Positive feedbacks associated with erosion of glacial and

ROGER LEB. HOOKE Department of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota 55455

ABSTRACT lower headwall, are not clear. Johnson (1904) rock ridge, or riegel, that shows effects of intense observed what he inferred to be the results of abrasion. From the riegel, a steep scarp leads The principal points of water input to a frost shattering during a descent into a berg- down to the next lower basin. Similar overdeep- are the bergschrund in cirques, and schrund that reached a floor, and thus enings are being found with increasing fre- fields lower on the glacier. Crevasse attributed erosion of lower headwalls to this quency in the course of radio-echo mapping of fields commonly occur over convexities at the process. Battle (Battle and Lewis, 1951; Thomp- the beds of valleys that still contain . The heads of overdeepenings in glacier beds. The son and Bonnlander, 1956; Battle, 1960) and of Storglaciaren, a small glacier in north- amplitude of subglacial water-pressure fluc- later Gardner (1987) demonstrated that temper- ern Sweden, has four (Fig. 1). tuations is large just down-glacier from these ature changes in a bergschrund during the Because it was inferred that higher parts of a points of water input. Erosion by quarrying is summer were small, however, and thus con- glacier bed should be worn down faster, litho- likely in such areas. Erosion is thus inferred cluded that frost shattering might not be signifi- logic and structural inhomogeneities were to be localized on the headwalls of cirques cant. Secular changes in temperature (Fisher, sought to explain these staircase profiles (Ritter, and overdeepenings. In the case of overdeep- 1955, p. 589-590), or of ice thickness and hence 1978, p. 390-391). Such inhomogeneities are, at enings, this leads to a positive feedback proc- pressure (Lewis, 1954), that might cause shatter- least, in part, responsible for the largest of the ess in which a perturbation in the bed causes ing at greater depths were invoked to resolve this overdeepenings on Storglaciaren (Jansson and crevassing at the surface, resulting in ero- apparent paradox, but they are too infrequent to Hooke, 1989, p. 207), but they are by no means sional forces that accentuate the perturbation. account for observed erosion rates. responsible for all overdeepenings. When subglacial water flows up an adverse More recently, it has become clear that large The realization that overdeepenings are a bed slope leading out of a cirque or over- variations in temperature are not necessary for common characteristic of glacier beds, not nec- deepening, much of the viscous energy dissi- frost shattering. Water trickling into a berg- essarily related to lithologic variations, suggests pated is used to warm the water to keep it at schrund can maintain rock surfaces at the melt- that they may reflect some form of instability, or the pressure melting temperature as the ice ing point while colder temperatures prevail positive feedback process, such that after a de- thins and the pressure decreases. In such sit- deeper within the rock. Chemical potential gra- pression of sufficient size has formed in the bed, uations, subglacial conduits are maintained dients that drive water toward zones of lower it erodes downward, and especially headward, by high water pressures rather than by temperature in frozen porous media then force faster than the rest of the bed. The morphologi- melting of conduit walls. In the limit, water the water into the rock where it can freeze cal similarity between headwalls of overdeepen- pressures apparently become so high that (Walder and Hallet, 1985, 1986). Frost shatter- ings and those of cirques, together with the water is forced out along the ice-bed interface ing in a bergschrund is, therefore, plausible. observation that overdeepened basins lie down- and the conduits collapse. The products of On the other hand, for more than 90% of the glacier from both types of headwall, motivates a erosion are then no longer flushed out, and a time during the past 2 m.y., glaciers were sub- search for a common mechanism of formation protective till layer accumulates. By limiting stantially larger than they are at present (Porter, for the two types of feature. erosion on such adverse bed slopes, this till 1989, p. 246). Thus, as recognized by Battle An analytical model that begins to address the layer controls the geometry of these over- (Thompson and Bonnlander, 1956), as well as positive feedback problem is that of Mazo deepened basins. others, much of the erosion of the cirques we see (1989), in which wave dispersion leads to a fa- today must have been a consequence of proc- vored wavelength for the distance between rie- INTRODUCTION esses that operate at depths well below those gels. In the case of Storglaciaren, the predicted reached by the bergschrund. The task at hand is wavelength is 1.8 km, which is significantly Cirque Erosion to clarify these processes. longer than observed. The fundamental differ- ence between Mazo's model and that presented Retreat of that part of a steep cirque headwall Overdeepenings herein is that Mazo assumes an initial perturba- that towers above a glacier surface is normally tion of infinitesimal height, and his analysis is attributed to frost shattering, but erosion of the Deglaciated valleys commonly have irregular not valid when bed relief is of the same order as cirque floor is assumed to be by abrasion and longitudinal profiles characterized by a series of the ice thickness, whereas the present model re- quarrying (Embleton and King, 1968, p. 2-14). overdeepenings that frequently contain lakes. quires initial perturbations that are large enough Details of the mechanism of retreat of the sec- The down-valley ends of such overdeepenings to affect the topography of the glacier surface. A tion of the headwall lying between the glacier are sometimes formed by , but often further difference is that Mazo assumes that the surface and the cirque floor, herein called the there is, instead or in addition, a transverse bed- erosion rate is proportional to the basal shear

