Together, the present Greenland and Antarctic ice sheets contain enough water to raise sea level by almost 70 m (Table 11.3), so that only a small fractional change in their volume would have a significant effect. The average annual solid precipitation falling onto the ice sheets is equivalent to 6.5 mm of sea level, this input being approximately balanced by loss from melting and iceberg calving. The balance of these processes is not the same for the two ice sheets, on account of their different climatic regimes. Antarctic temperatures are so low that there is virtually no surface runoff; the ice sheet mainly loses mass by ice discharge into floating ice shelves, which experience melting and freezing at their underside and eventually break up to form icebergs. On the other hand, summer temperatures on the Greenland ice sheet are high enough to cause widespread melting, which accounts for about half of the ice loss, the remainder being discharged as icebergs or into small ice-shelves.
Changes in ice discharge generally involve response times of the order of 102 to 104 years. The time-scales are determined by isostasy, the ratio of ice thickness to yearly mass turnover, processes affecting ice viscosity, and physical and thermal processes at the bed. Hence it is likely that the ice sheets are still adjusting to their past history, in particular the transition to inter-glacial conditions. Their future contribution to sea level change therefore has a component resulting from past climate changes as well as one relating to present and future climate changes.
For the 21st century, we expect that surface mass balance changes will dominate the volume response of both ice sheets. A key question is whether ice-dynamical mechanisms could operate which would enhance ice discharge sufficiently to have an appreciable additional effect on sea level rise.
Traditionally, the state of balance of the polar ice sheets has been assessed by estimating the individual mass balance terms, and making the budget. Only the mass balance of the ice sheet resting on bedrock (the grounded ice sheet) needs to be considered, because changes in the ice shelves do not affect sea level as they are already afloat. Recent mass balance estimates for Greenland and Antarctica are shown in Tables 11.5 and 11.6. Most progress since the SAR has been made in the assessment of accumulation, where the major obstacle is poor coverage by in situ measurements. New methods have made use of atmospheric moisture convergence analysis based on meteorological data, remotely sensed brightness temperatures of dry snow, and GCMs (see references in the tables). Recent accumulation estimates display a tendency for convergence towards a common value, suggesting a remaining error of less than 10% for both ice sheets.
For Greenland (Table 11.5), runoff is an important term but net ablation has only been measured directly at a few locations and therefore has to be calculated from models, which have considerable sensitivity to the surface elevation data set and the parameters of the melt and refreezing methods used (Reeh and Starzer, 1996; Van de Wal, 1996; Van de Wal and Ekholm, 1996; Janssens and Huybrechts, 2000). Summing best estimates of the various mass balance components for Greenland gives a balance of -8.5 ± 10.2% of the input, or +0.12 ± 0.15 mm/yr of global sea level change, not significantly different from zero.
During the last five years, some mass balance estimates have been made for individual Greenland sectors. A detailed comparison of the ice flux across the 2,000 m contour with total accumulation revealed most of the accumulation zone to be near to equilibrium, albeit with somewhat larger positive and negative local imbalances (Thomas et al., 1998, 2000). These results are likely to be only little influenced by short-term variations, because in the ice sheet interior, quantities that determine ice flow show little variation on a century time-scale. Recent studies have suggested a loss of mass in the ablation zone (Rignot et al., 1997; Ohmura et al., 1999), and have brought to light the important role played by bottom melting below floating glaciers (Reeh et al., 1997, 1999; Rignot et al., 1997); neglect of this term led to erroneous results in earlier analyses.
For Antarctica (Table 11.6), the ice discharge dominates the uncertainty in the mass balance of the grounded ice sheet, because of the difficulty of determining the position and thickness of ice at the grounding line and the need for assumptions about the vertical distribution of velocity. The figure of Budd and Smith (1985) of 1,620x1012 kg/yr is the only available estimate. Comparing this with an average value of recent accumulation estimates for the grounded ice sheet would suggest a positive mass balance of around +10% of the total input, equivalent to -0.5 mm/yr of sea level. Alternatively, the flux across the grounding line can be obtained by assuming the ice shelves to be in balance and using estimates of the calving rate (production of icebergs), the rate of melting on the (submerged) underside of the ice shelves, and accumulation on the ice shelves. This results in a flux of 2,209 ± 391x1012 kg/yr across the grounding line and a mass balance for the grounded ice equivalent to +1.04 ± 1.06 mm/yr of sea level (Table 11.6). However, the ice shelves may not be in balance, so that the error estimate probably understates the true uncertainty.
Provided that changes in ice and snow density and bedrock elevation are small or can be determined, elevation changes can be used to estimate changes of mass of the ice sheets. Using satellite altimetry, Davis et al. (1998) reported a small average thickening between 1978 and 1988 of 15 ± 20 mm/yr of the Greenland ice sheet above 2,000 m at latitudes up to 72°N. Krabill et al. (1999) observed a similar pattern above 2,000 m from 1993 to 1998 using satellite referenced, repeat aircraft laser altimetry. Together, these results indicate that this area of the Greenland ice sheet has been nearly in balance for two decades, in agreement with the mass budget studies mentioned above (Thomas et al., 2000). Krabill et al. (1999) observed markedly different behaviour at lower altitudes, with thinning rates in excess of 2 m/yr in the south and east, which they attributed in part to excess flow, although a series of warmer-than-average summers may also have had an influence. In a recent update, Krabill et al. (2000) find the total ice sheet balance to be -46x1012 kg/yr or 0.13 mm/yr of sea level rise between 1993 and 1999, but could not provide an error bar. Incidentally, this value is very close to the century time-scale imbalance derived from the mass budget studies (Table 11.5), although the time periods are different and the laser altimetry results do not allow us to distinguish between accumulation, ablation, and discharge.
Small changes of ± 11 mm/yr were reported by Lingle and Covey (1998) in a region of East Antarctica between 20° and 160°E for the period 1978 to 1988. Wingham et al. (1998) examined the Antarctic ice sheet north of 82°S from 1992 to 1996, excluding the marginal zone. They observed no change in East Antarctica to within ± 5 mm/yr, but reported a negative trend in West Antarctica of -53 ± 9 mm/yr, largely located in the Pine Island and Thwaites Glacier basins. They estimated a century-scale mass imbalance of -6% ± 8% of accumulation for 63% of the Antarctic ice sheet, concluding that the thinning in West Antarctica is likely to result from a recent accumulation deficit. However, the measurements of Rignot (1998a), showing a 1.2 ± 0.3 km/yr retreat of the grounding line of Pine Island Glacier between 1992 and 1996, suggest an ice-dynamic explanation for the observed thinning. Altimetry records are at present too short to confidently distinguish between a short-term surface mass-balance variation and the longer-term ice-sheet dynamic imbalance. Van der Veen and Bolzan (1999) suggest that at least five years of data are needed on the central Greenland ice sheet.
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