Electron backscatter diffraction (EBSD) based determination of crystallographic preferred orientation (CPO) in warm, coarse-grained ice: a case study, Storglaciären, Sweden

Microstructures provide key insights into understanding the mechanical behavior of ice. Crystallographic preferred orientation (CPO) develops during plastic deformation as ice dynamically 15 recrystallizes, with the dominance of intracrystalline glide on the basal plane. CPO patterns in fine-grained ice have been relatively well characterized and understood in experiments and nature, whereas CPO patterns in “warm” (T > -10oC), coarse-grained, natural ice remain enigmatic. Previous microstructural studies of coarsegrained ice have been limited to c-axis orientations using light optical measurements. We have developed a new sample preparation technique, by constructing composite sections, to allow us to use electron backscatter 20 diffraction (EBSD) to obtain a representative, bulk CPO on coarse-grained ice. We suggest that a grain sampling bias of large, branching crystals that appear multiple times as island grains in thin section may result in the typical multiple maxima CPOs previously identified in warm, coarse-grained ice that has been subjected to prolonged shear. CPOs combined from multiple samples of highly sheared ice from Storglaciären provide a more comprehensive picture of the microstructure and yield a pronounced cluster of c-axes sub-normal to the 25 shear plane and elongate or split in a plane normal to the shear direction, and a concomitant girdle of a-axes parallel to the shear plane with a maximum perpendicular to the shear direction. This pattern compares well with patterns produced by sub-sampling data sets from experimentally sheared ice at high homologous temperatures up to strains of ~1.5. Shear strains in the margin of Storglaciären are much higher than those in experimental work. At much lower natural strain rates, dynamic recrystallization, particularly grain boundary migration, may 30 have been more effective so that the CPO has been continuously reset and represents a smaller, final fraction of the shear history, rather than the entire finite strain history. A key result of this study is that the multimaxima CPOs in coarse grained ice reported in previous work may be due to limited sample size and a sampling bias stemming from the presence of island grains of a single host that appear several times in a thin section. 35

temperatures as ice flows, and glaciers represent natural tectonic systems that undergo the equivalent of regional high-grade metamorphism under known driving forces (Hambrey and Milnes, 1977;Van der Veen and Whillans, 1994). Similar to rocks in active orogens, flowing glacial ice develops both structures and CPOs that reflect the conditions and kinematics of deformation. Studying the internal structure of glaciers on the crystal 45 scale provides key insights into ice mechanics, and aids in the understanding of tectonic processes (Hambrey and Milnes, 1977;Hooke and Hudleston, 1978;Faria et al., 2014b;Wilson et al., 2014;Hudleston 2015).
Quantifying flow behavior of ice under natural conditions is essential for the accurate incorporation of glacier flow into climate models and for using ice as an analog for high temperature deformation of crustal and mantle rocks (Faria et al., 2014b). Glaciers move by two gravity-driven processes: (1) frictional sliding 50 (including deformation of underlying sediments) of the ice mass over the underlying rock surface (e.g. Flowers, 2010 and references therein), and (2) slow, continuous creep (flow) within the ice mass itself (e.g. Glen, 1955;Alley, 1992;Budd and Jacka, 1989;Cuffey and Paterson, 2010). Creep is governed by thermally-dependent, micro-scale deformation processes, and therefore participates in important thermo-mechanical feedbacks in the Earth's cryosphere, atmosphere and oceans. This is especially important because of the highly non-linear 55 dependence of strain rate on stress (Glen, 1955;Budd and Jacka, 1989;Bons et al., 2018) Terrestrial glaciers, ice sheets and ice shelves comprise crystals of hexagonal ice (Ih, Fig. 1a; Pauling, 1935;Faria et al., 2014b). As ice dynamically recrystallizes during flow, anisotropy in the form of a crystallographic fabric or crystallographic preferred orientation (CPO) develops due to a dominance of intracrystalline glide on the basal plane (Weertman, 1983;Duval et al., 1983;Faria et al., 2014b). Similar to other crystalline materials, 60 CPO development modifies the internal flow strength (e.g. Wenk and Christie, 1991); and thus documenting natural ice CPOs provides insight into the large-scale flow rates of glaciers and ice sheets (e.g. Faria et al., 2014b). The CPO of ice is commonly represented by the preferred orientation of c-axes. This is useful because the c-axis of an ice crystal is normal to the basal plane (Fig. 1a), and glide on this plane dominates deformation (Duval et al., 1983). However, the orientations of a-axes are needed to fully characterize the orientation of ice 65 crystals, and better understand deformation mechanisms.
Coarse-grained (highly variable, but typically greater than 20mm) ice is common at the base of ice sheets and in warm (T > -10ºC) glaciers. Work on coarse-grained ice is especially important because basal ice in ice sheets may accommodate much more of the ice flow than the colder ice higher up the ice column (e.g. Rignot and Mouginot, 2012;MacGregor et al., 2016). Previous studies on coarse-grained ice have likely only measured 70 partial CPOs, typically by optical methods (c-axes only), and identified apparent multiple-maxima patterns defined by isolated clusters of c-axes ( Fig. 1b; e.g. Rigsby, 1951;Kamb, 1959;Jonsson, 1970). However, these multiple-maxima patterns are incompletely understood and defined in part because there has been no practical method for measuring the a-axes associated with such patterns. Measuring the a-axes means that we can tell whether two grains (in a 2D slice) with the same c-axis orientation also have the same a-axes and may be two 75 slices through the same grain in 3D. Work on coarse-grained ice has been limited because methods used to measure CPOs are restricted to section sizes of 100mm x 100mm or smaller, which results in there being an insufficient number of grains needed to clearly define the CPO pattern.
We aim to (1) fully quantify the CPO patterns (c-and a-axes) associated with warm, coarse-grained ice using cryo-electron backscatter diffraction (cryo-EBSD), (2) understand how and why the apparent local deformation conditions in the ice. To address these objectives, we combine results from fieldwork and laboratory analyses on Storglaciären, a small valley glacier in northern Sweden. Fieldwork included detailed mapping of structural features to provide a large-scale kinematic framework for our lab-based, microstructural part of the study. Importantly, in the lab we developed a new sample preparation method to allow us to measure 85 a representative volume and number of grains necessary for robust CPO characterization in coarse-grained ice using cryo-EBSD.

