Tidewater Glaciers and Ice Shelves as Self-Organising Systems

Marine-terminating glaciers and ice shelves are notoriously complex, with a wide range of ice-dynamic and calving processes occuring in response to oceanographic, atmospheric and glaciological influences. Within this complexity, however, we can recognise order on at least two scales. First, marine ice fronts typically form vertical cliffs, reflecting competition between oversteepening (ice flow and melt-undercutting) and failure. Calving magnitude-frequency distributions have power-law form with an exponent of -1.2, characteristic of self-organising criticality (SOC). Such systems have a critical point as an attractor, such that the system converges on the failure threshold.The second scale is that of the whole ice tongue. Tidewater glaciers and ice shelves typically oscillate around stable positions for multiple years, punctuated by transitions to new quasi-stable positions. Stability is encouraged by pinning points which function as attractors at thresholds between stable and metastable states. Ice tongues may exist in metastable states for variable amounts of time, from days to decades. Factors encouraging rapid relaxation to the threshold include large stress gradients and rapid basal melt, and factors encouraging long relaxation times include low stress gradients, low melt rates, and buttressing from mélange or sea ice. Calving magnitude-frequency distributions have exponential form, reflecting the stochastic nature of calving in the metastable zone.Both scales of self-organisation emerge spontaneously from physically-based calving models such as the Helsinki Discrete Element Model (HiDEM) and the crevasse-depth (CD) calving law implemented in Elmer/Ice. Purely deterministic models, however, are not optimal for long-term simulations, especially in Antarctic contexts. We present results of preliminary simulations using a stochastic CD calving law, which opens up the possibility of a universal calving model applicable to both the Greenland and Antarctic ice sheets.