Borehole studies

Of the 47 holes discussed here, 66% connected with active englacial drainage conduits, 13% drained at the bed and 21 % did not drain. Holes that drained at the bed usually drained slowly; sometimes the fact that drainage was occurring was not detected until the following day. Hole 88–2, 132 m deep and near the south side of the glacier (Fig. 1), was one of those that drained at the bed and, when water was not actively flowing into it, the water level in it often dropped to or nearly to the bed.

In holes that drained, with the exception of hole 88-2, the water level was normally no more than 20–40 m below the surface (Fig. 2) and variations in level were relatively small (Fig. 3). Early in the season, the water pressure at the bed was commonly close to the ice-overburden pressure, as is evident from the proximity of the points in Figure 2 to the water-equivalent line. There was a tendency for levels to fall as the melt season progressed (Fig. 3), presumably reflecting enlargement of drainage conduits by energy dissipated by the flowing water.

Fig. 2. Longitudinal section of Storglaciären through the overdeepening, showing bed and surface topography and water-equivalent line. Also shown are water levels in bore-holes projected on to the plane of the section. These water levels are approximate averages over the period during which the hole was under observation; in some instances, this “period” included only one measurement made shortly after the hole was completed. In a few holes, the pressure appears to have exceeded the overburden pressure; whether these represent local areas of overpressure at the bed or errors in measurement of either the water level or the ice thickness is not known. Ice thicknesses were normally obtained from measurements of the length of hose required to reach the bed so, if holes were not plumb, as sometimes was evident, the thickness may have been overestimated. When a hole was known to be off vertical, radio-echo data were used to determine the thickness (Eriksson, unpublished map).

Fig. 3. Variation in water level through time in borehole 90-1.

These experiences are remarkably similar to those of Reference Brand, Pohjola and HookeHantz and Lliboutry (1983) in borehole experiments in the overdeepening of glacier d’Argentière. As on Storglaciären, they found that many holes drained englacially; that holes draining at the bed often drained slowly; that, except for holes near the valley sides, water pressures were commonly high, approaching overburden pressure; that holes near the valley sides were typically empty of water, suggesting the presence of a nearby conduit at approximately atmospheric pressure; that water-pressure fluctuations occurred over periods of days or weeks, but not diurnally; that water pressures tended to decline through the melt season; and that nearby holes behaved differently in some instances. These similarities suggest that our joint findings are typical of water behavior in glacier overdeepenings.

The salt-trace experiments established that active conduits had been intersected at the “drainage depth” or level where the drill tip stood when a hole drained. In experiments with crystalline salt, the salt was flushed from the upper part of the hole within a few hours, but remained concentrated below the drainage depth for over a day (Reference Hooke, Miller and KohlerHooke and others, 1988, Fig. 2). Below the drainage depth, the salt concentration decreased with depth, suggesting that water might be upwelling from the bed to drain through the englacial conduit. In the experiments using dissolved salt, the salt cloud could be followed down the hole until it disappeared at the drainage depth.

The video experiments in 1990 support these conclusions. After being allowed to stand for several days, water in the tops of the holes was clear enough for use of the camera. At greater depths, however, the water was invariably cloudy. The transition between the clear and cloudy water was normally abrupt. When the drainage depth was known, it coincided with the top of this sediment plume. We again infer that upper parts of these holes were flushed by clear water entering from the surface and that, near the bottom, fine sediment was held in suspension by upwelling of water from the bed. Observations during the more-detailed 1989 video surveys differed somewhat, in that in three of four holes the top of the sediment plume was from 3 to 70 m below the drainage depth and was quite diffuse.

The video surveys from 1989 revealed, on average, three or four openings in hole sides that could have served as englacial conduits. However, nylon string suspended in front of the camera usually hung motionless; either the string was too stiff to detect the low water velocities in these passages or there was, at the time of the surveys, little flow in the majority of them. Some of these openings contained a few sand or gravel particles that might once have been in transit. The passages ranged from ∼0.1 to ∼0.4 m in height. In cross-sectional shape, many were either irregular or oval, while some appeared to be sub-horizontal cracks that extended beyond the hole sides (Reference PohjolaPohjola, in press).

