Journal of Glaciology, Vol. 50, No. 170, 2004

Short-term variations in glacier flow controlled bysubglacial water pressure at Lauteraargletscher,
Bernese Alps, Switzerland
1

2

Shin SUGIYAMA,1;2 G. Hilmar GUDMUNDSSON2;3

Institute of LowTemperature Science, Hokkaido University, Sapporo 060-0819, Japan
Versuchsanstalt fu«rWasserbau, Hydrologie und Glaziologie (VAW), Eidgeno« ssischeTechnische Hochschule, ETH-Zentrum, CH-8092 Zu«rich,
Switzerland
E-mail: sugiyama@vaw.baug.ethz.ch
3
British Antarctic Survey, Natural Environment Research Council, Madingley Road, Cambridge CB3 0ET, England

ABSTRACT. Short-term variations in horizontal and vertical surface motion werestudied with high temporal resolution during the ablation season in Lauteraargletscher,
Bernese Alps, Switzerland. Horizontal surface flow speed oscillated diurnally, showing acorrelation with the water level in a borehole. Flow speed increased as a function of thewater level, with an asymptote at the ice overburden level. This observation implied thatthe flow variations were principally controlled by the local water pressure which
enhanced basal motions. Detailed examination of the diurnal variations, however,showed that the speed was larger when the pressure was increasing than when it was
decreasing. Greater speed with increasing pressure was interpreted by subglacial watercavity opening and/or longitudinal stress coupling with the upper reaches of the glacier.
Upward surface movements were observed when the glacier flow speed increased. Simultaneous measurement of internal vertical strain in a borehole showed that the uplift had
two different sources: vertical straining of ice and volume increase of subglacial water cavities. The vertical surface movement was largely affected by the vertical strain, and theuplift events could not be simply attributed to cavity opening.

INTRODUCTION
Horizontal flow velocity in a temperate valley glacier varies
over short periods of time during the ablation season (e.g.
Willis, 1995). In the extreme case, a heavy rainstorm or asudden drainage of a supraglacial lake can cause a doublingof velocity within a few hours (Naruse and others, 1992;
Gudmundsson and others, 2000; Mair and others, 2001;
Truffer and others, 2001). In this paper, we call this type ofsudden velocity increase in a period of hours to days amotion event. Intra-annual flow variations in temperateglaciers are caused by changes in basal conditions, in particular, by changes in subglacial water pressure. Water pressure is controlled by subglacial hydraulic conditions, surface
melt rate and precipitation, all of which give rise to complex
spatial and temporal flow variations.
Surface flow speed has been measured together with
subglacial water pressure in various glaciers, mostly using
conventional survey instruments operated daily to several
times a day. Results showed that glaciers accelerate as waterpressure increases, and maximum speed appears to coincidewith maximum pressure (Iken and Bindschadler, 1986;
Kamb and Engelhardt, 1987; Jansson, 1995). Despite theseclear correlations between flow speed and water pressure,sub-hourly velocity variations obtained by automatic distance measurement at Storglaciren, Sweden, were not directly related to basal water-pressure variations (Hanson andothers, 1998). In the basal sliding measurement with a dragspool at Trapridge Glacier, Canada (Blake and others,1994),
maximum sliding speeds coincided with rises in water pressure but not with pressure peaks. These high-frequency
measurements imply that the reaction of glacier flow topressure change is complex and its detail is obscured when
the temporal resolution of measurements is not sufficiently
high.
Surface speed increases are thought to be the result ofenhanced basal motion due to bed lubrication, cavity formation (Lliboutry,1968; Iken,1981; R˛thlisberger,1981; Fowler,1987) or the weakening of subglacial sediments (Boultonand Hindmarsh, 1987; Iverson and others, 1995). Although
greater basal motion is expected under high water pressure
for each of these processes, the exact pressure dependence ofthe flow speed seems to be different in each process. Numerical simulation by Iken (1981), for example, suggested that the
maximum sliding speed occurs not at the highest pressure,but when basal cavities are growing. For the bed deformation
process, subglacial measurements at Storglaciren implied
negative correlation between water pressure and strain rateof the sediments (Iverson and others,1995). It is implied thatdifferent basal processes give rise to different relationships
between flow speed and water pressure. Thus, the detailed
examination of flow speed and pressure variations based ona high-frequency velocity measurement is crucial to thestudy of basal flow processes.
Associated with short-term flow variations is the upward vertical movement of a glacier surface, commonly353

