Review of subglacial hydro-mechanical coupling: Trapridge Glacier, Yukon Territory, Canada

Quaternary International 86 (2001) 29–43

Review of subglacial hydro-mechanical coupling: Trapridge Glacier, Yukon Territory, Canada Urs H. Fischera,*, Garry K.C. Clarkeb b

a Laboratory of Hydraulics, Hydrology and Glaciology, ETH-Zentrum, CH-8092 Zurich, Switzerland Department of Earth and Ocean Sciences, University of British Columbia, Vancouver, B.C. Canada V6T 1Z4

Received 7 July 2001; accepted 7 July 2001

Abstract The interaction of basal processes with the subglacial drainage system is a critical issue in understanding glacier dynamics. Since the recognition that many glaciers and ice masses overlie soft sediments rather than hard bedrock, much research has been undertaken to investigate how mechanical and hydrological conditions of a deformable substrate control the coupling at the ice–bed interface and thus affect fast ice flow and glacier surging. In research undertaken on Trapridge Glacier, a small surge-type glacier in the St. Elias Mountains, Yukon Territory, Canada, we have combined extensive field investigations using novel measurement techniques and theoretical modelling to study hydromechanical coupling processes. Measurements of subglacial water pressure indicate that the basal water system can be dramatically inhomogeneous, both spatially and temporally. Since ice–bed coupling is strongly influenced by subglacial water pressure, the stresses at the bed are also markedly heterogeneous and are expected to form a patchwork distribution which mimics the pressure distribution of the basal water system. This heterogeneity in the stress field at the ice–bed interface introduces a pronounced variability to the basal motion mechanics. As such, basal sliding and subglacial sediment deformation are not steady and continuous processes. Instead, the variability of the subglacial water system leads to a spatial and temporal interplay of increased ice–bed coupling at low water pressures at one site or time with ice–bed decoupling during rising water pressures at other sites or times. Thus, on the one hand there is downglacier shear deformation of the bed and accumulation of elastic strain in ice and sediment, while on the other hand there is enhanced slip-sliding of the glacier and upglacier shear motion of the bed due to an elastic relaxation of the sediment. r 2001 Elsevier Science Ltd and INQUA. All rights reserved.

1. Introduction Improved understanding of the links between hydrological conditions at the bed of ice masses and changes in the rates and mechanisms of basal motion is important for elucidating the complex dynamical behaviour of glaciers and ice sheets. Interest in the dynamics of ice masses arises, in part, from the need to comprehend how the mass balance of ice sheets controls sea level. Since the volume of the modern Greenland and Antarctic Ice Sheets is to a great extent controlled by fast flowing outlet glaciers and ice streams, much research has focused on the subglacial processes that enable fast flow. Ice streams may move primarily by bed deformation (e.g. Alley et al., 1989) or sliding (e.g. Engelhardt and Kamb, 1998) depending on basal hydrological and mechanical conditions. As such, the *Corresponding author.

mechanisms of, and controls on, sliding and deformation processes beneath the ice are of primary interest. Similarly, the glacier flow instability known as surging is thought to be largely caused by basal rather than ice mechanical processes (Clarke, 1987a; Raymond, 1987). Surge-type glaciers oscillate between short periods of extremely rapid movement and long periods of relative inactivity or quiescence. During the active phase of the surge cycle, surface velocities and strain rates commonly reach 10–1000 times their quiescent value, and large volumes of ice are rapidly transported from an upglacier reservoir area to a downglacier receiving area (Meier and Post, 1969; Sharp, 1988). This fast flow is generally acknowledged to be the result of sustained, high subglacial water pressures. How basal hydrological conditions control coupling at the ice–bed interface, and whether rapid motion is promoted by sliding or deformation of weakened subglacial sediments, remain fundamental unsolved questions.

1040-6182/01/$ - see front matter r 2001 Elsevier Science Ltd and INQUA. All rights reserved. PII: S 1 0 4 0 - 6 1 8 2 ( 0 1 ) 0 0 0 4 9 - 0

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In this paper we aim to provide an overview of our investigations of the interactions between hydrological and mechanical conditions and processes at the ice–bed interface of Trapridge Glacier, Yukon Territory, Canada. We document the development of novel techniques for exploring the subglacial environment and present data of unique and heretofore unobserved basal processes that were recorded using these new techniques. We then describe the theoretical modelling that was indispensable for a comprehensive and consistent interpretation of our field measurements.

sediments? Do sliding and deformation processes vary in space and time? How do hydrological processes control the partitioning between basal sliding and sediment deformation? Two possibilities seem to be competing: high basal water pressure causes decoupling of the ice from the bed and thus promotes glacier sliding; at the same time however, high basal water pressure also has the potential to weaken basal sediments allowing the bed to deform.

