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Abstract Ice shelf fracture is responsible for roughly half of Antarctic ice mass loss in the form of calving and can weaken buttressing of upstream ice flow. Large uncertainties associated with the ice sheet response to climate variations are due to a poor understanding of these fracture processes and how to model them. Here, we address these problems by implementing an anisotropic, nonlocal integral formulation of creep damage within a large‐scale shallow‐shelf ice flow model. This model can be used to study the full evolution of fracture from initiation of crevassing to rifting that eventually causes tabular calving. While previous ice shelf fracture models have largely relied on simple expressions to estimate crevasse depths, our model parameterizes fracture as a progressive damage evolution process in three‐dimensions (3‐D). We also implement an efficient numerical framework based on the material point method, which avoids advection errors. Using an idealized marine ice sheet, we test the creep damage model and a crevasse‐depth based damage model, including a modified version of the latter that accounts for damage evolution due to necking and mass balance. We demonstrate that the creep damage model is best suited for capturing weakening and rifting over shorter (monthly/yearly) timescales, and that anisotropic damage reproduces typically observed fracture patterns better than isotropic damage. Because necking and mass balance can significantly influence damage on longer (decadal) timescales, we discuss the potential for a combined approach between models to best represent mechanical weakening and tabular calving within long‐term simulations. 

Abstract We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM‐SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub‐element scales, and a weak formulation based on well‐established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1‐D and 2‐D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid‐crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid‐crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM‐SSA framework is viable for the simulation of ice sheet‐shelf evolution and enables boundary tracking and error‐free advection of history or state variables, such as ice thickness or damage. 

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. 

Abstract. Linear elastic fracture mechanics (LEFM) models have been used to estimate crevasse depths in glaciers and to represent iceberg calving in ice sheet models. However, existing LEFM models assume glacier ice to be homogeneous and utilize the mechanical properties of fully consolidated ice. Using depth-invariant properties is not realistic as the process of compaction from unconsolidated snow to firn to glacial ice is dependent on several environmental factors, typically leading to a lower density and Young's modulus in upper surface strata. New analytical solutions for longitudinal-stress profiles are derived using depth-varying properties based on borehole data from the Ronne Ice Shelf and are used in an LEFM model to determine the maximum penetration depths of an isolated crevasse in grounded glaciers and floating ice shelves. These maximum crevasse depths are compared to those obtained for homogeneous glacial ice, showing the importance of including the effect of the upper unconsolidated firn layers on crevasse propagation. The largest reductions in the penetration depth ratio were observed for shallow grounded glaciers, with variations in Young's modulus being more influential than firn density (maximum differences in crevasse depth of 46 % and 20 %, respectively), whereas firn density changes resulted in an increase in penetration depth for thinner floating ice shelves (95 %–188 % difference in crevasse depth between constant and depth-varying properties). Thus, our study shows that the firn layer can increase the vulnerability of ice shelves to fracture and calving, highlighting the importance of considering depth-dependent firn layer material properties in LEFM models for estimating crevasse penetration depths and predicting rift propagation. 

Abstract. Full-thickness crevasses can transport water from the glacier surface to the bedrock where high water pressures can open kilometre-long cracks along the basal interface, which can accelerate glacier flow. We present a first computational modelling study that describes time-dependent fracture propagation in an idealised glacier causing rapid supraglacial lake drainage. A novel two-scale numerical method is developed to capture the elastic and viscoelastic deformations of ice along with crevasse propagation. The fluid-conserving thermo–hydro–mechanical model incorporates turbulent fluid flow and accounts for melting and refreezing in fractures. Applying this model to observational data from a 2008 rapid-lake-drainage event indicates that viscous deformation exerts a much stronger control on hydrofracture propagation compared to thermal effects. This finding contradicts the conventional assumption that elastic deformation is adequate to describe fracture propagation in glaciers over short timescales (minutes to several hours) and instead demonstrates that viscous deformation must be considered to reproduce observations of lake drainage rates and local ice surface elevation changes. As supraglacial lakes continue expanding inland and as Greenland Ice Sheet temperatures become warmer than −8 °C, our results suggest rapid lake drainage events are likely to occur without refreezing, which has implications for the rate of sea level rise. 

The phase field method is becoming the de facto choice for the numerical analysis of complex problems that involve multiple initiating, propagating, interacting, branching and merging fractures. However, within the context of finite element modelling, the method requires a fine mesh in regions where fractures will propagate, in order to capture sharp variations in the phase field representing the fractured/damaged regions. This means that the method can become computationally expensive when the fracture propagation paths are not known a priori. This paper presents a 2D hp-adaptive discontinuous Galerkin finite element method for phase field fracture that includes a posteriori error estimators for both the elasticity and phase field equations, which drive mesh adaptivity for static and propagating fractures. This combination means that it is possible to be reliably and efficiently solve phase field fracture problems with arbitrary initial meshes, irrespective of the initial geometry or loading conditions. This ability is demonstrated on several example problems, which are solved using a light-BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm. The examples highlight the importance of driving mesh adaptivity using both the elasticity and phase field errors for physically meaningful, yet computationally tractable, results. They also reveal the importance of including p-refinement, which is typically not included in existing phase field literature. The above features provide a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes.