1. Introduction
Earth’s polar ice sheets play an important role in modulating global sea level, but at present there is no accurate assessment of how much of the observed sea-level rise is due to changes in ice-sheet mass balance (Reference Rignot and ThomasRignot and Thomas, 2002). The West Antarctic ice sheet is a potential contributor, because observed changes in ice dynamics appear to be causing net mass loss. Recent remote-sensing studies indicate contrasting spatial patterns of ice-sheet behavior, characterized by a positive mass balance in the Siple Coast catchment (Reference Joughin and TulaczykJoughin and Tulaczyk, 2002) and rapid thinning in parts of the Amundsen Sea basin (Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998), which appear to be related to changes in ice dynamics. These studies describe the behavior of the ice sheet on short (~decadal) timescales but may not adequately describe longer-term change of the ice sheet. Independent measurements of ice-mass change, representative of longer timescales, are therefore useful for assessing current ice-sheet behavior and predicting future changes.
Estimates for the mass balance of the West Antarctic ice sheet are available from several different methods. Remote-sensing techniques, based on measurements of ice flow and surface elevation, provide the most spatially extensive estimates. One such study, by Reference Joughin and TulaczykJoughin and Tulaczyk (2002), compared the outgoing flux of ice, derived from widespread measurements of surface velocity obtained by satellite interferometry, with the distribution of basin-wide snowfall to show that the Siple Coast ice streams have an overall positive mass balance. Most of this positive budget was attributed to the rapid thickening of one currently inactive ice stream (Kamb Ice Stream). Other ice streams were shown to be thinning, albeit at slower rates (Reference Joughin and TulaczykJoughin and Tulaczyk, 2002). Another study, by Wingham and others
*Present address: Earth Science Agency, LLC, Stateline, NV 89449, USA. (1998), used repeat satellite altimeter measurements of surface elevations to show that while most of the interior West Antarctic ice sheet was changing at very slow rates, rapid thinning was occurring in parts of the Pine Island and Thwaites glacier basins in the Amundsen Sea sector. Because of the short timescale of observation (1992–96), it is difficult to assess whether the altimetry results are indicative of changes in ice dynamics or whether the elevation changes are dominated by interannual fluctuations in snowfall.
Here we describe local estimates of ice-sheet mass balance obtained at 15 sites in West Antarctica using the submergence velocity method (Reference Hulbe and WhillansHulbe and Whillans, 1994; Reference Hamilton and WhillansHamilton and Whillans, 2000). This technique provides long-term mass-balance estimates applicable to the timescales governing changes in ice flow and decadal–centennial accumulation rate. As such, the results provide a means of interpreting and validating altimetry studies, and of assessing changes at smaller length scales than can be investigated by remote-sensing techniques. Most of the field measurements were conducted at sites along traverse routes of the United States component of the International Trans-Antarctic Scientific Expedition (US ITASE). A few other sites were installed separately using aircraft support.
2. Submergence Velocity Method
The technique entails comparison of ice vertical velocity ż, derived from repeat global positioning system (GPS) surveys of markers, with the local accumulation rate _b, obtained from core stratigraphy. Any significant difference between measured values of ż and ḃ at a point location indicates a rate of ice-sheet thickness change Ḣ . Because both measured quantities are representative of long timescales (102–103 years), calculated values of Ḣ indicate longterm behavior of measurement locations on the ice sheet. The technique is described in detail by Reference Hamilton and WhillansHamilton and Whillans (2000).
In this study, vertical velocities were obtained from repeat GPS surveys of markers installed ~5–20m beneath the ice surface. Dual-frequency GPS data were acquired over a 12–24 hour period during each survey. These data were post-processed using precise satellite orbit and clock solutions (Reference Zumberge, Heflin, Jefferson, Watkins and WebbZumberge and others, 1997) to yield precise point positions for each marker. Marker velocities were computed using repeat positions obtained from surveys conducted 1–5 years apart.
Calculated vertical velocities include the effects of firn compaction beneath the markers and the horizontal flow of markers along a slope. Firn compaction was taken into account by installing several markers (four to eight) at different depths, and hence different densities, at each site. Depth–density profiles obtained from measurements of firn-core samples (obtained for the dual purpose of determining accumulation rates) were used to test for the steadiness of firn densification (Reference PatersonPaterson, 1994; Reference Hamilton and WhillansHamilton and Whillans, 2000). The adjustment for along-slope flow was made using calculated values of horizontal velocity obtained from kinematic GPS surveys around each marker site. These adjustments usually result in only a small change in vertical velocity, except for locations where marker sites have relatively large horizontal velocities.
