Ice fabrics in natural flows: beyond pure and simple shear

Ice fabrics are key for understanding and predicting ice flow dynamics. Despite its importance, the characteristics and evolution of ice fabrics beyond pure and simple shear flow has largely been neglected. However, 80 % of the flow of ice in Antarctica is outside the regimes of pure and simple shear. We use a new validated numerical model (SpecCAF), which has been shown to accurately reproduce experimentally observed fabrics in both compression and simple shear, to explore the fabrics produced between pure and simple shear, as well as those that are highly rotational. We present a definitive classification of all fabric patterns. We find that intermediate deformations between pure and simple shear result in a smooth transition between a fabric characterised by a cone-shape and a secondary cluster pattern. Highly-rotational fabrics are found to produce a weak girdle fabric. In addition we obtain complete predictions for the strain required for any fabric under a 2D deformation to reach steady state at any given temperature. Use of our data in current ice flow models as well as for ice core fabric and seismic anisotropy interpretation will enhance the communities' ability to predict future ice flow in a changing climate.

Ice fabrics in natural flows: moving away from pure and simple shear

<div>Antarctic ice flow shows deviation from the deformation regimes of pure and simple shear. By analysing the vorticity number from surface velocity data it is found that approximately 80% of the flow is outside these regimes. These deformations are both between pure and simple shear, as well as highly rotational, highlighting the need for fabric predictions away from the commonly studied regimes of pure and simple shear. </div><div>We use the numerical scheme SpecCAF, which has been shown to accurately reproduce experimentally observed fabrics with no free parameters, to study ice fabrics in such general deformations. By exploring the parameter space of temperature and vorticity number, we present a definitive classification of fabrics patterns which arise, and construct a universal regime diagram for ice fabrics under general two-dimensional deformation. We find that intermediate deformations see a smooth transition between a cone-shape fabric and a secondary cluster. We present the first investigation of the fabrics produced in highly rotational deformations, which produce a weak girdle fabric with the axis aligned to the vorticity axis. We also show that across deformation and temperature space fabrics only reach a true steady-state above strains of 200%, and there is significant variation in this across the parameter space.  </div>

Brief communication: Sampling c-axes distributions from the eigenvalues of ice fabric orientation tensors

For simulation purposes involving different realizations of ice fabrics, it can be necessary to generate arbitrarily large samples of c-axes based on the second-order orientation tensor, a commonly used descriptive statistics provided in publications of ice core measurements. This paper describes a sampling technique based on the combination of a vertical girdle and a single maximum Watson distributions.

Where is the 1-million-year-old ice at Dome A?

Ice fabric influences the rheology of ice, and hence the age–depth profile at ice core drilling sites. To investigate the age–depth profile to be expected of the ongoing deep ice coring at Kunlun station, Dome A, we use the depth-varying anisotropic fabric suggested by the recent polarimetric measurements around Dome A along with prescribed fabrics ranging from isotropic through girdle to single maximum in a three-dimensional, thermo-mechanically coupled full-Stokes model of a 70 × 70 km2 domain around Kunlun station. This model allows for the simulation of the near basal ice temperature and age, and ice flow around the location of the Chinese deep ice coring site. Ice fabrics and geothermal heat flux strongly affect the vertical advection and basal temperature which consequently control the age profile. Constraining modeled age–depth profiles with dated radar isochrones to 2∕3 ice depth, the surface vertical velocity, and also the spatial variability of a radar isochrones dated to 153.3 ka BP, limits the age of the deep ice at Kunlun to between 649 and 831 ka, a much smaller range than previously inferred. The simple interpretation of the polarimetric radar fabric data that we use produces best fits with a geothermal heat flux of 55 mW m−2. A heat flux of 50 mW m−2 is too low to fit the deeper radar layers, and 60 mW m−2 leads to unrealistic surface velocities. The modeled basal temperature at Kunlun reaches the pressure melting point with a basal melting rate of 2.2–2.7 mm a−1. Using the spatial distribution of basal temperatures and the best fit fabric suggests that within 400 m of Kunlun station, 1-million-year-old ice may be found 200 m above the bed, and that there are large regions where even older ice is well above the bedrock within 5–6 km of the Kunlun station.

