Recent in situ measurements of surface mass balance and improved calculation techniques are used to produce an updated assessment of net surface mass balance over Antarctica. A new elevation model of Antarctica derived from ERS-1 satellite altimetry supplemented with conventional data was used to delineate the ice flow drainage basins across Antarctica. The areas of these basins were calculated using the recent digital descriptions of coastlines and grounding lines. The delineation of drainage basins was achieved using an automatic procedure, which gave similar results to earlier hand-drawn catchment basins. More than 1800 published and unpublished in situ measurements of net surface mass balance from Antarctica were collated and then interpolated. A net surface mass balance map was derived from passive microwave satellite data, being employed as a forcing field to control the interpolation of the sparse in situ observations. Basinwide integrals of net surface mass balance were calculated using tools available within a geographic information system. It is found that the integrated net surface mass balance over the conterminous grounded ice sheet is 1811 Gton yr−1 (149 kg m−2 yr−1), and over the entire continent (including ice shelves and their embedded ice rises) it is 2288 Gton yr−1 (166 kg m−2 yr−1). These values are around 18% and 7% higher than the estimates widely adopted at present. The uncertainty in these values is hard to estimate from the methodology alone, but the progression of estimates from early studies to the present suggests that around ±5% uncertainty remains in the overall values. The results serve to confirm the great uncertainty in the overall contribution of the Antarctic Ice Sheet to recent and future global sea level rise even without a substantial collapse of the West Antarctic Ice Sheet.
Snowfall from clouds and clear skies, the formation of hoarfrost at the surface and within the snowpack, sublimation, melting and runoff, wind scouring, and drift snow deposition, all contribute to solid, liquid, and gaseous water transfer across the surface of the Antarctic Ice Sheet. Although the measurement of any one of these processes is still a difficult proposition (King and Turner 1997, 16), the net surface mass balance, the aggregate of them all, is measurable by a variety of glaciological techniques.
A precise evaluation of the amount and pattern of net surface mass balance over the Antarctic Ice Sheet (Fig. 1) will confer benefit on many active areas of research including the selection of ice coring sites before drilling (Clausen et al. 1988), comparison with poleward atmospheric moisture transport (Bromwich 1990), the validation of weather and climate models (Tzeng et al. 1993; Connolley and Cattle 1994; Genthon 1994; Genthon and Braun 1995; Connolley and King 1996; Ohmura et al. 1996; Starley and Pollard 1997), and investigations of ice flow (Fastook and Prentice 1994; Huybrechts 1994; Budd and Warner 1996).
Recent studies have shown distinct small-scale spatial variability in net surface mass balance over the Antarctic Ice Sheet (Richardson et al. 1997; Isaksson et al. 1996), whereas others have revealed temporal trends in net surface mass balance that are both positive (Petit et al. 1982; Jouzel et al. 1983; Goodwin 1991; Morgan et al. 1991; Peel 1992) and negative (Isaksson et al. 1996). Considered in isolation these studies could be taken to suggest that an attempt to draw a synoptic map of net surface mass balance for the continent might be unsound. This is, however, only true over a small-scale, and we proceed on the premise that there exist broad-scale, persistent patterns of net surface mass balance that can be mapped at a continental scale, in the same way that, for example, rainfall can be mapped across continental-scale areas without discounting the possibility of local variations and temporal trends.
Continent-wide maps of net surface mass balance have traditionally been compiled from in situ measurements of net surface mass balance from pits and cores. More data have been added to these maps as they have been collected, so that the maps of net surface mass balance have become progressively more detailed, and presumably more accurate, accepting the proviso that the data have been derived over progressively longer periods. In the last four decades at least 22 such compilations have been presented. The most significant reassessments have been presented at approximately 10-yr intervals: Kotlyakov (1961), Bull (1971), and Giovinetto and Bentley (1985). Giovinetto and Bull (1987) showed that the mean net surface mass balances calculated for these compilations were generally converging, although considerable scatter persists. The last significant reassessment (Giovinetto and Bentley 1985) can now be updated with more in situ measurements and more reliable methods of analysis. Thus this paper continues the process of reassessment, but introduces several improvements:
A new topographic model of the ice sheet that defines the pattern of flow and the drainage basins more accurately.