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher
FIELD MEASUREMENTS
Study site
Lauteraargletscher is part of a temperate valley glaciersystem in the Bernese Alps, Switzerland. It originates atabout 3000 m a.s.l. and merges with Finsteraargletscher at
2400 m a.s.l. into the common tongue of the glacier system,
Unteraargletscher. Below the confluence area, Unteraargletscher descends eastward to the terminus situated at2000 m a.s.l. (Fig. 1a). Unlike the lower part of the glaciersystem, where a thick debris layer covers the surface, Lauteraargletscher has a clean surface. FromJune to October 2001,
a camp was set up on Lauteraargletscher at 2480 m a.s.l. todrill boreholes and to conduct glacier flow measurements.
The snowline passed by the camp in late July and reachedapproximately 2600 m a.s.l. at the end of the ablation season
in 2001.
GPS survey

Fig. 1. (a) Map of Unteraar-, Finsteraar- and Lauteraargletscher and (b) the study site. Contour lines and broken contour
lines indicate the surface and bed elevation, respectively, in m.
Coordinates are from the official Swiss coordinate system.

called ‘‘uplift’’. Iken and others (1983) observed gradualuplift of 150 mm coinciding with increased flow speed at
Unteraargletscher, Switzerland, at the beginning of the melt
season. They proposed the idea that growth of subglacial
water cavities induced the uplift. Uplift was also observedat Variegated Glacier, Alaska, U.S.A., during motion events
called ‘‘mini-surges’’. The uplift was again interpreted interms of water-cavity growth (Kamb and Engelhardt,
1987). To confirm that uplift is caused by growth of basal
cavities, vertical strain must be measured with high temporal resolution. However, only a few such measurements havebeen reported (Harrison and others, 1993; Gudmundsson
and others, 1997; Gudmundsson, 2002), and clear evidence
indicating the mechanism of uplift has yet to be obtained.
This paper reports on glacier flow measurements withtemporal resolution of 1hour, using the global positioning
system (GPS) technique. Measurements at Lauteraargletscher, Switzerland, through the 2001ablation season display the details of a motion event and diurnal flow
variations under the control of basal conditions. The relationship between the surface flow speed and subglacial
water pressure is examined and the causes of uplift are determined from vertical-strain measurements.
354

A 6.5 m long aluminum pole was installed into the glaciersurface at site 313 (Fig. 1b), and the three-dimensional position of the pole was surveyed with GPS by the static relative
positioning technique (Hofmann-Wellenhof and others,
2000). One of the GPS receivers (TOPCON GP-SX1) was
fixed on the top of the pole, and the other one on bedrockon the left bank of the glacier as a reference station. L1phasesignals from GPS satellites were continuously collected by
the receivers and stored in data loggers to obtain hourly positions of the pole relative to the reference station by commercial software (TOPCON WAVE). The two receivers wereseparated by 700 m in the horizontal and 100 m in the vertical direction, and this relatively short baseline length was
crucial for obtaining high accuracy in the GPS measurement. A control experiment carried out with a baseline
length of 120 m and vertical separation of 12 m showed random positioning errors of 1.4 mm in the horizontal and
2.8 mm in the vertical direction.
On the glacier, the survey pole froze in the ice after the
installation because the subsurface ice layer was cold owing
to low air temperature during winter. The pole above thesurface was maintained at a length shorter than 1.5 m. Accordingly, measurement errors due to the leaning of the polecaused by ice melting or wind blowing were assumed to be
negligible. Because the measurement gives the position of aparticle of ice near the glacier surface, the surface velocity
or displacement refers to the movement of such particles,
and surface ablation is not relevant to the measured verticaldisplacement in this study.
Continuous GPS surveys were carried out during four
periods, each of 1^2 weeks in duration, from June to
October 2001. For these periods, hourly horizontal flow
speed was calculated from a 4 hour running mean of thehorizontal displacement of the pole. The minimum width
to remove high-frequency fluctuation from the data was 2hours of averaging time window. When the continuous survey was interrupted for a few hours, which mostly occurred
as a result of discharged batteries, data gaps were interpolated by spline interpolation.
Assuming a horizontal positioning error of 1.4 mm and adisplacement rate of 5 mm h^1, error propagation analysis
gives a relative error of 28% for hourly speed. However,
the actual error is hard to estimate because of the averaging
process and uncertainty in the positioning error.