Where is the 1-million-year-old ice at Dome A?

Ice fabric influences the rheology of ice, and hence the age/depth profile at ice core drilling sites. We use the depth varying anisotropic fabric suggested by the recent polarimetric measurements around Dome A along with prescribed fabrics ranging from isotropic through girdle to single maximum in a three-dimensional, thermo-mechanically coupled full-Stokes model of a 70 × 70 km2 domain around Kunlun station. This model allows to simulate the near basal ice temperature and age, and ice flow around the location of the Chinese deep ice coring site. Ice fabrics and geothermal heat flux strongly affect the vertical advection and basal temperature which in consequence controls the age profile. Constraining modeled age-depth profiles with dated radar isochrones to 2/3 ice depth, the surface vertical velocity, and also the spatial variability of a radar isochrones dated to 153.3 kyr BP, limits the age of the deep ice at Kunlun to 649–831 kyr, a much smaller range than inferred previously. The simple interpretation of the polarmetric radar fabric data that we use produces best fits with a geothermal heat flux of 55 mWm−2. A heat flux of 50 mWm−2 is too low to fit the deeper radar layers, and a heat flux of 60 mWm−2 leads to unrealistic surface velocities. The modeled basal temperature at Kunlun reaches the pressure melting point with a basal melting rate of 2.2–2.7 mm yr−1. Using the spatial distribution of basal temperatures and the best fit fabric suggests that within 400 m of Kunlun station, 1 million-year old ice may be found 200 m above the bed, and there are large regions where even older ice is well above the bedrock within 1–2 km of the Kunlun station.

Optical properties of sea ice doped with black carbon – an experimental and radiative-transfer modelling comparison

Radiative-transfer calculations of the light reflectivity and extinction coefficient in laboratory-generated sea ice doped with and without black carbon demonstrate that the radiative-transfer model TUV-snow can be used to predict the light reflectance and extinction coefficient as a function of wavelength. The sea ice is representative of first-year sea ice containing typical amounts of black carbon and other light-absorbing impurities. The experiments give confidence in the application of the model to predict albedo of other sea ice fabrics. Sea ices, ∼ 30 cm thick, were generated in the Royal Holloway Sea Ice Simulator ( ∼ 2000 L tanks) with scattering cross sections measured between 0.012 and 0.032 m2 kg−1 for four ices. Sea ices were generated with and without ∼ 5 cm upper layers containing particulate black carbon. Nadir reflectances between 0.60 and 0.78 were measured along with extinction coefficients of 0.1 to 0.03 cm−1 (e-folding depths of 10–30 cm) at a wavelength of 500 nm. Values were measured between light wavelengths of 350 and 650 nm. The sea ices generated in the Royal Holloway Sea Ice Simulator were found to be representative of natural sea ices. Particulate black carbon at mass ratios of ∼ 75, ∼ 150 and ∼ 300 ng g−1 in a 5 cm ice layer lowers the albedo to 97, 90 and 79 % of the reflectivity of an undoped clean sea ice (at a wavelength of 500 nm).

A comprehensive interpretation of the NEEM basal ice build-up using a multi-parametric approach

