Subglacial hydrology and sediment transport at Bondhusbreen, southwest Norway

Transcription

1 Subglacial hydrology and sediment transport at Bondhusbreen, southwest Norway ROGER LeB HOOKE* 1 > Hydrological Department, Norwegian Water Resources and Electricity Board, P. O. Box 5091 Majorstua, Oslo 3, Norway BJÖRN WOLD JON OVE HÄGEN Department of Geography, University of Oslo, P.O. Box 1042 Blindem, Oslo 3, Norway ABSTRACT Tunnels driven, in rock under the glacier Bondhusbreen in Norway, and thence upward to the ice-rock interface, provide a rare opportunity to study a subglacial drainage system. Early in the melt season, suspended sediment discharges in the subglacial water channels are lar ;e, and channels apparently change position. These effects are inferred to be a consequence of increased separation of ice from the bed due to increased water pressure. Water pressures are believed to be high at this time of year because water channels, having closed by plastic deformation during the winter when discharges are low, are too small to handle the increasing spring discharges. Water thus backs up in the channel system. Calculations suggest that further changes in channel position occur as discharges increase, because the potential energy released by the water is able to melt ice in the walls of channels faster than it is replaced by inward flow of ice. Channels can thus trend diagonally across the direction of glacier flow. Although such changes may occur at any time during the melt season in response to variations in discharge, there appears to be a seasonal evolution of the drainage pattern under Bondhusbreen that is repeated each year. These shifting channel patterns make the engineering task of locating and diverting water beneath glaciers more difficult than anticipated. INTRODUCTION Water from the three Folgefonni ice caps in southwestern Norway (60 N, 6 20'E) is used for hydroelectric-power production. The water is Permanent address: Department of Geology and Geophysics, University of Minnesota, Minneapolis, Minnesota U.S.A. collected and stored in artificial reservoirs situated at elevations between 850 and 1,050 metres above sea level (m.a.s.l.). Most of the water conies from parts of the ice caps that are higher than the reservoirs and thus can be readily diverted to them. About 10%, however, comes from Bondhusbreen, an outlet glacier that flows northwestward from the southernmost of the ice caps and extends down to an elevation of 450 m. In order to channel this water into the reservoirs by gravity, it was necessary to catch it at an elevation of -900 m under 160 m of glacier ice. To this end, tunnels were driven in the rock under the glacier, and in 1974 and 1975, nearly vertical intakes, each -2 m in diameter, were excavated from these tunnels to the glacier-rock interface in two areas (nos. "1" and "2", Fig. 1, inset A). There are 2 to 4 intakes in each of these areas. These intakes, however, catch only a small fraction of the subglacial discharge. Six additional intakes were thus excavated in a third location ("3" in Fig. 1) in Most of the remaining water is caught in two of these. In winter, when only minor amounts of water are present, ice creeps down through the intakes, forming large pillars. By melting away these pillars with hot-water jets, one can gain access to the glacier bed. It has thus been possible to install pressure transducers, temperature sensors, and strain gauges at the ice-rock interface and to make observations of channels and other features (Wold and 0strem, 1979; Hagen and others, 1983). From an engineering point of view, the project has been a success. The total cost of construction of the system was -$5,000,000, whereas the annual net income is now -$2,000,000. The objectives of this paper are to describe observations and measurements pertaining to the subglacial hydrology and sediment transport at Bondhusbreen made between 1975 and 1982 and to elucidate, where possible, some characteristics of the subglacial hydrological system. GENERAL DESCRIPTION The Folgefonni ice caps rest on an almost horizontal bedrock surface of granitic gneiss. Bondhusbreen and other outlet glaciers have eroded deep valleys into this surface, generally along tectonic joints and faults. The surface area of Bondhusbreen above the water intakes is 10.5 km 2. Another 2 km 2 of glacier and 2.5 km 2 of mountain slope drain to the intakes, in part through Lake Holmavatn (Fig. 1). The total drainage area is thus 15 km 2. The areas of mountain slope are mostly bare rock, occasionally covered with large boulders and more rarely with scattered patches of till. The southwestern part of the glacier seems to be thicker and more active than the eastern part. Although crevasses occur over the whole glacier, these two parts are divided by a significantly more heavily crevassed shear zone (Fig. 1, inset B). The surface velocity of the more active part is -300 mm/day 500 m upglacier from the intakes (Wold and Ostrem, 1979). The sliding speed near the intakes varies over short distances; measurements range from 0 to 80 mm/day (Hagen and others, 1983). Surface streams are rare; they are present only in the less active section draining to Lake Holmavatn. Elsewhere, water flows directly down into the glacier through crevasses. The rate of water input to the englacial and subglacial water systems per unit surface area is thus presumed to decrease with elevation in proportion to the decrease in summer balance (Fig. 2). Because most of the surface area of the glacier lies at higher elevations, about two-thirds of the water comes from levels above 1,400 m. Lake Holmavatn provides an additional point source of water. Large amounts of rock debris are transported by the water passing through the intakes. This debris is collected in a 10,000 m 3 sedimentation chamber in the bedrock tunnels. The chamber used to be emptied mechanically every winter. In 1983, however, an additional tunnel was ex- Geological Society of America Bulletin, v. 96, p , 7 figs., 1 table, March

