in the motion of glaciers. This is sometimes explained in terms of the water reaching the lower levels and acting as a form of lubricant to the frictional resistance at the rock interface. Why this explanation is less than convincing for all glacial motions is that if a lowering of the boundary shear failure stress were to always occur it would be extremely difficult to reconcile this with the extremely high shear forces that are clearly being generated at these boundaries That high shear forces are present is evidenced by the huge forces that are obviously needed to grind-away at the rock valleys and gouge out massive chunks of rock to form the glacial base and walls. Melt water could however, be having another very important action. The high volumes generated are probably an important component in the closing-up of the tension cracks and fissures. The latent heat stored in this runoff water will be considerable. When it is turned back into ice within the body of the fissured glacial ice it will release this latent heat energy into the lower regions of the underlying glacier. This form of latent heat flow from the surface into the body of the glacier could help to explain how the thermal expansion effects are more uniformly distributed through the thickness of the glacier. Increased forward motion experienced during periods of high rates of surface water melt might be expected to result from this most effective form of heat transfer. Such an alternative explanation would overcome one of the serious problems associated with the current models that ascribe this increased summer flow rate to just the effects of a form of bed fluidisation process.
Elastic-visco-plastic Distortions: The greater thermal activity in the upper layers of the glacier, together with the nature of the stress distributions through its thickness, as suggested in Figure 1(c), will increase the levels of shear with depth. Both elastic and visco-plastic creep shear straining will also increase with depth explaining why the rates of “flow” display typical vertical profiles like that shown in Figure 1(b). Relatively constant flow might be anticipated over the upper layers where the shear stresses will be low. Flow gradients will increase with depth. These gradients will be associated with the increasing shear strains occurring at depths approaching the lower layers. The high shear strains will accompany the build-up of shear stresses to levels required to fracture the rock and cause frictional failure at the ice-rock boundaries.
High edge shear stresses required to induce slip failures against the glacial valley walls will likewise result in shear stress gradients across the width of the glacier as suggested in Figure 2(b). Just as for the vertical variations in ice motion a shear strain, flow related, profile like that shown in Figure 2(a) would be expected.
Discontinuous Boundary Shear: While the basic ratchet motions were established in relation to idealised, uniform, kinematic bed friction failure, the same model would apply for ice-rock interfaces that display discontinuous failure properties. An extreme case could be that shown in Figure 3(a). Imagine that the section B is firmly bonded to a massive protruding rock, either on the glacial wall or bed. As the temperature is increased the compression force developed by the now restrained expansion relative to the fixed section A, will also build-up. Eventually a temperature might reach a level when the rock is fractured and gouged out from its surrounding rock face. This fracture will be associated with the sudden release of a huge amount of thermally induced strain energy, with a rapid (surge) motion of the glacial ice likely to follow. Similar discontinuous forms of forward behaviour could be experienced over the entire length of the glacier. The effects will be essentially similar to that described above for the smooth frictional behaviour. During the subsequent cooling period the tensions resulting from the restrained contraction will be most unlikely to cause a reversal of the bed friction motion for the simple reason that the ice is likely to fracture in tension well before it reaches the levels required to induce bed shear failure.
Burgess, M and Smith, S. (2001) Climate change indicators – permafrost. WG1, IPCC Third Assessment Report, Climate Change 2001: The Scientific Basis, Chapter 2.2.5.3 Permafrost. See also: http://sts.gsc.nrcan.gc.ca/permafrost.
comparing gravity and thermal forces in glacial motion
In the previous posting it has been suggested that the levels of compression potentially developed by restraining the expansion of glacial ice during the warm-up period can be immense. Just how large can be seen by considering a situation where glacial ice having a typical coefficient of thermal expansion alfa = 90x10-6m/m/oC, and modulus of elasticity E=10x10+6 kN/m2 is subjected to an averaged, through-thickness, seasonal temperature increase of say T=10oC. If fully restrained from expansion this situation will generate a compressive force in the ice of 9000t kN for every metre width of glacier. It would not require a great thickness, t, of ice to be subjected to such a temperature increase for the stresses to reach the levels required to cause both elastic-visco-plastic shear flow in the ice and/or overcome the shear resistance offered by an even rough bed friction.
In contrast, a glacier having a slope of say, 5o, and ice with a specific weight of 9 kN/m3, will be generating forces of a little under 0.8t kN for every 1m of glacier length and every 1m width. Even over a very long section of glacier these accumulated gravity forces will be orders of magnitude less than those arising from the thermal expansion. The stored energy from the thermal expansion will likewise be orders of magnitude greater than that from the effects of gravity. The relatively low magnitudes of the gravitational forces are such that it is almost inconceivable they will be entirely responsible for both the recorded motions and the erosive powers of glaciers.
In contrast, a glacier having a slope of say, 5o, and ice with a specific weight of 9 kN/m3, will be generating forces of a little under 0.8t kN for every 1m of glacier length and every 1m width. Even over a very long section of glacier these accumulated gravity forces will be orders of magnitude less than those arising from the thermal expansion. The stored energy from the thermal expansion will likewise be orders of magnitude greater than that from the effects of gravity. The relatively low magnitudes of the gravitational forces are such that it is almost inconceivable they will be entirely responsible for both the recorded motions and the erosive powers of glaciers.
thermal ratchet models for glacial motion
There appears to be two, thermally induced, ratchet processes that could be at work in the movement of glacial ice. Depending upon the nature of the glacial terrain either could be playing a major role in the flow, or more correctly the motion, of glacial ice. What they share is an energy source derived from the solar induced cyclical variations of temperatures. They differ only as to the effects these cyclic temperatures have upon the ice.
