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Ice slabs are multi-meter thick layers of solid reforzen ice that form on top of the porous firn layer in Greenland’s wet snow zone. Recent observations in Northwest Greenland highlight the ability of this relict firn layer to store meltwater in its pores after surface meltwater drains rapidly through cracks in the overlying ice slab. Current fracture mechanics (i.e., LEFM) assumes that the stored elastic energy in an impermeable solid matrix is instantaneously dissipated by creating new crack surfaces, which only holds for impermeable solid media. To better understand the fate of meltwater in the porous firn layer beneath ice slabs, we develop a two-dimensional, poroelastic continuum model to quantify the stress and pressure changes in the porous firn during meltwater penetration.We extend Biot’s poroelastic theory to two-phase immiscible flow by introducing meltwater saturation as an extra variable. By coupling the fluid continuity and force balance equations, we resolve the spatiotemporal evolution of 1) matrix deformations and effective stresses, 2) the water saturation field, and 3) the water pressure field. We adopt a fracture criterion for the cohesive porous firn layer: the maximum tensile effective stress should exceed the material tensile strength to generate fractures. We study the maximum tensile effective stress induced by water injection as a function of firn’s mechanical and hydraulic properties (bulk modulus, porosity, and permeability), and the infiltration conditions (constant infiltration pressure or flow rate). Our results show that the maximum tensile effective stress in the firn layer is no more than a quarter of that predicted for an equivalent solid ice column, because the imposed load is mostly transmitted into the pore pressure. Therefore our model predicts that surface-to-bed hydrofracture is unlikely to form if meltwater can leak into the firn layer. In “Vulnerability of Firn to Hydrofracture, Part II: Greenland’s Ice Slab Regions”, we apply this model to assess the vulnerability of Greenland’s ice slab regions.

Ice flows in response to stresses according to the flow law that involves ice viscosity. An accurate description of effective ice viscosity is essential for predicting the mass loss of the Antarctic Ice Sheet, yet measurement of ice viscosity is challenging at a continental scale. Lab experiments of polycrystalline ice shows that the effective viscosity of ice obeys a power-law relation with the strain rate, known as Glen’s flow law. However, it remains unclear how processes at ice-shelf scales impact the effective viscosity of glacial ice. Here, we leverage the availability of remote-sensing data and physics-informed deep learning to infer the effective ice viscosity and examine the rheology, i.e. flow law, of glacial ice in Antarctic Ice Shelves. We find that the rheology of ice shelves differs substantially between the compression and extension zones. In the compression zone near the grounding line the rheology of ice closely obeys power laws with exponents in the range 1

Ice shelves, the floating extensions of ice sheets, can reduce the rate of sea level rise by buttressing the upstream grounded ice. However, calving, or the fracturing that creates icebergs, can cut out regions that were resisting flow, and allow for increased ice flux and thus sea level contribution. In this work, I focus on the transition from basal crevasses, or seawater-filled fractures on the bottom surface, to full thickness fractures called rifts. Using RACMO ice shelf surface temperatures and holding the ice-ocean interface at -2℃, I find good agreement between observed rifts on the Larsen C and Ross Ice Shelves and rifts predicted to evolve from basal crevasses through 2D Mode I Linear Elastic Fracture Mechanics (LEFM). I also explore the influence of ice shelf geometry in rift formation by solving the Shallow Shelf Approximation (SSA) equations for idealized ice shelves with COMSOL’s Finite Element Analysis software. Using the stress field outputs with LEFM’s rift initiation criteria, I find qualitative agreement in the rift orientation between the predicted unstable basal crevasses and the observed rifts on the left margin of Pine Island Ice Shelf.

The drainage efficiency of the subglacial water system evolves during the melt season. However, direct measurement of drainage efficiency under 1000-meters thick ice is challenging. We previously demonstrated that surface observations of rapid lake drainage induced uplifts can be used to assess subglacial transmissivity beneath the ice sheet. When a lake drains, the water reaches the interface between the ice and bed and forms a water-filled blister. This water then drains through the subglacial drainage system. In this study, we use mathematical models to examine the behavior of surface uplift relaxation resulting from different types of drainage systems, including a laminar water sheet, a turbulent water sheet, and a turbulent subglacial channel. Combined with surface GPS observations of five lakes, we showed that the model can be used to study the evolution of subglacial drainage efficiency.

