Several modelling studies have been conducted for time periods of several centuries to millennia (Van de Wal and Oerlemans, 1997; Warner and Budd, 1998; Huybrechts and De Wolde, 1999; Greve, 2000). A main conclusion is that the ice sheets would continue to react to the imposed climatic change during the next millennium, even if the warming stabilised early in the 22nd century. Whereas Greenland and Antarctica may largely counteract one another for most of the 21st century (Section 220.127.116.11), this situation would no longer hold after that and their combined contribution would be a rise in sea level.
Greenland ice sheet
The Greenland ice sheet is the most vulnerable to climatic warming. As the temperature rises, ablation will increase. For moderate warming, the ice sheet can be retained with reduced extent and modified shape if this results in less ablation and/or a decrease in the rate of ice discharge into the sea, each of which currently account for about half the accumulation (Section 11.2.3). The discharge can be reduced by thinning of the ice sheet near the grounding line. Ablation can be reduced by a change in the area-elevation distribution. However, once ablation has increased enough to equal accumulation, the ice sheet cannot survive, since discharge cannot be less than zero. This situation occurs for an annual-average warming of 2.7°C for the present ice-sheet topography, and for a slightly larger warming for a retreating ice sheet (Huybrechts et al., 1991; see also Oerlemans, 1991; Van de Wal and Oerlemans, 1994). Models show that under these circumstances the Greenland ice sheet eventually disappears, except for residual glaciers at high altitudes. By using the AOGCM ratios of the Greenland temperature to the global average (Table 11.13) with the results of the calibrated simple model (Section 18.104.22.168 and Chapter 9, Section 9.3.3) we project increases in Greenland temperatures by 2100 of more than 2.7°C for nearly all combinations of SRES scenarios and AOGCMs. The maximum by 2100 is 9°C.
Huybrechts and De Wolde (1999) (Figure 11.16) (see also Letreguilly et al., 1991) find the Greenland ice sheet contributes about 3 m of sea level rise equivalent over a thousand years under their mid-range scenario, in which the Greenland temperature change passes through 4°C in 2100 before stabilising at 5.5°C after 2130. Taking into account the high-latitude amplification of warming, this temperature change is consistent with mid-range stabilisation scenarios (Chapter 9, Section 22.214.171.124 and Figure 9.17(b)). For a warming of 8°C, they calculate a contribution of about 6 m. Their experiments take into account the effect of concomitant increases in precipitation (which reduces sensitivity) but also of the precipitation fraction falling as rain (which strongly enhances sensitivity for the larger temperature increases). Disregarding the effects of accumulation changes and rainfall, Greve (2000) reports that loss of mass would occur at a rate giving a sea level rise of between 1 mm/yr for a year-round temperature perturbation of 3°C to as much as 7 mm/yr for a sustained warming of 12°C, the latter being an extreme scenario in which the ice sheet would be largely eliminated within 1,000 years.
West Antarctic ice sheet
The WAIS contains enough ice to raise sea level by 6 m. It has received particular attention because it has been the most dynamic part of the Antarctic ice sheet in the recent geological past, and because most of it is grounded below sea level - a situation that according to models proposed in the 1970s could lead to flow instabilities and rapid ice discharge into the ocean when the surrounding ice shelves are weakened (Thomas, 1973; Weertman, 1974; Thomas et al., 1979). Geological evidence suggests that WAIS may have been smaller than today at least once during the last million years (Scherer et al., 1998). The potential of WAIS to collapse in response to future climate change is still a subject of debate and controversy.
The discharge of the WAIS is dominated by fast-flowing ice streams, dynamically constrained at four boundaries: the transition zone where grounded ice joins the floating ice shelf (Van der Veen, 1985; Herterich, 1987), the interface of ice with bedrock that is lubricated by sediment and water (Blankenship et al., 1986; Anandakrishnan et al., 1998; Bell et al., 1998), the shear zone where fast-moving ice meets relatively static ice at the transverse margins of ice streams (Echelmeyer et al., 1994; Jacobson and Raymond, 1998), and the ice-stream onset regions where slowly flowing inland ice accelerates into the ice streams. Mechanisms have been proposed for dynamic changes at each of these boundaries.
