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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, F03010, doi:10.1029/2009JF001509, 2010

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ArticleSurface ice motion deviating toward the margins during
speed‐up events at Gornergletscher, Switzerland
S. Sugiyama,1,2 A. Bauder,2 P. Riesen,2 and M. Funk2
Received 31 August 2009; revised 22 March 2010; accepted 30 March 2010; published 27 July 2010.

[1] High frequency ice flow measurements during speed‐up events in Gornergletscher,
Switzerland, revealed intriguing ice motion which has never been reported in detail
before. During the summer 2005, more than a 100% flow speed increase was observed
three times at four GPS stations installed across Gornergletscher. The speed‐ups wereaccompanied by a decimeter scale surface uplift. Two of the events were triggered byintensive surface melt and rainfall, while the third one was due to the outburst of
Gornersee, a glacier‐dammed lake located 2 km upglacier. An interesting observation
was ice motion deviating toward the side margins during the events. As the glacieraccelerated, a transverse (cross glacier) velocity component was generated, turning theflow direction away from the central flow line toward the margins. When the glacierdecelerated, the transverse velocity component reversed so that the ice flowed back to
the azimuth of the initial flow direction. In the most significant case, the trajectory of thesurvey stake deviated from the original track by 0.2 m in the transverse direction. We
hypothesize that the observed lateral ice motion was caused by locally elevatedsubglacial water pressure. When the ice sole decoupled from the bed at a part of theglacier, a point source of vertical displacement was transmitted to the surface throughviscous ice. This caused the transverse as well as vertical surface motion, as observed inground motion during magma intrusion. The hypothesis was tested with a two‐dimensional
ice flow model applied to the transverse glacier cross section. The model confirmedthat the surface ice would move toward the margins as observed in Gornergletscher, if
subglacial water pressure exceeded the ice overburden pressure over a limited part ofthe bed.
Citation: Sugiyama, S., A. Bauder, P. Riesen, and M. Funk (2010), Surface ice motion deviating toward the margins during
speed‐up events at Gornergletscher, Switzerland, J. Geophys. Res., 115, F03010, doi:10.1029/2009JF001509.

1. Introduction[2] Glacier flow speed increases over a period of several
days, referred to as ‘speed‐up events’ in this paper, havebeen observed at a number of glaciers [e.g., Iken et al.,
1983; Kamb and Engelhardt, 1987; Hooke et al., 1989;
Naruse et al., 1992; Gudmundsson et al., 2000; Mair et al.,
2001; Truffer et al., 2001; Anderson et al., 2004]. Many
events have been observed early in summer, but may occur
throughout the ablation season. Surface flow speeds increaseby more than a factor of two within a day, and peak magnitudes widely vary with the glacier and events. Speed‐up
events are usually triggered by an increase in water input tothe subglacial drainage system, which is caused by intensivesnow‐ and ice melt, heavy rainfall, or a sudden release ofwater impounded in or beside a glacier. Outburst of a1
Institute of Low Temperature Science, Hokkaido University, Sapporo,
Japan.
2
Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich,
Zurich, Switzerland.

Copyright 2010 by the American Geophysical Union.
0148‐0227/10/2009JF001509

glacier‐dammed lake is one of these triggers, and it oftencauses extraordinary changes in the glacier flow regimes[e.g., Magnússon et al., 2007]. The acceleration is often
associated with high subglacial water pressure [Iken andBindschadler, 1986; Jansson, 1995; Sugiyama andGudmundsson, 2004]. This observation implies that basal
ice motion is enhanced by water pressure, which is elevated during the adjustment of the drainage system to thewater influx [Bindschadler, 1983; Nienow et al., 1998;
Bartholomaus et al., 2008]. Therefore, the study of speed‐
up events is particularly important to furthering the understanding of the mechanism of basal ice motion and its
connection to the subglacial hydraulic conditions.
[3] During the speed‐up, upward glacier surface motion(so‐called uplift) has been observed on many glaciers [e.g.,
Iken et al., 1983; Kamb and Engelhardt, 1987]. For example,
observations on Unteraargletscher showed that the surface
gradually moved upward by 0.15 m within a few days when
the glacier accelerated in early summer [Iken et al., 1983].
The surface uplift can be explained by the separation of theglacier from the bed due to elevated water pressure. Water
cavity formation at the lee side of bedrock bumps is one of