Active englacial drainage conduits were not encountered at depths less than 50 m (Fig. 4). This presumably reflects the existence of the surface layer of cold ice, which is typically 20–50 m thick in this part of the glacier (Reference Holmlund and ErikseonHolmlund and Eriksson, 1989). The deepest that such conduits occurred was within a meter or two of the bed. There was no apparent systematic variation in the depth to active conduits. In fact, in two instances in which holes were drilled within 1 m of each other (for electrical resistivity measurements), englacial conduits were encountered 2 and 4 m apart vertically, respectively (Reference Brand, Pohjola and HookeBrand and others, 1987).

Fig. 4. Longitudinal section of Storglaciären through the overdeepening, showing depths at which holes drained. Because depths were projected laterally on to the line of profile, square symbols, indicating holes that drained at the bed, may appear to lie somewhat above or below the bed in the figure. Dashed lines are traces of equipotential surfaces (see text).

(Experiences during the 1992 field season reinforced some of the above observations and gave a new perspective on others. Fourteen holes were drilled to the bed in a smaller overdeepening (site S3, Fig. 1). Penetrometer tests indicated that 13 of the holes bottomed in till. Water levels were initially well above the water-equivalent level in 12 holes, and from 20 to 22 July, water containing frazil ice and fine sediment overflowed from three of them. Presumably, the water was coming from the bed. Then on 23 July, following a storm, water levels dropped to depths of at least several tens of meters. We infer that the initial overpressures led to formation of connections between areas of thicker ice up-glacier and the borehole site, and hence in the overflow and that these connections were later extended to the down-glacier end of this overdeepening, resulting in the subsequent drop in water levels. In summary, as in the larger overdeepening further up-glacier, water pressures were high and subglacial till was present but, in contrast to the situation in the larger overdeepening, no englacial passages were encountered.)

Dye-trace experiments

Dye-return curves for the 1987 tests show well-defined single peaks (Fig. 5). However, the dispersivities derived from these tests (Table 1) are much higher than those of ∼2 m to, at most, ∼50 m obtained at about the same time of year from tracer tests from moulins over the riegel (Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others, 1988; Reference Hock and HookeHock and Hooke, 1993). Note also that dispersivity increases between the first and second tests. This is contrary to the normal pattern, in which dispersivity decreases as the conduit system becomes better integrated (Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others, 1988; Reference Hock and HookeHock and Hooke, 1993).

Fig. 5. Dye-return curves for tracer experiments 87: 1,87:2 and 87:3. The curves have been normalised to 1 kg of dye input to permit direct comparison of dye concentrations between tests.

The dye-return curve for test 88:1 (Fig. 6) has two peaks. Apparently much of the dye was retarded by about

, either in a storage from which dye is released only during the peak daily discharges, or in a separate conduit through which dye moved more slowly.

Fig. 6. Dye-return curve for tracer experiment 88:1.

The dye-return curve for tests 88:2,3 (Fig. 7) differs dramatically from those for the previous tests. The principal differences are attributed (below) to the fact that the boreholes in which these injections were made, 88-2 and 88-3, both drained at the bed rather than through englacial conduits. In addition, note that the declining dye concentrations during the first 4–7 d of this experiment may be the tail of the return curve from experiment 88:1. This would further imply that perhaps no dye was recovered from injection 88:2 in hole 88-2. If any dye was recovered from this test, it is indistinguishable from that from injection 88:3. Thus, henceforth, these tests are referred to as test 88:2,3.

Fig. 7. Dye-return curve for tracer experiment 88:2,3.

