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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.

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.

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.

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.

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 investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law.

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 lowest latitude sea ice in the world (excluding coastal freezing) is in the southern Sea of Okhotsk (south of 46°N), where it has significant impacts on freshwater input and primary production. This region is subject to climate change, and accordingly the monitoring of sea ice conditions is important. However, the interannual variability of the region's sea ice is poorly understood due to its logistical challenges. Sea ice observations have been conducted in this region every winter for the period 1996–2020. The interannual variability of the ice conditions and the likely factors responsible for it were investigated using visual observations following the international ASPeCt protocol, combined with satellite SSM/I‐SSMIS ice concentration data (1988–2020). AMSR‐derived ice drift data sets and ERA5 meteorological reanalysis data sets were also analyzed to examine the effects of dynamic and thermodynamic processes. Our analysis revealed that (a) sea ice area in this region varies differently from that in the central and northern Sea of Okhotsk, where decreasing trends are reported, (b) sea ice volume has remarkable interannual variation and the peaks appeared much to more affected by dynamically deformed ice than freezing conditions, and (c) prominently deformed ice can be explained by taking shear components into account based on sea ice rheology. These results suggest the importance of including the proper sea ice rheology in numerical sea ice models to reproduce the realistic sea ice volume and deformation processes, for all seasonal ice zones. Plain Language Summary: The southern Sea of Okhotsk (south of 46°N) is the southernmost area of the northern hemisphere, excluding coastal freezing, where there is wintertime sea ice cover. Although this sea ice has significant impacts on the surface heat and freshwater balance and biogeochemical cycles across a wide region, its interannual variability is not well understood yet. Long‐term field observations from the patrol vessel in this region for 1996–2020, in combination with satellite data, reveals that the variability of sea ice area south of 46°N is uncorrelated with that in the northern and central regions, and that the sea ice thickness and volume is mainly controlled by dynamical pile‐up processes, rather than the thermodynamical freezing conditions. Analysis of satellite‐derived ice drift datasets shows that the rheology traditionally used in many sea ice models, in which sea ice behaves like a plastic under the ordinary stress, holds consistently explaining the yearly variations of deformed ice contribution. Considering that sea ice rheology is essential to the dynamical part of sea ice models, our result promotes the possibility of accurately predicting sea ice thickness and volume in the seasonal ice zone. Key Points: The effect of sea ice dynamics on the variation of ice volume across the seasonal ice zone is examined based on field observations and remote sensing dataThe strong regionality of the interannual variability of sea ice area in the Sea of Okhotsk was revealed based on long‐term field observations and satellite dataThe effectiveness of the viscous‐plastic sea ice rheology in reproducing deformation processes were shown from observations and theory [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]

This paper establishes the local-in-time well-posedness of solutions to an approximating system constructed by mildly regularizing the dynamical sea-ice model of W.D. Hibler, Journal of Physical Oceanography, 1979. Our choice of regularization has been carefully designed, prompted by physical considerations, to retain the original coupled hyperbolic-parabolic character of Hibler’s model. Various regularized versions of this model have been used widely for the numerical simulation of the circulation and thickness of the Arctic ice cover. However, due to the singularity in the ice rheology, the notion of solutions to the original model is unclear. Instead, an approximating system, which captures current numerical study, is proposed. The well-posedness theory of such a system provides a first-step groundwork in both numerical study and future analytical study. [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.

Drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers. Simultaneously inferring these parameters is challenging since basal drag and ice viscosity are coupled in the momentum balance, which governs ice flow. We test the ability of adjoint-based inverse methods to infer the slipperiness coefficient in a power-law sliding law and the flow-rate parameter in the constitutive relation for ice using a regularization scheme that includes coefficients weighted by surface strain rates. Using synthetic data with spatial variations in basal drag and ice rheology comparable to those in West Antarctic Ice Streams, we show that this approach allows for more accurate inferences. We apply this method to Bindschadler and MacAyeal Ice Streams in West Antarctica. Our results show relatively soft ice in the shear margins and spatially varying basal drag, with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag. We interpret soft ice to reflect a combination of heating through viscous dissipation and changes in the crystalline structure. These results suggest that adjoint-based inverse methods can provide inferences of basal drag and ice rheology when regularization is informed by strain rates.

We investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law. [ABSTRACT FROM AUTHOR]

Further to systematic experiments on the flexural strength of laboratory-grown, fresh water ice loaded cyclically, this paper describes results from new experiments of the same kind on lake ice harvested in Svalbard. The experiments were conducted at −12 °C, 0.1 Hz frequency and outer-fiber stress in the range from ~ 0.1 to ~ 0.7 MPa. The results suggest that the flexural strength increases linearly with stress amplitude, similar to the behavior of laboratory-grown ice.

Streaming ice accounts for a major fraction of global ice flux, yet we cannot yet fully explain the dominant controls on its kinematics. In this contribution, we use an anisotropic full-Stokes thermomechanical flow solver to characterize how mechanical anisotropy and temperature distribution affect ice flux. For the ice stream and glacier geometries we explored, we found that the ice flux increases 1–3% per °C temperature increase in the margin. Glaciers and ice streams with crystallographic fabric oriented approximately normal to the shear plane increase by comparable amounts: an otherwise isotropic ice stream containing a concentrated transverse single maximum fabric in the margin flows 15% faster than the reference case. Fabric and temperature variations independently impact ice flux, with slightly nonlinear interactions. We find that realistic variations in temperature and crystallographic fabric both affect ice flux to similar degrees, with the exact effect a function of the local fabric and temperature distributions. Given this sensitivity, direct field-based measurements and models incorporating additional factors, such as water content and temporal evolution, are essential for explaining and predicting streaming ice dynamics.

Systematic experiments reveal that the flexural strength of freshwater S2 columnar-grained ice loaded normal to the columns increases upon cyclic loading. Specifically, over the range of stress amplitudes 0.1–2.6 MPa the flexural strength increases linearly with increasing stress amplitude. The experiments were conducted upon both reversed and non-reversed cyclic loading over ranges of frequencies from 0.03 to 2 Hz and temperatures from −25 to −3°C. Strengthening can also be imparted through bending-induced creep. The fundamental requirement for strengthening is that the surface that undergoes maximum tensile stress during failure must have been pre-stressed in tension. Flexural strength is governed by crack nucleation. We suggest that the process is resisted by an internal back-stress that opposes the applied stress and builds up through either crystal dislocations piling up or grain boundaries sliding.

Hydrofracturing can enhance the depth to which crevasses propagate and, in some cases, allow full depth crevasse penetration and iceberg detachment. However, many existing crevasse models either do not fully account for the stress field driving the hydrofracture process and/or treat glacier ice as elastic, neglecting the non-linear viscous rheology. Here, we present a non-local continuum poro-damage mechanics (CPDM) model for hydrofracturing and implement it within a full Stokes finite element formulation. We use the CPDM model to simulate the propagation of water-filled crevasses in idealized grounded glaciers, and compare crevasse depths predicted by this model with those from linear elastic fracture mechanics (LEFM) and zero stress models. We find that the CPDM model is in good agreement with the LEFM model for isolated crevasses and with the zero stress model for closely-spaced crevasses, until the glacier approaches buoyancy. When the glacier approaches buoyancy, we find that the CPDM model does not allow the propagation of water-filled crevasses due to the much smaller size of the tensile stress region concentrated near the crevasse tip. Our study suggests that the combination of non-linear viscous and damage processes in ice near the tip of a water-filled crevasse can alter calving outcomes.

This work quantifies the increased temperature sensitivity of the constitutive behavior of ice with proximity to the melting point in terms of dislocation mechanics. An analysis of quasistatic and dynamic cyclic loading data for several ice types leads to the conclusion that high temperature (e.g. T ≥ −8°C) behavior is the result of a thermally induced increase in the number of mobile dislocations rather than an increase in the activation energy of dislocation glide or the introduction of a new deformation mechanism. The relationship between dislocation density and temperature is quantified and the model is shown to adequately represent the published minimum creep rate vs stress data for isotropic granular freshwater ice for −48 ≤ T ≤ −0.01°C.

