Glacier Calving

What is modelled

A longitudinal strain rate stretches the ice at the front. Through Glen's flow law this sets a tensile stress, and a crevasse opens down to the depth where that stress is balanced by the weight of the ice (Nye). A crevasse partly filled with meltwater penetrates deeper. When it reaches the waterline, or the bed in thick grounded ice, a block of the front calves.

Equations

• Glen's law strain rate = A τ3, A(T) Arrhenius with 115 kJ/mol.
• Dry depth d0 = (2 / ρi g) (strain rate / A)1/3.
• Water filled to a fraction f: d = d0 / (1 - ρw f / ρi), with no finite depth above f = ρi/ρw.
• Flotation thickness ρw D / ρi; height above buoyancy H - ρw D / ρi.

Checks run in the page

• The Nye depth from the stress balance.
• The water-filled depth from the tip stress balance.
• The Glen rate factor against tabulated values.
• The flotation thickness from the weight balance.

Honest simplifications

One crevasse at a fixed distance behind the front, a uniform strain rate and temperature, a constant meltwater filling rate and a simple calving criterion without tides, undercutting by the sea or the full fracture mechanics of the stress intensity at the tip. The numbers are of the right order but not a prediction for any real glacier.

• Press Cold stiff ice: the dry crevasse is deeper but the front still needs water to calve.
• Press Thick grounded ice: the crevasse must reach the bed, which needs a nearly full crevasse.
• Press Near flotation: a thin front in deep water has a negative height above buoyancy.