2 SUBGLACIAL HYDROLOGY A N D SEDIMENT TRANSPORT, NORWAY 389 Figure 1. Map of Bondhusbreen showing inferred boundaries of drainage area. Inset "A" shows tunnels in rock under glacier and inferred subglacial water courses. As discussed in text, the principal subglacial channel is believed to change from position I to position II during the first weeks of the melt season. Inset "B" is an aerial photograph showing crevasse patterns and shear zone. cavated downward from the sedimentation chamber and back to the glacier. By opening a gate leading to this tunnel, it is now possible to empty the chamber in one or two hours in late summer when the water flow from the glacier is still high. MEASUREMENTS Water discharge has been measured at Bondhusbreen from the beginning of May until late fall since Early measurements were made with the use of a stage recorder in the stream at the glacier terminus. Since 1978, a stage recorder has been in operation near the outlet from the sedimentation chamber. Occasional spot measurements and qualitative observations of discharge are also available from other times of the year. Other stage recorders have also been used at various times to measure the discharge in the stream draining Lake Holmavatn and in the stream from the Brufossvatna lakes draining a glacierized area bordering Bondhusbreen on the north (Fig. 1). In 1972 and 1973, prior to excavation of the tunnel system, the total sediment discharge in the subglacial streams was measured below the glacier terminus (Ziegler, 1974; Haakensen, 1975). From 1979 to 1981, the suspended sediment discharge was determined by taking water samples twice a day at the entrance to the sedimentation chamber. Between 1978 and 1982, the sedimentation chamber was surveyed each winter to determine the volume of coarse sediment collected (Kjeldsen, 1983). An automatic meteorological station has measured air temperature, humidity, radiation, winds, and precipitation at Lake Holmavatn during the summers since 1979.

3 390 HOOKE AND OTHERS ma.s.l. TONS/D 1979 Figure 2. A. Mean summer balance for period Abscissa is in metres of water equivalent B. Area of glacier versus altitude. Area under curve is proportional to glacier surface area. One square = 4 km 2. C. Summer balance x area. Curve shows water yield for different elevations, excluding yield due to summer precipitation. HYDROLOGY The melt season usually starts during the first half of May, and the discharge begins to increase at the intakes two to four days later. The mean discharge during the summer is ~5 m 3 /s, but floods of significant size may be observed in all months from June to September (Fig. 3). Minor floods may occur even in October and November when warm North Atlantic storms reach the area. As soon as subzero temperatures become common in the autumn, however, the discharge drops steadily, reaching its winter level by the end of January. Thereafter, it remains fairly constant until May. The winter discharge varies from year to year, in a range from 0.05 m 3 /s to 0.20 m 3 /s. Nearly all of this water comes through the intakes at location "3". In the summer, during periods of stable fair weather, the flow has diurnal variations of ~0.5 m 3 /s. The minimum discharge usually occurs between 8 and 9 a.m., and the maximum discharge occurs at 9 p.m. (Fig. 4). As the maximum air temperature occurs between 4 and 6 p.m., this suggests a lag of ~4 hr. Summer discharges can, however, vary significantly from day to day in response to changes in weather (Fig. 3). Nearly every warm period lasting more than 4 or 5 days results in a significant increase in discharge; the lag between the peak temperature and the peak discharge averages 1 to 2 days. Precipitation seems to have less effect on the discharge, probably because it is often accompanied by colder weather and thus falls as snow (for example, Fig. 3, early August 1981). Intense rain storms during periods of warm weather are significant, however (Fig. 3, late August 1979). -i MAY JUNE JULY AUGUST Figure 3. Water and suspended-sediment discharge through intakes, together with temperature and precipitation records for Discharge from Lake Holmavatn During the summer, the daily mean discharge from Lake Holmavatn ranges from 0.3 m 3 /s to 1.5 m 3 /s, amounting to 10%-15% of the discharge at the intakes. Tracer experiments have shown that this water requires 12 min to reach the intakes ( 0.5 km from the lake outlet) and that it is caught by intakes in location "3" (Wold and Haakensen, 1978). Prior to development of the intakes, the transit time from Holmavatn to the glacier terminus was 45 min (Hagen, 1977). If this water follows a course that is basically orthogonal to the contours on the glacier bed, the above time intervals require mean water velocities of 0.7 m/s above the intakes and 1.5 m/s in the steeper area between the intakes and the terminus. During the summers of 1979 and 1980, the temperature of the water from Holmavatn was measured hourly by means of a thermistor on the river bed. The temperature seems to vary inversely with the discharge, especially 3n days without rain, apparently reflecting input of cold melt water to the lake. The mean temperature during the summer is between +3 and +4 C. Unfortunately, discharge measurements from Holmavatn have not been possible in the winter because the outlet fills up with snow 3 to 7 m deep during December and January.