1.1. Ice–bed coupling

Progress towards answering some of the above questions has been made by a number of research groups studying physical processes in situ at the ice–bed interface (e.g. Engelhardt et al., 1978, 1990a, b; Boulton and Jones, 1979; Boulton and Hindmarsh, 1987; Blake et al., 1992, 1994; Humphrey et al., 1993; Fischer and Clarke, 1994; Iverson et al., 1994, 1995; Hooke et al., 1997; Porter et al., 1997; Engelhardt and Kamb, 1997, 1998; Boulton, this issue). However, because of the difficulty of making direct measurements at the base of glaciers and ice sheets, a complete set of field data that is necessary to build a full physical description of the individual processes involved in ice–bed interactions is still lacking. To this end, theoretical and laboratory research have greatly helped to supplement and generalize field observations (e.g. Clarke, 1987b; Kamb, 1991; Fischer and Clarke, 1997a, b; Iverson et al., 1997, 1998, 1999; Iverson, 1999; Fischer et al., 1999; Tulaczyk, 1999; Tulaczyk and Scherer, this issue; Tulaczyk et al., 2000). Since geophysical investigations on Ice Stream B, West Antarctica revealed a metres-thick, water-saturated and highly dilated sediment layer (Blankenship et al., 1986, 1987; Rooney et al., 1987), numerous studies have advocated bed deformation as the primary mechanism of basal motion (Alley et al., 1986, 1987a, b, 1989; Alley, 1989; MacAyeal, 1992, 1993; Clark, 1994; Jenson et al., 1996). Support for this interpretation stems from simultaneous field measurements of sediment strain rates, pore-water pressures and shear stresses beneath the terminus of Breidamer. kurjokull, Iceland (Boulton and Jones, 1979; Boulton and Hindmarsh, 1987). The displacement of markers inserted into subglacial sediment indicated that up to 90% of the forward motion of the glacier can be accounted for by sediment deformation. Furthermore, the shear strain was observed to be distributed across a roughly 50–60 cm thick layer of the basal sediment and was taken as evidence for viscous behaviour. From these field data, empirical constitutive relations for sediment deformation were constructed (Boulton and Hindmarsh, 1987). The essential features of these flow laws are that sediment behaves as a linear-viscous or Bingham-type fluid and that shear-strain rate is proportional to the

Physical conditions beneath glaciers and ice sheets that lie on unlithified material can be complex. Sediment is inhomogeneous and rheological descriptions are challenging; influential parameters such as pore-water pressure, porosity and permeability can vary both spatially and temporally. Basal motion of an ice mass over such a sedimentary bed can arise from sliding between ice and bed, ploughing of clasts through the upper layer of the bed, pervasive deformation of the bed or shearing across discrete planes in the bed (Alley, 1989). However, whether a glacier deforms its bed, ploughs it or slides over it depends on the degree of coupling at the ice–bed interface. If the sedimentary bed is frozen to the overlying ice, sliding motion is inhibited and ice is strongly coupled to the bed. Strong coupling can also result from ice infiltrating unfrozen sediment; this process is promoted by low pore-water pressure within the sediment (Shoemaker, 1986; Iverson, 1993; Iverson and Semmens, 1995). Alternatively, complete decoupling of ice and sediment can result from increased ice–bed separation due to the presence of a water layer at the interface; now sliding can contribute to glacier motion (Shoemaker, 1986; Iverson et al., 1995; Alley, 1996). If the bed is incompletely coupled to the overlying ice, clasts that protrude across the ice–bed interface are potentially dragged through the upper layer of the sediment; this ploughing process requires that an increase in pore-water pressure causes the bed to weaken such that the local shear stress developed in front of these clasts is sufficient to deform the sediment locally (Brown et al., 1987). Further increases in pore-water pressure may cause the sediment yield strength to drop below the shear stress that can be supported by the ice–bed interface and may lead to pervasive deformation of the sedimentary bed (Alley, 1989). Important issues are linked to the strength of coupling between a glacier and its bed. What are the processes that control the coupling at the base of a glacier? Does a glacier overriding a soft bed primarily move by basal sliding or sediment deformation? What rheological models are appropriate to describe deforming subglacial

1.2. Previous investigations

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applied shear stress and inversely proportional to the effective pressure. In contrast, sediment deformation tests in the laboratory using a ring-shear device (Iverson et al., 1997) indicated that the rheology of subglacial sediment departs significantly from linear-viscous or Binghamtype models. In addition, direct-shear tests on sediment collected from beneath Ice Stream B (Engelhardt et al., 1990a) pointed to a strong rheological non-linearity (Kamb, 1991) implying that the sediment behaves as an essentially plastic material. This finding is consistent with classical soil mechanics (e.g. Lambe and Whitman, 1979). The additional finding that the rate of shearing did not affect the shear strength (Kamb, 1991; Iverson et al., 1998) is in agreement with field measurements at Storglaci.aren, Sweden. The force on instrumented objects (Fischer and Clarke, 1994; Iverson et al., 1994) as they were pulled through subglacial sediment did not vary systematically with the rate at which they were inferred to be dragged through the sediment (Hooke et al., 1997). However, the force varied directly with the effective pressure, which is consistent with the sediment being a Coulomb, or frictional material. These results suggest a Coulomb-plastic idealization as an appropriate description of deforming sediment. The apparent contradiction of a Coulomb-plastic rheology and distributed shear strain that has sometimes been recorded in sediment beneath glaciers can be reconciled with two recently proposed mechanisms (Iverson et al., 1998; Tulaczyk, 1999). A process known as dilatant hardening may distribute strain in glacier beds (Iverson et al., 1998) that are subject to cyclic deformation in response to fluctuations in water pressure (Blake et al., 1992; Iverson et al., 1995; Fischer and Clarke, 1997a; Hooke et al., 1997). During a deformation event, shear strain tends to focus in thin bands within the sediment. These discrete shear zones dilate and cause a reduction in pore-water pressure that strengthens these zones relative to the surrounding sediment. Consequently, the position of the shear zones will shift elsewhere, a process that when integrated over time, may yield the observed distributed strain (Iverson et al., 1998). Alternatively, ice-entrained clasts that plough through deformable till may exert the required control over subglacial strain distribution (Tulaczyk, 1999). Clast ploughing requires flow of sediment material from the stoss to the lee side of the clast. Model calculations based on the theory of perfect plasticity showed that this flow distributes the deformation associated with the passing clast downward into the sediment and, thus, may produce a distributed displacement field which resembles that observed beneath glaciers (Tulaczyk, 1999). Furthermore, this clast ploughing model (Tulaczyk and Scherer, this issue; Tulaczyk et al., 2000) provides a plausible explanation for the significant

