Introduction
Warm-based glaciers may drain subglacially via a number of different hydraulic configurations. These may be classified as either “discrete” or “distributed”. The former may be composed of channels incised upwards into ice (Reference RöthlisbergerRöthlisberger, 1972; Reference Hooke, Laumann and KohlerHooke and others, 1990) or downwards into bedrock (Reference NyeNye, 1973). In each case, channels link to form efficient networks with the capacity to drain, large amounts of meltwater rapidly. In contrast, distributed systems drain extensive areas of the glacier bed at lower flow rates. Such flow may occur via meltwater films (Reference WeertmanWeertman, 1957, Reference Weertman1972), through permeable subglacial sediments (Reference Boulton and CoatesBoulton, 1974; Reference ClarkeClarke, 1987) or via networks of either linked cavities over bedrock (Reference WalderWalder, 1986; Reference KambKamb, 1987) or “canals” above and within unconsolidated sediments (Reference Walder and FowlerWalder and Fowler, 1994). The existence of these different drainage configurations has been established empirically on the basis of proglacial bedrock mapping (e.g. Reference Walder and HalletWalder and Hallet, 1979; Reference Sharp and GemmellSharp and others, 1989), dye-tracer studies (e.g. Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others, 1988), meltwater hydrochemistry 1992) and observations at the glacier bed (eg. Reference Kamb and LaChapelleKamb and LaChapelle, 1964).
A full understanding of the co-existence of, and interaction between, these different subglacial drainage systems may be critical to models of glacier motion, since each configuration may be characterized by a distinctive steady-state relationship between discharge and water pressure (e.g. Reference RöthlisbergerRöthlisberger, 1972; Reference WalderWalder, 1986). The stability of distributed flow to channel development has therefore been investigated for films (e.g, Reference WalderWalder, 1982; Reference Weertman and BirchfieldWeertman and Birchfield, 1983), permeable sediments (e.g. Reference AlleyAlley, 1992) and linked cavities (Reference KambKamb, 1987). Reference KambKamb (1987) argued that certain linked-cavity geometries are inherently unstable to perturbations in subglacial water pressure and suggested that transitions between drainage via tunnels (at relatively low steady-state water pressures) and linked cavities (at relatively high steady-state water pressures) may be responsible for the initiation and termination of surges. Subglacial drainage systems beneath temperate glaciers may therefore develop or collapse in response to seasonal variations in meltwater supply (e.g Reference Hock and HookeHock and Hooke, 1993) Whilst a widespread distributed system can evacuate base flows during the winter, the onset of high and variable melt-season discharges may destabilize such a system and replace it, at least locally, with channelized drainage. This replacement may occur at glaciers that are underlain by bedrock or unconsolidated sediments (e.g. Reference FountainFountain, 1992, Reference Fountain1994). Dye-tracer studies at Haut Glacier d’Arolla provide strong empirical support for this model, indicating, first, that channelized drainage develops as the headward growth of channels replaces distributed flow during the melt season, and secondly, that the boundary between the two systems is associated with the retreat of the snow line at the glacier surface (Reference NienowNienow, 1994) Analysis of subglacial piezometric surfaces indicates that such replacement is laterally variable, with distributed drainage surviving the melt season in areas of the glacier bed separating the channels (Reference FountainFountain, 1994). Reduced surface melting during the winter results in the creep closure of melt-season channels and the re-esiablishment of a widespread distributed drainage system (paper in preparation by I. C. Willis and others).
Evidence from warm-based glaciers therefore indicates that the spatial extent of channelized and distributed drainage configurations varies seasonally and that the two at the glacier bed for much of the melt season, irrespective of the nature of the substrate. However, little is known about the transition between these drainage components or the manner in which they interact hydraulically. Borehole investigations provide a means of addressing such issues, since they allow spatially distinct drainage components to be accessed and studied simultaneously. In this paper, we present diurnal records of subglacial water pressure, electrical conductivity (EC) and turbidity recorded at the base of a dense network of boreholes drilled to the bed of Haut Glacier d’Arolla, Switzerland. Spatial variations in these properties are interpreted in terms of the presence of different subglacial drainage configuratrons and the nature of the hydraulic Linkages between them.
