Glacier Calving - 2D Terminus Cross-Section and Crevasse Depth Criterion

Crevasse depth criterion

Glen's flow law ε̇ = A τⁿ (n = 3, A = 2.4 × 10^-24 Pa^-3 s^-1 for temperate ice) gives the longitudinal tensile stress R_xx = 2 (ε̇_xx/A)^1/n. By the Nye zero-stress argument, a surface crevasse can open to the depth d_s = R_xx/(ρ_i g) + (ρ_w/ρ_i) d_w, where d_w is the depth of meltwater in it (Benn, Hulton and Mottram 2007). If d_s reaches the height of the ice above the waterline, the front is cut through and a block calves.

What the page computes

The crevasse deepens as dd/dt = (d_s - d)/τ, so it reaches the freeboard h_f after t = -τ ln(1 - h_f/d_s) if d_s > h_f and never otherwise. Between calving events the front advances at the flow speed u and each event removes one block of length L_b, so the mean terminus speed is u - L_b/t. Floating ice keeps ≈ 10 % of its thickness above water, h_f = H (1 - ρ_i/ρ_w).

Honest simplifications: one surface crevasse at a fixed distance, a first-order growth law instead of fracture mechanics, no basal crevasses, no buoyancy-driven bending, a single flow law and constant temperature. The animation of the falling block is illustrative.

• Start on Marginal front, then set meltwater to 0: the crevasse stalls below the freeboard and the glacier advances.
• Fill the crevasse with 25 m of meltwater: calving starts, the front retreats.
• Choose Deep fjord: a small freeboard means rapid calving.
• Raise the strain rate on the second graph and see where the blue curve crosses the freeboard line.