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fluctuations of basal sliding velocity that have been recorded beneath Ice Stream B (Engelhardt and Kamb, 1998). To address the question of what processes control the coupling at the ice–bed interface and the resultant partitioning between basal sliding and subglacial sediment deformation, simultaneous measurements of the individual contributing processes are necessary. To this end, measurements of bed deformation, bed shear strength, subglacial water pressure and surface speed at Storglaci.aren (Iverson et al., 1995; Hooke et al., 1997) showed that the shear-strain rates of the bed decreased during periods of high water pressure and increased surface flow rate. Elevated water pressures were therefore inferred to weaken the coupling of ice with the bed, allowing the glacier to move over the bed faster while deforming it less rapidly. This inference is further substantiated by continuous measurements of basal sliding and subglacial water pressure at Trapridge Glacier (Blake et al., 1994; Fischer and Clarke, 1997a) which indicated that there is substantial motion at the glacier sole during periods of rising water pressure. Similarly, recent investigations at the bed of Ice Stream B, where water pressure is continuously high (Engelhardt and Kamb, 1997), suggested that 83% of the basal motion was focused within 30 mm of the base of the ice stream (Engelhardt and Kamb, 1998). In contrast, measurements of basal sliding and bed strain rate above and below the surge front of Bakaninbreen, Svalbard (Porter, 1997; Porter et al., 1997) showed that active surging of this glacier is principally accomplished by deformation of basal sediments.

2. Study area Trapridge Glacier (Fig. 1a) is a surge-type glacier located in the St. Elias Mountains, Yukon Territory, Canada, that has been subjected to extensive scientific study since 1969 (e.g. Jarvis and Clarke, 1975; Clarke et al., 1984; Clarke and Blake, 1991; Blake, 1992; Stone, 1993; Fischer, 1995). The glacier last surged at some time between 1941 and 1949, and is currently believed to be in the late stages of its quiescent phase. Trapridge Glacier is small (length approx 4 km, width approx 1 km) and relatively thin (depth approx 70 m) (Clarke and Blake, 1991). Over much of its ablation area, the surface and basal slopes are both B71 in the direction of glacier flow. Over the past decade, the mean annual flow rate of the lower part of the glacier has varied somewhat from year to year, ranging from 80 to 100 mm/d. The thermal regime of Trapridge Glacier is sub-polar (Clarke et al., 1984; Clarke and Blake, 1991); the temperature in the upper layers is subfreezing whereas the base is at the melting point. The warm-based zone is bounded downslope by a margin of cold-based ice.

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Fig. 1. Study area. Tick marks indicate relative Easting and Northing coordinates in metres. (a) Location of Trapridge Glacier. Arrow indicates region shown in (b) where subglacial sensors were deployed during the 1992 summer field season. (Inset) Study area in southwestern Yukon, Canada. (b) Location map showing the 1992 boreholes instrumented with pressure sensors (C1,C2,A,U), ploughmeters (PL1,PL2) and sliding sensor (SL). Arrow indicates ice flow direction.

The glacier rests on a deformable and permeable sediment substrate (Blake et al., 1992; Stone and Clarke, 1993; Waddington and Clarke, 1995). The substrate is believed to be up to B10 m thick in places (Stone, 1993) of which the top 0.3 m have been shown to be deforming (Blake, 1992). The subglacial drainage of Trapridge

Glacier can be characterized as a diffusive Darcian system where water is assumed to follow preferential sub-horizontal flow paths through a porous softsediment environment rather than a network of conduits (Stone, 1993). Currently, most of our subglacial investigations, in particular those presented here, are

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conducted in the ablation area, approximately 600 m upglacier from the terminus (Fig. 1a).

3. Subglacial instrumentation On Trapridge Glacier, our approach to studying the processes that control the coupling of ice to the underlying sediment, has been to perform extensive subglacial measurements using a variety of instruments that were designed and constructed especially for this task. Earlier studies were confined to easily accessible parts of glaciers where the overlying ice is comparatively thin, such as natural subglacial cavities and tunnels excavated in the marginal regions. To remove these limitations our instruments were devised bearing in mind sizes and shapes that permit their in situ installation in the subglacial environment via narrow boreholes. The measurements we made included subglacial water pressure, basal sliding and bed deformation, and the assessment of sediment mechanical properties. For these measurements, holes were drilled through the glacier with the use of a hot-water drill and instruments were emplaced near or in the bed at the bottom of the holes. Data were recorded on Campbell Scientific CR-10 data loggers with a sampling interval of 5 min until 1989 and 2 min in subsequent years. 3.1. Water pressure Local subglacial water pressure was measured with the use of pressure transducers suspended in boreholes B0.25–0.5 m above the bed. We distinguish between two types of boreholes depending on whether the water level dropped or remained unchanged as soon as the drill reached the bed. We describe the first type of hole as ‘‘connected’’ to the subglacial drainage system and, assuming that the hole volume is small in comparison to that of accessible subglacial water, treat borehole water level as a manometric measure of water pressure at the bed. In contrast, the second type of hole, termed ‘‘unconnected’’, can in general not be used as a manometer, because the hole volume is large compared to that of accessible subglacial water. However, because of the subfreezing temperatures of near-surface ice at Trapridge Glacier, boreholes freeze closed at the top and we can measure water pressure in unconnected boreholes without relying on the manometric principle. The distinction between connected and unconnected boreholes further implies a distinction between connected and unconnected regions of the bed. The components of the subglacial water system that occupy these regions are referred to as the connected and unconnected systems, respectively.