Long-term snow accumulation rates were derived from ice-core stratigraphy. Accumulation records of several centuries duration were obtained at most sites, based on multiparameter annual-layer dating of 50–120m deep cores (Reference KaspariKaspari and others, 2004). For the remaining sites, ~40 year average accumulation rates were determined by detecting elevated levels of gross beta radioactivity (cf. Reference Whillans and BindschadlerWhillans and Bindschadler, 1988) in shallow (<20m deep) firn cores.
The field measurements were used to solve
for each marker, where ρ is density. Uncertainties in Ḣ were obtained from the propagation of variances in each measured term (Reference Hamilton and WhillansHamilton and Whillans, 2000) which were usually small and well constrained. Uncertainties in ż ż and ḃ usually dominated the error budget, with nearly equal contributions from each term.
For accumulation rates, the uncertainty incorporates measurement errors and spatial–temporal variability. Core diameter is the principal measurement error in determining accumulation rate because it enters into the calculation of sample volume and density (cf. Reference Hulbe and WhillansHulbe and Whillans, 1994). The influence of temporal variability was minimized by averaging long-term (centennial) accumulation rate estimates. There is no apparent long-term trend in accumulation rates at most of the measurement sites (Reference KaspariKaspari and others, 2004). Spatial variability in snowfall is a source of uncertainty in point determinations of accumulation rate, like those used here. We estimated this variability from ground-penetrating radar surveys of firn stratigraphy around several of the measurement sites (Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others, 2004). Accumulation rates vary by about 10% over a distance of 2 km from ice-core sites. Because this variability increases significantly beyond 50km (Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others, 2004), we emphasize that the rates of thickness change calculated in our study are local estimates. Errors in ice velocity were the result of positioning uncertainties, and were usually smaller for modern surveys (due to improved GPS receiver performance) and for sites with multiple occupations (due to the longer interval between surveys). Combined 1 – σ uncertain- ties in Ḣ are typically ~0.02ma–1 or less, except in cases where a rapid propagates a large uncertainty in the adjustment for along-slope flow of a marker.
We neglect the effect on ż of isostatic adjustment of the crust due to glacial loading and unloading. Bedrock elevation changes due to short-term elastic and longer-term viscoelastic effects are poorly constrained in West Antarctica. The best estimate (Reference James and IvinsJames and Ivins, 1998) of present- day glacial rebound in the study region indicates only a small (~0.008ma–1) potential isostatic contribution to ż.
Field measurements were made at 15 sites in West Antarctica (Fig. 1; Table 1). These sites were located in and close to zones of rapid flow in the Siple Coast and the Amundsen Sea basin, on slow-moving flanks in the ice-sheet interior and across the main ice divide in West Antarctica. One site was located in the upper catchment of Rutford Ice Stream.
Table 1. Location of measurement sites and dates of survey occupation. Elevations are meters above the World Geodetic System 1984 (WGS84) ellipsoid
Fig. 1. Shaded relief image of the OSU DEM (digital elevation model; Reference Liu, Jezek and LiLiu and others, 1999) showing the location of submergence velocity stations in West Antarctica. Illumination is from 90˚ W.
3. Results
3.1. Siple Coast ice streams
Six sites were installed on or close to the main trunks of several ice streams draining the Siple Coast. There are reasons to expect mass-balance changes in this part of West Antarctica because of observations of recent large-scale changes in ice dynamics (e.g. Reference Joughin, Tulaczyk, Bindschadler and PriceJoughin and others, 2002).
UpB is located on the fast-flowing central part of Whillans Ice Stream. Results of calculations using the submergence velocity technique show that rapid thinning of ~1.32ma–1 (1 – σ uncertainty 0.09ma–1) is occurring at this site (Table 2). We note the fast horizontal motion of this site introduces a large along-slope component in vertical velocity which is difficult to remove with confidence, as indicated by the large uncertainty. The thinning rate, however, is more than an order of magnitude larger than the local 40 year average accumulation rate (~0.09ma–1), implying either an ice-dynamics forcing or a substantial change in accumulation rate. An observed reduction of flow speeds in this part of Whillans Ice Stream (Reference Hulbe and WhillansHulbe and Whillans, 1997; Joughin and others, 2002; Reference Stearns, Jezek and van der VeenStearns and others, 2005; this study) might account for some of the calculated thinning by decreasing the incoming mass flux. The horizontal velocity at UpB, adjusted for down-glacier advection of the survey site, decelerated from ~430ma–1, as measured in 1991–92 (Reference Hulbe and WhillansHulbe and Whillans, 1997), to ~416ma–1, as measured in 1996–97 in the current study. Because of this non-steady flow, however, we caution that the thinning results be interpreted carefully.
