Numerical modelling of ice sheets and glaciers has become a useful tool in glaciological research. A model described here deals with the vertical mean ice velocity, is time dependent, computes bedrock adjustment and uses an empirical diagnostic relationship to derive the distribution of ice thickness in ice shelves. The rate of snowfall and ice/snow melt depends on the (prescribed) sea-level temperature, surface slope, elevation and distance to open water. The model is able to reproduce the major. features of the Antarctic Ice Sheet. When it is run to a steady state for present climatic conditions, the main difference with the present ice sheet is that the shallow parts of the Weddell Sea become covered by grounded ice. To understand ice-sheet histories from proxy data, and to see whether they are physically plausible, numerical ice-sheet models can have an important role. Although the theory of ice flow is formulated reasonably well (this does not apply to what happens at the ice-bedrock interface), modelling of large ice sheets requires a pragmatic approach. It is not possible to solve the full stress-strain rate relationships, together with the ther-modynamic equation, for the whole Antarctic Ice Sheet, for example. This certainly applies if one wants to carry out integra-tions over 100,000 yr or so.-In recent years, ice-sheet models based on a flow law for the vertical mean ice velocity have become popular1-4; they have been used mainly for palaeoclimatic studies, and in complexity come between perfectly plastic models$ and three-dimensional models'. In these models temperature is not calculated, so constant bulk flow parameters have to be used. In spite of the simplifications involved, the vertically integrated models capture most of the characteristics of large ice sheets. Based on these observations, I have :developed a vertically integrated model of the Antarctic Ice Sheet. In fact the Antarctic Ice Sheet is an excellent test case for thèvertical mean approach', because it has a very irregular bedrock topography Grid 0028-0836/82/240550-04$01.00 and subtle grounding line dynamics at some places, and its present-day physical characteristics are well documented'. The first version of the present model was used to investigate how sensitive the Antarctic Ice Sheet is to changes in the .ice accumulation rate2. However, this version did not include bed-rock adjustment and ice shelves, and could only be used for short .integrations.. The second version, results of which are presented here, has much more internal freedom. The response of the bedrock topography to a varying ice load is computed, and a diagnostic relation for ice shelves (though simple) is included. A varying! bedrock topography introduces the problem of initial condi-,' tions. It is not very well known how close the present bedrock topography is to isostatic equilibrium. A 100-m error in the equilibrium bedrock elevation will be insignificant in the central parts of`of`the East Antarctic Ice..Sheet, but is very important in such marginal regions ...
