A

Changes in surface profile

CB O

Changes in surface profile

20 15 10 5

Distance from head of glacier, km

15 10 5

Distance from head of glacier, km

Figure 8.23. Evolution of the: (a) surface profile, and (b) speed of Variegated Glacier during its build up to a surge. (c) Surface speed of the upper part of Variegated Glacier during its surge in 1982-1983. ((a) and (b) from Raymond and Harrison, 1988, Figures 4 and 5b; (c) from Kamb et al., 1985, Figure 2b. Reproduced with permission of the authors, the International Glaciological Society, and the American Association for the Advancement of Science.)

Oct Nov Dec Jan Feb Mar Apr May June July 1982 1983

Figure 8.23. Evolution of the: (a) surface profile, and (b) speed of Variegated Glacier during its build up to a surge. (c) Surface speed of the upper part of Variegated Glacier during its surge in 1982-1983. ((a) and (b) from Raymond and Harrison, 1988, Figures 4 and 5b; (c) from Kamb et al., 1985, Figure 2b. Reproduced with permission of the authors, the International Glaciological Society, and the American Association for the Advancement of Science.)

by continental ice sheets during the late Pleistocene. Some are tens of meters in height and tens or hundreds of kilometers in length.

Eskers often appear to follow bizarre paths when viewed from the perspective of people accustomed to the courses of subaerial streams. Eskers may climb hills, trend diagonally down valley sides, and run along valley sides instead of in valley bottoms. Shreve (1972, 1985a, 1985b) has shown that these characteristics can be readily understood from consideration of the hydraulic potential field beneath an ice sheet.

We have noted (Figure 8.6) that englacial water is expected to move in directions that are normal to equipotential planes in a glacier. Similarly, along the bed of a glacier water flow should be normal to the intersections of these equipotential planes with the bed. This is equivalent to saying that water flow down a hillslope should be normal to topographic contours, as topographic contours are the intersections of surfaces that are a constant height above sea level (= equipotential surfaces) with the topography.

Let us consider a couple of examples of this. The solid lines on the map in Figure 8.24a are topographic contours. They depict a gentle slope leading down to a valley that drains to the south. East of the valley there is a ridge that varies in elevation. Now, visualize the situation when an ice sheet covered the landscape, as shown in Figure 8.24b. The surface of the glacier sloped to the east, so the equipotential planes dipped westward. The dashed contours show the intersections of these planes with the landscape. These intersections are precisely analogous to the outcrop pattern that would be formed on the landscape by a westward-dipping sedimentary rock unit.

Under subaerial conditions, creeks would run down the gentle slope on the west side of the map, and then turn south. However, when ice covered the area, subglacial water would not have turned south. Instead, flowing normal to the contours of equipotential, it would have been deflected toward the low point in the ridge. If such a subglacial stream could not carry all of the sediment delivered to it, we might now find an esker crossing the ridge at its lowest point. This is commonly observed in situations in which ridges cross the paths of eskers.

The equipotential planes in the vicinity of the ridge are distorted. This is because the ice is flowing and the pressure is thus higher on the stoss side of the ridge than on the lee. To understand why the planes are distorted as shown, remember that in a situation in which z is constant, the decrease in potential from A to C is the result of a decrease in pressure, Pw (Equation (8.1)). Thus, if some distance away from the ridge a potential drop of 10 units occurs over the horizontal distance AB, nearer the stoss side of the ridge a longer distance, BC, is required for the same drop because the pressure at C is elevated. In the lee of the ridge, the distortion is in the opposite sense.

JaJach er<

Ice flow

^Higher pressure

Figure 8.24. (a) Contour map of a landscape on which are superimposed contours (dashed) of equipotential from a time when an ice sheet covered the landscape. (b) Topographic cross section from a time when ice was present, showing the equipotential surfaces in the ice sheet.

400 m

Because the velocity of water in the tunnel is proportional to d$/ds (Equations (8.13) and (8.14)), this distortion of the potential field affects the velocity. In particular, where d^/ds is higher over the crest of the ridge, the velocity would be higher. This is consistent with the observation that eskers are commonly discontinuous across the crests of such ridges; the higher velocity flow there presumably inhibits deposition.

Another hypothetical situation is shown in Figure 8.25. Here, a topographic valley drains southeastward, diagonally across the direction of glacier flow. As a result, the trough in the equipotential contours is on the valley side rather than in the valley bottom, and this is where an esker would be found if conditions were otherwise suitable for its formation. Again, eskers are commonly found in such positions under these circumstances.

Figure 8.25. Topographic map of a valley trending diagonally across the direction of ice flow, showing how an esker formed in such a situation would be on the side of the valley.

Figure 8.25. Topographic map of a valley trending diagonally across the direction of ice flow, showing how an esker formed in such a situation would be on the side of the valley.

With an understanding of the physical processes that determine the locations of eskers in situations such as those in Figures 8.24 and 8.25, it is sometimes possible to determine the surface slope of the glacier beneath which the esker formed. As an example of this, consider the section of the Katahdin esker near the town of Medway in Maine shown in Figure 8.26a. Ice flow was roughly from north to south in this area. In the northern part of the map, the two branches of the esker follow respective branches of the Penobscot River, but are slightly offset from the river, up onto the valley sides, in the downglacier direction. However, south of the junction between the two branches, the esker departs from the valley of the Penobscot to run up the valley of a small tributary and then across the divide between this tributary and another small southward-flowing creek. To clarify the reasons for this, Shreve (1985a) constructed a series of maps of the potential field in the Medway area for different possible ice surface slopes. The one that best explained the course of the esker (Figure 8.26b) utilized a surface slope of 0.0048.

By determining ice-surface slopes in this way at a number of locations along a single esker system, one might be able to reconstruct the surface profile of an ice sheet, and from this calculate the basal shear stress. For such a reconstruction, however, the entire esker system must have been active simultaneously. In situations in which contemporaneity can be demonstrated, this is one of the few techniques available for determining surface profiles of vanished ice masses.

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