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F03010

tions. The primary objective of the field campaign was tostudy a glacier‐dammed lake outburst which was expected tooccur in the summer. We aligned the GPS receivers acrossthe glacier to detect the location of the lake water drainage
from the changes in the ice motion. We expected that themagnitude of the acceleration and uplift would be greater
above the drainage path than elsewhere. When the lakedrained, in addition to the expected speed‐up and uplift, weobserved intriguing ice motion toward the glacier margins.
The transverse motions coincided with the uplift and they
were distributed systematically across the glacier. These
details are revealed for the first time in this study as a resultof the multiple GPS installations across the glacier. Similar
ice motion was recognized in two other speed‐up events
earlier in the melt season.
[5] In this paper we report the details of the three speed‐
up events that occurred in Gornergletscher in summer 2005,
with special focus on the surface ice motion in transverse
and vertical directions. The observed ice motion can be
reproduced with a two‐dimensional numerical ice flow
model by assuming that the subglacial water pressure exceeds the ice overburden pressure over a limited part of theglacier. Thus, we propose that the glacier decouples fromthe bed at a pressurized subglacial drainage path, resulting in
the upward and transverse motion on the surface. Our fielddata reveal a peculiar dynamic behavior during a speed‐up
event, and the numerical modeling demonstrates a possible
procedure to assess basal ice motion and hydraulic conditions from surface observations.
Figure 1. (a) Map of Gornergletscher and Grenzgletscher
with the study site indicated by the box and the Gornersee
indicated by the gray hatch. Surface contour spacing is
100 m. Coordinates are in the official Swiss coordinate system. (b) Locations of the GPS stations (open circles), theodolite and reflectors (triangle), boreholes (solid circles), andautomatic weather station (AWS, plus sign). The vectors
are horizontal flow velocities measured from May 15 toAugust 25, 2005. Surface contour spacing is 20 m.
the mechanisms proposed for the basal separation [e.g.,
Röthlisberger and Iken, 1981]. Although the occurrence ofbasal separation is likely during a high velocity period, thevertical surface motion may not be solely attributed to a
separation of the glacier from its bed. Vertical strain
integrated over the ice thickness is an important component of the vertical motion, and temporal variation in thestrain rate is significant under changing subglacial and englacial stress conditions [Gudmundsson, 2002; Sugiyama andGudmundsson, 2003]. Sliding along an inclined bed may
contribute to vertical surface motion as well [Hooke et al.,
1989; Mair et al., 2002; Anderson et al., 2004], making it
more difficult to interpret surface observations. To fully
understand the cause of the surface uplift, it is crucial tomeasure flow speed, water pressure, strain regimes, and bed
geometry, and compare them with the details of verticalsurface motion. High frequency Global Positioning System(GPS) survey techniques, and water pressure and strain
measurements in boreholes provide a possibility to collectdata for an accurate understanding of the uplift mechanisms.
[4] During summer 2005, we installed four GPS receivers
on Gornergletscher to measure short‐term ice flow varia-

2. Field Measurements
2.1. Study Site
[6] Gornergletscher is the second largest glacier system in
the Swiss Alps with a surface area of 38 km2 for major
tributaries and 53 km2 for the whole system [Bauder et al.,2007]. The upper part of the 12‐km long mainstream isnamed Grenzgletscher; it merges with Gornergletscher at
about 5 km from the common terminus of the glacier system(Figure 1a). Due to the thinning of the upper part of
Gornergletscher, ice flux and flow regime in the confluence
area are dominated by the flow from Grenzgletscher[Sugiyama et al., 2007]. Borehole temperature and ice radarmeasurements showed the existence of a cold ice body inthe confluence area at temperatures down to 2.5 K below
the pressure melting point [Ryser, 2008; Eisen et al., 2009].
The cold ice occupies the central part of the glacier from thesurface to more than 50% of the ice thickness, and this coldlayer is underlain by a temperate basal layer. The lateral andvertical extent of the cold ice decreases downglacier.
[7] One of the characteristic features of Gornergletscher isthe formation of a glacier‐dammed lake, Gornersee, at theeastern margin of the confluence (Figure 1). Gornersee forms
every spring as water from snow‐ and ice melt collects, andthen drains away that same summer, releasing several million
cubic meters of water. We studied the outburst events from2004 to 2008 by conducting detailed field observations[Huss et al., 2007; Sugiyama et al., 2007, 2008; Walter et al.,2008; Werder et al., 2009; Werder and Funk, 2009]. Our
observations revealed that the triggering and drainage mechanisms of the outburst vary from year to year. However,significant changes in the ice flow regime, e.g., acceleration,

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direction change, uplift, accompanied by an increase insubglacial water pressure, have been observed in each of theevents.
[8] The 2005 field measurements began in April by
installing GPS receivers and an automatic weather station,
followed by a borehole drilling campaign in June. The iceflow and water pressure data presented in this paper wereobtained at about 1–2 km downglacier from Gornersee. The
glacier surface of this region became snow‐free in late May.
Lake water level was measured with a pressure sensor
installed near the deepest point in Gornersee. The lake level
dropped on June 11 when the lake water volume was lessthan a third of the full capacity. It was difficult to determine
the true onset of the outburst as the water had begun to leakabout a week before the lake level began to decrease.
According to the lake discharge, about 80% of the lake waterdrained during the three days from June 12 to 14 [Huss et al.,2007].
2.2. Method
2.2.1. Ice Flow Measurements[9] Surface ice motion was measured either with GPS or atheodolite by surveying the three‐dimensional coordinatesof aluminum stakes installed on the glacier. The stakes were
drilled several meters deep into the ice and stake length
above the surface was maintained to be less than 2 m inorder to reduce the influence of wind on survey accuracy.
The locations of the stakes used for this study are shown in
Figure 1b together with summer flow vectors obtained forthe period from May 15 to August 25, 2005.
[10] Four stakes named GPS13‐16 were installed acrossthe glacier at distances of 250 to 350 m from each other(Figure 1b). From May to September 2005, these stakes
were surveyed by GPS (Leica System 500) at intervals of
3 hours. The L1 and L2 GPS phase signals were recordedwith a GPS antenna mounted on the top of the stake andpost‐processed in a static mode using Leica SKI‐Pro software with reference data recorded by a fixed GPS station on
bedrock at the northern glacier flank (Figure 1b). The
accuracy of the positioning was estimated from wintermeasurements at the study site (December 1–31, 2003, n =121). Assuming a constant flow speed and direction during
the winter measurement period, standard deviations fromexpected stake locations were 3.4 and 4.2 mm in the horizontal and vertical directions, respectively. From May 12 toJune 4, stake GPS16 was measured by a theodolite instead of
GPS using the technique described below.
[11] Stakes 12 and 24 were equipped with reflectors on
the top to be surveyed with a theodolite (Leica TCA1800)
installed on the bedrock at the northern flank (Figure 1b).
The theodolite was automatically operated every hour from
May to September 2005, unless the operation was interrupted by weather conditions or equipment failure. The dataobtained were corrected by surveying reference reflectors
fixed on bedrock in the vicinity of the margin. The standard
deviation of the positioning is about 5–10 millimeters,
depending on the distance from the theodolite to the reflectors[Sugiyama et al., 2008].
[12] The surveyed coordinates were smoothed using a
Gaussian filter to calculate horizontal flow speed and strain
rate. The smoothing bandwidth was fixed in the range of
0.125–0.75 days depending on the magnitude of the posi-