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher
Borehole length
A 300 m deep borehole was drilled with the hot-water technique at about 200 m from the GPS measurement site
(Fig. 1b). Ice thickness was estimated to be 400 m fromradio-echo soundings and by drilling to the bed. In order
to measure the vertical strain of the ice, borehole length
was measured one to eight times a day with the magnetic
ring technique (Gudmundsson and others, 1997; Gudmundsson, 2002). A ring-shaped magnet was mounted outside a 1m long, 56 mm diameter plastic pipe and installed at
the bottom of the borehole.When a magnetic sensor fixed at
the end of a measuring tape was lowered into the borehole, asignal indicated the position of the magnet, so that the distance from the magnetic ring to a reference bar fixed on theglacier surface could be measured. The elastic stretching of
the measuring tape made of Teflon was negligibly small andits thermal expansion was ignored based on the stable temperature of the water-filled boreholes. Judging from the deviations in repeated measurements and daily inspection of
the magnetic sensor with a reference magnet installed 1m
deep in a borehole, measurement error was estimated to be3 mm.
Changes in the borehole length are due to the horizontal
shear and the vertical strain of the ice. Assuming simple
shear deformation and Glen’s flow law with the parametern ¼ 3, the extension rate of an originally vertical borehole
was estimated at 4  10^6 m d^1 for a 300 m borehole which
was smaller by three orders of magnitude than measured
length changes. The contribution of the shear strain to borehole-length changes was thus neglected.
Borehole measurements were carried out from 25 June
to 5 July and from 18 July to 1 August using the same borehole and magnet. The borehole closed in late August at
173 m depth below the surface, probably because the waterlevel in the borehole was too low to counteract the hydrostatic pressure of the ice. Without signals from the magnetic
ring, the measurement was continued by sensing thepinched-off point with the measuring tape from 24 to
26 August. When the magnetic sensor sat on the boreholebottom, the tension of the tape reduced as the weight of thesensor and tape was supported by the ice. The measuring
tape was read when the tension was decreased. Because successive measurements did not show monotonic shortening,
we attributed borehole-length changes to the vertical strain
but not to freezing or closing at the bottom. Repeated measurements showed the reliability of the reading was 5 mm.
The borehole closed again at 119 m in September and wasmeasured with the same method from 28 September to
2 October.
Water pressure
From 30 June to 28 September, water level was measured
every 10 min in a 380 m deep borehole at the study site
(Fig. 1b). A vibrating-wire pressure transducer (Geokon
Model 4500) was installed 100 m above the bed. The accuracy of the pressure measurement was equivalent to a waterlevel of 0.35 m. Two more transducers were installed in twoother boreholes, one close to the borehole-length measurement site and the other near the right margin of the glacier.
Water levels in the three boreholes fluctuated in phase,showing connections to a common subglacial drainage
system. Because these two boreholes were disconnected

Fig. 2. Stake movement in the vertical plane (diamonds) anddaily variation of surface speed against horizontal displacement obtained by GPS measurement, 15 June^2 October
2001.
from the drainage system in early August, only the dataobtained from the 380 m deep borehole are presented here.
Air temperature and precipitation
A meteorological station was established on the left bank of
Unteraargletscher at 2400 m a.s.l. (Fig. 1a). Air temperatureand precipitation were measured from 13 June to 30 September at 30 min intervals with a ventilated thermistor sensor(Vaisala T107) and with a tipping bucket rain gauge (JossTognini), respectively.
RESULTS
Figure 2 shows the vertical displacement of the survey stake,and daily variation in horizontal speed, during the study
period. The vertical movement of the stake was generally
downward from June to October, but clear upward movements were observed in June and July. Both of the uplift
events were accompanied by sharp increases in horizontal
speed. Details of short-term fluctuations in horizontal speed
and vertical movement during four measurement periods
are shown with water level, borehole length and meteorological data in Figure 3.
Period I (25 June^5 July)
During the first period, 25 June^5 July, snowline elevation
was approximately 2400 m a.s.l. and the study site was still
covered with 1^2 m of snow.
The main feature of the flow variation in this period is amotion event on 27 June. After a period of fine weather withsurface ablation of 30^50 mm w.e. d^1, a heavy rainstorm
started at 1500 h on 27 June and precipitation reached
6.3 mm h^1 at 1800 h. Horizontal flow speed started to increase at 1700 h and a maximum speed was recorded at
2200 h. As the flow speed reached its maximum, the glaciersurface rose by 20 mm within a few hours. Borehole length
decreased by 5 mm over the night of the motion event, incontrast to the steady increase until 27 June.
Period II (21^27 July)
After the cold weather with snow precipitation from 18 to355

