Crystallographic analysis of temperate ice on Rhonegletscher, Swiss Alps

, Abstract. The crystal orientation fabric (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) fabrics (cid:58) (COF) (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) provide (cid:58)(cid:58)(cid:58) key (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) information (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) about (cid:58)(cid:58)(cid:58) the (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) mechanics (cid:58)(cid:58) of (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) The COF was studied at an ice core that was obtained from the temperate Rhonegletscher, located in the Central Swiss Alps. Seven samples, extracted at depths between 2 and 79 m, were analysed with an automatic fabric analyser. The COF analysis revealed conspicuous four-maxima patterns of the c-axis orientations at all depths. Additional data, such as microstructural images, produced during the ice sample preparation process, were considered to interpret these patterns. Furthermore, repeated high-precision Global Navigation Satellite System (GNSS) surveying allowed the local glacier ﬂow direction to be determined. The relative movements of the individual surveying points indicated horizontal compressive stresses parallel to the glacier ﬂow. Finally, numerical modelling of the ice ﬂow permitted to estimate eigenvector (cid:58) align with the compressive stress directions obtained from numerical modelling. The clustering of the c-axes in four maxima surrounding the predominant compressive stress direction is most likely the result of a fast migration recrystallisation in combination with the presence of signiﬁcant shear stresses. This interpretation is supported by air bubble analysis of the LASM images. Our results indicate that COF studies, which were so far predominantly performed at cold ice samples from the polar regions, can also provide valuable insights on the stress and strain distribution within temperate glaciers. with the c-axes are thus predominantly horizontal , but with increasing depths, their colatitudes decrease. Ice ﬂow modelling results support the assumption that this is an effect of combined compressive horizontal stresses in ice ﬂowdirection and depths-increasing vertical stresses caused by the ice overburden. The presence of multi-maxima patterns (instead of a single maximum) can be explained by (i) migration recrystallisation and (ii) the presence of shear stresses. The multi-maximum patterns are also indicative that a fast and complete migration recrystallisation must have occurred. This interpretation is supported by air bubble analyses in LASM images Author contributions. This study was initiated and supervised by HM, AB, IW and MS. The ﬁeld and laboratory data were collected by MS, SH, MG, AB and JK and analysed by SH with support from JK and under supervision of IW and MS. Data processing and calculations were 510 made and interpreted by SH and discussed with JK, IW, and MG. The ice ﬂow was modelled by GJ with input data from MG. The paper was written by SH with comments and suggestions for improvements from all co-authors.