4 SUBGLACIAL HYDROLOGY AND SEDIMENT TRANSPORT, NORWAY 391 water. Detailed measurements of the relative discharges through the three intakes are not available to support this conclusion. Pressure Variations in Boreholes Figure 4. Diurnal variation in temperature and discharge, July Nonsynchronous Discharge Variations From 1975 until the opening of the intakes at location "3" in 1978, several instances of nonsynchronous discharge variation were documented (Wold and Repp, 1979). The first occurred in the spring of Water came through intakes in location "2" on May 10th and through intakes in location "1" a few days later. During the next one or two weeks, the discharge through intakes in area "2" decreased and stopped while the discharge through intakes in area "1" increased. Later, flow through intakes in area "1" decreased but still continued at a moderate level all summer. This pattern was repeated in Between 1978 and 1980, observations were not detailed enough to document similar nonsynchronous changes in locations "1" and "2", but it is known that the combined discharge from these two locations generally peaked during the first week or two of the melt season and then decreased. As the discharge at the terminus did not appear to increase, we infer that some channels that initially led to intakes in areas "1" and "2" shifted to intakes in area "3". Somewhat more information is available from In this year, the water appeared first at intakes in areas "1" and "2", and then, within a day, at intakes in area "3". During the ensuing weeks, the discharge increased in areas "1" and "3" and continued through the summer. Approximately one-third of the water came through intakes in area "1", and two-thirds came through intakes in area "3". A second kind of nonsynchronous discharge variation occurred in late June In response to a period of warm weather, the discharge from Brufossvatna and that from Holmavatn increased markedly. About a week later, a flood of ~4 m 3 /s came through the intakes in areas "1" and "2". The increase at Bondhus occurred while the discharges at Brufossvatna and Holmavatn were declining due to cooler weather. A third kind of nonsynchronous discharge variation occurred during the first week of July Warm weather resulted in simultaneous increases in discharge at the Bondhus intakes, Brufossvatna, and Holmavatn. This initial increase lasted about two days. Discharge in the latter two streams then decreased rapidly while that at the Bondhus intakes continued to increase for five more days. Simultaneously, the discharge in the river at the terminus of Bondhusbreen decreased. The discharge at the Bondhus intakes then decreased rapidly while those at Brufossvatna, Holmavatn, and Bondhus terminus again increased in response to renewed melting. The first example strongly suggests that the location of water courses beneath Bondhusbreen changes seasonally. The second and third examples probably also can be explained by a change in location of channels beneath the glacier; only 10% to 15% of the total subglacial discharge was being caught at the time, and so shifting of water courses toward or away from the intakes could account for the variations at Bondhus. Alternatively, the second example, in particular, could reflect temporary storage of water in or beneath the glacier. Nonsynchronous variations similar to the second and third examples have not been recorded since the opening of intakes in area "3". On the contrary, variations have been synchronous at Brufossvatna, Holmavatn, and the Bondhus intakes. As virtually all of the Bondhus water is now being caught by the intakes, this supports the hypothesis that the earlier, nonsynchronous variations were due to shifting of flow between water courses leading to intakes in areas "1" and "2" and water courses bypassing these intakes rather than to release of stored During construction of the tunnels in the rock under the glacier, between 80 and 100 holes, 40 mm in diameter, were drilled through the rock to the ice-rock interface in order to locate water and to determine the geometry of the interface. About 85% of these holes are always dry, perhaps in part because they are plugged with ice or moraine. Of the remaining holes, about half are upglacier from intake area "2" and half are upglacier from intake area "3". Water flow through the former is under high pressure during most of the melt season, but pressures are highest early in the season before the discharge in the main intakes increases. Later in the season, pressures are lower, but diurnal variations may continue and high pressures may occur during periods of heavy water inflow. Pressures in the holes upglacier from intake area "3" are normally low. Relatively little water comes through these holes, despite the fact that the main channel system appears to pass close to, if not over, the point where they reach the glacier bed. Exceptional Water Discharge Events The summer 1979 discharge records from the sedimentation-chamber outlet show three extraordinary events (Fig. 5) (Haakensen and Wold, 1981). Although the discharge variations during these events differ in detail, there are many similarities. All three events occurred during periods of gradually increasing discharge. In each case, the rate of increase was also increasing (d 2 Q/dt 2 positive) just before the event. The events began with a sharp drop in discharge to a rather low value, as if a major conduit had suddenly become blocked. This was followed within an hour by a rapid increase in discharge to a value substantially above that preceding the drop. The excess volume of water released during this rise was estimated as being approximately equal to the deficit resulting from the preceding fall, again suggesting a temporary damming of a conduit. Usually there is little ice in the water entering the intakes, but during these last abrupt increases, it contained numerous large ice blocks, reminiscent of the situation after the collapse of a tunnel near a glacier terminus. No similar events have been detected since Another type of unusual event was reported by Wold and Ostrem (1979). From June 12 to 18,1976, the discharge oscillated with an amplitude of 0.15 to 0.80 m 3 /s and a period of 1-2 hr. At the time of these oscillations, the mean

