Glacier movement

Information about glacier movement has been obtained from mathematical and numerical modelling, laboratory experiments, measurements in boreholes, observations in natural and artificial ice cavities, and interpretation of landforms and sediments in formerly glaciated regions.

Snow and ice are transferred from the accumulation area to the ablation area by glacier flow. Flow takes place as sliding, deformation of the ice, and deformation of the bed under the glacier. The deformation and sliding due to gravity slowly transports snow and ice from the accumulation area and the interior of ice sheets to the marginal areas where ablation takes place. The rates of ice flow are related to the climatic input to the glacier and the geometry of the glacier catchment. For a glacier with no changes in size and shape, the ice flow through a cross section must be equal to the accumulation and ablation, illustrated by the wedge concept in Fig. 4.43, p. 102. Commonly, the maximum ablation occurs at the glacier snout, while the minimum

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Figure 4.40 The annual net (upper panel) and cumulative (lower panel) mass balance variations on Griesgletscher between 1962 and 1997. (Data from Funk et al, 1997, and WGMS)

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Figure 4.40 The annual net (upper panel) and cumulative (lower panel) mass balance variations on Griesgletscher between 1962 and 1997. (Data from Funk et al, 1997, and WGMS)

ablation is recorded in the upper part of the glacier. The opposite is the case for accumulation. In order to be in a steady-state condition, glacier ice must move from the accumulation to the ablation area. Velocities calculated in this manner are termed balance velocities. As a consequence of this behaviour, ice velocities increase from the upper part, reaching a maximum at the equilibrium line. Below the equilibrium line the velocity decreases, reaching a minimum velocity at the glacier margin. Glacier velocities are highest on glaciers with steep mass balance gradients, and where glacier ice from wide accumulation basins is focused into a narrow valley. The mass balance gradient at the equilibrium line is therefore an indication of the glacier activity. As a rule, glaciers in humid, maritime areas flow more rapidly than glaciers in arid, cold and continental regions. Consequently, glacier activity commonly increases with decreasing latitude and more maritime climates. However, glacier geometry highly influences glacier behaviour and therefore no simple relationship occurs

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Figure 4.41 The annual (upper panel) and cumulative (lower panel) net balance variations on Sarennes from 1949 to 1997. (Data from WGMS)

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Figure 4.41 The annual (upper panel) and cumulative (lower panel) net balance variations on Sarennes from 1949 to 1997. (Data from WGMS)

between mass balance gradient and glacier discharge.

In the short term, significant deviations from the balance velocity occur as a result of the balance between driving and resisting forces being out of phase with variations in glacier mass balance. The driving forces are the stresses caused by the surface slope and the weight of the ice, and therefore influenced by variations in mass balance. The resisting forces are the result of the strength of the glacier ice, the glacier/bed contact and the bed itself. The driving and resisting forces are kept in balance over longer periods by glacier flow. Glaciers therefore adjust their surface slope to produce driving forces sufficient to maintain the mass balance of the glacier. Temporary and significant changes in resisting forces may occur as a result of variations in water at the base of the glacier.

Stress and strain are important concepts for the understanding of glacier movement. Stress is a measure of how hard a material is pushed or pulled as the result of external

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Figure 4.42 The annual (upper panel) and cumulative (lower panel) net balance on Lewis Glacier between 1979 and 1996. (Data from WGMS)

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Figure 4.42 The annual (upper panel) and cumulative (lower panel) net balance on Lewis Glacier between 1979 and 1996. (Data from WGMS)

forces, while strain is a measure of the amount of deformation that takes place as a result of this stress. To understand stress, it is first useful to understand the concept of force, which is mass multiplied by acceleration. The downward force at the base of a glacier is the product of the mass of the overlying ice and the acceleration due to gravity, normally measured in newtons (N; kg m s ). Stress is defined as force per unit area. As a result, a given force acting on a small area will result in a greater stress than the same force acting over a larger area. The most commonly used units of stress are pascals (1 Pa = 1N m~2) and bars (lbar = 100 kPa). The high stresses under the glacier make it more convenient to use kilopas-cals (1 kPa = 1000 Pa). The surface stress can be divided into two components: normal stress (the stress acting at right angles to the surface) and shear stress (the stress acting parallel to the surface). For normal stress, two opposing tractions either press the material together across the surface, termed compressive stress, or tend to pull the material apart across the surface,

