GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 2, 1090, doi:10.1029/2002GL016160, 2003

Diurnal variations in vertical strain observed in a temperate valley glacierShin Sugiyama
Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan

G. Hilmar Gudmundsson
British Antarctic Survey, Cambridge, United Kingdom
Received 22 August 2002; revised 3 October 2002; accepted 25 November 2002; published 30 January 2003.

[1] During a period of diurnal fluctuations in glacial flow
speed, vertical strain was measured with sub-daily temporal
resolution on Unteraargletscher, Switzerland. Mean verticalstrain in boreholes up to 300-m deep in 400-m-thick ice wasfound to fluctuate diurnally. Vertical strain rates were tensile
in the daytime and compressive at night, with a magnitudeof up to 10 3 day 1. Horizontal surface strain was observed
to fluctuate in a manner consistent with the verticaldeformation. Diurnal surface flow speed variations
correlated well with basal water pressure suggesting abasal control on temporal flow variations. Nevertheless, thestrain rate measurements indicated that changes in surface
flow speed are affected by internal ice deformation and nota direct measure of local basal motion. Basal conditions inthe surrounding neighborhood and their temporal variations
take an important role in short-term glacial flow
INDEX TERMS: 1827 Hydrology: Glaciology
fluctuations.
(1863); 1863 Hydrology: Snow and ice (1827); 0915 Exploration
Geophysics: Downhole methods. Citation: Sugiyama, S., andG. H. Gudmundsson, Diurnal variations in vertical strain observedin a temperate valley glacier, Geophys. Res. Lett., 30(2), 1090,
doi:10.1029/2002GL016160, 2003.

1. Introduction[2] Temperate valley glaciers often exhibit diurnal variations in surface flow speeds. These variations appear to
be triggered by changes in subglacial conditions such as
subglacial water pressure and mechanical properties ofsubglacial sediments [e.g., Willis, 1995]. Because corresponding changes in surface slope and ice thickness are
small, englacial deformation is generally assumed to havean insignificant effect on surface speeds. Consequently,
diurnal variations in surface flow speeds are usually
thought to directly express temporal variations in basal
motion.
[3] A few direct short time scale studies of basal motion
are reported [Blake et al., 1994; Iverson et al., 1995;
Engelhardt and Kamb, 1998], but none of short-term
variations in englacial strain during a period of diurnal
fluctuations in surface speeds. In this paper, we present
surface flow speeds and vertical strain-rate variation withdepth measured on Unteraargletscher in the Bernese Alps of
Switzerland in summer. The measurements demonstrate thatenglacial vertical strain-rate can vary diurnally and significantly affect ice motion at the surface. Horizontal surface
strain also varied over short time scales suggesting that
Copyright 2003 by the American Geophysical Union.
0094-8276/03/2002GL016160$05.00

stresses are being transmitted horizontally, possibly inresponse to spatially non-uniform temporal changes in basal
lubrication. It is concluded that in temperate glaciers, basal
motion and internal ice deformation cannot be considered as
independent processes.

2. Methods[4] Unteraargletscher is a temperate valley glacier in the
Swiss Alps with length of 11 km and area of 26 km2(Figure 1A). Motion events, characterized by an increases
in surface flow speed of 200% or more over a few days,
usually occur several times in the ablation season on thisglacier [Iken et al., 1983; Gudmundsson et al., 2000]. With
the initial goal of better understanding such short time scalevariations in glacial motion, an extended field experiment
was carried out on Lauteraargletscher, a tributary of Unteraargletscher, from June to October 2001. All measurements
were made at an altitude of 2480 m, about 100-m below theequilibrium line altitude (Figure 1B). Maximum ice thickness at the measuring site was about 400 m [Funk et al.,
1994; Bauder, 2001].
2.1. Measurements[5] Vertical strain variation with depth was measured
through repeated high-accuracy borehole depth measurements. We used a hot water technique to drill 50, 150, and
300-m deep boreholes of about 100-mm diameter withroughly 5-m spacing [Iken, 1988]. A 1-m long, 64-mm
diameter plastic pipe with a 12-mm thick ring-shaped
magnet on its upper rim was placed at the bottom of eachborehole. The distance from the magnets to reference bars
drilled into the surface ice directly above each of theboreholes was measured 1 –8 times a day with a TEFLON
measuring tape equipped with a magnetic sensor on its end[Gudmundsson et al., 2002]. The measurement error was
estimated to be ±3 mm.
[6] Surface velocities close to the drilling site (site 313 inFigure 1B) were determined using static relative GPS
measurements [Hofmann-Wellenhof et al., 2001]. The reference station was situated on the north flank of the glacier
about 700 m from the drilling site (Figure 1B). From a test
performed with two fixed antennas the positioning error was
estimated to be about ±3 mm. Hourly surface flow speed
was calculated from a 4-h running mean of the horizontal
displacement. In addition, twice a day (within 2-h of 6:00
and 18:00) from 22 to 27 August, the positions of threeother poles forming a triangle with sides of about 300 m(strain array in Figure 1B) were surveyed. These surveys
were used to examine the surface strain pattern.

