Introduction

Whillans Ice Stream (formerly Ice Stream B), Antarctica (Fig. 1), is the most studied ice stream in the world, but continues to surprise researchers. Scientific investigations on this ice stream began in 1957, when its downstream portion was crossed during the International Geophysical Year, well before the existence of ice streams was recognized. This area was later included in the Ross Ice Shelf Geophysical and Glaciological Survey (RIGGS) during the 1970s, when this entire area was thought to be part of the floating Ross Ice Shelf. Since the discovery of ice streams, this ice stream has received intensive surface-based work, airborne surveys and satellite monitoring (see review by Reference Whillans, Bentley, van der Veen, Alley and BindschadlerWhillans and others, 2001). Much of our current understanding of ice-stream mechanics results from these studies, including the discovery and sampling of the weak subglacial till that supports rapid ice-stream motion (Reference Blankenship, Bentley, Rooney and AlleyBlankenship and others, 1987; Reference Engelhardt and KambEngelhardt and Kamb, 1998; Reference Kamb, Alley and BindschadlerKamb, 2001) and the first recognition that ice-stream margins are the sites of major resistive forces determining ice-stream speed (Reference Whillans and van der VeenWhillans and Van der Veen, 1997). Currently, this ice stream is decelerating (Reference Bindschadler and VornbergerBindschadler and Vornberger, 1998; Reference Joughin and TulaczykJoughin and Tulaczyk, 2002), providing scientists with a magnificent natural experiment in ice-stream response behavior.

Fig. 1.

Map of study area. Station names are centered on station locations. Lines of different types represent different interpretations of grounding line: solid, Reference BindschadlerBindschadler (1993); dashed, S. Shabtaie (unpublished information); dotted, Reference GrayGray and others (2002). Grounded ice is recognized by the more undulated surface character in this composite of SPOT (smaller squares) andRADARSAT (background) imagery. The “ice plain” is the area of grounded ice downstream of the stations B18, DNB and A19 and upstream of Crary Ice Rise.

The mouth of Whillans Ice Stream contains a region called an “ice plain” (Fig. 1), where surface slopes are intermediate between those of active ice streams (order10⁻²) and ice shelves (order 10⁻⁴), the ice thickness above buoyancy is only tens of meters, the basal shear stress is extremely low (order 1kPa), and the bed is a till delta comprised of fore-setted stratigraphy (Reference Shabtaie and BentleyShabtaie and Bentley, 1987; Reference Alley, Blankenship, Rooney and BentleyAlley and others, 1989; Reference BindschadlerBindschadler, 1993). The heritage of field observations of the ice plain made it an obvious site to extend the measurements of deceleration and to examine their spatial variation, if any. A program designed to efficiently collect these data revealed the unexpected behavior of sudden, short-lived motions of the ice, interspersed with much longer periods of stagnation. This paper reports on this behavior and offers hypotheses to explain it.

Tides are known to affect the motion of tidewater glaciers (Reference Meier and PostMeier and Post, 1987; Reference Walters and DunlapWalters and Dunlap, 1987; Reference O’Neel, Echelmeyer and MotykaO’Neel and others, 2001). The floating portions of these glaciers rise and fall with the tide, while their horizontal speeds decrease as the tide rises and increase as the tide falls. The opposite relationship between tides and horizontal motion was reported in Greenland on Jakobshavn Isbræ (Reference O’Neel, Echelmeyer and MotykaO’Neel and others, 2001).

Tides also affect the vertical position of ice shelves, but it has only recently been reported that tides also affect the horizontal motion of both floating ice and adjacent grounded ice in Antarctica. Direct measurements have been made on Amery, Brunt and Ross Ice Shelves. Several sites on the Amery Ice Shelf exhibit unidirectional horizontal motion based on global positioning system (GPS) measurements (King and others, in press). However, GPS records from the Brunt Ice Shelf show that ice shelf experiences quasi-cyclonic horizontal motions that are related to the ocean tides or currents, with the maximum downstream velocity reached about 4 hours before high tide. These motions result in horizontal velocity reductions typically 50%, and even 4100%, of the long-term velocity (Reference DoakeDoake and others, 2002). Where it enters the Ross Ice Shelf, Ice Stream D exhibits a 50% variation in the downstream speed inanti-phasewith the tide (Reference Anandakrishnan, Voigt, Alley and KingAnandakrishnan and others, 2003). This variation is diminished 40 km upstream and is not seen 80 kmupstream, although the site of this final observation may be poorly chosen to detect residual tidal influence on ice motion.

