172

Journal of Glaciology, Vol. 53, No. 181, 2007

Reversal of ice motion during the outburst of a glacier-dammedlake on Gornergletscher, Switzerland
Shin SUGIYAMA,1,2 Andreas BAUDER,2 Patrik WEISS,2 Martin FUNK2
1

Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan
E-mail: sugishin@lowtem.hokudai.ac.jp
2
Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie (VAW), Eidgenössische Technische Hochschule ETH Zentrum,
CH-8092 Zürich, Switzerland
ABSTRACT. During the outburst flood of a glacier-dammed lake on Gornergletscher, Switzerland, in
July 2004, the drained lake water triggered anomalous glacier motion. At the onset of the outburst, theice-flow direction in the vicinity of the lake became closer to the central flowline. When the lake
discharge magnitude decreased, the flow direction altered such that the ice moved back to the azimuthof the initial motion. At one of the survey points, where the ice flows parallel to the central flowline, theice accelerated along the pre-event flow direction followed by a 18088 backward motion that lasted over
2 days. These observations indicate the impact of the lake outburst on the subglacial and englacial stressconditions; however, the reversal in the flow direction is difficult to explain by drawing on our current
understanding of glacier mechanics. The timing and the timescale of the flow-direction changes suggestthat the elastic glacier motion and its rebound played a role under the rapidly changing stressconditions, but the Young’s modulus of ice is too large to cause the observed ice motion. Other
processes, including basal separation and subglacial sediment deformation, are discussed as possible
mechanisms for the reversal of the ice motion.

INTRODUCTION
The sudden drainage of a glacier-dammed lake provides aunique opportunity to study the influence of subglacialhydrological conditions on glacier dynamics. Since anenormous amount of lake water drains into the glacier bed
within a short period, the glacier flow regime is expected tochange dramatically during an outburst event due to thechanging subglacial conditions. According to the diurnal
flow variations and motion events observed in the alpine
glaciers, a sudden water input into the bed enhances thebasal ice motion by increasing the subglacial water pressure(e.g. Iken and Bindschadler, 1986; Naruse and others, 1992;
Jansson, 1995; Sugiyama and Gudmundsson, 2004). The iceflow speed significantly increases as the pressure approaches
the ice overburden pressure and the glacier sole decouples
from the bed (e.g. Iverson and others, 1995, 1999; Fischer
and Clarke, 2001). Since the water flux from a draining lake
is generally much larger than the meltwater input, the lakedrainage may cause flow changes that are not observable
under the usual hydrological conditions. The study of glacier
dynamics with a special emphasis on subglacial hydrology isof critical importance because the basal flow processes
assume a key role, not only in small mountain glaciers, butalso in fast-flowing ice streams on large ice sheets (e.g.
Engelhardt and Kamb, 1998; Kamb, 2001). In addition to thegeneral interest in the glacier dynamics, it is also important
to study ice motion near a glacier-dammed lake because it
plays an active role in the lake drainage process. The motionof an ice dam may control the water discharge from a lake;
therefore, ice dynamics in the vicinity of the lake is crucial tounderstanding the triggering mechanism of the outburst.
Despite the critical importance and keen interest
indicated above, few ice-flow measurements have been
conducted during lake outburst events. This is because theprediction of an outburst is difficult. One successful
measurement was carried out during the drainage of Hidden

Creek Lake at Kennicott Glacier, Alaska, USA, in 2000.
Stake surveys on the ice dam suggested that a fault
penetrating from the glacier surface to the bed caused asurface uplift before the drainage (Walder and others, 2005,
2006). Stake motion near the central flowline showed anincrease in the flow speed accompanied by surface uplift,
thereby suggesting enhanced basal sliding and subglacial
cavity enlargement (Anderson and others, 2005). These
measurements, together with the observations of subglacialhydrology and hydrochemistry (Anderson and others, 2003),
provided important information for the study of the impact of
the outburst on glacier dynamics. In Iceland, the ice surface
motion of Skeiðarárjökull was continuously measured by aglobal positioning system (GPS) during the outburst event ofGrı́msvötn in 2004 (Roberts and others, 2005). A ten-foldincrease in the horizontal flow speed and a decimeter-scalesurface uplift were observed near the glacier terminus. The
surface elevation permanently increased by 0.3 m, representing a lasting impact of the flood on the glacier.
To better understand the dynamic response of a glacier toa lake outburst, we conducted an intensive field campaign
on Gornergletscher, Switzerland, in 2004. The aim of thestudy was to obtain a comprehensive dataset describing theglacier dynamics and hydraulics during the outburst event ofGornersee, a glacier-dammed lake on Gornergletscher.
During the outburst in July 2004, ice-flow measurements
showed extraordinary ice motion triggered by the lakedrainage. This paper reports the details of the ice-flowchanges during the event and discusses possible mechanisms of the anomalous ice motion.