Geological Society of America Bulletin, v. 103, p. 1104-1108, 3 figs., August 1991.

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their heads. Pressure fluctuations are much greater immediately down-glacier from these points of water input than up-glacier from them. These water inputs and resulting pressure fluc- tuations thus appear to occur at precisely the points where erosion is necessary to maintain the headwalls. In the present model, crevassing over a minor convexity in the bed, the initial perturbation, localizes water input and hence erosion. As ero- sion progresses, the convexity in the bed is am- plified, resulting in further crevassing. This is the positive feedback process sought. In the rest of this paper, I expand upon the diverse theoretical developments and field evi- dence on which this model is based. Recent studies of the quarrying problem are discussed next, followed by an overview of water-pressure data from Storglaciaren collected over the past 9 years. Finally, the role of a subglacial till layer is examined.

EROSIONAL PROCESSES

Glaciers erode by a combination of abrasion and quarrying. Herein we concentrate on quar- rying, as it is probably quantitatively more im- portant than abrasion in the general case (Jahns, 1943, p. 81-94; Drewry, 1986, p. 90) and is certainly more important on cirque and over- deepening headwalls in particular. In quarrying, blocks of bedrock must first be loosened, either along preglacial joints or along fractures formed by subglacial processes. They then must be en- trained by the basal ice. Rapid water-pressure fluctuations within cavities in the lee of a bump on a glacier bed may play a role in both the fracture and entrainment processes (Rothlis- berger and Iken, 1981; Iverson, 1989). We con- sider fracture first. Water inputs to a glacier due to rain or melt may vary rapidly, causing subglacial cavities in the lees of bumps on the bed to fill and drain faster than they can adjust by flow of the ice. Figure 1. Map of Storglaciaren, showing surface and bed topography, and locations of The resulting pressure fluctuations transfer the boreholes discussed in text. Bed topography from Eriksson (1990). weight of the glacier first to, and then from, the tops of the bumps. Under 250 m of ice, for example, the pressure could vary from a rela- stress. Headwall morphology, however, points Theoretical studies suggest that quarrying may tively uniform 22 bars on all faces of a bump to to quarrying as the dominant erosional mecha- be due to water-pressure fluctuations on time more than 60 bars, say, on the top, and nearly nism, and, as discussed below, the rate of quarry- scales of a few hours to a few days (Ròthlis- zero on the lee face. Such stress differences can ing is apparently determined more by variations berger and Iken, 1981; Iverson, 1989 and in lead to propagation of tensile fractures at the tips in normal stress than by the absolute value of the press). Subglacial water pressures fluctuate of favorably oriented pre-existing cracks (Grif- shear stress. when water inputs to a glacier alternately fall fith, 1924), even at stresses well below the exper- below or exceed the ability of the glacial drain- imentally determined tensile strength of the rock THE INSTABILITY age system to transmit the flow (Iken and Bind- (Atkinson and Rawlings, 1981; Atkinson, 1984; schadler, 1986; Hooke and others, 1989). In the Segall, 1984). The likelihood of crack growth As noted above, the steep headwalls of both case of cirques, the water input is localized by increases when the water pressure within cracks cirques and overdeepenings are herein presumed the bergschrund; in the case of overdeepenings, remains elevated while that in an adjacent cavity to be eroded principally by glacial quarrying. by that form over the convexities at drops, or when stress corrosion reduces the

