Velocity measurements

The primary data analyzed here are water pressures and surface speeds (Fig. 2). The measurements were made during field seasons lasting from late June to late July in 1991 and 1992, and from early July to mid-August 1993 and 1994 (table 1). Distance data were collected using Automatic Distance Measurement (ADM) systems, each consisting of an infrared laser range finder controlled by a pocket-sized computer that also serves as a data logger (described in Reference Hanson and HookeHanson and Hooke (1994)). In 1991, one such system was placed on a stationary rock near the south side of the glacier (DM, Fig. 1) and aimed at a triple prism at site 2 (S2). Two ADMs were deployed from 1992 onward. In 1992 and 1993, velocity (V) measurements were made from DM to S3 (V92-S3, V93 S3) and strain-rate (SR) data were obtained between S2 and S3, using a distance meter anchored to stakes at S2 (SR92, SR 93; Table 1). In 1994, speeds at S2 were again measured from DM and speeds at a new site. SO, were also measured from a distance meter located on the north moraine (H, Fig. 1).

Points on the glacier consisted of 5 cm diameter iron pipes, 6 m long, that were drilled 4-5 m into the ice. All of these had more than 3 m still embedded in the ice at the end of the season, so they all remained firmly anchored, although increasingly capable of swaying, throughout the period of measurements. The distance meter al S2 was fixed to three such slakes, drilled in a firmly cross-braced triangle approximately 70 cm on a side.

Distance measurements were attempted every 10 min, with more frequent attempts made if visibility prevented a scheduled measurement. Caps in the measurement series are caused by technical problems, primarily battery failures, and weather-related visibility problems. Visibility failures caused by fog or precipitation were common when shooting the > 800 m distance from DM to S2. Visibility from DM to S3 or H to SO was only interrupted in the most severe rain storms, which did, nevertheless, result in very interesting water-pressure events. Strain-rate measurements from S2 to S3 were never interrupted for significant lengths of time by weather, owing to the short distance of measurement.

Fig. 2. ADM speeds, ADM strain rates and water-pressure measurements. Vertical scale on speed/strain-rate axes is the same for all diagrams: water-pressure scale varies. Hater pressures are given as height above the bed of the water level in the borehole. Some data series ore truncated (in time) from the periods listed in Table 1 in order to highlight the periods of correlated measurements. In (b) and (c), strain rate is shown as the rate at which S2 and S3 were getting closer; positive is compressive. (a) 1991: all measurements at S2. (b) 1992: speed at S3, water at S2, S2-S3 strain rate included. (c) 1993: speed at S3, water at S2 until 20 July and at S2.5 thereafter, S2-S3 strain rate included. (d) 1994: upper diagram is S2 speed and water, lower diagram is SO speed and water. Shaded bars on the time a is indicate periods averaged to form the diurnal composite diagrams (Fig. 3).

Table 1 Data series collected for short-term velocity and bore hole water pressure

The ADM data were supplemented by three-dimensional surveys from the base lines NM- 18.5 or H 18.5 (Fig. 1), using an electronic theodolite and distance meter. These surveys were made nine—ten times in each field season (every 2-3 days as weather permitted) (table 2). They provided directions of motion for each of the stakes and were made sufficiently often to show that the direction does not vary appreciably during acceleration events. Thus, the events shown by the ADM experiments appear to consist of speed changes only, without accompanying directional change, at least within the limits of these surveys.

Table 2 Summary of three-dimensional surveys of stakes used for ADM experiments. (a). Speeds in mm d⁻¹, horizontal azimuth relative to due east, vertical direction relative to the horizontal plan

* S2.5 is roughly half-way between S2 and S3. It was used for water pressure only in 1993.

Speeds calculated as first derivatives of ADM distance data are based on the directly measured distance changes; they were not “corrected" for angles between the measurement line and the direction of motion of the stake. For S2 and S3, the stakes primarily discussed in this paper, the angles between the actual motion of surveyed stakes and the components of that motion directly towards the distance meter are very small anyway (Table 2b).