5 392 HOOKE AND OTHERS m3/ s 18-3,0 2,5 2, JUNE H D JULY Figure 5. Exceptional water discharge events discharge was declining. When these oscillations occurred, the main intakes were not in operation and only 15% of the water was being collected. The same type of oscillation occurred from June 9 to at least June 13, 1982 (Fig. 6), when the recorder failed. During this period, the discharge decreased from 2.6 m 3 /s to 1.8 m 3 /s. The amplitude of the oscillation was 0.2 to 0.4 m 3 /s and the period was 1 to 2 hr. All intakes were operative during this time, and nearly 100% of the melt water was captured. Radioecho soundings suggest that there are at least one and possibly two overdeepened areas in the glacier bed 2.5 km upglacier from the intakes. Subglacial channels in these areas are probably full much of the time, and this may provide an explanation for these oscillations: they may have resulted from an alternate making and breaking of a siphon over the threshold at the downglacier end of one of the overdeepened areas. We suppose that as the water flow into the overdeepened area decreased, a JUNE 1982 Figure 6. Pulsating discharge, June AUGUST siphon formed that could draw out water faster than it was replaced. Such a siphon would l)e broken after the water level had been drawn somewhat below the threshold level and would reform as soon as cavities in the overdeepened area had been refilled. The rarity of such events suggests that an unusual combination of channel size and discharge variations is required to produce them. Observations of Subglacial Water Channels During work in the artificial ice-tunnels that were melted at the glacier bed, natural water channels were observed on three occasions. The first was in April An empty englacial channel, trending approximately parallel to the direction of glacier flow, was found 2 m above the bed near intake area "2". No water was observed in the channel, although trapped water may have escaped during the melting operation. The channel was -100 mm in diameter and had a bed of well-rounded, 50- to loo-mm-dianeter stones partly imbedded in the ice. This is ail area in which the discharge is usually -1 m 3 /:> during the first week of summer drainage and a few hundred liters/s later in the season. The size that this conduit may have had at the end of the melt season, 0.6 yr earlier, can be estimated using Nye's (1953) theory for the closure of a cylindrical hole. The result, even choosing a rather high viscosity for the ice. is a diameter of 200 m! Although the uncertainties in such a calculation are large, possibly in excess of a factor of 10, it seems clear that the conduit could have been large enough to carry 1 m 3 /s during the early summer. Furthermore, it very probably was closed off or water-filled and thus not at atmospheric pressure for very long after the end of the melt season (see also Haefeli, 1970, p. 208). A second observation was made in April An artificial ice tunnel was melted perpendicular to the main stream near the intakes at location "3". Where this tunnel crossed the stream, the latter was split into one main branch and two smaller branches with a total discharge of-0.05 to 0.10 m 3 /s. The three branches were separated by ice pressing against higher parts of the glacier bed, and so the water followed natural depressions in the rock. From the orientations of these branches, it appeared that they joined each other a few metres upstream. The main branch was in a more or less semicircular channel 0.3 m across in the rock. The other two channels were 0.5 m wide but only 10 to 30 mm high. The main branch was never observed to be more than approximately twothirds full; the other two seemed to be nearly full. The last observation was made in May Work was being done in a tunnel that was melted along the glacier sole above the intakes at location "1" when the first melt water came. Two jets of water of perhaps 2 to 5 liters/s entered the artificial tunnel from englacial conduits a couple of metres above the bed. One of the conduits dipped upglacier 15, and water in it was moving upglacier, although this might not have been the case had the artificial tunnel not been present. The other conduit was not as accessible, but it appeared to dip downglacier and had a lens-shaped cross section. SEDIMENT TRANSPORT The total amount of sediment transported by the subglacial streams for each year of record is given in Table 1. For convenience in discussion, the material is classified as either bed load or suspended load, the boundary between the two being taken arbitrarily atv2 mm.

6 SUBGLACIAL HYDROLOGY AND SEDIMENT TRANSPORT, NORWAY 393 TABLE ]. SEDIMENT TRANSPORT [N STREAM IN FRONT OF BONDHUSBREEN ( ) AND IN THE DIVERTED WATER BENEATH BONDHUSBREEN ( ) Coarser than Vi mm Finer than Vi mm Total Metric 7 of total Metric % of total tons transport tons transport transport , , , , , , , , , , , , , , , , ,300 Suspended Load Temporal variations in the transport of suspended material are shown in Figure 3. The most noteworthy characteristic of these curves is a major peak in transport during the early days of the first flood each year. Unless subsequent floods are considerably higher, they do not carry nearly as much material. For example, in 1980, the first flood carried 26% of the total suspended load for the season. Each of two later floods of about the same size, one at the end of July and the other in mid August, carried -9% of the total load in the same number of days. Peak sediment concentrations during these early floods ranged from 250 to nearly 800 g/m 3 ; during ordinary discharges the concentration is normally between 15 and 70 g/m 3 (Kjeldsen, 1981). These variations are similar to those observed on other Norwegian glaciers (Ostrem, 1975; Kjeldsen, 1981, 1983). Bed Load The bed-load discharge has shown a progressive decrease during the period of observation (Table 1). The change between 1973 and 1978 may be due to the change in sampling location from the terminus to the sedimentation chamber and could thus provide a measure of the amount of erosion in the ice fall below the intakes. The decline since 1978 could reflect some sort of "flushing" process resulting from excavation of the intakes. In the absence of more data, however, such interpretations are speculative. The number of boulders (>200 mm) transported by the streams and caught in the sedimentation chamber ranges from 200 to 500/yr; usually 10 to 20 of these are 1 m 3 or larger. In contrast, in