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Figure 2. Longitudinal section of Storgiaciaren along an approximate flowline (Fig. 1), showing relationship between water-input points (crevasse zones and bergschrund) and presumed sites of quarrying (triangles). Water levels (circles) in boreholes in the are close to water equivalent line (w.e.l.). Water-level records from boreholes 83-5,84-1, and 90-1 are shown in Figure 3. Dashed line labeled "riegel" shows profile of riegel projected onto line of profile.

strength of the rock (Iverson, in press). Even exceed frictional forces tending to hold them in ess is more effective at higher sliding velocities; higher and more concentrated stress differences place (Iverson, 1989). Both are affected by fluc- thus increases in subglacial water pressure that can result when a cobble or boulder is dragged tuations in water pressure. Pressure-release freez- cause increases in sliding speed should increase over a bump by the ice. Thus it now seems safe ing may occur on tops of bumps when increases its effectiveness. to conclude, as field data (for example, Sharp, in water pressure in cavities transfer part of the Frictional forces resisting dislodgment of 1982) have suggested, that even sound crystal- weight of a glacier away from the bumps. The loosened blocks are reduced as water pressures line rocks can be fractured subglacially through drag exerted by the ice is thus increased (Robin, rise (Iverson, 1989). This is because the normal the action of ice and water, despite the fact that 1976). Similar cold patches can also develop pressure that ice exerts on a bedrock surface the ice is much weaker than the underlying rock. due to simple flow of the ice from the stoss side up-glacier from a cavity is reduced, thus decreas- Entrainment requires that bed-parallel forces of a bump to its crest (Robin, 1976). This proc- ing the friction along fractures that bound loos- tending to slide loosened blocks out of position ened blocks. In addition, after fractures are well

July August

Figure 3. Water-level records from three boreholes. Borehole locations are shown in Figures 1 and 2. Holes 83-5 and 84-1 were below the riegel. Records from them were obtained in 1984. As the dynamic range of the transducers was less than the change in water pressure, the transducer in Hole 83-5, which was emplaced at a greater depth than that in Hole 84-1, did not record peak water levels, but it did record levels lower than those recorded in Hole 84-1. Where they overlap, the two records are nearly identical. Hole 90-1 was above the riegel at the lower end of the main overdeepening, and the record from it was obtained in 1990.

