Positive feedbacks associated with erosion of glacial cirques and overdeepenings 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- glacier are the bergschrund in cirques, and schrund that reached a cirque floor, and thus enings are being found with increasing fre- crevasse 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 glaciers. The heads of overdeepenings in glacier beds. The son and Bonnlander, 1956; Battle, 1960) and valley 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 moraines, 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. 1104 Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/103/8/1104/3381435/i0016-7606-103-8-1104.pdf by guest on 24 September 2021 EROSION OF GLACIAL CIRQUES AND OVERDEEPENINGS 1105 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).