Thickening

Equilibrium line

Thinning

Thickening

Equilibrium line

Thinning

Mass Movements Wind And Glaciers
Figure 4.43 The wedge model of glacier flow. Glacier B has a steeper mass balance gradient than glacier A and therefore requires higher velocities to balance the mass gained and lost in the two wedges. (Adapted from Sugden and John, 1976, and Benn and Evans, 1998)

termed tensile stress. The tractions are parallel, but act in opposite directions for shear stresses. The shear stress t at the base of the glacier is a result of the weight of the overlying ice and the slope of the glacier surface, expressed as t — rgh sin a

where r is the density of ice (ca. 0.9 g cm ), g is gravitational acceleration (9.81ms 2), h is ice thickness in metres, and a is the surface slope. One implication of this formula is that the stress increases with ice thickness. Irregularities in the glacier bed may, however, result in stress variations that influence subglacial erosion and deposition. In addition, the pushing and pulling effect, termed longitudinal stress, is compressive where the velocity is slowing down and tensile where the velocity is accelerating. Normal stress is greatest on the upstream side of subglacial bumps and lowest on the downflow side.

Strain, the change in shape and sometimes size of materials due to stress, can be divided into elastic (recoverable) strain and permanent (unrecoverable) strain. The degree of stress where permanent deformation occurs is termed the yield stress. Permanent deformation takes place as brittle failure (breaks along fractures) or ductile deformation (material is subject to flow or creep). Deformation involving volume changes is termed dilation (expansion or contraction), whereas deformation without volume changes is called constant-volume deformation. Strain types normally related to glacier flow are pure shear and simple shear (Fig. 4.44). Studies of glacier

Brittle deformation

Brittle deformation r~nr

A Ductile deformation

A Ductile deformation

E Simple shear

E Simple shear

Figure 4.44 Styles of deformation in glaciers. (Modified from Benn and Evans, 1998)

movement commonly involve studies of strain rate (strain that occurs per unit time) and the cumulative strain (net amount of strain in a given period of time).

Strain my occur either by deformation of ice, deformation of the subglacial bed, or sliding at the interface between the ice and the bed. Surface movement on a glacier is the cumulative movement of one or all of these effects. Resistance to flow depends on several factors like temperature, debris content in the ice, bed roughness and water pressure.

Creep is ice deformation as a result of movement within or between ice crystals. Internal crystal movement can occur by sliding along cleavage planes, which are weakness lines related to crystal molecular structure, or movement along crystal defects. Movement between crystals leads to changes in shape or size by recrystallization at boundaries between crystals. Glen's flow law (Glen, 1955), first adapted for glaciers by Nye (1957) is written:

where e is strain rate, A and n are constants, and t is shear stress. Parameter A decreases with ice temperature; colder ice deforms less readily than ice at a higher temperature. The exponent n is normally close to 3 (Fig. 4.45). However, the orientation of ice crystals (ice fabric) and the presence of impurities (solutes, gas bubbles and solid particles) may cause strain rates different from those predicted from the flow law.

Fracture takes place when glacier ice can not move fast enough to allow the glacier to adjust its shape under stress. Crevasses are examples of fractures formed where ice is pulled apart by tensile stress. Tensile fractures are formed near the surface, because at depths greater than 15-20 m, the compressive force is larger than the tensile one. On temperate glaciers,

Glacier Movement

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Shear stress (kPa)

Figure 4.45 Relationships between stress and strain for different types of material: (a) perfectly plastic material; (b) Newtonian viscous material; (c) non-linearly viscous material (such as ice). (Adapted from Paterson, 1994)

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Shear stress (kPa)

Figure 4.45 Relationships between stress and strain for different types of material: (a) perfectly plastic material; (b) Newtonian viscous material; (c) non-linearly viscous material (such as ice). (Adapted from Paterson, 1994)

crevasses are rarely deeper than 30 m, whereas on polar glacier, where the ice is stiffer than in temperate glaciers, the crevasses may be considerably deeper. Fractures can also form where ice is subject to compression where movement takes place along a shear plane.