In this posting these thermal ratchet processes will be described for an idealised conceptual model based upon the assumptions that the temperature increases are uniform through the thickness of the ice and that the movement of the ice is resisted by an idealised bed shear failure taking the form of a, so called, fully mobilised, kinematic friction. Furthermore, vertical sections through the ice before the temperature change will be considered to remain vertical after the temperature change. These assumptions are invoked merely to allow the mechanisms at work to be more clearly established. Later, brief consideration will be given to the more realistic circumstances of thermal gradients existing through the ice thickness, giving rise to stress gradients both through the thickness and laterally in the case of alpine glaciers. The ways that these stress gradients would develop non-uniform elastic-plastic shear distortions through the ice, in addition to the shear failures at the glacier-rock interfaces will also be considered in a later posting. Furthermore, in real glacial situations discrete obstructions will occur, such as protruding rocks, which will present a localised constraint to the motions. How these thermally based mechanisms would be modified to account for the sudden fracture of such obstacles will also be briefly touched upon in a later blog.
Material Ratchet: This process is closest to that described for the development of pingos (Croll. 2004b). It is also most likely to be the major driving force in the motions of continental ice, including the well documented outward flows of our contemporary ice-caps and those of even greater extent that occurred during glacial periods of the ice ages. Because these continental glacial motions account for the major part of the earth’s continuing ice movements, this mechanism is suggested to be potentially the more important ratchet process affecting glacial behaviour.
Consider a length l of essentially horizontal ice sheet depicted in Figure 1(a). This would be typical of that occurring at the upper glacier basin (cirques), or on the continental ice shelves. When during the spring to summer warm-up period an average increase in temperature of T occurs, a section B would if unrestrained move out relative to a section A which is assumed to remain effectively fixed in position. For a continental ice shelf the section A might be thought of as a central location of the ice sheet. For the upper reaches of an alpine glacier the section A could be thought of as the rigid rock face on the upstream side of the glacier or cirque containing the upper ice lake – like the flat accumulation zones talked about in the earlier posting. However, it is likely that the bedrock and valley walls will present a rough surface with the bond between the rock and the ice constraining movement by the development of friction between the underside of the glacial ice and the bedrock. If the friction between sections A and B, as shown in Figure 1(b), prevents all relative movement then for a temperature increase of T a compression force per unit width of magnitude C=alfa.T.E.t will be generated, where alfa is the coefficient of thermal expansion, E the modulus of elasticity, and t the assumed thickness of the ice sheet. As simple scoping calculations will later show these forces C can for even quite modest rises in temperature become immense, partly as a result of the extremely high coefficient of thermal expansion of ice. It is likely therefore, that at an early stage during this warm-up period the induced bed shear will become great enough to cause shear failure. When this occurs the interface in the present idealised model is taken to develop an assumed uniform mobilised frictional resistance of q per unit length. In this mobilised state the maximum compression force at A will remain at the level C=q.l, with section B moving outwards from A to relieve the thermal energy that would otherwise have been developed. By the end of the warm period it is likely that there will have been a number of such sudden releases of thermal energy, at various locations over the length of the glacier. In this way the glacial ice will have moved forward over its entire length, with a maximum outward motion of alfa.T.l, as shown in the sketch of Figure 1(c).
Another consequence of this form of slip-stick, fracture, behaviour will have been the release of the energy and an associated loss of the compressive energy stored within the ice. This means that at the end of the warm period the compression force will be considerably lower than that which would have been present had no shear failures occurred. As a consequence, when the cold season starts it will take only a small decrease in temperature before this residual compression force is overcome by the tensile strains arising from the constraint to thermal contraction. Continuing decreases in temperature will induce tensions in the ice. If the contraction was to occur about the geometric centre of the ice sheet then major fissures and crevices would be expected at the rigid restraint of the ice wall at A. At the free end B the fissures would likely be less pronounced and instead some recovery of the former outward deformation would occur. With ice being so weak in tension the tensile stresses at an early stage of the cooling cycle will cause tensile cracking, both in the form of discrete cracks and fissures, or major crevices. These tension failures would be likely to occur at force levels considerably lower than those needed to induce reversed bed shear failure at the interfaces between the ice and the bedrock. Consequently there would be little recovery of the glacial advances that had occurred during the warm period and the relative deformation that had occurred between sections B and A will not be recovered during the succeeding cooling period. This is suggested in Figure 1(d). Into the major fissures will flow precipitation and surface melt water runoff which will be quickly turned to ice. By the start of the next warm season the glacial ice will to a great extent have recovered its continuity and present a new, relatively stress free, integral ice sheet for the compressive actions to be repeated during the next cycle of warm-up. Over long periods it might be envisaged that the depth and the outward movement of the ice would reach a mass equilibrium with the rates of precipitation falling over the body of the ice sheet.