Basal ice of glaciers and ice sheets frequently contains a well-developed stratification of distinct, semi-continuous, alternating layers of debris-poor and debris-rich ice. Here, the nature and distribution of shear within stratified basal ice are assessed through the anisotropy of magnetic susceptibility (AMS) of samples collected from Matanuska Glacier, Alaska. Generally, the AMS reveals consistent moderate-to-strong fabrics reflecting simple shear in the direction of ice flow; however, AMS is also dependent upon debris content and morphology. While sample anisotropy is statistically similar throughout the sampled section, debris-rich basal ice composed of semi-continuous mm-scale layers (the stratified facies) possesses well-defined triaxial to oblate fabrics reflecting shear in the direction of ice flow, whereas debris-poor ice containing mm-scale star-shaped silt aggregates (the suspended facies) possesses nearly isotropic fabrics. Thus, deformation within the stratified basal ice appears concentrated in debris-rich layers, likely the result of decreased crystal size and greater availability of unfrozen water associated with high debris content. These results suggest that variations in debris-content over small spatial scales influence ice rheology and deformation in the basal zone.

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.

Experimental data from creep tests on polycrystalline ice samples highlight not only the non-Newtonian behavior of ice but also suggest a critical dependence of the various rheological parameters upon the applied hydrostatic pressure. We propose a new modeling framework, based on implicit theories of continuum mechanics, that generalizes two well-known constitutive models by taking into account the effect of the pressure in the description of ice in creep. To ascertain the validity of the proposed models, we fit the physical parameters with experimental data for the elongational flow of ice samples. The results show good agreement with the experimental creep curves. In particular, the proposed generalized models reproduce the increase of the creep rate due to the presence of hydrostatic pressure.

Abstract Sea ice dynamics determine the drift and deformation of sea ice. Nonlinear physics, usually expressed in a viscous‐plastic rheology, makes the sea ice momentum equations notoriously difficult to solve. At increasing sea ice model resolution the nonlinearities become stronger as linear kinematic features (leads) appear in the solutions. Even the standard elastic‐viscous‐plastic (EVP) solver for sea ice dynamics, which was introduced for computational efficiency, becomes computationally very expensive, when accurate solutions are required, because the numerical stability requires very short, and hence more, subcycling time steps at high resolution. Simple modifications to the EVP solver have been shown to remove the influence of the number of subcycles on the numerical stability. At low resolution appropriate solutions can be obtained with only partial convergence based on a significantly reduced number of subcycles as long as the numerical procedure is kept stable. This previous result is extended to high resolution where linear kinematic features start to appear. The computational cost can be strongly reduced in Arctic Ocean simulations with a grid spacing of 4.5 km by using modified and adaptive EVP versions because fewer subcycles are required to simulate sea ice fields with the same characteristics as with the standard EVP.

This contribution discusses results obtained from 3-D neutron diffraction and 2-D fabric analyser in situ deformation experiments on laboratory-prepared polycrystalline deuterated ice and ice containing a second phase. The two-phase samples used in the experiments are composed of an ice matrix with (1) air bubbles, (2) rigid, rhombohedral-shaped calcite and (3) rheologically soft, platy graphite. Samples were tested at 10°C below the melting point of deuterated ice at ambient pressures, and two strain rates of 1 × 10−5 s−1 (fast) and 2.5 × 10−6 s−1 (medium). Nature and distribution of the second phase controlled the rheological behaviour of the ice by pinning grain boundary migration. Peak stresses increased with the presence of second-phase particles and during fast strain rate cycles. Ice-only samples exhibit well-developed crystallographic preferred orientations (CPOs) and dynamically recrystallized microstructures, typifying deformation via dislocation creep, where the CPO intensity is influenced in part by the strain rate. CPOs are accompanied by a concentration of [c]-axes in cones about the compression axis, coinciding with increasing activity of prismatic- slip activity. Ice with second phases, deformed in a relatively slower strain rate regime, exhibit greater grain boundary migration and stronger CPO intensities than samples deformed at higher strain rates or strain rate cycles.

