Propagation of glacier surges - Canadian Science Publishing

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Propagation of glacier surges has been discussed in terms of stresses acting in the three major zones of the surge. The steeply sloping front of a surge appears ...

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Propagation of glacier surges Article  in  Canadian Journal of Earth Sciences · February 2011 DOI: 10.1139/e69-101





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Propagation of glacier surges1 G . DE Q.ROBIN Can. J. Earth Sci. Downloaded from by Harbin Industrial University on 06/06/13 For personal use only.

Scott Polar Research Institute, Cambridge, England AND

P. BARNES Cavendish Laboratory, Cambridge, England Received February 10, 1969 Accepted for publication April 23, 1969

Propagation of glacier surges has been discussed in terms of stresses acting in the three major zones of the surge. The steeply sloping front of a surge appears sufficient to explain the thickening of a glacier and the rise in velocity of ice motion which takes place across this zone in terms of accepted stress-strain rate data for ice. Explanation of the high velocities which occur in the next zone in spite of little change in the available shear stress is more difficult, but the experimental results of Barnes and Tabor on ice close to the melting point appear to offer an explanation of the unusually high rates of flow. In the tensile zone, where velocities slow down, the net lowering of the glacier surface after the surge has passed is explained in terms of the depth of crevassing and easier flow of ice at melting point when under tensile and shear stresses.

Propagation of Glacier Surges In a preceding paper (Robin 1969), the possibility of initiating a glacier surge by a switch from extending to compressive flow in the accumulation zone, or the opposite switch in the ablation zone, was put forward. This paper is intended to relate the forces released by such a switch to laboratory studies of the deformation and sliding of ice by Glen (1955), Barnes and Tabor (1966), Barnes ( 1968), and Barnes et al. (in preparation). For discussion we have redrawn Figs. 3 and 4 of Robin (1969) as Figs. I (a)and 1(b) and have divided the profiles into zones A, B, C, and D. In Fig. I (a), we show the situation which might initiate a surge in the accumulation zone, in Fig. 1( b ) the comespunding situation in the ablation zone, and in Fig. 1(c) the possible form of the wave as it travels down a uniform section of the glacier. The zones have been chosen as follows: Zone A:-The zone of strong compression across which the ice flow accelerates. In Fig. 1(b) there may be some doubt as to the exact location of zone A. Zone B:-The main zone of high velocity flow of ice. Zone C:-The tension zone in which the ice velocity slows down. 1Presented at the Seminar on the Causes and Mechanics of Glacier Surges, St. Hilaire, Quebec, !ieptember 10-11, 1968. t hadian

Journal of Earth Sciences, 6,969 (1969)

Zone D:-The stagnant zone in which ice movement is low. This zone may either be formed after the wave has passed a given point, or may be upstream in a region not affected by the surge. The above zones fit our postulated model of causes which initiate a surge, and in a propagating surge (Fig. 1 ( c ) ) they appear to correspond to features described by Harrison ( 1964) for the surge of the Muldrow Glacier in 1956-57 as follows: His "velocity jump" where the rapidly moving ice meets relatively stagnant ice would correspond to the leading edge of zone A. His "compression-tension boundary" would lie in zone B, while his point where the ice level has dropped 15 m would lie in zone C. On July 6-7, 1956, it was 4.8 km from the velocity jump to the compression-tension boundary, and a further 4.8 km to the 15 m drop in ice level. On August 13, the first two features had moved about 13 km down glacier, the distance separating the velocity jump from the compression-tension boundary still being 4.8 km, while the location of the 15 m drop in ice level had trailed to 6.3 km behind the compressiontension boundary. The total length of the glacier is about 60 km, and the earliest motion associated with the surge was seen about 6 km down glacier from the ikn line. It seems possible that the surge could have started either in the accumulation zone or the ablation zone, the latter being more likely.

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VOL. 6,


FIG. 1. l(a) and 1 (b) Figure show suggestedbedrock and surface profiles associated with formation of a glacier surge. Figure l(a) shows the possible situation in the accumulation zone while Fig. l(b) shows the postulated situation in the ablation zone (see Robin 1969). Figure l ( c ) shows the suggested profile of the upper surface of a surge as lt IS propagated down the glacier, in comparison with a probab!e steady-state profile. Zones B and C.should be drawn with their length an order of magnitude greater than their thickness. This has not been shown 1x1 t h ~ schematic s d~agcamIn order to maintain an effective impression of relative surface slopes.