An updated compilation of in situ measurements that gives improved resolution in the net surface mass balance map.
The use of an independent background field to control the interpolation between sparse in situ measurements.
Improved techniques of basinwide integration within a geographic information system (GIS) that removes the uncertainty introduced by manual analysis.
2. Delineation of drainage basins
a. Antarctic digital elevation model
This study is based on a digital elevation model (DEM) of Antarctica previously presented and discussed by Bamber (1994) and Bamber and Huybrechts (1996). For most of the continent, the DEM was derived from more than 20 000 000 measurements of surface elevation retrieved from the eight 35-day repeat cycles of the ERS-1 satellite radar altimeter. Over areas where slopes are less than 0.5°, the vertical accuracy is better than ±1 m. In areas of higher surface slope, accuracy is reduced. Around the coast and in mountainous areas where the altimeter failed to maintain track on the ice sheet surface, the altimeter measurements were supplemented with data taken from the Antarctic digital database (ADD; SCAR 1993; Thompson and Cooper 1993). Beyond the orbital limit of ERS-1, south of 81.5°S, data from the Scott Polar Research Institute folio series (Drewry 1983) and data from the original airborne radar sounding flights have been used. In some areas the only data available were collected during the Tropical Wind Energy Conversion Reference Level Experiment (TWERLE) 1975–76 (Levanon et al. 1977; Levanon 1982).
All these data were gridded to 10-km resolution using methods described by Bamber and Huybrechts (1996). Throughout the paper this DEM will be referred to as the Observed DEM. Figure 2 presents the Observed DEM as a series of images designed to highlight complementary aspects of the topography. The two shaded-relief maps (Figs. 2a and 2b) give an impression of the overall shape of the ice sheet, whereas the map showing magnitude of surface slope (Fig. 2c) highlights flatter areas such as ridges, domes, and subglacial lakes. Finally, Fig. 2d shows the direction of maximum slope and serves to highlight the exact position of the ice divides and ridges.
b. Delineation of basins
In common with all glaciers, ice flow within the Antarctic Ice Sheet is driven by stresses generated as the result of surface and basal slopes. For most of the Antarctic Ice Sheet, the stress resulting from the surface slope is dominant (Paterson 1994, 241) and the flow of the ice sheet is generally parallel to the direction of maximum surface slope, or aspect. Exceptions to this rule will be discussed in a later section. This reasoning was first used to determine drainage basins by Giovinetto (1964). Drewry (1983) also used this reasoning to plot flowlines for the entire continent by determining the direction of maximum surface slope on a grid (111-km resolution) of the best available surface elevation model. From this he drew the flow vectors by hand. Drewry’s contours and flowlines were used by Giovinetto and Bentley (1985) to determine the catchment areas that feed 26 physiographically distinct sectors of the coastline of Antarctica. A similar approach was taken by Radok et al. (1986, 1987) using a computer analysis of a gridded version of the same data to produce a simpler set of drainage basins.
A catchment basin delineation similar to that done by Drewry has been performed for this study by applying standard hydrological modeling tools available in the proprietary GIS, ARC/Info (version 7.0), to the Observed DEM. Several steps were required to determine the drainage pattern.
The Observed DEM was made hydrologically consistent by artificially filling any closed surface depressions (sinks) deeper than 50 m. In practice, this involved the filling of only one depression within the ice sheet between Hercules Dome and Horlick Mountains (85°55′ S, 114° W). This depression was also present in the DEM shown by the British Antarctic Survey (1993, hereafter BAS), although it is not clear if it represents a real and unexplained surface depression or is an artifact of the data.
For each cell in the Observed DEM the direction of steepest descent (aspect) was determined by reference to adjacent grid points and a new grid of containing the aspect generated. Where the descent to all the adjacent cells was the same, the search was extended until the steepest descent was found. Where the steepest descent was found for two directions, both directions were recorded (Jenson and Domingue 1988). Because no interpolation was allowed, only eight primary directions were allowed.