Soft rocks and sediments underneath a glacier can experience strain as a result of stress by the glacier. This process of subglacial sediment deformation may explain certain types of unstable glacier behaviour and fast flow of some ice streams (e.g. Boulton and Jones, 1979). Studies of subglacial sediment deformation have been conducted in tunnels dug into glaciers, by placing instruments into boreholes, and by means of seismic sounding techniques. Studies have shown that subglacial material will not deform until a threshold stress is achieved, termed the yield stress or critical shear siress. The critical shear stress varies considerably, the most important factor being the effective normal pressure on the material from the overlying ice and sediment. The shear strength of a material is the sum of cohesion and intergranular frictional strength. Cohesion describes the forces keeping the material together, whereas frictional strength is the resistance of grains to sliding and grain crushing. The deforming sediment layer is normally confined to the uppermost part of the bed, because the frictional strength increases downwards. Consequently, changes in the shear stress or in the porewater pressure will affect the thickness of the deforming sediment layer. The strain rates, increasing with increasing porewater pressure, commonly increase upwards, reaching a maximum value at the top of the deforming layer. Very high porewater pressure at the glacier-till interface, however, may cause decoupling and reduction of basal deformation rates.

Sliding is the movement between the glacier and the bed. The most important factors controlling the rate of basal sliding are adhesion due to freezing of ice to the bed, bed roughness, the quantity and distribution of water at the bed, and the amount of rock debris at the base of the ice. The rate of sliding is determined by the basal temperature, and effective sliding takes place when the ice is at the pressure melting point. The adhesive strength of frozen glacier beds is high even on a smooth surface. Until recently, therefore, sliding of cold-based glaciers was considered unlikely. Recent laboratory work and field evidence have, however, si i own that , slow basal sliding can take place

Figure 4.46 The relative effectiveness of regelation and creep for different obstacle sizes. (Adapted from Boulton, 1975)

Figure 4.46 The relative effectiveness of regelation and creep for different obstacle sizes. (Adapted from Boulton, 1975)

underneath polar glaciers. Measurements below Urumqihe S. No. 1 in China showed sliding rates of 0.01 mm day-1 (annual sliding of less than 4 mm) at -5°C (Echelmeyer and Wang, 1987; Echelmeyer and Zhong Xiang, 1987).

In nature, glacier beds are not smooth over wide areas, but have irregularities at different scales. The resistance to glacier movement around and above obstacles is termed form drag, which is an important factor controlling the rate of sliding. Two mechanisms of glacier movement over obstacles are regelation sliding and enhanced creep. During the regelation process, glacier ice slides over rough beds by melting on the upglacier side and refreezing on the downglacier side of the obstacle. Regelation sliding on the upstream side occurs from locally high pressures and lowering of the pressure melting point. The subglacial meltwater moves to the downglacier, low-pressure side of the obstacle, where it refreezes. The theory of regelation sliding suggests that this process is most effective when the latent heat on the downstream side of the obstacle is advected through the obstacle to melt the ice on the upglacier side (Weertman, 1964). The mechanism of enhanced creep is the result of stress concentrations around the upglacier sides of obstacles, leading to accelerated sliding over the obstacle. The shape of the basal ice therefore changes continuously due to sliding. The creep rates are much lower in cold ice due to the temperature influence of the flow law (Glen, 1955). While regelation is most effective around small bumps, enhanced creep is most effective around large obstacles. A critical obstacle size (where neither of the two mechanisms is efficient and which represents maximum resistance to sliding) is found to be in the range 0.05-0.5 m (e.g. Kamb, 1970) (Fig. 4.46).