Early studies emphasised the role of the ice shelf boundary in ice discharge by introducing the concept of a "back-stress" believed to buttress the grounded ice sheet and prevent it from collapsing. Recent work, however, both modelling and measurement, places greater emphasis on the other ice stream boundaries. Force balance studies on Ice Stream B show no evidence of stresses generated by the Ross ice shelf, and mechanical control emanates almost entirely from the lateral margins (Whillans and Van der Veen, 1997). If confirmed for the other Siple Coast ice streams, this suggests ice stream flow fields to be little influenced by conditions in the ice shelf, similar to the situation elsewhere at the Antarctic margin (Mayer and Huybrechts, 1999).
Nonetheless, there is a considerable body of evidence for ice stream variability, and the above analyses may not apply to dynamic situations involving large thinning or grounding line change. Ice Stream C largely stopped about a century ago (Retzlaff and Bentley, 1993) and Ice Stream B decelerated by 20% within a decade (Stephenson and Bindschadler, 1988). The mechanisms for these oscillations are not well understood and have been ascribed to processes such as basal water diversion to a neighbouring ice stream (Anandakrishnan and Alley, 1997) or thermomechanical interactions between competing catchment areas (Payne, 1998). Despite ice stream variability in the latter model on the millenial time-scale, the overall volume of the WAIS hardly changed, supporting the suggestion that ice streams may act to remove the imbalance of individual drainage basins and to stabilise rather than destabilise WAIS (Hindmarsh, 1993).
The WAIS was much larger during the LGM and has probably lost up to two thirds of its volume since then (Bindschadler, 1998). The largest losses have been from grounding line retreat below the present WAIS ice shelves (Ross and Filchner-Ronne), most likely as a gradual response to rising sea levels subsequent to melting of the Northern Hemisphere ice sheets (Ingolfsson et al., 1998). Local imbalances, both positive and negative, are presently occurring (Shabtaie and Bentley, 1987; Whillans and Bindschadler, 1988; Bindschadler and Vornberger, 1998; Hamilton et al., 1998; Rignot, 1998a,b; Wingham, et al., 1998), but there is no conclusive observational evidence (from monitoring of surface elevation, see Section 126.96.36.199) that WAIS overall is making a significant contribution to global average sea level change (Bentley, 1997, 1998a,b; Bindschadler, 1998; Oppenheimer, 1998; Wingham et al. 1998). Conway et al. (1999) suggest that grounding line retreat since the LGM may still be ongoing, giving an average rate of recession corresponding to a rate of sea level rise of 0.9 mm/yr (Bindschadler, 1998). If projected into the future, this would imply disappearance of WAIS in 4,000 to 7,000 years (Bindschadler, 1998). However, geological estimates of ocean volume increase over the last 6,000 years place an upper limit of about half this amount on global sea level rise (Section 11.3.1).
Recent spectacular break-ups of the Larsen ice shelves in the Antarctic Peninsula (Vaughan and Doake, 1996; Doake et al., 1998) demonstrate the existence of an abrupt thermal limit on ice shelf viability associated with regional atmospheric warming (Skvarca et al., 1998). However, the WAIS ice shelves are not immediately threatened by this mechanism, which would require a further warming of 10°C before the -5°C mean annual isotherm reached their ice fronts (Vaughan and Doake, 1996). Although atmospheric warming would increase the rate of deformation of the ice, causing the ice shelf to thin, response time-scales are of the order of several hundred years (Rommelaere and MacAyeal, 1997; Huybrechts and de Wolde, 1999).
In view of these considerations, it is now widely agreed that major loss of grounded ice, and accelerated sea level rise, is very unlikely during the 21st century. An interdisciplinary panel of international experts applying the techniques of risk assessment to the future evolution of WAIS concluded that there is a 98% chance that WAIS will not collapse in the next 100 years, defined as a change that contributes at least 10 mm/yr to global sea level change (Vaughan and Spouge, 2001). The probability of a contribution to sea level (exceeding 0.5 m) by the year 2100 was 5%. These results are broadly consistent with an earlier assessment by Titus and Narayanan (1996) based on a US-only panel, who found a 5% chance of a 0.16 m contribution and 1% chance of a 0.3 m contribution to sea level rise from WAIS by 2100. We note that Vaughan and Spouge also report a probability of 5% for WAIS giving a sea level fall exceeding 0.4 m within the same time frame, while Titus and Narayanan give 0.18 m.
