Implementation of calving processes in large-scale ice sheet models

Concepts and ideas related to implementation of calving in large-scale ice-sheet models are presented and discussed, and new model verification experiments proposed. For unconfined ice shelves, any calving law where the calving rate increases with cliff height (free board) must lead to an unstable advance or retreat. No other solutions are possible and all calving front positions are always unstable. If in contrast, calving rate is a monotonically decreasing function of cliff height, both stable and unstable positions are possible. An example of such a configuration and simple analytical solution for the transient evolution of the calving front is provided, which can be used for numerical verification purposes. It is argued that cliff-height based calving laws are, at least for the case of buttressed ice shelves, arguably unphysical as they can result in a multi-valued function for the calving rate as a function of local state of stress. Implementation of a new variational form of the level-set method, involving forward-and-backward diffusion, for capturing the evolution of calving fronts is discussed and several applications to Pine Island and Thwaites glacier shown.