Glacier Calving: A Numerical Model of Forces in the Calving-Speed/Water-Depth Relation

Empirical data suggest that the race of calving of grounded glaciers terminating in water is directly proportional to the water depth. Important controls on calving may be the extent to which a calving face tends to become oversteepened by differential flow within the ice and the extent to which bending moments promote extrusion and bottom crevassing at the base of a calving face. Numerical modelling suggests that the tendency to become oversteepened increases roughly linearly with water depth. In addition, extending longitudinal deviatoric stresses at the base of a calving face increase with water depth. These processes provide a possible physical explanation for the observed calving-rate/water-depth relation.

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.