While the data analysis is done really well, the interpretation in terms of stress state is not as thorough and rigorous. Their qualitative interpretation of the stress state and its relation to fabric and recrystallization processes is confusing and in a few places incorrect. The paper would benefit from a summary of the key states of stress, key metamorphic processes, citing the original research (going beyond Cuffey and Paterson and the Faria reviews). As a reader, if I am to trust their interpretation of the fabric, I need to trust that they understand the underlying physics. At this point, the physics is description is still lacking. It is imperative that the interpretation of the fabric in terms of the stresses be written with the same care and rigor that that fabric was measured.
First, it would be helpful to clarify when deviatoric stress is being used versus total stress. Deviatoric stress control most of the deformation and pressure plays a minor, if any, role in deformation, therefore describe the deviatoric stress states rather than "absolute" stress and "overburden." For example, the authors suggest that there is less deformation in the surface layers because the "absolute" stress there is low, but this is not the case -the vertical compressive deviatoric stress is no necessarily smaller at the surface, it is typically about the same -it is only the pressure term in the total stress that is smaller at the surface and pressure does not drive fabric (only gradients in pressure or overburden can drive flow). I would suggest that they re-write the description of the stress state in terms of more formal tensor components, and more specific (and correct) wording. And please be explicit about what is behavior linked to stress and what is behavior linked to strain rate (and discuss with respect to the statement that strain rate ultimately drives fabric development not stress). In terms of writing, there are numerous run-on sentence, imprecise wording, and extensive use of passive voice, all of which slows down the reader. I provide examples of a few of these (but not all of them) below, I encourage the authors to edit carefully for these three writing issues.
We will check for any passive structures and run-on sentences and appreciate your particular recommendations below. In the revised version, we introduce a subsection about the physical details. We also show the deviatoric stresses for each depth in a separate table and use the particular values for an improved discussion. Of course, the overburden pressure is not responsible for deformation of the ice. We have rectified this blunder.
Indeed, the core barrel and drill head could rotate, but a magnetometer was integrated into this core barrel. After each drilling we turned this core barrel until reaching the orientation at beginning. Then the core segment was retrieved and its orientation was marked with a knife. Afterwards we tried to attach the segment to the previous one. If this was possible we added a notch with a soldering iron on both segments. However, if this was not possible, we opened up the notch of the knife. Later, we could retrieve the orientation of the core barrel during the drilling process. Assuming that the core segment was not rotating within the core barrel (e.g. due to sudden shocks which we avoided by a decent winch speed), we could retrieve the actual core orientation. The data also reveal that there is no 360°-spinning around the cable (just slight movements). The water-filled borehole damped any rotation of the core barrel. We actually calculate the strain rates as constraint for our model. We will add this information and discuss whether it could replace  We did not measure this value at this position. However, a reference station about 50 m away from the boreholes shows an emergence of 1.5-2 m a -1 .
Line 89 -This paragraph seems to shift to modeling methods, from drilling methods. While it mostly reads ok, perhaps make this a different section? Especially since the section is titled "field site and data acquisition" I also think one paragraph describing the model is a bit thin. If you are actually using the model to interpret your data, please describe it more rigorously and explain the weaknesses with the model outputhow much do you trust the modeled principal strain rates and directions? Given that you just assumed a rate factor from another glacier and tuned the sliding to fit this glacier site? Did you conduct a sensitivity study to assess the impact of your parameter selection on the stress and strain rate output from the model? Given that the model inputs are approximate, I'm not entirely sure that the model provides any better qualitative assessment of the expected principal stresses and strain rates than a simpler flow band description explained with clear assumptions.
We improved the modelling description and moved it to a new section (see substantial changes). According to your questions: As you point out in your comment for line 97, the model is only used to constrain our interpretation. However, we could have used a flow band description or our borehole data to interpret. The main task behind employing the model is to get some quantitative values rather than just speculating qualitatively about different stresses (namely compressional in-flow and shear stress). The most important weakness is that we use the stress information of a single point to explain the stress conditions for a certain area of the glacier. Local stress effects cannot be captured by such a model. Furthermore, we also do not have reliable bed velocities and we have to admit that the model is only constrained by surface velocity and ice thickness information. To overcome these weaknesses, we will consider strain rates derived from our borehole experiments (Table 3).
Line 91 -delete "simply"; say "steady state" model or something like that.
We revised the whole paragraph and removed it.
Line 97 -I realize that the model is not intended to be a perfect match, but tuning the model to only one surface velocity is limiting. But I think that's ok, if you are mostly going for the style of stresses and not the real magnitudes (but see my comment above about just using a simpler flow band description because models like this not tuned well can induce complexities that might be interpreted as real). Importantly, the stress distribution with depth at the site of the borehole is highly dependent on the sliding coefficient. When you use these results to interpret the data, please discuss this with respect to the limitations of the model (see my comment above about the vertical distribution of stresses). Oh -and what was used for accumulation/ablation rates? The vertical strain rate at the core site will depend on the ablation rate. Did you measure the vertical velocity at the surface?
We do not model a time-transient evolution but only calculate the stress field for the actual geometry. Therefore, we did not consider the accumulation and ablation rates. The limitation is that the model only provide stresses and not strain rates or directions. We can calculate strain rates with Glen's flow law. Please regard the model as constraining information for the interpretation. We do not intend to setup a perfect model that describes the ice flow and stress + strain rates. This needs additional measurements and is beyond the scope of this work. In the revised interpretation, we also consider strain rates derived from the borehole data.
Line 123 -delete "as discussed later" and "important" -they don't provide any useful information here.
Changed. We add the other two eigenvectors (Fig 5), symbol size decreases accordingly. The eigenvalues are not 100% equal but both around 0.10-0.31 (we added the particular ranges in the text, line 181). Usually the second eigenvector is laying in the vertical plane of the diamond shape pattern. We also add the number of grains for 6 grain size classes (<1/1-5/5-20/20-100/100-500/>500 mm 2 ) to Table 2 and show a histogram for a selected depth and put the others to the supplement. We will use this additional figure in our interpretation as the small grains (<1mm 2 ) clearly emphasis one of the four clusters. This provides some evidence that recently recrystallized grains in the deeper and intermediate parts of the glacier prefer one of the clusters rather than equally distribute to all four clusters.
Here (and more in detail in the discussion), we introduce the concept of Faria et al. and also show, where their concept differs from previous literature (see substantial changes). Faria clearly state that the tripartite paradigm is wrong and our interpretation is based on their assumptions (which has been proven by other authors in the last years). They particularly distinguished between strain-induced boundary migration with new grains (SIBM-N) and strain-induced boundary migration with keeping the old grains (SIBM-O).
Line 233 Because normal and shear stresses are the two types of stresses, then the statement that a combination of normal and shear must have been involved to create the fabric is minimally useful. Please provide more specific description.
We completely removed this immature part. Instead we refer more to the recrystallization processes to describe the diamond shape pattern.
Line 239 what does it mean for a tensor to provide "hints" (that seems to me like an anthropomorphism)?
This line has been removed. See comments to Line 233 and substantial changes.
Line 239/240 Do you mean that this site is not 100% sliding? That's the only way to avoid borehole shearing. It seems like the model set up already defined a limited amount of sliding, there must be some non-zero component of tau xz. So that was an input to the model, not an output.
Our model assumes basal sliding (parameter c > 0) and we removed this line during our revision. However, we also considered no basal sliding in our model for a sensitivity analysis. This would lead to giant rate factors which are unrealistic. Therefore, basal sliding is, indeed, a prerequisite.
Line 241 A parabola is typically for an xˆ2 relationship, that is not the case for the curve resulting from Glen's flow law.
It is a hyperbolic curvature.
Line 243 -how long ago was "recently" can you provide estimates for the timescale of the last significant change in stress state and express that timescale as a percent strain the crystal experiences?
"Recently" must be within the last four decades as the ice flow direction changed about 1000 m up-glacier and our pattern is in good agreement with the current flow direction. The strain % is difficult to assess as we do not have information about the surface velocities in that area further up-glacier.
Line 244 -I think the authors mean "latter" not "later"