Corrections for temporal changes in atmospheric density were applied to the distance measurements. The temperatures required for this calculation were measured beneath a data-logger shelter directly at S2 during much of the 1991 season. During the remainder of the 1991 season and the entire 1992 season, temperatures were taken from a weather station higher on the glacier. Temperatures for 1993 and 1991 were obtained from a station maintained ~200 m down-glacier from S3. All of these temperature stations were within the same sun and shade conditions as the sight line of the distance meter for nearly all of the day. by Reference CutlerCutler (1997) showed that meteorological stations within the larger region of the main overdeepening and riegel had similar, strongly correlated diurnal temperature cycles. Atmospheric-pressure measurements were taken from a barograph at Tarfala station in the valley below the glacier and corrected lo glacier height using a temperature-compensated form of the altimeter equation. Corrections for atmospheric density had minimal effects on the liming and placement of the speed peaks and valleys discussed here; un-corrected measurements used for preliminary graphs in the field showed mostly the same results.

The distance meters used in these experiments have a stated absolute accuracy of 6-9 mm over the distances measured here. The ADM experiments depend upon the relative accuracy of a succession of measurements being more precise than this. That is, any systematic errors in a distance meter must affect successive measurements similarly and hence have a very small effect on their first time derivative. Each data point recorded by an ADM consisted of an average of three distance measurements, recorded to the nearest miltimeter. Normally, the glacier does not move 1 mm during every l0 min interval, and random errors cause the measurements to fluctuate up and down 1-2 mm. The unsmoothed distance measurements thus produce a quanli-tized set of velocities, as the glacier appears to move -1,0,1 or 2 mm in each 10 min interval. Smoothing is necessary to turn these measurements into usable velocity data.

The smoothing method used here, as in Reference Hanson and HookeHanson and Hooke (1994), is an error-correcting cubic spline applied to distance data (routine DCSSMH in 1MSL, 1994). More precisely, the spline is applied lo distance data from which a trend line has been removed and hence it smoothes deviations from die average velocity of the entire record. Smoothing was tuned by specifying what percentage of the standard deviation of the detrended data consisted of error. Lacking an objective criterion for tins smoothing parameter, we have used for each ADM series the minimum smoothing that removes negative velocities. In the resulting velocity curves, the timing and duration of major velocity fluctuations are insensitive to the smoothing parameter (Fig. 2), However, the absolute amplitudes of fluctuations shown here are uncertain, even though one can compare the relative amplitudes of durèrent velocity fluctuations in the same series.

Series SR92 and SR 93 are measurements of strain rates, for which negative values are possible. Strain rates are graphed and discussed here as rates of compression, in mmd⁻¹, between S2 and S3, so that the strain-rate curve can also be interpreted as a simple speed-difference curve, The strain-rate series were smoothed by forcing their qualitative appearance, in frequency and duration of graphically visible fluctuations, to mimic that of the corresponding velocity series for S3. Vector summing the S2-S3 strain rate with the S3 velocity in these cases yields slight k negative velocities for S2 during extreme compressional strain events, indicating that at least one of the series was under-smoothed.

Smoothing techniques are inherently subjective, but the method used here does little violence to the spectrum of variations, and it preserves the timing of peaks and valleys better than low-pass spectral smoothing methods. If integrated over time, this method reproduces the total observed motion of a stake. Our smoothing procedure is substantially more stringent than methods used in Columbia Glacier ADM experiments, reported by Wallers and Dunlop (1987: and Meier and others (1994), as the order-of-magnitude smaller velocity on Storglaeiaren produces a noisier distance-meter dataset.

ADM raw data were obtained at unevenly spaced times, as the 10 min intervals mentioned above were times between attempted measurements, not necessarily between obtained measurements. Furthermore, with cubic-spline smoothing techniques, there is no particular advantage in calculating first derivatives directly at the raw-measurement times. Therefore, for calculational and graphical convenience, speed data were extracted at an evenly spaced time grid with 0.01 d intervals.

