Progress in understanding and modelling calving

The importance of calving losses from marine-terminating ice margins in a warming world has highlighted the need for reliable representation of calving in predictive ice-sheet models. However, there is currently no consensus regarding the most appropriate form for calving functions (so-called 'calving laws'), and the calving problem remains open. We advocate an integrated approach, in which observations, theory and high-fidelity modelling are used to develop and calibrate optimal, general calving functions for continuum ice-sheet models. Our work has demonstrated that calving is a stochastic process that gives rise to self-organising behaviour at a range of scales, including calving-size distributions, waiting times, and ice-front fluctuations. Individual calving events occur in response to critical and/or sub-critical crack propagation under tensile, shear or mixed stress regimes. We have used these insights to develop a position-based stochastic calving function, in which calving probabilities are scaled to the state of stress in the ice. When implemented in the full-stress continuum model Elmer/Ice, the calving function exhibits a wide range of realistic self-organising behaviour, and successfully reproduces observed ice-front fluctuations of Jakobshavn Isbrae and Store Glacier without the need for site-specific tuning. A calving algorithm suitable for vertically integrated ice-sheet models is in development.