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Floating ice shelves that fringe the coast of Antarctica resist the flow of grounded ice into the ocean. One of the key factors governing the amount of flow resistance an ice shelf provides is the rigidity (related to viscosity) of the ice that constitutes it. Ice rigidity is highly heterogeneous and must be calibrated from spatially continuous surface observations assimilated into an ice-flow model. Realistic uncertainties in calibrated rigidity values are needed to quantify uncertainties in ice sheet and sea-level forecasts. Here, we present a physics-informed machine learning framework for inferring the full probability distribution of rigidity values for a given ice shelf, conditioned on ice surface velocity and thickness fields derived from remote-sensing data. We employ variational inference to jointly train neural networks and a variational Gaussian Process to reconstruct surface observations, rigidity values and uncertainties. Applying the framework to synthetic and large ice shelves in Antarctica demonstrates that rigidity is well-constrained where ice deformation is measurable within the noise level of the observations. Further reduction in uncertainties can be achieved by complementing variational inference with conventional inversion methods. Our results demonstrate a path forward for continuously updated calibrations of ice flow parameters from remote-sensing observations. [ABSTRACT FROM AUTHOR]

Understanding the dynamic behaviour of ice shelves, specifically the controls on their ability to buttress the flow of ice into the ocean, is critical for predicting future ice-sheet contributions to sea level rise. Many large ice shelves, which are predominantly composed of meteoric ice, have a basal layer of marine ice (formed from accumulated platelets at the ice–ocean interface), comprising up to 40% of their thickness locally. Differences in temperature, chemistry and microstructure between marine and meteoric ice mean the rheological properties of the ice vary throughout the ice shelf. These differences are not explicitly accounted for in ice-sheet modelling applications, and may have an important influence on ice shelf dynamics. We tested the sensitivity of a model of an idealised ice shelf to variations in temperature distribution and flow enhancement, and found that incorporating a realistic thermal profile (where the marine ice layer is isothermal) had an order of magnitude greater effect on ice mass flux and thinning than incorporating the mechanical properties of the marine ice. The presence of marine ice at the ice shelf base has the potential to significantly increase deviatoric stresses at the surface and ice mass flux across the front of an ice shelf. [ABSTRACT FROM AUTHOR]

We compare different ways the bulk flow nonlinearity of glacier ice can be captured in an orthotropic rheology. Specifically, we compare the unapproximated orthotropic rheology, derived from plastic potential theory, to existing approximations that assume either the nonlinear viscosity or fluidity is identical to that of Glen's isotropic flow law. We find, overall, a reasonable agreement between the three orthotropic rheologies, and with existing Dye 3 ice-core deformation tests, although assuming Glen's viscosity provides the best approximation to the unapproximated rheology. Our results therefore suggest that previous studies based on either approximation to the orthotropic rheology are on relatively safe ground in the sense that both approximations generally agree with the unapproximated rheology and experimental data. Finally, we provide the forward and inverse analytical forms of all three rheologies for use in future numerical ice-flow modelling. [ABSTRACT FROM AUTHOR]

The once-contiguous Ellesmere Ice Shelf, first reported in writing by European explorers in 1876, and now almost completely disintegrated, has rolling, wave-like surface topography, the origin of which we investigate using a viscous buckling instability analysis. We show that rolls can develop during a winter season (~ 100 d) if sea-ice pressure (depth-integrated horizontal stress applied to the seaward front of the Ellesmere Ice Shelf) is sufficiently large (1 MPa m) and ice thickness sufficiently low (1–10 m). Roll wavelength initially depends only on sea-ice pressure, but evolves over time depending on amplitude growth rate. This implies that a thinner ice shelf, with its faster amplitude growth rate, will have a shorter wavelength compared to a thicker ice shelf when sea-ice pressure is equal. A drawback of the viscous buckling mechanism is that roll amplitude decays once sea-ice pressure is removed. However, non-Newtonian ice rheology, where effective viscosity, and thus roll change rate, depends on total applied stress may constrain roll decay rate to be much slower than growth rate and allow roll persistence from year to year. Whether the viscous-buckling mechanism we explore here ultimately can be confirmed as the origin of the Ellesmere Ice Shelf rolls remains for future research. [ABSTRACT FROM AUTHOR]

