- The linear model uses the apparent linear correlation between the average summer temperature, for
*T*_{avg}> - 2^{o}*C*, and the ablation observed at a few measurement stations in Greenland as the basis for the parameterization (Ohmura et al. (1996), Wild and Ohmura (1999)). - The degree-day model uses the sum of temperatures above the melting point as a ``melting potential''. Snow and ice are melted successively at different rates to account for the change in albedo between these two surfaces. A prescribed fraction of the meltwater refreezes to form superimposed ice (Braithwaite and Olesen (1989), Huybrechts et al. (1989), Braithwaite (1995)).
- The snowpack model developed at M.I.T. relies on a representation of the physical processes which occur in the snow cover to obtain an estimate of runoff. The uppermost 15
*m*of the snow, firn and ice are divided into a maximum of 12 layers. Each layer settles under the weight of the overlying snow until it is compressed into ice. The temperature distribution is calculated from a heat diffusion equation which includes the effect of the latent heat released or absorbed by the changes of phase of water. Melt- and rainwater percolation is modeled by prescribing the maximum volume fraction of water which saturates the firn, the excess filtering down layer by layer until it reaches ice, at which point it is assumed to contribute to runoff. The surface energy balance provides the boundary condition at the surface and a vanishing heat flux is imposed at 15*m*depth. Many components of the surface energy balance are calculated internally by the snowpack model, notably the surface albedo, the upwelling longwave radiation and the turbulent fluxes of latent and sensible heat. This model allows an explicit calculation of the formation of meltwater, of the fraction of meltwater which refreezes and of runoff in the ablation region. This was not the case in past modelling efforts (Thompson and Pollard (1997), Ohmura et al. (1996), DeWolde et al. (1997), Wild and Ohmura (1999)) which neglected the effect of latent heating on the temperature and density structure of the snow cover which was not modelled explicitely.

The model is computationally sufficiently efficient to be solved on a 20 *km* grid on the Greenland ice sheet and 40 *km* on Antarctica. The resolution used for Greenland has been shown by Glover (1999) to be sufficient to resolve the features of the melt zone on the margins of that ice sheet. The model is allowed to equilibrate with the 1990 climate by developing temperature and density structures appropriate for each location on the ice sheet before proceeding with the transient climate change calculations.

The conditions at Qamanârssûp Sermia on the Greenland ice sheet, as predicted by the MIT climate model (see the next section for details about the model), provide an example of the differences in behavior of the three models. The average summer temperature is 5.4^{o} which leads the linear model to predict
0.51^{ . }5.4 + 0.93 = 3.68 *m*. of runoff. This location experiences 4 months with temperatures above the melting point for a total of 527 positive degree-days (PDD). Melting the winter's snow accumulation uses only 19 PDDs and 60% of that meltwater is assumed to refreeze. The remaining PDDs are used to melt ice for a total runoff of 4 *m*. The snowpack model relies on the surface energy balance to generate 3.27 *m* of meltwater, 8 *cm* of liquid water is added in the form of rain, 4 *cm* refreezes within the snow cover and 3.31 *m* contribute to the runoff from the ice sheet. The potential for refreezing is for the most part eliminated between July, when the winter's snow is melted and bare ice outcrops, and September, when temperatures drop below the melting point.
Because the snowpack model is based on well established physical principles, it can be expected to respond in a believable way to substantial changes in atmospheric forcing. The results obtained with the simpler temperature based models will therefore be assessed by comparison to those obtained with the snowpack model.

Because of the size of the ice sheets, the response of the internal ice dynamics of Greenland and Antarctica to changes in the surface forcing will take place on time scales greater than a century and will therefore be neglected (Greve (1997), Huybrechts (1990a)). Dynamic changes which could take place over less than a century, such as the partial collapse of the West Antarctic ice sheet (M.Oppenheimer (1998)) or rapid local changes in glacier dynamics (Krabill et al. (1999)) are still difficult to model accurately and will be neglected in this analysis.