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developed and in hydraulic communication needed to warm the flowing water to keep it at the riegel changed from its mean value of about with cavities, increases in water pressure in the the pressure melting point is supplied by freezing -0.003 a"1 (compressive) to +0.002 a-1 aver- fractures reduces the effective pressure across of some of the water on conduit walls. To main- aged over about 7 days (Hooke and others, fracture surfaces. tain the conduit size under these conditions, 1983, Fig. 2 and p. 274). More recent measure- In summary, fluctuations in subglacial water water pressures must become so high that they ments show similar changes in strain rate over pressure and associated transient changes in exceed the pressure in the ice. Conduits would the riegel itself during July 1983 and June 1984 glacier sliding speed appear to be necessary for then be enlarged by plastic flow. In reality, it (Hooke and others, 1989, Fig. 5). quarrying. Abrupt reductions in water pressure seems likely that before this condition obtains, Exactly where water entering a or promote subglacial fracture, whereas increases, water will be squeezed out into a thin film along crevasse system reaches a glacier bed is a rele- whether rapid or more gradual, promote the dis- the bed. Subglacial conduits then cease to exist, vant question. Studies of moulins developed lodgment of loosened blocks. and, as noted, the water is forced to find engla- over the riegel at the down-glacier end of the cial ones. We infer that this is why drainage main overdeepening on Storglaciaren demon- SPATIAL AND TEMPORAL through the main overdeepening on Storgla- strate that the water goes down essentially verti- VARIATIONS IN WATER PRESSURE ciaren is englacial (Hooke and others, 1988; cally for nearly half the glacier thickness ON STORGLACIAREN D. W. Wiberg and R. LeB. Hooke, unpub. (Holmlund, 1988). If it were then to flow nor- data). mal to equipotential surfaces in the ice, as sug- The principal drainage system through the In the absence of subglacial drainage that is gested by Shreve (1972), it would reach the bed main overdeepening on Storglaciaren (Fig. 2) is sufficient to flush sediment from a glacier sole, a several hundred meters down-glacier from the known to be englacial (Hooke and others, 1988; subglacial layer of till may accumulate. It is in- riegel (Fig. 2). Such flow, however, is expected D. W. Wiberg and R. LeB. Hooke, unpub. ferred that this is why such a layer appears to only when water pressures in the conduits are data). Of 47 boreholes drilled in this part of the have formed in the main overdeepening on controlled, in part, by the pressure in the sur- glacier in the past 9 years, 66% encountered en- Storglaciaren (Brand and others, 1987; J. Paetz rounding ice. In steep conduits at moderate glacial conduits, but only 13% drained subgla- and R. LeB. Hooke, unpub. data; N. R. Iverson depths, the energy dissipated by water flowing in cially (the remainder did not drain). Further- and R. LeB. Hooke, unpub. data). As noted, the conduits will enlarge them faster than they more, dye injected in englacially draining however, dye-trace data suggest that an ineffi- close by plastic flow of the ice (Hooke, 1984). boreholes appears at the in a cient drainage system exists between the ice and Water pressures then do not depend on the pres- single slug after only a few hours, bilt that in- this till. sure in the ice, and the water will tend to move vertically downward, solely under the influence jected in holes draining subglacially appears spo- In contrast to the situation in the overdeepen- of gravity. That such is the case on Storglaciaren radically, in very small quantities, over many ing, water pressures measured below the riegel is suggested by the fact that dye injected in mou- days or weeks. The frequency with which engla- on Storglaciaren