Table 2. Measured and derived quantities at each of the sites discussed in the text, and accompanying 1 – σ uncertainties. Horizontal velocities were derived from repeat GPS surveys. Accumulation rates ḃ were derived from ice-core stratigraphy (Reference KaspariKaspari and others, 2004) and represent long-term averages (100–400 years). Asterisks denote ~40 year average accumulation rates derived from detection of bomb horizons. Rates of thickness change Ḣ were obtained by solving Equation (1). Our results are compared, where possible, with other mass-balance estimates aSpatial averages over 143 000km2 (for the UpC comparison) and 153 400 km2 (for the UpB comparison), from Reference Joughin and TulaczykJoughin and Tulaczyk (2002). b5000 km2 spatial average over the region closest to UpB and a crossover measurement at UpC, from Reference Spikes, Csathó, Hamilton and WhillansSpikes and others (2003).cSpatial averages for slow-moving ice (<20ma–1) (~20 000km2) and intermediate ice (~50–200ma–1) (50 000km2) in the Amundsen Sea basin, from Reference Shepherd, Wingham, Mansley and CorrShepherd and others (2001).
A marker site was installed in the high-elevation catchment of Whillans Ice Stream to test for longitudinal variations in mass balance. The Inland-WIS station is ~100km up-glacier of the region of rapid flow. Here, results of the calculations indicate steady-state conditions (Table 2). These conditions have persisted for at least the length of the accumulation rate record (~40 years) and may indicate that sustained drawdown of the catchment due to the rapid flow of Whillans Ice Stream is nearing an end.
The Snake site is located <500m outboard of the northern shear margin (the ‘snake’) to Whillans Ice Stream. Horizontal velocities at this location (~12.7ma–1; Table 2) show that slow-flowing interstream ridge ice is accelerating as it approaches the shear margin. A thinning rate of 0.20 ± 0.02ma–1 was calculated for this site, which is slightly faster than similar calculations indicated for the Dragon site on the opposite shear margin (Reference Hamilton, Whillans and MorganHamilton and others, 1998). This thinning rate is within the range of thinning calculated farther down-glacier on the ‘snake’ shear margin using a different dataset (Reference Stearns, Jezek and van der VeenStearns and others, 2005).
UpC is the only submergence velocity station on the stagnant Kamb Ice Stream. The horizontal velocity over the period 1995–97 was 13.5ma–1. Submergence velocity calculations show that this site is currently thickening at ~0.56 ± 0.02ma–1. This thickening rate is several times larger than the measured local accumulation rate of 0.1ma–1 (Table 2). It is unlikely the thickening rate is due to a recent change in accumulation rate, because it implies a severalfold increase in snowfall which is inconsistent with other accumulation rate evidence in this region (e.g. Reference HamiltonHamilton, 2002). An ice-dynamics cause is more likely. Flow speeds farther up-glacier are ~100ma–1 or larger (Reference Joughin, Tulaczyk, Bindschadler and PriceJoughin and others, 2002), indicating a steady incoming flux of ice to the UpC site. The outgoing flux, however, is very small because Kamb Ice Stream is stagnant down-glacier of UpC (Reference Anandakrishnan, Alley, Jacobel, Conway, R.B. and BindschadlerAnandakrishnan and others, 2001). This flux imbalance is inferred as the cause of the calculated ice-sheet thickening (cf. Reference Price, Bindschadler, Hulbe and JoughinPrice and others, 2001).
One site (99-2; Fig. 1) was installed close to the onset of rapid motion of a tributary to Bindschadler Ice Stream, in a region of intermediate-speed ice (Table 2). The results of calculations indicate slow thinning at ~0.1 ± 0.01ma–1. This thinning might be a result of continued drawdown of tributary ice by Bindschadler Ice Stream.
3.2. Amundsen Sea basin
The largest outlet glaciers in this basin are Pine Island and Thwaites Glaciers. Mass-flux calculations (Reference RignotRignot, 1998) and satellite altimeter measurements (Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998; Reference Shepherd, Wingham, Mansley and CorrShepherd and others, 2001) suggest that rapid thinning is occurring in parts of each catchment, although Reference Vaughan, Alley and BindschadlerVaughan and others (2001) suggest that, input–output as a whole, Pine Island Glacier is close to balance. Independent ground-based estimates of change are, however, lacking for this part of Antarctica.
One submergence velocity station was installed in the upper reaches of Thwaites Glacier. Site 01-1 is approximately 100km from the ice divide, in a region of inland flow (Fig. 1). Thinning of ~0.22 ± 0.016ma–1 was calculated for this location (Table 2).
