Study site

Gornergletscher is the second largest valley glacier system in the Swiss Alps, with a surface area of 68 km² (Raymond and others, 2003). The upper part of the 12 km long main stream is named Grenzgletscher; it merges with Gornergletscher ~5 km from the common terminus of the glacier system (Fig. 1a). Many investigations have been conducted at Gornergletscher with regard to glacier hydrology and ice dynamics (e.g. subglacial water-pressure measurements (Röthlisberger and others, 1979), hydrological study of glacier run-off (Collins, 1989) and combined measurements of subglacial hydrology and glacier dynamics (Iken and others, 1996)).

Fig. 1. (a) Map of Gornergletscher and Grenzgletscher with surface contour lines at intervals of 100 m. The study area is indicated by the box. (b) Location of the GPS and theodolite survey stakes with annual flow vectors obtained for the period October 2003 to September 2004. The borehole drilling site is labeled BH430.

At the eastern margin of the confluence area of Gornergletscher and Grenzgletscher, a glacier-dammed lake named Gornersee forms in the spring; it collects snowmelt and drains every summer (Figs 1 and 2). The historical records of its formation and outburst date back to the 18th century (Huss and others, 2007). The lake water flows through the glacier for 5 km before it drains into the outlet river Gornera. The maximum ice thickness between the lake and the glacier snout is about 450 m according to an ice-penetrating radar survey carried out in 2004 (Huss, 2005). The volume of water stored in the lake before the outburst shows an annual variation. In 2004, the maximum water volume was estimated to be 4.0 ×10⁶ m³ from the water level and the hypsometry of the lake floor, obtained by processing an aerial photograph taken after the lake was emptied (Huss and others, 2007).

Fig. 2. The confluence area of Gornergletscher and Grenzgletscher, and Gornersee in the center of the photograph. The photograph was taken on 1 July 2004 from Gornergrat, the northern flank of Gornergletscher.

Ice-flow measurements

In order to measure the ice motion, aluminum stakes were installed in the glacier surface in October 2003, using either GPS or an automatically operated theodolite. The length of the stakes above the surface was maintained at less than 2 m to reduce the influence of wind on the survey accuracy. In addition to the high-frequency measurements described below, the stakes were surveyed with GPS in October 2003 and September 2004 to determine the annual flow speeds. The locations of the stakes and annual flow vectors are indicated in Figure 1b.

The three-dimensional positions of four of the stakes (GPS14, GPS24, GPS37 and GPS42) were surveyed by GPS receivers (Leica System 500) mounted on the top of the stakes (see Fig. 4 for the locations). From 18 June to 12 July 2004, the L1 and L2 phase signals from the GPS satellites were recorded eight times a day for 1 hour at regular 3 hour intervals. The GPS data were post-processed using Leica SKI-Pro software with reference data recorded by a receiver fixed on the bedrock at the glacier flank (Fig. 1b). The accuracy of the survey depends on the horizontal distance and the elevation difference from the reference station, satellite configuration and wind conditions. Control experiments and past measurements on glaciers provide an estimate of the positioning errors, 3 and 5 mm in the horizontal and vertical directions, respectively (Sugiyama and Gudmundsson, 2004).

Fig. 4. Horizontal flow speed vectors before the lake outburst from 25 June to 1 July (gray bold) and during the first half of the outburst from 2 to 4 July (black thin).

Theodolite reflectors were mounted on the remaining stakes to survey the positions from the glacier flank. The theodolite installed on the bedrock (Fig. 1b) was automatically operated every hour from May to September 2004, unless operation was interrupted by weather conditions or equipment failure. The data obtained were corrected by surveying the reference reflectors fixed on the bedrock in the marginal vicinity. The errors in the measurement vary from several millimeters to centimeters, depending on the distance from the theodolite to the stakes (Gudmundsson and others, 2000).

The surface flow speed at each stake was calculated from the horizontal displacement after filtering the surveyed coordinates by kernel regression smoothing with adaptive plug-in bandwidth (Seifert and others, 1994). The open-source Fortran routine employed for this uses a filtering bandwidth determined to correspond to the estimated survey errors. The code is available at http://www.unizh.ch/biostat/Software/kernf77.html.

Hydrological measurements

Measurement of lake level began in May 2004. A water-pressure transducer (Keller, PAA-36W) with an accuracy of ±60 Pa was installed near the deepest point in the lake to record the water depth every 10 min. The measurement was terminated when a floating ice block cut the sensor cable during the outburst on 5 July. The discharge from the lake for the period 2–5 July was computed from the change in water level and the hypsometry of the lake floor.