Water-pressure measurements

Each year, a number of holes was drilled through the glacier near S2 and S3 with the use of a hot-water drill. Most of these were for an investigation of the till layer beneath the ice but water-pressure transducers were installed in some (table 1). Rustrak Ranger data loggers were used in 1991 and 1992. These, however, proved to be unreliable, particularly in 1992 and, in addition, they sampled data at a time grid of their own choosing, using a proprietary algorithm that is not available to us. Hence, the few data extracted from these devices were interpolated to the same 0.01 d time grid as the velocity data using cubic-spline interpolation (not smoothing).

In 1993, water pressures were measured again at S2 and S3 (using other data loggers: and also at an intermediate location clubbed S2.5. The longest available water-pressure series was from S2.5, as the series at S2 ended early when the borehole became disconnected from the conduit system and tin- series at S3 both started late and failed early. During a few days of overlapping records among these three locations, we were unable to detect a significant or consistent timing difference among them. That is, no evidence for propagation of a water-pressure wave was seen, although this conclusion is based on an unfortunately short period of overlapping record and on measurements over a relatively small distance (300 m). In 1994, S2 and SO were instrumented with pressure transducers and these were trouble-free. Even over this greater distance (>700m), there is little evidence of a water-press tire wave propagating between the two sites. Although 1993 and 1994 data were mostly measured at 10 min intervals, these were also interpolated to a 0.01 d time grid for correlation with other data series.

Velocity- and water-pressure peaks

Lagged correlations

The common 0.01 d time grid allowed calculation of direct correlations as well as correlations at all possible lags within ±2 days for various pairs of time series (table 3). Looking first at correlations between water-pressure series and their corresponding or nearby surface speeds (first block in Table 3), the best positive correlations are always obtained with a negative lag, meaning that increases in velocity normally preceded local increases in water pressure. These lags in the less-expected direction were as much as a quarter day in 1991 but were usually less than that.

Reference IkenIken’s (1981) modeling suggested that speeds may be highest on rising water pressures while subglacial cavities are expanding. by Reference Iken, Röthlisberger, Flotron and HaeberliIken and others 1983} found field support for this idea on Unteraargletscher using approximately daily speed measurements but only for periods during which water pressures were extremely high. Using our liner time-scale data, lagged correlations with surface speed were calculated for the first-time derivative of the water-pressure series. This set of lagged correlations also showed peaks in surface speed generally preceding peaks in dp_w/dt and rises in surface speed often began while the local water pressure was still falling.

The correlations presented in Table 3 are for the entire season. Pearson correlations are always strongly influenced by a few large values, in t his case the large, precipitation-induced velocity events. This events, in turn, have the least reliability as to their exact timing, because the distance meters were unable to “see" their targets during heavy rainfall. The full-season correlations could thus be misleading. Correlations among shorter time series with smaller, diurnal signals revealed less consistency in cither size or direction of the lagged correlations. However, examining stretches of these smaller, diurnal variations in Figure 2, one can see many cases where a velocity minimum precedes a water-pressure minimum and a velocity peak precedes a water-pressure peak. These support the full-season calculations and the conclusion that local water pressure is not driving the surface speed.

Table 3 Summary of lagged and unlagged correlation s among water pressure, velocity and strain-rate measurements. A range of ± 2 days of lag was explored in each case. Lags are given in days and correlations (R) in percent

There is a lack of agreement between these data and the results found byjansson (1995), who found a good correlation between effective pressure (ρ_i — ρ_w) and surface speed in(u_s): u_s = 30 (ρ_i — ρ_w) ^−0.4 (pressures in MPa, speeds in mm d⁻¹). Some of Jansson’s measurements were made in the vicinity of S2, the rest were separated from ours by a series of large crevasses and the riegel. Jansson’s velocity data were based on daily conventional surveys rather than ADMs and thus were of much lower time resolution. Furthermore, his high correlations were obtained for incidents in which high water pressures were maintained over a period of several days. We aggregated our data temporally to see whether results similar to Jansson’s would result. Smoothing yielded slight improvements in some of the correlations shown in Table 3 but nothing like his 90% R² value was approached.

Composite diagrams

By inspection of Figure 2, we selected several days in each year during which all data series were available for the entire day without interpolating over data gaps. The days were not necessarily contiguous. (To produce a reasonable composite, some days with no water-pressure records were included in 1992.) Days chosen from each year were stacked to produce a number of composite single days (Fig. 3). Days with large precipitation were excluded; they are small in number and unique in character.