show large variations, often on lins over the riegel appears in a dirt-laden stream cial conduits are encountered in boreholes, a diurnal time scale (Fig. 3). It is inferred that at the terminus (Seaberg and others, 1988). In however, implies that there are a great many this behavior is representative of that which oc- contrast, dye injected in englacially draining such conduits. They must, therefore, be small, curs just down glacier from other points of water boreholes in the overdeepening appears in a and dye-trace data suggest that they are easily input, such as the bergschrund or the crevasse stream that carries a comparatively low sedi- disrupted (Hooke and others, 1988; D. W. Wi- field above the head of the overdeepening. ment load. Also noteworthy is the fact that the berg and R. LeB. Hooke, unpub. data). Water-pressure measurements in these locations diurnal fluctuations in water pressure in holes Water is probably forced to find englacial have not been successful, however, as holes 83-5 and 84-1 (Fig. 3) lag atmospheric tempera- conduits when the viscous energy dissipated as it either failed to drain or drained so completely ture peaks by only ~4 h, suggesting that the flows up an adverse bed slope from an over- that no water-level variations were recorded in water input site is the nearby moulin field. deepening is either insufficient or only barely the few days during which they were monitored. sufficient to warm it at the same rate that the The down-glacier decrease in the amplitude pressure melting temperature increases. This oc- of pressure fluctuations thus inferred can be ex- ROLE OF THE SUBGLACIAL curs when the magnitude of the adverse slope plained, in part, by the fact that when the averge TILL LAYER exceeds about 1.5 to 2 times the slope of the water pressure must be high and the maximum glacier surface (Shreve, 1972; Rothlisberger and pressure is bounded by the overburden pressure, The steepness of adverse slopes leading out of Lang, 1987, p. 245). The exact multiplication pressure variations must be small. A possible cirques and overdeepenings may be limited by factor depends upon whether or not the water is contributing factor is damping of fluctuations as the ability of water to flow along the bed. As saturated with air. Under such circumstances, they are transmitted through the till layer and noted, a layer of till should then accumulate. there is little or no viscous energy available for the deranged englacial conduit system. Continuity considerations suggest that this layer enlarging conduits through melting. Theoretical Further evidence for a significant difference in will increase in thickness until the down-glacier considerations suggest that conduits are then the pattern of subglacial water-pressure varia- mass transfer by deformation within it equals held open principally by water pressure, and tions across a riegel is provided by velocity sediment production by erosion. Such a sedi- water pressures become very high (Rothlis- measurements, as temporal changes in velocity ment layer should protect the bed throughout berger, 1972, p. 186). Field measurements sup- are apparently commonly caused by changes in the down-glacier reaches of an overdeepening, port this conclusion; observed pressures in the water pressure (Iken and Bindschadler, 1986). thus concentrating erosion at its head. It is postu- main overdeepening on Storglaciaren approach In July 1981, for example, a period of warm lated that this is why overdeepenings exist, and the overburden pressure (Figs. 2 and 3). weather resulted in so rapid an acceleration of why their longitudinal profiles are characteristi- Theoretical analysis (Rothlisberger, 1972) the lowermost part of Storglaciaren that the lon- cally asymmetrical, with the deepest point at suggests that in the limit, some of the energy gitudinal strain rate in ice just up-glacier from their up-glacier ends.

