## Patterns And Rates Of Ice Flow

Within a glacier flow usually follows the direction of the surface slope. Figure 3.3 shows a cross-section through both an ice sheet and a glacier. In an ice sheet the ice flows in two opposite directions from the summit or ice divide (Figure 3.3). In the accumulation area, flow takes place downwards into the ice, counteracting the upward growth of the surface through accumulation. In the ablation zone the surface is lowered by ablation, which causes ice to effectively rise towards the surface. Ice may also rise towards the surface in the ablation zone due to compressional flow at the glacier margin. Flow within a valley glacier or channel shows a similar pattern. Ice flow is maximum in the centre of the channel or valley and near the surface: the point furthest from the frictional resistance of the valley sides (Figure 3.14).

Increasing velocity

Increasing velocity Increasing velocity Figure 3.14 The pattern of ice flow in a glacierised valley. (A) The flow pattern in cross-section where no basal sliding is present. (B) The flow pattern in cross-section where basal sliding is present. (C) The flow pattern in plan view where no basal sliding is present. (D) The flow pattern in plan view where basal sliding is present. [Modified from: Summerfield (1990) Global Geomorphology, Longman, figure 11.5, p. 265]

In an ideal ice sheet the rate of flow will tend to increase from the ice divide towards the equilibrium line, where it will reach a maximum, before decreasing towards the terminus. This observation can be explained schematically with reference to Figure 3.15. If we assume a constant average velocity through the whole thickness of the ice sheet, then at a point at a given distance (x) from the ice divide the horizontal flow velocity (u) must be sufficient to remove by flow all the accumulation (a) which occurs up-ice of that point. The amount of ice or discharge that can pass through this point is given by:

discharge = uh where u is the average ice flow velocity (m s_1) and h is ice thickness (m).

B: Ice profile

C: Ice velocity

Ice margin o

Ice divide

Ice margin Ice divide Distance from the ice divide

Figure 3.15 Pattern of ice flow within an ice sheet. (A) A simplified mass balance pattern on the ice surface. (B) The ice sheet in profile. (C) Ice-flow velocity within the ice sheet. Velocity rises from zero at the ice divide to a maximum near the equilibrium line, after which it declines. [Modified from: Boulton (1993) in: Holmes' Principles Of Physical Geology (ed. P.McL.D. Duff), Chapman and Hall, figure 20.14, p. 412]

### Distance from the ice divide

Figure 3.15 Pattern of ice flow within an ice sheet. (A) A simplified mass balance pattern on the ice surface. (B) The ice sheet in profile. (C) Ice-flow velocity within the ice sheet. Velocity rises from zero at the ice divide to a maximum near the equilibrium line, after which it declines. [Modified from: Boulton (1993) in: Holmes' Principles Of Physical Geology (ed. P.McL.D. Duff), Chapman and Hall, figure 20.14, p. 412]

This discharge must equal the accumulation rate up-ice of that point if the ice sheet is to maintain a steady state (i.e. size). Therefore the amount of ice to be discharged by the glacier is given by:

discharge = xa where x is the distance from point x to the ice divide (m) and a is the average accumulation (m yr-1)

It follows therefore that average ice velocity (u) can be calculated from:

66 Mass Balance and the Mechanisms of Ice Flow This can be rearranged to give:

xa u = xa where u is the average ice-flow velocity (m s-1), h is ice thickness (m), x is the distance from point x to the ice divide (m) and a is the average accumulation (m yT_1).

Using this simple equation, ice-flow velocity increases from zero at the ice divide (x = 0) to a maximum at the equilibrium line, thereafter it decreases. Clearly the assumptions made in calculating the velocity pattern in Figure 3.15 are considerable, but the pattern produced holds as a general model or first approximation of Figure 3.16 A surge-type glacier, Lowell Glacier in the Yukon. Note the folded and looped medial moraines on the ice surface. [Photograph: M.J. Hambrey]

the velocity pattern within an ideal ice sheet. This pattern is significant because it implies that: (i) little or no geomorphological work will take place beneath ice divides due to low ice velocities; and (ii) that most geomorphological work will be done beneath the equilibrium line, which is usually located relatively close to the ice margin.

Most glaciers have velocities in the range of 3-300 m per year, but their velocity can reach 1-2 km per year in steep terrain or where there is a high mass balance gradient. A few glaciers flow at speeds that are much higher. These are commonly associated with large outlet glaciers from ice sheets such as that in Greenland or Antarctica. In these the flow of ice streams is channelled down valleys and velocities may reach as much as 7-12 km per year. These ice streams may drain significant areas of an ice sheet and because they are fed by a large accumulation area their velocities are not normally limited by the supply of ice (i.e. the rate of accumulation).

Some glaciers may also experience periodic surges in ice flow, often 10-100 times greater than previous ice velocities (Figure 3.16). Surges are usually limited by the amount of ice available in the accumulation zone so that increased flow rates cannot be sustained. Not all glaciers are prone to surges and those that do, appear to surge at regular intervals. It has been suggested that only about 4% of all glaciers surge, although they tend to be concentrated in certain geographical areas, such as in Svalbard and Alaska.

It has been suggested that there are two modes of glacier flow: one 'normal' and one 'fast' (Figure 3.17). In an ice stream the 'fast' flow mode is maintained because of the availability of ice within the large accumulation zone of the ice

Figure 3.17 Modes of glacier flow. Two states exist: 'fast flow' and 'normal flow'. The existence of 'fast flow' is dependent on some critical bed condition (e.g., changes in the subglacial hydrological system or thermal regime), without which it cannot occur. A surge-type glacier is able to switch between fast and normal flow rates through time. Figure 3.17 Modes of glacier flow. Two states exist: 'fast flow' and 'normal flow'. The existence of 'fast flow' is dependent on some critical bed condition (e.g., changes in the subglacial hydrological system or thermal regime), without which it cannot occur. A surge-type glacier is able to switch between fast and normal flow rates through time.

### Basal shear stress i

Basal shear stress i sheet that it drains. In the case of surging valley glaciers the pulse of 'fast' flow is limited by the amount of ice available in the much smaller accumulation zone. Once this ice has been discharged the flow must return to 'normal'. It is possible to conceptualise a surge as the product of an excess of accumulation of ice above that which 'normal' flow can discharge. This excess accumulation may be stored in the accumulation area until it reaches a critical level, when it may trigger a pulse of 'fast' flow. The periodic nature of a surge is explained in this model by the time necessary between pulses of 'fast' flow to build up the excess of ice or the stress necessary to trigger the event. This will vary from one glacier to next, which explains why different glaciers surge with different periodicities. The exact nature of the instability that generates a surge and the mechanisms of 'fast' flow are not well understood at present (Box 3.5: see also Section 4.5).

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