For 1991, figure 3a shows the calculated quarter-day lag (table 3) in that a velocity peak at 10.30 h was followed by a broad water-pressure peak at 16.00- 19.00 h. The water-pressure peak is easily understood in terms of the diurnal melt cycle; the velocity peak in mid-morning is less easily understood. The 1994 measurements (fig. 3e) show a similar water-pressure cycle (note the change in water-pressure scale between figure 3a and e) but a much later S2 speed cycle. However, speed still leads water pressure in the 1994 diagram.

Graphical composites for 1992 and early season 1993 (fig. 3b and c), when the speed measurements were at S3, are a little more ambiguous owing to lower coherence in both water pressure and velocity. Relatively small diurnal speed cycles are a feature of all S3 composites, implying that this area does not respond strongly or coherently to water inputs. Speeds tend to lead water pressures but not as dramatically as in the data from S2 (fig. 3a and e). Water pressures in the 1992 composite (Fig. 3b) have a tiny amplitude but the deepest valley and highest peak are at times similar to other years.

To further summarize the 1991 93 graphs, a multi-year composite was created, in which all of the days included in figure 3a-c were averaged (Fig. 4). In this slacking, S2 speeds for 1992 and 1993 were estimated by summing the S3 speed and the strain rate for those years and averaging the results with the 1991 data. (This procedure, while conceptually accurate, is only a rough estimate of S2 speeds, because of the different and uncertain smoothing procedures used for strain-rate and velocity curves. If the method were perfect and the periods averaged in all three curves were the same, then the strain-rate curve shown in Figure 4 would be exactly the difference between the two velocity-curves.)

Fig. 3. One-diunal-cycle composite diagrams, constructed by stacking the days listed on each figure. Curve types are the same as in Figure 2: solid is speed, dashed is strain rate, dulled is water pressure, with additional SO curve types labelled in (e). Water pressures are given as height above the bed of the water level in the borehole: (a) 1991: (h) 1992: (c) 1993 early season; (d) 1993 late season; (e) 1994.

Fig. 4. One diurnal cycle in which curves labelled “91-93" were created by averaging together the days in Figure 3 a-c for S2 and S3 early season, including S2 velocities estimated by adding S3 speed to S2-S3 strain rate fur 1992 and 1993. The velocity curve for 1994 is the same as that in figure 3e. Water pressures are given as height above the bed of the water level in the borehole.

The 1994 speed data from S2 were substantially more coherent diurnally than previously measured (1991) or calculated (1992-93) S2 speeds. It the 1994 data were averaged with those from the preceding 3 years, the resulting curve would look essentially like the 1994 curve, albeit damped. The 1994 curve was added to Figure 4 for comparison but left as a separate curve rather than included in the 1991 93 average. The 1994 S2 water-pressure composite (fig. 3e) has identical timing and nearly identical amplitude (note again the scale change) to the 1991-93 water-pressure curve shown m Figure 4, so it was omitted.

Although Figure 4 is restricted to days that visibly showed diurnal cycles, it reinforces the correlation results. To the extent dial we can Grid diurnal water-pressure cycles, they are remarkably consistent in all locations and in all years, with a late-afternoon peak and an early-morning-minimum that are consistent with melt input driven by a diurnal temperature cycle. Timing and amplitude of velocity cycles are less consistent inter-annually and between locations but, in all cases the peak speed occurs earlier in the day than the peak water pressure, both at S2 and at S3, but most noticeably at S2.

Strain rates between S2 and S3

Simultaneous measurement of both S3 speed and S2-S3 strain rate from 1992 and 1993 clearly show that peak speeds al S2 precede those at S3. In the composite diagrams [fig. 3b and c), this is shown by the consistency with which a peak in compressive strain rate precedes peak speed at S3, indicating a push from behind at S3. These composites include only a few days, restricted to early season in the 1993 case, but the same result can be inferred from the lagged correlations over the entire measurement period. The best positively correlated lags between S3 speed and S2—S3 strain showed lags of 0.7 and 13 days, respectively (table 3). If we allow shifting the indicated lags by ±1 day to correlate proximal peaks with each other, then strain-rate peaks lead S3 speed peaks by 0.3-0.5 days.