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SUMMARY In only a few localities has a subglacial till layer Eriksson, M., 1990, Storglaciaren bottentopografi uppmâtt genom radioeko- sondering (Storglaciaren bottom topography measured by radio echo in an overdeepening been identified by geophys- sounding): Examensarbete. Department of Physical Geography, Uni- The thesis of this paper is as follows: ical techniques (Brand and others, 1986; J. Paetz versity of Stockholm, Sweden, 29 p. Fisher, J. E., 1955, Internal temperature of a cold glacier and conclusions there (1) cirques and overdeepenings are products and R. LeB. Hooke, unpub. data) or directly from: Journal of , v. 2, p. 583-591. Gardner, J. S., 1987, Evidence for headwall weathering zones. Boundary of basically the same erosional processes, and sampled (N. R. Irverson and R. LeB. Hooke, Glacier, Canadian Rocky Mountains: Journal of Glaciology, v. 33, unpub. data). Its probable presence throughout p. 60-67. (2) there is a positive feedback process that Griffith, A. A., 1924, Theory of rupture: First International Congress on Ap- amplifies perturbations in the longitudinal pro- the overdeepening on Storglaciaren, and by ex- plied Mechanics, Delft, Proceedings, p. 55-63. Holmlund, P., 1988, Internal geometry and evolution of moulins, Storglaciaren, file of a glacier valley. Specifically, the principal tension other overdeepened basins, is inferred on Sweden: Journal of Glaciology, v. 34, no. 117, p. 242-248. erosional process on headwalls of either cirques the basis of the processes believed to be respon- Hooke, R. LeB., 1984, On the role of mechanical energy in maintaining subgla- cial water conduits at atmospheric pressure: Journal of Glaciology, or overdeepenings is probably quarrying result- sible for its formation. That these processes re- v. 30, no. 105, p. 180-187. Hooke, R. LeB., Brzozowski, J., and Bronge, C., 1983, Seasonal variations in ing from rapid fluctuations in subglacial water sult in localization of erosion on headwalls of surface velocity, Storglaciaren, Sweden: Geografiska Annaler, v. 65, pressure occasioned by variations in water input. cirques and overdeepenings and in an adverse ser. A, p. 263-277. Hooke, R. LeB., Miller, S. B., and Kohler, J, 1988, Character of the englacial In overdeepenings, the water input occurs by bed slope down-glacier from these headwalls, and subglacial drainage system on Storglaciaren, Sweden, as revealed by dye trace studies: Journal of Glaciology, v. 34, no. 117, p. 228-231. way of moulins developed in crevasses that form and thus, over time, accentuate the overdeepen- Hooke, R. LeB., Calla, P., Holmlund, P, Nilsson, M„ and Stroeven, A., 1989, over the riegel at the up-glacier end of the over- A three-year record of seasonal variations in surface velocity, Storgla- ing, is based on this inductive reasoning. ciaren, Sweden: Journal of Glaciology, v. 34, no. 120, p. 235-247. deepening. These crevasses occur at precisely the Iken, A., and Bindschadler, R. A., 1986, Combined measurements of subglacial water pressure and surface velocity of Findelengletscher, Switzerland: point where water access to the bed is required ACKNOWLEDGMENTS Conclusions about drainage system and sliding mechanism: Journal of to reinforce the erosional process. The water Glaciology, v. 32, no. 110, p. 101-119. Iverson, N. R., 1989, Theoretical and experimental analyses of glacial abrasion pressure variations are much higher immediately I am indebted to B. Hanson for productive and quarrying [Ph.D. thesis]: Minneapolis, Minnesota, University of Minnesota, 233 p. down glacier from the input point than they are discussions of the cirque problem and especially 1991, Potential effects of subglacial water-pressure fluctuations on quar- further down glacier. Thus quarrying is localized rying: Journal of Glaciology (in press). for his interpretation of Mazo's paper, and to Jahns, R. H., 1943, Sheet structure in granites: Its origin and use as a measure of on the headwall. In cirques, the point of water N. R. Iverson for elucidating the mechanics of glacial erosion in New England: Journal of Geology, v. 51, p. 71-98. input is the bergschrund. Water-pressure meas- Jansson, P., and Hooke, R. LeB., 1989, Variations in surface tilt on Stor- the quarrying process. V. A. Pohjola drilled glaciaren, northern Sweden: Journal of Glaciology, v. 35, p. 201-208. urements have not been obtained near a Johnson, D. W., 1904, The profile of maturity in Alpine glacial erosion: many of the holes from which water-level data Journal of Geology, v. 12, p. 569-578. bergschrund, but B. Hanson and R. LeB. Hooke were obtained. The constructive critical com- Lewis, W. V., 1954, Pressure release and glacial erosion: Journal of Glaciology, (unpub. data) have demonstrated that diurnal v. 2, p. 