The grid of aspect data was converted to a vector description of the ice flow trajectories. Whereas the improved resolution of this operation (10 km) over that achieved by Drewry (111 km) allowed for a considerable improvement in the detail in the map of flow direction, it was clear that there existed some problems with this description of the flow. Primarily, there is a mismatch between the area north of 81.5°S for which ERS-1 data were available and that south of this line, for which only terrestrial, airborne, and TWERLE balloon data were available. The derived flowlines appear to skirt the boundary of this area, indicating some mismatches in DEM slopes. Furthermore, whereas the flowlines outside this area have a well-formed dendritic appearance, inside they are parallel over wide areas, indicating that the sparse data has resulted in unrealistically planar areas.
The watershed or basin was defined as the upslope area contributing to flow across a defined section of coast and simply calculated from the flow trajectories. The overall pattern of drainage was controlled by defining sections of grounding line manually. In the present analysis these sections were defined to be the same as those used by Giovinetto and Bentley (1985), rather than according to any particular topographic criterion, allowing direct comparison with the earlier work.
Since the above analysis assumes that ice flow is parallel to the aspect, which is not necessarily true for floating ice, we have chosen to limit the flow analysis to the grounded continental ice sheet, and not extend it to the ice shelves. Figure 3 shows the results of the automatically derived basin delineation procedure.
c. Amendments to the automatically derived basins
Although the automatic procedure described above provided an adequate delineation of the drainage basins over most of the ice sheet, there exist two locations where we believe it needs amending.
1) The effect of subglacial lakes
Around 64 subglacial lakes have now been identified in Antarctica (Siegert et al. 1996). They occur mostly under thick ice in East Antarctica and are generally only a few kilometers in extent. Although, most of the lakes were identified by the characteristically strong and uniform echoes on ice sounding radar (Oswald and Robin 1973; Steed 1980; McIntyre 1983), many are also visible as unusually flat areas on surface maps derived from satellite radar altimetry (Cudlip and McIntyre 1987; Ridley et al. 1993), showing that subglacial lakes have a strong influence in the surface topography of the ice sheet. Without basal restraint, the dynamics of the ice sheet over the lakes is similar to those of a confined ice shelf; local flow is determined by the local strain rate and ice velocity around the margins. Such behavior could disrupt our determination of ice divides over the lakes. Fortunately, most of the lakes have dimensions similar to the ice thickness (Siegert et al. 1996). This is smaller than the present grid resolution, and so they are unlikely to disrupt the determination ice divide position. There are two possible exceptions, Lake Vostok (241 km × 43 km; Kapitsa et al. 1996) and the 30-km lake in Terre Adelie, identified by Cudlip and McIntyre (1987).
The Terre Adelie lake had little impact on the determination of the catchment basin, as it lies entirely within one basin. Lake Vostok was, however, bisected by the automatically derived drainage divide (Fig. 3). Only one ice velocity measurement has been made, at the southern extremity of the lake. From this measurement Kapitsa et al. asserted that ice flow over the lake was controlled solely by local surface gradient, and thus was parallel to the long axis of the lake, in agreement with the automatically derived ice divides. We prefer the interpretation that the flow of ice on the lake is driven largely by ice velocities around its boundaries, not local strain rate, and that ice flow is generally perpendicular to the axis of the lake. This implies that we should calculate the basin boundaries ignoring the local topography over the lake. This line of reasoning has required a manual amendment to the automatically derived ice divide as shown in Fig. 3.
2) The effect of data sparsity
There is an area inland of Support Force Glacier, beyond the limit of ERS-1 data, where the sparsity of data produces a poorly constrained ice divide. In this area we have decided to edit manually the ice divide to maintain agreement with ice surface contours and form lines given in the ADD.
d. Drainage basin areas
Figure 3 shows a direct comparison of the ice drainage basins derived by Giovinetto and Bentley (1985) and those derived above. There are no gross differences between the two sets of drainage basins and most of the divides lie very close to those derived by Giovinetto and Bentley (1985). In one minor area the Giovinetto and Bentley delineation does seem questionable; they suggested that four drainage basins adjoined at a single junction near Dome A. Hindmarsh (1993) has discussed the likelihood of such a juxtaposition and determined that it would represent a nongeneric, or unlikely random occurrence. In the drainage basin delineation derived in this study there are no four divide junctions.
