## Abstract

Satellite radar altimeter measurements show that the average elevation of the Antarctic Ice Sheet interior fell by 0.9 ± 0.5 centimeters per year from 1992 to 1996. If the variability of snowfall observed in Antarctic ice cores is allowed for, the mass imbalance of the interior this century is only −0.06 ± 0.08 of the mean mass accumulation rate.

The best estimate of 20th century sea-level rise is 1.8 mm year^{−1} (1). Of this, known sources are insufficient by 360 Gt year^{−1} of water (1). This missing water may reflect uncertainties in sea-level rise, ocean thermal expansion (2), change in the Greenland Ice Sheet (3) and other land ice (4), and groundwater storage (5). It could equally signal a source as large as 500 Gt year^{−1} within the grounded Antarctic Ice Sheet (1, 6). However, one part of the grounded ice area (42%) has been estimated (7) from sparse glaciological data to be growing at 118 Gt year^{−1}. If this part is characteristic of the whole grounded ice sheet, Antarctica has been a 435 Gt year^{−1}sink of ocean mass (7).

Here we use 5 years of spatially continuous ERS satellite measurements to estimate the rate of change of thickness of 63% of the grounded Antarctic Ice Sheet. Between 1992 and 1996, 4 × 10^{6}ice-mode ranges were recorded by the ERS-1 and ERS-2 satellite altimeters (8) at crossing points of the satellites' orbit ground tracks. The ranges were corrected for the lag of the leading-edge tracker (9), surface scattering (10), dry atmospheric mass (11), water vapor (11), ionosphere (11), slope-induced error (9), solid Earth tide (11), ocean loading tide (11), and isostatic rebound (12). The satellite location was determined with the DGM-E04 orbit model (13). After data editing, we formed time series of 35-day averages of elevation change (Fig. 1). From these time series (14), we determined the average 5-year rate of elevation change for 1° by 1° cells (Fig. 2), the major drainage basins, and the entire region of coverage (ROC) (Table 1).

We also estimated the total error covariance (Fig. 3) of the elevation change by summing its contributions. For errors that decorrelate over less than 35 days, we determined the covariance of elevation rate that arose when crossover sums were replaced with differences (14). This method should account for the speckle-induced error and much of the atmospherically related and satellite-location errors. The variability was 4.10 cm year^{−1}, decorrelating to ∼0.4 cm year^{−1} at separations larger than 200 km. For satellite-location errors with longer correlations, we examined the difference in elevation change that arose on replacing the satellite locations with those from the TEG-3 orbit model (15). These errors are negligible. We estimated that the variability due to instrument system drift was 0.13 cm year^{−1} by differencing the ice-free Southern Ocean elevations measured by the ERS and TOPEX/Poseidon (16) altimeters south of 50°S. Instrument changes (particularly to gain control in December 1992 and orbit altitude in April 1994 and March 1995) result in a residual error in the tracker-lag correction. By replacing the leading-edge tracker with echo cross correlation, we estimated that the variability of this error was 0.5 cm year^{−1}. We were unable to estimate from independent measurements a residual error in the surface-scattering correction. This correction is large in places, but were it substantially in error, we would expect to find correlation between the correction and the elevation rate. However, the largest correlation coefficient at any value of separation was 0.06.

Elevation changes corrected for isostatic rebound reflect thickness changes due to changes in ice flow, bottom melting, snow accumulation, and ablation. In the interior, bottom melting is small and few places experience net ablation. If we assume that in the interior, ice is flowing by internal shear over a frozen or rough bed, the flow is unlikely to have altered on century to millennial time scales. Accumulation since the middle of the 19th century (17–23) has fluctuated in the interior about a constant mean accumulation rate (MAR). A change in elevation should result from either a century-scale mass imbalance or a contemporary fluctuation in accumulation rate. (We assume a century scale because there are few records of accumulation before 1850.)