Nonetheless, on a longer time-scale, changes in ice dynamics could result in significantly increased outflow of ice into the ice shelves and a grounding line retreat. Large-scale models show both of these phenomena to be sensitive to basal melting below the ice shelves (Warner and Budd, 1998; Huybrechts and De Wolde, 1999). Model studies do not agree on the sensitivity of the basal melting to an oceanic warming: for instance, one shows a quad-rupling of the basal melting rate below the Amery ice shelf in East Antarctica for an adjacent sea warming of 1°C (Williams et al., 1998), while another claims that warmer sea temperatures would reduce melting rates below the Ronne-Filchner ice shelves through alteration to sea-ice formation and the thermohaline circulation (Nicholls, 1997). Changes in open ocean circulation may also play a role. Warner and Budd (1998) suggest that even for moderate climatic warmings of a few degrees, a large increase in bottom melting of 5 m/yr becomes the dominant factor in the longer-term response of the Antarctic ice sheet. In their model, this causes the demise of WAIS ice shelves in a few hundred years and would float a large part of the WAIS (and marine portions of East Antarctica) after 1,000 years. Predicted rates of sea level rise are between 1.5 and 3.0 mm/yr depending on whether accumulation rates increase together with the warming. Allowing for runoff in addition to increased accumulation, Huybrechts and De Wolde (1999) find a maximum Antarctic contribution to global sea level rise of 2.5 mm/yr for an extreme scenario involving a warming of 8°C and a bottom melting rate of 10 m/yr. These figures are upper limits based on results currently available from numerical models, which do not resolve ice streams explicitly and which may not adequately predict the effect of ice shelf thinning on grounding line retreat owing to physical uncertainties.
Based on a wide-ranging review, Oppenheimer (1998) argues that WAIS could disintegrate within five to seven centuries following a warming of only a few degrees. Such a collapse implies a rate of sea level rise of 10 mm/yr and an average speed-up of the total outflow by at least a factor of 10 (Bentley, 1997, 1998a,b). However, the majority opinion of a recent expert panel reported by Vaughan and Spouge (2001) is that such outflow rates are not attainable. It is, therefore, also plausible that WAIS may not make a significant contribution to sea level rise over time-scales less than a millennium. Vaughan and Spouge (2001) attribute a 50% probability to the latter scenario, but retained an equally large probability that the sea level rise will be larger than 2 mm/yr after 1,000 years, emphasising the inadequacy of our current understanding of the dynamics of WAIS, especially for predictions on the longer time-scales.
Independent of bottom melting below the ice shelves and the possibility of an ice-dynamic instability, surface melting sets an upper temperature limit on the viability of the Antarctic ice sheet, because runoff would eventually become the dominant wastage mechanism (as would be the case for Greenland in a climate several degrees warmer than today). For warmings of more than 10°C, simple runoff models predict that an ablation zone would develop around the Antarctic coast, making the mass balance at sea level sufficiently negative that the grounded ice would no longer be able to feed an ice shelf. Also the WAIS ice shelves would disintegrate to near to their inland limits as summer temperatures rise above the thermal limit of ice shelf viability believed to be responsible for the recent collapse of ice shelves at the northern tip of the Antarctic Peninsula. Disintegration of WAIS would in that case result, because the WAIS cannot retreat to higher ground once its margins are subjected to surface melting and begin to recede (Huybrechts, 1994). Depending on the strength of the warming, such a disintegration would take at least a few millennia.
East Antarctic ice sheet
Thresholds for disintegration of the East Antarctic ice sheet by surface melting involve warmings above 20°C, a situation that has not occurred for at least the last 15 million years (Barker et al., 1999), and which is far more than thought possible under any scenario of climatic change currently under consideration. In that case, the ice sheet would decay over a period of at least 10,000 years. However, the recent inference of complex flow patterns in the interior of the East Antarctic ice sheet demonstrates the existence of ice-streaming features penetrating far inland, which may be indicative of a more dynamic regime than believed so far (Bamber et al., 2000; Huybrechts et al., 2000)
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