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50, 150, and 300 m were measured at the same times andthen linearly interpolated (relative vertical speed is zero atz = 0 m) to obtain a vertical speed distribution through out
the day. These data, temporally interpolated to each 0.25day interval, are plotted in Figures 2C and 3C. From thespatially interpolated data, the vertical strain rate wascalculated as the derivative of the speed with respect tothe depth.
[9] From 22 to 27 August, we calculated the horizontal
strain rate on the surface from the displacements of threepoles surveyed twice a day using the method described by
Jaeger [1969]. The strain rates in Figure 4C were determined
as a function of compass bearing for each period of 6:00 –18:00 and 18:00 – 6:00 everyday. Deformational ellipses,
representing deviation from a unit circle due to the deformation of the ice after a unit time, were averaged in the two
periods and are shown in a magnified form in Figure 4D.

3. Results

Figure 1. (A) Map of Unteraargletscher and its tributaries.
The solid square is the precipitation measurement site. (B)The study area on Lauteraargletscher (smaller square in (A)).
Solid and broken contour lines indicate the surface and bed
topography, respectively. Elevations are in meters above sea
level. Solid circles are positions of a pair of GPS antennas forcontinuous measurement of surface flow. Open circles
connected with solid lines are the strain array, the open
square is the location of the boreholes, and the solid triangle isthe location of the water pressure measurements. Coordinatescorrespond to the official Swiss coordinate system.

[10] We focus on measurements from three distinct
observational periods in summer 2001: from 20 June to 5
July, from 18 July to 1 August, and from 22 to 27 August.
The first series of measurements shows how the ice
responded to a heavy rainstorm on 27 June, which caused
a clear change in surface speed (Figure 2A). The storm
started at 15:00 with precipitation reaching 6.3 mm per hour
at 18:00. Shortly thereafter around 17:00, the surface flow
speed started to increase to a maximum speed of 0.2 m[7] Subglacial water pressures were registered every 15–
30 min with a vibrating wire pressure transducer lowered
into a 380-m bottom-reaching borehole at 200-m away fromthe survey site (Figure 1B). Measurement accuracy of thetransducer is equivalent to the water level of 3.5 m. Daily
surface ablation was measured by stake measurements at the
GPS survey site.
2.2. Calculation of Strain Rates[8] Successive measurements of the borehole depths
were used to determine the vertical strain-rate variation.
The relative displacements plotted in Figures 2B, 3B, and
4B reflect both the vertical strain and horizontal shear
between each magnet and the surface. Assuming laminarflow and Glen’s flow law with n = 3, the horizontal
shearing over the uppermost 300 m was estimated to be
2  10 4 m day 1 or less from the surface position
measurements [Paterson, 1994], which is negligible compared with the measured displacements. Therefore, we
assume that the relative displacement equals the total
vertical strain over the borehole depth, and its rate ofchange is the vertical flow speed relative to the surface ice
at the depth of each magnet. The vertical flow speeds at

Figure 2. (A) Surface flow speed (red) and hourly
precipitation rate. (B) Borehole depth changes in the 50-m
(solid square), 150-m (open circle), and 300-m (solid circle)
boreholes. (C) Depth distribution of vertical flow speed andvertical strain rate (right side) during late June and earlyJuly 2001. Ticks on the temporal axes indicate 0:00 local
time. The arrow in (A) shows the motion event described in
the text. In (B), measurements in the 150-m borehole wereinterrupted 1 – 4 July because snow temporarily clogged in
the borehole. In (C), z-axis is pointing upward from theorigin at the glacier surface.

