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Only a few localised ice streams drain most of the ice from the Greenland Ice Sheet. Thus, understanding ice stream behaviour and its temporal variability is crucially important to predict future sea-level change. The interior trunk of the 700 km-long North-East Greenland Ice Stream (NEGIS) is remarkable due to the lack of any clear bedrock channel to explain its presence. Here, we present a 3-dimensional analysis of the folding and advection of its stratigraphic horizons, which shows that the localised flow and shear margins in the upper NEGIS were fully developed only ca 2000 years ago. Our results contradict the assumption that the ice stream has been stable throughout the Holocene in its current form and show that upper NEGIS-type development of ice streaming, with distinct shear margins and no bed topography relationship, can be established on time scales of hundreds of years, which is a major challenge for realistic mass-balance and sea-level rise projections.

Creep due to ice flow is generally thought to be the main cause for the formation of crystallographic preferred orientations (CPOs) in polycrystalline anisotropic ice. However, linking the development of CPOs to the ice flow history requires a proper understanding of the ice aggregate's microstructural response to flow transitions. In this contribution the influence of ice deformation history on the CPO development is investigated by means of full-field numerical simulations at the microscale. We simulate the CPO evolution of polycrystalline ice under combinations of two consecutive deformation events up to high strain, using the code VPFFT (visco-plastic fast Fourier transform algorithm) within ELLE. A volume of ice is first deformed under coaxial boundary conditions, which results in a CPO. The sample is then subjected to different boundary conditions (coaxial or non-coaxial) in order to observe how the deformation regime switch impacts the CPO. The model results indicate that the second flow event tends to destroy the first, inherited fabric with a range of transitional fabrics. However, the transition is slow when crystallographic axes are critically oriented with respect to the second imposed regime. Therefore, interpretations of past deformation events from observed CPOs must be carried out with caution, particularly in areas with complex deformation histories.

Creep due to ice flow is generally thought to be the main cause for the formation of crystallographic preferred orientations (CPOs) in polycrystalline anisotropic ice. However, linking the development of CPOs to the ice flow history requires a proper understanding of the ice aggregate's microstructural response to flow transitions. In this contribution the influence of ice deformation history on the CPO development is investigated by means of full-field numerical simulations at the microscale. We simulate the CPO evolution of polycrystalline ice under combinations of two consecutive deformation events up to high strain, using the code VPFFT (visco-plastic fast Fourier transform algorithm) within ELLE. A volume of ice is first deformed under coaxial boundary conditions, which results in a CPO. The sample is then subjected to different boundary conditions (coaxial or non-coaxial) in order to observe how the deformation regime switch impacts the CPO. The model results indicate that the second flow event tends to destroy the first, inherited fabric with a range of transitional fabrics. However, the transition is slow when crystallographic axes are critically oriented with respect to the second imposed regime. Therefore, interpretations of past deformation events from observed CPOs must be carried out with caution, particularly in areas with complex deformation histories.

This data set contains the output files with the crystal orientation of each simulation presented in the article Can changes in deformation regimes be inferred from crystallographic preferred orientations in polar ice? https://doi.org/10.5194/tc-16-2009-2022 in this repository http://hdl.handle.net/10261/270644 (run using the open-source software platform ELLE; Bons et al., 2008). For the visualization of the crystallographic preferred orientation the information contained in these output files can be loaded to the software toolbox MTEX (Bachmann, F., Hielscher, R. and Schaeben, H. Grain detection from 2d and 3d EBSD data—Specification of the MTEX algorithm. Ultramicroscopy, 111(12), pp.1720-1733. 2011).