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling. [ABSTRACT FROM AUTHOR]

Over a year of seismic observations, ~5000 short duration icequakes were detected by a permanent broadband station installed at the Princess Elisabeth base, located ~180 km inland in eastern Dronning Maud Land, East-Antarctica. Icequake detection via seismic waveform pattern recognition indicates the presence of two dominating clusters of events, totalizing ~1500 icequakes. The corresponding icequake locations point towards two distinct zones of outcropping blue ice areas (BIAs) located respectively at 4 and 1 km from the seismic station, both on the leeward side of a nunatak protruding through the ice sheet. The temporal occurrence of these icequakes suggests a close genetic link with thermal contraction of ice caused by significant surface cooling controlled, in summer by variations in diurnal solar radiation and in winter by strong cooling during cold katabatic regimes. Further analysis demonstrates the dependence of these icequakes on the absolute surface temperature and on its temporal change. Besides providing information on the ice fracture mechanics and rheology, investigations of thermal icequakes may be regarded as a ground-based proxy for the monitoring of the thermal state of BIAs, and characterization of ice-sheet ablation zones. [ABSTRACT FROM AUTHOR]

We investigate the relationship between four ice-shelf characteristics in the area close to the calving front: ice flow speed, strain rate, ice thickness and shelf width. Data are compiled for these glaciological parameters at the calving fronts of 22 Antarctic ice shelves. Clarification concerning the viscous supply of ice to the calving front is sought following the empirical calving law of Alley and others (2008), derived from a similar but smaller dataset, and the scaling analysis of Hindmarsh (2012). The dataset is analysed and good agreement is observed between the expected theoretical scaling and geophysical data for the flow of ice near the calving front in the case of ice shelves that are laterally confined and have uniform rheology. The lateral confinement ensures flow is aligned in the along-shelf direction, and uniform rheological parameters mean resistance to flow is provided by near-stationary ice in the grounded margins. In other cases, the velocity is greater than predicted, which we attribute to marginal weakening or the presence of ice tongues. [ABSTRACT FROM AUTHOR]

In this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized. [ABSTRACT FROM AUTHOR]

At Taylor Glacier, a cold-based outlet glacier of the East Antarctic ice sheet, observed surface speeds in the terminus region are 20 times greater than those predicted using Glen's flow law for cold (-17°C), thin (100 m) ice. Rheological properties of the clean meteoric glacier ice and the underlying deformable debris-rich basal ice can be inferred from surface-velocity and ablation-rate profiles using inverse theory. Here, with limited data, we use a two-layer flowband model to examine two end-member assumptions about the basal-ice properties: (1) uniform softness with spatially variable thickness and (2) uniform thickness with spatially variable softness. We find that the basal ice contributes 85-98% to the observed surface velocity in the terminus region. We also find that the basal-ice layer must be 10-15 m thick and 20-40 times softer than clean Holocene-age glacier ice in order to match the observations. Because significant deformation occurs in the basal ice, our inverse problem is not sensitive to variations in the softness of the meteoric ice. Our results suggest that despite low temperatures, highly deformable basal ice may dominate flow of cold-based glaciers and rheologically distinct layers should be incorporated in models of polar-glacier flow. [ABSTRACT FROM AUTHOR]