With the above mechanism being repeated each year, and to a lesser extent during any shorter periods, even daily thermal cycles, it is possible to envisage a gradual outward movement u of the glacial ice sheet relative to the assumed stationary section A. This thermal cycle and its associated internal compression force C, together with the outward motion u, are depicted in Figure 2. Figure 2 is of course a gross simplification since there will be a lot of other complexity occurring over a typical thermal cycle. However, it should serve to illustrate the mechanics involved in the postulated thermally induced, material property dependent, ratchet process. During the early warm-up period there will be a fairly rapid build-up of compression stress associated with the force C, shown by the line ab in Figure 2(b), but little forward movement u. When the compressive energy reaches levels required to overcome the static bed shear friction resistance there could be a fairly sudden, surge, forward movement u and a possible relief of the compression; this is depicted by the line bc. A period of steady forward motion would then accompany relatively steady compressive stresses required to overcome the assumed constant kinematic friction during the warmest season, shown as line cd. This residual compression would be quickly overcome during the start of the cooling period, line de, with an associated halt in the forward advance of the ice. Continuing cooling would be expected to result in a period of maximum tension cracking and an associated unstable form of glacial motion with relatively little net advance, as suggested by the jagged section ef.
It is significant that this form of slick-slip, thermal ratchet, behaviour could occur without any gravity forces being present. For this reason the ratchet action made possible by the discontinuous material failure characteristics of ice, provides a mechanism that could be important in both alpine but especially ice-sheet and continental glacial ice motions. This phenomenon of material failure induced ratchet is closely related to the process observed to occur in the motions of lake ice (Frellson, 1963).
Gravity Ratchet: Where the ice sheet sits upon an inclined plane as shown in Figure 3(a), a second form of thermal ratchet process can be set in motion. This ratchet continues to have thermal energy as its driving force but no longer requires the material to display discontinuous material failure properties. The trigger for this ratchet effect is provided by the relatively small component of gravity force acting parallel to the slope.
Consider a section of glacial ice similar to that of Figure 1(a) to be now located on a plane having slope θ. When subject to a temperature increase T, sufficient to overcome the static friction, the downhill section B will move downwards while an uphill section A would move upwards, with these relative motions being resisted by the fully mobilised bed kinematic friction q. These opposing motions will occur about a stagnation point D that remains fixed in position, as shown in Figure 3(b). This stagnation point will be located at a position offset by a distance x from the geometric centre O of the sheet, in such a way that the net upward friction force 2.q.x will equilibrate the downhill component of gravity force 2.gamma.t.l.sin theta, where gamma is the weight of ice per unit volume. Ignoring the elastic shortening associated with the compressive forces in the ice, the point O will as a result of the expansion move downward relative to the stationary point D through a distance given by u = alfa.T.x, where x = gamma.t.l.sin theta / q, so that
u = alfa.T.gamma.t.l.sin theta / q (1)
If the temperature is now lowered by T the ice sheet will contract with kinematic friction forces being developed as shown in Figure 3(c). During this phase of the thermal cycle the relative motions will occur about a stagnation point E located a distance x downhill from O so that the uphill friction force will now provide the equilibrant to the downhill gravitation component. Relative to the point E that does not move, the geometric centre O of the ice sheet will again move downhill by amount given by eqn (1). Each increase or decrease in temperature will cause the geometric centre of the ice mass to move a little further down the slope.
This form of thermal ratchet is directly related to the magnitude of the downhill gravitational component 2.gamma.t.l.sin theta. It might be anticipated to occur whenever the overlying sheet has a thermal expansion coefficient that is greater than the underlying bed material, or where the sheet has an average temperature change higher than in the bed material. With ice having such a high coefficient of thermal expansion, this form of ratchet action might be expected to be of considerable significance in the observed motions of certain forms of alpine glaciers.
Just to stress the point that above all relates to fairly idealised models of how thermal ratchets could be at work in glacial motion. It is intended to illustrate mechanical phenomena rather than reality. Some more realistic and practical considerations will be briefly covered in a future posting.
In this posting these thermal ratchet processes will be described for an idealised conceptual model based upon the assumptions that the temperature increases are uniform through the thickness of the ice and that the movement of the ice is resisted by an idealised bed shear failure taking the form of a, so called, fully mobilised, kinematic friction. Furthermore, vertical sections through the ice before the temperature change will be considered to remain vertical after the temperature change. These assumptions are invoked merely to allow the mechanisms at work to be more clearly established. Later, brief consideration will be given to the more realistic circumstances of thermal gradients existing through the ice thickness, giving rise to stress gradients both through the thickness and laterally in the case of alpine glaciers. The ways that these stress gradients would develop non-uniform elastic-plastic shear distortions through the ice, in addition to the shear failures at the glacier-rock interfaces will also be considered in a later posting. Furthermore, in real glacial situations discrete obstructions will occur, such as protruding rocks, which will present a localised constraint to the motions. How these thermally based mechanisms would be modified to account for the sudden fracture of such obstacles will also be briefly touched upon in a later blog.
Material Ratchet: This process is closest to that described for the development of pingos (Croll. 2004b). It is also most likely to be the major driving force in the motions of continental ice, including the well documented outward flows of our contemporary ice-caps and those of even greater extent that occurred during glacial periods of the ice ages. Because these continental glacial motions account for the major part of the earth’s continuing ice movements, this mechanism is suggested to be potentially the more important ratchet process affecting glacial behaviour.