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3.2. Bed deformation Bed deformation was measured with the use of tiltmeters inserted into the subglacial sediment. To obtain measurements at several levels within the bed, three dual-axis tilt cells, each 47 mm long and 16 mm in diameter, were assembled into a string at a centre-tocentre spacing of 75 mm (Fig. 2a; Blake et al., 1992). Within each cell two leaf-spring pendula measure the tilt angle along perpendicular axes, thus allowing determination of tilt from vertical and azimuth of this tilt with respect to the internal coordinates of the cell. Under the assumption that the principal direction of tilt is downglacier, we can further decompose the net tilt and azimuth values into down-flow and cross-flow components of tilt (Fig. 2b). Calculation of the bed strain rates (averaged over the length of the cell) can then be accomplished by numerical differentiation of the tilt time series. This method essentially treats the tilt cell as a clast experiencing rigid-body rotation as a result of being placed in a straining medium. 3.3. Basal sliding Basal sliding was measured with a sliding sensor that we refer to as drag spool (Blake et al., 1994; Fischer and Clarke, 1997a). This sensor enabled the first direct, continuous and long-term observations of basal sliding over a soft substrate. The device consists of an anchor and a multi-turn potentiometer connected to a spooled string (Fig. 3a). In response to glacier sliding, the drag spool, which is suspended within the borehole, continuously measures the length of string paid out to the anchor inserted in the basal sediment and is essentially interpreted in terms of the displacement of the glacier ice with respect to the underlying bed (Fig. 3b). Subsequent calculation of the displacement rate by differentiation of the displacement record provides an estimate of the basal sliding velocity. 3.4. Sediment properties Mechanical properties of sediments were assessed in situ at the base of the glacier with a ploughmeter (Fischer and Clarke, 1994, 1997b). The device is a 1.5 m long steel rod which is driven B0.1–0.2 m into the sediment bed and is then dragged through the sediment as the glacier slides forward (Fig. 4a). Elastic bending of the rod in two mutually orthogonal directions is recorded by strain gauges bonded onto the immersed tip and, with the use of a laboratory calibration, is converted into a force on the rod and azimuth of this force with respect to the internal coordinates of the device (Fig. 4b). Azimuth variations are interpreted in terms of temporal changes in the direction of glacier flow or translational motion in a direction perpendicular

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Fig. 3. Drag spool. (a) Schematic diagram of drag-spool operation. As the glacier slides forward, the length of string paid out to an anchor in the bed is continuously measured. (b) Sample record showing the displacement of the borehole with respect to the anchor in the bed as a function of time. After: Blake et al., 1994; Fischer and Clarke, 1997. Fig. 2. Tiltmeter. (a) Schematic diagram of a string of tilt cells emplaced within subglacial sediments. As the sediment deforms, the cells are tilted. (b) Sample record showing down-flow tilt (solid curve) and cross-flow tilt (dashed curve) as a function of time for one tilt cell. After: Blake, 1992; Blake et al., 1992.

to the glacier flow rather than the rotation of the ploughmeter within the borehole about its long axis. Interpretation of the force record depends on the ploughmeter geometry and the rheological model of

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Fig. 5. Schematic diagram of the percussion hammer used to insert sensors into basal sediments. The hammer can be fitted with either an insertion sheath (for tiltmeter) or a dowel attachment (for drag spool and ploughmeter). After: Blake et al., 1992.

3.5. Sensor insertion

Fig. 4. Ploughmeter. (a) Schematic diagram of a ploughmeter installed at the bottom of a borehole. As the glacier slides forward, the immersed tip is dragged through basal sediments. (b) Sample record showing the force applied to the tip (solid curve) and azimuth of this force with respect to the internal coordinate system of the ploughmeter (dashed curve) as a function of time. After: Fischer and Clarke, 1994.

sediment behaviour. In the case of a Coulomb-plastic material, the force scales with the yield strength of the sediment, whereas for a viscous fluid the force is proportional to the velocity of motion through the sediment and to the sediment viscosity.

With the exception of pressure transducers, a percussion hammer was required to insert sensors into basal sediments. The hammer (Blake et al., 1992) consists of a 2 m long tubular stainless-steel body (Fig. 5). Dependent on the type of sensor to be inserted, an insertion sheath (tiltmeter) or dowel attachment (drag spool and ploughmeter) can be screwed onto the thread at the lower end of the body. A tubular steel striker that slides over the body can be raised by a single steel wire operated from the glacier surface, and then dropped onto an anvil. When the striker hits the anvil, a percussive force results that is used to drive the sensor into the sediments. Depth of insertion is measured by observing the vertical displacement of the instrument cable with respect to the ice surface. However, the final position of the sensor with respect to the ice–bed interface remains uncertain because hydraulic excavation by the hot-water drill is believed to loosen subglacial material to a depth of several decimetres through which the hammer likely penetrates by its own weight prior to the hammering procedure (Blake et al., 1992). On completion of insertion, the steel wire is used to retrieve the hammer from the bed by pulling on it until the striker reaches the upper stop. At this point continuing to pull on the wire lifts the hammer up the borehole leaving the sensor emplaced in the bed.

4. Field measurements One of the original aspirations of our study at Trapridge Glacier was simultaneously to measure basal

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sliding, bed deformation, mechanical properties of the basal sediment and subglacial water pressure. For several field seasons we battled the difficulties associated with installing and operating arrays of drag spools, tiltmeters, ploughmeters and pressure transducers. Recording data using these four types of instruments at the same location and over the same time period is an important requirement for a comprehensive analysis. Due to the short life span and proneness to failure of some of our devices, in particular the tiltmeters, we never succeeded in making simultaneous measurements involving all four types of instruments for any significant length of time. We were nevertheless able to identify fundamental aspects of the coupling process at the ice–bed interface. In the following we highlight these aspects by focussing on combined measurements of hydrological and mechanical conditions and processes from 1992. First, however, we briefly describe the most important results from individual measurements of basal sliding, mechanical sediment properties and bed deformation which provided key insights to the ice–bed coupling question. At this point, we also note that all data presented and discussed in this paper were collected during the summer months. Therefore, results of this work are actually based on melt-season conditions and processes. 4.1. Basal sliding measurements Results from our sliding measurements at the bed of Trapridge Glacier using drag spools indicated displacement rates that ranged between B40 and B80 mm/d (Blake et al., 1994; Fischer, 1995). We dismissed the possibility that different depths to which anchors of different instruments were inserted, could account for differences in measured displacement rates because we could not discern a clear relationship between insertion depth and displacement rate from the available data (Fischer, 1995). Instead we accepted the alternative explanation that different displacement rates measured at different points across the glacier bed within a given year reflect a spatial variability in basal sliding. With uniform surface motion observed over large parts of the glacier, these results implied a spatially varying partitioning between sliding and subglacial sediment deformation. Similarly, changes in displacement rate that we observed from year to year probably resulted from temporal variations in this partitioning (Blake et al., 1994). We can attempt to quantify, in a very general sense, the partitioning between sliding and subglacial sediment deformation by recalling that the surface motion of Trapridge Glacier at our study site was around 100 mm/d. Observations of lateral deformation of boreholes revealed that the velocity contribution from internal ice creep for this glacier did not exceed