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher

Fig. 3.Time series of data during periods I^IV. (a) Horizontal flow speed of the stake (thin solid line) and water level in the borehole(bold line).The dash-dotted line indicates the overburden level. (b) Vertical displacement of the stake (solid line) and borehole length(diamond and dotted line). (c) Air temperature (solid line) and precipitation.
20 July, 50^70 mm w.e. d^1 of surface ablation took place for10 days. Glacier surface conditions turned from water-saturated snow to bare ice, and many moulins opened aroundthe study site.
Clear diurnal oscillations in the surface speed wereobserved from 22 to 25 July, with maximum and minimumin the evening and early in the morning, respectively. The
water level also showed diurnal variations. It rose above
the overburden level in the evening, and the daily maxima
coincided with peaks in the flow speed. Vertical displacement of the glacier surface appears to correlate with borehole-length variation during this period.

Diurnal oscillation in the flow speed was still observed,
but both amplitude of the oscillation and daily mean speed
were smaller than those observed in July. The water levelchanged by 4100 m d^1 in a diurnal manner and it neverexceeded the overburden level. The borehole measurement
confirmed that the borehole length varied diurnally. Diurnal signals were also found in surface elevation, low in thedaytime and high at night. Surface speed, vertical displacement, water level and borehole length all appear to oscillate
in phase throughout this observation period.
Period IV (28 September^3 October)

Period III (22^27 August)In late August, the snowline was about 1km up-glacier fromthe study site. Fine weather caused surface ablation of 40^
60 mm w.e. d^1, and the meltwater was fed into the moulins
that were well developed by this time.
356

The study site was covered with 0.5 m of fresh snow, and surface ablation was small, when the measurements were restarted on 28 September. Surface flow speed was low,
without diurnal signals, and borehole length increased
monotonically.

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher

Fig. 4. (a) Horizontal surface speed against water pressure measured from 21 to 27 July 2001 (solid symbols) and from 22^27 August
2001 (open symbols). (b) Same data as (a), but with the speed obtained when the effective pressure was decreasing (open symbols) andincreasing (solid symbols).The lines are regression curves for the different phases of the pressure change.
INTERPRETATION
Relationship between water pressure and surface
speed
Horizontal surface speed fluctuated diurnally in July andAugust, when substantial meltwater was produced on thesurface. Surface speed oscillated in phase with the borehole
water level, implying that high water pressure enhanced
basal motion. In order to examine the effect of the subglacial water pressure on the flow-speed change, hourly surface speeds measured in periods II and III are plottedagainst the effective pressure Pe in Figure 4. The effective
pressure was obtained from the measured water pressure
Pw and the ice overburden pressure Pi determined by theice thickness ðPe ¼ Pi  Pw Þ.
A scatter plot of the data obtained in the two observation
periods shows that the surface speed increases as theeffective pressure approaches zero (Fig. 4a). This relationship is similar to the observation at Findelengletscher, Switzerland (Iken and Bindschadler,1986), atVariegated Glacier(Kamb and Engelhardt, 1987) and at Storglaciren (Jansson, 1995). Presumably, basal ice decoupled from the bed
when the overburden pressure was cancelled by subglacial
water pressure. Although the flow speed appears to correlate with the effective pressure in Figure 4a, the speed scatters over a broad range of up to 20^30%. This scattering
can be attributed partly to GPS measurement errors; however, Figure 4b reveals two distinct relationships. Figure 4b
plots the same dataset as in Figure 4a, but with the data
points grouped according to whether the effective pressure
is decreasing or increasing. It appears that the surface speed
is larger when the effective pressure is decreasing, i.e. thesubglacial water pressure is increasing. To test this hypothesis, two regression models, (1) common regression for allof the data and (2) separate regression for each of the pressure-increasing and -decreasing periods, were compared bya standard statistical method, the F-test (Weisberg, 1985).
After the data of negative effective pressure were removed,
flow speeds and effective pressures were log-transformed tofit a power function ðus ¼ kPe Þ, where us is the surface
speed, Pe is the effective pressure and k and  are regression