Another consequence of this form of slip-stick, fracture, behaviour will have been the release of the energy and an associated loss of the compressive energy stored within the ice. This means that at the end of the warm period the compression force will be considerably lower than that which would have been present had no shear failures occurred. As a consequence, when the cold season starts it will take only a small decrease in temperature before this residual compression force is overcome by the tensile strains arising from the constraint to thermal contraction. Continuing decreases in temperature will induce tensions in the ice. If the contraction was to occur about the geometric centre of the ice sheet then major fissures and crevices would be expected at the rigid restraint of the ice wall at A. At the free end B the fissures would likely be less pronounced and instead some recovery of the former outward deformation would occur. With ice being so weak in tension the tensile stresses at an early stage of the cooling cycle will cause tensile cracking, both in the form of discrete cracks and fissures, or major crevices. These tension failures would be likely to occur at force levels considerably lower than those needed to induce reversed bed shear failure at the interfaces between the ice and the bedrock. Consequently there would be little recovery of the glacial advances that had occurred during the warm period and the relative deformation that had occurred between sections B and A will not be recovered during the succeeding cooling period. This is suggested in Figure 1(d). Into the major fissures will flow precipitation and surface melt water runoff which will be quickly turned to ice. By the start of the next warm season the glacial ice will to a great extent have recovered its continuity and present a new, relatively stress free, integral ice sheet for the compressive actions to be repeated during the next cycle of warm-up. Over long periods it might be envisaged that the depth and the outward movement of the ice would reach a mass equilibrium with the rates of precipitation falling over the body of the ice sheet.
It is significant that this form of slick-slip, thermal ratchet, behaviour could occur without any gravity forces being present. For this reason the ratchet action made possible by the discontinuous material failure characteristics of ice, provides a mechanism that could be important in both alpine but especially ice-sheet and continental glacial ice motions. This phenomenon of material failure induced ratchet is closely related to the process observed to occur in the motions of lake ice (Frellson, 1963).
Gravity Ratchet: Where the ice sheet sits upon an inclined plane as shown in Figure 3(a), a second form of thermal ratchet process can be set in motion. This ratchet continues to have thermal energy as its driving force but no longer requires the material to display discontinuous material failure properties. The trigger for this ratchet effect is provided by the relatively small component of gravity force acting parallel to the slope.
u = alfa.T.gamma.t.l.sin theta / q (1)
If the temperature is now lowered by T the ice sheet will contract with kinematic friction forces being developed as shown in Figure 3(c). During this phase of the thermal cycle the relative motions will occur about a stagnation point E located a distance x downhill from O so that the uphill friction force will now provide the equilibrant to the downhill gravitation component. Relative to the point E that does not move, the geometric centre O of the ice sheet will again move downhill by amount given by eqn (1). Each increase or decrease in temperature will cause the geometric centre of the ice mass to move a little further down the slope.
This form of thermal ratchet is directly related to the magnitude of the downhill gravitational component 2.gamma.t.l.sin theta. It might be anticipated to occur whenever the overlying sheet has a thermal expansion coefficient that is greater than the underlying bed material, or where the sheet has an average temperature change higher than in the bed material. With ice having such a high coefficient of thermal expansion, this form of ratchet action might be expected to be of considerable significance in the observed motions of certain forms of alpine glaciers.
Just to stress the point that above all relates to fairly idealised models of how thermal ratchets could be at work in glacial motion. It is intended to illustrate mechanical phenomena rather than reality. Some more realistic and practical considerations will be briefly covered in a future posting.
Monday 3 May 2010
from pingos to glacial motion
Over the past 15 years one of my more pleasant distractions has been the gradual exploration of the Mediterranean coastline in my much loved little yacht Rebellion II. By summer of 2004 I had reached the Bay of Naples and over the winter months had left Rebellion out of the water adjacent to the charming little port of Chiaiolella on the Isola di Procida about 10 miles west of Naples. If you have not visited Procida I would strongly recommend putting it on your list of places to go; it has all the geographic charm of its better known and larger neighbours of Capri and Ischia, but has the great advantage of having been largely overlooked by a tourist trade which really has come to blight its larger neighbours and especially Capri - but perhaps more about the delights of Procida and the rest of the Italian coastline in later postings. Its significance for the present is how it is relevant to the next theme of my blogs?
It was while flying down to Naples that the flight path from London had us crossing the Alps which even in late spring were still heavily shrouded in snow and ice. From my 35,000 ft vantage point on a perfectly clear day and while I was mulling over the little paper I intended to prepare for the upcoming IUTAM Symposium in Warsaw, I started thinking about the movement of glaciers, some wonderful examples of which could be clearly seen below. I had not really had a great deal of cause to think about glacial motion in the recent past but was aware that the driving mechanism was considered to be the gravitational components of force dragging the visco-plastic solid down through glacial valleys which were consequently gouged out by the massive forces being developed. And yet this did not seem to square with some of the features I was observing. At the heads of the glaciers there were large accumulation zones over which the lack of any shadows made it clear the ice surface was largely horizontal. (Being a bit of a skinflint I always tended to catch the very early but cheaper flights since anyone in their right mind would prefer to travel at more sociable hours. But this did mean there were still long early morning shadows highlighting the relief of the alpine topography below). Ice was evidently being shoved out of these accumulation zones over ice falls from which the valley glacier flowed. I say shoved because it was clear from the highly fissured and creviced outfalls from the accumulation zones that any possibility of tensile pull from the weight of the ice below could be dragging the ice from the accumulation zones was effectively ruled out. I had done enough geology during my engineering training to know that these accumulation zones would when the glaciers receded and eventually disappeared leave the distinctive features known as cirques. Now cirques tend to be gouged-out rock bowls surrounded by rock walls but usually with a lip leading out to the relic glacial valley. How I wondered did the ice in these horizontal bowls get extruded out over the lips to start what would become the downward flow of the alpine glacier? The Matterhorn was also clearly visible. Like a lot of the horns it was clear that this had been formed by the gouging-out of the rock from the back walls of at least 3 cirques that had eventually overlapped, with the steep sides of their back rock walls coalescing to form the characteristic horn shape. But where on earth did all the force required to chisel out such a shape come from? Again, it was pretty evident that gravity could not be providing this force. Having not resolved these and a few other question on arrival in Naples, I then spent any moments of mental calm, for sailing can often be a demanding activity in which there is not a lot of spare mental space, thinking about the questions of how all that ice is shoved out of the accumulation bowl to make its way down the steeper inclines of the glacial valleys. Could whatever was this motivating force also account for the tremendous erosion accompanying this glacial motion? And of course, given my own preoccupation at the time, I particularly wondered whether the ratchet model I was invoking to explain the upward distortions of permafrost to form pingos, might just provide at least some of the energy required to move this mass of glacial ice.