The prominent North East Greenland Ice Stream (NEGIS) is an exceptionally large ice stream in the Greenland Ice sheet. It is over 500 km long, originates almost at the central ice divide, and contributes significantly to overall ice drainage from the Greenland Ice sheet. Surface velocities in the inland part of the ice stream are several times higher inside NEGIS than in the adjacent ice sheet. Modelling NEGIS is still a challenge as it remains unclear what actually causes and controls the ice stream. An elevated geothermal heat flux is one of the factors that are being considered to trigger or drive the fast flow inside NEGIS. Unfortunately, the geothermal heat flux below NEGIS and its upstream area is poorly constrained and estimates vary from close to the global average for continental crust (ca. 60 mW/m2) to values as high as almost 1000 mW/m2. The latter would cause about 10 cm/yr of melting at the base of the ice sheet. We present a brief survey of global geothermal heat flux data, especially from known hotspots, such as Iceland and Yellowstone. Heat fluxes in these areas that are known to be among the hottest on Earth rarely, if ever, exceed 300 mW/m2. A plume hotspot or its trail can therefore not cause heat fluxes at the high end of the suggested range. Other potential factors, such as hydrothermal fluid flow and radiogenic heat, also cannot raise the heat flux significantly. We conclude that the heat flux at NEGIS is very unlikely to exceed 100-150 mW/m2, and future modelling studies on NEGIS should thus be mindful of implementing realistic geothermal heat flux values. If NEGIS is not the result of an exceptionally high heat flux, we are left with the exciting challenge to find the true trigger of this fascinating structure.

Smith-Johnsen et al. (The Cryosphere, 14, 841–854, https://doi.org/10.5194/tc-14-841-2020, 2020) model the effect of a potential hotspot on the Northeast Greenland Ice Stream (NEGIS). They argue that a heat flux of at least 970 mW m−2 is required to have initiated or to control NEGIS. Such an exceptionally high heat flux would be unique in the world and is incompatible with known geological processes that can raise the heat flux. Fast flow at NEGIS must thus be possible without the extraordinary melt rates invoked in Smith-Johnsen et al. (2020).

Ice 1h shows a strong viscoplastic anisotropy, as the resistance to activate dislocation glide on basal planes is at least one order of magnitude smaller than on the other slip planes. During flow the viscoplastic anisotropy leads to the development of a crystallographic preferred orientation (CPO). The anisotropic behaviour of flowing ice can lead to strain localisation. Only when the ice is layered (e.g. due to cloudy bands) it may be possible to identify localisation structures, as ice otherwise has no readily recognisable strain markers. We use the Viscoplastic Full-Field Transform (VPFFT; Lebensohn and Rollett, 2020) crystal plasticity code coupled with the modelling platform ELLE (http://www.elle.ws; Piazolo et al., 2019) to simulate the deformation of intrinsically anisotropic ice 1h with an initial single maximum CPO in dextral simple shear up to very high strains. The VPFFT-approach simulates deformation by dislocation glide, taking into account the different available slip systems and their critical resolved shear stresses. We use an anisotropy similar to that of ice 1h, systematically vary the orientation of the initial CPO, and use passive markers/layers to visualise deformation structures. The localisation behaviour strongly depends on the initial CPO, but reaches a consistent steady state after very high shear strains of about 30. The fabric and stress evolution reach a steady-state situation as well. The orientation of the CPO controls the style of deformation, which varies from (1) synthetic shear zones with a stable shear-direction parallel orientation and that widen with ongoing strain to unstable, (2) rotating antithetic shear bands, (3) initial formation of antithetic shear bands and subsequent development of synthetic shear bands and (4) distributed localisation. Furthermore, evolving visual structures depend on the presence and orientation of a visual layering in the material. However, at very high strains, the material is almost always strongl