Field Site and Methods
Haut Glacier d’Arolla is a predominantly warm-based valley glacier located at the head of Val d’Hérens, Valais, Switzerland (Fig. 1). The glacier extends fram c. 2560 m a.s.l. at its snout to c. 3500 m a.s.l. at its headwall and covers an area of c. 6.3 km2. A dense array of 24 boreholes was drilled during July and August 1993 close to the eastern margin of the ablation area of the glacier, about 1.5 km from the terminus (Fig. 2). This site was chosen on the basis of reconstructed subglacial hydraulic potentials that predicted the presence of a major melt-season channel beneath this part of the glacier (Reference SharpSharp and others, 1993). Ice-marginal and subglacial observations invariably reveal that the glacier is underlain by unconsolidated sediments. The recovery of such sediment within and on borehole probes further indicates that such a substrate extends beneath the borehole array. It is unlikely that the debris recovered on these probes was derived from the melting of debris-rich basal ice, since no thick basal-ice layers have been observed at the glacier (Reference HubbardHubbard, 1992). Available evidence therefore indicates that Haut Glacier d’Arolla is underlain by unconsolidated sediments.
Fig. 1. Haut Glacier d’Arolla. The borehole array is located on the eastern side of the glacier tongue c. 1500 m from the terminus.
Boreholes were drilled to the glacier bed using hot water. The bed was considered to have been reached and drilling was halted when no further progress could be made at a depth consistent with radio-echo sounding (Reference SharpSharp and others, 1993) and the depths of neighbouring boreholes. Borehole depths varied from 23 m for borehole 38, located close to the glacier margin, to 142 m for horehole 46, located towards the glacier centre line (Fig. 2). Inclinometry of 12 of these boreholes indicated a mean horizontal deviation of 2.9 ± 0.7 m across the glacier (east-west) and 4.6 ± 1.3 m parallel to ice flow (north-south). The mean depth of these boreholes was 87 m (min. = 23 m; max. = 132 m; σ = 41.5 m). Contact with the bed was occasionally marked by a rapid fall in water level as equilibrium was reached with the subglacial water pressure at the base of the borehole. Less immediate connections were also recorded, with many boreholes connecting during the night within some days of being drilled. Once drilled, boreholes were isolated from supraglacial water inflow by channel diversion. However, minor inflow through the surface ice layer could not be prevented. Water levels were monitored initially by manual sounding and subsequently, in 12 of the boreholes, by automated sensors (Fig. 2). The sensors measured water pressure, electrical conductivity (EC) and turbidity within a few tens of centimetres of the glacier bed. Their output was stored on microloggers (Campbell Scientific CR-10) that recorded the means of 30 readings every 10 min. Water pressures and ECs were calibrated against known values and are accurate to within 0.5 m of water head and 5 σS cm−1, respectively. ECs are presented as measured in water at c. 0°C.
Fig. 2. The 1993 borehole array. Boreholes indicated by dots were monitored automatically and those indicated by cricles were monitored manually (every 1-3 h during daylight). Quantitative analysis presented in the text is based on data recorded in boreholes 35,29,40, 42 and 43 (crosses).
Borehole turbidities were measured by light-sensitive and light-emitting diodes that were separated by the sample. The difficulties involved in calibrating lurbidity-sensor records in terms of suspended-sediment concentrations are well-documented (e.g. Reference GippelGippel, 1988; Reference Stone, Clarke and BlakeStone and others, 1993). These data are therefore presented and interpreted predominantly in terms of “relative turbidity” (Tu[r]), defined as
where Tu[c] and Tu[s] are the turbidity signals recorded in clear water and the sample, respectively. Clear water;, therefore, has a relative turbidity of 0 and opaque water a relative turbidity of 1. However, turbidity sensors were also calibrated against suspended-sediment concentration (SSC) using the Erie fraction (< 125 μm) of fluvially deposited sediments sampled from the proglacial area of Haut Glacier d’Arolla. These calibrations define a relationship of the form
where SSC is in gl−1 (Fig. 3). Despite the good fit of these data, the influence of variations in sediment grain-size and lithology remains unconstrained. Calibrated SSCs are therefore used only as an approximate indication cf actual concentrations.
Fig. 3. Turbidity calibration curve for borehole sensors used during the 1993 field season. Sediments were recovered from fluvial deposits in the proglacial area of the glacier and were sieved to remove particles coarser than 125 μm prior to calibration.