front of the glacier, rocks larger than 200 mm are rare; this suggests that boulders may be broken in the ice fall downglacier from the intakes. At location " 1", more boulders were caught in 1975, the first year of operation, than in any other season (Wold and 0strem, 1979). Since 1975, boulders have rarely come through the intakes in this area. This lends some support to the suggestion that excavation of the intakes resulted in flushing of sediment from the glacier bed. Debris at the Base of the Glacier The debris content in the basal ice has been studied in artificial ice tunnels covering, at various times, most of the bed area between the three intake areas. In general, the debris concentration is relatively low and decreases rapidly with height above the bed; the mean concentration is 15 kg/m 3 in the lowermost 2 m of ice, but near the subglacial water courses, it is approximately an order of magnitude less (Hagen and others, 1983). Much of the debris is siltsized and is evenly distributed in the ice, giving it a grayish color. Coarser material sometimes occurs in debrisbearing layers that are congruent to, but some decimetres above, the bed and that contain rocks as much as 150 mm in diameter. Rocks larger than 150 mm are usually found at the bed or in the lower metre of ice. Appreciable thicknesses of bottom moraine beneath the basal ice are not common. Where such moraine occurs, it is generally less than a metre thick and is concentrated in depressions and lee-side areas. It appears to be stagnant. The contact between this bottom moraine and the basal ice is usually sharp, although ice may penetrate down into it locally. The mean debris concentration in the basal ice is -15 kg/m 3, and the basal ice flux is -2,400 m 3 /yr (2 m thick x 400 m wide x 30 m/yr). The debris flux past the intakes in the ice is thus only 360 mt/yr. In contrast, the diverted water transports -8,000 mt/yr (Table 1). DISCUSSION It is now widely accepted (Elliston, unpub. data; Haefeli, 1970; Rothlisberger, 1972; Shreve, 1972; Hodge, 1974) that englacial and subglacial water conduits are smallest in the early spring after closing by plastic deformation during the winter when discharges are low. As surface melting accelerates in the spring, discharges increase and passages are enlarged by melting. The energy needed for this melting is derived partly from sensible heat carried by the water from the surface and partly from conversion of potential energy to heat as the water falls in elevation. Pressures in the water system are high early in the melt season when melt-water production is increasing faster than conduit size can adjust. As the rate of water production begins to stabilize at normal summer values, the conduits are still being opened by melting, and water pressures thus decline. Recent observations (Iken and others, 1983; Holmlund, unpub. data) have shown that temporary periods of high water pressure can occur later in the summer, however, in response to increased melt-water production during periods of warm weather. Our observations of water pressures in small boreholes, described above, are consistent with these interpretations. Theoretical studies suggest that high water pressures result in cavity formation in the lee of bedrock irregularities and hence in increased separation of the glacier from its bed (Lliboutry, 1968; Iken, 1981). Although each of these cavities must be of local extent, their total volume can be substantial. Hooke and others (1983) found that the cavity volume beneath a part of Storglaciaren, Sweden, was equivalent to an average separation of 0.2 to 0.3 m, and Tangborn and others (1975) estimated the volume of water stored in and under South Cascade Glacier and found that it was equivalent to a layer >1 m thick. More recent observations (Kamb and Engelhardt, unpub. data; Holmlund and Hooke, 1983) indicate that at times, water pressures may be sufficient to float a glacier locally, resulting in extensive, audible ice-quake activity. Under certain circumstances, these zones of separation may propagate downglacier. With this background, we now turn to a discussion of some of our observations at Bondhusbreen. Winter Discharge For the five winter months from December to April, inclusive, the mean discharge from the glacier ranges from 0.05 to 0.20 m 3 /s, giving a total discharge of between 0.7 and 3.1 x 10 6 m 3. Possible sources for this water include melting of ice due to geothermal and frictional heating, release of water from storage in cavities within or under the glacier, ground water, and drainage from Lake Holmavatn. Assuming a geothermal heat flux of 0.05 J/m 2 s and a subglacial area of 10.5 km 2, the

7 394 HOOKE AND OTHERS water production due to geothermal heating is m 3 /s. To estimate water production due to frictional heating, we need first to estimate the mean ice velocity, u. The ice flux past the intakes is ~7,500 m 3 /day. As the intakes are about halfway from the equilibrium line to the terminus, it is reasonable to use this as an estimate of the mean ice flux for the glacier. The mean cross-sectional area is ~43 x 10 4 m 2. The mean velocity is thus m/day. If the mean basal shear stress is 0.1 MN/m 2, the water production would be ~T u -A/L = m 3 /s, where L is the latent heat of fusion and A is the area of the glacier bed. The total production of melt water by geothermal and frictional heating thus appears to be more than an order of magnitude too small to account for the winter flow. If draining of subglacial cavities provides most of the winter discharge, the amount of water stored corresponds to a water layer 50 to 250 mm thick under the whole glacier. As noted, this is comparable to cavity sizes estimated on other glaciers (Tangborn and others, 1975; Iken and others, 1983; Hooke and others, 1983). Lliboutry (1983) believes that subglacial ground water is ari important source of winter drainage in alpine valley glaciers. We have no information on the ground-water flow in this area, but due to the massive character of the granitic bedrock and the lack of soil, we think that this is a less li kely source here than in an alpine environment. Furthermore, considering the topography, it is probable that the geometry of the water table will be such as to cause ground water to reach the surface below the intakes rather than above them. Another possible source for some of the winter