Deformation of foliated rocks commonly leads to crenulation or micro-folding, with the development of cleavage domains and microlithons. We here consider the effect of mechanical anisotropy due to a crystallographic preferred orientation (CPO) that defines the foliation, for example by of alignment of micas. Mechanical anisotropy enhances shear localisation (Ran, et al., 2018; de Riese et al., 2019), resulting in low-strain domains (microlithons) and high-strain shear bands or cleavage domains. We investigate the crenulation patterns that result from moderate strain simple shear deformation, varying the initial orientation of the mechanical anisotropy relative to the shear plane. We use the Viscoplastic Full-Field Transform (VPFFT) crystal plasticity code coupled with the modelling platform ELLE (http://www.elle.ws; Llorens et al., 2017) to simulate the deformation of anisotropic single-phase material with an initial given CPO in dextral simple shear in low to medium strain. Deformation is assumed to be accommodated by glide along the basal, prismatic and pyramidal slip systems of a hexagonal model mineral. An approximately transverse anisotropy is achieved by assigning a small critical resolved shear stress to the basal plane. An initially point-maximum CPO at variable angles to the shear plane defines the initial straight foliation at different angles to the shear plane, limiting ourselves to orientations in which the foliation is in the stretching field. The resulting crenulation geometries strongly depend on the orientation of the foliation and we observe four types of localisation behaviour: (1) synthetic shear bands, (2) antithetic shear bands, (3) initial formation of antithetic shear bands and subsequent development of synthetic shear bands, and (4) distributed, approximately shear-margin parallel strain localisation, but no distinct shear bands. The numerical simulations not only show the evolving strain-rate field, but also the predicted finite strain patt

The prominent North East Greenland Ice Stream (NEGIS) is an exceptionally large ice stream in the Greenland Ice sheet. It is over 500 km long, originates almost at the central ice divide, and contributes significantly to overall ice drainage from the Greenland Ice sheet. Surface velocities in the inland part of the ice stream are several times higher inside NEGIS than in the adjacent ice sheet. Modelling NEGIS is still a challenge as it remains unclear what actually causes and controls the ice stream. An elevated geothermal heat flux is one of the factors that are being considered to trigger or drive the fast flow inside NEGIS. Unfortunately, the geothermal heat flux below NEGIS and its upstream area is poorly constrained and estimates vary from close to the global average for continental crust (ca. 60 mW/m2) to values as high as almost 1000 mW/m2. The latter would cause about 10 cm/yr of melting at the base of the ice sheet. We present a brief survey of global geothermal heat flux data, especially from known hotspots, such as Iceland and Yellowstone. Heat fluxes in these areas that are known to be among the hottest on Earth rarely, if ever, exceed 300 mW/m2. A plume hotspot or its trail can therefore not cause heat fluxes at the high end of the suggested range. Other potential factors, such as hydrothermal fluid flow and radiogenic heat, also cannot raise the heat flux significantly. We conclude that the heat flux at NEGIS is very unlikely to exceed 100-150 mW/m2, and future modelling studies on NEGIS should thus be mindful of implementing realistic geothermal heat flux values. If NEGIS is not the result of an exceptionally high heat flux, we are left with the exciting challenge to find the true trigger of this fascinating structure.

C' shear bands are common structures in ductile shear zones but their development is poorly understood. They occur in rocks with a high mechanical strength contrast so we used numerical models of viscoplastic deformation to study the effect of the proportion of weak phase and the phase strength contrast on C' shear band development. We employed simple shear to a finite strain of 18 in 900 steps and recorded the microstructure, stress and strain distribution at each step. We found that C' shear bands form in models with ¿5% weak phase when there is a moderate or high phase strength contrast, and they occur in all models with weak phase proportions ¿15%. Contrary to previous research, we find that C' shear bands form when layers of weak phase parallel to the shear zone boundary rotate forwards. This occurs due to mechanical instabilities that are a result of heterogeneous distributions of stress and strain rate. C' shear bands form on planes of low strain rate and stress, not in sites of maximum strain rate as has previously been suggested. C' shear bands are ephemeral and they either rotate backwards to the C plane once they are inactive or rotate into the field of shortening and thicken to form X- and triangle- shaped structures.