The result was a little paper entitled “The Movement of Glaciers”, which upon return to London was submitted to the J of Glaciology, I think sometime in late 2004. I say think since it too has not yet seen the light of day and until now has languished on a memory stick along with those thousands of photographs that also never seem to see the light of day.
But more on this and where it all led in later blogs.
It was while flying down to Naples that the flight path from London had us crossing the Alps which even in late spring were still heavily shrouded in snow and ice. From my 35,000 ft vantage point on a perfectly clear day and while I was mulling over the little paper I intended to prepare for the upcoming IUTAM Symposium in Warsaw, I started thinking about the movement of glaciers, some wonderful examples of which could be clearly seen below. I had not really had a great deal of cause to think about glacial motion in the recent past but was aware that the driving mechanism was considered to be the gravitational components of force dragging the visco-plastic solid down through glacial valleys which were consequently gouged out by the massive forces being developed. And yet this did not seem to square with some of the features I was observing. At the heads of the glaciers there were large accumulation zones over which the lack of any shadows made it clear the ice surface was largely horizontal. (Being a bit of a skinflint I always tended to catch the very early but cheaper flights since anyone in their right mind would prefer to travel at more sociable hours. But this did mean there were still long early morning shadows highlighting the relief of the alpine topography below). Ice was evidently being shoved out of these accumulation zones over ice falls from which the valley glacier flowed. I say shoved because it was clear from the highly fissured and creviced outfalls from the accumulation zones that any possibility of tensile pull from the weight of the ice below could be dragging the ice from the accumulation zones was effectively ruled out. I had done enough geology during my engineering training to know that these accumulation zones would when the glaciers receded and eventually disappeared leave the distinctive features known as cirques. Now cirques tend to be gouged-out rock bowls surrounded by rock walls but usually with a lip leading out to the relic glacial valley. How I wondered did the ice in these horizontal bowls get extruded out over the lips to start what would become the downward flow of the alpine glacier? The Matterhorn was also clearly visible. Like a lot of the horns it was clear that this had been formed by the gouging-out of the rock from the back walls of at least 3 cirques that had eventually overlapped, with the steep sides of their back rock walls coalescing to form the characteristic horn shape. But where on earth did all the force required to chisel out such a shape come from? Again, it was pretty evident that gravity could not be providing this force. Having not resolved these and a few other question on arrival in Naples, I then spent any moments of mental calm, for sailing can often be a demanding activity in which there is not a lot of spare mental space, thinking about the questions of how all that ice is shoved out of the accumulation bowl to make its way down the steeper inclines of the glacial valleys. Could whatever was this motivating force also account for the tremendous erosion accompanying this glacial motion? And of course, given my own preoccupation at the time, I particularly wondered whether the ratchet model I was invoking to explain the upward distortions of permafrost to form pingos, might just provide at least some of the energy required to move this mass of glacial ice.
The result was a little paper entitled “The Movement of Glaciers”, which upon return to London was submitted to the J of Glaciology, I think sometime in late 2004. I say think since it too has not yet seen the light of day and until now has languished on a memory stick along with those thousands of photographs that also never seem to see the light of day.
But more on this and where it all led in later blogs.
Friday 30 April 2010
problems in publishing the new hypothesis for pingo growth
My own first thoughts on the the thermal ratchet model for the devlopment of pingos were presented in a paper given to the 21st International Congress of Theoretical and Applied Mechanics (ICTAM-04) held in Warsaw in Auggust, 2004. While this was received with polite interest by the mechanics community it was disappointing that few people from the periglacial and permafrost communites were present. For this reason I prepared a slightly amended version of the paper for possible publication in the Proceedings of the Royal society, thinking that this would provide a suitably interdisciplinary venue to encourage discussion. Sadly this was not to be. The reviewers raised objections to the new model which it would have been very helpful to have been able to discuss. But peer review processes generally do not encourage dialogue between author and reviewer and so despite a second try with an amended manuscript and a few years of back and forth the manuscript remains unpublished. A similar fate awaited more recent attempts to publish in more specialist journals. And even an application for research funding was met by a similar range of objections to the new model. This was my first real experience of meeting a publication brick wall and made me realise all too clearly how resilient are the barriers for change and obstacles put in the way of anyone daring to try and publish work in disciplines outside their own little patch.