Flow at the bed

The dye-return curve from tracer test 88:2,3 suggests that flow along the bed is sporadic. Dye appears to be trapped in pockets for extended periods of time. Releases some-times, but not always, appear to be triggered by high water inputs. These results are consistent with those of an earlier tracer test in a stream flowing into a crevasse about 400 m northwest of hole 87-3 (Reference Hooke, Miller and KohlerHooke and others, 1988). We suppose that the storage pockets are between the glacier sole and the subglacial till layer that we believe is present throughout most of the overdeepening. The multiplicity of dye releases over many days suggests that these pockets are multiply interconnected so that the dye is split into numerous separated packets that have widely differing residence times beneath the glacier. During the 1989 video surveys, we observed a part of this release process in action. While the camera was focused on the bed, a sediment cloud entered the borehole along the ice-bed interface and progressed across the field of view, obscuring the bed (Reference PohjolaPohjola, 1993).

Discharge in englacial conduits

There appear to be a large number of englacial conduits, each carrying a small fraction of the total discharge. For example, if holes were to be drilled in a straight line across the central 600 m of the glacier, roughly the region over which our drilling program extended, the 1989 video surveys suggest that we would intersect an average of four englacial passages per hole. Based on the frequency with which holes drained during drilling, one of these passages would be expected to be active in two-thirds of the holes. Given that the conduits were observed to be a few decimeters across, we could argue that holes drilled on 0.5 m centers would intersect different conduits. Thus, in the 600 m transect, we would have 1200 independent boreholes intersecting 4800 conduits of which ∼800 (one-quarter of two-thirds) would be active. Our dye-trace experiments indicate that water draining through these conduits appears in Nordjåkk which has a mean discharge of ∼1.1 m³ s⁻¹ (Reference Hock and HookeHock and Hooke, 1993). Dividing this evenly among the 800 conduits gives a mean discharge per conduit of ∼0.0014 m³ s⁻¹. These figures will be used in some of the calculations that follow.

Theoretical considerations

The reason for the high pressures in the overdeepening is readily understood; as an adverse bed slope becomes increasingly steep, more of the viscous energy is needed to warm the water as the pressure-melting point beneath the down-glacier thinning ice increases. Thus, less energy is available to enlarge conduits by melting and the tendency for conduit closure must be balanced by high water pressures rather than by melting.

Where the adverse bed slope exceeds ∼1.3–2.0 times the surface slope, the viscous energy available may not be sufficient to keep water warmed to the pressure-melting point. (The lower figure is appropriate for air-saturated water and the higher one for pure water (Reference Röthlisberger, Lang, Gurnell and ClarkRöthlisberger and Lang, 1987, p. 245)). In conduits exceeding this critical slope, supercooling would occur. Conduits might then freeze up or, perhaps more likely, ice crystals may nucleate on impurities in the water, forming frazil ice (verbal communication from D.E. Lawson, July 1992). Such frazil ice could form aggregates that would clog smaller conduits (Reference Strasser,, Lawson, Evensen, Gosse and AlleyStrasser and others, 1992).

Reference ShreveShreve (1972) showed that equipotential surfaces in a glacier should dip up-glacier with a slope of ~11 times the slope of the glacier surface. Three such equipotential surfaces are shown in Figure 4. Englacial water flow is expected to be normal to these surfaces. Upon reaching the bed, water should flow along the ice-bed interface in a direction normal to contours of equipotential defined by the intersection of these surfaces with the bed. Reference ShreveShreve (1985) successfully explained a number of characteristics of eskers using this model. Shreve’s model assumed that the difference between the pressure in the conduits and that in the surrounding ice is small and that there are no significant spatial variations in this difference.

When the slope of a bed leading out of an over-deepening exceeds the critical value noted above, there is an obvious inconsistency: Shreve’s model requires the water to descend to the bed and then flow along it, while

Röthlisberger’s, which is supported by our field obser-vations, suggests that conduits would then become blocked.

