It is now practicable to construct complete three-dimensional primitive- equation models of ice flow in which all the input may be time dependent. The input consists of bedrock and ocean distribution, accumulation net balance, ice-surface elevation- temperature relation, and the thermal and flow parameters of the ice. The main limitations on this type of model is the extensive demand of computation time. Thus simplified two-dimensional models have been developed for detailed flow-line studies, and single-column models have been used extensively for analysing the few deep bore-hole temperature profiles.
The main feature of the measured temperature profiles reflect the current steady-state regime at each location. Deviations from the steady state are caused by time variations of any of the variables such as surface temperature, accumulation rate, ice thickness, velocity, etc.
Measurements of stable-isotope ratios in the ice cores provide an indication of past temperatures which has been confirmed by the analysis of the temperature profiles. However the temperature changes could be either due to surface elevation changes or climate changes. Gas volumes in the core show promise of providing an indication of past elevations. Annual variations of the isotopes give indications of past accumulation rates. The determination of past velocities, however, requires velocity-temperature coupled models with more precise flow-law information.
Three-dimensional models are necessary to study past variations of the flow-line pattern. Finally the sliding and surging models recently developed need to be incorporated into the cold ice-sheet models.