F03010tioning errors (GPS or theodolite) and the smoothness
required for the calculations (speed or strain rate).
2.2.2. Water Pressure Measurements[13] Subglacial water pressure in borehole BH430(Figure 1b) has been measured since the summer 2004.
Pressure measurements in four additional boreholes BH2–5(Figure 1b) began in early June 2005, shortly before theoutburst event. These boreholes were drilled down to the bed
by a hot‐water drilling system. According to the length of
the hose used for the drilling, the ice thicknesses at thedrilling sites BH430, and BH2–5 were 430, 251, 354, 384,
and 227 m, respectively. These values are in good agreementwith the thicknesses obtained by radio echo soundings[Sugiyama et al., 2008]. Errors due to the stretching of thehose are about 2–3% of the ice thickness. The thickness at
BH430 is not as accurate as the others because of surface
melting and vertical straining after the drilling in 2004. The
water pressure was measured near the bottom of the boreholes
with vibrating wire pressure transducers (Geokon Model
4500) and recorded with data loggers (Campbell CR10X) atintervals of 10 min. The accuracy of the measurement was
equivalent to a change in water level of ±0.35 m. In borehole
BH430, the water level may have an error of up to ±10 m
because of the uncertainty in the distance between the bed andthe sensor.
2.2.3. Meteorological Measurements[14] A meteorological station was established on the glacier flank near the theodolite at 2600 m a.s.l. (Figure 1b).
Air temperature and precipitation were measured from April
2005 at 30 min intervals with a ventilated thermistor sensor(Vaisala T107) and with a tipping bucket rain gauge (Joss‐
Tognini), respectively.

3. Results
3.1. Speed‐Up Events[15] Three speed‐up events were observed during thestudy period, twice in May and once in June. At each event,flow speed increase and surface uplift occurred for about
5 days (Figures 2a and 2b). We refer to these speed‐up eventsas Event 1 (May 20 0000 h–May 24 1200 h), Event 2 (May
26 0000 h–May 31 1200 h), and Event 3 (June 11 0000 h–
June 16 1200 h).
[16] Event 1 began on May 20 when the air temperaturerose after a cold period (Figure 2c). The horizontal surface
speed increased with weak diurnal signals, and it peaked on
May 22 about a day after heavy precipitation (Figures 2aand 2c). The peak speeds were about three times greaterthan those before the event. GPS13–15 recorded a surface
uplift of 0.05–0.1 m during the period of acceleration(Figure 2b). The horizontal speed decreased to the pre‐event
level when the air temperature dropped on May 24, whereas
the surface remained elevated at a higher level. The waterlevel slightly dropped over the course of the event, but nosignificant fluctuation was observed (Figure 2d).
[17] Event 2 was characterized by strong diurnal variations in the flow speed (Figure 2a). The diurnal signals werealso present in the vertical displacement (Figure 2b). The
flow speed increased and the ice surface moved upward in
the afternoon, whereas the speed decreased and the surface
moved downward in the morning. The flow speeds at
GPS13–16 peaked on May 28 and they were about three

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F03010Figure 2. Time series of (a) horizontal flow speed, (b) vertical displacement, (c) air temperature (line)
and precipitation (column), and (d) borehole water level in BH430 (black) and discharge from Gornersee(gray bold). The gray bands indicate the periods of speed‐up events. The stake GPS16 was surveyed by atheodolite until June 4. The GPS and theodolite data used for the horizontal speed calculations were filtered with bandwidths of 0.125 and 0.375 d, respectively. The error bars in Figure 2b correspond to thestandard deviations of the GPS (±4.2 mm) and theodolite (±10 mm) measurements. The lake discharge
was derived from the lake level and modeled meltwater input [Huss et al., 2007].
times greater than the speeds before the event. The magnitude of the uplift was greater at the glacier center, reaching
0.2 m at GPS14. After this event, the generally upwardvertical motion since the beginning of the measurements
turned into a downward trend at GPS14 and GPS15. Thisobservation contrasts to GPS13 and GPS16, which showed
upward motion trend throughout the measurement period.
The air temperature showed steady diurnal variations at a
relatively high level (Figure 2c) suggesting a large amountof meltwater production during the daytime. The borehole
water level began to show diurnal signals at the onset of theevent (Figure 2d). The pressure dropped at the end of theevent, coincided with the beginning of clear diurnal oscillations with an amplitude of about 20 m.
[18] Event 3 was caused by the outburst of Gornersee. The
flow speeds at GPS13–16 increased with diurnal variations