The data presented in this paper were recorded during a 7 d period of stable meteorological and hydrological conditions from 16 to 22 August 1993 (Julian Day [JD] 228-234). This time period was long enough to exclude daily meteorological variability and short enough to exclude seasonal trends in the hydraulic development of the subglacial drainage system. The latter of these forms the subject of another paper (paper in preparation by I. C. Willis and others). The data presented in this paper, and the interpretations based on them, are therefore considered to represent typical, late melt-season conditions at Haut Glacier d’Arolla.
Diurnal Subglacial Water-Pressure Variations
Minimum daily borehole water levels and daily borehole water-level ranges have been interpolated spatially across the full borehole array (UNIRAS, 1990). The resulting surfaces for JD 229 demonstrate that much of this area of the glacier is characterized by subglacial water pressures that are high (approaching overburden pressure; Fig. 4a) and diurnally constant (Fig. 4b). However, the surfaces are clearly bisected by an axis, greater than 100 m wide and aligned sub-parallel to the general direction of ice flow, that is characterized by low minimum water pressures and large pressure variations. The centre of this “variable pressure axis” (VPA) passes through the borehole array at an easting of c. 185 m; close to borehole 36 in the southern transect, between boreholes 35 and 29 in the middle transect and between boreholes 37 and 28 in the northern transect (Fig. 2).
Fig. 4. Interpolated subglacial water-pressure surfaces for the full borehole array for JD 229, 1993: (a) minimum water level (m a.s.l.); (b) water-pressure variation (percentage of overburden).
Subglacial water pressures have also been investigated using time series of water levels recorded in boreholes 35, 29, 40, 42 and 43 in the middle transect (Fig. 5). These records confirm a progressive drop in minimum water level and an increase in diurnal water-level range towards the centre of the VPA. Water levels in the two boreholes located closest to the centre of the VPA (boreholes 35 and 29) rise to within 10 ra of the ice surface during the day and fall to the glacier bed for some hours overnight. These temporal variations take the general form of quasi-sinusoidal cycles, with a wavelength of 1 d and a phase relationship that lags c. 2 h behind glacier-surface air temperature. Closer inspection of the form of these cycles reveals a systematic asymmetry, with steep rising and attenuated falling limbs.
Fig. 5. Water-level time series recorded in boreholes across the middle transect on JD 229 and 230 1993.
Interpretation
The water-pressure characteristics and orientation of the VPA are consistent with the location of a hydraulically efficient subglacial channel at its centre. In contrast, water pressures adjacent to the VPA are uniform and high-standing, indicating the presence of a widespread and less efficient drainage system. The parabolic cross-sectional form of the VPA indicates that the two systems interact hydraulieally and are possibly transitional, over tens of metres.
The nature of this hydraulic interaction may be investigated on the basis of diurnal water-level variations recorded across the middle borehole transect (Fig. 5). Water levels (in m a.s.l.) in boreholes 35 and 29, located close to the centre of the VPA, rise above and fall below those in boreholes 40, 42 and 43 each day. A diurnally reversing hydraulic gradient therefore exists between the channel and the surrounding glacier bed. Reconstructions of the direction and magnitude of this gradient between adjacent boreholes located to the west of the channel (Fig. 6) indicate that water is driven laterally out from the in the early afternoon and back to it overnight. The magnitude of the hydraulic gradient also diminishes with distance from the channel, as would the velocity of the consequent water flows under a uniform basal hydraulic configuration. The relatively minor diurnal water-pressure variations recorded in boreholes 42 and 43 suggest that the influence of these channel-initiated water flows decays rapidly over some tens of metres. No waterlevel variations were apparent in boreholes 44, 45 or 46, each of which was monitored manually several times a day. Even though these boreholes reached the glacier bed, water levels in them remained high and constant. Although such boreholes are “connected” to the subglacial hydrological system, the local capacity of that system may be inadequate to transmit water away from their bases rapidly enough to drain surface meltwater inputs. Water levels in such boreholes may not, therefore, reflect accurately the magnitude of local subglacial water-pressure variations. Such boreholes may fill with water drilling and never subsequently drain to their equilibrium levels.