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Much of the pre-existing research on CPO development in natural ice has been done on ice cores from Antarctica and Greenland, and this has been nicely synthesized by Faria et al. (2014a). Schytt (1958) produced the first microstructural study of deep polar ice from the ice core extracted from the Norwegian-British-Swedish-Antarctic Expedition of 1949-1952. Many studies of ice cores have been subsequently undertaken, on both Antarctica (Gow and Williamson, 1976;Lipenkov et al., 1989;EPICA community members, 2004;Seddik 95 et al., 2008;Durand et al., 2009;Weikusat et al., 2009b;Azuma et al., 1999Azuma et al., , 2000Weikusat et al., 2017) and Greenland (Herron and Langway, 1982;Herron et al., 1985;Langway et al., 1988;Thorsteinsson, 1997;Gow et al., 1997;Wang et al., 2002;Svensson et al., 2003b;Montagnat et al., 2014). Studying microstructures in ice sheets offers the advantages of examining an extensive record of ice deforming under relatively simple kinematic conditions. As a result, CPOs in ice caps have been well defined and interpreted from ice cores.

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There are two typical end member c-axis CPO patterns that have been identified in experimental work. At warm temperatures and lower strain rates under uniaxial compression, the c-axes define an open cone shape or small circle girdle at 30-60 o about the axis of compression on a CPO plot ( Fig. 1c; e.g. Jacka and Maccagnan, 1984;Alley, 1988;Budd and Jacka, 1989;Jacka and Jun, 2000;Treverrow et al., 2012;Piazolo et al., 2013;Montagnat et al., 2015;Vaughan et al., 2017;Qi et al., 2017). Whether this CPO occurs in nature is less clear.