Water pressures in englacial and subglacial conduits

We next investigate water pressures in an englacial conduit that is parallel to, but some distance above the bed, vis-á-vis one lying along the bed. The conduits are assumed to be hydraulically connected. Thus, water would tend to flow from the conduit at the higher potential towards that at the lower potential. Reference RöthlisbergerRöthlisberger (1972), Reference LliboutryLliboutry (1983, p. 224) and Reference Röthlisberger, Lang, Gurnell and ClarkRöthlisberger and Lang (1987, p. 261) have all approached this problem by assuming that discharges in the two conduits were different and asking which would carry the larger discharge. Lliboutry concluded that the higher conduit would carry most of the flow, but Röthlisberger and Lang argued that Lliboutry had misinterpreted his equations and that they actually demonstrated the opposite result.

Here, we approach the problem slightly differently; instead of asking which conduit will carry more water, we assume that both carry the same discharge and ask which will have the higher hydraulic grade line. The result is not obvious from the governing differential equation (Reference RöthlisbergerRöthlisberger, 1972, equation (20)) so we integrated it numerically for the specific geometry of Storglaciären, and show the resulting energy grade lines in Figure 8. In performing this integration, we assumed that subglacial conduits are broad and low, or lenticular, as Reference Hooke, Lauman and KohlerHooke and others (1990) argued should be the case. Water pressures in such conduits are much higher than those in classical circular or semi-circular Röthlisberger conduits because plastic flow of the ice closes lenticular conduits more rapidly. We also assumed that the drainage system down-glacier from the riegel consists of an arborescent network of conduits in which, for modeling purposes, the discharge is halved five times between the terminus and the riegel. Velocities in such an arborescent conduit system match observed velocities much better than is the case for a system consisting of a single conduit (Reference Hock and HookeHock and Hooke, 1993). Above the riegel, the discharge per conduit is taken to be 0.0014 m³ s⁻¹, as discussed above. We assume a Manning roughness of 0.05 m ^−1/3s, which would seem to be reasonable for conduits entirely in ice, though possibly slighdy low for those at the bed.

Fig. 8. Energy grade lines through overdeepening calculated for different drainage configurations. As discussed in the text, an arborescent network of broad, low conduits is assumed to exist down-glacier from the riegel. Up-glacier from the riegel, conduits that are “above bed” are assumed to be horizontal until they reach an elevation of 15 m above the bed. Thereafter, they parallel the bed. Water levels in boreholes (Fig. 2) are shown by square symbols.

When both the englacial and subglacial conduits are assumed to be lenticular, the conduit above the bed has an energy grade line that is slightly higher throughout most of the overdeepening (Fig. 8). This would imply a tendency for water to move from the higher conduit to the one at the bed whenever the opportunity presented itself. However, if we assume that the englacial conduit is circular in shape, it will close much more slowly, thus requiring a lower water pressure and hence lower hydraulic grade line (Fig. 8). Using a higher roughness for the conduit at the bed, say 0.2 ^−1/3s,, also increases the pressure here above that in an englacial lenticular conduit. In either case, water would tend to move from the lower to the higher conduit. As noted, this is what is inferred to be happening in the boreholes when they provide a pathway between the bed and an englacial conduit. Some of the water ascending in this way might be expected to freeze, much as it would while flowing up an adverse bed slope. However, water ascending from the bed may have a solute content sufficient to inhibit such freezing.

A conduit receiving water from another will be enlarged at the expense of the other (Reference ShreveShreve, 1972). Then, because the steady-state water pressure in a conduit decreases as discharge increases, the conduit at the lower potential would continue to increase in size in a positive feed-back (Reference RöthlisbergerRöthlisberger, 1972).

As a result of these temporal and spatial variations in conduit roughnesses, in conduit sizes and shapes, and in locations of blockages, we infer that the potential field near the bed is distorted in such a way as to induce flow of water from subglacial to englacial conduits. Thus, we conclude that Reference ShreveShreve’s (1972) model for the potential field breaks down near a bed with a sufficiendy steep adverse slope.