FIELD MEASUREMENTS
Study site
Gornergletscher is the second largest valley glacier system in
the Swiss Alps, with a surface area of 68 km2 (Raymond andSugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

173

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

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 withannual flow vectors obtained for the period October 2003 to
September 2004. The borehole drilling site is labeled BH430.

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 measurementsof subglacial hydrology and glacier dynamics (Iken andothers, 1996)).
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 anddrains 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 theglacier for 5 km before it drains into the outlet river Gornera.
The maximum ice thickness between the lake and theglacier snout is about 450 m according to an ice-penetratingradar survey carried out in 2004 (Huss, 2005). The volume
of water stored in the lake before the outburst shows anannual variation. In 2004, the maximum water volume wasestimated to be 4.0 106 m3 from the water level and the
hypsometry of the lake floor, obtained by processing anaerial photograph taken after the lake was emptied (Hussand others, 2007).

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 areindicated 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 hourintervals. 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 distanceand the elevation difference from the reference station,satellite configuration and wind conditions. Control experiments and past measurements on glaciers provide anestimate of the positioning errors, 3 and 5 mm in thehorizontal and vertical directions, respectively (Sugiyama
and Gudmundsson, 2004).
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 orequipment failure. The data obtained were corrected bysurveying the reference reflectors fixed on the bedrock in themarginal vicinity. The errors in the measurement vary fromseveral 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 fromthe horizontal displacement after filtering the surveyed
coordinates by kernel regression smoothing with adaptiveplug-in bandwidth (Seifert and others, 1994). The opensource Fortran routine employed for this uses a filtering
bandwidth determined to correspond to the estimated174

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

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.

survey errors. The code is available at http://www.unizh.ch/biostat/Software/kernf77.html.

RESULTS

Hydrological measurements

In 2004 the lake began to form in mid-May. The lake filledwith water extending over a surface area of 0.27 km2 by theend 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 lakelevel measurements and could be observed by the formationof a strandline at the lake shore. This incident suggests thetransfer of 8 104 m3 of water into the subglacial spaceprior to the main drainage.
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 indicatesthat nearly 70% of the stored water drained during the days
from 3 to 5 July (Fig. 3c). Peak discharge from the lakeoccurred 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 theeastern margin of the glacier. However, after the event, wefound several water channels (the diameters of which wereof the order of a few meters) excavated into the ice at thelake floor (Weiss, 2005), indicating that a part of the water
also drained englacially.

Measurement of lake level began in May 2004. A waterpressure transducer (Keller, PAA-36W) with an accuracy of
60 Pa was installed near the deepest point in the lake torecord the water depth every 10 min. The measurement was
terminated when a floating ice block cut the sensor cableduring the outburst on 5 July. The discharge from the lake forthe period 2–5 July was computed from the change in waterlevel 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 is430  20 m according to the length of the hose used for the
drilling and ice-penetrating radar survey. A vibrating wirepressure 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 awater level of 0.35 m. Due to the uncertainty in the distancefrom the glacier bed to the sensor, the absolute value of thewater level from the bed may have an error of up to 10 m.
Water discharge from the glacier is measured by theGrande 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

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

175

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).