Previous to these studies, variations in vertical strain and in basal water pressure at tidally synchronous periods were observed 300 km upstream of the grounding line onWhillans Ice Stream (Reference Harrison, Echelmeyer and EngelhardtHarrison and others, 1993; Reference Engelhardt and KambEngelhardt and Kamb, 1997) and in the seismicity of the lower 86 km of the nearly stagnant Ice Stream C (Reference Anandakrishnan and AlleyAnandakrishnan and Alley, 1997). In this latter study, a flow relationship was inferred that predicted higher flow rates at low tide (as later observed on Ice Stream D).

Our report describes the most extreme example of known tidal influence on horizontal ice motion. During most of the tidal cycle much of the ice plain is completely stationary, only moving forward during brief periods at high tide and at the midpoint of the falling tide. These short-period motion events are observed to propagate across the ice plain and onto the ice shelf.

Data

The motion described in this paper was not anticipated. The data used were collected originally to better quantify the known multi-decadal deceleration of the Whillans Ice Stream ice plain (Reference Bindschadler and VornbergerBindschadler and Vornberger, 1998), and the collection strategy was designed for that purpose. To avoid the spatial interpolations and extrapolations necessary in previous velocity-change calculations, stations for the designed study were selected from sites occupied during either RIGGS, about 25 years earlier, or the Siple Coast Project (SCP), about 15 years earlier. Geodetic-quality Ashtech Z-12 GPS receivers were used with data stored internally and power supplied by deep-cycle marine batteries. Receivers were deployed by a one-mancrew transported by TwinOtter using on-board GPS navigationto ensure accurate positioning of the receivers at former RIGGS and SCP sites. A minimum occupation time of 4hours was imposed to determine an accurate site position. The minimum interval between surveys was set at 1week. Based on the average velocity of the ice plain (400 m a⁻¹) and the anticipated ±10 cm precision of the site coordinates, this plan ensured a velocity precision well under 1%, meeting the goal of precise velocity measurements at many locations determined over a relatively short period of time in a single season.

Twenty-nine stations were occupied twice during January 1999 (Fig. 1). Occupation times varied widely depending on aircraft logistics. Often receivers were left overnight or, in cases of inclement weather, for multiple days with data collection continuing until the external battery drained. Multiple receivers were deployed during a given flight, usually in the same vicinity, to minimize flight times between stations. Subsequent flights picked up and redeployed receivers. Data were downloaded to laptop computers during redeployment flight legs, and batteries were recharged overnight at Siple Dome, the base used during the survey. Figure 2 shows the temporal record of station occupations.

Fig. 2.

Temporal plot of station occupations, motion events and composite tidal curve. Date of 1999 is indicated across station is listed along the vertical. Thick horizontal lines indicate when a GPS receiver occupied a station. Solid circles identification of a motion event from the GPS positions. Vertical lines connect events seen at multiple stations and are across the bottom to allow discussion in the text. Thin oscillatory curve is a composite of predicted tidal magnitude discussed

We processed the GPS data using the Precise Point Positioning (PPP) techniqueas implemented in the GIPSY/OASIS software (Reference Zumberge, Heflin, Jefferson, Watkins and WebbZumberge and others, 1997), estimating site coordinates and tropospheric zenith delay parameters every 5 min. The effects of the solid-Earth and pole tides were modeled, while ocean loading effects were left unmodeled. The magnitude of the total ocean load in the study region has a maximum of ∼30mm in the vertical and ∼10mm in the horizontal components. We modeled the site motion as a random walk, constraining the motion to 1mm s^−1/2, chosen to maximize the coordinate precisions while not biasing the coordinate estimates. The weighted root mean square of the coordinates of a uniformly moving site suggests that the coordinate precisions are better than 25 mm in each component. This kinematic approach was adopted after we initially attempted to process the data using a static processing strategy where site coordinates were estimated every 3hours (Reference ZumbergeZumberge, 1999). Not only did this static approach lead to results that had a lower temporal resolution compared to those using the kinematic approach, but the horizontal coordinate components also contained spurious signals. This was due to the application of a static processing methodology to data collected at a non-stationary site (King and others, in press).