Figure 4 includes S2 speeds inferred from the combination of S3 speed with S2-S3 strain rate. Both stake velocities begin to rise in the morning while water pressure is still rising. The more rapid acceleration at S2 creates a compression peak in the strain-rate curve at about 09.00 h that is then dissipated both by the ongoing acceleration of S3 and the decreasing acceleration of S2. By the time S3 reaches its velocity peak in mid-afternoon, both S2 speed and the strain rate have decreased sharply.

Although the timing of the onset of acceleration at S3 is consistent with rising strain rate, the onset of deceleration does not have a consistent timing with respect to the decreased strain rate. We can conclude that S3 begins its acceleration with a push from behind but it is not necessarily slowed by the decrease in magnitude of that push later in the day. Another implication of this inconsistency is that we cannot say whether the pushing of S3 consistently blocks the further acceleration of S2 or whether the ongoing motion of S3 sometimes decreases the back-pressure on S2.

As noted above, the 1994 S2 speed peak is much later in the day than in the previous 3 years. Even though it maintains its timing with respect to water pressure, the peak in S2 speed in 1994 nearly matches the timing of S3 speed peaks from 1992 and 1093. In the field, we noted that 1994 was an unusual year in that fewer crevasses opened up-glacier from S2 and new crevasses appeared elsewhere. We lack measurements that would confirm whether the pattern of ice S2 pushing ice at S3 was maintained in 1994.

Early season stress coupling

We generally see that velocities begin to increase before water pressure. The implication is that changes in the local velocity are driven by changing conditions elsewhere on the glacier, with speed conveyed to the region via stress coupling. Speculation on how this operates is significantly constrained by the presence of crevasses just up-glacier from the study area: a clear sign of extending flow.

Force-balance calculations for the area of the glacier in the vicinity of S2 (Hooke and others, 1989) suggest that during the winter about 20% of the driving force is balanced by side drag, 20% by a longitudinal stress gradient and 60 % by basal drag. The longitudinal stress gradient arises from a combination of extending strain up-glacier from S2 and compressive strain down-glacier from it. The driving force is effectively constant on the time-scales we are considering. Hence, if we assume that changes in basal drag not responsible for initiating surface-velocity fluctuations (since water pressure is not changing appropriately), accelerations at S2 must result from: (1) decreases in side drag, (2) decreases in longitudinal pull from up-glacier, or (3) decreases in longitudinal back-pressure from down-glacier. The strain rate between S2 and S3 normally becomes more compressive as S2 accelerates (Fig. 4), so we can eliminate the third possibility.

Accelerations at S2 via reduction in side drag cannot be eliminated as a possibility but are unlikely. On the north side, water emerging from the glacier has a low sediment content, indicating little basal contact, and water emerges quite high along the left margin. On the south side, the lateral position of the largest surface-water inputs suggests that the large conduits are very near the margin where ice is thinner. It is thus unlikely that they are pressurized.

The remaining potential source of acceleration at S2 is reduction in longitudinal tension due to accelerations up-glacier from S2. This is consistent with the 1994 measurements, showing that accelerations at SO lead those at S2 (fig. 3e). The small acceleration at SO is insufficient to cause the larger one at S2 but SO is off to the side of the glacier, so the magnitude of its acceleration may not be representative of what is happening along the center line. Hooke and others (1989) observed that compression can occur in areas of normally extending flow just down-glacier from the riegel during high water-pressure events that last a few days. That further supports the suggestion that reduction in tensile stress across the riegel is responsible for the acceleration of S2.

Pressures in the overdeepening up-glacier from S2 are consistently high (Hooke and Pohjola, 1994). Diurnal water-pressure variations found at SO in 1994 typically had amplitudes of only 10- 15m (fig. 2d). Although these are small, they are superimposed on water pressures that are often near overburden, so the small fluctuations must have a disproportionate effect on surface speed. We therefore conclude that early-season velocity changes at S2 are driven by speed changes in the main overdeepening above the riegel.