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 thehydrological conditions underneath the borehole site. The
water level dropped by 200 m 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 thedrainage 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 theannual mean vertical speed, which is 2.5 mm d–1 at GPS14.
The daily elevation peaks lagged several hours behind theborehole 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 Julyand 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 theoutburst (2 to 4 July) are compared with those before theevent (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 andGPS37, and the clockwise rotation at stakes 31, 32 and 41
and GPS42. In the lower reaches, the flow vectors are moreto the north, as observed at stake 22, GPS14 and GPS24. In
general, the glacier flow field became more parallel to thecentral 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 anddirection were observed at stakes 44–46 at the west shoreof 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, theupward vertical displacement during the outburst was inrange 0.5–3.0 m, one order of magnitude larger than at theother 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 thisregion, the huge uplift was probably a local response of themarginal ice to buoyancy force. We assume that englacial
fractures acted as a hinge under the direct influence of thedraining 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 thedrainage event continuous stake measurements showed
complex flow-direction changes, hereafter referred to as
the ‘reversal of ice motion’. The southwest ice flow at GPS42changed its direction to the northwest during the first half ofthe outburst (Fig. 5a). It then turned south on 4 July andmoved 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 lakebecame empty. It appears that a transverse (northwest–
southeast) flow component was superimposed on the preevent flow direction (southwest) over the course of theoutburst, and the transverse component reversed on 4 July.

176

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

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 thestake 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 theflow direction occurred not only near the lake but also at
GPS24 and GPS14 at reaches several kilometers below thelake. This deviation is not as evident as those at GPS37 andGPS42 because the flow speed is relatively high in the lower
reaches; however, the stake moved away from the azimuth ofthe motion towards the northeast at GPS24 (Fig. 5d) andtowards the north at GPS14 (Fig. 5e). The change intransverse velocity and the subsequent switch back to theazimuth of the initial motion are similar to the flow variations
observed at Hansbreen during a speed-up event triggered byenhanced snowmelt (Vieli and others, 2004). The mostintriguing ice motion was observed at stake 43 (Fig. 5c). The
ice flowed northwest until the morning of 5 July; it thenstarted to flow backward towards the southeast for about
2 days. This observation of a glacier flowing up-glacier isvery 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.

INTERPRETATION AND DISCUSSION
The flow-speed increase and the surface uplift are probably
caused by the subglacially drained lake water. Because theborehole water level was very high from 2 to 6 July (Fig. 3d),the pressurized subglacial water enhanced the basal ice
motion and the surface flow speed increased. The uplift canbe attributed to the water storage underneath the glacier,which occurred as a result of the time lag between the
discharge peaks from the lake and the glacier (Fig. 3c and b).
The magnitude and the timing of the uplift is similar to theobservation on Kennicott Glacier during the drainage of
Hidden Creek Lake (Anderson and others, 2005). The
correlations of the peaks in the flow speed, uplift rate andwater level are as expected from previously reported fieldobservations and numerical investigations (Iken, 1981; Iken
and others, 1983; Sugiyama and Gudmundsson, 2004). An
unexpected observation was the reversal of ice motion
characterized by the flow-direction changes at the onset,
during and after the outburst, which correspond to thechanges on 1, 4 and 8 July in the case of GPS42 and GPS37(Fig. 5a and b).
During the first half of the lake outburst, the glaciermotion became more parallel to the northwest ice flow at thecentral part of the confluence area, as described in theprevious section (Fig. 4). Since the ice is thick at this part of
the glacier, the most plausible interpretation of the flowchange is that an accelerated central glacier flow pulled or
pushed the surrounding ice by longitudinal stress coupling.
For example, the change in the flow direction from the northto the northwest on 1 July at GPS37 (Fig. 5b) can be
attributed to the dragging of the ice by the longitudinal stresstransmitted from the accelerated northwest ice flow at thecenter of the glacier. Although the first change in the flow
direction can be explained in this way, the second and thethird changes are still unclear. If the glacier flow field had
been influenced by the drained lake water, it should havereturned to the pre-event pattern subsequently without

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

177

Fig. 6. Schematic diagrams showing the trajectories of stake motion
during the lake outburst.

switching back to the azimuth of the original motion(Fig. 6a). Even if the flow conditions before and after the
event were different, the flow direction should not havereturned to the pre-event direction after the outburst (Fig. 6b).
Hereafter, we focus on the interpretation of the observed
reversal of ice motion, which is sketched in Figure 6c.