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Possible examples are described at the center of ice domes (e.g. Hooke and Hudleston, 1981;Lile et al., 1984;Gow and Meese, 2007). Representations of open cone CPOs do not appear in syntheses of polar bore holes (Faria et al., 2014a). Under simple shear conditions, the basal planes of ice crystals dominantly align with the shear plane, and the c-axes form an asymmetric bimodal distribution with both a strong maximum perpendicular to the shear plane and a weaker secondary cluster offset at an angle antithetic to the rotation associated with the 110 shear direction (Fig. 1c). The angle between the two clusters varies with shear strain, and the weaker cluster ultimately disappears with increasing strain leaving a strong single maximum pattern normal to the shear plane (Fig. 1d;e.g. Duval, 1981;Bouchez and Duval 1982;Budd and Jacka, 1989;Budd et al., 2013;Qi et al., 2019;Journaux et al., 2019). This dual maxima pattern of CPO development under simple shear has been described in nature (Hudleston, 1977a;Jackson and Kamb, 1997). It is probable that the strong single vertical maxima seen 115 in many ice cores from Antarctica and Greenland are associated with zones of sub-horizontal simple shear ).
An enigmatic CPO pattern can develop in valley glaciers and deep in ice sheets in coarser grained ice that has undergone significant recrystallization. This pattern is always associated with warmer (T > −10ºC) conditions and an increase in grain size, and is characterized by 3-4 maxima (sometimes with submaxima), 120 arranged around an axis that is vertical in ice sheets (Gow and Williamson, 1976;Thwaites et al., 1984; https://doi.org/10.5194/tc-2020-135 Preprint. Discussion started: 8 June 2020 c Author(s) 2020. CC BY 4.0 License. Goossens et al., 2016), and perpendicular to foliation in valley glaciers (Fig. 1b, Fig. 2; Kamb, 1959;Allen, 1960;Budd, 1972;Jonsson, 1970). In most cases, given the coarse grain size (Fig. 2a), the number of grains measured per thin section is small, usually no more than ~100. This may or may not be enough to reveal a mechanically significant CPO pattern ( Fig. 2b; Rigsby, 1960). By contrast, CPO plots produced for other 125 deformed crystalline materials typically include data from several hundred unique grains/crystals, which can usually be collected from a single sample section. This would be difficult or impossible to accomplish with coarse-grained ice.
Previous studies on valley glaciers done by Rigsby (1951) on Emmons glacier, Kamb, (1959) on Blue Glacier, and Jonsson (1970) on Isfallsglaciären used light optical measurements to delineate a CPO 130 characterized by a multimaxima pattern of the type described above, but were limited to measuring c-axis orientations. Such studies used a Rigsby universal stage to individually orient c-axes (Langway, 1958), and they demonstrated a relationship of the overall c-axis CPO to other structural elements, with the pole to foliation typically located centrally among the maxima (Jonsson, 1970).
Possible analogues to the multimaxima CPOs found in nature have been produced in experiments by 135 Steinemann (1958) and Duval (1981), in both cases done at temperatures near the melting point and under torsion-compression conditions. The maxima developed at high angles to the shear plane. It should be noted however, that the grain size in the experiments is much smaller than in natural ice with these CPOs.
Ice with the multi maxima CPO in valley glaciers (Rigsby, 1951;Kamb, 1959;Jonsson, 1970) and deep in ice sheets (Gow and Williamson, 1976) is comprised of large, branched crystals that lack undulose extinction 140 and have irregular, lobate grain boundaries ( Fig. 2a; Fig. 3). The branching nature of these crystals may result in sectioning artifacts that lead to apparent "island grains"-branches of the same grain appearing multiple times throughout one 2D thin section ( Fig. 3: e.g. as observed by Dempsey and Langhorne (2012) in sea ice). Without a complete crystal orientation -one which includes ice a-axes -it is difficult to confirm the existence of such island grains and determine their effect of the characterization of a representative CPO.

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Earlier studies made efforts to quantify an angular relationship between clusters of c-axes, but no consistent relationship could be found, and a mechanism that produces such a pattern -with regular angular relationships or otherwise -has not been established, although it has been proposed that the multimaxima pattern may be the result of twinning (Matsuda and Wakahama, 1978) alteration of a preexisting CPO (Kamb, 1959), or somehow related to the kinematics of combined shear and compression (Duval, 1981).