and reached their maxima on June 14 (Figure 2a), one day
before the lake discharge peaked (Figure 2d). The magnitude of the uplift at GPS14 and GPS15 was about 0.2 m,
while no significant vertical displacement was observed at
GPS16 (Figure 2b). The large uplift at GPS14 and GPS15
was followed by a similar magnitude of downward motion.
A substantial amount of precipitation (26 mm in total) wasrecorded during this period (Figure 2c). The borehole waterlevel had risen since several days before the onset of the
speed‐up, and the high pressure condition lasted longer after
the event (Figure 2d).
3.2. Ice Motion Deviating Toward the Margins[19] During the speed‐up events, anomalous ice motion
was observed. The trajectory of the stake motion at GPS13
indicates that the ice moved toward the right margin

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F03010Figure 3. Plan view of the stake motion measured with GPS (plus signs) and theodolite (crosses) at(a) GPS13, (b) GPS14, (c) GPS15, and (d) GPS16 from May 15 to June 21, 2005. The flow directions
are from right to left. The gray bands indicate the periods of speed‐up events. The gray line for GPS16
is drawn by filtering the theodolite data with bandwidths of 0.375 d.
(looking down the glacier) during the first half of the eventsand switched back to the original track during the second
half (Figure 3a). In other words, the transverse (cross glacier) velocity component was generated at the onset of theevent, and then the transverse velocity became negative until
it returned to zero after the event. Among the three events,
the deviation from the original track was greatest in Event 3,
but smaller deviations were also recognized in the other two
events. Similar flow changes were observed at GPS14(Figure 3b), although the magnitude was smaller than that at
GPS13. At GPS15 and GPS16, the directions of the flowchanges were opposite to those at GPS13 and GPS14, i.e.,
toward the left margin (Figures 3c and 3d). It was clearlyobserved in Event 3 that the directions of the deviation wereto the right in the right half of the glacier and to the left in
the left half. In the remainder of this paper, we refer to theseice movements in the transverse directions as ‘marginward
ice motion’.
[20] The marginward ice motion coincided not only withthe speed‐up, but also with the surface uplift. Figure 4
shows the trajectories of the stake motion in the verticaland cross glacier (south‐north) directions after removing thelinear trends between the onset and the end of the events.
The detrended trajectories indicate correlations between thetransverse ice motion and uplift. The maximum displace-ment in the transverse and vertical directions occurred at
approximately the same time. The trajectories exhibit hysteresis, but the stake motion basically follows the lines
pointing to the maximum displacements, as represented by
GPS13 during Events 2 and 3 (Figures 4b and 4c). Thus, thetransverse displacement was linearly correlated to the vertical displacement. The direction of the ice motion at eachstake was similar in the three events. For example, thetransverse ice motion at GPS15 was toward the south, andits magnitude was about half of the vertical displacement ineach event. Therefore, the proportion of the transverse to thevertical velocity was approximately the same in the three
events, and the only difference was the magnitude of thedisplacement.
[21] The marginward ice motion gave rise to significant
changes in the transverse strain rate regime. Strain rates
were computed between the survey stakes (GPS13–14,
GPS14–15, and GPS15–16) and the right margin (margin–
GPS13), using the south‐north displacements of the stakes
and assuming no lateral ice movement at the margin where
ice is confined by the sidewall (Figure 5a). The strain rates at
GPS13–14 and GPS14–15 were well correlated throughout
the study period. During the speed‐up events, the strain rates
were tensile (positive) in the first half of the events, andthen reversed to compressive (negative) in the second half.

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F03010erated (second half of the events or morning). The spatial andtemporal variations shown in Figure 5b clearly display such
trends during the study period.

4. Interpretation of the Field Data
4.1. Cause of the Speed‐Up Events[22] The climatic data and subglacial water pressure indicated that the three speed‐up events were related to increased
water input to the glacier bed. Event 1 was caused by the
combination of temperature increase and rainfall as observedin Figure 2c. The glacier reacted to them in a sensitive way,
probably because the hydraulic system was undeveloped at
this time of the season. The uplift during Event 1 was smaller
than those during other events (Figure 2b), which implies
that this event was triggered by a relatively small amount ofwater input.
[23] Event 2 was a typical speed‐up event in the early melt
season triggered by a period with high temperature. It is
likely that a large amount of meltwater drained along theglacier bed and increased the subglacial water pressure as
recorded in the borehole water level (Figure 2d). The pressure began to fluctuate diurnally after this event, suggestingthat the subglacial drainage became more efficient by
opening drainage conduits. The surface snow in the studysite disappeared approximately at this time of the season,
which has been observed to coincide with transformationfrom an inefficient distributed drainage system into a conduit system [Nienow et al., 1998].
[24] It is evident that Event 3 was triggered by the outburst of Gornersee. Its magnitude and rate of uplift weregreater than those during the other two events, as expectedfrom the sudden release of a large amount of lake water tothe glacier bed (Figure 2d). During the outburst event,temporary water storage in the glacier system attained 54%of the total lake water [Huss et al., 2007].
[25] These events showed various interesting responses of
the glacier dynamics to the changes in the subglacial
hydraulic conditions. Nevertheless, here we focus on themarginward ice motion.