10 mm/d (Blake, 1992). Therefore, almost the entire surface motion of the glacier was attributable to sliding and deformation processes at the bed. However, we recognize that the measurements taken with a drag spool yielded only an upper limit on glacier sliding because the anchor was placed within deformable sediment and we estimate that about 5–10% of the motion between the anchor and the ice was caused by deformation of the intervening sediment (Fischer, 1995). Thus, basal sliding can account for 45–65% of the total flow observed at the glacier surface (Blake et al., 1994). 4.2. Measurements of sediment properties Measurements with two ploughmeters installed beneath Trapridge Glacier along a single flowline approximately 10 m apart yielded data with contrasting character suggesting that the texture of subglacial sediment across the bed of the glacier was not uniform; one of the instruments appeared to have been immersed in a region that predominantly consisted of fine-grained material, whereas the other seemed to interact with a clast-rich sediment (Fischer and Clarke, 1994). These measurements represent the first long-term observations of mechanical processes at the ice–bed interface. We interpreted these contrasting ploughmeter observations either in terms of a translational motion through a homogeneous, unlithified sediment layer or as collisions with clasts. The first interpretation allows the estimation of rheological parameters of Trapridge sediment, although some prior assumption of the rheological model of sediment behaviour is required. If subglacial sediment is assumed to behave as a linear viscous fluid then, based on a quantitative analysis of the force distribution along the section of ploughmeter that was immersed in the bed, we calculate an effective viscosity for the sediment between 3.0
109 and 3.1
1010 Pa s. Alternatively, if the sediment is assumed to behave as an ideal solid plastic, the estimated yield strength is 48–57 kPa (Fischer and Clarke, 1994). Although our simple model rheologies neglected the influence of pore-water pressure or the deformation history and heterogeneity of subglacial materials, they nevertheless offer some indication of the ability of the bed to resist deformation. Assuming a plane-slab geometry, the applied basal driving stress beneath our study site is B77 kPa. Thus, for both the viscous and plastic rheologies, the estimates of sediment strength yielded by the ploughmeter analysis suggest that the deformational resistance of the bed is comparable to, but somewhat less than, that required to ensure mechanical stability in this region of Trapridge Glacier (Fischer and Clarke, 1994). For a heterogeneous or clast-rich sediment, a purely linear viscous assumption was inappropriate and the rate of collision between clasts and a ploughmeter

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dragged through such a sediment should be related to the glacier sliding rate. By assuming that proglacial measurements of sediment granulometry represented the subglacial granulometry of Trapridge Glacier, we were able to use the collision frequency as indicated by a ploughmeter to obtain an estimated basal sliding velocity of B45 mm/d (Fischer and Clarke, 1997b), in good agreement with drag spool measurements described above. 4.3. Bed deformation measurements Fig. 6a shows the down-flow and cross-flow strainrate data for a string of leaf-spring tilt cells that was inserted into the bed of Trapridge Glacier (Blake, 1992; Blake et al., 1992). These data represent the first continuous observations of subglacial sediment deformation in a realistic setting under a representative thickness of ice. The records of subglacial water pressure measured in the same borehole, and in another that was located about 40 m upglacier, are also included (Fig. 6b) and plotted along the same time axis. The data reveal several interesting characteristics. (1) The records for the three tilt cells are similar, which indicates that the three cells were moving essentially in unison and suggests uniform deformation over the 20 cm length of the sensor string. (2) Strain rates varied strongly in amplitude and

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rapidly in polarity. However, for each of the three cells, the average strain rate over the course of the measurement was on the order 10 a1, indicating net strain within the deforming layer. (3) There is a diurnal signal evident throughout the record, which is strongest in the last three days. In general, positive strain rates in the morning were followed by negative strain rates in the afternoon. (4) The pressure records and the strain rate curves are weakly correlated, sharing some diurnal cycling towards the end of the measurement period (Blake, 1992; Blake et al., 1992). These continuous measurements demonstrate that on a local spatial scale and over short time intervals, bed deformation is a more complex process than previous work had suggested. There is a time-varying nature of subglacial deformation which was not captured in measurements of net strain such as those made by Boulton and Hindmarsh (1987). Although not sustained over long periods of time, strong negative strain rates are a striking characteristic of Fig. 6a. A negative strain rate results from upglacier rotation of a tilt cell, irrespective of its net motion. Blake (1992) proposed an interpretation for these negative strain rates based on the idea of extrusion flow. In response to vertical movement of the ice–bed interface, the subglacial sediment moves laterally and is squeezed into zones where basal ice is uplifted. The resultant local thickening of the sediment layer causes tilt cells tilted downglacier to rotate upglacier. We explore this and another mechanisms in more detail in a later section below. 4.4. Combined hydrological and mechanical measurements In July 1992, we instrumented densely a 20 m
20 m region of the bed (Fig. 1a) with water pressure transducers, sliding sensors and ploughmeters (Fig. 1b). The results from these measurements are presented in Figs. 7–9. Pressure sensors C1 and C2 were installed in boreholes that connected to the subglacial water system. Both sensors tracked each other very closely and registered a strong diurnal cycle (Fig. 7) with maximum

Fig. 6. Records showing (a) down-flow strain rate (solid curves) and cross-flow strain rate (dashed curves) for three tilt cells assembled in a string and (b) subglacial water pressure in the same (solid curve) and a nearby (dashed curve) borehole. After: Blake, 1992.