As future blogs will show I am becoming something of an expert in this experience.
Croll, J. G. A. (2004) An alternative model for “pingo” formation in permafrost regions, paper presented at 21st Int Congress of Theoretical and Applied Mechanics, ICTAM-04, Warsaw, 15-21 Aug., 2004, Abstracts and CD Rom Proceedings, 99.
As future blogs will show I am becoming something of an expert in this experience.
Croll, J. G. A. (2004) An alternative model for “pingo” formation in permafrost regions, paper presented at 21st Int Congress of Theoretical and Applied Mechanics, ICTAM-04, Warsaw, 15-21 Aug., 2004, Abstracts and CD Rom Proceedings, 99.
Monday 26 April 2010
why don't pingos disappear in winter?
Why the upward deformation of the pingo occurring during the warming period is not recovered during the following cooling period is believed to be the result of two important and interacting processes.
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.
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.
Friday 23 April 2010
pingos as a form of thermally induced upheaval buckling
Whether it be the bulges observed on lake ice or those so commonly experienced on asphalt pavements the thermal cycles described in previous blogs as being responsible for their development occur over time scales measured in terms of hours, days or possibly a few days. Such short term fluctuations in temperature are clearly not going to provide the driving force for the development of pingos. Pingos emerge from permafrost that can, even at the start of the upward growth, be many metres thick. Short term surface temperature changes will propagate just a few centimetres into the permafrost so that any expansion and contraction forces associated with these near surface temperature changes will be small, and insufficient to induce the levels of force required to cause an upheaval buckle to form. However, it is possible that the temperature variations experienced over typical annual seasonal cycles could be enough to induce levels of force sufficient to induce uplift of the permafrost.
Reports indicate that average seasonal changes of surface temperature could be as high as 15oC, and in the areas covered by Mackay et al (2002) and Burn (2004) the measured annual changes in ground temperature show that at ground surface, fluctuations in the region of 10oC can occur which with attenuation still show small changes at depths just above the aggrading lower permafrost boundary. MacCarthy (1952) reports seasonal maximum and minimum average daily temperatures varying at the ground surface by almost 20oC, with some changes still being experienced to a depth of 20 m. Ground water temperatures in the saturated talik remain fairly constant at just below zero. That being so it is more than conceivable that during the spring to late summer warm-up periods the average temperature through the permafrost thickness will rise sufficiently to induce in-plane compressive forces great enough to either initiate a thermal uplift buckle or, where one has already begun, allow it to further propagate. This would be especially likely if the pore water pressure increases that might have taken place over the autumn to winter period had approached the levels required to reduce the effective specific weight of the permafrost overburden. Let us consider in a little more detail how this process might occur and why any incremental uplift experienced by the permafrost during warming is not simply reversed when it is subsequently cooled.
Figure 1(a) depicts an area of locally thinned permafrost. This could be the result of an old lake being drained. The lake would have acted as a damper on the propagation of permafrost so that beneath the lake bed the permafrost remains relatively thin. Suppose that the permafrost layer has over the period of possibly a few winters extended some metres into the old bed of the lake, but the thickness beneath the old lake bed remains less than the surrounding more ancient permafrost. It is possible that frost heave or frost mounds could develop over this initial period. Naturally the bed of the lake will not be perfectly flat, and it is likely to contain areas where residual ponds occur. These could continue to act as a an insulator to the downward propagation of the permafrost so that an even thinner area exists. Frost heave will have resulted in mild upward convexity over both the old lake bed as well as the residual pond area. This will be especially so as a result of the differential frost heave that will have occurred as a consequence of the differential rates of aggradation of the lower permafrost boundary.This situation is depicted in Figure 1(b) within an area of the recently formed permafrost layer.
It has been observed in many cases that pingos initiate in areas where the drained lake has left shallow ponding. With the relatively thinner permafrost beneath this pond any lake bed convexity within the thinned area would be a prime target for the development of a thermal buckle. That the resulting upward bulges of the pingo are so often of a generally regular axisymmetric form, even within irregular ponds, is again highly suggestive that an important element in their origins might be from thermal buckling effects rather than as currently proposed just being pressure driven. As the permafrost layer warms during the spring to summer period, compressive forces will be generated over the entire area as a result of the restraint provided by the older and deeper permafrost surrounding bed of the lake, as suggested in Figure 1(c). Figure 1(c) represents an expanded horizontal scale of the central portion of the sketch of Figure 1(b). As seems to often be the case the pingo bulge does not necessarily occupy the full area of the thinner residual pond area. This too is suggestive of a mechanical cause other than, or at least additional to, underlying excessive ground water pressure.
