Calving laws and where to find them

Calving from tidewater glaciers and ice shelves is an important component of global mass balance and may contribute significantly to future sea-level rise. Current prognostic ice-sheet models cannot predict future calving losses because they lack a robust calving law. We argue that the key to finding a general calving law is to recognise that calving glaciers are stochastic dynamic systems that exhibit self-organisation. Collectively, calving events have statistical properties that reflect underlying fragmentation processes. These reflect distinct styles of calving and give rise to persistent patterns of advance and retreat, including fluctuations around pinning points and periods of instability and transition. These patterns motivate a stochastic calving function scaled to the stress within the ice, which we demonstrate in a set of model experiments with Elmer/Ice, for synthetic geometries representative of a Greenland outlet glacier and an Antarctic ice shelf. Self-organising behaviour emerges spontaneously from the model, including expected calving-size distributions and system convergence on quasi-stable states. The model simulates calving behaviour over a wide range of spatial and temporal scales and produces short calving cycles for a Greenland-type geometry and long cycles for an Antarctic shelf-type geometry. The long-standing calving law problem may yield to this kind of approach.