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We argue that no previously employed method has been able to determine a representative CPO for glacial ice consisting of coarse, branching crystals. Optical studies using the Rigsby stage, which accommodates 100mm x 100mm thin sections, are time consuming, and are limited not only by incomplete crystal orientations, but also by data resolution. Automatic ice texture analyzers (AITA), which can also accommodate larger grain sizes, use an image-analysis technique under cross-polarized light to determine c-axes (Russell-Head and 155 Wilson, 2001;Wilen et al., 2003). AITA analyses are attractive for speed and data resolution, but are also limited by incomplete crystal orientations (Russell-Head and Wilson, 2001). Three methods: etching (Matsuda 1979;Matsuda and Wakahama 1978), Laue diffraction (Miyamoto et al 2011;Weikusat et al 2011), and EBSD (Dingley, 1984;Prior et al., 1999)  Cryo-EBSD as a technique was first applied to ice in 2004 (Iliescu et al 2004), and modern cryo-EBSD methods enable routine work on water ice (Prior et al 2015). CPOs derived from EBSD datasets include a-axis orientations and provide a comprehensive view of ice microstructure that can improve our knowledge of the CPO and its relation to ice flow mechanisms on the grain scale. In addition, the speed, angular precision, and 165 spatial resolution attainable with modern EBSD systems offer major advantages over optical methods. However, until now, EBSD has not been applied to warm, coarse-grained ice because a sample of maximum size for analysis (60mm x 40mm: Prior et al., 2015;Wongpan et al., 2018) will only contain a few grains. The procedure we propose in this paper addresses this limitation.

3 Geologic Setting
Storglaciären is a small polythermal valley glacier located in the Tarfala Valley in northern Sweden (Fig.   4). The glacier is 3.2km long, extending in an E-W direction, with a total surface area of 3.1km 2 . A cold surface layer (annual mean of -4.0ºC) (Hooke et al., 1983a;Holmlund and Eriksson, 1989;Pettersson et al., 2007) of 175 variable thickness (20-60m) (Holmlund and Eriksson, 1989;Holmlund et al., 1996;Pettersson et al., 2003), and a cold-based margin and terminus (annual mean of -4.0ºC) (Holmlund et al., 1996;Pettersson, 2007), characterize the ablation zone of Storglaciären (Holmlund et al., 1996b). The thermal regime influences glacier dynamics; the center of the glacier undergoes basal sliding, but the margins and terminus are frozen to the overlying and marginal rock (Holmlund et al., 1996), causing most of the deformation in these areas to be a where shearing, which combines with shortening, is most intense. Folds range from centimeter to meter amplitude, and generally have axial surfaces that are vertical near the margins and contain the flow direction.

Field Work
Detailed mapping in 2016 and 2018 on the surface of the glacier provides the structural framework for this study. Data collection was focused on multiple transects across the glacier in the ablation zone. Relevant data, 205 presented in Figure 4, highlight the relationship of the structures to one another and the known kinematics.
We collected samples from eight areas of intense deformation in the ablation zone during the 2018 field season. For the purposes of this paper, we are focusing on three samples from the intensely sheared southern margin (SG23, SG27, and SG28) (Fig. 4). We excavated 10-20cm of surficial ice before sampling to avoid a layer of solar-damaged, recrystallized ice. Damaged ice was broken up using an ice axe and removed with a 210 shovel. Blocks of ice were removed from the glacier using a small chainsaw. Each sample was ~15x15x30cm, oriented such that the top of the block was parallel to the glacier surface, and the long axis was N-S, perpendicular to the flow direction. The shear plane, used to define the kinematic reference frame for subsequent microstructural analyses, is assumed to be parallel to the foliation. Samples were immediately shaded with a tarp upon removal to avoid solar damage, then labelled and insulated with ice and jackets to be transported off the 215 glacier. We trimmed samples with a band saw in a cold room at the University of Stockholm, Sweden, and marked the top north edge with a notch. We transported these samples to the University of Otago, New Zealand, in doubly insulated Coleman Xtreme 48L wheeled coolers to be stored in a biohazard freezer set to -31ºC.
Samples remained below -20ºC for the entire transport pathway.