discharge is Lake Holmavatn. The lake is normally ice-covered by the end of November, but the accumulating winter snow pack could displace 2 to 3 x 1C 6 m 3 of water by depressing the ice. On the other hand, ice forming in the thick snow pack iri and downstream from the outlet of the lake should have a damming effect. We therefore suspe;t that this is a minor source of water. Occasional winter rain storms are another possible source of water, but temperatures in the snow pack are normally low enough to freeze this water before it penetrates into the glacier. Most of the winter discharge is thus believed to be water slowly forced out of subglacial cavities through millimetre-scale channels. Such drainage would be E.ccompanied by gradual closure of the cavities. Variations in Suspended Sediment Discharge The large, suspended sediment flux accompanying the first really high discharge of the melt season is interpreted as being, for the most part, a result of flushing of fine particles produced by abrasion since the last period of high water pressure, possibly as long ago as the previous spring. The high water pressures cause separation, thus giving water access to sediment that has accumulated at the ice-rock interface. This interpretation is consistent with observations of Raymond and Malone (1981), who recorded high sediment concentrations in water issuing from the terminus of Variegated Glacier, Alaska, in connection with certain high water-pressure events that caused uplift of the glacier. Large discharges later in the summer have appreciably lower sediment concentrations. This is presumably because the channel system is now well developed, and so water pressures are lower and separation less extensive. Alternatively, there may be less material available in such a short time after the initial flushing (0strem and others, 1967). Some of the suspended sediment load early in the spring and much of that later in the summer may come from melting of dirt-bearing ice in conduit walls. If, while flowing at the base of the glacier, a cubic metre of water falls through a vertical distance of 250 m (on the average), the mechanical energy released will be able to melt m 3 of ice. The average concentration of fine material in the basal metre of ice near the intakes is -6 kg/m 3 (Hagen and others, 1983). If this can be used as an average value for basal ice elsewhere under the glacier, then m 3 of ice would contribute kg of suspended sediment to the cubic metre of water. This sediment concentration is comparable to normal middle- and late-summer concentrations, exclusive of periods of flood. Characteristics of Channels The shapes of the subglacial conduits leading to the intakes should reflect the relative importance of tunnel enlargement by melting and of closure by creep. If the potential rate of en - largement greatly exceeds that of closure, the tunnel should be relatively broad and flat and normally only partly full of water (Shreve, 1972). The pressure in the tunnel would thus be atmospheric, or close to it. On the other hand, if the rate of closure equals or exceeds the rate of melting, the tunnel would normally be completely full of water, and because viscous energy dissipation will be greater where the water is deeper, the tunnel shape should be more nearly semicircular (Shreve, 1972). We now proceed to make some calculations that strongly suggest that subglacial channels beneath Bondhusbreen are at atmospheric pressure for some distance above the intakes, and we examine some consequences of this conclusion. For purposes of illustration, we will make calculations for a standard summer discharge of 5 m 3 /s (Fig. 3). From pipe flow theory we have (Hunsaker and Rightmire, 1947, equation 8.11) P P Z2- Zl+ H l2 = 0 (1) where P is the pressure, z is the elevation, p is the density of water, g is the acceleration due to gravity, and H is the head loss. The subscripts 1 and 2 identify two cross sections of the conduit a distance L apart. H is given by H = flv 2 /2Dg, where f is the friction factor, D is the conduit diameter, and V is the mean velocity. For an initial calculation, we assume (P2 - P])/pg << (Z2 - Z[). Then (z 2 - z,)/l is the slope of the tunnel, which we assume is parallel to th; bed near the intakes. A value of 30 is adopted. The friction factor, f, depends on the roughness of the tunnel walls; a plausible value is 0.05 (Hunsaker and Rightmire, 1947, p. 127). Equation 1 is now solved for D, making use of the continuity relation, Q = V 7rD 2 /4, with the result that D = 0.7 m and V = 12.7 m/s. The diameter, D', of a semicircular tunnel of identical hydraulic radius would be 1.1 m. An alternate calculation can be made by assuming that P is approximately equal to the ice overburden pressure (Shreve, 1972). In this case, D' = 1.3 m and V = 7.4 m/s if the presence of the intakes is ignored, thus approximating conditions prior to their excavation. If an intake is assumed to be present and at atmospheric pressure, D' = 0.8 m and V = 10 m/s. (These velocities are an order of magnitude higher than those estimated earlier, based on the time required for salt to travel between Hclmavatn and the intakes. This is in part because the average slope between Holmavatn and the intakes is about one-fourth of that near the intakes and in part because the average discharge in the channel from Holmavatn is much less than the discharge at the intakes. Two other possible sources of discrepancy are incorrect estimates of the friction factor, f, and of the length of the channel from Holmavatn to the intakes.) With a 1.0-m-diameter semicircular conduit, the rate of closure, f, can be obtained from Nye's (1953) theory for closure of a cylindrical hole. The result is 2 x 10" 4 mm/s if the ice viscosity is assumed to be relatively high (0.2 MPa-yr 1/n,

