The upper part of the englacial hydraulic system

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Veins and the initial development of passages

Nye and Frank (1973) argued that veins should be present along boundaries where three ice crystals meet, and that at four-grain intersections these veins should join to form a network of capillary-sized tubes through which water can move. They thus concluded that temperate ice should be permeable.

Such capillary passages have been observed in ice cores obtained from depths of up to 60 m on Blue Glacier, Washington (Figure 8.1a) (Raymond and Harrison, 1975). The veins are triangular in shape (Figure 8.1b) and roughly 25 ^m across.

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Figure 8.1. (a) Veins in ice from Blue Glacier. (b) Cross section of a vein with approximate scale. (c) Millimeter-sized tubes from a depth of 20 m in Blue Glacier. ((a) and (c) from Raymond and Harrison, 1975. Reproduced with permission of the authors and the International Glaciological Society.)

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Figure 8.1. (a) Veins in ice from Blue Glacier. (b) Cross section of a vein with approximate scale. (c) Millimeter-sized tubes from a depth of 20 m in Blue Glacier. ((a) and (c) from Raymond and Harrison, 1975. Reproduced with permission of the authors and the International Glaciological Society.)

Estimates of the permeability of glacier ice resulting from this vein system vary widely. Expressed in terms of the thickness of a water layer that would be transmitted downward into the ice, values range from ~ 1 mm a-1 in coarse-grained ice with relatively few crystal boundaries perunitvolume (Raymond and Harrison, 1975)to1ma-1 in fine-grained

The upper part of the englacial hydraulic system

Figure 8.1. (cont.)

ice (Nye and Frank, 1973). Lliboutry (1971) noted that the existence of supraglacial streams precludes the possibility of significantly higher permeabilities. He further argued that, at permeabilities near the upper end of this range, the potential energy released by the descending water would rapidly enlarge the conduits to the point of completely melting the glacier.

Lliboutry (1971) concluded that deformation and recrystallization of ice must constrict the veins, rendering the ice essentially impermeable. Alternatively, air bubbles located along the veins might block water movement. Lliboutry considered and rejected the latter idea, but Raymond and Harrison thought that it might have merit in coarse ice with few veins.

When water moves through such a vein system, viscous energy is dissipated in the form of heat. The amount of heat produced is proportional to the water flux. To a first approximation, the ice is already isothermal and at the pressure melting point. Thus, the heat cannot be conducted away from the veins, but instead must be consumed by melting ice. In this way, passages are enlarged. Shreve (1972) and Rothlisberger (1972) argued that when two such passages of unequal size separate and rejoin, the larger passage carries more flow per unit of wall area and is thus enlarged at the expense of the smaller passage. They suspected that some of the capillary passages would thus become enlarged to millimeter-scale tubes a short distance below the surface.

Raymond and Harrison confirmed the existence of such tubes in a slab of ice cut from a core from a depth of 20 m in Blue Glacier (Figure 8.1c). The tubes formed an upward-branching arborescent network, as expected. Because the Shreve-Rothlisberger argument applies equally well to larger anastomosing passages, we may imagine that at greater depths, the arborescent network continues to evolve, with ever larger conduits developing. These conduits drain water produced by strain heating in the deforming ice in addition to that from the surface.

Connections to the surface

In the accumulation area, one can visualize continuous connections between the vein system and the overlying porous firn. As the veins do not necessarily transmit downward all of the percolating meltwater, a local water table commonly forms in the firn (Vallon et al., 1976; Fountain, 1989). Measurements of the slope of this water table in the vicinity of crevasses demonstrate that the latter are actually the principal conduits for movement of water deeper into the glacier (Fountain, 1989).

In the ablation area there may be a surface layer of cold ice, several meters in thickness, in which the veins are frozen. This cold layer forms on glaciers in more continental climates where snow fall is low enough to allow appreciable cooling of the ice by conduction during the winter (Hooke et al., 1983). It is less likely to form in maritime climates where larger snow falls form an effective insulating layer. When present, it is likely to persist well into the melt season, if not entirely through it, and thus forms an effective barrier to penetration of surface meltwater. Because of this cold layer, and because the vein system, even on glaciers without such a cold layer, is relatively ineffective in transmitting water downward, it is, again, principally by way of crevasses that surface water in the ablation area is able to reach the interior of the glacier.

When a crevasse first forms, it may fill with water and overflow. In larger crevasses, however, this situation normally does not persist for long. It seems probable that once a crevasse penetrates deep enough to intersect the millimeter-scale conduit system, increasing the water supply to these conduits dramatically, the conduits are quickly enlarged until they can transmit all of the incoming water downward into the glacier.

Crevasses may close as they are moved into areas or are rotated into orientations with lower tensile stresses. However, where melt streams in the ablation area pour into such a crevasse, the viscous energy dissipated maintains a connection to the englacial conduit system. The hole thus formed in the glacier surface is called a moulin.

When a crevasse opens across a melt stream upglacier from a moulin, it cuts off the water supply to the moulin. In the absence of further dissipation of viscous heat, the moulin's connection to the deeper drainage system is then constricted by inward flow of ice, and during the winter the upper part of the moulin fills with snow. In due course, the snow becomes saturated with water which eventually freezes. These processes result in distinctive structures in the ice.

Figure 8.2. Illustration of difference between pressure field and potential field.

Over a period of several years Holmlund (1988) carefully mapped such structures on Storglaciaren as ablation exposed ever deeper levels in the glacier. He also descended into some of the moulins during the winter. He found that moulins are typically 30-40 m deep, although deeper ones occur on other glaciers, that channels leading from the bottoms of moulins are typically meandering and trend in the direction of the initiating crevasse, and that after some distance the meandering channel ends in a vertical conduit leading deeper into the glacier.

Shreve (1972) has compared the drainage system we have just described with one developed in a permeable limestone in which karst has developed. The anastomosing vein system provides the basic permeability, while the moulins and larger arborescent network of conduits are the analog of the karst system. Our task now is to consider the geometry of the system of larger conduits deeper in the glacier, below the level of Holmlund's mapping. One possibility is that these conduits are not vertical, but rather slope steeply downglacier, normal to equipotential surfaces in the glacier. We develop the theory behind this idea next, following closely the analysis of Shreve (1972).

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