The timing of the flow-direction changes
To reveal the mechanism of the reversal of ice motion, thetimings 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 from29 June to 9 July is examined by comparing it with theavailable lake discharge data and vertical surface motion(Fig. 7b and c).
First, the transverse motion had begun several days before
the onset of the discharge (see also Fig. 5a), suggesting theinfluence of the lake water on the subglacial conditions
before the outburst event. It is inferred from the sudden dropin the lake level on 1 July that lake water had alreadyconnected to some part of the ice–bed interface under theice 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 thenorthwest 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). Whenthe discharge was maximum at midnight from 3 to 4 July, thetransverse velocity had decreased to nearly zero. The
transverse flow component reversed from the northwest to
the southeast at noon on 4 July, coinciding with thesignificant 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 thatthe direction of the transverse motion was determined bywhether the discharge was increasing or decreasing: the ice
flowed northwest or southeast when the discharge wasincreasing 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 sametime 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).

Fig. 7. (a) Plan view of the stake motion at GPS42. The open circles
on the smoothed trajectory indicate the locations of the stake at0000 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.

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 thelake discharge, the magnitude of the discharge is presumably related to the basal decoupling and flow-speed increasein the region. If we take the discharge as the measure of thestress 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 responseto the increasing longitudinal stress perturbation, thesubsequent south movement is explained as its rebound,178

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

vertical and horizontal length scales, respectively, of thestudied 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.

Basal separation due to pressurized water

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

caused by the stress reverting to the pre-event condition. The
maximum rate of the northwest motion coinciding with theincreasing lake discharge and the reversal of the motion at
the time of the discharge reduction are in agreement withthe characteristic feature of elastic motion.
It is not surprising to observe elastic behavior in glaciermotion 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 (Anandakrishnan 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 isdependent on the stress magnitude and temporal scale. This
needs to be examined if the 100% recovery of thedisplacement 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 alinear combination of elastic and viscous components.
When a constant stress, , is applied to initially stress-free
ice for a time t, the proportion of elastic strain is
"e
=E
,
¼
"e þ "v =E þ A  3 t

ð1Þ

where "e and "v are the elastic and viscous strain, respectively, E is the Young’s modulus and A is the rate factor. We
use E ¼ 5.1 109 Pa (Jellinek and Brill, 1956), which lies
within the range of values determined by laboratory studies(Vaughan, 1995), and A ¼ 6.4 1024 Pa–3 s–1, which is suggested for temperate ice (Paterson, 1994). The elastic
property of glacier ice does not differ significantly from thatof artificial ice (Gammon and others, 1983), and the effects
of temperature and pressure on the Young’s modulus are verysmall under the conditions at Gornergletscher (Dantl, 1969;
Gagnon 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 lessthan 103 Pa under the considered timescale of 5–10 days
(Fig. 8). However, the stress required to produce 0.1 m ofelastic ice deformation over a distance of 0.1–1 km (theThe correlation between transverse ice motion and surface
uplift suggests that the reversal of ice motion was associatedwith 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 tothe 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 Iken, 1981). Since the bedrock beneath Gornersee is inclined towards the west, thiseffect can explain the westward motion at GPS37 andGPS42. 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 towater-pressure variations exert a bed-normal force (Truffer
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 (Iken and others, 1996; Huss, 2005), thehorizontal component of the bed-normal ice motion(44 mm  0.5 ¼ 22 mm) accounts for about 35% of theobserved horizontal motion. If the water penetrated beneaththe glacier, prying off the ice near the lake, the horizontal ice
motion away from the lake would be larger than thisestimation.
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 subglacialpressure is elevated locally at a drainage conduit along theglacier center, surface uplift would be accompanied byhorizontal motion towards the glacier margins. Such ice
motion is expected by analogy of vertical and horizontal
ground surface displacements due to the changes in thepressure exerted by the intrusion of magma (e.g. Mogi,
1958; Walsh and Decker, 1971). If this was the case, it isalso possible that the flow-direction changes near the lakewere influenced by the location and direction of the lakewater 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