Table 1 allows us to make a more detailed comparison based on the areas of the derived catchment basins. Areas of the derived basins have been calculated with reference to the 1:30 million scale coastline presented in the ADD after reprojection to the Lambert equal area projection. These areas can be compared directly with those calculated by Giovinetto and Bentley (1985), which are also given in Table 1. As Giovinetto and Bentley used a different grounding line and measured the area of each drainage basin graphically at 1: 10 000 000 scale, correcting for scale distortion by using a single scale factor, updated estimates of areas for the Giovinetto and Bentley drainage basins are also listed in Table 1. These were calculated using the updated grounding line on a Lambert equal area projection.
Clearly, the change in the grounding line and method of calculation has caused some considerable changes in the areas of the drainage basins. In some cases (e.g., E"F) this is largely due to an updated grounding line, whereas in others (e.g., C′D) there is some disparity that is more probably due to improved methodology.
The sums of the areas of the of the basin polygons representing the conterminous grounded ice sheet (∼12 100 000 km2) agree closely with the area of the single polygon as given in the ADD. This value is, however, 1.5% larger than the area of the contiguous continent calculated from the same data in BAS (1993), 11 900 000 km2. It seems likely that this discrepancy results because the calculations described in BAS (1993) were performed using polar stereographic rather than an equal area projection.
The sum of the areas comprising the conterminous ice sheet, ice shelves, and ice rises (13 828 km2) agrees to within 0.8% with the figure calculated by Fox and Cooper (1994, 13 949 km2). These minor discrepancies result from the use of a generalized coastline in the present study.
3. Updated compilation of net surface mass balance measurements
Most of the Antarctic Ice Sheet experiences little surface melting (Zwally and Fiegles 1994) and there is a general year-on-year accumulation of snow that becomes locked into the ice sheet. Two notable exceptions that will be discussed later are areas of perennially exposed rock and areas of blue ice. The flux of snow into the ice sheet system at any geographical point has been termed the net balance by Paterson (1994, 28), here we use the term net surface mass balance to avoid confusion with ice dynamics effects and surface energy balance.
Net surface mass balance can be measured in situ by a variety of methods in common use; stratigraphic interpretation of the layers seen in snow pits and shallow ice cores (e.g., Alley and Bentley 1988); the burial of single stakes and farm of stakes (e.g., Goodwin et al. 1994); counting the annual layers in ice cores using some seasonally varying chemical marker, such as oxygen isotope analysis (e.g., Reinwarth et al. 1985); and finding the beta-radioactivity that is a marker of the snow deposited during above-ground testing of nuclear weapons (e.g., Whillans and Bindschadler 1988). Each method has its own strength and weakness and likely error limits, although, as noted throughout the literature (e.g., Giovinetto et al. 1989) those based on stratigraphic interpretations alone are generally considered as the least reliable method.
For the purposes of this study we assume that the mechanisms of accumulation and ablation are unimportant, we simply require the net surface mass balance. We shall assume, unless otherwise specified, that in situ measurements of net surface mass balance can be taken as regionally and temporally representative. In future, increasing spatial and temporal resolution of data will highlight geographic and temporal variability, but for the present we are content to consider only in broadscale geographic variability. We are, however, mindful of results that do suggest recent changes in the net surface mass balance at particular sites (e.g., Morgan et al. 1991;Moseley-Thompson et al. 1995).
a. Data sources
A compilation of in situ measurements of net surface mass balance containing a total of 1860 points has been established for this study (Fig. 4) and is reported in full by Vaughan and Russell (1997). For the vast majority of these measurements an original reference has been found in the literature and is recorded alongside the observation in the compilation. Around 360 points have, however, been drawn without checking from earlier compilations, notably Bull (1971). Estimates of uncertainty were given for around 10% of the measurements, and the period of the observation is known for 30%. Occasionally where measurements were made densely in some specific locality or along a traverse route the data have been consolidated.
b. Zero accumulation areas
It should be noted that there are many areas across the Antarctic Ice Sheet where the net accumulation is zero or significant ablation causes the net surface mass balance to be negative. These are areas of bare ice (blue ice) and areas of rock outcrop.