Dimensions of Surge Zones Although detailed evidence is scarce, we have concluded that the dimensions of the zones on a surging glacier are as follows: Zone A:-Length is thought to be of similar order to the ice thickness.

Zones B and C:-It is clear from observations on the Muldrow Glacier and elsewhere that the length of these zones is an order of magnitude greater than the ice thickness. Zone D:-In Fig. 1 (a) this is the portion of the glacier not affected by the surge. In some

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cases the surge appears to extend to the headwall of the glacier, while in other cases such as the Muldrow Glacier, a large portion of the accumulation zone is not affected by the surge. In Fig. 1(c) this zone may include the whole glacier when the surge is finished. In developing our discussion we must note that zones B and C are so long that the motion and strain rates in each of these zones must be produced by the stress field characteristic of each zone. Surface Slopes and Main Stress Systems We will discuss the surge in terms of basal shear stress 7 , the longitudinal stress uO, as used in the preceding paper by Robin, and the surface slope a. The equation connecting these terms has been discussed in the earlier paper, namely

and in most cases the last term is negligible and it is reasonable to simplify equation [ I ] to doxO pgha = T - h -dx Zone A In a propagating surge (Fig. 1(c) ), this is the zone of steep frontal slope. In our models of Figs. 1(a) and 1(b), this is the zone where the ice thickness of a slowly moving glacier increases by about 30 m in the negative x direction over the thickness necessary if the same glacier was flowing at greater speed. In all cases it appears that we have an extra "head" of pressure of about 30 m which can produce longitudinal stresses in the glacier of the order of 3 bars. According to the results of Glen (1955), such a stress at -1.5 OC will produce longitudinal strain rates of 1 year - l or of 5 year-l at -0.02 "C. These stlain rates are of the order needed to produce the thickening of the glacier as the surge front passes a given point-since the estimated thickening of the order of 10% in a week or a month is produced by a strain rate of 1-4 year-l. Corresponding to these figures for vertical thickening we must have acceleration of velocity across the zone of 0.5-2.0 km/year. Thus the stresses and longitudinal strain rates of a moving surge in


zone A appear to fit laboratory results, while the models in Figs. 1(a) and 1(b) could produce the conditions to initiate the surge. As the velocity increases across zone A, we may also have a sharp rise in basal shear stress to, say, double its normal value, since this may be necessary to accelerate the ice motion across this zone to the higher speeds existing in zone B. Associated with the increased deformation in zone A will be a certain amount of warming of ice because of the work done. Rough estimates put this at about calories per cm3 throughout the ice mass due to the general thickening, whilst the increased basal sliding across the zone will liberate something like per cm2, which if distributed lO+alories through a column 10 m high would raise the ice temperature by perhaps 0.1-0.2 "C, or produce an equivalent amount of melting. The purpose of these rough figures is to indicate that the work done on the ice in zone A may put it into the state where it will react easily to pressure melting phenomena in zone Bespecially in the basal layers of ice, since as the surge moves down glacier, any portion of the glacier will be affected successively by the phenomena of zones A, B, C, and D in that order. Zone B In this zone, which is an order of magnitude greater-in length than the ice thickness, velocities of ice movement of several kilometers per year occur commonly. The surface slopes do not differ greatly from those of other glaciers, nor from that of the glacier before the surge. On our model in Figs. 1(a) and 1(b) the ice thickness may be of the order of 30 m greater than that required for steady-state flow, and this could produce a basal shear stress of the order of 10% above that necessary for normal flow. We attempt in this paper to see if there is any evidence from laboratory results to explain this anomalously high rate of flow. The only available theories to explain this phenomenon are those of Weertman (1964) and Lliboutry (1968), but these theories have not been verified directly by experiment. Barnes (1968) analyzed the results of the friction of sliding a steel ball over a smooth ice surface. By measuring the depth and width of the resultant groove, he was able to calculate the component of friction due to ploughing and

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FIG.2. Comvonents of sliding - friction of a steel ball on ice (Barnes 1968). The diameter of the steel ball was

5 cm.