To appreciate the levels of compressive force that may be generated in the permafrost layer consider the effect of an average temperature increase of 10oC, in the sense of representing the average of the change over the depth of the permafrost, from the midwinter minimum to the summer maximum temperatures. This might be considered reasonable in regions where, say, the surface temperatures exhibit seasonal surface temperature variations from minimum to maximum of say 30oC. With a coefficient of thermal expansion taken to be 50x10-6 / oC (coefficients of expansion for permafrost are not terribly well recorded but some reports have quoted values as 90x10-6 / oC or even higher, but a more representative figure of 50x10-6 / oC has, for example, been given by Washburn, p39, 1978) a fully restrained sheet will develop a stress producing, average, compressive strain of 500x10-6 which for a permafrost layer having an average modulus of elasticity E=5 GPa (again, the permafrost literature is a little bashful in terms of giving values of elastic modulus. One of the few publications making use of E values was that of Mackay (1986) which used a value of 19 MPa which seems extraordinarily low, so here I have adopted a value of 5 GPa that seems to be somewhat more representative - perhaps more on this in a later contribution) will generate an in-plane isostatic stress of 2.5 MPa. This would be more than enough incidentally to cause cracking when similar levels of temperature decrease occur over the next six month cycle. For a permafrost layer of thickness 5 m an average compressive stress of 2.5 MPa will result in compressive forces of 12.5 kN (one and a quarter tonne) for every 1 mm width of permafrost, or 12500 kN/m (1250 tonne for every 1 m strip width of permafrost). These extremely high levels of compressive force could conceivably produce an uplift buckle of the form shown as a detail to Figure 1(c).
Continuing with the above example, and assuming that the hypothetical pingo had over the previous years reached a state in which a total uplift of 5 m had occurred for the pingo of base radius a0 = 50 m. Under the extreme assumption that there were to be no underlying pore water pressure, so that q=75 kN/m2 (it being assumed that the specific weight of the permafrost is 15 kN/m3), then the temperature required to initiate first uplift from the talik would be around 2.25oC. An underlying ground water pressure having a head equal to the thickness of the permafrost layer would reduce this to around 0.7oC. For the case of pingo 14, having an assumed radius of the deforming portion of the pingo of 70 m and an uplift amplitude of 10 m above the surrounding ground surface, a local thickness t=22 m, and taken to also have coefficient of thermal expansion of 50x10-6 / oC, modulus of elasticity E=5 GPa, and Poisson’s ratio nu = 0.4, the temperature increase required to initiate uplift is effectively unchanged at T=2.2oC for no pore pressure and 0.7oC when the pore pressure reaches a head equal to the thickness of the permafrost sheet, ie the pore water would be enough to cause a gentle surface run-off from a borehole drilled into the underlying talik.
It appears that the amount of thermal energy associated with typical seasonal increases in temperature through the full thickness of the agrading permafrost layers, would be more than enough to induce the incremental seasonal uplifts of pingos. For more extensive discussion of the temperatures required to induce the typically observed levels of seasonal incremental uplift I would refer you to Croll (2004, 2005, 2007 pingos1). But a subsidary question must be, why do the pingos not just subside when during the late autumn to winter cooling period the average temperatures drop?
References:
Burn, C. R. (2004) A field perspective on modelling of “single-ridge” ice wedge polygons, Permafrost and Periglacial Processes, 15, 59-65.
Croll, J. G. A. (2004) An Alternative Model for “Pingo” Formation in Permafrost Regions, Paper presented at 21st Int Congress of Theoretical and Applied Mechanics, ICTAM-04, Warsaw, 15-21 Aug., 2004.
Croll, J. G. A. (2005) Aspects of the mechanics of pingo formation in permafrost regions, Internal UCL Research Report, 2004, submitted to Proc Royal Society for possible publication.
Croll, J. G. A. (2007) Mechanics of thermal ratchet uplift buckling in periglacial morphologies, Proceedings of the SEMC Conference, At Cape Town, September, 2007 (pingos1)
Mackay, J. R. (1998). Pingo growth and collapse, Tuktoyaktuk Peninsula area, Western Arctic Coast, Canada: a long-term field study, Geographie physique et Quarternaire, 52, 271-323.
Washburn, A. L. (1979) Geocryology: A survey of periglacial processes and environments, Edward Arnold, 406pp.
Reports indicate that average seasonal changes of surface temperature could be as high as 15oC, and in the areas covered by Mackay et al (2002) and Burn (2004) the measured annual changes in ground temperature show that at ground surface, fluctuations in the region of 10oC can occur which with attenuation still show small changes at depths just above the aggrading lower permafrost boundary. MacCarthy (1952) reports seasonal maximum and minimum average daily temperatures varying at the ground surface by almost 20oC, with some changes still being experienced to a depth of 20 m. Ground water temperatures in the saturated talik remain fairly constant at just below zero. That being so it is more than conceivable that during the spring to late summer warm-up periods the average temperature through the permafrost thickness will rise sufficiently to induce in-plane compressive forces great enough to either initiate a thermal uplift buckle or, where one has already begun, allow it to further propagate. This would be especially likely if the pore water pressure increases that might have taken place over the autumn to winter period had approached the levels required to reduce the effective specific weight of the permafrost overburden. Let us consider in a little more detail how this process might occur and why any incremental uplift experienced by the permafrost during warming is not simply reversed when it is subsequently cooled.
Figure 1(a) depicts an area of locally thinned permafrost. This could be the result of an old lake being drained. The lake would have acted as a damper on the propagation of permafrost so that beneath the lake bed the permafrost remains relatively thin. Suppose that the permafrost layer has over the period of possibly a few winters extended some metres into the old bed of the lake, but the thickness beneath the old lake bed remains less than the surrounding more ancient permafrost. It is possible that frost heave or frost mounds could develop over this initial period. Naturally the bed of the lake will not be perfectly flat, and it is likely to contain areas where residual ponds occur. These could continue to act as a an insulator to the downward propagation of the permafrost so that an even thinner area exists. Frost heave will have resulted in mild upward convexity over both the old lake bed as well as the residual pond area. This will be especially so as a result of the differential frost heave that will have occurred as a consequence of the differential rates of aggradation of the lower permafrost boundary.This situation is depicted in Figure 1(b) within an area of the recently formed permafrost layer.
