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

2. Methods

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 for continuous 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 is the location of the water pressure measurements. Coordinates correspond to the official Swiss coordinate system.

[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 this glacier [Iken et al., 1983; Gudmundsson et al., 2000]. With the initial goal of better understanding such short time scale variations 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 the equilibrium 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 with roughly 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 each borehole. The distance from the magnets to reference bars drilled into the surface ice directly above each of the boreholes 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 in Figure 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 three other 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.

[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 from the survey site (Figure 1B). Measurement accuracy of the transducer 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

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 and vertical strain rate (right side) during late June and early July 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 were interrupted 1–4 July because snow temporarily clogged in the borehole. In (C), z-axis is pointing upward from the origin at the glacier surface.

Figure 3. (A) Surface flow speed (red) and water level in the bottom-reaching borehole measured from the glacier bed (black). (B) Borehole depth changes in the 150-m (open circle), and 300-m (solid circle) boreholes. (C) Depth distribution of vertical flow speed and vertical strain rate (right side) during late July 2001.

Figure 4. (A) Surface flow speed (red) and borehole water level. (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 the daytime and at night during late August 2001. These represent the original state (black), after the deformation from 6:00 to 18:00 (blue) and that from 18:00 to 6:00 (red) in magnified 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 rate in N-S and the equivalent compression in W-S.

[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 laminar flow 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 of change is the vertical flow speed relative to the surface ice at the depth of each magnet. The vertical flow speeds at 50, 150, and 300 m were measured at the same times and then linearly interpolated (relative vertical speed is zero at z = 0 m) to obtain a vertical speed distribution through out the day. These data, temporally interpolated to each 0.25-day interval, are plotted in Figures 2C and 3C. From the spatially interpolated data, the vertical strain rate was calculated as the derivative of the speed with respect to the depth.

[9] From 22 to 27 August, we calculated the horizontal strain rate on the surface from the displacements of three poles 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.

Citation: Sugiyama, S., and G. H. Gudmundsson, Diurnal variations in vertical strain observed in a temperate valley glacier, Geophys. Res. Lett., 30(2), 1090, doi:10.1029/2002GL016160, 2003.