Figure 4. Surface ice motion projected on the south‐northvertical plane at GPS13 (open circles), GPS14 (triangles),GPS15 (squares), and GPS16 (plus signs) during (a) Event 1,(b) Event 2, and (c) Event 3. Linear trends between the onset
and the end of the events were removed from the motion. The
GPS and theodolite data were filtered with bandwidths of
0.25 and 0.75 d, respectively.
Superimposed on these changes were diurnal variations,which showed tensile strain rates in the afternoon and compressive strain rates in the morning. These variations in thecentral part of the glacier were inversely correlated to those in
the marginal regions (margin–GPS13 and GPS15–16).
Therefore, the observed changes in the transverse strain rate
were as follows. During the period of velocity increase(i.e., first half of the events or afternoon), the glacier ice wasstretched in the central part and compressed in the marginal
regions. The strain rates were reversed when the ice decel-

4.2. Mechanism of the Marginward Ice Motion[26] The marginward ice motion in Gornergletscher is notunique to the observations made in 2005. Field measurements in Gornergletscher were repeated from 2006 to 2008,
and essentially the same ice motion was observed duringlake outbursts by means of stake measurements and interferometric radar technique [Riesen et al., 2009]. Similar
flow direction changes were recognized in Hansbreen during a speed‐up event [Vieli et al., 2004], although it was notpossible to determine if the flow change was systematically
distributed across the glacier as the survey points werelimited. Direction changes during summer acceleration arereported in Greenland as well [Zwally et al., 2002]. Theseobservations suggest that such ice motion commonly occurs
in other glaciers. The marginward ice motion was clearly
related to the speed up and surface up lift, which werecaused by changes in the subglacial conditions. Based on
the magnitude and the direction of the transverse ice motion
at GPS13–16 together with their close relationship with the
uplift, we discuss a mechanism which connects basal perturbation to the marginward ice motion.

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F03010Figure 5. (a) Time series of transverse strain rate and (b) its distribution across the glacier. Intervals of
the contour lines are 0.25 × 10−4 d−1 with gray lines for negative (compressive) strain rate. The gray bands
indicate the periods of speed‐up events. The GPS and theodolite data used for the strain rate calculations
were filtered with bandwidths of 0.25 and 0.75 d, respectively.
[27] The mean flow vectors during the first half of Event 3(June 11 0000 h–June 14 0000 h) are projected on the verticalglacier cross section along the GPS stations (Figure 6). The
linear trend during the event (June 11 0000 h–June 16 0000 h)
is subtracted from the stake displacement. As a mechanismof this transverse and upward motion, we propose basal
separation beneath the central part of the glacier caused by
locally elevated subglacial water pressure. When the glacier
bed is pressurized above the overburden pressure, the glaciersole is decoupled from the bed. If we assume that the basal
separation is spatially limited in the central part and the ice inthe remaining regions is still in contact with the bed, thesurface moves vertically upward above the decoupled zone
while it moves up and marginward at off‐center locations.
Such surface motion is expected when a point source ofvertical motion propagates through a viscous medium, andcan be understood by analogy with vertical and horizontal
ground motion due to the intrusion of magma [e.g., Mogi,
1958; Walsh and Decker, 1971]. It is most likely that thereversal in the transverse ice motion occurred when the waterpressure dropped and the space created by the basal separation collapsed owing to the ice pressure.
[28] The ice surface motion shown in Figure 6 can be
expected when a subglacial drainage or a highly pressurizedzone is located approximately beneath GPS14. Flow speed
and surface elevation before, during, and after Event 3
provide insights into the location of subglacial drainage dueto the lake outburst. The flow speed profile across the glacier shows that the right side of the glacier was more
accelerated during the outburst (Figure 7a). The surface

uplift was also greater in the right side and the maximum
elevation change was observed at GPS14 (Figure 7b). The
surface lowering after the event at GPS14 and GPS15 implies a closure of the drainage conduit underneath. Theseobservations indicate that the lake water was routed throughthe right side of the glacier and the bed became morepressurized in that region, resulting in enhanced basal ice
motion and separation. A hydraulic potential analysis alsosuggested the location of the main drainage channel in theregion beneath GPS14–15 [Werder and Funk, 2009]. Similar flow speed variations across a glacier have been used to

Figure 6. Vertical cross section of Gornergletscher along
the GPS stations. The mean flow vectors for the first half ofEvent 3 (June 11 0000 h–June 14 0000 h) are projected on
the vertical plane. Linear trends between the onset (June 110000 h) and the end (June 16 0000 h) of Event 3 are subtracted from the flow vectors.

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F03010speed. Our data show that the uplift rates in Event 3 aregreater than those in Event 2, whereas the surface speeds in
Event 3 are smaller than those in Event 2 (Figures 2a and 2b).
Thus, the observed ice motion cannot be explained by basal
separation due to cavity formation. Basal sliding along an
up‐glacier inclined bed slope also causes vertical ice motion[Hooke et al., 1989]. Anderson et al. [2004] found a similar
upward slope (proportion of horizontal to vertical displacement) in surface ice trajectories during two speed‐up eventsin Bench Glacier, Alaska. They suggested sliding over stoss
slopes of bedrock bumps as an interpretation of the verticalsurface motion which was consistent during each event. In
Gornergletscher, upward slopes of the trajectories projected
on a vertical plane along ice motion are not consistent during
each event (Figure 9). For example, the slopes at GPS13–15
during Event 3 are greater than those in Event 2. Because of
the reasons above, we hypothesize basal separation due topressurized water as the key mechanism of the marginward
ice motion.