8 SUBGLACIAL HYDROLOGY AND SEDIMENT TRANSPORT, NORWAY 395 Hooke, 1981) and 16 x 10" 4 mm/s for half this viscosity. The measured closure rate in a 1,5-mdiameter, semicircular artificial tunnel was 18 x 10" 4 mm/s (Hagen and others, 1984), suggesting a viscosity of 0.14 MPa-yr 1/,n. In these calculations, we have assumed that the conduit is at atmospheric pressure and that there is no shear stress on the bed perpendicular to the tunnel axis. If the tunnel is flowing full and thus at a pressure in excess of atmospheric, or if there is a shear stress perpendicular to the axis, the closure rate will be slower. We also have assumed that other deviatoric stresses in the ice are negligible compared with the pressure causing closure. The potential rate of melting of the tunnel walls by viscous energy dissipation, M v, can be most easily estimated from the loss in mechanical energy as the water falls through a distance of 1 m. This energy is expended over the walls of a semicircular tunnel that is 1 /Tan 30 in length. The result is M v = 0.05 mm/s. In addition, the sensible heat in the water from Lake Holmavatn, which makes up -10% of the water reaching the intakes, will melt some ice. If the temperature of this water drops from +3 C to 0 C between the point where it enters the subglacial water system and the intakes, and if the distance followed by the water between these two points is 500 m, the heat released will be capable of melting the walls at an average rate Mj = 0.03 mm/s over the 500-m length of the passage. Much of this melting may, of course, occur near the point where Holmavatn water enters the subglacial water system rather than near the intakes. In summary, it appears that the potential rate of melting, M v + M^ is significantly larger than f, even allowing for as much as an order of magnitude error in our estimate of r. Thus the tunnels, for a considerable distance upstream from the intakes, should thus be relatively wide and not very high. To get a feeling for the dimensions of such a channel, note that a melt rate of 0.05 mm/s is equivalent to 4 m/day. As soon as a large channel develops, of course closure rates will be much higher, and heat exchange between the water and the tunnel walls will be less efficient. We thus should not expect to find a 15-mwide x 1-m-high tunnel with a rushing stream occupying < 10% of this 15 m 2 cross section. A 4-m-wide x '/2-m-high tunnel flowing about half full is, however, entirely conceivable. Splashing of "warm" water against the walls and roof of the tunnel would transfer the energy necessary to keep it open. For the most part, we might also expect to find this stream in topographically low areas in the glacier bed, as it could readily melt its way laterally down a transverse slope. This expectation may not be realistic, however; in view of the amount of rock debris carried by such subglacial streams, they should be able to erode a significant channel in the bedrock if they remained in the same place for a long period of time (H. Rothlisberger, 1983, oral commun.), but such bedrock channels are only rarely observed in valley bottoms from which the ice has retreated. If the channels were semicircular, ice would be expected to flow toward them from the sides as well as from the top, and sediment concentrations in ice bordering the tunnels should not be significantly different from those elsewhere in the basal ice. If the channels are broad and flat, however, the ice flux in from the top should be appreciably higher, and as this ice is cleaner than that at the bed, ice bordering the channels should be relatively clean. The fact that clean ice is found bordering the channels near the intakes supports the conclusion that these channels are broad and flat. Evolution of Drainage in the Spring The change in location of the water from intakes in areas "1" and "2" during initial phases of the melt to intakes at location "3" after the first week or so suggests a well-defined, systematic evolution of the subglacial drainage during this time period. The high water pressures in small drill holes in the vicinity of location "2" further suggest a connection between these pressures and the changes in drainage. To study this process, we need to make some further calculations of melt and closure rates in the subglacial conduits. A cylindrical channel under 150 m of ice should close to -0.05% of its original size between late September and early May (Nye, 1953). Unless conduits remain water filled during the winter, they will thus effectively cease to exist by spring (Haefeli, 1970). The conduits that do persist during the winter will be those carrying water draining from the englacial or subglacial storage reservoirs which we believe supply the normal winter discharge. On an 8 slope under 150 m of ice, conditions approximating those somewhat upglacier from the intakes, the mechanical energy released by the water will normally be able to melt the walls of a conduit substantially faster than the conduit can close by plastic flow (Fig. 7). The conduits, in general, should thus be only partly filled with water. This water still may not flow directly down the subglacial bedrock slopes, however. If ice is moving obliquely across such slopes, the mechanical energy dissipated in the water may not be able to melt the ice as rapidly as it is flowing. Conduits might then be forced into an oblique course such that M v = u b Sin 0, where u b is the basal ice velocity and 6 is the angle which this velocity vector makes with the conduit. These ideas are explored more fully in a separate paper (Hooke, 1984). One interpretation of the observed changes in location of the water early in the melt season is thus that low flows in the winter result in low melt rates, M v, and conduits thus become aligned more nearly parallel to the ice flow (so that 6 is small). As water pressures increase in the spring, separation occurs at numerous locations in the lee of bumps on the glacier bed, and small conduits develop, connecting these zones of separation. As water flows increase in these conduits, more mechanical energy is converted to heat in those conduits that trend more directly downslope; these thus have a higher melt rate and may be enlarged at the expense of others. M v is high enough to maintain these channels trending across the ice flow direction even when pressures drop as channel size increases later in the melt season. The hypothesized change in course is sketched as pathways I and II in Figure 1 (inset A). More detailed analysis of this problem suggests that orientations of these conduits may be unstable to small perturbation in discharge (Hooke, 1984). Figure 7. Rate of enlargement of a semicircular tunnel by melting due to mechanical energy dissipation on an 8 slope, M v, and rate of tunnel closure under 150 m of ice, r. Conduit diameter for various discharges was calculated from equation 1. r was obtained from Nye (1953) using an ice viscosity of 0.16 MPa-yr 1/n.