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]

Drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers. Simultaneously inferring these parameters is challenging since basal drag and ice viscosity are coupled in the momentum balance, which governs ice flow. We test the ability of adjoint-based inverse methods to infer the slipperiness coefficient in a power-law sliding law and the flow-rate parameter in the constitutive relation for ice using a regularization scheme that includes coefficients weighted by surface strain rates. Using synthetic data with spatial variations in basal drag and ice rheology comparable to those in West Antarctic Ice Streams, we show that this approach allows for more accurate inferences. We apply this method to Bindschadler and MacAyeal Ice Streams in West Antarctica. Our results show relatively soft ice in the shear margins and spatially varying basal drag, with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag. We interpret soft ice to reflect a combination of heating through viscous dissipation and changes in the crystalline structure. These results suggest that adjoint-based inverse methods can provide inferences of basal drag and ice rheology when regularization is informed by strain rates. [ABSTRACT FROM AUTHOR]

Further to systematic experiments on the flexural strength of laboratory-grown, fresh water ice loaded cyclically, this paper describes results from new experiments of the same kind on lake ice harvested in Svalbard. The experiments were conducted at −12 °C, 0.1 Hz frequency and outer-fiber stress in the range from ~ 0.1 to ~ 0.7 MPa. The results suggest that the flexural strength increases linearly with stress amplitude, similar to the behavior of laboratory-grown ice. [ABSTRACT FROM AUTHOR]

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics.

Streaming ice accounts for a major fraction of global ice flux, yet we cannot yet fully explain the dominant controls on its kinematics. In this contribution, we use an anisotropic full-Stokes thermomechanical flow solver to characterize how mechanical anisotropy and temperature distribution affect ice flux. For the ice stream and glacier geometries we explored, we found that the ice flux increases 1–3% per °C temperature increase in the margin. Glaciers and ice streams with crystallographic fabric oriented approximately normal to the shear plane increase by comparable amounts: an otherwise isotropic ice stream containing a concentrated transverse single maximum fabric in the margin flows 15% faster than the reference case. Fabric and temperature variations independently impact ice flux, with slightly nonlinear interactions. We find that realistic variations in temperature and crystallographic fabric both affect ice flux to similar degrees, with the exact effect a function of the local fabric and temperature distributions. Given this sensitivity, direct field-based measurements and models incorporating additional factors, such as water content and temporal evolution, are essential for explaining and predicting streaming ice dynamics. [ABSTRACT FROM AUTHOR]

Systematic experiments reveal that the flexural strength of freshwater S2 columnar-grained ice loaded normal to the columns increases upon cyclic loading. Specifically, over the range of stress amplitudes 0.1–2.6 MPa the flexural strength increases linearly with increasing stress amplitude. The experiments were conducted upon both reversed and non-reversed cyclic loading over ranges of frequencies from 0.03 to 2 Hz and temperatures from −25 to −3°C. Strengthening can also be imparted through bending-induced creep. The fundamental requirement for strengthening is that the surface that undergoes maximum tensile stress during failure must have been pre-stressed in tension. Flexural strength is governed by crack nucleation. We suggest that the process is resisted by an internal back-stress that opposes the applied stress and builds up through either crystal dislocations piling up or grain boundaries sliding. [ABSTRACT FROM AUTHOR]

Hydrofracturing can enhance the depth to which crevasses propagate and, in some cases, allow full depth crevasse penetration and iceberg detachment. However, many existing crevasse models either do not fully account for the stress field driving the hydrofracture process and/or treat glacier ice as elastic, neglecting the non-linear viscous rheology. Here, we present a non-local continuum poro-damage mechanics (CPDM) model for hydrofracturing and implement it within a full Stokes finite element formulation. We use the CPDM model to simulate the propagation of water-filled crevasses in idealized grounded glaciers, and compare crevasse depths predicted by this model with those from linear elastic fracture mechanics (LEFM) and zero stress models. We find that the CPDM model is in good agreement with the LEFM model for isolated crevasses and with the zero stress model for closely-spaced crevasses, until the glacier approaches buoyancy. When the glacier approaches buoyancy, we find that the CPDM model does not allow the propagation of water-filled crevasses due to the much smaller size of the tensile stress region concentrated near the crevasse tip. Our study suggests that the combination of non-linear viscous and damage processes in ice near the tip of a water-filled crevasse can alter calving outcomes. [ABSTRACT FROM AUTHOR]