Figure 7. (a) The mean horizontal flow speed and (b) meansurface elevation before (June 6 1200 h–June 11 1200 h),
during (June 11 1200 h–June 16 1200 h), and after Event
3 (June 16 1200 h–June 21 1200 h). The elevation is measured relative to the surface before Event 3.
estimate basal stress distributions in Haut Glacier d’Arolla[Hubbard et al., 1998; Nienow et al., 2005] and Black
Rapids Glacier [Amundson et al., 2006]. These studies
attributed the changes in transverse flow speed profiles to a
localized subglacial drainage pattern, as we assume here.
[29] The borehole water levels in BH2–5 provide more
direct information on the location of the subglacial drainage
path (Figure 8). The water level was elevated in BH3 during
Event 3, and it began to show clear diurnal variations after
the event. Similar water level variations were observed in
BH4. In contrast to BH3 and BH4, the boreholes near themargins, BH2 and BH5, filled up with water and showed nosignificant variations during the event. Small fluctuations
after Event 3 at BH2 may indicate poor connection to adrainage system, but BH5 showed no evidence of connection. These observations and the borehole locations imply
that the flow path of the lake water was located in the region
beneath GPS13–15, resulting in greater acceleration anduplift in the right side of the glacier. Surface ice motion as a
response to locally elevated subglacial water pressure isdiscussed more in detail in the next section by using a
numerical ice flow model.
[30] The water levels in BH3 and BH4 were nearly equal tothe overburden levels during Event 3 (Figure 8). Thisobservation supports our assumption that basal separation
occurred because of water pressure exceeding the ice overburden. Another mechanism of basal separation is watercavity formation due to ice sliding over bedrock bumps [e.g.,
Röthlisberger and Iken, 1981]. Growth of cavities at spatiallylimited area of glacier bed may cause similar vertical andtransverse ice motion as we discussed above. In this case, therate of surface uplift should be related to the basal sliding

4.3. Strain Rate Regime[31] The transverse strain rate at the glacier center became
tensile during the first half of the events, and turned tocompressive during the second half (Figure 5). These strain
rates are one to two orders of magnitude greater than themean transverse strain rate derived from the summer flow
velocities at GPS13 and GPS16 (5.7 × 10−6 d−1 for theperiod from May 15 to August 25, 2005). Thus, theobserved changes cannot be explained by sudden acceleration or deceleration of ice along a narrowing or widening
valley.
[32] The transverse extension and compression could becaused by longitudinal compression and extension, respectively. Such changes in the strain rate regime may have been
generated by a wave of accelerated ice motion propagating

Figure 8. Time series of water level in the boreholes
BH2–5. The ice overburden level at each borehole site isshown by the dashed line. The gray band indicates theperiod of Event 3.

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F03010SUGIYAMA ET AL.: ICE MOTION DEVIATING TOWARD THE MARGINS

F03010motion was caused by longitudinal compression andextension.

5. Numerical Experiments[34] To test the hypothesis that the marginward ice motion
was generated by locally elevated subglacial water pressure,numerical experiments were carried out by applying a two‐
dimensional ice flow model to the transverse glacier crosssection. The aim of the experiments was to compute verticaland transverse velocity fields in the cross section to investigate whether the model reproduces marginward surface
motion as a response to a subglacial water pressure being
locally higher than the ice overburden pressure.
5.1. Model[35] The cross section of Gornergletscher along the GPS
stations was approximated with a quadratic function forthe bed and a flat surface (Figure 11a). By taking y‐ andz‐coordinates in the transverse and vertical directions,
momentum and mass balance equations in the y‐z plane are

Figure 9. Surface ice motion projected on a vertical plane
parallel to the ice motion at (a) GPS13, (b) GPS14, (c) GPS15,
and (d) GPS16 from May 15 to June 21, 2005. The graybands indicate the periods of speed‐up events.

down the glacier. Downglacier propagation of accelerated
motion has been observed in other glaciers [Kamb andEngelhardt, 1987; Gudmundsson, 2002; Vieli et al., 2004],
and used to interpret short‐term variations in longitudinal
and vertical strain rates [Raymond and Malone, 1986;
Gudmundsson, 2002]. Although changes in the transverse
strain rate were not observed in these studies, longitudinalstrain rate variations during the events should be analyzed asa possible cause of the marginward ice motion.
[33] Longitudinal strain rate was computed for the periodof Event 3 from the horizontal flow speed measured by thetheodolite at stakes 12 and 24. The result was comparedwith the transverse strain rate from the GPS data to assess
whether the transverse extension and compression werecounteracted by longitudinal compression and extension,respectively (Figure 10). The flow speed at stake 24 wasgreater than that at stake 12, except for a short period in the
middle of the event (Figure 10a). From June 13 to 14, thespeed at stake 12 exceeded that at stake 24, resulting in thereversal of the longitudinal strain rate from compressive totensile (Figure 10b). The strain rate then became compressive toward the end of the event as the speed decreased atstake 12. If this strain rate reversal was the cause of themarginward ice motion, an inverse correlation should beobserved between the longitudinal and transverse strain
rates. However, the observed strain rates do not support thishypothesis (Figure 10c). Moreover, the transverse strain rateis one order of magnitude greater than the longitudinal strain
rate. Therefore, it is not likely that the marginward ice@yy @yz
þ
¼ 0;
@y
@z