The GPS data collected in this project are not of sufficient duration to accurately extract the tidal contribution to the total vertical displacement signal. We therefore obtain estimates of tidal displacement (and currents) from a numerical tidal model, the Circum-Antarctic Tidal Simulation, version 02.01, CATS02.01 (Reference Padman, Fricker, Coleman, Howard and ErofeevaPadman and others, 2002, in press). CATS02.01 is a high-resolution two-dimensional model of barotropic tides of the Southern Ocean and Antarctic Seas. The model domain extends southward from 58° S, and explicitly includes the ocean cavities under the Amery, Filchner–Ronne, George V I and Ross Ice Shelves. The resolution is 1/4° east/west and 1/12° north/south, for a typical grid spacing of ∼ 10 km at 70° S. The model is forced by height fields along 58° S obtained from the Oregon State University TPXO5.1 global tidal solution. Ten constituents are modeled, four diurnal (O₁, K₁, P₁, Q₁) , four semi-diurnal (M₂ , S₂, N₂ , K₂) and two long-period (month and fortnight) ( M_m, Mf). Most of the model details are similar to the model described by Robertson and others (1998), with the exception that CATS02.01 uses linear bottom friction. Output fields are constituent amplitudes and phases for sea surface height and depth-averagedvelocity components.

CATS02.01 performs well under the Ross Ice Shelf, as is seen by comparisons with gravimeter records (Reference Williams and RobinsonWilliams and Robinson, 1980) and synthetic aperture radar (SAR) interferometry (Reference Padman, Fricker, Coleman, Howard and ErofeevaPadman and others, 2002, in press). Much of the improvement in CATS02.01 compared with earlier models can be attributed to revising the grounding line based on SAR images from RADARSAT (Reference GrayGray and others, 2002). The choice of linear bottom friction instead of the more usual quadratic formulation also improves the model comparisons with data.

Data Analysis

Observations of stick–slip motion

Our data show that horizontal motion throughout most of this region is not steady. Instead, most stations exhibit strongly episodic motion consisting of extended periods with little movement interspersed with large and rapid displacements. Following Reference Fischer and ClarkeFischer and Clarke (1997) who measured similar sudden displacements on Trapridge Glacier, Canada, we refer to this as “stick–slip” motion.This surprising result for the ice stream is best illustrated by the GPS-calculated positions during the second occupation of G2 (Fig. 3). Most of the daily motion occurs in two distinct and brief motion events, between which the station is essentially stationary. In some cases, most of the forward motion took place between only two 5 min processing intervals. By comparing the times of these motion events with the predicted tide at the nearest floating location, the first motion event occurred near the end of the high tide, and the second event occurred during the midpoint of the falling tide. This correlation was observed frequently at several stations.

Fig. 3.

GPS positions and tidal predictions during second occupation of ice-plain station G2. Upper panel connects station positions every 5 min from processed GPS data with a gray circle every hour and date indicated every 12 hours. Open circle indicates typical mean error of a single GPS position. Lower panel shows vertical position (thin line), predicted tidal magnitude for a nearby floating position (dashed line) and horizontal displacement (thick line) calculated from 5 min GPS positions. Motion events are indicated by numbered arrows. The spike in displacement at day 29.0 is an artifact of the GPS processing.

Stick–slip motion events are seen at all stations to varying degrees. Most stations grounded on the ice plain exhibit an extremely low background velocity, with most downstream displacement confined to rapid slip events. Stations on the ice shelf exhibit a higher background velocity than ice-plain stations, but move slower during slip events. Figure 4 shows an example of this behavior from station G10. Station E2.3a, nestled closely against the upstream boundary of the nearly stationary Crary Ice Rise, is perhaps the most firmly grounded station of all, showing the least motion with little evidence of a stick–slip character. A second notable exception for a grounded station is B18, located within 1km of the ice-stream shear margin. Although this station shows numerous motion events, they are considerably less intense and more frequent than at the neighboring station DNB (Fig. 5).

Fig. 4.

GPS positions and tidal predictions during second occupation of floating station G10. Legend is identical to Figure

Fig. 5.