Fig. 5. Horizontal surface speed against water pressure connected in a time sequence from 24 July 1130 h to 26 July 1230 h (a) and from
24 August 1030 h to 26 August 0330 h (b).
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Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher

Fig. 6. One-diurnal-cycle composite diagrams constructed by stacking the data from 22 July 0600 h to 27 July 0600 h (a) and from
23 August 0600 h to 27 August 0600 h (b).Vertical displacement shows surface elevation relative to the mean elevation of a day.
parameters. The F-test for model (1) against (2) showed asignificance level much smaller than 0.01, providing strong
support for model (2).
Flow-speed variations were examined in detail by connecting the data in a time sequence for the periods 24^
26 July and 24^26 August (Fig. 5). Connected lines show
clear hysteresis loops in the counterclockwise direction.
Although the loops vary in shape from day to day, the speed
is consistently smaller when the effective pressure increases.
This cannot be ascribed to uncertainties in the measurements, since the control experiment of GPS measurement
showed only random errors.
Our observation does not contradict the direct correlations reported from the three other glaciers mentioned
above, because such a precise feature may have been obscured in the measurements with low temporal resolutions.
The relationship in Figure 4a implies that basal motion at
the study site was generally related to the effective pressure
as previously suggested. Nevertheless, the relationship forthe pressure-increasing period differs from that for the decreasing period.
To further discuss the hysteresis loops in Figure 5, a composite day’s time-series plots were constructed for the time
periods showing clear diurnal variations inJuly and August.
Flow speed, water level and surface vertical displacementfrom 22 July 0600 h to 27 July 0600 h and from 23 August
0600 h to 27 August 0600 h were stacked by averaging at
each time of day (Fig. 6). Displacement relative to the meansurface elevation of a day was used for the vertical displacement. Important features observed in both periods are:(A) Horizontal flow speed decreases when water level
drops at a greater rate than the speed increases whenwater level rises.
(B) The maximum horizontal speed coincides with the
maximum water level.
(C) The maximum horizontal speed occurs during uplift
before vertical displacement reaches its peak.
(D) The peak in water level slightly precedes the peak invertical displacement.
358(A) is equivalent to the findings in Figures 4b and 5.Thisfeature is less clear in July, but can be recognized when
speeds are compared before and after the peak at the samewater level. (B) is distinct from the results of the previously
reported high-frequency measurements. Hanson and others(1998) obtained maximum surface speeds generally before
pressure peaks, and Blake and others (1994) found enhanced
basal motion coincided with increased pressure. (C) showsthat the maximum speed occurred when the surface waselevated but not when it was at the highest elevation.
Because vertical surface movement can be attributed to thevolume change of subglacial water cavities or vertical strainover ice thickness, (C) implies that the increase in the surface speed was linked to cavity formation or change in thestrain regime. Based on these inspections, we suggest two
processes that may cause the characteristic diurnal flow
variations at Lauteraargletscher.
One of the possible processes is basal sliding with cavity
formation. Iken (1981) investigated basal sliding on a wavy
bedrock while water-filled cavities were growing or shrinking. The main finding of this numerical modeling was thatthe largest sliding velocity occurred when cavities weregrowing rather than at the steady state with their maximum
size. This result is consistent with the field measurements on
Unteraargletscher (Iken and others, 1983) showing that thelargest surface speed coincided with the highest rate of uplift. Observation (C) agrees with these previous studies, suggesting that growing cavities enhanced basal motion in
Lauteraargletscher. Iken’s modeling also predicted that asmall fall in water pressure below the steady-state valuecauses a rapid decrease in the sliding velocity. This prediction is consistent with observation (A) and thus it can interpret the hysteresis loop. (D) does not perfectly conform to
the general idea that cavities expand when water pressure
increases. Presumably, cavity evolution under the transientstate of water pressure is difficult to estimate.
The above interpretation is plausible if we regard thevertical surface movement as a result of the volume changeof water cavities. However, vertical strain also affects thesurface elevation, and borehole-length measurements show
this happening in the time period 24^26 August (Fig. 3b). If
the diurnal uplift was caused by the vertical strain, it is expected that the flow-speed gradient along the flowline