ð1Þ

@zy @zz
þ
¼ g;
@y
@z

ð2Þ

@uy @uz
þ
¼ 0;
@y
@z

ð3Þ

and

Figure 10. (a) Time series of horizontal flow speed atstakes 12 (black) and 24 (gray bold), (b) longitudinal strain
rate at stakes 12–24, and (c) transverse strain rates at
GPS13–14 and GPS14–15. The GPS and theodolite data
were filtered with bandwidths of 0.25 and 0.375 d, respectively. The gray band indicates the period of Event 3.

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F03010SUGIYAMA ET AL.: ICE MOTION DEVIATING TOWARD THE MARGINS

F03010where "_ ij and t ij are the components of the strain rate anddeviatoric stress tensors, respectively, and t e is the effective
stress. We took n = 3 for the flow‐law exponent and A =75 MPa−3 a−1 as a value of the rate factor for a temperateglacier [Gudmundsson, 1999]. In Gornergletscher, the extent
of the cold ice in the modeled cross section was estimated as
300 m wide and 100–200 m thick [Ryser, 2008; Eisen et al.,2009]. For simplicity of the model, the influence of the coldlayer on A was not considered here.
[36] Equations (1)–(4) were solved for uy and uz with thefinite element method. The code was originally developed
for longitudinal ice flow modeling [Sugiyama et al., 2003]
and tested in the benchmark experiments for higher‐orderand full‐Stokes ice sheet models (ISMIP‐HOM) [Pattyn
et al., 2008]. The nonlinear ice rheology was taken into
account by computing the effective stress in an iterative way
until the velocity solution converged. Furthermore, theeffect of the ice flow downglacier was included by solving
the momentum balance along the flow line (x‐direction),@xy @xzþ¼ g sin :
@y
@z

ð5Þ

The surface slope sin = 0.04 was taken from the map ofGornergletscher with a length scale of ice thickness. The
shear stresses sxy and sxz obtained from equations (4) and(5) were used to compute the effective stress t e. The
effective stress was updated by iterating the two partial
differential equation systems (1)–(4) and (4)–(5) until thevelocity field (uy, uz) converged.
[37] The modeled domain was discretized with 224 triangular quadratic elements as shown in Figure 11a. Spatial
resolutions at the glacier center were 50 and 25 m in thehorizontal and vertical directions, respectively. The stress‐
free boundary condition was imposed on the glacier surface.
The bottom boundary nodes were fixed (uy = uz = 0) except
for those located in a central region defined by y0 < y < y1(pressurized zone). For the pressurized zone, instead of the
fixed boundary condition, a stress boundary condition was
imposed along the glacier sole:

Figure 11. (a) Vertical cross section of Gornergletscher
along the GPS stations GPS13–16 (looking downglacier)and a finite element mesh used for the numerical experiments. Flow vectors computed by (b) Experiment 1 and(c) Experiment 2. The bold lines at the glacier bed indicate
the locations of the pressurized zones. (d) Horizontal(solid) and vertical (dashed) surface velocities in Experiment 1 (bold) and Experiment 2 (thin). The velocities in
Figure 11d are normalized with the maximum verticalvelocities.
where sij are full stresses, r = 910 kg m−3 is the density ofice, g = 9.81 m s−2 is the gravitational acceleration and uy
and uz are transverse and vertical velocities. The constitutive
equation is given by Glen’s flow law [Glen, 1955],"_ ij ¼ Aen1 ij ;ð4Þny yy þ nz zy ¼ ny pw ðyÞð6Þ

ny yz þ nz zz ¼ nz pw ðyÞ:ð7ÞThe normal vector n = (ny, nz) is pointing outward from theglacier sole, and the subglacial water pressure pw(y) is givenaspw ðyÞ ¼ pi ðyÞ;ð8Þ

where pi is the ice overburden pressure and the constant a
was prescribed so that the magnitude of the vertical velocity
at the glacier surface became similar to the observation in
Gornergletscher. We assumed that the water pressure wasgreater than the ice overburden pressure (a > 1) in thepressurized zone, which led to basal separation and surface
uplift.
5.2. Results and Discussion[38] Figure 11b shows the flow vectors obtained for a
200‐m wide pressurized zone located at the glacier center