that due to adhesion. The result is shown in Fig. 2. Although the total friction increased as the melting point was reached, this was calculated to be a result of increased depth of ploughing at warmer temperatures, while the adhesion component decreased as melting point was approached. However, under a glacier which is sufficiently thick (say 200-400 m) to ensure the ice remains in contact with bedrock, one would expect a constant depth of ploughing, irrespective of temperature, for a glacier sliding over relatively few obstacles of horizontal dimensions ranging from a few centimeters to tens of meters. In order to sort out the two types of friction, the friction of an ice slider moving over a flat steel surface was measured by Barnes. In this case ploughing is considered negligible, so that we are dealing only with the adhesion term. The results are shown in Figs. 3 and 4, the former showing the change in the coefficient of friction ( p ) with temperatures for two different sliding rates, while Fig. 4 shows the coefficient of friction ( p ) plotted against speed of sliding for a series of different temperatures. Speeds of 10-4-10-5 cm/s are typical of the sliding velocity of temperate glaciers, whereas

a surging glacier is likely to be sliding at about cm/s or faster. We note a tendency for the coefficient of friction to increase around cm/s, after which the increase is small for considerable increases in velocity. Such a situation fits the character of surges, except that close to the melting point the coefficient of friction is down to 0.002, corresponding to a retarding force of about 0.05 bar under 300 m of ice. In other words, the adhesion component of friction appears to be so low that it alone cannot account for the frictional retardation of glaciers, and we have to consider the ploughing term as the major component of basal friction. The results indicate that the models of basal friction used by Weertman and Lliboutry would be applicable even in the absence of any appreciable water fYm to make friction between "obstacles" negligible. Evidence on the stress-strain rate relationship due to the ploughing term is available from the hardness tests reported by Barnes and Tabor (1966) and from further results of Barnes (1968). It should be emphasized that these experiments started as a series of tests of sliding a steel ball over an ice surface, and it was found that the results of such sliding ex-


, , 2.2. lo-'c m./s Can. J. Earth Sci. Downloaded from by Harbin Industrial University on 06/06/13 For personal use only.






FIG. 3. Sliding l5iction of polycrystaIline ice on smooth steel shown as a function of temperature for two sliding velocities.

FIG.4. Sliding friction of polycrystalline ice on smooth steel shown as a function of velocity of sliding at different temperatures.




6 , 1969




, 'melt~nqcurve




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Loadinq time (t)

FIG.5 . Indentation hardness of ice shown in relation to temperature for different loading times. The broken curve indicates the temperature at which pressure melting will occur at different stresses given by the hardness scale.

periments were directly comparable to the results of the hardness tests. In the former experiment one set up a system to produce a groove in an ice surface, as opposed to a simple indentation in a hardness test. The hardness tests are much simpler to carry out. They also possess the advantage in this case that they are essentially related to the ploughing term in friction, but not to the adhesion term. The results of Barnes (1968) are shown in Fig. 5, which presents hardness against loading time for a pyramidal steel indenter. At the lower hardness figures of 0.1-0.2 kg/mm2 (corresponding to 10-20 bars), we see that in ice which is only 0.25 "C warmer, we have an order of magnitude increase of strain rate for the same applied stress. The point is perhaps brought out more clearly in relation to strain rate by a comparative plot of Barnes7hardness and Glen's stress-strain results in Fig. 6. A detailed study of the deformation zone around the indentations showed that in the pressure melting regime the crystal size was much larger than for corresponding deformation of colder ice, and in this zone air bubbles

were largely eliminated when pressure melting was present. It was pointed out by Barnes and Robin (1966) that the sole of temperate glaciers had similar characteristics. In addition, studies on Blue Glacier by Karnb and La Chapelle ( 1964) showed that the sole of 50-cm thickness deformed more rapidly than the ice immediately above. Although regelation processes are of major importance around small obstacles, when we are dealing with larger obstacles and rapid deformation throughout a thickness of 0.5 m or more we need an alternative mechanism of rapid deformation such as the grain boundary effect postulated by Barnes (1968). The laboratory results therefore appear very relevant to studies of deformation of the basal layers of a temperate glacier, although the experimental data are not yet in a form in which they can readily be incorporated into current theory. Even so, they suggest that we may well explain the surges by means of a glacier sole ten times as thick as the usual half meter or so, throughout which the strain rates are ten times greater than normal.









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pressure 'Meltmq Curve



t=1&s 1.10s





t=rds t=rds


- 320 years-'