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher

Fig. 7. Horizontal surface speeds measured at the study site
(dotted line), 1.5 km up-glacier (thin solid line) and 1.5 km
down-glacier (bold line).
varied diurnally. Figure 7 shows surface velocities measured
at the borehole-length measurement site, 1.5 km up- anddown-glacier from the study site, with GPSs operated ninetimes a day.These GPSs were operated independently of theone at site 313, with another reference station fixed near themeteorological station. Because positioning error in thesemeasurements was larger than that at site 313 owing to thelonger distance to the reference station, flow speeds werecomputed after smoothing the data with the kernel regression method.The amplitude of the diurnal variation is larger
in the upper region, implying that enhanced compressive
flow contributed to the uplift as the surface speed was increasing. Hence, an alternative interpretation of the hysteresis loop is proposed as follows. Flow speed was generally
controlled by the local water pressure (observation B). As asecondary effect, flow speed was increased by longitudinal
stress conveyed from the upper reach during the upward surface movement. The upward movement occurred mostly
when water pressure was increasing (observation D), consistent with the greater speed with increasing pressure.
Hanson and others (1998) found that surface speed increased earlier than water pressure in the lower part of Storglaciren and attributed this observation to the longitudinal
stress coupling with the upper region of the glacier. Theirstudy suggests the importance of a spatially varying basal
condition to short-term flow variations in temperate valley
glaciers. Fischer and Clark (1997) proposed stick^slip sliding
behaviour to interpret the maximum sliding rate at increasing water pressure measured at the bed of Trapridge
Glacier. We do not consider this process applicable to ourobservation, because Lauteraargletscher is underlain byhard bedrock (Knecht and Sˇsstrunk, 1952; Funk andothers, 1995), while the proposed model assumed a deformable bed. We conclude that the variations in surface flow
speed at Lauteraargletscher were principally controlled bysubglacial water pressure. In addition, basal motion
enhanced by cavity formation and/or stress coupling toupper reaches of the glacier caused the characteristic relationship between surface flow speed and subglacial waterpressure.

Fig. 8.Vertical displacement of the stake (cross and solid line)
and borehole length (diamond with error bar and dotted line)
measured in periods (a) I, (b) II, (c) III and (d) IV. Effectof basal sliding on the vertical movement is excluded from thevertical displacement, as described in the text.
The relationship (us ¼ kPe ; us in mm d^1 and Pe in
MPa) obtained by data fitting in this study was comparedwith those in other glaciers. Jansson (1995) found the same
regression parameter  ¼ 0:40 in Storglaciren and in
Findelengletscher (Iken and Bindschadler, 1986) and suggested the possibility of a common basal flow process. Linear regression on the two pressure-transition phases gave
k ¼ 110 and  ¼ 0:18; with a correlation coefficient of
r ¼ 0:66 for the effective-pressure decreasing phase andk ¼ 86 and  ¼ 0:20 with r ¼ 0:68 for the increasingphase (Fig. 4b). Presumably, the relationship is not entirely
related to the basal processes and it varies in space and timewithin the same glacier, reflecting the influence of both
local and surrounding subglacial conditions.
Uplift mechanism
From June to August, conspicuous vertical surface movements were observed, such as the sudden uplift by a few
359

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher

Fig. 9. (a) Water level in the borehole measured from 30 June to 28 September.The dash-dotted line indicates the overburden level, and theshaded bands show the periods of the GPS and borehole-length measurements. (b) Air temperature (solid line) and hourly precipitation
recorded at the meteorological station.
centimeters on 27 June and the diurnal upward and downward movements observed in August. The measured vertical displacements are much larger than the estimatedmeasurement error.
The vertical component of surface velocity ws is given as_ þ V_ ;ws ¼ ub tan  þ h"ih