Densification of firn at the North Greenland Eemian Ice Drilling (NEEM) camp is investigated using density surrogates: dielectric permittivities ϵv and ϵh at microwave frequencies with electrical fields in the vertical and horizontal planes, respectively. Dielectric anisotropy Δϵ (=ϵv - ϵh) is then examined as a surrogate for the anisotropic geometry of firn. Its size, fluctuations and mutual correlations are investigated in samples taken at depths from the surface to ~90 m. The initial Δϵ of ~0.06 appears within the uppermost 0.2 m. After that, Δϵ decreases rapidly until 21-26 m depth. Below this, Δϵ decreases slowly. Layers with more ions of fluorine, chlorine and some cations deposited between the autumn and the subsequent summer deform preferentially during all these stages. This layered deformation is explained partly by the textural effects initially formed by the seasonal variation of metamorphism, and partly by ions such as fluorine, chlorine and ammonium, which are known to modulate dislocation movement in the ice crystal lattice. Insolation-sensitive microstructure appears to be preserved all the way to the pore close-off, within layers of the summer-to-autumn metamorphism. Like previous authors, we hypothesize that calcium is not the active agent in the reported deformation- calcium correlations. [ABSTRACT FROM AUTHOR]

Compression experiments on laboratory-grown columnar S2 saltwater ice loaded triaxially through proportional loading at T = -20°C at applied strain rates of ϵ = 10-5-10-1 s-1 demonstrate that plastic (P) faulting is a mode of failure in saltwater ice when rapidly loaded under a high degree of confinement. In terms of microstructure, mechanical behavior and strength, saltwater ice that fails via P-faulting is almost indistinguishable from columnar S2 freshwater ice that fails via P-faulting loaded under the same conditions. The results also demonstrate that saltwater ice loaded rapidly may exhibit yet another mode of failure, in addition to P-faulting, through what appears to be a mechanism of pore collapse• [ABSTRACT FROM AUTHOR]

Abstract: We have implemented the Jacobian-free Newton–Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8–3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods. [Copyright &y& Elsevier]

Water ice I rheology is a key factor for understanding the thermal and mechanical state of the outer shell of the icy satellites. Ice flow involves several deformation mechanisms (both Newtonian and non-Newtonian), which contribute to different extents depending on the temperature, grain size, and applied stress. In this work I analyze tidally heated and stressed equilibrium convection in the ice shell of Europa by considering a composite viscosity law which includes diffusion creep, basal slip, grain boundary sliding and dislocation creep, and. The calculations take into account the effect of tidal stresses on ice flow and use grain sizes between 0.1 and 100 mm. An Arrhenius-type relation (useful for parameterized convective models) is found then by fitting the calculated viscosity between 170 and 273 K to an exponential regression, which can be expressed in terms of pre-exponential constant and effective activation energy. I obtain convective heat flows between ~40 and ~60 mW m, values lower than those usually deduced (~100 mW m) from geological indicators of lithospheric thermal state, probably indicating heterogeneous tidal heating. On the other hand, for grain sizes larger than ~0.3 mm the thicknesses of the ice shell and convective sublayer are ~20-30 km and ~5-20 km respectively, values in good agreement with the available information for Europa. So, some fundamental geophysical characteristics of the ice shell of Europa could be arising from the properties of the composite water ice rheology. [ABSTRACT FROM AUTHOR]

Structural analyses were conducted in the basal zone of an Antarctic glacier. The studied basal ice sequence was retrieved from a 20-m-long subglacial tunnel dug at the margin of the glacier and is at the temperature of −17°C. For the first time, rotating clast systems embedded within debris-rich ice were thin-sectioned using specially designed cutting techniques. The observed structures reflect the occurrence of pervasive shearing at the base of the glacier, and can be used as shear sense indicators. In addition, some of these structures provide evidence for the presence of thin liquid films at the time of formation despite the marked freezing temperature of the ice. It is showed here that cautious analysis of deformation structures present in debris-bearing ice may bring insights not only into the flow dynamics of the embedding matrix, but also into the behaviour of the interstitial fluid network at the base of cold glaciers and ice sheets. [ABSTRACT FROM AUTHOR]