At about 1 km down-glacier from the lake, a borehole (BH430 in Fig. 1b) was drilled to the bed using the hot-water drilling technique. The ice thickness at the drilling site is 430 ± 20 m according to the length of the hose used for the drilling and ice-penetrating radar survey. A vibrating wire pressure transducer (Geokon Model 4500) was installed in the borehole to measure the water pressure at intervals of 10 min. The accuracy of the measurement was equivalent to a water level of ±0.35 m. Due to the uncertainty in the distance from the glacier bed to the sensor, the absolute value of the water level from the bed may have an error of up to ±10 m.

Water discharge from the glacier is measured by the Grande Dixence hydroelectric power company. The company operates a water intake system ~1 km down the valley from the glacier terminus and measures the river discharge every hour.

Formation and outburst of Gornersee in 2004

In 2004 the lake began to form in mid-May. The lake filled with water extending over a surface area of 0.27 km² by the end of June and the lake water began to flow over the ice surface on 1 July. The water level had increased steadily, showing no clear indication of water leakage until it suddenly dropped by 30 cm on 1 July (Fig. 3a). The 30 cm drop occurred within the 10 min recording interval of lake level measurements and could be observed by the formation of a strandline at the lake shore. This incident suggests the transfer of ~8 × 10⁴m³ of water into the subglacial space prior to the main drainage.

Fig. 3. Time series of (a) lake water level, (b) discharge from the glacier, (c) discharge from the lake, (d) water level in borehole BH430 and (e) horizontal flow speed and (f) vertical displacement at GPS14. The vertical displacement is relative to the elevation at the beginning of the GPS survey on 15 April. The dashed line indicates the flotation water level at the borehole site with an error bar. The vertical gray lines show the correlation of the water level, flow speed and vertical displacement.

The lake outburst began on 2 July and the water level dropped continuously until the lake emptied on 7 July. Although the water-level figure is available only until late in the evening on 5 July, the discharge from the lake indicates that nearly 70% of the stored water drained during the days from 3 to 5 July (Fig. 3c). Peak discharge from the lake occurred on 3 July, while discharge at the terminus peaked 3 days later on 6 July (Fig. 3b). In the latter half of the event, we observed that the water drained subglacially from the eastern margin of the glacier. However, after the event, we found several water channels (the diameters of which were of the order of a few meters) excavated into the ice at the lake floor (Weiss, 2005), indicating that a part of the water also drained englacially.

During the outburst, the water level in borehole BH430 was consistently high and was close to the flotation level (Fig. 3d). In contrast to the large oscillations observed before the outburst, the magnitude of the diurnal variations is small, showing a clear influence of the drained lake water on the hydrological conditions underneath the borehole site. The water level dropped by ~200m on 7 July, corresponding to the decrease in the discharge from the glacier (Fig. 3b).

Surface flow speed and uplift

The horizontal flow speed and vertical displacement measured at GPS14 are plotted in Figure 3e and f, for comparison with the hydrological data. From 2 to 4 July, during the drainage period, the flow speed shows clear diurnal variations (Fig. 3e) and the daily maxima in the evening coincide with peaks in the borehole water level (Fig. 3d). The mean speed during this period is 150% of the mean before the outburst (0.063 m d⁻¹ for the period 24 June to 1 July). After 6 July, the flow speed and its variations are similar to those before the outburst. During the same period, the glacier surface lifted up diurnally by about 0.1 m d⁻¹, resulting in a total uplift of 0.2 m over the 3 days (Fig. 3f). Hereafter, we use the term ‘uplift’ to refer simply to the upward vertical displacement by paying attention to the annual mean vertical speed, which is 2.5 mm d⁻¹ at GPS14. The daily elevation peaks lagged several hours behind the borehole water-level peaks; thus, the maximum uplift rate corresponded to the maximum water level (Fig. 3d). The diurnal vertical motion had also been observed before drainage, but the elevation change did not accumulate because the daily uplift was cancelled out by the subsequent downward motion. The surface started to lower on 6 July and reached the same level as the pre-event elevation after 2 days. Similar elevation changes were observed at most of the other survey stakes.

The horizontal flow vectors during the first half of the outburst (2 to 4 July) are compared with those before the event (25 June to 1 July) in Figure 4. The surface speed increased and the flow direction changed at most of the stakes. Near the lake, the direction of the flow vectors during the first half of the event is more to the west, as indicated by the counterclockwise vector rotation at stakes 33–36 and GPS37, and the clockwise rotation at stakes 31, 32 and 41 and GPS42. In the lower reaches, the flow vectors are more to the north, as observed at stake 22, GPS14 and GPS24. In general, the glacier flow field became more parallel to the central flow direction at the confluence area (stakes 23, 25 and 27), which is dominated by the fast inflow from Grenzgletscher (see Fig. 1b).

