Theoretical Calving Rates from Glaciers Along Ice Walls Grounded in Water of Variable Depths

Calving has been studied for glaciers ranging from slow polar glaciers that calve on dry land, such as on Deception Island (63.0-degrees-S, 60.6-degrees-W) in Antarctica, through temperate Alaskan tide-water glaciers, to fast outlet glaciers that float in fiords and calve in deep water, such as Jakobshavns Isbrae (69.2-degrees-N, 49.9-degrees-W) in Greenland. Calving from grounded ice walls and floating ice shelves is the main ablation mechanism for the Antarctic and Greenland ice sheets, as it was along marine and lacustrine margins of former Pleistocene ice sheets, and is for tide-water and polar glaciers. Yet, the theory of ice calving is underdeveloped because of inherent dangers in obtaining field data to test and constrain calving models. An attempt is made to develop a calving theory for ice walls grounded in water of variable depth, and to relate slab calving from ice walls to tabular calving from ice shelves. A calving law is derived in which calving rates from ice walls are controled by bending creep behind the ice wall, and depend on wall height h, forward bending angle-theta, crevasse distance c behind the ice wall and depth d of water in front of the ice wall. Reasonable agreement with calving rates reported by Brown and others (1982) for Alaskan tide-water glaciers is obtained when c depends on wall height, wall height above water and water depth. More data are needed to determine which of these dependencies is correct. A calving ratio c/h is introduced to understand the transition from slab calving to tabular calving as water deepens and the calving glacier becomes afloat.

Bending Shear: The Rate-Controlling Mechanism for Calving Ice Walls

Bending shear was observed to produce nearly vertical shear bands in a calving ice wall standing on dry land on Deception Island (Iat. 63.0 oS., long. 60.6 W.), and slabs calved straight downward when shear rupture occurred along these shear bands (Hughes, 1989). A formula for the calving rate was developed from the Deception Island data, and we have attempted to justify generalizing this formula to include ice walls standing along beaches or in water. These are environments in which a wave-washed groove develops along the base of the ice wall or along a water line above the base. The rate of wave erosion provides an alternative mechanism for controlling the calving rate in these environments. We have determined that the rate at which bending creep produces nearly vertical shear bands, along which shear r upture occurs, controls the calving rate in all environments. Shear rupture occurs at a calving shear stress of about I bar. Our results justify using the calving formula to compute the calving rate of ice walls in computer models of ice-sheet dynamics. This is especially important in simulating retreat of Northern Hemisphere ice sheets during the last deglaciation, when marine and lacustrine environments were common along retreating ice margins. These margins would have been ice walls standing along beaches or in water, because floating ice shelves are not expected in the ablation zone of retreating ice sheets.