SUGIYAMA AND GUDMUNDSSON: DIURNAL VARIATIONS OBSERVED IN A GLACIER

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18– 27 July. Furthermore, the strain rate was spatially nonuniform, particularly from 30 July to 1 August, with the
deeper regions being compressive while the shallower
regions were tensile.
[12] Clear diurnal fluctuations in the surface flow speed
were again observed from 22 to 27 August (Figure 4A), but
fluctuations were smaller than in the previous period. By 22
August, the 150-m borehole was frozen near the surface andthe 300-m borehole was closed at 173-m below the surface,probably due to the ice deformation. However, the measurement was continued without the magnet by feeling thedecreased tension in the tape when the magnetic sensor
contacted the pinched-off point at 173 m. Repeated measurements indicated an uncertainty of ±5 mm. Although data
are available only for 4 days, diurnal oscillations in borehole depth are clearly observed (Figure 4B).
[13] The horizontal strain rate showed diurnal oscillationin the direction of and perpendicular to the glacier flow
except on 24 August (Figure 4C). Strain ellipses in Figure
4D display general figures of surface strain regimes in thedaytime (6:00 – 18:00) and at night (18:00 – 6:00). Theirdistinguishing features are compressive strain along the
Figure 3. (A) Surface flow speed (red) and water level inthe bottom-reaching borehole measured from the glacier bed(black). (B) Borehole depth changes in the 150-m (opencircle), and 300-m (solid circle) boreholes. (C) Depth
distribution of vertical flow speed and vertical strain rate(right side) during late July 2001.
day 1, about twice the pre-storm speed, occurred at 22:00.
Before this event, the depths of the three boreholes had
increased monotonically (Figure 2B) and the vertical strain
rates were positive (tensile) and constant with time throughout the depth (Figure 2C). On 28 June, the strain rate
became negative. Close inspection of the data revealed thatthe compression started near the surface and then moved
deeper into the ice. In the following days, rather complex
patterns of temporal and spatial variation in vertical strain
were observed. For example, large temporal variations inborehole depths were observed with the 300-m borehole
becoming 50-mm deeper overnight from 30 June to 1 July.
Although the surface flow speed reverted to its pre-storm
pattern, the speed up on 27 June left a lasting impact on theenglacial strain-rate distribution.
[11] Another conspicuous event occurred from 18 July to
1 August (Figure 3). In the beginning of this period, weather
was cold with occasional snowfall, but on 21 July, dailymean air temperature rose sharply by about 10°C causing
intense surface melting of 70-mm water equivalent day 1.
Then a clear diurnal variation in the surface flow speed wasestablished as a result of substantial melt water input in thedaytime (Figure 3A). The maximum speed occurred in theevening and the minimum speed in the morning. By 18 July,
the 50-m borehole had closed off due to the freezing ofwater near the surface, but depth measurements could becontinued for the other two boreholes. From 27 July to 1
August, large diurnal fluctuations in vertical strain wereobserved with the depths of the boreholes changing by up to30– 40 mm a day (Figure 3C). In the daytime, the strain ratein the shallower region was tensile, on the order of 10 3
day 1, while at night it became compressive. Weaker, butsimilar, diurnal signals also occurred throughout most of

Figure 4. (A) Surface flow speed (red) and borehole waterlevel. (B), Changes in the 173-m borehole depth. (C),Horizontal strain rate on the surface. Strain rates were
measured twice a day at 0:00 and 12:00, and the contours
estimated by linear interpolation along the time axis. (D),Mean strain rate ellipses of horizontal deformation in thedaytime and at night during late August 2001. These
represent the original state (black), after the deformationfrom 6:00 to 18:00 (blue) and that from 18:00 to 6:00 (red) inmagnified forms by a factor of 5  103. On the right side in(D) is a scale that shows 10 4 day 1 of tensile strain ratein N-S and the equivalent compression in W-S.