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F03010SUGIYAMA ET AL.: ICE MOTION DEVIATING TOWARD THE MARGINS

Figure 12. Surface flow vectors computed by Experiment 3(black thin) and measured during the first half of Event 3(June 11 0000 h–June 14 0000 h) (gray bold). Linear trends
between the onset (June 11 0000 h) and the end (June 160000 h) of Event 3 are subtracted from the measured flow
vectors. The bold line at the glacier bed indicates the location of the pressurized zone. The shaded area shows theactual glacier cross section along the GPS stations.
(Experiment 1: y0 = −100 m, y1 = 100 m, a = 1.138). The
vertical basal motion is transmitted to the surface and causes
uplift in a region broader than the pressurized zone. The
surface flow vectors have horizontal components of uy > 0 at
y > 0 and uy < 0 at y < 0, resulting in ice motion toward themargins as observed in Gornergletscher. This result indicates that a locally elevated subglacial water pressure
generates marginward ice motion as well as uplift on theglacier surface. When the pressurized zone is extended
closer to the margins (Experiment 2: y0 = −500 m, y1 = 500 m,
a = 1.0125), the direction of the surface ice motion is morestraight upward and the transverse motion is less significant
near the glacier center (Figure 11c). The surface velocity
distributions show transverse velocity peaks near the edgesof the pressurized zone (Figure 11d). The peak locations are
100 m outside of the pressurized zone (y = y0 − 100 m andy1 + 100 m) in Experiment 1, yet 100 m inside (y = y0 + 100 m
and y1 − 100 m) in Experiment 2. The magnitude of thetransverse peak velocities are 33% of the maximum verticalvelocity in Experiment 1 and 26% in Experiment 2.
[39] We repeated the experiment by changing the valuesof y0, y1, and a to obtain surface flow vectors similar to
those observed during the first half of Event 3. A reasonableagreement with the observation was achieved by taking y0 =−100 m, y1 = 500 m, and a = 1.033 (Experiment 3) asshown in Figure 12. The important features in the observation, such as nearly vertical motion at GPS14, marginward ice motion at GPS13 and GPS15, and relatively
smaller motion at GPS16, were well reproduced by themodel. The location of the pressurized zone prescribed inExperiment 3 is consistent with the discussion in the previous section. The model assumes that the flow path of thelake water is located in a region beneath GPS13–15, assuggested by the velocity change and uplift data (Figure 7)
and the borehole water levels (Figure 8).
[40] A perfect agreement with the field data was not feasible since the assumed bottom boundary condition was too
simple to simulate complex subglacial conditions. Moreover,the influence of the cold ice body was not considered andthe elastic component in the ice mechanics was neglectedin the model. Nevertheless, our experiments confirmed that

F03010the marginward motion occurs when the subglacial waterpressure is locally elevated slightly above the ice overburdenpressure.
[41] Another important aspect of the modeling results isthe transmission of the ice motion from the bed to the surface. Such a problem has been investigated earlier for thetransfer of basal sliding to horizontal surface motion [e.g.,
Balise and Raymond, 1985], but never studied for the basal
separation and surface uplift. The flow vectors obtained byExperiments 1 and 2 clearly show that a greater portion of
the vertical velocity is transferred to the surface when abroader pressurized zone is given (Figures 11b and 11c).
The ratios of the surface to the basal vertical velocities at y =0 are 0.36 and 1.07 for Experiments 1 and 2, respectively.
Our numerical experiments indicate that the magnitude ofsurface uplift is not necessarily equal to the separation
underneath the glacier, even if vertical strain of ice is negligible. Therefore, care should be taken when the magnitudeof the basal separation is discussed from a point measurement on the surface. However, if the measurements arecarried out at multiple locations across the glacier, spatial
variations of the uplift and transverse motion can be used asa tool to estimate the location and magnitude of basal separation and distribution of subglacial water pressure.

6. Conclusion[42] This study reports ice motion deviating toward themargins observed in Gornergletscher during three speed‐up
events in summer 2005. The high‐frequency GPS measurements showed that the transverse velocity component
increased as the glacier accelerated, resulting in ice motion
toward the margins. The transverse ice motion reversed
direction during the second half of each event, so that thesurvey stakes switched back to their original track. Four
GPS receivers installed across the glacier revealed that themagnitude and the direction of the transverse velocity
component were distributed systematically across the glacier. Our measurements also indicate that the transverse
motion was correlated with surface uplift.
[43] Based on the detailed analysis of the transverse andvertical velocities, we propose the following mechanism forthe marginward ice motion. When a limited part of theglacier bed is pressurized above the ice overburden pressure,the ice sole decouples from the bed and the vertical ice
motion is transmitted from the bed to the surface. As thevertical basal motion propagates through the ice, transverse
velocity components are generated, as also observed inground motion during magma intrusion. The location of thesubglacial drainage path estimated from the velocity change,
uplift magnitude, and subglacial water pressure is consistent
with this hypothesis.
[44] Numerical experiments with a two‐dimensional ice
flow model confirmed that the marginward ice motion occurs when the subglacial water pressure locally exceeds theice overburden pressure. The measured surface flow vectors
were well reproduced by tuning the location and magnitudeof a high pressure zone at the bed. The location of thepressurized zone assumed in the model was in good
agreement with the drainage path suggested by the surface
speed and subglacial pressure measurements. Our observations and the modeling results reinforce our understanding

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F03010SUGIYAMA ET AL.: ICE MOTION DEVIATING TOWARD THE MARGINSof glacier dynamics, and create a possibility to quantify the
distributions of basal separation and subglacial water pressure from surface observations.
[45] Acknowledgments. We would like to thank the members of the
field campaign at Gornergletscher in 2005. The lake‐discharge data was provided by M. Huss. We are grateful to R. Greve and H. Blatter for insightfulcomments on the manuscript, and M. Truffer for helpful discussion. The
paper was improved by careful reviews from D. Mair, R. S. Anderson,
and an anonymous reviewer. S. Braun‐Clarke and S. Hesse corrected theEnglish. This research was funded by the Swiss National Science Foundation grant 200021‐103882/1.

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