Exceptionally large changes in the flow speed and direction were observed at stakes 44–46 at the west shore of the lake. The ice motion accelerated towards the west at stake 44 and southwest at stake 45, whereas the flow speed became very small at stake 46. At these three stakes, the upward vertical displacement during the outburst was in range 0.5–3.0 m, one order of magnitude larger than at the other stakes (Weiss, 2005) and far different from the annual mean vertical motion at these stakes (−5.9 to −1.4 mm d⁻¹). Since the glacier surface was heavily crevassed in this region, the huge uplift was probably a local response of the marginal ice to buoyancy force. We assume that englacial fractures acted as a hinge under the direct influence of the draining water, but details of the ice motion in the vicinity of the lake will be presented elsewhere.

Reversal of ice motion

Figure 4 shows the difference in the glacier flow field before and after the onset of the outburst. Moreover, during the drainage event continuous stake measurements showed complex flow-direction changes, hereafter referred to as the ‘reversal of ice motion’. The southwest ice flow at GPS42 changed its direction to the northwest during the first half of the outburst (Fig. 5a). It then turned south on 4 July and moved south during the second half of the outburst until the stake returned to the azimuth of the pre-event ice motion. The flow direction returned to the southwest when the lake became empty. It appears that a transverse (northwest–southeast) flow component was superimposed on the preevent flow direction (southwest) over the course of the outburst, and the transverse component reversed on 4 July.

Fig. 5. Plan view of the stake motion at each survey site. The contour lines on the map indicate the surface elevation at intervals of 50 m. The vertical axes in (d) and (e) are exaggerated by a factor of two to emphasize the transverse stake motion. The dotted line in (d) connects the stake positions at 0000 h on 20 June and 12 July.

Similar ice motion was observed at GPS37 (Fig. 5b). The trajectory of the stake movement deviated west from the preevent flow direction during the outburst. The changes in the flow direction occurred not only near the lake but also at GPS24 and GPS14 at reaches several kilometers below the lake. This deviation is not as evident as those at GPS37 and GPS42 because the flow speed is relatively high in the lower reaches; however, the stake moved away from the azimuth of the motion towards the northeast at GPS24 (Fig. 5d) and towards the north at GPS14 (Fig. 5e). The change in transverse velocity and the subsequent switch back to the azimuth of the initial motion are similar to the flow variations observed at Hansbreen during a speed-up event triggered by enhanced snowmelt (Vieli and others, 2004). The most intriguing ice motion was observed at stake 43 (Fig. 5c). The ice flowed northwest until the morning of 5 July; it then started to flow backward towards the southeast for about 2 days. This observation of a glacier flowing up-glacier is very unusual. The time of the reversal in the transverse ice motion is 4 July near the lake at GPS42 and GPS37 and about 1 day later down-glacier at GPS14 and GPS24.

The timing of the flow-direction changes

To reveal the mechanism of the reversal of ice motion, the timings of flow-direction changes are analyzed by plotting the daily locations of GPS42 (Fig. 7a). A smooth trajectory was obtained from the GPS positioning data by kernel regression smoothing. We define the flow component perpendicular to the average flow vector from 20 June to 12 July as transverse ice motion. The transverse motion from 29 June to 9 July is examined by comparing it with the available lake discharge data and vertical surface motion (Fig. 7b and c).

Fig. 7. (a) Plan view of the stake motion at GPS42. The open circles on the smoothed trajectory indicate the locations of the stake at 0000 h. (b) Water discharge from the lake. The shaded bands show the day of the maximum northwest displacement and the timing of the reversal of the transverse ice motion. (c) Vertical displacement at GPS42 relative to the elevation at 0000 h on 1 July.