Sample preparation
We prepared samples for microstructural analysis in a cold room (-20ºC) at the University of Otago. To prepare coarse-grained, natural polycrystalline samples for EBSD mapping, we developed a novel composite sample preparation method to maximize the number of grains collected and minimize the number of repeated 225 grains, in order to obtain a representative CPO. We made at least two composite sections for imaging from each of the eight samples, totalling 18 composite sections.
The procedure is highlighted in figure 5. We initially cut each sample block into three 5cm thick slabs perpendicular to the foliation. We then divided each slab into rods, spaced by 5cm, perpendicular to the flow direction and to the foliation. These rods were cut such that they were staggered between sequential slabs, and a 230 series of ~2mm thick slices were cut off of the bottom or top of each rod (easiest to divide each rod into equally spaced cubes before cutting slices due to the delicacy of individual slices). Each slice was labelled, oriented, and stacked sequentially between two wooden blocks within a clamp to hold loose slices together before being cemented. We wrapped wet paper towels around the compiled stack to adhere the slices into a coherent block, ~3.6x5x5 cm. We then cut these blocks in half to generate a flat composite surface, labelled each half, and 235 returned one to storage for future use. We mounted sections on 4x6cm copper and aluminium ingots in the cold room using the freeze-on technique outlined by Craw et al. (2018) and, to ensure secureness, used thin slices of wet paper towels around the edges in contact with the ingot. The exposed surface was then flattened and polished using progressively finer sand paper and then cooled slowly to ~ -90ºC before being inserted into the SEM.
Whole sections of certain areas of the original blocks were prepared for examination, to mitigate loss of information on internal structure due to the small slices for the composite sections. Slabs cut perpendicular to foliation (first step in composite preparation) were polished using progressively finer sandpaper and allowed to sublimate overnight, then illuminated using low angle light, which revealed grains intersecting the surface.
Areas of interest in these slabs were targeted for whole section analysis. At least two whole sections were taken 245 from each sample.

Orientation data collection
A Zeiss Sigma variable pressure field-emission-gun Scanning Electron Microscope (SEM) fitted with a 250 Nordlys EBSD camera from Oxford Instruments was used for EBSD analyses. The instrument is fitted with a custom-built cryo-stage that is continuously cooled by liquid nitrogen from an external dewar via a copper braid connection (Prior et al., 2015). The stage is cooled below -100ºC prior to sample insertion. During the transfer process, the sample did not exceed -80ºC. Once the stage cooled back down to -100ºC, we vented the SEM chamber, allowing the stage temperature to rise to -75ºC, inducing a sublimation cycle outlined by Prior et al.

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(2015) to remove any residual frost from the sample surface before imaging.
We collected full cross-sectional orientation maps of whole sections (e.g. Fig. 6a,b) and composite sections (e.g. Fig. 7a) at a 50µm step size in order to balance data resolution with such a coarse grain size. SEM settings for EBSD acquisition were a stage temperature of ~-90ºC, a chamber pressure of 3-5Pa, an accelerating voltage of 30kV, a beam current of ~60-70nA, and a sample tilt of 70º. EBSD data were collected using the Aztec 260 Software from Oxford Instruments and exported into Oxford-HKL Channel 5. We used EBSDinterp 1.0, a graphic user interface based MATLAB® program developed by Pearce (2015) to reduce noise and interpolate nonindexed EBSD data points using band contrast variations. Noise reduced data were then processed using MTEX, a texture analysis toolbox for MATLAB® (Bachmann et al., 2010), to determine full crystallographic orientations (CPOs), intergranular misorientations and grain boundaries (Mainprice et al., 2015). The overall 265 CPO in our samples is best represented using one-point-per-grain plots rather than all-pixel orientation plots due to the area bias introduced by larger grains in a small sample size. The kinematic reference frame used for plotting CPO is shown in figure 4.

Field Work
Orientation measurements of bedding and foliation are consistent with previous observations on Storglaciären and other valley glaciers. Bedding is difficult to distinguish from foliation at the margins of

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Storglaciären, but more obviously recognizable in the center of the glacier. Although locally variable due to folding, in the center of the ablation zone, bedding generally dips shallowly west. Along the margins, the foliation is subvertical, dipping steeply inwards towards the center of the glacier (Fig. 4). In the center towards the front of the glacier, the foliation becomes progressively shallower and dips shallowly up glacier where sheared basal ice is closer to the surface (Fig. 4). The combination of transformed stratification and foliation in the ablation zone forms a series of arcs on the surface reflecting in three dimensions an overall nested spoon arrangement, opening up glacier, much as described by Kamb (1959) for the Blue Glacier.

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Grains are locally variable in size, ranging from 1mm to >90mm, and shape, and have no apparent consistent shape preferred orientation (SPO). Air bubbles exist as a secondary phase and are found both within grains and on grain boundaries (Figs. 2a and 6a,b). Broadly, there is an inverse correlation between bubble concentration and grain size, and also between bubble concentration and grain boundary smoothness.