Hydrofracture and rapid lake drainage can transport surface meltwater to the bed of the Greenland Ice Sheet, thereby coupling surface mass balance processes and dynamic mass loss. Vertical hydrofracture is widely assumed to occur in the ablation zone, where abundant surface runoff that can fill fractures. However, in Greenland, the runoff line has expanded into the accumulation zone due to the development of ice slabs in the firn. It remains unclear whether surface runoff from these ice slab regions also drains locally to the bed. Recent observations in Northwest Greenland suggest that when meltwater penetrates ice slabs via surface fractures, it leaks off into a relict firn layer and does not initiate unstable vertical hydrofracture that propagates throughout the ice thickness. At the same time, buried supraglacial lakes have been observed to drain to the ice sheet bed this same region. Therefore, to assess the mass balance impact of ice slab expansion, it is important to understand if and when surface-to-bed hydrofracture may occur in these regions.In “Vulnerability of Firn to Hydrofracture, Part I: Poromechanical Modeling”, we developed an analytic expression for the maximum tensile effective stress within the firn layer beneath a water-filled fracture in an ice slab. Here we apply this model to Greenland’s ice slab regions. We use an ensemble of in situ and remote sensing observations to constrain the physical, mechanical, and hydraulic parameters in our model. We then run a Monte Carlo analysis to constrain the physically-plausible range of maximum tensile effective stress in the firn for two scenarios: a water-filled crevasse in an ice slab or a supraglacial lake over a fractured ice slab. Our results show that the maximum stress in the firn layer is always less than in an equivalent solid ice column, and typically remains compressive, because the imposed load is partially accommodated by a change in pore pressure. An overlying lake further stabilizes the system by increasing the lithostatic stress that acts to close the fracture. Therefore, in Greenland, the relict firn layer can be an important stabilizing factor that suppresses surface-to-bed hydrofracture under ice slabs, despite the abundance of both surface crevassing and meltwater.

Greenland supraglacial lakes sometimes drain to the ice-sheet base only hours to days apart in time, leading to the hypothesis that stress transmission following one drainage may be sufficient to induce hydro-fracture-driven drainages of other lakes. However, available observations characterizing the time- and length-scales of drainage-induced stress perturbations are insufficient to evaluate this hypothesis, hindering our understanding of whether lower-elevation lake drainages could generate stress changes that initiate hydro-fracture beneath lakes in inland ice-sheet regions. Here, we invert ice-sheet surface displacement observations from a dense Global Positioning System (GPS) array deployed around three supraglacial lakes in the Greenland Ice Sheet ablation zone to estimate the space-time history of slip and opening along pre-defined planes within an elastic half-space that best reproduces GPS observations during two rapid drainage events. We then use these slip and opening estimates to forward model ice-sheet surface stresses across all three neighboring lake basins and investigate stress transmission between the basins. We find that drainage of a central lake places neighboring basins in either tensional or compressional surface stress relative to their individual hydro-fracture scarp orientations, which, respectively, promotes or inhibits hydro-fracture initiation beneath those lakes. Surface-stress-change direction is asymmetric across the lake-draining fracture of the central lake and highly dependent on where surface uplift occurs. On elastic timescales, lake-drainage-induced stresses within the extent of the GPS array in the inland direction remain low within ~3 km of the central lake. This short length-scale for stress coupling in the inland direction is consistent with idealized lake-drainage scenarios for different lake volumes and ice-sheet thicknesses. Our observations and idealized-model results support the stress-transmission hypothesis for inducing hydro-fracture-driven drainage of lakes located within the region of uplift produced by the initial drainage, but refute this hypothesis for distal lakes not located down the subglacial hydraulic catchment from the initial drainage.