Discussion

The combined effect of increasing accumulation and runoff from the Greenland and Antarctic ice sheets on the level of the oceans are summarized in Table 4. The range obtained with the MIT / snowpack model combination is -4.5 - -2.5  cm, with a best guess of -4 cm. At -5.5 cm, the number obtained with the ECHAM climate input, when coupled to the snowpack model, is not very different. The reasonable agreement between the results obtained for both Greenland and Antarctica by the ECHAM and MIT-REF gives some confidence in the results obtained with the MIT model for the other climate change scenarios and the Kyoto runs. The thermal expansion associated with the REF run is 17 cm (Prinn et al. (1997)), thus the contribution of Greenland and Antarctica represents a 25 % reduction, bringing this number down to 13 cm. The small changes over the next century which are estimated with the snowpack model stand in sharp contrast with the conclusions from previous studies (Ohmura et al. (1996), Thompson and Pollard (1997), DeWolde et al. (1997)) which were as large as +10 cm for Greenland and -10 cm for Antarctica. The discrepancies between these projections can however be explained by differences in climate models, in the use of transient vs. equilibrium simulations, by differences in the resolution at which melting is calculated and in the models used to estimate runoff. The scaling factor used to obtain a realistic total accumulation over the Antarctic ice sheet also has an important effect in reducing the contribution to sea-level change from that continent.

The results obtained with the snowpack model certainly have more credibility than those derived with simple parameterizations. Temperature based methods such as the degree-day and linear models are calibrated to the range of temperatures and conditions observed in southern Greenland and are prone to failure outside of that range, as can be seen from the results obtained in Antarctica. As could be expected in snow or ice covered areas, the parameterization of the surface albedo has a determining influence on the results, and both the non-linear dependence of snow albedo on surface temperature and the absence of dependence of the ice albedo on temperature critically affects the results obtained with the snowpack model. The importance of the surface energy balance and of the temperature and density structures within the snow cover in determining runoff is highlighted by the ability of the snowpack in Antarctica to refreeze most of the melt- and rainwater which is added at the surface, thereby adding an important delay in the onset of melting. Significant changes can however be expected to take place on the Antarctic Peninsula for a warming of more than a few degrees.

In order to avoid excessive computation requirements, simplifications in climate models are however required to perform many transient simulations. The weakness of this study lies in the inability of the MIT climate model to capture regional climate changes, for example the changes in location and intensity of the Atlantic storm track which would affect the accumulation of snow on the Greenland ice cap. Local climate changes could also affect the temperature structure of the atmosphere and the lapse rates which were assumed to remain constant in this study. The zonal model does however capture global scale changes in the atmospheric circulation and in the moisture transport.

The assumptions made about the intensity of oceanic heat uptake are shown to play a dominant role in determining melting on the Greenland ice sheet. The constant ocean diffusion coefficient which is used below the mixed layer ocean model does not allow to capture the changes in the thermohaline circulation which could accompany the modifications of the atmospheric circulation, as reported by Cubasch et al. (1992), Manabe and Stouffer (1994) or Wood et al. (1999). A reduction in the intensity of the thermohaline circulation would induce a relative cooling in the region around Greenland which would further reduce, or reverse the direction of the changes in melting and runoff. However, comparisons with coupled A/O-GCM results have shown that the global effect is small for 100 year projections (Sokolov and Stone (1998)).

The freshwater flux from Greenland increases from $\sim$ 0.0015 Sv in 1990 to $\sim$ 0.003 Sv at the end of the 21^st century in the reference run. This is only a fraction of the freshwater flux which occurred during the Younger Dryas and peaked at 0.44 Sv Fairbanks (1989), and which is thought to have been sufficient to lead to the temporary collapse, or at least to a transition to a different state of overturning, of the thermohaline circulation (Broecker et al. (1985), Lehman and Keigwin (1992)). It is also much less than the freshwater pulses artificially added to the North Atlantic basin in model simulations aimed at switching the state of the thermohaline circulation away from its current equilibrium (Marotzke and Willebrand (1991), Manabe and Stouffer (1995), Rahmsdorf and Willebrand (1995)). Enhanced poleward atmospheric moisture transport also leads to a weakening of the thermohaline circulation in simulations of future climate changes in coupled atmosphere-ocean GCM's. The contribution of Greenland to the freshwater forcing is smaller by a factor of 5-10 than the increase over the North Atlantic basin due to atmospheric transport ( 0.15 Sv North of 50^oN with the assumption of a geographically uniform increase) reported by Manabe and Stouffer (1994) after the first hundred years of their 1% per year increase in CO₂ experiment. Because the freshwater produced by the melting of snow and ice on the Greenland ice sheet flows into the Labrador and Greenland Seas very close to the sites of deep water formation, a small increase in runoff may not have a negligible impact on the convective overturning. The assesment of effects such as these would however require an interactive coupling between the snowpack model and an atmosphere-ocean GCM.

Acknowledgements

I am grateful to the ETH Zürich (Prof. A. Ohmura, Dr. M. Wild) for providing the ECHAM 4 data. Insightful coments on earlier drafts were provided by G. Roe, P. Stone and M. Wild. This research was supported by the Alliance for Global Sustainability, the M.I.T. Joint Program on the the Science and Policy of Global Change and NASA Grant NAG 5-7204 as part of the NASA GISS Interdisciplinary EOS Investigation.