Basal ice is a common expression to describe bottom ice layers of glaciers, ice caps and ice sheets in which the ice is primarily conditioned by processes operating at the bed. It is chemically and/or physically distinct from the ice above and can be characterized by a component of basally derived sediments. The study of basal ice properties provides a rare opportunity to improve our understanding of subglacial environments and processes and to refine ice sheet behaviour modelling. Here, we present and discuss the results of water stable isotopes (δ18O and δD), ice fabrics, debris weight/size distribution and gas content of the basal part of the NEEM (North Greenland Eemian Ice Drilling Project) ice core. Below a depth of 2533.85 m, almost 10 m of basal debris-rich material was retrieved from the borehole, and regular occurrence of frozen sediments with only interstitial ice lenses in the bottom 5 m suggest that the ice–bedrock interface was reached. The sequence is composed of an alternation of three visually contrasting types of ice: clear ice with specks (very small amounts) of particulate inclusions, stratified debris-rich layers and ice containing dispersed debris. The use of water stable isotope signatures (δ18O and δD), together with other parameters, allows discrimination between the different types of ice and to unravel the processes involved in their formation and transformation. The basal debris-rich material presents δ18O values [−39.9 ‰; −34.4 ‰] within the range of the above last 300 m of unaltered meteoric ice [−44.9 ‰; −30.6 ‰] spanning a glacial-interglacial range of values. This rules out the hypothesis of a basal ice layer originating from pre-ice sheet ice overridden by the growing ice sheet, as previously suggested e.g. in the case of GRIP (Greenland Ice Core Project). We show that clear basal ice with specks corresponds to altered meteoric glacial ice where some of the climatic signal could have been preserved. However, the stratified debris-rich layers and the ice containing dispersed debris layers respectively express an “open” or “closed” system melting/refreezing signature, somewhat blurred by mixing processes in the upper part of the sequence. Climatic reconstruction is therefore prohibited from these ice types. We propose a first interpretative framework for the build-up of the NEEM basal ice sequence, based on the origin of the various ice types.

A comprehensive interpretation of the NEEM basal ice build-up using a multi parametric approach

Basal ice is a common expression to describe debris-laden ice layers found close to the ice–bedrock interface under glaciers and ice sheets. The study of basal ice properties provides a unique opportunity to improve our understanding of subglacial environments and processes and to refine ice sheet behaviour modelling. Here, we present and discuss the results of water stable isotopes (δ18O and δD), ice fabrics, debris weight and gas content of the basal part of the NEEM (North Greenland Eemian Ice Drilling Project) ice core. Below a depth of 2533.85 m, almost 10 m of basal debris-rich material were retrieved from the borehole. The sequence is composed of an alternation of three visually contrasting types of ice: clear ice with specks of particulate inclusions, stratified debris-rich layers, and ice containing dispersed debris. The use of water stable isotope signatures (δ18O and δD) together with other parameters, allows to discriminate between the different types of ice and to unravel the processes involved in their formation and transformation. The basal debris-rich material presents δ18O values [−39.9 ‰; −34.4 ‰] within the range of the above last 300 m of unaltered meteoric ice [−44.9 ‰; −30.6 ‰] spanning a glacial–interglacial range of values. This rules out the hypothesis of a basal ice layer originating from pre-ice sheet ice overridden by the growing ice sheet (as previously suggested e.g. in the case of the GRIP ice core), since the latter would result in an heavier isotopic signature for ice formed at a much lower altitude. We show that clear basal ice with specks corresponds to altered meteoric glacial ice where a climatic signal is preserved. On the other hand, both stratified debris-rich layers and ice containing dispersed debris layers express an "open" or "closed" system melting/refreezing signature, somewhat blurred by mixing processes. Climatic reconstruction is therefore prohibited from these ice types. We propose a first interpretative framework for the build-up of the NEEM basal ice sequence, based on the origin of the various ice types.

Propagation of elastic waves through textured polycrystals: application to ice

The propagation of elastic waves in polycrystals is revisited, with an emphasis on configurations relevant to the study of ice. Randomly oriented hexagonal single crystals are considered with specific, non-uniform, probability distributions for their major axis. Three typical textures or fabrics (i.e. preferred grain orientations) are studied in detail: one cluster fabric and two girdle fabrics, as found in ice recovered from deep ice cores. After computing the averaged elasticity tensor for the considered textures, wave propagation is studied using a wave equation with elastic constants c =〈 c 〉+ δc that are equal to an average plus deviations, presumed small, from that average. This allows for the use of the Voigt average in the wave equation, and velocities are obtained solving the appropriate Christoffel equation. The velocity for vertical propagation, as appropriate to interpret sonic logging measurements, is analysed in more details. Our formulae are shown to be accurate at the 0.5% level and they provide a rationale for previous empirical fits to wave propagation velocities with a quantitative agreement at the 0.07–0.7% level. We conclude that, within the formalism presented here, it is appropriate to use, with confidence, velocity measurements to characterize ice fabrics.