The Crevasse Depth Calving Law Applied to Ice Shelves: Insights from a 1D Flowline Model

The crevasse depth (CD) calving law predicts the position of glacier termini from the penetration of surface and basal crevasses computed from stresses in the ice. When applied to Greenland tidewater glaciers, it has high skill when implemented in a full-Stokes 3D model, although its performance in 2D and 1D models is still subject to debate, especially its ability to induce ice shelf calving without the addition of unrealistic amounts of  water in surface crevasses.  This study re-evaluates the CD law within a 1D flowline model of an ice shelf. We show that the model predicts deep crevasse penetration at locations where drag at the shelf boundaries diminishes,such as the grounding line or embayment mouths. Crevasse depth depends on the rate at which these resistance sources decrease along-flow, influencing the longitudinal stress gradient. While full-depth penetration may occur in thinned shelves (due to extensive basal melt), full-depth calving is generally not predicted for unconfined ice shelves. Observations of Antarctic ice shelves and floating ice tongues well beyond embayments or basal pinning points suggest that additional triggers, like slow rift growth, basal melting, or oceanographic stresses, are essential for calving. The addition of water to surface crevasses can greatly facilitate calving. In some cases, reflecting real-world conditions, such as the hydrofracturing-induced collapse of vulnerable ice shelves. However, the need for water-depth tuning in other situations has raised concerns about the physical fidelity of the model. We propose a modified stochastic CD calving criterion in which the probability of calving ramps from zero for a threshold crevasse depth to one for full-depth penetration. This non-deterministic approach captures the statistical structure of calving events, and allows a range of observed behaviours to emerge, such as long Antarctic ice shelf calving cycles (ice-tongue advance punctuated by rare calving events), and short-term fluctuations of tidewater glaciers (frequent calving retreat back to pinning points). We argue that a probabilistic approach represents an important step towards a universal calving law.