Fig. 7. Measured subglacial water-pressure records at connected (C1, solid curve; C2, dashed curve), unconnected (U, long-dashed curve) and alternating (A, dotted curve) sites. After: Murray and Clarke, 1995.

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Fig. 8. Records showing (a) force and (b) azimuth as measured with two ploughmeters at sites PL1 (solid curves) and PL2 (dashed curves). After: Fischer et al., 1999.

Fig. 9. Records showing (a) displacement and (b) displacement rate (obtained by numerical differentiation of the time series shown in (a)) as measured with a drag spool at site SL. After: Fischer and Clarke, 1997.

water pressure typically occurring in the late afternoon in response to increased input of surface-derived meltwater. In contrast, pressure sensor U was situated in a region that was not hydraulically connected to C1 and C2, and showed water-pressure variations of opposite polarity (Fig. 7). Pressure sensor A recorded semidiurnal pressure fluctuations (Fig. 7) and seems to represent an intermediate case as it alternated between the response of C1 and C2 in the connected system and the response of U in the unconnected system. Murray and Clarke (1995) argued that this behaviour can be explained by thinking of the water pressure in the connected system as a forcing function to which the water pressure in the unconnected system responds. This explanation follows from considering the force balance between a glacier and its bed and involves the transfer of mechanical support of the ice overburden from one point to another. As the water pressure in the connected system increases, the overlying ice is hydraulically

uplifted in this region and relieves the pressure in the adjacent unconnected region; hence a drop in water pressure in the unconnected system is to be expected. Furthermore, the area of the connected region expands at high pressure and regions of the bed that are isolated during periods of low water pressure become hydraulically connected, thereby accounting for regions of the bed that switch back and forth between the connected and unconnected states (Murray and Clarke, 1995). Both ploughmeters, PL1 and PL2, registered strong diurnal variations (Fig. 8) which are correlated with large and rapid fluctuations in subglacial water pressure (Fig. 7). If we follow the interpretation of Murray and Clarke (1995), that water pressure variations in the connected system can be viewed as a forcing function, then there is a conspicuous difference in how the two ploughmeters responded to this forcing. In the case of PL2, variations in subglacial water pressure (C1 in Fig. 7) are in-phase with variations in the force response (Fig. 8a): high and low water pressures corresponded to high and low forces, respectively. In fact, the similarity of the two records is striking, as they share even fine details. In contrast, peak water pressures appear to coincide with low forces experienced by PL1 and vice versa (C1 in Figs. 7 and 8a). Thus, the force magnitude recorded with PL1 is anti-correlated with that of PL2 (Fig. 8a). At the same time, however, the azimuth records (Fig. 8b) indicate ploughmeter responses that are correlated with each other: for both ploughmeters the force angle appeared to be rotating in the same sense back and forth. The displacement record from the sliding sensor (Fig. 9a) also shows variations that are correlated with the strong diurnal pressure fluctuations in the connected water system (C1 in Fig. 7). Superimposed onto a general trend, distinct step-like increases in displacement can be discerned that coincide with rises in water pressure. The computed sliding velocity (rate of displacement; Fig. 9b) further emphasizes that peak displacement rates occur during periods of rising water pressure in the connected system and not when the water pressure has reached its maximum. The correlations between diurnal signals recorded with ploughmeters and drag spools and fluctuations in subglacial water pressure suggest that mechanical conditions at the bed varied temporally in response to changes in the basal hydrological system. However, the anti-correlated force responses in conjunction with correlated azimuth responses of the two ploughmeters, as well as the 901 phase shift between water pressure and sliding rate, also indicate that the role of the subglacial water system appears to be complex and not always intuitive. In the following section we use a theoretical framework to analyze the sliding motion of glacier ice over a surface having a temporally and spatially variable basal

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drag and show that a consistent explanation for our 1992 field measurements can be developed.

5. Conceptual models of ice–bed coupling dynamics The mathematical details of the models have been described by Fischer and Clarke (1997a) and Fischer et al. (1999), so here we confine our discussion to their conceptual framework. The measurements of water pressure beneath Trapridge Glacier (Fig. 7) revealed pronounced spatial and temporal variations in conditions of the subglacial water system (Murray and Clarke, 1995). Since glacier flow mechanics are strongly linked to variations in ice–bed coupling due to changes in subglacial water pressure, it is no surprise that the measurements of sliding and ploughmeter response also display a spatial and temporal heterogeneity. Our theoretical models are built around the interpretation that a lubricating water film is associated with high subglacial water pressure, which effectively decouples the glacier from its bed and promotes sliding. In contrast, low pressures cause increased bottom drag. This idea follows from theory and observation that in a distributed subglacial drainage system, ice–bed separation by water increases with water pressure and that glacier sliding velocity increases with ice–bed separation (Alley, 1996; and references therein). We numerically implemented this description of water-pressure effects on bed coupling by the linear glacier sliding law

Fig. 10. Results for model ST-SP showing computed (a) force and (b) azimuth records of two numerical ploughmeters positioned in a flow field of a linear viscous medium flowing over a surface with a basal drag that varies in response to the water-pressure fluctuations C1 shown in Fig. 7. After: Fischer et al., 1999.

where Tb denotes the basal shear traction vector. Here we assume that the glacier bed is an inclined ‘‘flat’’ surface with a variable drag coefficient e over which the ice moves with variable basal sliding velocity *b : The variability in the resistance to sliding is caused by spatial and temporal changes in basal drag. The origin of increased drag is the absence of a lubricating water film at the ice–bed interface during periods of low basal water pressures. To maintain overall stress balance we impose the condition that the spatial average of the drag coefficient corresponds to a constant background drag.