The boundary around an area of blue ice, although variable from year-to-year, is an isopleth of zero net surface mass balance. Inclusion in the database is not, however, straightforward as there are many hundreds of isolated bare ice areas and there is no single source for the location and extent of such areas over the continent. The meteorological conditions that cause bare ice fields are generally local, and so a bare ice area should not be considered as having a wide influence on the regional net balance. Indeed, Bintanja and van den Broeke (1995) noted that while blue ice areas are widespread, “their surface area is too small to play an important role in the total surface mass balance regime of Antarctica.” For these reasons we have decided not to make a correction to the estimates of net surface mass balance for most of the areas of blue ice.
The exception to this is Lambert Glacier where several authors have noted that there is an extensive area of blue ice and zero net accumulation. McIntyre (1985) identified this area using satellite imagery and measured its extent as 56 000 km2, or 4% of the area of basin BC as measured in this study. The 0 kg m−2 yr−1 isopleth given by Higham and Craven (1997) has thus been taken as an accurate delineation of the blue ice area, and we have used this contour as an additional constraint during gridding and contouring of the data.
A correction for the area of exposed rock is more simply calculated and is discussed in section 5a.
Giovinetto and Bentley (1985) made corrections for deflation (where snow that falls on a steep slope near the sea is blown into the sea and lost from the ice sheet) and ablation (areas in the coastal zone that suffer net ablation), based on a discussion by Giovinetto (1964). Determination of the size of these corrections was largely arbitrary and is not adopted in the current study.
4. Contouring of net surface mass balance data
An overriding problem in any attempt to draw contours of net surface mass balance over Antarctica from in situ net surface mass balance measurements is that the data are unevenly distributed and too sparse to produce a reasonable map without significant manual intervention. Large parts of the continent have not been sampled whereas other areas lying along traverse routes have a high density of measurements. A simple-minded automatic contouring of the data would make little sense when considered in terms of the known topography of the continent. Thus far, maps have been drawn by hand to be consistent with particular features of the continent thought to be important. Giovinetto and Bull (1987) summarized these factors as surface elevation and slope, assumed surface air drainage routes, direction of incoming lower-tropospheric flow, distance from the coast and the distance to the seasonal sea-ice edge, and polynyas.
One method to improve the interpolation of the sparse net surface mass balance data is to use a background field to guide the contouring in areas with few data. This approach was suggested by Giovinetto and Bull (1987), who suggested that microwave emission data had been shown to correlate with net surface mass balance (Zwally 1977; Rotman et al. 1982; Doake 1985; Thomas et al. 1985) and would eventually provide useful control for this purpose. This is precisely the approach that we will eventually adopt for the present study, although first some alternatives were considered.
a. Choice of background field
To be useful, a background field introduced to control the contouring of sparse data should be highly correlated with the parameter to be contoured. It should have adequate coverage and resolution and be derived from data independent from that which is to be contoured. Several candidate fields were considered
Fortuin and Oerlemans (1990) looked for correlations between net surface mass balance and saturated vapor pressure of the free atmosphere above the inversion (SVP), the surface slope, and the surface convexity. They found no significant correlations over the entire continent, but found a significant correlation with SVP and surface convexity over the interior of East Antarctica. A similar exercise was performed to determine the usefulness of various fields as background fields for forcing our contouring of net surface mass balance. Values were extracted from each of the candidate fields at locations where in situ net surface mass balance measurements are available. A linear correlation was performed on the observed net surface mass balance and the extracted values. Table 2 shows the results of this exercise for several candidate fields.