This work quantifies the increased temperature sensitivity of the constitutive behavior of ice with proximity to the melting point in terms of dislocation mechanics. An analysis of quasistatic and dynamic cyclic loading data for several ice types leads to the conclusion that high temperature (e.g. T ≥ −8°C) behavior is the result of a thermally induced increase in the number of mobile dislocations rather than an increase in the activation energy of dislocation glide or the introduction of a new deformation mechanism. The relationship between dislocation density and temperature is quantified and the model is shown to adequately represent the published minimum creep rate vs stress data for isotropic granular freshwater ice for −48 ≤ T ≤ −0.01°C. [ABSTRACT FROM AUTHOR]

Two debris bands associated with an overdeepened basin in the terminus region of the Fláajökull glacier, Iceland, have been sampled for their ice and debris. Here the kinematics of deformation are investigated through anisotropy of magnetic susceptibly (AMS), microstructural analyses, and c-axis preferred orientations. Comparison of the crystallographic orientations of 180 grains and the AMS shape orientations of mineral inclusions in polycrystalline ice reveals a multi-maximum girdle oblique to the planar stratification and a record of near vertical triaxial ellipsoids. These two distinct fabrics can be attributed to both pure and simple shear suggesting a complex deformational history. In addition, AMS from an ice-free sediment ridge on the glacier surface indicates pure shear locally dominated strain. The physical properties of the debris bands, sedimentology and field observations suggest that they were sourced from the glacial bed and emplaced by highly pressurized water into localized fractures. • A composite fabric of debris-rich ice suggests a complex history of both pure and simple shear deformation. • AMS fabrics from a sediment ridge indicate pure shear dominated strain resulting from longitudinal ice flow. • The physical properties of the debris bands suggest that they were sourced from the glacial bed. [ABSTRACT FROM AUTHOR]

Tidal flexure in ice shelf grounding zones has been used extensively in the past to determine grounding line position and ice properties. Although the rheology of ice is viscoelastic at tidal loading frequencies, most modelling studies have assumed some form of linear elastic beam approximation to match observed flexure profiles. Here we use density, radar and DInSAR measurements in combination with full-Stokes viscoelastic modelling to investigate a range of additional controls on the flexure of the Southern McMurdo Ice Shelf. We find that inclusion of observed basal crevasses and density dependent ice stiffness can greatly alter the flexure profile and yet fitting a simple elastic beam model to that profile will still produce an excellent fit. Estimates of the effective Young's modulus derived by fitting flexure profiles are shown to vary by over 200% depending on whether these factors are included, even when the local thickness is well constrained. Conversely, estimates of the grounding line position are relatively insensitive to these considerations for the case of a steep bed slope in our study region. By fitting tidal amplitudes only, and ignoring phase information, elastic beam theory can provide a good fit to observations in a wide variety of situations. This should, however, not be taken as an indication that the underlying rheological assumptions are correct.

Grounding zones are vital to ice-sheet mass balance and its coupling to the global ocean circulation. Processes here determine the mass discharge from the grounded ice sheet, to the floating ice shelves. The response of this transition zone to tidal forcing has been described by both elastic and viscoelastic models. Here we examine the validity of these models for grounding zone flexure over tidal timescales using field data from the Southern McMurdo Ice Shelf (78° 15′S, 167° 7′E). Observations of tidal movement were carried out by simultaneous tiltmeter and GPS measurements along a profile across the grounding zone. Finite-element simulations covering a 64 d period reveal that the viscoelastic model fits best the observations using a Young's modulus of 1.6 GPa and a viscosity of 1013.7 Pa s (≈ 50.1 TPa s). We conclude that the elastic model is only well-constrained for tidal displacements >35% of the spring-tidal amplitude using a Young's modulus of 1.62 ± 0.69 GPa, but that a viscoelastic model is necessary to adequately capture tidal bending at amplitudes below this threshold. In grounding zones where bending stresses are greater than at the Southern McMurdo Ice Shelf or ice viscosity is lower, the threshold would be even higher.