patches by slowing down and diverging laterally at these points, thereby permitting the ice to move forward. Correspondingly, it speeds up and converges behind the sticky spots, in response to the reduced drag on the downstream sides. The ‘‘sticky-spot’’ model, denoted ST–SP, computes the velocity field for the ice immediately above the glacier bed as a function of bottom drag. The temporal evolution of the basal drag is controlled by the variations in subglacial water pressure in the connected region (C1 in Fig. 7) such that low water pressures correspond to a sticky spot in the centre of our model domain whereas high water pressures result in a ‘‘slippery’’ patch. The results for model ST–SP are presented in Fig. 10 which shows the computed force and azimuth responses of two ploughmeters positioned in this flow field, one within the sticky/slippery patch and the other in the surrounding region. The simulated records (Fig. 10) capture well the main characteristics of the field data shown in Fig. 8: the force records (Fig. 10a) indicate variations that are anti-correlated with each other, while the azimuth records (Fig. 10b) show an in-phase rotation of the force angle.

5.1. Model of sticky-spot response

5.2. Model of stick–slip sliding

In a first set of simulations, the flow of ice is analyzed for a configuration in which the glacier is treated as a planar, parallel-sided slab of linear viscous rheology that rests on a hard bed. Glacier sliding is controlled by spatially and temporally varying patches of increased drag at the ice–bed interface. These patches of increased drag are dynamically similar to ‘‘sticky’’ spots in that they are localized regions of the bed where the basal shear stress is concentrated (Alley, 1993). Ice responds to the increased drag on the upstream sides of sticky

The spikes in the velocity record in Fig. 9b might be an expression of short-term enhanced basal motion suggesting an elastic relaxation during the slip phase of a stick–slip sliding process, whereby accumulated elastic strain at the base of the glacier is released as the rising water pressure decouples the ice from the bed. Therefore, in a further set of simulations, we draw analogies between the stick–slip behaviour of the glacier and a slider block pulled by a spring which begins to slip once the pulling force exceeds the frictional resistance to

Tb ¼ e*b ;

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Fig. 11. Results for model ST–SL showing a computed displacement record of an elastically deforming medium with respect to an elastic substrate in response to the water-pressure fluctuations C1 shown in Fig. 7. After: Fischer and Clarke, 1997.

sliding on the surface. Here, the extension in the spring is associated with the build-up of elastic strain at the bed and the slip of the block corresponds to the momentary enhancement of sliding. Our ‘‘stick–slip’’ model, denoted ST–SL, is a modification of the simple springblock model in which the sliding motion of a purely elastic ice over an elastic substrate is analyzed. The resistance to sliding along the ice–substrate interface is allowed to vary according to fluctuations in subglacial water pressure. In response to increased basal drag, ice and substrate deform and begin to accumulate elastic strain. Upon reduction in basal drag, this stored elastic strain is relieved resulting in a momentary displacement of the ice with respect to the substrate. The model computes this displacement as a function of subglacial water pressure in the connected region (C1 in Fig. 7) such that low water pressures correspond to increased bottom drag. The result for model ST–SL (Fig. 11) shows that the calculations closely simulate the postulated stick–slip relaxation process: although the glacier continues to slide as the water pressure continues to rise, its highest velocity is during the initial release of stored elastic strain that occurs before the water pressure reaches its maximum.

6. Synthesis With the theoretical framework developed to describe the sliding motion of ice over a surface having basal resistance which is allowed to vary in space and time, we were able to shed some light onto the complex, and not always intuitive, interaction of basal processes with the subglacial hydrological system as recorded during the 1992 field season. Our model results show that the strongly anti-correlated force responses in conjunction with correlated azimuth responses of the two ploughmeters can be interpreted in terms of a sticky spot being created and destroyed. These spatial and temporal variations of a sticky spot are linked to changes in basal lubrication in response to fluctuations in

Fig. 12. Conceptual diagram showing a possible relationship of connected (C1,C2), alternating (A) and unconnected (U) holes to the subglacial drainage system at times of (a) low subglacial water pressures and (b) high subglacial water pressures in the connected region. The shading indicates the extent of the connected region. After: Murray and Clarke, 1995

subglacial water pressure. Furthermore, we have demonstrated that the 901 phase shift between water pressure and sliding rate can be interpreted to result from a stick–slip sliding process at the glacier base, whereby accumulated elastic strain in the ice and the substrate is released as the rising water pressure reduces the coupling at the bed. In this section we revisit the 1992 measurements and use the field and modelling results presented above as a basis for discussing the effects of the subglacial hydrological system on basal coupling processes. We also tie our measurements of subglacial bed deformation and results from field studies by other investigators into this discussion. In the final section below we view our field measurements, modelling results and associated interpretations in a larger context and address some implications for glacier dynamics. Now, we start with the pressure data (Fig. 7). Fig. 12 shows a possible spatial relationship between water pressure sensors and the connected water system. Rising pressures are believed to cause an increase in the areal coverage of the connected system, which appears to be affected by local uplift of ice in the vicinity of a connected water flow path. The alternation of sensor A between the response of hydraulically connected and unconnected boreholes can, hence, be attributed to the areal expansion of the connected region. At the same time, the transfer of ice overburden pressure between connected and unconnected regions of the bed can account for the anti-phase relationships observed for sensors C1 and C2 and sensor U (Murray and Clarke, 1995). Since ice–bed coupling is strongly influenced by subglacial water pressure, a spatial and temporal heterogeneity in basal motion is to be expected. This

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Fig. 13. Conceptual model of the dynamic response of the glacier to the hydrological forcing shown in Fig. 12. The locations of ploughmeters (PL1,PL2) and sliding sensor (SL) are indicated. The different levels in shading represent differences in resistance to basal sliding as a result of varying degrees of ice–bed coupling. The direction and magnitude of ice flow at the bed are depicted by arrows and are exaggerated to emphasize the difference in basal flow field at times of (a) low subglacial water pressures and (b) high subglacial water pressures in the connected region.