Late-season conduit development

In past years (Hooke and others, 1983b, 1989), we have found that velocities, averaged over several days, decreased gradually through the melt season and into the autumn. Such a pattern would be consistent with an evolution of the conduit system in which a better capacity for rapid through-put of water develops through the season, so that each succeeding water-input event will have less effect on the water pressure and hence velocity (Seaberg and others, 1988; Reference Hock and HookeHock and Hooke, 1993; Reference Iken and TrufferIken and Truffer, 1997). The 1993 and 1994 measurement series were continued long enough into August to suggest that such a decrease might be starling but these measurements did not extend long enough to confirm it (fig. 2c and d). Such behavior was also noted by Jansson (1995) for water pressures above the riegel in the summer of 1987. He found that he could not detect late-season water-pressure fluctuations in response to the diurnal temperature cycle. Only water inputs from precipitation events were large enough to show in the record.

Some observations relevant to the intra-seasonal development of the subglacial drainage system below the riegel were made in late July 1992 at S3. By 20 July, several holes had been drilled to the bed. Water levels in most of them had remained within 1 m of the glacier surface since completion. In the morning of 20 July, dirty water was observed emerging from two holes. The following day, a plug of frazil ice had formed in a third hole. When this was broken, slightly dirty water began to flow from the hole at a rate of about 1.61s. On 22 July, a stormy day with wind and 33 mm of rain, dirty water was still emerging from another hole, although two of the others had stopped flowing. Then, on 23 July, all holes had drained. Observations on 24 July suggested that water levels were as much as 70 m below the surface in some.

From these observations, we infer that at this location and in the small overdeepening up-glacier from it (Fig. 1), the ice—bed interface was effectively impermeable before 20 July. This is consistent with our understanding of water flow through such overdeepenings (Hooke and Pohjola, 1994). Most of the subglacial water flow from the moulin area over the riegel probably flowed southward to join a branch of subglacial Sydjâkk that, as noted, we suspect runs at a relatively shallow depth along the south side of the glacier (Fig. 1). As the melt season progressed, high water pressures along this course probably gradually pried open small conduits leading through the shallow overdeepening and more directly to the terminus. This conduit system, we hypothesize, reached the vicinity of S3 during the night of 19-20 July, resulting in the excess pressures that produced artesian flow. The storm on 22 July then, we suppose, caused the conduit system, which had by this time reached areas somewhat down-glacier from the overdeepening to extend rapidly lo the terminus, draining the holes.

Although drainage systems change continuously, major water-pressure events cause a proportionally greater increase in conduit capacity. In 1993, for example, there were a few major storm-induced high water-pressure events, two of which occurred between the series of days covered by figure 3c and d, respectively. The timing and amplitude of the diurnal water-pressure cycle are basically the same before and after these events, but the amplitude of the diurnal speed cycle at S3 and of the S2-S3 strain-rate cycle increase markedly after the storms. Furthermore, the speed peak at S3 occurs later in the day and in now in phase with the water-pressure peak! Observations at S2 were similarly in phase with those at S3 in this late-season situation, as can be seen by the corresponding peak and valley of speed at S3 and strain rate at S2-S3 strain rate in figure 3d.

We conclude from these observations that subglacial cavities were probably more interconnected aller the mid-season storms in 1993 and that high water-pressure events thus affected a larger fraction of the glacier bed. This reinforces a conclusion recently reached by Reference Iken and TrufferIken and Truffer (1997), who found that the relation between speed and water pressure on Findelengletscher had changed dramatically between 1982 and 1994; they attributed the change to a change in the degree to which subglacial cavities were hydraulically interconnected and thus responding simultaneously to changes in water pressure.

In other words, on any given glacier, even holding the driving stress constant, it is unlikely that there is a unique relation between speed and water pressure. Equation (1) therefore needs to be modified to include a term describing the coherence of the hydraulic system. Jansson’s (1995) data, demonstrating that at comparable water pressures sliding speeds on Storglaciären and Findelengletscher vary by an order of magnitude, are probably a manifestation of the same phenomenon.