Fig. 6. Hydraulic gradients, calculated by linear interpolation, between borekole pairs across the middle transect an JD 229 NW 230 1993: (a) borehole 29 to borekole 40, (b) borehole 40 to borehole 42 and (c) borehole 42 to borekole 43. (Calculations are based on borehole separation as surveyed at the glacier surface. Inclinometry suggests that these distances may be ± c. 20% of borehole separation at the glacier bed. The magnitude of the reconstructed hydraulic gradients may therefore also be ± c.20%).
The asymmetric form of the borehole water-pressure time-series records (Fig. 5) may also reflect the nature of these lateral subglacial water flows Reference AlleyAlley (in press) argues that asymmetry arises in such systems because variations in effective pressure result in flow paths opening up first and closing down first at the channel boundary. Thus, according to Alley, cavities at the ice-bedrock interface progressively open up as water is driven away from the channel but have already closed down at the channel (due to falling channel pressures) as the water drains back to it. Return drainage is thereby impeded relative to outflow from the channel. Although Alley envisages such a process in terms of water flow through a film-cavity system over bedrock, our data suggest that similar cycles occur at Haut Glacier d’Arolla, which is underlain by unconsolidated sediments. Asymmetry in lateral water flows beneath such soft-bedded glaciers may reflect the effects of variable channel-marginal effective pressures on sediment consolidation rather than (or as well as) the capacity of flow pathways at the ice-substrate interface.
The significance of the diurnal, transverse water fluxes at Haut Glacier d’Arolla may he investigated on the basis of subglacial water-quality records across the middle borehole array (Fig. 7). Time series of basal EC recorded in boreholes 29, 40 and 42 have been compared with the hydraulic gradient between boreholes 29 and 40 for JD 229 and 230 (Fig. 7a). Borehole 29 is characterized by a strong diurnal EC cycle, rising gradually to c. 20 μS cm−1 overnight and falling rapidly to c.2μS cm−1 in the late morning. This pulse of solute-poor water represents the new day’s melt wave arriving (from the channel) at horehole 29 as the hydraulic gradient is established from this borehole towards borehole 40 (Fig. 7a). The low EC of this water indicates, first, that the channel transports locally derived, surface meltwater at this time and, secondly, that little solute has been acquired during flow from the channel to borehole 29. In contrast, the high-EC signal recorded overnight in borehole 29 coincides with waters flowing back to the channel under the reversed hydraulic gradient. These waters have acquired solute within the distributed drainage system. ECs at the base of borehole 40 are generally higher (15-20 μS cm−1) and less variable than those at the base of borehole 29, suggesting less subglacial hydrological mixing and longer water-rock contact times beneath the former. However, a distinct fall in EC is recorded at the base of borehole 40 during the afternoon. If we assume that this event reflects the arrival of the same low-EC pulse that in recorded in borehole 29, then the approximate velocity of that pulse may be calculated from the time it takes to pass between the two horeholes: 0.24 d (2.1 × 104s) on JD 229. The two boreholes are c. 16 m apart, indicating a mean flow velocity between them of c 67 m d−1 (8× 10−4 m s−1). No such pronounced EC variations were recorded in either borehole 42 or borehole 43.
Fig. 7. Comparisons of the hydraulic gradient (heavy lines) calculated between boreholes 29 and 40 with (a) ECs recorded in boreholes 29, 40 and 42 and (b) relative turbidities recorded in boreholes 29 and 40 on JD 229 and 230 1993.