Sugiyama and others: Reversal of ice motion during a glacier-dammed lake outburst

pressure, they possibly play an important role in the reversalof ice motion. The basal sliding speed is usually formulated
by a power function of the basal shear stress and theeffective pressure (e.g. Weertman, 1957; Fowler, 1981;
Bindschadler, 1983); thus, the sliding displacement would
not recover when the magnitude of the stress or waterpressure changes. The elastic behavior of subglacial sediment has been observed by tilt-sensor measurements
conducted under glaciers (Iverson and others, 1995; Fischer
and Clarke, 2001; Porter and Murray, 2001). In thesemeasurements, tilt sensors installed in a subglacial sedimentlayer periodically showed up-glacier rotation, suggesting
recovery of the elastic part of the deformation. Iverson andothers (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, theexistence of a subglacial sediment layer up to 50 m thick
was suggested by drilling and seismic measurements(Bezinge 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 respondelastically to basal condition changes. A drawback of thisinterpretation is that the timing of the reported strain
recovery in the sediment layer is not consistent with ourmeasurements. The up-glacier rotation of the tilt sensor
occurred when the glacier sole decoupled from the bed
owing to increasing water pressure (Iverson and others,
1995; Fischer and Clarke, 2001), whereas in Gornergletscher the surface motion reversed when the lake
discharge decreased.

179

also cause complex glacier responses to changing basal
conditions. It is difficult to provide a complete explanation ofwhat we observed, based on the current knowledge of theseprocesses and available data. Further study of the subglacial
drainage pattern and viscoelastic property of the glacier isneeded to verify the hypotheses.
Since the reversal of ice motion was observed in thevicinity of the lake on the ice dam, it possibly played a keyrole in the triggering and drainage mechanisms of theoutburst. Moreover, the reversal was observed as being
pervasive, from the lake vicinity to several kilometers lower,
implying that the phenomenon commonly occurs under the
influence of changing stress conditions. Thus, similar ice
motion is expected during glacial events such as glacier
surge, calving and stick–slip glacier motion (Fischer andClarke, 1997; Bindschadler and others, 2003). Our study
maintains that the response of a glacier to these events may
not be explained by our current understanding of glaciermechanics; thus, further investigation of glacier motion
under rapidly changing stress conditions is required.

ACKNOWLEDGEMENTS
We thank the members of the field campaign at Gornergletscher in 2004. Special thanks are due to B. Müller,
M. Huss, U.H. Fischer and T. Wyder for their contribution to
the field measurements. The river discharge data were kindly
provided by Grande Dixence SA. The quality of the paper
was substantially improved by careful reviews by J.S. Walder(scientific editor), M. Truffer and S. Anandakrishnan. Theinterpretation of the observed ice motion is indebted to thediscussion with the editor and the referees. R. Greve and
H. Blatter provided helpful comments on the manuscript.
This research was funded by Swiss National Science
Foundation grant No. 200021-103882/1.

CONCLUSIONSIn order to study the impact of the sudden drainage of a
glacier-dammed lake on glacier dynamics, high-frequency
ice-flow measurements were carried out with hydrologicalobservations at Gornergletscher. During the outburst eventof Gornersee in July 2004, the flow speed increased by 50%
and the surface rose by 20 cm; these changes were triggeredby 4 106 m3 of water draining from the lake within 5 days.
The borehole water level was consistently high near the
flotation level, suggesting that the elevated subglacial waterpressure enhanced the basal ice motion and the subglacial
water cavity formation.
The most intriguing observation was that of the reversal ofice motion, including the 1808 backward ice flow recorded
at one of the survey stakes. The flow-direction change can be
attributed to stress coupling with accelerated ice flow at thecentral part of the glacier, but its reversal is difficult to
explain. Detailed analysis of the ice motion shows that therate of the transverse flow was correlated with the changing
rate of lake discharge and the surface uplift rate. This analysis
and the timescale of the event suggest that the elastic glacier
response to the rapidly changing stress conditions and its
rebound assume an important role. Nevertheless, the Young’s
modulus of ice is too large to explain the observed recoveryof almost the entire transverse motion. Alternatively, theseparation of the glacier sole from the inclined bed due toelevated water pressure may have caused the observed
transverse ice motion. Subglacial sediment deformation can

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MS received 1 May 2006 and accepted in revised form 20 January 2007