9 396 HOOKE AND OTHERS Time Lags As noted, the time lag from a temperature peak to a discharge peak is about one-fourth day for diurnal variations, but it increases to 1 to 2 days for variations with a period of several days. To study this difference in lag times, we consider a hypothetical glacier of uniform width and of length, L. We assume that the input, q, of melt water into the hydraulic system per unit length of glacier varies sinusoidally with time, t, thus q = q () + A 0 Sin (wt) (2) where q 0 is a base flow, A 0 is the amplitude of the oscillation, T is its period (1 day for a diurnal variation), and w = 2TT/T. The discharge at the terminus (or intakes) due to an input of this magnitude at a point a distance, x, upglacier will be q (x, t) = q 0 + A (x) Sin {w[t - ]} (3) v(x) where A is now taken as a function of x because the amplitude of the input signal will presumably be damped by diffusion as the water flows through the glacier. v(x) is the mean velocity of the water as it passes through the glacier, and so x/v is the time required for water to flow from position x to the intakes. To obtain the total discharge at the terminus, Q(t), we need to integrate q(x, t) over L. As the correct forms of the functions A(x) and v(x) are not known, the resulting Q(t) will not have quantitative significance, but it can be used qualitatively to study the dependence of Q(t) on T. Making the simplifications v(x) = constant, independent of x, and A(x) = A 0 - ax, integrating over x, and taking the derivative with respect to t yields jjq- = V (A () Sin (wt) - (A 0 - al) L av Sin [w (t - )] + { Cos (wt) - V w Cos [w(t - }). (4) v Two interesting :ases can be considered. If a = 0, Q(t) is a maximum (dq/dt = 0) when L/v = mt where m is an integer. Q(t) is then equal to q 0 L, and is independent of time, as would be expected from superimposing a large number of sinusoidal variations, each slightly out of phase with the others. Tius for periodic variations in input to result in similar variations in discharge, the dependence of A 0 (or possibly v) on x must be taken into consideration. Alternatively, suppose that a is not 0, and that the length of the glacier is chosen so that L/v = mt. As m» 1, this is not a serious restriction on L. Q(t) is then a maximum when val Sin (wt) = 0 or when t = mt/2. In other words, the lag from the time of maximum input, which occurs at t = mt/4 (equation 2), to the time of maximum discharge, is l AT. The fact that observed time lags are approximately this amount is probably coincidental, considering the assumptions made; the essential point is that, according to this simplified model, the lag increases as the period of oscillation increases, as observed. A plausible explanation for the observed increase in lag time with increasing period of the temperature variation is thus as follows: The input that occurs at a point a distance of ~vt/4 upglacier from the intakes will give its maximum contribution to the discharge at a time, T/4, after the peak input. At this time, locations closer to the intakes will still be contributing more than their mean discharge, q 0, and waves originating farther from the intakes, up to a distance vt/2 from them, will be just beginning to contribute more than their mean discharge. These contributions will thus reinforce each other, so that this will be the time of peak discharge at the intakes. Thereafter, the contributions from the closer points will begin to drop below q 0, and, due to diffusive damping of signals from farther upglacier, this deficit will not be balanced by the still increasing contributions from upglacier points. The discharge at the intakes will thus begin to decline. CONCLUSIONS Many of the observations we have made in the subglacial environment at Bondhusbreen are consistent with earlier work based on surface measurements. Our data thus support the conclusion that water pressures increase early in the melt season as the water influx exceeds the capacity of the channel system, that this increase in water pressure results in separation of ice from the bed and hence in a high sediment flux, and that the declining winter discharge is a result of gradual draining of water-filled cavities, probably at the glacier bed. On the other hand, the short-term and seasonal changes in position of subglacial water courses, although possibly anticipated, have not been as well documented previously. Our calculations suggest that these changes may be a consequence of separation of ice from the bed during periods of high water pressure coupled with the ability of channels that are only partly filled with water to maintain courses diagonally across the ice-flow direction. They can do this because the amount of mechanical energy released is more than that necessary to balance tunnel closure, and the excess energy available can thus offset the general ice flow. Such shifting of water courses makes the task of finding and trapping water beneath glaciers more difficult than originally anticipated. Fortunately, the channel systems under Bondhusbreen appear to be relatively sable, once the initial evolution of the system in the spring has occurred. This might not be the case under a different part of the glacier or under another glacier, however. Furthermore, future changes in regime of the glacier, involving an advance or a retreat, could change the sliding speed and pressure distribution in the ice and hence the location of channels. An additional complication associated with locating the water arose from the fact that high water pressures are not necessarily indicative of major channels. In fact, when channels are only partly full, low pressures may be more meaningful than high pressures. The type of extensive probing that was done with small drill holes to locate water under Bondhusbreen is thus less useful than might have been anticipated. In any such engineering effort, it is important to consider the extent to which man's activities have altered the natural system. There are two indications that permanent changes may have occurred in the present case. (1) The extraordinary variations in discharge during the summer of 1979 (Fig. 5), the second year of operation of intakes in area "3", suggest the possibility of collapse of a conduit and temporary subglacial damming of the flow. Such events have not been observed subsequently. Does this mean that the intakes somehow altered the drainage system under the glacier and that the extraordinary events described were an indication of this change? (2) The steady decline in bedload transport (Table 1) and in the concentration of large boulders also suggests a permanent change of some type. More dramatic changes in glacier regime might be expected downglacier from the intakes, of course, due to removal of water and sediment at the intake level. Such changes are most likely in locations where subglacial channels frequently flowed full and were under pressure prior to diversion of the water. We, as yet, have not detected any evidence for such changes downglacier from the intake level, and those changes so far identified upglacier from the intakes do not appear to be cause for concern.