Borehole turbidity-time series provide further evidence for diurnal suhglacial water flows across the VPA. Reversals in the hydraulic gradient between boreholes 29 and 40 are coincident with turbidity pulses in both horeholes (Fig. 7b), indicating that the diurnal water flows are responsible for mobilizing fine sediments. However, the two turbidity cycles are out of phase and peak turbidities in borehole 29 are an order of magnitude higher than in borehole 40. These differences may he interpreted in terms of the source areas and relative amounts of sediment involved. During the early afternoon, when the hydraulic gradient drives water away from the channel, clear water is recorded at the base of borehole 29 (Tu[r] < 0.001) and a (relatively) turbid pulse is recorded at the base of borehole 40 (Tu[r] > 0.002). In contrast, when the reversed hydraulic gradient drives water back to the channel overnight, a prominent turbidity peak is recorded in borehole 29 (Tu[r] = c. 0.07) and very low turbidities are recorded in borehole 40 Tu[r] = c. 0 0005). These patterns suggest, first, that the rate of water flow diminishes away from the channel such that, by horehole 40, only relatively low suspended-sediment concentrations are recorded, and secondly, that waters returning to the channel are more turbid than those leaving it. Substitution of these data into Equation (2) suggests that, at borehole 29, waters leaving the channel in the morning have a SSC of < 0.1 gl−1, while those returning to it overnight have a SSC c. 1-10 gl−1. A net transfer of fine debris towards the channel is therefore inferred, with peak transfer rates occurring during the descending limb of the diurnal flow cycle. Overnight bulk meltwater suspended sediment yields may therefore comprise debris supplied principally by lateral water fluxes returning to subglacial channels. The nature of this erosion depends largely on the precise hydraulic configuration of the distributed system flow pathways. In the absence of evidence to the contrary, we adopt the working hypothesis that this occurs as pore-water flow through the subglacial sediment layer. The permeability of such a layer may be investigated on the basis of the speed and amplitude of water-pressure waves as they propagate through it.
The Hydraulic Diffusivity of the Subglacial Sediment Layer
Borehole data from Haut Glacier d’Arolla indicate that diurnal pressure waves are initiated at the centre of the VPA and migrate laterally through the surrounding distributed system. Standard heat-flow theory (Reference Ingersoll, Zobel and IngersollIngersoll and others, 1954; Reference Carslaw and JaegerCarslaw and Jaeger, 1959) provides analytical solutions that relate the propagation velocity (Reference FountainFountain, 1994) and the amplitude attenuation of these pressure waves to the hydraulic conductivity of the sediments through which they migrate. According to this analysis, the driving pressure is treated as a boundary condition that varies as a harmonic function of time and the glacier bed is treated as a uniform half-solid with a steady water pressure at infinity.
Pressure-Wave Propagation Velocity
The propagation velocity of a subglacial pressure change may he related to the frequency of the initiating pressure fluctuation and the hydraulic conductivity and specific storage of the sediments through which the wave passes. The time t it takes for a pressure inflection to arrive at a point of distance x from the channel is given by
where S s is specific storage of the sediments (defined as the volume of water released from saturated storage by a unit volume of material under a unit decline of hydraulic head; m−1 ω is the angular frequency of the periodic boundary condition (2π/t = 7.27 × 10−5s−1 for a diurnal cycle) and K is the hydraulic conductivity of the sediments (m s −1). Since both K and S s are related to the material properties of the sediments, we base our analysis on the ratio parameter hydraulic diffusivity (D) defined as
(Reference Freeze and CherryFreeze and Cherry, 1979, p. 61; m2s−1). Solving Equation (3) for D gives
Equation (5) can be solved in one dimension across the middle borehole transect using the recorded pressure-wave arrival times at boreholes 35, 29, 40, 42 and 43. For the purpose of these calculations, we assume that borehole 35 marks the westward margin of the channel. We therefore take distance x = 0 at borehole 35 and t = 0 as the time at which the direction of pressure change reverses in this borehole. Plotting the mean time of arrival of diurnal pressure inflections (maxima and minima) along this transect for the 7 d period, JD 228-234, reveals a quasi-exponentially increasing delay in arrival time away from the channel (Fig. 8a). The diurnal pressure wave therefore propagates at a progressively lower velocity as it migrates away from the channel. These pressure-wave velocities may he compared with that predicted under the assumption of a constant hydraulic diffusivity for the sediments underlying the VPA (Fig. 8b). Substituting a typical value of D for subglacial sediments (3.4 × 10−3s−1; Reference Murray and ClarkeMurray and Clarke, 1995;Table 1) into Equation (5) yields a propagation velocity (x/t) of c. 7 × 10−4 m s−1 (Fig. 8b). This velocity contrasts markedly with those recorded across the VPA: measured pressure-wave velocities are, first, markedly higher than 7 × 10−4 m s−1, suggesting that subglacial sediments beneath the VPA are characterized by a higher hydraulic diffusivity than typical glacial tills, and secondly, decrease away from the channel, suggesting an associated decrease in the hydraulic diffusivity of the subglacial layer. Fitting a curve to these data indicates that the hydraulic diffusivity (D) of the layer decreases exponentially with distance (x; in m) according to
(Fig. 8c). Solving Equation (6) for D at the channel margin (x = 0) and at the “edge” of the VPA (x = 70), yields hydraulic diffusivities of 4 × 10−1 m2s−1 and 7 × 10−2 m2s−1, respectively. The range of hydraulic conductivities associated with these diffusivities may be approximated by substituting a typical value of S s for subglacial sediments (6.4 × 10−6 m−1; Reference Murray and ClarkeMurray and Clarke, 1995;Table 1) into Equation (4). The resulting hydraulic conductivities are 3 × 10−4 m s−1 for sediments located close to the channel and 5 × 10−7 m s−1 for sediments located c. 70 m away (bearing in mind that the assumption of constant S s may reduce the accuracy of the analysis by an order of magnitude (Reference Freeze and CherryFreeze and Cherry, 1979, p. 55)). Whilst the latter value is typical of Dardan flow through subglacial till (Table 1), the former a more typical of flow through clean sand (Reference Freeze and CherryFreeze and Cherry, 1979, p. 29).