Concurrent records of displacement at six stations showing the near coincidence of motion events across the study area. Station locations are shown in Figure 1. Dashed lines are predicted tidal magnitudes at nearby floating locations. Thin curves are vertical GPS positions every 5 min. Thick curve is horizontal displacement calculated from GPS positions every 5 min.

Propagation speed of slip motion

While slip events are seen at multiple stations at about the same time, even with a 5 min parsing of the data we notice that the precise time of a single event at different stations can vary by many minutes. Assuming each event recorded at multiple stations has a single cause, the precise arrival times can be analyzed to locate the source and determine the mean propagation velocity of the event across the region. To estimate the time of maximum displaced motion at better than the 5 min temporal resolution of the GPS-derived positions, a parabola was fit to the five displacement measurements nearest each event. The maximum displacement of the fitted parabola was taken as the precise time of the event at that station.

Ice-shelf stations more than a few kilometers from the grounding line had to be excluded from this analysis because arrival delays for floating stations well removed from the grounded ice were very small − often a fraction of a minute. This indicates propagation velocities through the ice shelf very much faster than those calculated for propagation between grounded stations. Given the uncertainties of 1min or more in our interpolation of arrival times, the velocities from grounded to floating stations are not reliable; however, they are consistent with the elastic wave velocity in ice of 3830 ms⁻¹ (Reference Blankenship, Bentley, Rooney and AlleyBlankenship and others, 1987).

In principle, four arrival times at four independent sites allow the calculation of the source location as well as propagation velocity. While there were a few opportunities for this calculation, the imprecision of the arrival times made the source location extremely uncertain. Instead, three arrival times were used to calculate the propagation velocity and the direction, but not distance, to the source event by assuming a plane wave and constant velocity. When four stations recorded an event, calculations were completed for each possible station triplet. Table 1 presents the results. The 19 estimates of propagation velocity vary considerably and uncertainties are large. Omitting the two largest velocities produces a mean velocity of 88 ±79 m s⁻¹. For events 1–4, the sources were generally southeast of the stations (A2, G2, O and W8); for events 8 and θ, the sources were south of the stations (A19, DNB, M0 and N4). Both of these directions point toward areas at the south edge of Whillans Ice Stream where comparison ofairborne radar soundings indicate ice thickness has increased from mid-1985 to 1999 (R. A. Bindschadler and others, unpublished information). For events 11–13, the sources were located upstream of the stations (G2, G3 and Hθ), also in a region that airborne radar suggests has thickened.

Table 1.

Relative arrival time (in minutes) for numbered events at different stations. Derived velocities for each triplet of stations are presented along the last rows

Interpretation

Stick–slip motion is a common phenomenon of tectonic processes. Reference Fischer and ClarkeFischer and Clarke (1997) observed stick–slip sliding of Trapridge Glacier and suggested it is caused on that glacier by a relaxation process driven by diurnal fluctuations in surface meltwater production. Surface meltwater is not produced on Whillans Ice Stream, but we hypothesize that fluctuations in the normal pressure, forced by tidal oscillations, may drive a similar relaxation process on the ice plain of Whillans Ice Stream. The process involves the build-up of stored elastic strain in a viscoelastic material, coupled with the sudden elastic release of this strain after failure on a slip plane. The impulsive nature of the events implies some non-linear response to an imposed force. Till samples collected 400 km upstream on Whillans Ice Stream have been characterized as highly non-linear after laboratory testing (Reference Tulaczyk, Kamb and EngelhardtTulaczyk and others, 2000). In their characterization, water content (expressed as a void ratio) and effective normal stress are the key parameters that determine the failure shear strength of the till. Following Reference Fischer and ClarkeFischer and Clarke (1997), we suggest stored elastic strain may also be important.

The ice plain is a lightly grounded region experiencing very small driving stresses. Ice thicknesses in the region are only a few meters, to a few tens of meters, above flotation (Reference Shabtaie and BentleyShabtaie and Bentley, 1987). Subglacial water pressure would reduce the effective normal stresses further. Ice from the upstream portion of Whillans Ice Stream discharges ice into this area and is met by ice from Ice Stream A, creating a modest lateral compression of 24 kPa (Reference Bindschadler, Stephenson, MacAyeal and ShabtaieBindschadler and others, 1987), while the Ross Ice Shelf pulls ice from this area under modest tension on the floating ice. Driving stress for the entire region was calculated as 2.6 kPa, most of which is balanced by shear stress to the north along the shear margin ofWhillans Ice Stream and to the south along the boundary with Ice Stream A and, across A, along the Transantarctic Mountains. The resultant basal shear stress is not significantly different from zero (Reference Bindschadler, Stephenson, MacAyeal and ShabtaieBindschadler and others, 1987). Low stresses in this area make it sensitive to even small changes in external forces.