First, the transverse motion had begun several days before the onset of the discharge (see also Fig. 5a), suggesting the influence of the lake water on the subglacial conditions before the outburst event. It is inferred from the sudden drop in the lake level on 1 July that lake water had already connected to some part of the ice–bed interface under the ice dam. A relatively small change in the basal condition before the outburst had enough influence on the ice motion to initiate the flow-direction change. Second, the rate of the northwest transverse motion was greatest on 2 July, when the water discharge was increasing, but not when the discharge was at the maximum level (Fig. 7a and b). When the discharge was maximum at midnight from 3 to 4 July, the transverse velocity had decreased to nearly zero. The transverse flow component reversed from the northwest to the southeast at noon on 4 July, coinciding with the significant drop in discharge from the maximum level. These features show that the rate of transverse motion was related to the changing rate of lake discharge. It is likely that the direction of the transverse motion was determined by whether the discharge was increasing or decreasing: the ice flowed northwest or southeast when the discharge was increasing or decreasing, respectively. Third, the transverse motion and its reversal were correlated with the surface vertical motion (Fig. 7a and c). The surface rose up during the lake outburst, showing the uplift peak at nearly the same time as the reversal in the transverse flow component. The surface vertical motion appears to be related also to the lake discharge (Fig. 7b and c).

These features of the stake motion at GPS42 suggest several processes which may have caused the observed ice motion. Although a conclusive interpretation is not reached, possible mechanisms of the reversal of ice motion are discussed below.

Viscoelastic ice deformation

As implied by the surface uplift peak at the same time as the lake discharge, the magnitude of the discharge is presumably related to the basal decoupling and flow-speed increase in the region. If we take the discharge as the measure of the stress perturbation exerted by the accelerated central part of the glacier, the northwest and southeast ice motion at GPS42 appear to be driven by the increase and decrease in the stress perturbation, respectively. These observations lead us to suggest elastic glacier motion and its rebound as possible mechanisms of the reversal of ice motion. For example, at GPS42, if the northwest ice movement is an elastic response to the increasing longitudinal stress perturbation, the subsequent south movement is explained as its rebound, caused by the stress reverting to the pre-event condition. The maximum rate of the northwest motion coinciding with the increasing lake discharge and the reversal of the motion at the time of the discharge reduction are in agreement with the characteristic feature of elastic motion.

It is not surprising to observe elastic behavior in glacier motion since ice is a viscoelastic material. When an englacial stress field changes rapidly, elastic ice deformation is significant, and it recovers when the stress perturbation disappears. In fact, the tidal flexure of ice shelves (Vaughan, 1995) and tidal effects on an ice stream near the grounding line (Reference Anandakrishnan and AlleyAnandakrishnan and Alley, 1997) have been well explained by considering ice as an elastic material. Nevertheless, the relative importance of viscous and elastic components in the deformation of a viscoelastic material is dependent on the stress magnitude and temporal scale. This needs to be examined if the ~100% recovery of the displacement observed over a period of 5–10 days is to be explained by the viscoelastic nature of ice.

The importance of elastic strain in total ice deformation was estimated using linear elasticity and Glen’s viscous flow law with a stress exponent of 3. For simplicity, onedimensional stress and strain were considered, assuming a linear combination of elastic and viscous components. When a constant stress, τ, is applied to initially stress-free ice for a time t, the proportion of elastic strain is

(1)

where ε _e and ε _v are the elastic and viscous strain, respectively, E is the Young’s modulus and A is the rate factor. We use E = 5.1 ×10⁹ Pa (Reference Jellinek and BrillJellinek and Brill, 1956), which lies within the range of values determined by laboratory studies (Reference VaughanVaughan, 1995), and A = 6.4 × 10²⁴ Pa⁻³ s⁻¹, which is suggested for temperate ice (Reference PatersonPaterson, 1994). The elastic property of glacier ice does not differ significantly from that of artificial ice (Reference Gammon, Kiefte, Clouter and DennerGammon and others, 1983), and the effects of temperature and pressure on the Young’s modulus are very small under the conditions at Gornergletscher (Reference Dantl, Riehl, Bullemer and EngelhardtDantl, 1969; Reference Gagnon, Kiefte, Clouter and WhalleyGagnon and others, 1988). Plots of Equation (1) for various stresses show that almost the entire portion of the total strain can be attributed to elasticity only when the stress is less than 10³ Pa under the considered timescale of 5–10 days (Fig. 8). However, the stress required to produce 0.1 m of elastic ice deformation over a distance of 0.1–1 km (the vertical and horizontal length scales, respectively, of the studied area) is ~10⁵–10⁶ Pa. The proportion of elastic strain is even smaller than shown in Figure 8 because the effect of initial stress and three-dimensional stress components on the non-linear viscosity of ice is neglected. Although the above estimation relies on a simplified rheology and stress–strain regime, it appears to be difficult to attribute the entire observed glacier motion to ice elasticity.

Fig. 8. Ratio of elastic to total strain under various stresses (τ), as calculated by Equation (1).