Table 1. Reported values of hydraulic conductivity and speCific storage for typical Subglacial sedimenls
Fig. 8. Analysis of the propagation velocity of the diurnal pressure wave across the middle borehole transect (boreholes 35, 29, 40, 42 and 43) for JD 228-234 1993: (a) time delay to arrival of pressure-wave inflections following initiation at borehole 35 (error bars = 1σ); (b) associated propagation velocity (the velocity predicted for typical subglacial tills (explained in text) is shown for comparison); (c) calculated variation in hydraulic diffusivity (D).
Analysis of the propagation velocity of the diurnal pressure wave at Haut Glacier d’Arolla therefore indicates that the hydraulic diffusivity of the subglacial sediment layer increases markedly towards the centre of the VPA. This is consistent with the progressive removal of fines from such a layer by diurnal water flows that are initiated at, and return to, a subglacial channel located at the centre of the VPA.
Pressure-Wave Amplitude
The hydraulic diffusivity (D) of the subglacial sediment layer may also be estimated from the amplitude attenuahon of the diurnal pressure wave as it propagates across the VPA. Following Reference Carslaw and JaegerCarslaw and Jaeger (1959), the deray of wave amplitude (a) with distance (x) from the channel is given by
This relation may be used to predict the amplitude attenuation of diurnal pressure waves as they migrate across the middle borehole transect (boreholes 35, 29, 40, 42 and 43) under two assumptions; first, that the hydraulic diffusivity of the underlying sediments is uniform (D = 3.4 × 10−3 m−2s−1) and, secondly, that the hydraulic diffusivity of the underlying sediments decreases away from the channel in accordance with the propagation velocity the diurnal pressure wave. Under the second scenario, a(0) is redefined at each borehole according to the recorded amplitude and D changes continuously across the VPA according to Equation (6). Predicted amplitude-attenuation patterns under the two scenarios are compared with those recorded across the transect on JD 234 (Fig. 9). None of the water levels fell below the sensors on this day, providing records of the full magnitude of the pressure wave cycles in all boreholes. The assumption of homogeneous subglacial sediments yields amplitudes that are similar to those recorded in boreholes 40-43, but which decay too rapidly close to the centre of the VPA (Fig. 9a). This comparison therefore indicates that the hydraulic diffusivity of the subglacial sediment layer between the channel and borehole 40 is higher than that of typical subglacial sediments. Indeed, with the exception of borehole 42, recorded pressure-wave amplitudes correspond much better with those predicted on the basis of an exponential decrease in diffusivity away from the channel (Fig. 9b). However, a much smaller amplitude is recorded in borehole 42 than is predicted. The hydrological system beneath this borehole may he unable to transport the water flux that is required to reflect accurately the magnitude of the subglacial pressure wave. This anomalous behaviour suggests that the analysis of pressure-wave amplitudes (that is, based on water levels in open boreholes) may be susceptible to local variations in the capacity of the subglacial hydrological system. In contrast, the analysis of pressure-wave velocities (based on the timing of a pressure change) is less sensitive to such variations since wave propagation does not require significant water transfer. This interpretation is supported by the consistency of the timing of the pressure variation recorded in borehole 42 with arrival times in boreholes 40 and 43 that are adjacent to it (above).