Liquid water at the glacier bed is fundamental for effective sliding, because of lack of adhesion at the bed and the need for water during the regelation process. Water pressure and the distribution of water are now recognized as the most important factors for modern sliding theory, explaining velocity fluctuations and glacier surge. The presence of a water film underneath glaciers moving over rock beds may accelerate sliding by submerging millimetre-scale surface irregularities. In addition, increased water pressure in cavities may have a similar effect. Field evidence suggests that water-filled cavities cause increased sliding velocity due to hydraulic jacking and uplift of the glacier (e.g. Willis, 1995). In other cases, glacier uplift may be related to variations in strain rate due to velocity variations and changes in longitudinal stress (e.g. Hooke et ai, 1989). The threshold water pressure for formation of cavities is termed separation pressure, which is high for short-wavelength, high-amplitude bumps and low for long-wavelength, low-amplitude surface irregularities (e.g. Willis, 1995).

Basal ice commonly contains rock debris, and where the debris is in contact with the bed, frictional drag will influence basal sliding. In general, the larger the drag is, the lower is the sliding velocity. Three models explaining subglacial friction have been suggested, called the 'Coulomb', 'Hallet' and 'sandpaper' models (Schweizer and Iken, 1992). The Coulomb friction model is based on the assumption that friction between rock particles in basal ice and a rigid bed is proportional to the normal pressure pressing the surfaces together (e.g. Boulton, 1979). In addition, the model infers that basal friction increases with ice thickness and is inversely proportional to basal water pressure. Hallet's (1981) friction model was based on the assumption that ice deforms completely around subglacial particles, and that contact forces are independent of ice thickness. The sandpaper model was introduced for debris-rich basal ice where particles are close or in contact. In this case, ice cannot flow around particles and the ice is the 'glue' holding the mass together. The ice rich in debris is deformable and therefore in contact with the bed. The drag force at the base of the debris-rich ice is a function of water pressure and the area of the bed occupied by cavities between particles in the basal ice layer. The sandpaper model is considered to be the best where the concentration of basal debris is more than about 50 per cent by volume, and the Hallet model the most appropriate when basal-debris concentrations are less than ca. 50 per cent by volume (Willis, 1995).

In a glacier, velocities vary commonly systematically with depth, the velocities being greatest at the surface at the centre of the glacier. The increase in velocity with height is most rapid near the bottom of the ice due to high strain rates. Near the surface, velocity increases more slowly with height due to lower strain rates in the upper ice layers, as illustrated by the velocity distribution of Athabasca Glacier in Canada (Harbor, 1992).

Positive mass balance in the accumulation zone of a glacier may be transmitted in waves of increased velocity, termed kinematic waves (e.g. Paterson, 1994), in which zones of increased velocity may travel downglacier at a rate approximately four times faster than the ice itself. Because the surface profile is constantly adjusting to mass-balance variations, kinematic waves are difficult to distinguish on non-surging glaciers (Benn and Evans, 1998).

Glaciers flow at a wide range of velocities. Cold-based glaciers with small balance velocities flow almost entirely by internal deformation, and velocities are relatively small (Echelmeyer and Wang, 1987). Wet-based glaciers, on the other hand, may reach high velocities. The fastest-moving glacier so far recorded is the Jacobshavn Isbrse, a tidewater outlet glacier on the western margin of the Greenland ice sheet, reaching maximum observed annual flow rates of 8360 m close to the calving margin (Echelmeyer and Harrison, 1990). For glaciers with annual velocities in the range of 10-100 m, basal shear stresses are relatively high (40-120 kPa), whereas the basal shear stresses under fast outlet glaciers and ice streams are considerably lower (1030 kPa) (e.g. Paterson, 1994).

Velocity measurements carried out on Hintereisferner, central Alps, Austria (Span et al., 1997), show three periods of accelerated flow between 1894 and 1994. These occurred around 1920, in 1940 and during the 1970s. The period of accelerated velocity around 1920 resulted in an advance of about 60 m. The mean annual advance increased from 30 m in 1914 to more than 120 m in 1919, and doubled during the accelerations in 1940 and 1980. The authors found that an increase in ice thickness alone cannot explain the enormous change in surface velocity, and that sliding may contribute to the total measured velocity during periods of accelerated ice flow.

supraglacial ice morphology 107

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