Basal separation due to pressurized water

The correlation between transverse ice motion and surface uplift suggests that the reversal of ice motion was associated with basal separation beneath the glacier. When the lake discharge rapidly increases, subglacial water pressure exceeds ice overburden pressure and lifts the glacier sole. The separation of the glacier sole in the direction normal to the inclined bed should produce horizontal as well as vertical ice motion. Such an effect at the lee side of a subglacial bump is the manifestation of a hydraulic jacking mechanism (Röthlisberger and Reference IkenIken, 1981). Since the bedrock beneath Gornersee is inclined towards the west, this effect can explain the westward motion at GPS37 and GPS42. The magnitude of the separation increases when the discharge is rising, as implied by the correlation between surface uplift and discharge. When the separation reduces owing to the drop in discharge, the horizontal ice motion possibly reverses its direction. In addition to the basal separation, volume changes of subglacial sediments due to water-pressure variations exert a bed-normal force (Reference Truffer, Echelmeyer and HarrisonTruffer and others, 2001). The stake motion at GPS42 from 1 to 4 July shows that the horizontal displacement was ~60 mm northwest while the vertical displacement was ~30 mm (Fig. 7a and c). Taking the annual mean vertical speed (−4.6 mm d⁻¹) into consideration, 44 mm of vertical displacement may be attributed to the bed separation. Because the bed slope beneath Gornersee is approximately 0.5 towards the west (Reference Iken, Fabri and FunkIken and others, 1996; Reference HussHuss, 2005), the horizontal component of the bed-normal ice motion (44 mm × 0.5 = 22 mm) accounts for about 35% of the observed horizontal motion. If the water penetrated beneath the glacier, prying off the ice near the lake, the horizontal ice motion away from the lake would be larger than this estimation.

In the lower reaches, away from the lake, the northward ice motion at GPS14 and GPS24 seems to be difficult to explain by basal separation. However, if the subglacial pressure is elevated locally at a drainage conduit along the glacier center, surface uplift would be accompanied by horizontal motion towards the glacier margins. Such ice motion is expected by analogy of vertical and horizontal ground surface displacements due to the changes in the pressure exerted by the intrusion of magma (e.g. Reference MogiMogi, 1958; Reference Walsh and DeckerWalsh and Decker, 1971). If this was the case, it is also possible that the flow-direction changes near the lake were influenced by the location and direction of the lake water intrusion into the bed. The viscoelastic property of ice presumably played an important role in the short-term glacier response to the basal separation and subsequent pressure drop.

Subglacial sediment deformation

Ice sliding over bedrock and subglacial sediment deformation are crucial in glacier motion. Because these processes are mostly controlled by basal stress and subglacial water pressure, they possibly play an important role in the reversal of ice motion. The basal sliding speed is usually formulated by a power function of the basal shear stress and the effective pressure (e.g. Reference WeertmanWeertman, 1957; Reference FowlerFowler, 1981; Reference BindschadlerBindschadler, 1983); thus, the sliding displacement would not recover when the magnitude of the stress or water pressure changes. The elastic behavior of subglacial sediment has been observed by tilt-sensor measurements conducted under glaciers (Reference Iverson, Hanson, Hooke and JanssonIverson and others, 1995; Reference Fischer and ClarkeFischer and Clarke, 2001; Reference Porter and MurrayPorter and Murray, 2001). In these measurements, tilt sensors installed in a subglacial sediment layer periodically showed up-glacier rotation, suggesting recovery of the elastic part of the deformation. Reference Iverson, Baker, Hooke, Hanson and JanssonIverson and others (1999) tested subglacial sediment collected from Storglaciären, Sweden; these tests yielded a Young’s modulus of 1.0–1.8 × 10⁶ Pa. Assuming this value, the shear deformation of a 10 m thick sediment layer by a stress of 10⁴ Pa results in ~0.1 m horizontal displacement. At Gornergletscher, although it has not been confirmed, the existence of a subglacial sediment layer up to 50 m thick was suggested by drilling and seismic measurements (Reference Bezinge, Perreten and SchaferBezinge and others, 1973). It is debatable whether the subglacial motion can be transferred directly to the surface through an ice layer that is several hundred meters thick; however, sediment deformation has the potential to respond elastically to basal condition changes. A drawback of this interpretation is that the timing of the reported strain recovery in the sediment layer is not consistent with our measurements. The up-glacier rotation of the tilt sensor occurred when the glacier sole decoupled from the bed owing to increasing water pressure (Reference Iverson, Hanson, Hooke and JanssonIverson and others, 1995; Reference Fischer and ClarkeFischer and Clarke, 2001), whereas in Gornergletscher the surface motion reversed when the lake discharge decreased.