Analysis of both pressure-wave velocities and pressure-wave amplitudes at Haut Glacier d’Arolla suggest a systematic increase in hydraulic diffusivity (to levels significantly above those of typical subglacial sediments) close to the centre of the VPA. This increase is interpreted in terms of a coarsening of the subglacial sediment layer. This inference may be assessed by comparing the hydraulic conductivity of a channel-marginal subglacial sediment sample (recovered from a basal cavity at Haut Glacier d’Arolla; Fig. 10) with that determined on the basis of the pressure-wave analyses. The hydraulic conductivity (K in m s−1) of this sample may be approximated from its effective grain-size (the diameter at which 10% by weight of the particles are finer than d 10 in mm) according to
where A is a coefficient with a value of c. 1 (m−1 s−1) (Reference Freeze and CherryFreeze and Cherry, 1979, p. 350). The effective grain-size (d 10) of the sample is c. 0.3 mm, indicating (from Equation (8))a hydraulic conductivity of c.9 × 10−4m s−1. This hydraulic conductivity is consistent with that determined for channel-marginal sediments on the basis of the diurnal pressure-wave propagation velocity and amplitude attenuation (3 × 10−4m s−1; above)
Summary and Discussion
Diurnal water-level variations in boreholes in the ablation area of Haut Glacier d’Arolla indicate the late melt-season presence of a variable pressure axis (VPA) that is aligned broadly parallel to the direction of ice flow. This axis is characterized by a gradual rise from low minimum diurnal water pressures and high diurnal water-pressure variations at its centre to high minimum diurnal water pressures and Low diurnal water-pressure variations at its margins, about 70m away. These patterns indicate the presence of a major subglacial channel (located at the centre of the VPA) that is bounded by, and interacts with, an extensive “distributed” hydrological system. Reconstructed subglacial hydraulic gradients suggest that this interaction is driven by large diurnal water-pressure variations within the channel: high pressures in the day force water out from the channel, and into the adjacent distributed system, and low channel pressures overnight drive that water back. Analyses of the velocity and amplitude attenuation of the associated diurnal pressure waves indicate that the hydraulic efficiency of the distributed system increases markedly close to the channel. In the foregoing analysis, we have postulated that these flows occur by permeating the subglacial sediment layer that underlies the VPA. Whilst such flows must occur where a hydraulic gradient acts on saturated, permeable sediments, the apparent increase in hydraulic diffusivity close to the channel may also be interpreted in terms of flow concentration at the ice-sediment interface. Such concentration may take three forms: first, as film flow at the ice-till interface (Reference Weertman and BirchfieldWeertman and Birchfield, 1983), secondly, as pore-water flow through coarser, and therefore more hydraulically transmissive, clasts at the upper surface of the subglacial sediment layer (Reference FountainFountain, 1994), and thirdly, as flow through a network of small channels located at the ice-sediment interface (Reference Walder and FowlerWalder and Fowler, 1994). Although any of these configurations may exist beneath the VPA at Haut Glacier d’Arolla, no independent evidence is currently available to suggest that this is the case. In contrast, the correspondence of the hydraulic conductivity of a channel-marginal suhglacial sediment sample with that determined from the pressure-wave analyses suggests that the inferred hydraulic diffusivities may be accounted for by pore-water flow alone.
Lateral, diurnal water flows at the glacier bed involve the temporary storage of waters in the distributed hydrological system, the transport of subglacial debris and systematic variations in the pattern of subglacial water pressures. These may have important implications for glacier erosion, hydrochemistry and motion.
Fig. 9. Comparison of the amplitude attenuation of the diurnal pressure wave recorded across the middle borehole transect (boreholes 35, 29, 40, 42 and 43) on JD 234 with that predicted for subglacial sediments with (a) a uniform hydraulic diffusivity (3.4 × 10−3 m2 s−1) and (b) a hydraulic diffusivity that decreases with distance from the channel (according to Equation (6); see text).