New experiments reveal that the flexural strength of fresh water, columnar-grained ice loaded normal to the columns may be increased by about a factor of two upon reversed cyclic loading at a frequency of ~0.1 Hz at stress amplitudes of 1.3–2.6 MPa. The effect is explained in terms of a reduction in deformation-induced stress concentration through the activation of grain boundary sliding, which is evident through boundary decohesion.

Basal ice of glaciers and ice sheets frequently contains a well-developed stratification of distinct, semi-continuous, alternating layers of debris-poor and debris-rich ice. Here, the nature and distribution of shear within stratified basal ice are assessed through the anisotropy of magnetic susceptibility (AMS) of samples collected from Matanuska Glacier, Alaska. Generally, the AMS reveals consistent moderate-to-strong fabrics reflecting simple shear in the direction of ice flow; however, AMS is also dependent upon debris content and morphology. While sample anisotropy is statistically similar throughout the sampled section, debris-rich basal ice composed of semi-continuous mm-scale layers (the stratified facies) possesses well-defined triaxial to oblate fabrics reflecting shear in the direction of ice flow, whereas debris-poor ice containing mm-scale star-shaped silt aggregates (the suspended facies) possesses nearly isotropic fabrics. Thus, deformation within the stratified basal ice appears concentrated in debris-rich layers, likely the result of decreased crystal size and greater availability of unfrozen water associated with high debris content. These results suggest that variations in debris-content over small spatial scales influence ice rheology and deformation in the basal zone. [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]

Experimental data from creep tests on polycrystalline ice samples highlight not only the non-Newtonian behavior of ice but also suggest a critical dependence of the various rheological parameters upon the applied hydrostatic pressure. We propose a new modeling framework, based on implicit theories of continuum mechanics, that generalizes two well-known constitutive models by taking into account the effect of the pressure in the description of ice in creep. To ascertain the validity of the proposed models, we fit the physical parameters with experimental data for the elongational flow of ice samples. The results show good agreement with the experimental creep curves. In particular, the proposed generalized models reproduce the increase of the creep rate due to the presence of hydrostatic pressure. [ABSTRACT FROM AUTHOR]

This contribution discusses results obtained from 3-D neutron diffraction and 2-D fabric analyser in situ deformation experiments on laboratory-prepared polycrystalline deuterated ice and ice containing a second phase. The two-phase samples used in the experiments are composed of an ice matrix with (1) air bubbles, (2) rigid, rhombohedral-shaped calcite and (3) rheologically soft, platy graphite. Samples were tested at 10°C below the melting point of deuterated ice at ambient pressures, and two strain rates of 1 × 10−5 s−1 (fast) and 2.5 × 10−6 s−1 (medium). Nature and distribution of the second phase controlled the rheological behaviour of the ice by pinning grain boundary migration. Peak stresses increased with the presence of second-phase particles and during fast strain rate cycles. Ice-only samples exhibit well-developed crystallographic preferred orientations (CPOs) and dynamically recrystallized microstructures, typifying deformation via dislocation creep, where the CPO intensity is influenced in part by the strain rate. CPOs are accompanied by a concentration of [ c ]-axes in cones about the compression axis, coinciding with increasing activity of prismatic- slip activity. Ice with second phases, deformed in a relatively slower strain rate regime, exhibit greater grain boundary migration and stronger CPO intensities than samples deformed at higher strain rates or strain rate cycles. [ABSTRACT FROM AUTHOR]