The events we observe correlate with the tidal cycle. Even with no pressurized subglacial water system, the effective pressures on the ice plain are often less than the equivalent of 10 m of ice. Thus, a 1m increase in the tide represents a substantial change to the effective normal stress. By our observations, this tidal magnitude is sufficient to cause regular motion events, whereas the smaller tides seen during the earlier portion of the field period are less able to drive a regular event pacing. Our favored hypothesis is that the tides are forcing changes to the basal condition of the ice plain. Measurements of the surface-horizontal strain rates at many sites on the ice plain show a spatially variable stress field that cannot be easily correlated to the surface topography (Reference BindschadlerBindschadler, 1993). Thus, we conclude that there is spatial heterogeneity in the basal stress field, which is associated with ice overburden pressure on the till. The directions we calculate to event sources point to regions where repeat airborne radar soundings indicate thickening of the ice plain (R. A. Bindschadler, unpublished information). These may be the stickiest spots within the ice plain and control the stick–slip behavior.

Another hypothesis is that the tides change the lateral shear resistance at the shear margin and along the Transantarctic Mountains. The directions to the source locations are consistent with this shear-margin hypothesis but we reject it for two reasons. First, station B18, closest to the shear margin, shows one of the weakest sets of motion events. Second, if the Transantarctic Mountains shear margin was the source of a tidally coupled variation of resistance, we expect the events to occur either at low tide, when the colder upper layers of the ice shelf are in tension and the warmer, lower layers are being compressed, or at mean tide, when lateral compression is minimal. Neither correlation matches our observations.

Any causal mechanism must also explain the falling-tide events. We are less confident of the causes for these events, but suggest that they arise through the influence of lateral stress on the ice base from the sub-shelf tidal current. For our observation period, this current is strongest at falling tide and is directed roughly parallel to the mean ice-flow direction. The ocean tidal currents in this region flow roughly parallel to the peninsula that forms Crary Ice Rise. The predicted spring-tide currents exceed 0.1 m s⁻¹ during falling tide, and there may be sufficient sub-shelf roughness caused by bottom crevasses in the area (Reference Jezek and BentleyJezek and Bentley, 1983), or by smaller-scale features, to transmit sufficient momentum to the basal ice and draw the ice plain forward at the location of the event sources. With nearly negligible basal shear stresses as the mean, even minor increases to the basal shear stress could prove sufficient to trigger falling-tide motion events. They are seen at every falling tide when we have data. During rising tides, ice-shelf basal stress associated with currents flowing against the mean ice-flow direction oppose the driving stresses of the ice-plain system and may help establish the exact timing of the slip events associated with high tide. Thus, the interaction between effective pressure associated with tide height and lateral stresses associated witht idal currents may be significant.

The rapid propagation of events across the ice plain suggests propagation is achieved through an elastic phenomenon. Viscous behavior would tend to dampen the events over even short distances, but they are seen to travel many tens of kilometers. The observations on Ice Stream C by Reference Anandakrishnan and AlleyAnandakrishnan and Alley (1997) lend further credence to this concept. At the Upstream B site (400km from the grounding line), Reference Blankenship, Bentley, Rooney and AlleyBlankenship and others (1987) reported a compression (P) wave velocity of 1700ms⁻¹ and a shear (S) wave velocity of 150 ms⁻¹ in the till and an effective normal stress of 50 kPa. Our mean value of propagation velocity is similar to this shear wave velocity, and the normal stresses are likely in the same range. S. Anandakrishnan (personal communication, 2002) suggested our events might be Stokely waves. This type of wave is caused by the shearing motion of one medium against another and travels at about 80%of the S-wave speed. This possibility was considered by him and Alley in their analysis of the Ice Stream C seismic observations, but rejected because their observed speeds were only 1.6 ms⁻¹. The rough agreement of the Stokely wave speed (i.e. 120m s⁻¹) with our calculations (88±79 ms⁻¹) is appealing. This explanation also provides a mechanism by which neither compression wave effects nor vertical motion would be produced, while allowing the floating stations to respond to an elastic (compression) wave with propagation speeds faster than our coarse temporal resolution permits us to measure.