1. Implications for glacier erosion
It has long been recognized that pore-water flow has the capacity to eluviate fine debris through unconsolidated sediments (e.g. Reference Ingles and LeeIngles, 1968). Reference Boulton and DentBoulton and Dent (1974) linked vertical grain-size variations in proglacial tills at Breiðamerkurjökull, Iceland, to eluviation by permeating rain water, whilst Reference ClarkeClarke (1987) suggested that suhglacial pore-water flows could result in lateral variations in the texture of the sediment layers through which they pass. We believe that evidence from Haut Glacier d’Arolla provides the first empirical support for this process of subglacial erosion. Borehole-turbidity pulses are synchronous with systematic changes in the direction of the subglacial hydraulic gradient and analyses of the propagation rate and amplitude attenuation of the diurnal pressure wave indicates that subglacial sediments are characterized by systematic transverse variations in hydraulic conductivity, varying from c. 10−4 m s−1 at the channel margin to c. 10−7 m s−1 70 m away. These values suggest, first, that fine material has been removed from sediments underlying the borehole array and, secondly, that such removal is greatest close to the subglacial channel, along which fines may be transported to the glacier portal. The spatial extent of this erosion may be approximated by the area of the glacier bed affected by the permeating diurnal water flux. Borehole EC and turbidity records from Haut Glacier d’Arolla indicate that such a zone may be about 20-40m wide. Borehole-turbidity records further suggest that waters returning from this zone to the central channel may transport fine sediments at concentrations of 1-10 g l−1.
2. Implications for Glacier Hydrochemistry
The occurrence of diurnal, lateral subglacial water flows suggests the presence of three subglacial weathering environments. First, waters flowing within melt-season conduits will be characterized by solute-acquisition signatures that are indicative of the dissolution of relatively high suspended-sediment concentrations for short periods (tens of minutes to hours). Secondly, waters flowing through sediments beneath the VPA will be characterized by solute loads that are acquired from in-situ subglacial sediments and (possibly) suspended sediments over some hours. These effects may be most evident in bulk meltwaters forming the recession limb of diurnal hydrographs, since that is when these cycled pore waters return to subglacial drainage channels and exit the glacier Solute acquisition within the distributed system represents the third weathering environment, where waters are in contact with sediments containing a high proportion of reactive fines for periods of perhaps weeks to months. Such waters may exit the glacier relatively continuously, as an ionically concentrated “base-flow” component.
3. Implications for Glacier Motion
High subglacial water pressures increase basal sliding, either via slip at the ice-bedrock (Reference Iken and BindschadlerIken and Bindschadler, 1986) or ice-sediment (Reference Iverson, Hanson, Hooke and JanssonIverson and others, 1995) interface or via the deformation of a subglacial sediment layer (e.g. Reference Boulton and HindmarshBoulton and Hindmarsh, 1987). Our borehole investigations at Haut Glacier d’Arolla reveal that subglacial water pressures approach overburden within a band 50 m wide at the centre of the VPA (Fig. 4b) for some hours each day (Fig. 5) during the late melt season. Reconstructed subglacial hydraulic potentials indicate that two such channels drain the glacier for most of its length (Reference SharpSharp and others, 1993), suggesting that these high transient subglacial water pressures affect c. 10% of of the glacier (which is c. 1 km wide). This proportion may increase down-glacier as the net melt-water flux increases and glacier width decreases. The inferred lateral variations in subglacial sediment texture may also influence glacier motion, since laboratory studies indicate that shear strength may be increased by the removal of fines (e.g. Reference Rodine and JohnsonRodine and Johnson, 1976).
Fig. 10. Grain-size distribution of a near-channel subglacial till sampled from a cavity in the ablation area of Haut Glacier d’Arolla. Grain-size fractions were determined by dry-sieving from 5ø to 3ø (32-0.125 mm) and by laser granuiometry from 3ø to 9ø (0.125-0.002 mm; Reference HubbardHubbard, 1992).
Lateral subglacial water flows, such as those identified at Haut Glacier d’Arolla, therefore have time-dependent consequences for patterns of subglacial pore-water pressure and sediment texture (and therefore rheology). These influences may be reilected in high-resolution temporal and spatial variations in glacier motion.
Acknowledgements
We thank A. Hubbard and M. Tulley for their assistance in the field. Y. Bams and P. and B. Bournissen provided essennal logistical support in Arolla. Additional logistical support was provided by M. Beytreyson of Grande Dixence S.A. The manuscript has been greatly improved by comments on an earlier draft by R. Hooke, N. Iverson and A. Fountain. The research was funded by the U.K. Natural Environment Research Council (grant GR3/8114) and the Royal Society.
