2019, Schlemm, T., Levermann, A.

Over large coastal regions in Greenland and Antarctica the ice sheet calves directly into the ocean. In contrast to ice-shelf calving, an increase in calving from grounded glaciers contributes directly to sea-level rise. Ice cliffs with a glacier freeboard larger than ≈100 m are currently not observed, but it has been shown that such ice cliffs are increasingly unstable with increasing ice thickness. This cliff calving can constitute a self-amplifying ice loss mechanism that may significantly alter sea-level projections both of Greenland and Antarctica. Here we seek to derive a minimalist stress-based parametrization for cliff calving from grounded glaciers whose freeboards exceed the 100 m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs.

To this end we compute the stress field for a glacier with a simplified two-dimensional geometry from the two-dimensional Stokes equation. First we assume a constant yield stress to derive the failure region at the glacier front from the stress field within the glacier. Secondly, we assume a constant response time of ice failure due to exceedance of the yield stress. With this strongly constraining but very simple set of assumptions we propose a cliff-calving law where the calving rate follows a power-law dependence on the freeboard of the ice with exponents between 2 and 3, depending on the relative water depth at the calving front. The critical freeboard below which the ice front is stable decreases with increasing relative water depth of the calving front. For a dry water front it is, for example, 75 m. The purpose of this study is not to provide a comprehensive calving law but to derive a particularly simple equation with a transparent and minimalist set of assumptions.

2011, Martin, M.A., Winkelmann, R., Haseloff, M., Albrecht, T., Bueler, E., Khroulev, C., Levermann, A.

We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.

2014, Rosier, S.H.R., Green, J.A.M., Scourse, J.D., Winkelmann, R.

Tides play an important role in ice sheet dynamics by modulating ice stream velocity, fracturing, and moving ice shelves and mixing water beneath them. Any changes in ice shelf extent or thickness will alter the tidal dynamics through modification of water column thickness and coastal topography but these will in turn feed back onto the overall ice shelf stability. Here, we show that removal or reduction in extent and/or thickness of the Ross and Ronne-Filchner ice shelves would have a significant impact on the tides around Antarctica. The Ronne-Filchner appears particularly vulnerable, with an increase in M2 amplitude of over 0.5 m beneath much of the ice shelf potentially leading to tidally induced feedbacks on ice shelf/sheet dynamics. These results highlight the importance of understanding tidal feedbacks on ice shelves/streams due to their influence on ice sheet dynamics.

2021-1-7, De Rydt, Jan, Reese, Ronja, Paolo, Fernando S., Gudmundsson, G. Hilmar

Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Over the last 2 decades, the glacier has lost in excess of a trillion tons of ice, or the equivalent of 3 mm of sea level rise. The ongoing changes are thought to have been triggered by ocean-induced thinning of its floating ice shelf, grounding line retreat, and the associated reduction in buttressing forces. However, other drivers of change, such as large-scale calving and changes in ice rheology and basal slipperiness, could play a vital, yet unquantified, role in controlling the ongoing and future evolution of the glacier. In addition, recent studies have shown that mechanical properties of the bed are key to explaining the observed speed-up. Here we used a combination of the latest remote sensing datasets between 1996 and 2016, data assimilation tools, and numerical perturbation experiments to quantify the relative importance of all processes in driving the recent changes in Pine Island Glacier dynamics. We show that (1) calving and ice shelf thinning have caused a comparable reduction in ice shelf buttressing over the past 2 decades; that (2) simulated changes in ice flow over a viscously deforming bed are only compatible with observations if large and widespread changes in ice viscosity and/or basal slipperiness are taken into account; and that (3) a spatially varying, predominantly plastic bed rheology can closely reproduce observed changes in flow without marked variations in ice-internal and basal properties. Our results demonstrate that, in addition to its evolving ice thickness, calving processes and a heterogeneous bed rheology play a key role in the contemporary evolution of Pine Island Glacier.