Equilibrium profile of ice shelves

Using expressions for ice-shelf creep derived by Weertman (1957) and Thomas (1973[b]) a general method is developed for calculating equilibrium thickness profiles, velocities, and strain-rates for any ice shelf. This is done first for an unconfined glacier tongue and the result agrees well with data for Erebus Glacier tongue (Holdsworth, 1974). Anomalies occur within the first 3 km after the hinge zone and these are too great to be the result of local bottom freezing; they are probably due to disturbance of the velocity field. Secondly, profiles are calculated for bay ice shelves. Thickness gradients are largely independent of melt-rate or flow parameters but are inversely proportional to the width of the bay. Data from Antarctic ice shelves agree with this result both qualitatively and quantitatively. The theory is readily extended to ice shelves in diverging and converging bays. An ice shelf in a diverging bay can only remain intact if it is thick enough and slow enough to creep sufficiently rapidly in the transverse direction. If it cannot, it will develop major rifts or will come adrift from the bay walls. It is then likely to break up. The presence of ice rises or areas of grounding towards the seaward margin can radically alter the size of the ice shelf which can form. The theory could be used as a starting point to study non-equilibrium behaviour.