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Abstract The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects. 

The largest uncertainty in future sea-level rise is loss of ice from the Greenland and Antarctic Ice Sheets. Ice shelves, freely floating platforms of ice that fringe the ice sheets, play a crucial role in restraining discharge of grounded ice into the ocean through buttressing. However, since the 1990s, several ice shelves have thinned, retreated, and collapsed. If this pattern continues, it could expose thick cliffs that become structurally unstable and collapse in a process called marine ice cliff instability (MICI). However, the feedbacks between calving, retreat, and other forcings are not well understood. Here we review observed modes of calving from ice shelves and marine-terminating glaciers, and their relation to environmental forces. We show that the primary driver of calving is long-term internal glaciological stress, but as ice shelves thin they may become more vulnerable to environmental forcing. This vulnerability—and the potential for MICI—comes from a combination of the distribution of preexisting flaws within the ice and regions where the stress is large enough to initiate fracture. Although significant progress has been made modeling these processes, theories must now be tested against a wide range of environmental and glaciological conditions in both modern and paleo conditions. ▪ Ice shelves, floating platforms of ice fed by ice sheets, shed mass in a near-instantaneous fashion through iceberg calving. ▪ Most ice shelves exhibit a stable cycle of calving front advance and retreat that is insensitive to small changes in environmental conditions. ▪ Some ice shelves have retreated or collapsed completely, and in the future this could expose thick cliffs that could become structurally unstable called ice cliff instability. ▪ The potential for ice shelf and ice cliff instability is controlled by the presence and evolution of flaws or fractures within the ice. 

Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner. 

Abstract Iceberg calving, the process where icebergs detach from glaciers, remains poorly understood. Moreover, few parameterizations of the calving process can easily be integrated into numerical models to accurately capture observations, resulting in large uncertainties in projected sea level rise. Recent efforts have focused on estimating crevasse depths assuming tensile failure occurs when crevasses fully penetrate the glacier thickness. However, these approaches often ignore the role of advecting crevasses on calculations of crevasse depth. Here, we examine a more general crevasse depth calving model that includes crevasse advection. We apply this model to idealized prograde and retrograde bed geometries as well as a prograde geometry with a sill. Neglecting crevasse advection results in steady glacier advance and ice tongue formation for all ice temperatures, sliding law coefficients and constant slope bed geometries considered. In contrast, crevasse advection suppresses ice tongue formation and increases calving rates, leading to glacier retreat. Furthermore, crevasse advection allows a grounded calving front to stabilize on top of sills. These results suggest that crevasse advection can radically alter calving rates and hint that future parameterizations of fracture and failure need to more carefully consider the lifecycle of crevasses and the role this plays in the calving process. 

Abstract Marine ice-cliff instability could accelerate ice loss from Antarctica, and according to some model predictions could potentially contribute >1 m of global mean sea level rise by 2100 at current emission rates. Regions with over-deepening basins >1 km in depth (e.g., the West Antarctic Ice Sheet) are particularly susceptible to this instability, as retreat could expose increasingly tall cliffs that could exceed ice stability thresholds. Here, we use a suite of high-fidelity glacier models to improve understanding of the modes through which ice cliffs can structurally fail and derive a conservative ice-cliff failure retreat rate parameterization for ice-sheet models. Our results highlight the respective roles of viscous deformation, shear-band formation, and brittle-tensile failure within marine ice-cliff instability. Calving rates increase non-linearly with cliff height, but runaway ice-cliff retreat can be inhibited by viscous flow and back force from iceberg mélange. 

Portions of ice sheets grounded deep beneath sea level can disintegrate if tall ice cliffs at the ice-ocean boundary start to collapse under their own weight. This process, called marine ice cliff instability, could lead to catastrophic retreat of sections of West Antarctica on decadal-to-century time scales. Here we use a model that resolves flow and failure of ice to show that dynamic thinning can slow or stabilize cliff retreat, but when ice thickness increases rapidly upstream from the ice cliff, there is a transition to catastrophic collapse. However, even if vulnerable locations like Thwaites Glacier start to collapse, small resistive forces from sea-ice and calved debris can slow down or arrest retreat, reducing the potential for sustained ice sheet collapse. 

Abstract The ice sheets of the Amundsen Sea Embayment (ASE) are vulnerable to the marine ice sheet instability (MISI), which could cause irreversible collapse and raise sea levels by over a meter. The uncertain timing and scale of this collapse depend on the complex interaction between ice, ocean, and bedrock dynamics. The mantle beneath the ASE is likely less viscous (â<88>Œ1018 Pa s) than the Earth's average mantle (â<88>Œ1021 Pa s). Here we show that an effective equilibrium between Pine Island Glacier's retreat and the response of a weak viscoelastic mantle can reduce ice mass lost by almost 30\% over 150 years. Other components of solid Earth responseâ<80><94>purely elastic deformations and geoid perturbationsâ<80><94>provide less stability than the viscoelastic response alone. Uncertainties in mantle rheology, topography, and basal melt affect how much stability we expect, if any. Our study indicates the importance of considering viscoelastic uplift during the rapid retreat associated with MISI.