The best correlation was obtained with a map of accumulation rate (MBz) produced using the firn emissivity method (Zwally 1977) by combining the radiative transfer equation with a grain-growth function. The solution of these equations gave a single hyperbolic function to derive net mass balance (MBz) to satellite derived parameters:
where Tb are the satellite measurements of brightness temperature in kelvins and Tm is the mean annual surface temperature in kelvins, based on the equations given by Zwally (1977). We have used coefficients a0 = −5.5, and a1 = 6.50, which are similar to those chosen by Zwally and Giovinetto (1995) to match in situ measurements of net surface mass balance at 367 sites selected for their reliability. Although the single function showed robust correlation between the surface data and the emissivity derived values (r2 = 0.82), it gave relatively high residuals (rms = 90 kg m−2 yr−1). These high residuals led Zwally and Giovinetto (1995) to adopt different functions with different sets of coefficients based on in situ measurements using only stable-isotope or radioactive-isotope methods. The approach reduced the number of data sites (82 in East Antarctica, 69 in West Antarctica) but improved the fit between the in situ data and the emissivity derived values. Nevertheless, because the net surface mass balance values for the sites compiled for the present study include all measurement techniques, we use a map based on the single function, with the coefficients given above.
By avoiding the use of fields generated by climate models, we have avoided contamination of the final net surface mass balance map that might exclude its use for testing such models in future. The least squares regression of the values of in situ net surface mass balance measurements, MBobs, against coincident values of MBz is given by
The correlation coefficient (r = 0.46) and standard deviation of the residuals (±131 kg m−2 yr−1) for this relation indicates that although MBz represents much of the variation in field observations, it cannot be considered to represent all of it, as estimates of uncertainty given in the original publications have a mean of ±52 kg m−2 yr−1. This is further confirmed by considering the areal distribution of the residuals, which shows a coherent pattern across the ice sheet, with extended areas of positive residuals exceeding 200 kg m−2 yr−1 [e.g., along the Bryan Coast (75°–105°W) and west coast of the Antarctic Peninsula] and areas of negative residuals exceeding −200 kg m−2 yr−1 [e.g., along the Amundsen Sea Coast (105°–150°W)].
b. Choosing between differing datasets
Giovinetto et al. (1989) described in some detail the technique they used to produce a contour map of net surface mass balance (Giovinetto and Bentley 1985) by choosing between apparently disagreeing datasets. In summary, where they were suspicious about the apparent mismatch between nearby or overlapping data, they generally rejected measurements obtained by stratigraphic methods alone.
Comparing the residuals (MBobs − MBz) of subsets of the data used in this study indicates that this may be unsound (Table 3). Data from the early compilation by Bull (1971), which contained many observations from stratigraphic data, have lower rms residuals than either the dataset used by Zwally and Giovinetto (1995), which contained no stratigraphically derived data, or other data published since 1985, which also included few stratigraphically derived points. Thus it seems unrealistic to make the general assumption that the stratigraphically derived data are per se unreliable. Therefore we have chosen not to make arbitrary choices between datasets but to include all the data, except where the (MBobs − MBz) residuals for a single or small group of points are unbelievably large (see step 2 below).
c. Interpolation of net surface mass balance
Having accepted the MBz field as the best available forcing field, the derivation of the final net surface mass balance grid and map has proceeded through several steps:
Step 1: Subtraction of MBz field scaled using (2) from observed net surface mass balance (MBobs) to yield values of residuals at the observation sites.
Step 2: Manual editing and removal of a handful of suspect isolated points that appear to show unfeasibly large residuals (>200 kg m−2 yr−1). Editing data such that observations with very low residuals (less than 20 kg m−2 yr−1) are put to zero.
Step 3: Imposition of further constraints on the gridding of residuals. Mountain ranges are represented by discontinuities (faults); major ice divides and ridges are represented by sharp changes in gradient in the residual field.
Step 4: Gridding of residual values using Delauney triangulation with the other constraints applied.
Step 5: Addition of gridded residual file to the Zwally accumulation field (MBz) scaled using (2) to reconstruct the net surface mass balance grid.