ð1Þ_ is vertical strain rate averwhere  is bed inclination, h"iaged over the glacier thickness and V_ is the vertical component of basal cavity opening rate (Hooke and others,1989). The first term on the righthand side of Equation (1)was estimated from the vertical surface velocity and theaverage vertical strain rate over the period 25 June^
1 August. The rate of the volume change of basal cavities
during this period was assumed to be zero. Substitution of_ ¼ 1:8 mm d^1 and V_ ¼ 0 in Equaws ¼ 6:3 mm d^1, h"ihtion (1) yields ub tan  ¼ 8:1 mm d^1 for the mediumterm contribution of basal sliding to surface vertical movement. After subtraction of this steady downward movement,
surface elevation was compared with borehole lengthchange (Fig. 8). It is debatable whether the 300 m boreholelength change accurately represents the vertical strain overthe glacier thickness, since measurements in the boreholes
with different depth showed that the vertical strain rate
was not uniform from the bed to the surface (Sugiyama
and Gudmundsson, 2003). As a rough approximation, however, we take the strain measured in the upper 300 m as thetotal strain over the whole thickness.
For the motion event on 27 June, the upward movementof the surface cannot be ascribed to vertical straining sinceborehole measurements show slightly compressive verticalstrain during the uplift from 27 to 28 June (Fig. 8a). Thisimplies that the uplift was caused by the volume increase of
subglacial water cavities. It should be noted that the coincidence of the surface speed peak with the maximum rate ofvertical displacement, rather than the maximum elevation(Fig. 3a and b), conforms to Iken’s theory of cavity formation discussed before. After the motion event, the surface
360

started to move downward, suggesting a closing of the cavities. Over the night of 30 June/1 July, the borehole length
increased by 50 mm and the surface moved upward at thesame time. This uplift appears to be a consequence of vertical stretching.
In period II (Fig. 8b), the upward surface movementfrom 21 to 25 July and subsequent lowering are consistent
with the borehole-length change. Thus, the surface verticalmovement was generally controlled by the vertical strainingof the ice and presumably caused by the regional flow
regime turning from compressive to extending flow overthe night of 25 July. A possible reason for the change in flow
regime is spatially and temporally non-uniform basal conditions related to transient development of the subglacial
drainage system.
As also shown in Figure 6, diurnal vertical movements were observed in July and August. Superimposedon the long-term variation, the vertical displacementshows upward movement at night from 22 to 26 July.
Because there is no diurnal signal in the borehole measurement, cavity opening is a plausible interpretation for
the uplift at night. From 24 to 26 August, surface elevation is correlated with borehole length (Fig. 8c), suggesting vertical strain as the cause of the diurnal uplift.
According to the discussion in the previous subsection,
the source of these uplifts is crucial to the interpretationof diurnal flow-speed variations. From the field data, weare not able to eliminate either of the two processes. It
is most likely that vertical strain and cavity opening
were both relevant to the diurnal uplift.
During period IV, a reasonable interpretation for thesteady upward movement of the surface is that the glacier
was gradually thickening (Fig. 8d). The annual surface
speed distribution shows that the flow is slightly compressiveat the study site (Gudmundsson and Bauder,1999). It is suggested that the glacier flow regime switched to winter mode,in which internal ice deformation accounts for the dominantpart of the surface flow speed.

Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher
Influence of subglacial drainage conditions onwater pressure
Although the characteristics of the short-term flow
variations changed markedly in the course of the ablationseason, they were controlled by the subglacial water pressure. Water pressure itself is strongly influenced by drainage
efficiency, which increases from early spring to the midablation season. To investigate the seasonal evolution of thedrainage condition and how it influences the subglacial
water pressure, water-level variations throughout the summer are examined and compared to meteorological records
in Figure 9.
Until period II, diurnal oscillations in water level are notsignificant. This feature can be attributed to the snow layer
which covered the study site until late July, because snow
absorbs meltwater and dampens the diurnal signal of water
input to the bed. Water level rose sharply up to the overburden level on 6 and 15 July, and these incidents coincidewith heavy precipitation. Water level dropped quickly after
the events, then remained low for several days followed byan increase to the overburden level. These are implicationsof the opening of drainage conduits by the precipitation andsubsequent closing due to insufficient water pressure. The
motion event observed on 27 June seems to be accompanied
by high water pressure, like those recorded on 6 and 15 July.
When surface snow disappeared in the beginning of
period II, surface ablation increased and meltwater started
to drain into the bed directly through moulins and crevasses. Consequently, water level rose and remained close
to the overburden level for 4 days. Then, under similar meteorological conditions, mean water level started todecrease on 26 July while the amplitude of the diurnal oscillation increased. This suggests that the basal conduit systemdeveloped during this period because a large amount ofwater was supplied into the bed. The efficient drainage condition reduced the mean pressure and enhanced the diurnal
oscillations.
Nienow and others (1998) conducted dye-tracing
experiments and discharge measurements at Haut Glacierd’Arolla, Switzerland. From these measurements, they concluded that a hydraulically efficient basal channel systemdevelops up-glacier as the snowline ascends over the courseof the ablation season. Our observations also indicate
changes in the drainage system after the surface snow disappeared in lateJuly. In August, meteorological conditions are
similar to those in July, but the water-level variation differs
in the following ways. The amplitude of the diurnal variation is generally large, although the water level never exceeds the overburden level. During this period theamplitude of the diurnal flow-speed variation was greater
up-glacier than at the study site. The upper reaches of theglacier were still covered with snow, suggesting drainage efficiency there was less than at the study site. Daily meanwater level in August is correlated with air temperature
rather than with precipitation. A sudden water input by precipitation has less effect on water pressure under well-developed drainage conditions.
The diurnal water-level variation disappeared soonafter the temperature dropped in September. It is suggested
that the basal conduit system collapsed and the basal hydrological system was disconnected.
The foregoing examinations imply that there are two
distinguishable hydrological basal conditions at the studysite during the ablation season. One is a poor drainage condition characterized by high sensitivity to changes in water
input. The other is an efficient drainage condition characterized by large diurnal amplitude in water-pressure variations (and relatively low daily mean pressure), and in suchconditions daily mean pressure correlates with surface ablation rate. In summer 2001, the transition occurred in lateJuly, when the surface snow layer disappeared and a large
amount of meltwater started to drain into the bed.

CONCLUSION
GPS measurements with high temporal resolution wereused to determine short-term variations in horizontal andvertical surface movements on a temperate valley glacierduring the ablation season. Horizontal speed was generally
correlated with subglacial water pressure, and increased significantly when the pressure rose close to the overburdenpressure. Detailed analysis of the relationship between surface speed and water pressure showed characteristic featuresof the observed diurnal variations.When water pressure wasincreasing, the speed was greater than that under the samepressure in the decreasing phase. This hysteresis was attributed to the basal sliding with cavity formation and/or pushing force exerted by the faster flow in the upper reaches.
Vertical movement of the glacier surface was comparedwith borehole-length change to study the uplift mechanism.
Two intrinsically different types of uplifts were observed;
one was caused by vertical straining and the other presumably originated from the volume increase in subglacial watercavities. Our results suggested subglacial cavity opening
during the motion event, but also suggested that uplift accompanied by a speed increase could not be simply related
to cavities. As the glacier accelerated non-uniformly, vertical strain rate changed within a short period, leading to vertical movement of the surface.
Subglacial drainage efficiency played a crucial role indetermining water-pressure variations under the influenceof the surface snow layer. When the surface was covered
with snow, diurnal variation in water pressure was damped
and heavy precipitation caused pressure to increase up to
the overburden pressure. After the snowline ascended upglacier, the amplitude of the diurnal variation increased
while mean pressure decreased. Water pressure was thenmore directly controlled by surface melt rate and was lesssensitive to precipitation in the late ablation season.

ACKNOWLEDGEMENTS
We are grateful to the members of the 2001 Unteraargletscher field campaign from the Section of Glaciology,
VAW-ETHZ. Special thanks are due to J. Helbing for organizing the campaign and measuring the water pressure.
T. Schuler provided the meteorological dataset. The qualityof the manuscript was improved by careful reviews by
J. Walder, B. Hanson and an anonymous reviewer. We also
thank R. Naruse and H. Blatter for their suggestions on the
manuscript. This research was funded by the Swiss National
Science Foundation through grant No. 2100063770.00 and by
The Inoue Scientific Field Study Foundation.
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Sugiyama and Gudmundsson: Short-term flow variations at Lauteraargletscher
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MS received 12 March 2003 and accepted in revised form 22 January 2004

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