First, a snapshot solution was obtained for ice velocities, strain-rates, stresses and temperatures, using measured values of ice thickness and inflow velocities of tributary glaciers and ice streams. Ice rheology and its temperature dependence were prescribed to be compatible with laboratory and ice-shelf measurements, and ice temperatures were calculated using observed surface temperatures and snow-accumulation rates, and basal melt rates that are consistent with available data (Reference MacAyealMacAyeal 1984). The model results show close agreement with measured velocities, except in regions where ice movement is locally constrained by nearby ice rises or ice-shelf margins. In these areas, the model velocities are too low (generally by less than 30%), and we believe this is because ice in the marginal shear bands is softened by strain heating, ice-crystal fabric, and crevassing. We intend to incorporate these sub-grid-scale effects in future development of the model.

The other simulations project future ice-shelf behavior (temperatures, strain-rates, stresses, velocities, ice thickness, etc.) in response to contrasting climates, i.e. present-day conditions and a warmer climate induced by doubling atmospheric CO ₂. Climate parameters for the CO₂ scenario are from the Goddard Institute for Space Studies (GISS) climate model (Hansen personal communication): a 6.5°C increase in surface temperatures and a 30% increase in snow accumulation. Basal melting rates are assumed also to increase (to 1.8 m a⁻¹ along the Siple Coast and to double present-day values near the seaward ice front) in response to greater influx of warm Circumpolar Deep Water beneath the ice shelf (Reference MacAyealMacAyeal 1984).

Time-marching the ice shelf with present-day climate indicates only minor changes in ice-shelf configuration over the next 400 a, apart from progressive grounding in the mouth of ice stream B, and diversion of downstream flowlines in the ice shelf. For CO₂ warming, however, major changes occur. In one simulation, we increased only the basal melting rates. This resulted in ice-shelf thinning by as much as 400 m upstream of Crary Ice Rise and Roosevelt Island, and a slowing of the ice-front velocity by 200 m a⁻¹. Slowing is due mainly to a reduction in mean ice-shelf temperatures associated with increased basal melting. In a second simulation, we increased basal melting rates, snow accumulation and surface temperatures. Ice-shelf thinning was more pronounced than for basal melting only, and ice velocities finally increased above present-day values. In this case, the effects of surface warming and increased snowfall counterbalanced those of basal melting, and average ice-shelf temperatures increased. The thickness and velocity differences between the present and the “full CO₂” simulation after 400 a are displayed in Figures 1 and 2.

Fig. 1 Changes in Ross Ice Shelf thickness associated with CO₂-induced climatic warming. Note that drainage rates of tributary glaciers were not allowed to change for this simulation. In reality, their drainage rates would increase, and ice-shelf thinning would be less pronounced than shown here.

Fig. 2 Changes in Ross Ice Shelf velocities caused by CO₂-induced climatic warming. These estimates represent the effect of ice softening only; actual velocity increases would probably be greater due to acceleration of glacier drainage rates.

Our simulations indicated that changes in ice-shelf temperature have a major influence on future behavior. To emphasize this, we compared the influences on ice-shelf thickness of basal melting and freezing. We used the analytic expression for isotropic spreading (Reference WeertmanWeertman 1957) to project thickness responses of two icebergs, each initially I 000 m thick. The temperature-depth profiles of the icebergs were simulated using a one-dimensional and time-dependent model of the heat equation. On one, we imposed basal melting of 3.0 m a⁻¹ for 50 a, and on the other we imposed basal freezing of 3.0 m a⁻¹ for 50 a. Each iceberg has a surface temperature of −30°C and zero snow accumulation. Initially, the melting iceberg rapidly thins by both melting and creep, but, as the average ice temperature decreases in response to the melting, creep thinning also decreases. After basal melting ceases, thinning rates are very low. The freezing iceberg also thins, initially very slowly because creep thinning is almost balanced by freezing. But, as the depth-averaged temperature increases, creep rates increase and, once freezing ceases, thinning rates are considerably larger than for the melting iceberg. Indeed, after 100 a it actually becomes thinner than the melting iceberg. This is an extreme example, but it does highlight the importance of changes in ice-shelf temperature. Clearly, these can be induced by factors other than basal melting; changes in either surface temperature or snow-accumulation rates will have a similar effect.

Our Ross Ice Shelf simulations indicate the potential for major changes in ice-shelf configuration as a consequence of CO₂-induced warming. However, we stress that our study was confined to ice-shelf responses; discharge from ice streams into the ice shelf was held constant throughout. Currently, we are Incorporating this response by including a simple analytic treatment of ice streams that will provide first-order estimate of ice-stream discharge. In brief, we believe the effects of ice-stream feedback are to reduce ice-shelf thinning rates and to increase ice velocities.