Step 6: Editing to fix areas of negative net surface mass balance to zero and smooth the derived grid over 30 km.
Step 7: Contours were drawn for the gridded data and then smoothed using a Douglas–Peuker filter to remove contour deviations smaller than the pixel size (10 km).
The final map of net surface mass balance for the entire continent including ice shelves is shown in Fig. 5c.
d. Comparison of new net surface mass balance map with Giovinetto and Bentley (1985)
In general terms, Fig. 5 shows that the present compilation has the same broadscale pattern of net surface mass balance variations as that presented by Giovinetto and Bentley (1985). There are, however, some significant differences, the central desert in East Antarctica (as defined by the 50 kg m−2 yr−1 contour) is smaller in the present representation. The Filchner–Ronne and Ross ice shelves show a less pronounced minimum of net surface mass balance. More spatial variability is evident in the coastal regions around the whole continent.
5. Integration of basinwide balances
Giovinetto and Bentley (1985) estimated the total net surface mass balance for each basin directly from the isopleth map, using manual procedures to convert the areas contained between the isopleth lines to evaluate net surface mass balance. Where the rate of change of balance between isopleths is not linear, these techniques will give biased values. With the application of modern GIS techniques to calculate integrals as the summation of values at grid points, here at 10-km spacing, these limitations can be largely overcome.
Table 4 shows the results of the basinwide integration of the net surface mass balance distribution shown in Fig. 5c and the basin’s delineations shown in Fig. 3. For the area II" (Antarctic Peninsula) the value calculated by Frolich (1992) has been used. Frolich made this calculation at higher resolution and precision than is obtainable here. The comparable values calculated by Giovinetto and Bentley (1985) are also included in Table 4. The present determination shows the mean net surface mass balance rates for most basins are higher than those estimated by Giovinetto and Bentley (1985).
a. Rock outcrops
Areas of permanent rock outcrop are necessarily areas of zero net surface mass balance and the integrations performed above should be reduced to account for these areas. Generalized polygons describing rock outcrop are taken from a generalization of the ADD, it includes around 11 000 outcrop polygons, around 10 000 of which lie on the conterminous continent. For each outcrop we have found a value of the net surface mass balance from the gridded data, this is a simple matter as all the outcrop polygons are smaller than the grid size. Multiplying the area of each outcrop by the mean net surface mass balance gave a net surface mass balance correction for each outcrop and these were summed to give a total correction. The total area of the generalized outcrops is 98 000 km2, and the total correction for them is 30 × 1012 kg yr−1. The total area of generalized outcrops is, however, greater than the area of outcrops before generalization (48 000 km2; BAS 1993). Thus the integrated net surface mass balance is reduced accordingly, giving a final correction due to the zero mass balance over rock outcrops of −14.8 × 1012 kg yr−1 (see Table 4).
b. Uncertainty estimation
Because most of the numerical calculations are now done digitally using relatively fine grids, there is little reason to suspect systematic errors in either the calculation of basin areas or the integration of the net surface mass balance field over these areas. We estimate that together these numerical errors are likely to account for no more than a 1% error in the final basin integrals.
The dominant uncertainty continues to arise in the gridding process. Since there is some manual intervention in the procedure an objective measure of the uncertainty in final compilation cannot be directly obtained from a consideration of the methodology. An estimate of the uncertainty must be made by other means.
The progression of mean net surface mass balance estimates described by Giovinetto and Bull (1987, their Table 2) and other sources are shown in Fig. 6 with a comparable value from this analysis. Since most in situ measurements were used in more than one study, the progression of the estimates of mean net surface mass balance may give some indication of the uncertainty in the method. In a general sense the mean net surface mass balance is converging toward a more uniform value. This can be seen in the reduction of standard deviations from the mean in each decade, 2.4 kg m−2 yr−1 (1960s), 0.5 kg m−2 yr−1 (1970s), 1.0 kg m−2 yr−1 (1980s), and 0.4 kg m−2 yr−1 (1990s). The spread of estimates since Giovinetto and Bentley (1985) suggests a likely uncertainty of around ±5%.