idea is conceptualized in Fig. 13. The area which is occupied by sensor A is hydraulically isolated at low water pressures (Fig. 12a) and acts effectively as a localized sticky spot because the ice preferentially moves over surrounding regions that are lubricated by water associated with the connected water flow paths (Fig. 13a). As the water pressure rises and the areal coverage of the connected water system increases (Fig. 12b), resistance to sliding decreases and the area around sensor A essentially turns into a slippery patch over which the ice is routed efficiently (Fig. 13b). In order to maintain overall stress balance at the bed, the basal shear stress that cannot be supported in this area must be taken up in the adjacent unconnected region, i.e. reduced ice–bed coupling in the slippery patch is compensated by increased ice–bed coupling in the surrounding sticky region (Fig. 13b). The changes in the direction and magnitude of ice flow at the base of the glacier that result from this redistribution of shear stresses in response to fluctuations in subglacial water pressure, thus, lead to the anti-correlated responses of the two ploughmeters PL1 and PL2 (Fig. 8). As with the case of pressure transducer A, the sliding sensor SL appears also to be located in a region of the bed that switches back and forth between the connected and unconnected systems. Associated with the areal expansion of the connected region, the decoupling of the ice from the bed (Fig. 13) leads to an elastic relaxation of ice and substrate which manifests itself as enhanced slip events during periods of rising subglacial water pressure (Fig. 9). The transfer of ice overburden pressure between connected and unconnected regions of the bed provides an explanation for the strain rate fluctuations observed with our tiltmeters (Fig. 6a) which relates to the

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aforementioned extrusion flow idea (Blake, 1992). In response to pressure variations in the connected water system, lateral transfer of the normal loading on the bed leads to an alternation of uplift and lowering of basal ice which causes the underlying subglacial sediment to be expanded or compressed. Depending on whether the sediment layer is thickening or thinning, tilt cells respond by rotating upglacier or downglacier, respectively. However, because the pressure fluctuations recorded in the vicinity of the bed deformation measurements were small (Fig. 6b), we are surprised to see such large changes in strain rate (Fig. 6a) and we suspect that the correlation is not direct and that there is some other mechanism at work. Furthermore, as pointed out by Iverson et al. (1999), the difficulty with the interpretation of a lateral transfer of ice overburden pressure is that, while some parts of the sediment bed are thinning during a given period others should thicken, suggesting that while some tiltmeters rotate downglacier others should rotate upglacier during these periods. However, bed deformation measurements conducted at different locations in three consecutive years beneath Storglaci a. ren (Iverson et al., 1995; Hooke et al., 1997) consistently only showed upglacier rotation of tiltmeters during periods of rising subglacial water pressure. A more appealing explanation for the strongly fluctuating strain rates (Fig. 6a) is based on the lateral transfer of basal shear stress and relates to the sticky/ slippery model of the bed, described above in connection with the sliding measurements (cf. Fig. 13). In this alternative explanation, positive strain rates recorded with tiltmeters are interpreted as downglacier deformation of subglacial sediments due to high shear loading on the bed during periods of low water pressures and strong ice–bed coupling (Fig. 13a). In contrast, as water pressure rises, the ice reduces its coupling with the bed (Fig. 13b), causing the sediment to relax elastically. During such periods of elastic relaxation, the sense of shearing in the sediment reverses and tiltmeters rotate upglacier. Thus, calculated rates of shear strain are negative.

7. Concluding discussion The picture that seems to emerge from the above discussion is one of extreme heterogeneity of conditions and processes at the base of a glacier. Measurements of water pressure beneath Trapridge Glacier show that at any given time, basal water pressure is not uniform over the glacier bed (Stone and Clarke, 1996). In fact, the subglacial water system displays dramatic variability across distances of even few metres. Furthermore, temporal variations in subglacial water pressure are significant over time scales of hours (Murray and Clarke, 1995). Due to the close linkage between changes in water pressure and variations in the way the ice is

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coupled to the bed, the stress field at the ice–bed interface is also markedly heterogeneous, which introduces a pronounced variability to the basal motion mechanics. As such, the flow field of ice immediately above the bed is not uniform, sliding at the base of the glacier is not temporally smooth, nor is deformation of subglacial sediments a steady and continuous process. Instead, at places or times of low subglacial water pressure and increased ice–bed coupling, there is high resistance to sliding leading to a downglacier shear deformation of the bed and accumulation of elastic strain in the ice and sediments. In contrast, during rising water pressure and ice–bed decoupling at other places or times, the glacier slips forward while the bed relaxes elastically in shear upglacier. We realize that we have demonstrated consistency for hydro-mechanical interactions beneath Trapridge Glacier only on a scale of B10 m for a single example. However, it is conceivable that high-drag, slow sliding sites exist all across the bed of our main study region. Sticky patches appear to be created and destroyed in response to fluctuations in subglacial water pressure, leading to time-varying lateral transfer of shear stress beneath the glacier. By associating high water pressures with slippery patches and low water pressures with sticky patches, we expect the stresses at the bed to form a patchwork distribution which is similar to the pressure distribution in the subglacial water system.

Acknowledgements We gratefully credit Erik W. Blake, Dan B. Stone, Tavi Murray, Brian S. Waddington and Shawn J. Marshall for their enormous contributions to this work. Special thanks go to K. Dieter Schreiber for his technical assistance in the construction of the subglacial instruments. Comments made by Bryn Hubbard and an anonymous reviewer led to considerable improvements of this manuscript. This research was funded by the Natural Sciences and Engineering Research Council of Canada, the University of British Columbia and the Canadian Northern Studies Trust of the Association of Canadian Universities for Northern Studies. Parks Canada and the Yukon Territorial Government kindly permitted our field studies in Kluane National Park, and the Kluane Lake Research Station, owned and operated by the Arctic Institute of North America, provided logistical support for our field programme.

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