Three sites were located in the upper part of Pine Island Glacier (Fig. 1). Sites 01-3 and 01-4 are located in a ‘neck’ between the northern and southern lobes of the glacier basin identified by Reference Vaughan, Alley and BindschadlerVaughan and others (2001). Thinning was calculated for both sites, in the range ~0.15–0.25 ± 0.02ma–1 (Table 2). The third site, 01-6, was installed within ~25 km of the ice divide separating Pine Island Glacier from Rutford Ice Stream, as indicated by the very slow flow speeds (Table 2). Results of the submergence velocity technique show this site is close to steady state (Table 2), although we note that the accumulation rate record for this location is relatively short (~18 years).
One site, 01-5, was installed in the upper catchment of Rutford Ice Stream (Fig. 1), about 75km from the ice divide with Pine Island Glacier. The rate of thickness change at this site indicates a negative mass balance (~0.15 ± 0.016ma–1).
These large rates of change in ice thickness are likely due to ice dynamics, because an analysis of accumulation rates from ice cores collected at these sites indicates no significant trend or variations in snowfall over the last ~200 years (Reference KaspariKaspari and others, 2004). Unfortunately, with just two sites in the ‘neck’, we are unable to test the hypothesis that the presence of two catchment lobes is an indication of unsteady flow conditions in the basin (cf. Reference Vaughan, Alley and BindschadlerVaughan and others, 2001). However, both sites (01-3 and 01-4) are thinning at ~0.2ma–1, and it is tempting to speculate that this represents evidence of increased drawdown of ice from the southern lobe and the ‘neck’ region.
3.3. Main West Antarctic ice divide
This divide separates the Siple Coast from the Amundsen Sea basin. It is a broad, flat feature (Reference Liu, Jezek and LiLiu and others, 1999) at approximately 1750m elevation.
Three submergence velocity stations were installed in the vicinity of a proposed deep ice-core drilling site (Reference Morse, Blankenship, Waddington and NeumannMorse and others, 2002). The sites, 00-1A, 00-1B and 00-1C, are arranged along a ~50km transect approximately orthogonal to the divide ridge (Fig. 1). All three sites appear to be located slightly off the flow divide in the catchment of Bindschadler Ice Stream, based on flow azimuths (Table 2). Results indicate near-steady-state conditions at each location, with very small residual rates of thickening in excess of the calculated uncertainties. There does not appear to be any difference in mass-balance conditions between the sites, although there is a detectable gradient in accumulation rate (Table 2). We are unable to test for divide migration, for example by detecting differential rates of thickness change (Reference HamiltonHamilton, 2002), because these sites do not span both flanks of the ridge.
Flow vectors indicate that site 00-5 (Fig. 1) lies slightly within the Amundsen Sea sector. Steady-state conditions were calculated for this location (Table 2). Although the four sites (00-1A, 00-1B, 00-1C and 00-5) do not fall on a straight line orientated orthogonal to the divide axis, the absence of differential rates of thickness change might be indirect evidence that the divide is not currently migrating.
4. Discussion
The results from our distributed set of submergence velocity stations reveal the largest rates of change in ice thickness are occurring in and very close to regions of enhanced flow identified by Reference Bamber, Vaughan and JoughinBamber and others (2000). Conversely, we find that interior regions of the ice sheet characterized by slow sheet flow appear to be close to steady-state conditions. This broad spatial pattern is consistent with earlier results of calculations using the submergence velocity technique at a smaller number of sites (Reference Hamilton, Whillans and MorganHamilton and others, 1998; Reference HamiltonHamilton, 2002).
Our results are also consistent with larger-scale remote-sensing estimates of mass balance for West Antarctica (Table 2). Mass-flux calculations based on space-borne measurements of ice velocity (Reference Joughin and TulaczykJoughin and Tulaczyk, 2002) indicate rates of thickness change for Whillans, Kamb and Bindschadler Ice Streams that are in line with our results. Reference Spikes, Csathó, Hamilton and WhillansSpikes and others (2003) conducted repeat airborne laser altimeter surveys over selected regions of Whillans and Kamb Ice Streams, and, for sites where measurements overlap (Table 2), their results agree with our local rates of thickness change from the submergence velocity technique. Ordinarily, short-term repeat altimeter surveys (<5 years apart) might not be expected to agree with long-term rates of change from other methods, such as the submergence velocity technique, because of interannual variability in snowfall and the effects of firn compaction. The close agreement between our results and those of Reference Spikes, Csathó, Hamilton and WhillansSpikes and others (2003) is probably due to the large size of the ice-dynamics-forced changes (~0.1ma–1) relative to short-term accumulation rate variability in this part of West Antarctica.
