Evaluating calving functions: emergent dynamics from a position-based calving function and the limits of rate-based calving functions.

A wide range of calving functions is currently available but there is no consensus on the best approach. Current assessments of calving functions are often crudely done by fitting functions to observed terminus positions, neglecting the physical processes that drive changes in calving dynamics. Here, we use 3D simulations of synthetic tidewater glacier domains in Elmer/Ice, to determine whether natural behaviours emerge from the crevasse-depth and von Mises calving functions, and to provide a basis for more robust assessments of the potential capabilities of calving functions. Both functions are derived from the full 3D Cauchy stress tensor and are simple functions that can be exported to ice sheet models. The crevasse-depth calving function is shown to be able to simulate both serac and full thickness calving events and simulates how their relative proportion is altered by changing the ice freeboard or submarine melting. A clear distinction between rate- and position-based calving is shown with the von Mises calving function unable to respond to imposed changes in topography or glacier geometry. Importantly, any feedback between glacier dynamics and the von Mises calving function is through an unphysical velocity feedback loop.  

Through these simple experiments we show both steady state and transient behaviour can modelled using a position-based calving function while rate-based functions can only capture an imposed state. It is clear we must look beyond just terminus positions when assessing the suitability of a calving function. Manual tuning can mask unphysical calving behaviour and restrict behaviour to that of the tuned period. Furthermore, we show that a robust calving function does not require site or timeframe specific tuning using the crevasse-depth calving function at Store Glacier (Sermeq Kujalleq) and Jakobshavn Isbrae (Sermeq Kujalleq). 

By comparing the two calving functions, it is apparent that full-depth calving is irrefutably position-based. Consequently, future projections must not be made using rate-based calving functions. Using a position function, calving rates vary with time and glacier state, so cannot be assumed to be a constant function of stress.