Whole Section
The size of an individual whole-section is determined by the technique used for the analysis. For U-stage work it is 100mm x 100mm, whereas for EBSD work it is 40mm x 60mm. Neither section size is large enough to clearly measure the coarse crystal size, but such sections capture the complexity of grain boundaries and 295 crystal shapes. Larger crystals have lobate-cuspate boundaries ( Fig. 2a; Fig. 6a,b), and many grains are larger than the size of the thin section. Many larger grains within one measured section have the same color in thin section under cross-polarized light and are shown to have the same crystallographic orientations by EBSD data, with near identical c-axis and a-axis orientations ( Fig. 2; Fig. 6,b,c).
Misorientation profiles A-A' (Fig. 6a) and B-B' (Fig. 6b) show that the orientation gradient across 300 individual grains is low. The pixel-to-pixel scatter, mostly less than ±0.5º is typical of the angular error for fast EBSD acquisition (Prior et al., 1999). Profile A-A' shows an abrupt change of about 4º across a subgrain boundary, and no distortion within the grain or subgrain. In nine whole sections analyzed for this study, ~15% of grains contain subgrain boundaries, with misorientations ranging between 2.5º and 5.5º (e.g. Fig. 6a). Profile B-B' shows a grain that has no internal distortion, and profile C-C' shows an orientation change of about 2.5º 305 across ~20mm. The statistics of misorientation between every pixel and the average orientation for that grain (Fig 6e) shows that 99% of these misorientations are below 2.5º. There is very little orientation spread, a measure of lattice distortion in the grains in this and all of the other sections shown.

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Several c-axis maxima clustered around the normal to the shear plane are present in individual samples and this is largely independent of whether we plot all measured pixel orientations or one-point-per-grain orientations (Fig. 7b,c,d). The maxima in the all-pixel diagrams (Fig. 7b) have different relative intensities compared to those in the one-point-per grain CPO plots (Fig. 7c,d), reflecting the increased weight given to the larger grains 315 in the per pixel data. In either case, many c-axes within an individual cluster are only separated by 2-3 degrees.
These slight misorientations are likely due to small misalignments of individual slices in the composite section that occurred during the sample preparation process. The a-axes define a diffuse girdle, parallel to sub-parallel with the shear plane, containing three distinct clusters (Fig. 7e). Each cluster is elongate towards the pole to foliation.
When composites SG23, SG27 and SG28, which are in the same kinematic reference frame, are individually plotted as one point per grain, and these results are combined on one CPO plot, the multimaxima nature of the pattern diminishes (Fig. 8). The composite pattern has one c-axis maximum perpendicular to the shear plane, that is elongate or split in a plane normal to the shear direction, and an a-axis girdle parallel with the shear plane with a concentration of a-axes perpendicular to the shear direction (parallel to the inferred vorticity 325 axis of flow). Two weak c-axis sub-maxima are offset from the main maximum in a plane perpendicular to the vorticity axis: the more distinct one ~30º synthetic to the shear direction and the less distinct one ~50º antithetic to the shear direction (Fig. 8).
6 Discussion 330 6.1 Whole sections EBSD maps of whole sections confirm that island grains are likely part of the same larger grain (Fig. 6a,b).
Individual grains within a two-dimensional surface that have exactly the same orientation or a slight 335 misorientation are likely branching segments of the same grain, or subgrains of the larger grain in three dimensions ( Fig. 3; Fig. 6b,c). Even small (30mm x 50mm) 2D sections can contain 3-5 island grains that have the same orientation (Fig. 6b,c). By appearing several times in the same section, some of the larger crystals likely amplify individual maxima within the overall CPO pattern typically identified in warm, coarse-grained ice. This may particularly be the case in studies that only use ~100 or fewer grains to identify a c-axis pattern, 340 because if 10-15 islands comprising the same grain were measured as separate grains, that would automatically lead to a c-axis maximum due to that grain.
Whole section analyses also allowed us to better understand the deformation mechanisms. While some subgrains are present in the suite of whole sections analyzed, most crystals show little evidence of significant lattice distortion. Individual grains are relatively strain free (Fig. 6e). A lack of intragranular distortion, 345 combined with the presence of lobate-cuspate grain boundaries suggests that recrystallization in these samples is dominated by grain boundary migration (Urai et al., 1986). These interpretations are consistent with those in microstructural studies of experimentally deformed ice at high temperatures (e.g. Kamb, 1972;Montagnat et al., 2015;Vaughan et al., 2017;Journaux et al., 2019), and natural ice samples deformed at relatively high temperature (Duval and Castelnau, 1995).