417^122. ments of B. Hallet and K. Echelmeyer forced my Mazo, V. L., 1989, Waves on glacier beds: Journal of Glaciology, v. 35, and longer accelerations occur high in the ac- no. 120, p. 179-182. ideas into much sharper focus and resulted in Porter, S. C-, 1989, Some geological implications of average Quaternary glacial cumulation area of Storglaciaren, only a few conditions: Quaternary Research, v. 32, p. 245-261. significant improvements in the paper. tens of meters from the bergschrund. These ac- Ritter, D. F., 1986, Process geomorphology: Dubuque, Iowa, W. C. Brown, This research was financed by the United 603 p. celerations are correlated with changes in Robin, G. deQ., 1976, Is the basal ice of a temperate glacier at the pressure States National Science Foundation (Grants melting point?: Journal of Glaciology, v. 16, p. 183-196. temperature or with rainfalls that would increase Rôthlisberger, H., 1972, Water pressure in intra- and subglacial channels: Jour- DPP-8619086, INT-8712749, and DPP- water input to the glacier. They are, therefore, nal of Glaciology, v. II, p. 177-203. 8822156) and the Swedish Natural Sciences Rôthlisberger, H., and Iken, A., 1981, as an effect of water-pressure presumed to be caused by water-pressure variations at the glacier bed: Annals of Glaciology, v. 2, p. 57-62. Research Council. Rôthlisberger, H., and Lang, H., 1987, Glacier hydrology, in Gurnell, A. M., variations. and Clark, M. J., eds., Glacio-fluvial sediment transfer: London, En- gland, John Wiley and Sons, p. 207-284. This model is based on a combination of Seaberg, S. Z„ Seaberg, J. Z„ Hooke, R. LeB., and Wiberg, D. W„ 1988, Character of the englacial and subglacial drainage system in the lower theoretical analysis, numerical modeling, field part of thé area of Storglaciaren, Sweden, as revealed by dye- trace studies: Journal of Glaciology, v. 34, no. 117, p. 217-227. observations, and inductive inference. The me- Segall, P., 1984, Rate-dependent extensional deformation resulting from crack chanics of glacier quarrying are yet to be firmly REFERENCES CITED growth in rock: Journal of Geophysical Research, v. 89, p. 4185-4195. Sharp, M., 1982, Modification of clasts in lodgement tills by glacial erosion: established, but Iverson's (1989, 1991) theoreti- Atkinson, B. K., 1984, Subcrilical crack growth in geological materials: Journal Journal of Glaciology, v. 28, no. 100, p. 475^181. of Geophysical Research, v. 89, no. B6, p. 4077-4144. Shreve, R. L., 1972, Movement of water in glaciers: Journal of Glaciology, cal and numerical studies suggest that water- Atkinson, B. K., and Rawlings, R. D., 1981, Acoustic emission during v. II, no. 62, p. 205-214. pressure fluctuations greatly accelerate erosion stress corrosion cracking in rocks, in Simpson, D. W. and Richards, Thompson, H. R., and Bonnlander, B. H., 1956, Temperature measurements at P. G., eds.. Earthquake prediction: An international review (Ewing a cirque bergschrund in Baffin Island: Some results of W.R.B. Battle's by quarrying. Water levels in holes drilled below Series, Volume 4): Washington, D.C., American Geophysical Union, work in 1953: Journal of Glaciology, v. 2, p. 762-769. p. 605-619. Walder, J., and Hallet, B., 1985, A theoretical model of the fracture of rock a riegel fluctuate widely. It is inferred that this Battle, W.R.B., 1960, Temperature observations in bergschrunds and their during freezing: Geological Society of America Bulletin, v. 96, behavior is representative of that which would relationship to frost shattering, in Lewis, W. V., Norwegian cirque p. 336-346. glaciers: Royal Geographical Society Research Series 4, p. 83-95. 1986, The physical basis of frost weathering: Toward a more fundamen- be found elsewhere near other headwalls, BatUe, W.R.B., and Lewis, W. V., 1951, Temperature observations in berg- tal and unified perspective: Arctic and Alpine Research,v . 18, p. 27-32. schrunds and their relationship to cirque erosion: Journal of Geology, whether of cirques or overdeepenings. In con- v. 59, p. 537-545. trast, water-pressure measurements farther Brand, G„ Pohjola, V., and Hooke, R. LeB., 1987, Evidence for a till layer beneath Storglaciaren, Sweden, based on electrical resistivity measure- down-glacier in an overdeepening have shown ments: Journal of Glaciology, v. 33, no. 115, p. 311-314. Drewry, D., 1986, Glacial geologic processes: London, England, Edward Ar- that pressures there are high and relatively con- nold, 276 p. MANUSCRIPT RECEIVED BY THE SOCIETY JUNE 11, 1990 stant. This is consistent with theoretical analysis. Embleton, C-, and King, C.A.M., 1968, Glacial and periglacial geomorphology: REVISED MANUSCRIPT RECEIVED DECEMBER 11, 1990 London, England, Edward Arnold Ltd., 608 p. MANUSCRIPT ACCEPTED JANUARY 7,199!

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