We map polygonally patterned ground formed in sublimation tills that overlie debris-covered glaciers in Mullins Valley and central Beacon Valley, in southern Victoria Land, Antarctica, and distinguish five morphological zones. Where the Mullins Valley debris-covered glacier debouches into Beacon Valley, polygonal patterning transitions from radial (orthogonal) intersections to non-oriented (hexagonal) intersections, providing a time-series of polygon evolution within a single microclimate. We offer the following model for polygon formation and evolution in the Mullins Valley system. Near-vertical cracks that ultimately outline polygons are produced by thermal contraction in the glacier ice. Some of these cracks may initially be oriented radial to maximum surface velocities by pre-existing structural stresses and material weaknesses in the glacier ice. In areas of relatively rapid flow, polygons are oriented down-valley forming an overall fan pattern radial to maximum ice velocity. As glacier flow moves the cracks down-valley, minor variations in flow rate deform polygons, giving rise to deformed radial polygons. Non-oriented (largely hexagonal) polygons commonly form in regions of stagnant and/or near-stagnant ice. We propose that orientation and morphology of contraction-crack polygons in sublimation tills can thus be used as an indicator of rates of subsurface ice flow. [ABSTRACT FROM AUTHOR]

An experimental investigation of flexural-gravity waves was performed in the Hamburg Ship Model Basin HSVA ice tank. Physical characteristics of the water-ice system were measured in several locations of the tank with a few sensors deployed in the water and on the ice during the tests. The three-dimensional motion of ice was measured with the optical system Qualisys; water pressure was measured by several pressure sensors mounted on the tank wall, in-plane deformations of the ice and the temperatures of the ice and water were measured by fiber optic sensors; and acoustic emissions were recorded with compressional crystal sensors. The experimental setup and selected results of the tests are discussed in this paper. Viscous-elastic model (Burgers material) is adopted to describe the dispersion and attenuation of waves propagating below the ice. The elastic modulus and the coefficient of viscosity are calculated using the experimental data. The results of the measurements demonstrated the dependence of wave characteristics from the variability of ice properties during the experiment caused by the brine drainage. We showed that the cyclic motion of the ice along the tank, imitating ice drift, and the generation of under ice turbulence cause an increase of wave damping. Recorded acoustic emissions demonstrated cyclic microcracking occurring with wave frequencies and accompanying bending deformations of the ice. This explains the viscous and anelastic rheology of the model ice. [ABSTRACT FROM AUTHOR]

Ice in both terrestrial and planetary settings often contains rock particles. Here we present an experimental investigation of the influence of intergranular particles on the rheological behavior of ice. Experiments were performed on samples fabricated from 10‐μm ice powders +1‐μm graphite or 0.8‐μm alumina particles and subjected to elevated confining pressures. A critical particle fraction, ∼6%, was observed, below which samples behave like pure ice and deform by both grain boundary sliding (GBS) and dislocation creep, and above which GBS creep is impeded. Above this critical fraction, ice grains occur in particle‐free clusters surrounded by bands of particles mixed with fine‐grained ice, resulting in the impedance of GBS in the bands as well as sliding between the ice clusters. Our results imply that South Polar Layered Deposits and midlatitude lobate debris aprons on Mars must contain >94% ice and that the shallow subsurface of Ceres could contain >90% ice. Plain Language Summary: Ice on Mars, Ceres, and icy satellites often contains rock particles. The presence of particles in ice changes its flow behavior and thus is important for understanding the composition and evolution of planetary ice masses. Based on laboratory experiments on samples made of fine‐grained ice and intergranular particles, we determined a critical quantity of particles, about 6% by volume, below which the ice‐particle samples flow like pure ice, and above which, sliding between grains (so‐called grain boundary sliding, or GBS) is impeded. The impedance of GBS by particles has not previously been observed. At planetary conditions, GBS is often the dominant flow mechanism for pure ice. Our result thus imply that the South Polar Layered Deposits and midlatitude lobate debris aprons on Mars must contain >94% ice and that the shallow subsurface of Ceres could contain more than 90% ice. Key Points: Below the critical fraction, ∼6%, particle‐bearing ice behaves like pure ice and deforms by both grain boundary sliding and dislocation creepAbove the critical fraction, ∼6%, GBS creep is impeded in particle‐bearing ice, as bands of particles separate ice clustersIcy masses on Mars, Ceres, and outer planet satellites could contain more ice than previously expected [ABSTRACT FROM AUTHOR]