Water pressures calculated using the model with lenticular conduits are remarkably consistent with those measured (Fig. 8). The measured hydraulic gradient, which is relatively flat in the middle of the overdeepening and steeper toward the riegel, is also well reproduced. This agreement suggests that the circular approximation for the cross-sectional shape of englacial conduits may not be a good one. However, of the conduits observed in the 1989 video experiment, 70% were oval or sub-circular, while the rest were lenticular (Reference PohjolaPohjola, in press).

Flow speeds in the conduits

The average hydraulic gradient through the overdeepening is ∼0.041 m m⁻¹ (Fig. 2). Using, again, a roughness of 0.05 m^−1/3s, we find that circular conduits with a diameter of ∼0.08 m would be required to transport a discharge of 0.0014 m³ s⁻¹, and the flow speed in the conduit would be ∼0.3 m s⁻¹. For the particular geometry assumed for the lenticular conduits (Reference Hooke, Lauman and KohlerHooke and others, 1990, Table 1), the cross-sectional area of the conduit is somewhat larger but its height is < 0.01m. The velocity in this case is ∼0.2ms⁻¹. These conduit sizes are smaller to much smaller than those observed in the 1989 video experiments, while the velocities are 2 to nearly 30 times those recorded in the 1987 dye-trace experiments (Table 1). Because the flow is actually in much larger conduits over much of the distance between borehole 87-3 and the terminus, the actual discrepancy in the velocities is even worse.

To match the highest velocities from the 1987 tracer experiments would require a circular conduit with a diameter of 0.14 m and roughness of 0.25 m^−1/3s. The former is consistent with observation but the latter borders on the unreasonable. To match the lower velocities would require still larger conduits with grossly unreasonable roughnesses.

One resolution of this apparent inconsistency is to assume that passageways are constricted locally. In the case of the ∼75% of the conduits that are inactive, we hypothesize that these constricions have closed the passages completely. Suppose we assume that constrictions in active circular conduits are 50 mm long and 20 mm in diameter and that they, too, have a roughness of 0.05 m^−1/3s. Suppose further that, between constrictions, the conduit has a diameter D of 0.2 m. Then, if the conduit is carrying a discharge Q of 0.0014 m³ s⁻¹, one constriction every 70 m would suffice to increase the head loss to that observed. Because the constrictions are such a small fraction of the total conduit length, the average velocity will be essentially Q/π(D/2)² or, in this case, 0.045 m s⁻¹. This is near the middle of the observed range (Table 1).

However, as noted, velocities in conduits in the overdeepening must be less than the mean, as those in the trunk conduits further down-glacier are much higher. To match these lower velocities would require larger conduits or lower discharges per conduit, or both, along with appropriate changes in the distance between constrictions. As mean conduit size is constrained by the video observations and is unlikely to be much larger than 0.2 m, the actual number of active conduits through any given cross-section of the overdeepening may be under-estimated.

This model of the conduit system provides a possible explanation for the unexpected increase in dispersivity between tests 87:1 and 87:2, and the subsequent decrease to test 87:3 (Fig. 5; Table 1). Some conduits may have become constricted between the first two injections, and either the same conduits or others may have opened between the second and third tests. This suggests a rather more dynamic englacial drainage system than previously suspected.

Such constrictions would raise pressures in the conduits. In the case of the circular conduits, this could explain why observed pressures are higher than those calculated (Fig. 8). These elevated pressures serve to offset the higher closure rates that would otherwise occur in larger conduits.

The origin of these constrictions, if they actually exist, is unclear. Ice flow over the riegel or freezing of ascending supercooled water might be factors. Once formed, however, we presume that they can persist, in part because energy dissipated by water flowing through them is carried downstream and consumed by melting of ice in larger parts of the passages rather than in the constrictions themselves.