Deformation localisation can lead to a variety of structures, such as shear zones and bands that range from grain to crustal scale, from discrete zones to anastomosing networks, and shear zone related folds. We present numerical simulations of the deformation of an intrinsically anisotropic material with a single maximum crystal preferred orientation (CPO) in simple shear. We use the Viscoplastic Full-Field Transform (VPFFT) crystal plasticity code coupled with the modelling platform ELLE to achieve very high strains. The VPFFT-approach simulates deformation by dislocation glide, taking into account the different available slip systems and their critical resolved shear stresses. We vary the anisotropy of the material from isotropic to highly anisotropic, as well as the orientation of the initial CPO. To visualize deformation structures, we use passive markers, for which we also systematically vary the initial orientation. At low strains the amount of strain rate localisation and resulting deformation structures depend on the initial CPO in all anisotropic models. Three regimes can be recognised: distributed shear localisation, synthetic shear bands and antithetic shear bands. However, at very high strains localisation behaviour always tends to converge to a similar state, independent of the initial CPO. Shear localisation is often detected by folded layers, which may be parallel to the anisotropy (e.g. cleavage formed by aligned mica), or the deformation of passive layering, such as original sedimentary layers. The resulting fold patterns vary strongly, depending on the original layer orientation. This can result in misleading structures that seem to indicate the opposite sense of shear.

Deformation localisation can lead to a variety of structures, such as shear zones and shear bands (from grain to crustal scale), from isolated zones to anastomosing networks. The heterogeneous strain field can furthermore result in a wide range of highly diverse fold geometries. In anisotropic materials the deformation behaviour is controlled by the viscoplastic anisotropy of the material and their ability to form a crystallographic preferred orientation (CPO). Here we present a selection of a series of numerical simulations which aim to investigate (1) the influence of an initial CPO in an anisotropic material on localization behaviour and (2) the role of layering/passive markers on the development of deformation structures.

To describe the rheology of ice, it is customary to employ a flow law that relates the (differential) stress to the strain rate, typically as a function of temperature. The flow law thus predicts a single strain rate for a given stress and temperature. However, ice 1h is highly anisotropic when deforming by dislocation creep as is usually assumed to be the case in glaciers and polar ice sheets. Ice is effectively much softer in shearing parallel to the basal plane compared to deformation that requires activation of the non-basal crystallographic slip planes. Numerical simulation of ice deformation with the full-field crystal plasticity code (VPFFT, Lebensohn & Rollett, 2020) coupled with the numerical simulation platform Elle (Llorens et al., 2016) show that deformation in aggregates of ice grains is highly heterogeneous and typically shows strong strain heterogeneity and strain localisation in shear zones. This localisation remains when lattice rotation has resulted in a strong crystallographic preferred orientation (CPO) with basal planes all oriented approximately parallel to the shear plane in simple-shear deformation. Plots of the differential stress versus strain rate of all points of the full field model at one point in time show a wide scatter within the polycrystal. Although most basal planes have an orientation close to optimal for slip along this plane, few, if any material points actually show a stress-strain rate state close to the one predicted by the flow law for basal glide. On the contrary, the hard nonbasal slip planes contribute significantly to the overall deformation. Shear zones show a stronger alignment of basal planes than the surrounding material. However, differential stress tends to be highest inside these shear zones, suggesting that shear zones are not simply the result of the presence of "soft" ice. The results give insight in the highly complex behaviour of the strongly anisotropic material ice.

C′ shear bands are ubiquitous structures in shear zones but their development is poorly understood. Previous research has determined they mostly occur in rocks with a high mechanical strength contrast. Using numerical models of viscoplastic deformation, we studied the effect of the proportion of weak phase and the phase strength contrast on C′ shear band development during simple shearing to a finite strain of 18. We found that C′ shear bands form in models with ≥5% weak phase when there is a moderate or high phase strength contrast, and they occur in all models with weak phase proportions ≥15%. Contrary to previous research, we find that C′ shear bands form when layers of weak phase parallel to the shear zone boundary rotate forwards. This occurs due to mechanical instabilities that are a result of heterogeneous distributions of stress and strain rate. C′ shear bands form on planes of low strain rate and stress, and not in sites of maximum strain rate as has previously been suggested. C′ shear bands are ephemeral and they either rotate backwards to the C plane once they are inactive or rotate into the field of shortening and thicken to form X- and triangle-shaped structures.