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flow direction in the daytime and transversal tensile strain atnight of about 10 4 day 1. Combined with the verticalstrain rate measured in the borehole, the ice deformation in
the upper half of the glacier can be described as follows.
From morning to evening, ice contracts horizontally in theflow direction and expands vertically. From evening to thenext morning, it expands horizontally across the flow
direction and contracts vertically.

4. Discussion[14] The important aspect of the vertical strain measurements in the first period is the temporal reversal in verticalstrain rate at the rainstorm. Similar strain-rate reversal has
been observed previously during a major motion event in
the same glacier [Gudmundsson, 2002]. Until the fast flow
on 27 June, the observed steady and uniformly distributed
tensile vertical strain rate is consistent with the spatial
distribution of annual surface velocities that show compressive flow at the study site [Gudmundsson and Bauder,1999]. The compressive vertical strain from 27 to 28 Juneis presumably related to spatially uneven acceleration of theglacier as a response to the large amount of water input by
the rainstorm. This event may have triggered changes insubglacial hydrology, which caused the subsequent verticalstrain rate fluctuations.
[15] An unexpected finding in this study is the diurnal
fluctuations in the strain rate at the end of July and in
August. One of the clues to understand the cause for thestrain oscillation can be found in the subglacial waterpressure variations. The water level was well correlatedwith the flow speed and relative borehole depth (Figures 3A
and 3B, 4A and 4B). Furthermore, during the period of
diurnal strain rate oscillations, water levels changed bymore than 100 m a day, indicating a high drainage efficiency for the subglacial hydrological system. The drainage
efficiency was expected to increase in a progressively
upglacier direction through the ablation season since it has
been observed in other valley glaciers [Nienow et al., 1998].
Evidence for this is seen in the water level trend from 23
July to 2 August (Figure 3A). While the melt rate remained
approximately constant, the diurnal peak-to-peak variationin water level increased with time and the daily minimum
level decreased. This suggests the following interpretationof the diurnal fluctuations in the strain regime. When thewater pressure increases in the daytime, the glacier accelerates. This acceleration is higher in the upper reach because
the subglacial drainage system there has not developed aswell as that in the study area, and so the water pressure ishigher in the upper reach. Higher flow speed in the upper
reach causes longitudinal compression in the study area,
which affects the vertical and surface strain regime in thedaytime. At night, the flow speed in the upper reachdecreases to about the same speed as that in the study area
and then the longitudinal compression disappears.
[16] Interestingly, the vertical strain rate was not uniformwith depth when the vertical strain varied diurnally. This
sort of vertically non-uniform strain rate has been suggested
theoretically to be associated with short-scale spatial variations in basal motion [Balise and Raymond, 1985]. Whenthe basal conditions are non-uniform along the glacier, as
we expect for the periods of the diurnal strain rate signals at
Unteraargletscher, predicted vertical strain rate is no longer
constant with depth. Although the previous theoreticalworks have been limited to small amplitude perturbations
and linear rheology, non-uniformity in vertical strain-rate
distribution has been also revealed in a numerical study withmore realistic ice rheology. [Sugiyama et al., in press].

[17] Acknowledgments. We thank J. Helbing for his substantial
assistance throughout the measurements on the glacier. T. Schuler contributed on the precipitation and the water pressure measurements, andother members in Section of Glaciology, VAW-ETH, Zurich supported thefield research activity. Discussions with R. Naruse was beneficial for the
study. H. Blatter, R. C. A. Hindmarsh, D. Vaughan, and two anonymous
reviewers carefully reviewed the paper. This work was funded by a Swiss
National Science Foundation grant No. 2100-063770.100 and by the Inoue
Scientific Field Study Foundation.

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S. Sugiyama, Institute of Low Temperature Science, Hokkaido
University, Sapporo, Japan. (sugishin@pop.lowtem.hokudai.ac.jp)
G. H. Gudmundsson, British Antarctic Survey, High Cross, Madingley
Rd., Cambridge, CB3 0ET, U.K.