Composite sections
c-axis patterns for individual samples appear to represent typical multimaxima CPO patterns of the kind that have previously been identified in warm, coarse-grained ice (Fig. 7b,c) during the sample preparation process. As such, we propose that multimaxima patterns such as those described in previous studies may be an apparent result caused by grain sampling bias, with some samples containing fewer than 30 unique grains within a set of 100 apparent grains (i.e. the case assuming no multiple counting).
Thus, even for the composite samples, the data may not truly provide a representative one-point-per-grain CPO.

Comparison with Experimental Results
We compare our CPOs from natural ice to experimentally obtained CPOs from two warm temperature (-5ºC) direct shear experiments done by Qi et al. (2019), at relatively low (γ=0.62) and high (γ=1.5) strains.
Except for grain size, we interpret microstructures in the ice from Qi et al. (2019) to be similar to those in our 370 samples from Storglaciären (including c-and a-axis CPOs) and to other examples (including c-axis only CPOs) of warm, natural ice (Rigsby, 1951;Kamb, 1959;Jonsson, 1971). Individual grains from these "warm" experiments done by Qi et al. (2019) are characterized by amoeboidal shapes and lobate boundaries, and portray little to no shape preferred orientation in the two dimensional plane. A major advantage of using the Qi et al.
(2019) dataset for our comparison is that it comprises hundreds more grains than can be measured in a single 375 sample of coarse-grained glacial ice -even with using the novel composite-section sampling techniques addressed in this paper. Given the similarity in grain-shape characteristics and deformation temperature, and owing to the greater number of analyzed crystal orientations, we argue that CPO patterns from the Qi et al.

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Orientation data from Qi et al. (2019) show well-defined CPO patterns with a two-cluster c-axis pattern: a strong c-axis maximum perpendicular to the shear plane, and a c-axis sub-maximum rotated from the dominant maximum 45º-70º in a direction antithetic to the shear induced rotation (Fig. 9). The angle between the strong maximum and sub-maximum decreases with increasing shear strain. Clusters of c-axes are somewhat elongate in a plane normal to the shear direction. This elongation is clear in many previous studies (e.g. Kamb, 1972; 385 Duval, 1981;Bouchez andDuval, 1982, Li et al., 2000;Qi et al., 2019). Kamb (1972), and Budd et al. (2013) suggest that this may be due to compression perpendicular to the shear plane during deformation based on experiments that allow compression in addition to shear or torsion. However, Bouchez and Duval (1982), Li et al. (2000) and Journaux et al. (2019) observed these elongate CPOs in torsion experiments using fixed platens, so compression could not have been a factor in these cases.

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The a-axes in both the low-and high-strain experiments of Qi et al. (2019) define a girdle parallel with the shear plane (Fig. 9). In the lower-strain experiments the a-axes cluster mostly perpendicular to the shear direction (parallel to the vorticity axis), whereas in the higher-strain experiments they mostly cluster parallel with the shear direction (Fig. 9). This change in a-axis maximum from normal to shear to parallel to shear with increasing strain is also observed by Journaux et al. (2019).

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In an attempt to mimic a possible grain sampling bias similar to that which we propose when dealing with warm coarse-grained ice, we randomly resampled subsets of 50 grains -allowing for random duplicates in the resampling (thus one grain may appear more than once in the resampling) -from the two warm experiments by Qi et al. (2019) at low and high strains and compared these to the stacked suite of natural samples in the same kinematic reference frame (Fig. 9). Subsets of the experimental data produce patterns that are more-diffuse and patchy than those for the full dataset and are broadly similar to patterns observed in natural coarse-grained ice.
Importantly, the Qi et al. (2019) study does not suffer from grain sampling biases common to CPO characterization in warm glacial ice, due to the significantly finer and more consistent grain size (Fig. 9).
Compared to the experimental results, the main c-axis maxima in the stacked data from our glacial ice samples ( Fig. 8) are more elongate or "pulled apart" than those in the subsampled experimental data, and the girdle of a-405 axes is broader, with a cluster perpendicular to the shear direction, similar to the pattern observed in the lower strain experiments (Fig. 9). The more distinct c-axis sub-maximum in our combined data (Fig. 8) is offset from the main maximum in a synthetic sense with respect to the shear direction, rather than an antithetic sense as might be expected from the experimental data (Fig. 9). However, the less distinct sub-maximum, offset in the antithetic sense ~50º from the main maximum, is consistent with the secondary maximum in the experiments.