Similarly good agreement is found between our results and satellite radar altimeter-derived estimates of elevation change (Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998; Reference Shepherd, Wingham, Mansley and CorrShepherd and others, 2001) on the main West Antarctic ice divide and in the Amundsen Sea basin (Table 2). The sites with the fastest rates of thickness change calculated using the submergence velocity technique (01-1, 01-2 and 01-4) fall in regions noted by Reference Shepherd, Wingham, Mansley and CorrShepherd and others (2001) as having large changes in elevation during the period 1992–99. Sites with conditions calculated to be close to steady state (00-1A, 00-5, 01-6 (Table 1) and Byrd Station (Reference Hamilton, Whillans and MorganHamilton and others, 1998)) showed little change in elevation during the radar altimeter surveys. The agreement between the two sets of results suggests that the conclusion reached by Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others (1998), that of steady-state conditions for most of Antarctica and rapid changes in a few isolated catchments, i.e. the Amundsen Sea basin and the Siple Coast, is largely correct.
An independent analysis (Reference KaspariKaspari and others, 2004) of ice-core accumulation rate records from the Amundsen Sea basin provides a useful context for interpreting the present results and those of Reference Shepherd, Wingham, Mansley and CorrShepherd and others (2001). No significant trends or changes in snowfall over the past ~200 years were present in these records (Reference KaspariKaspari and others, 2004), suggesting that the thinning rates calculated from the submergence velocity technique are an ice-dynamics effect. In addition, Reference KaspariKaspari and others (2004) report there was no anomalous variability in snowfall during the 1990s which might account for the surface elevation lowering observed in satellite altimeter results (Reference Shepherd, Wingham, Mansley and CorrShepherd and others, 2001), further supporting an ice-dynamics forcing of current mass balance in the Amundsen Sea basin.
One potential concern of interpreting our results as indicators of long-term ice-sheet behavior is recent evidence of short-period changes in ice flow (e.g. Reference Bindschadler, King, Alley, Anandakrishnan and PadmanBindschadler and others, 2003). The submergence velocity technique assumes that ice-sheet vertical velocities are steady on timescales similar to those used to determine accumulation rates (102– 103 years). This assumption might not be valid for sites on or near active ice streams, where decadal trends in velocity (e.g. Reference Joughin, Tulaczyk, Bindschadler and PriceJoughin and others, 2002) and tidal-forced daily velocity fluctuations (Reference Bindschadler, King, Alley, Anandakrishnan and PadmanBindschadler and others, 2003) have been observed. We argue, however, that sub-annual-scale velocity variations are unimportant, on the basis of results from several ice-stream sites that have more than one measurement epoch (Table 1). In those cases, rates of thickness change are similar when calculated using individual epochs or all available data. The effect of decadal-scale trends in velocity is more difficult to assess, but perhaps implies that rates of change calculated at sites of rapid flow might only apply to the periods of measurement (a few years) rather than longer accumulation rate timescales.
5. Conclusions
Local rates of ice-thickness change were obtained using measurements of ice vertical velocity and accumulation rate at 15 sites in West Antarctica. Calculated rates of change are very different at each site. In general, the largest changes are occurring in or near regions of rapid flow in the Siple Coast and Amundsen Sea sectors. Near-steady-state conditions were calculated for sites in the slow-moving ice-sheet interior and close to the main ice divide.
The results are consistent with larger-scale elevation change and mass-balance estimates from remote-sensing methods (e.g. Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998; Reference Joughin and TulaczykJoughin and Tulaczyk, 2002; Reference Spikes, Csathó, Hamilton and WhillansSpikes and others, 2003). This level of agreement suggests that the remote-sensing results, appropriately adjusted for short-term fluctuations in surface mass balance, are valid indicators of long-term ice-sheet behavior.
In general, most parts of the ice sheet currently do not appear to be undergoing significant changes in mass. However, large rates of change are calculated for several sites in or close to regions of rapid flow. Because of the importance of ice streams and outlet glaciers in controlling ice-sheet mass balance, and in light of a complex series of changes observed on Whillans Ice Stream, we believe there is merit in continuing to monitor ice-sheet mass balance at local scales.
Acknowledgements
The fieldwork was made possible by the hard work of S. Price, E. Venteris, I. Whillans, the air crews of Kenn Borek Air, and members of US ITASE. S. Kaspari and D. Dixon supplied most of the accumulation rate data. Comments from R. Arthern, A. Shepherd and D. Vaughan improved the final manuscript. This research was supported by the US National Science Foundation (OPP-9419396 and OPP-0196441).