Solid-state convection has been proposed to occur within Europa's ice shell based both on the interpretation of observed geological activity during Galileo spacecraft exploration and theoretical investigations. Laboratory experiments have investigated the effect of grain size insensitive creep and grain size sensitive creep on the ductile behaviour of polycrystalline ice. The ice grain size and the ice impurities content and, consequently, the viscosity of the ice within Europa's ice shell are poorly constrained, limiting the possibility to understand if solid-state convection can occur under Europa's ice shell conditions. To investigate how diurnal tidal flexing and the internal dynamics of Europa's ice shell influence the ice grain crystals' evolution, we adopted a thermal-mechanical numerical model that uses finite differences and marker-in-cell techniques, implementing the dynamic recrystallization of the ice and the ice grain evolution in a self-consistent way with the numerical model. We found that solid-state convection within Europa's ice shell can occur if it is diurnally tidally deformed, as the tidal stresses within the ice shell operate to reduce the ice grain sizes and the ice viscosity. We discuss future radio science experiments, in combination with radar sounder investigations, that will be capable of characterizing the possible presence of solid-state convection within Europa's ice shell. • Numerical solid-state convection model of self-consistent ice grain size evolution in Europa's ice shell • The diurnal tidal flexing of the ice shell influences the ice crystals evolution and, consequently, the onset of convection, and its stability. • The tidal stresses within the ice shell reduce the ice grain size, allowing the onset of solid- state convection within Europa's ice shell [ABSTRACT FROM AUTHOR]

Recent studies have suggested a physical link between Ca++ ions and an increase in the ductility or ‘softening’ of polycrystalline ice. In order to investigate the potential effects of Ca++ on deformation, we created sets of both undoped and CaSO4-doped specimens of polycrystalline ice for testing in uniaxial tension or compression. Deformation tests in tension were carried out under a constant load at an initial stress of 0.75 MPa and a temperature of −6°C. Compression tests were carried out at −10 and −20°C at constant strain rates of 1×10−4 s−1, 1 × 10−5 s−1 and 1 × 10−6 s−1 and taken to 5% strain. Our results show that CaSO4 increases the strength of polycrystalline ice at higher strain rates and lower temperatures, an effect that decreases with decreasing strain rate and higher temperatures. A microstructural analysis of the post-test compression specimens reveals mean grain diameters much larger in the CaSO4-doped specimens tested at the lowest applied strain rate of 1 × 10−6 s−1. Precipitates were found to have formed along grain boundaries in some doped specimens and evidence of intergranular fracture was observed in all specimens tested at 1 × 10−4 and 1 × 10−5 s−1. In tension-tested specimens, there was no difference in the mean grain diameter between doped and undoped specimens at 25% strain.

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics. [ABSTRACT FROM AUTHOR]

Abstract: In times of warming in polar regions, the prediction of ice sheet discharge is of utmost importance to society, because of its impact on sea level rise. In simulations the flow rate of ice is usually implemented as proportional to the differential stress to the power of the exponent n = 3. This exponent influences the softness of the modeled ice, as higher values would produce faster flow under equal stress. We show that the stress exponent, which best fits the observed state of the Greenland Ice Sheet, equals n = 4. Our results, which are not dependent on a possible basal sliding component of flow, indicate that most of the interior northern ice sheet is currently frozen to bedrock, except for the large ice streams and marginal ice. [ABSTRACT FROM AUTHOR]

Abstract: The validity of the sea ice rheological model formulated by Hibler (1979), which is widely used in present numerical sea ice models, is examined for the Sea of Okhotsk as an example of the seasonal ice zone (SIZ), based on satellite‐derived sea ice velocity, concentration and thickness. Our focus was the formulation of the yield curve, the shape of which can be estimated from ice drift pattern based on the energy equation of deformation, while the strength of the ice cover that determines its magnitude was evaluated using ice concentration and thickness data. Ice drift was obtained with a grid spacing of 37.5 km from the AMSR‐E 89 GHz brightness temperature using a maximum cross‐correlation method. The ice thickness was obtained with a spatial resolution of 100 m from a regression of the PALSAR backscatter coefficients with ice thickness. To assess scale dependence, the ice drift data derived from a coastal radar covering a 70 km range in the southernmost Sea of Okhotsk were similarly analyzed. The results obtained were mostly consistent with Hibler's formulation that was based on the Arctic Ocean on both scales with no dependence on a time scale, and justify the treatment of sea ice as a plastic material, with an elliptical shaped yield curve to some extent. However, it also highlights the difficulty in parameterizing sub‐grid scale ridging in the model because grid scale ice velocities reduce the deformation magnitude by half due to the large variation of the deformation field in the SIZ. [ABSTRACT FROM AUTHOR]