Stability of the Junction of an Ice Sheet and an Ice Shelf

TLDR

The study analyzes the steady‑state size of a two‑dimensional ice sheet resting below sea level and ending in floating ice shelves. The analysis finds that a stable ice sheet can exist only when the bed depth is below a critical threshold; above this depth no steady state is possible, while a sloping bed permits a stable width that increases with accumulation or lower sea level, leaving the West Antarctic ice sheet’s equilibrium status uncertain and possibly disintegrating.

Abstract

An analysis is made of the steady-state size of a two-dimensional ice sheet whose base is below sea-level and which terminates in floating ice shelves. Under the assumption of perfect plasticity it is found that an ice sheet placed on a bed whose surface was initially flat cannot exist if the depth of the bed below sea-level exceeds a critical depth. If this depth is less than the critical level, the ice sheet extends out to the edge of the continental shelf. Similar results are found with more realistic assumptions about the laws governing the flow of ice. If the bed slopes away from the centre, the ice sheet can have a stable width that increases in value as the accumulation rate increases or as sea-level is lowered. It is not possible to decide whether or not the West Antarctic ice sheet is in stable equilibrium. It is entirely possible that this ice sheet is disintegrating at present, as suggested by Hughes.