We also make the observation that the magnitude of motion displacement is relatively constant for each grounded station. Thus, the displacement for the high-tide event is not three times as large as for the falling-tide event even though the quiescent time for strain to accumulate is roughly three times as long. This suggests that there is some viscous dissipation of the elastic strain, limiting the amount of stored strain for any event. Alternatively, the motion itself may involve deformation of the till, and “dilatancy hardening” could limit the displacement magnitude (Iverson and others, 1998). We favor viscous dissipation because the dilatancy effect would have to be cyclic on the order of minutes to harden and hours to relax. Viscous dissipation may also explain why there were some instances (10 out of 71) where an event was not recorded even though it was expected from the tidal state and the behavior of other stations. Viscous dissipation may be more dominant upstream of the ice plain. At the Upstream B site 400 km upstream, Reference Harrison, Echelmeyer and EngelhardtHarrison and others (1993) observed no diurnal variation in surface velocity, but vertical strain varied diurnally in summer only. Thus, at some distance upstream of the ice plain the inflow of ice must be steady. Our observations show this is yet upstream of the A19/DNB/B18 transect, but, based on the smoother motion of B18 relative to DNB, it may not be far upstream.

We return to the results on Ice Stream D where an inverse correlation between ice speed and tide, i.e. faster flow at low tide, was observed (personal communication from S. Anandakrishnan, 2002). The ice accelerates at falling tide, similar to our observations, but fast motion is sustained at about 50% above the mean through the entire low-tide period and decelerates at rising tide. This may be similar to the effect we report here if the resistive effect of lateral shear is considered. Our observations are on an ice-plain peninsula surrounded by ice shelf and far from laterally resistive mountains or slow-moving ice. The observed region of Ice Stream D is more narrowly confined and shear is expected to form a significant part of the force balance. Thus, in both cases, the bed may be fully lubricated, allowing the ice plain to move very rapidly (up to 15 km a⁻¹) without much resistance while Ice Stream D’s shear margins prevent unrestrained motion (up to 0.75 km a⁻¹). Anandakrishnan’s data also include the characteristic that the faster motion is not directly downstream but includes a significant lateral component. This may represent the influence of drag imposed by sub-shelf currents, but, because the direction of this current is different underneath D, its influence on the ice-stream motion is different.

Conclusions

Stick–slip motion on the ice plain of Whillans Ice Stream is a surprising result. We conclude that the source events are caused by the tides influencing the stress field at the base of the lightly grounded ice plain in two ways. The need for two mechanisms is forced by our observation that, especially during spring tides, there are impulsive motion events at high tide and during the falling tide. At high tide, the mechanism we favor is the release of accumulated stress through the reduction of normal stress of the ice on the till. At falling tide, we propose that the sub-shelf tidal currents, which at this phase of the tidal flow are roughly parallel to the mean ice motion, increase the net basal stress sufficiently to release the ever-accumulating stress over the ice plain.

Slip events propagate from one station to another at a mean speed of 88 ±79 m s⁻¹. This value is intermediate between the rapid elastic wave speed in ice (3830m s⁻¹) and the slower 1.6 m s⁻¹ deduced for the till underneath the stagnant Ice Stream C. Our value is close to the shear wave or Stokely-wave velocity and we suggest that these waves trigger the release of stored elastic strain as slip events across the ice plain. The displacement magnitudes are not correlated to the length of the preceding quiescent period, suggesting that some viscous dissipation may occur within the till. Our data did not allow the event-origin sites to be located with confidence, although the calculated directions toward the source events consistently point to regions where the ice plain has thickened since 1985.

The causal mechanics of these events may be similar to those underneath Ice Stream D and represent a characteristic of motion in the mouths of ice streams. On the other hand, we cannot reject the possibility that this peculiar motion is related to the observation of a sustained deceleration of the ice plain and the possible eventual stagnation of Whillans Ice Stream.