It has been observed in many cases that pingos initiate in areas where the drained lake has left shallow ponding. With the relatively thinner permafrost beneath this pond any lake bed convexity within the thinned area would be a prime target for the development of a thermal buckle. That the resulting upward bulges of the pingo are so often of a generally regular axisymmetric form, even within irregular ponds, is again highly suggestive that an important element in their origins might be from thermal buckling effects rather than as currently proposed just being pressure driven. As the permafrost layer warms during the spring to summer period, compressive forces will be generated over the entire area as a result of the restraint provided by the older and deeper permafrost surrounding bed of the lake, as suggested in Figure 1(c). Figure 1(c) represents an expanded horizontal scale of the central portion of the sketch of Figure 1(b). As seems to often be the case the pingo bulge does not necessarily occupy the full area of the thinner residual pond area. This too is suggestive of a mechanical cause other than, or at least additional to, underlying excessive ground water pressure.
To appreciate the levels of compressive force that may be generated in the permafrost layer consider the effect of an average temperature increase of 10oC, in the sense of representing the average of the change over the depth of the permafrost, from the midwinter minimum to the summer maximum temperatures. This might be considered reasonable in regions where, say, the surface temperatures exhibit seasonal surface temperature variations from minimum to maximum of say 30oC. With a coefficient of thermal expansion taken to be 50x10-6 / oC (coefficients of expansion for permafrost are not terribly well recorded but some reports have quoted values as 90x10-6 / oC or even higher, but a more representative figure of 50x10-6 / oC has, for example, been given by Washburn, p39, 1978) a fully restrained sheet will develop a stress producing, average, compressive strain of 500x10-6 which for a permafrost layer having an average modulus of elasticity E=5 GPa (again, the permafrost literature is a little bashful in terms of giving values of elastic modulus. One of the few publications making use of E values was that of Mackay (1986) which used a value of 19 MPa which seems extraordinarily low, so here I have adopted a value of 5 GPa that seems to be somewhat more representative - perhaps more on this in a later contribution) will generate an in-plane isostatic stress of 2.5 MPa. This would be more than enough incidentally to cause cracking when similar levels of temperature decrease occur over the next six month cycle. For a permafrost layer of thickness 5 m an average compressive stress of 2.5 MPa will result in compressive forces of 12.5 kN (one and a quarter tonne) for every 1 mm width of permafrost, or 12500 kN/m (1250 tonne for every 1 m strip width of permafrost). These extremely high levels of compressive force could conceivably produce an uplift buckle of the form shown as a detail to Figure 1(c).
Continuing with the above example, and assuming that the hypothetical pingo had over the previous years reached a state in which a total uplift of 5 m had occurred for the pingo of base radius a0 = 50 m. Under the extreme assumption that there were to be no underlying pore water pressure, so that q=75 kN/m2 (it being assumed that the specific weight of the permafrost is 15 kN/m3), then the temperature required to initiate first uplift from the talik would be around 2.25oC. An underlying ground water pressure having a head equal to the thickness of the permafrost layer would reduce this to around 0.7oC. For the case of pingo 14, having an assumed radius of the deforming portion of the pingo of 70 m and an uplift amplitude of 10 m above the surrounding ground surface, a local thickness t=22 m, and taken to also have coefficient of thermal expansion of 50x10-6 / oC, modulus of elasticity E=5 GPa, and Poisson’s ratio nu = 0.4, the temperature increase required to initiate uplift is effectively unchanged at T=2.2oC for no pore pressure and 0.7oC when the pore pressure reaches a head equal to the thickness of the permafrost sheet, ie the pore water would be enough to cause a gentle surface run-off from a borehole drilled into the underlying talik.
It appears that the amount of thermal energy associated with typical seasonal increases in temperature through the full thickness of the agrading permafrost layers, would be more than enough to induce the incremental seasonal uplifts of pingos. For more extensive discussion of the temperatures required to induce the typically observed levels of seasonal incremental uplift I would refer you to Croll (2004, 2005, 2007 pingos1). But a subsidary question must be, why do the pingos not just subside when during the late autumn to winter cooling period the average temperatures drop?
References:
Burn, C. R. (2004) A field perspective on modelling of “single-ridge” ice wedge polygons, Permafrost and Periglacial Processes, 15, 59-65.
Croll, J. G. A. (2004) An Alternative Model for “Pingo” Formation in Permafrost Regions, Paper presented at 21st Int Congress of Theoretical and Applied Mechanics, ICTAM-04, Warsaw, 15-21 Aug., 2004.
Croll, J. G. A. (2005) Aspects of the mechanics of pingo formation in permafrost regions, Internal UCL Research Report, 2004, submitted to Proc Royal Society for possible publication.
Croll, J. G. A. (2007) Mechanics of thermal ratchet uplift buckling in periglacial morphologies, Proceedings of the SEMC Conference, At Cape Town, September, 2007 (pingos1)
Mackay, J. R. (1998). Pingo growth and collapse, Tuktoyaktuk Peninsula area, Western Arctic Coast, Canada: a long-term field study, Geographie physique et Quarternaire, 52, 271-323.
Washburn, A. L. (1979) Geocryology: A survey of periglacial processes and environments, Edward Arnold, 406pp.
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