Accumulation fluctuations occur at annual to decadal scales (17–23) and will appear (24) in the elevation rate with the density of snow. Their 5-year point variability is ∼0.15 of the MAR (hereafter 0.15 MAR) (25). The density of snow is ∼350 kg m^{−3}; Table 1 gives the spatial average of MAR (hereafterM̅A̅R̅). With these data, the average temporal variability of the fluctuation within the ROC is 5.5 cm year^{−1}. At any point, the total elevation error from satellite observation is similar. Its variability is 4.13 cm year^{−1}(Fig. 3). However, the elevation error decorrelates rapidly with distance (Fig. 3). For the ROC as a whole, it is 0.5 cm year^{−1}. The extent to which the elevation change can be used to estimate the century-scale imbalance at large scales depends on how snow accumulation has fluctuated with distance.

Accumulation has fluctuated greatly this century at ice-core sites in separate drainage basins in the Antarctic interior, and there seems to be little or no correlation among these sites (26). On the other hand, if a substantial covariability survives at 1° by 1° (∼100 km by 30 km), it should be apparent in the measured elevation change. We compared the covariance of the measured elevation change with the total error covariance (Fig. 3). The difference between them is the actual covariance of the elevation rate. The variability of the difference was 2.7 cm year^{−1}, and the correlation scale was ∼200 km throughout the ROC. We therefore take 200^{2}π km^{2} as the areal correlation scale for snow accumulation. To estimate (27) the variability of snowfall of a basin (Table 1), we assumed that the snowfall variance reduces as the ratio of the basin area to this reference area.

To estimate the century-scale imbalance, we treated the elevation change error and snowfall variability as equivalent sources of uncertainty. From Table 1, the estimated ice imbalances of individual basins range from 0.42 to −0.28 M̅A̅R̅; the average uncertainty is 0.30 M̅A̅R̅. For East Antarctica (basin J"-E′), the estimated imbalance is −1 ± 53 Gt year^{−1} or 0.00 ± 0.08 M̅A̅R̅; for West Antarctica (basin E′-J"), it is −59 ± 50 Gt year^{−1}or −0.17 ± 0.15 M̅A̅R̅; and for the ROC as a whole, it is −60 ± 76 Gt year^{−1} or −0.06 ± 0.08M̅A̅R̅. This last value of imbalance has a lower uncertainty than the range of −0.28 to 0.24 M̅A̅R̅, which is equivalent to the −500 to 435 Gt year^{−1} that previous observations (1, 6, 7) allow for the grounded ice. Fifty gigatons per year equals 0.14 mm year^{−1} of eustatic sea-level change (6). It appears that the interior of the Antarctic Ice Sheet has been at most only a modest source or sink of sea-level mass this century. The data also provide evidence that the fluctuations in snowfall observed in the sparse Antarctic ice-core record (for example, *17*–*23*) are not characteristic of the continent but have a spatial scale of 200 km on average.

It is possible that a larger imbalance has been compensated for by a fluctuation in accumulation of the opposite sign that is larger than we estimate. The estimate of snowfall variability is made from observations (25) at locations outside the ROC that are not contemporary with the elevation change; the spatial scale of fluctuation may vary over the ice sheet, and the elevation change extends over one 5-year interval. Nonetheless, an imbalance of −0.28 or 0.24 M̅A̅R̅ makes a heavy demand on the contemporary snowfall. For example, an imbalance of −0.28 M̅A̅R̅requires (28) that the accumulation increased throughout the ROC by greater than half the point variability (0.08M̅A̅R̅). However, in general, recent accumulation in Antarctica does not look unusual. Between 1955 and 1996, accumulation has been high at some sites (6, 29) and low (18) or close to the century mean (6,18, 22, 23, 30) at others. Although a recent increase in mean annual Antarctic temperature has occurred (29), it is too small to explain a fluctuation of ∼0.25 M̅A̅R̅. A large century-scale imbalance for the Antarctic interior is unlikely. This conclusion is in keeping with a body of relative sea-level and geodetic evidence supporting the notion that the grounded ice has been in balance at the millennial scale (31).