This paper presents a compilation and interpretation of data to assess the net surface mass balance of the Antarctic Ice Sheet. Besides updating the body of in situ measurements, this study introduces several important refinements to the method that improve both reliability and repeatability: basin delineation using automated techniques on an improved DEM, digital calculation of surface areas and basinwide integrations, and interpolation of sparse data using an independent background field. The results indicate a total net surface mass balance for the conterminous grounded ice sheet is 1811 Gton yr−1 (149 kg m−2 yr−1) and for the entire ice sheet including ice shelves and embedded ice rises, 2288 Gton yr−1 (166 kg m−2 yr−1). Whereas the uncertainty is difficult to calculate systematically, a comparison to earlier compilations suggests an uncertainty of at least ±5%.
The total net surface mass balance calculated in this way represents an increase of 15% (20% for the contiguous grounded ice sheet) above the estimate mostly widely used until now (Giovinetto and Bentley 1985). Indeed, it is more in line with other estimates published before Giovinetto and Bentley (1985); whose estimate was 8% lower than the mean of 12 earlier estimates (Jacobs et al. 1992). This is a surprising result since Giovinetto and Bentley (1985) stated that although “the surface balance isopleth pattern . . . is likely to change as additional data become available . . . we believe that the changes will not be large enough to alter the total and mean balance rates by more that a few percent in most of the systems. . . .”
A change in the estimated total net surface mass balance of the Antarctic Ice Sheet clearly has direct implications for the attribution of measured sea level change. Jacobs et al. (1992) stated that each millimeter of sea level rise is roughly equivalent to the addition of 360 Gton of water to the world’s oceans. This implies that the accumulation of ice falling on the grounded ice sheet is thus equivalent to 5.0 mm of sea level each year. Jacobs et al. (1992) estimated the total mass of ice lost from the ice sheet (including ice shelves) to be 2613 Gton yr−1; their analysis suggests they consider this to have an uncertainty of ±530 Gton yr−1. Jacobs et al. compared this with the total net surface mass balance for the continent given by Giovinetto and Bentley (1985) and Frolich (1992) and calculated a net imbalance of (−469 ± 639) Gton yr−1. Using the estimates from the present study, (2288 ± 114) Gton yr−1, we can refine this estimate of net imbalance to (−325 ± 594 Gton yr−1). In terms of uncertainty, this is only a small improvement and realistically we are still unable to determine even the sign of the contribution of the Antarctic Ice Sheet to recent sea level change. But it is now clear that the major uncertainty resides in the determination of the attrition components and not the accumulation components.
These calculations perhaps highlight a disturbing truth for those engaged in the effort of attributing observed sea level rise to its contributing sources. Only a simple calculation is required to show that a massive reduction in the uncertainties in the attrition components will be required before a useful attribution is possible. Warrick et al. (1995) give the best estimate for sea level rise over the last century as 18 cm, or a yearly addition of around 650 Gton of water, which is roughly equal to the uncertainty in the yearly surface mass balance of Antarctica. If the present method of evaluation is ever to allow determination of the contribution of the Antarctic Ice Sheet to sea level that has an uncertainty of less than 10% of the observed sea level trend, both accumulation and attrition terms must be calculated to an uncertainty of around 1%–2%. This is unlikely to be feasible with present methods. It is most probable that significant progress will in the future come not by reducing uncertainty in net surface mass balance and attrition components, but by the direct measurement of the difference between these values using radar or laser satellite altimetry of the ice sheet surface (Zwally et al. 1989). Meanwhile the study described here will, perhaps, be of greatest value to researchers involved in the validation and tuning of numerical weather prediction and climate models.
We thank S. R. Jordan who pointed out several sources of accumulation measurement, H. J. Zwally, who provided the SMMR derived accumulation field, and C. S. M. Doake and E. M. Morris, who provided useful discussions.
Corresponding author address: Dr. David G. Vaughan, British Antarctic Survey, Natural Environment Research Council, High Cross, Madingley Road, Cambridge CB3 OET, United Kingdom.