Modelling of the past history of the ice sheets and their underlying beds over a glacial cycle is a way to obtain an estimate of the present ice-dynamic evolution unaffected by short-term (annual to decadal) mass-balance effects. The simulation requires time-dependent boundary conditions (surface mass balance, surface temperature, and sea level, the latter being needed to model grounding-line changes). Current glaciological models employ grids of 20 to 40 km horizontal spacing with 10 to 30 vertical layers and include ice shelves, basal sliding and bedrock adjustment.
 Figure 11.3: Modelled evolution of ice sheet volume (represented as sea level equivalent) centred at the present time resulting from ongoing adjustment to climate changes over the last glacial cycle. Data are from all Antarctic and Greenland models that participated in the EISMINT intercomparison exercise (From Huybrechts et al., 1998). |
Huybrechts and De Wolde (1999) and Huybrechts and Le Meur (1999) carried out long integrations over two glacial cycles using 3-D models of Greenland and Antarctica, with forcing derived from the Vostok (Antarctica) and Greenland Ice Core Project (GRIP) ice cores. The retreat history of the ice sheet along a transect in central west Greenland in particular was found to be in good agreement with a succession of dated moraines (Van Tatenhove et al., 1995), but similar validation elsewhere is limited by the availability of well-dated material. Similar experiments were conducted as part of the European Ice Sheet Modelling Initiative (EISMINT) intercomparison exercise (Huybrechts et al., 1998). These model simulations suggest that the average Greenland contribution to global sea level rise has been between –0.1 and 0.0 mm/yr in the last 500 years, while the Antarctic contribution has been positive. Four different Antarctic models yield a sea level contribution of between +0.1 and +0.5 mm/yr averaged over the last 500 years, mainly due to incomplete grounding-line retreat of the West Antarctic ice sheet (WAIS) since the Last Glacial Maximum (LGM) (Figure 11.3). However, substantial uncertainties remain, especially for the WAIS, where small phase shifts in the input sea level time-series and inadequate representation of ice-stream dynamics may have a significant effect on the model outcome. Glacio-isostatic modelling of the solid earth beneath the Antarctic ice sheet with prescribed ice sheet evolution (James and Ivins, 1998) gave similar uplift rates as those presented in Huybrechts and Le Meur (1999), indicating that the underlying ice sheet scenarios and bedrock models were similar, but observations are lacking to validate the generated uplift rates. By contrast, Budd et al. (1998) find that Antarctic ice volume is currently increasing at a rate of about 0.08 mm/yr of sea level lowering because in their modelling the Antarctic ice sheet was actually smaller during the LGM than today (for which there is, however, little independent evidence) and the effect of the higher accumulation rates during the Holocene dominates over the effects of grounding line changes.
Model simulations of this kind have not included the possible effects of changes in climate during the 20th century. The simulations described later (Section 11.5.1.1), in which an ice sheet model is integrated using changes in temperature and precipitation derived from AOGCM simulations, suggest that anthropogenic climate change could have produced an additional contribution of between –0.2 to 0.0 mm/yr of sea level from increased accumulation in Antarctica over the last 100 years, and between 0.0 and 0.1 mm/yr from Greenland, from both increased accumulation and ablation. The model results for Greenland exhibit substantial interannual variability. Furthermore, because of rising temperatures during the 20th century, the contribution for recent decades is larger than the average for the century. These points must be borne in mind when comparing with results of the direct observation methods for short periods in recent decades (Sections 11.2.3.1 and 11.2.3.2). Note also that the observational results include the ongoing response to past climate change as well as the effect of 20th century climate change.
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