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We interpret these results to mean that the grain sampling bias issue was not entirely resolved by making composite sections, due to the very large grain size with interlocking shapes that still have not been entirely characterized. However, the overall similarity between the stacked data from composite sections from the three samples in the same kinematic reference (Fig. 8) to the CPO pattern presented by Qi et al. (2019) for finegrained ice that has undergone low shear strains at high homologous temperature (Fig. 9, PIL91) suggest that the 415 operative deformation mechanisms are similar.
It is important to note that we do not know the exact deformational history experienced by the ice in our natural samples, but the recent part of that history corresponds most closely to simple shear parallel to the ice margin. An additional similarity between the experiments (Qi et al., 2019) and the conditions of deformation experienced by our samples is that there is a component of compression, which for our natural samples is 420 perpendicular to the margins of the glacier, associated with the narrowing of the valley in the direction of flow (Fig. 10a). Thus our samples may represent similar kinematics to those in the experiments conducted by Duval (1981) and Budd et al. (2013) that involved simple shear combined with compression normal to the shear plane ( Fig. 10b). Hudleston (2015) calculated the shear strain required to rotate fractures towards parallelism with the flow 425 direction along the margins of Storglaciären, and this indicated that the shear strain where we collected ice samples for our study is greater than 2. This estimate exceeds the strain of the "high-strain" experiments done by Qi et al. (2019) and we might therefore expect our data to best match the "high-strain" experimental data.
However, the a-axis pattern of our samples best matches the pattern for the "low-strain" experiments. One likely reason for this comes from considering strain rate. In the experiments, shear strain rate was ~10 -4 s -1 whereas in 430 natural ice along the south margin of Storglaciären, strain rate calculated from velocity measurements (Hooke et al., 1983b;Hooke et al., 1989) and modeling (Hanson, 1995) is ~10 -10 s -1 . At low strain rates (Zener and Hollomon, 1944;Hirth and Tullis, 1992;Takahashi, 1998;Qi et al., 2017) and at high temperatures (Cross and Skemer, 2019), dynamic recrystallization and grain growth will be enhanced. The resulting CPO (Fig. 10b) will thus likely reflect a small part of the deformational history and have been continually reset as deformation 435 proceeded.
are able to use cryo-EBSD to obtain complete (c-and a-axes) crystallographic orientation measurements for interpreting CPO patterns in natural, coarse-grained glacial ice. A single composite section captures a relatively large number (~50-100) of grains, in our case from an ice sample of ~200mm x 150mm x 75mm dimensions and with >20mm grain size. The larger number of grains in this new approach allows us to better characterize CPO patterns in coarse-grained ice than has been done previously, and it sheds new light on the significance of 445 microstructural processes associated with previously identified multi-maxima CPO patterns. Specifically, we conclude that a grain sampling bias of interlocking, large (>20mm) branched crystals that appear multiple times as apparent island grains in thin section contributes to the apparent multiple maxima CPOs displayed in our natural ice samples. Such bias also likely contributed to similar CPOs that have long been identified in other studies of natural, warm, coarse-grained ice. Without better establishing 3D grain size and shape, it will be 450 difficult to fully eliminate or account for this bias, but a combination of systematic sampling, composite sample preparation, and data stacking will help more accurately define CPOs.
We suspect that in our study, a more representative CPO, if enough data from a large enough volume of ice were sampled, would consist of: 1) a c-axis CPO with one maximum that may be extended or "pulled apart" in a plane perpendicular to the shear direction, and a weaker maximum 45º-60º from the shear plane; and 2) a broad 455 girdle of a-axes parallel to the shear plane with a cluster perpendicular to the shear direction. Such a pattern assumes that the dynamic recrystallization of ice under slow strain rate and high temperature conditions results in the observed large grain size and resetting of CPO to reflect the local kinematic conditions.
Our new sample preparation method allows for faster and more accurate collection of complete crystallographic orientation data and microstructural analyses of coarse-grained ice. This opens a range of 460 opportunities for further analyses to aid in the understanding of micromechanical processes governing rheological properties of such ice. Future work will benefit from better quantification of 3D grain size and shape to help improve the sample preparation methods in order to minimize any grain sampling bias. Additionally, more work should be done to quantify the effects of dynamic recrystallization in the context of shear strain along the margins of glaciers and should be taken into account when assessing these CPO patterns.