Changed.
Line 244 -I'm not quite sure why a mean grain size reduction would necessarily occur after a change in flow direction, unless you are suggesting that the change in direction is triggering specific recrystallization (migration or rotation). I am also not sure I understand the citation to Faria here, as recrystallization has been described in many papers before. Perhaps you can be more specific about what Faria contributed that is specific to this analysis? And please more carefully cite the statements here (alternativly, if you write an overview of the stress state and metamorphism of the crystals in the beginning that describes and cites each process as background and properly cited, you can avoid having to add too many citations in this discussion section. As described in our answer to line 228, Faria was (to our knowledge) the first, who distinguished between SIBM-O and SIBM-N. Others only referred to dynamic and rotational recrystallization (RRX). This distinction is particularly important for observed grain-size changes at high temperatures as in our case. That even leads to a new process understanding, e.g. Steinbach et al (2017) in Frontiers in Earth Science, Vol 5. We include a paragraph in the discussion and describe in detail, how the findings of Faria et al. differ from previous studies (see substantial changes).

Line 256 I really like the images of the bubbles and the grain boundaries -it does show fast grain boundary migration and active interaction between bubbles and boundary movement. How do you know it was a "complete" recrystallization?
We actually do not need this Figure anymore and do not use the observations in our revised version.
Line 258 The image of bubbly and bubble free ice brings up a question I have as to whether there are signs of refrozen water in these thin sections. Water filled crevasses refreeze with a different microstructure that is typically bubble-free or with patterns of bubbles and distinctly different crystals. Some of the small grain "fracture" noted in the paper also might be a post-depositional process. Perhaps it is ok to include these in your analyses, as the same crystal evolution processes are happening, but it might be useful to discuss the ice from snow compaction versus any refrozen water and how that might influence the fabric and grain size distribution (and bubble) We have seen those fracture traces in two depths (22+45 m). We also analysed these fracture grains separately and can provide information about their orientation. Some of them are perfectly aligned with the surrounding large grains (especially if the fracture is thin). Others (if not a fracture but rather a patch of small grains) show a girdle structure. This girdle is aligned with the glacier flow (extension in transverse direction). We could exclude these grains from our analysis. This would emphasise the diamond pattern in 22 and 45 m.
This paragraph was revised. The strain rate and also the deviatoric stress is not smaller at the surface compared to other depth (Table 2).

Line 310 -how do you judge "good agreement"?
We wanted to point out that the stress conditions in these laboratory experiments are in a similar range as we find them in the glacier. During our revision, we rephrased this part.
Line 317 -"clearly" is not a helpful word -at this point, I am a bit bogged down in generalities and imprecise wording in the fabric and stress/strain relationship, that I am struggling to judge for myself what the source of the 4 maxima are.
We avoid these words in the revised version.
Line 335 -I do believe twinning has been observed use EBSD (such as Obbard's work on the Fremont glacier and/or at Siple Dome), I can't remember which one she noted the a-axis alignment that would suggest twinning.
Up to date, we could not find the respective part in the papers of R.W Obbard. However, her work is worth to consider as it clearly points out the ambiguities of our technique (analysing the c-axis without the a-axes information).
Line 340 -This statement isn't correct, at least the way I am understanding it (increasing overburden/pressure). Please describe the fabric in terms of deviatoric stress tensor as a function of depth, and, in addition, explain more clearly why 4 single maxima are created rather than a girdle, I think you tried to explain this, but it didn't come through very clearly.
Indeed, this needed a revision. The overburden pressure is hydrostatic and not responsible for strain rates that drive c-axis developments. We removed this argumentation and included a paragraph in which we describe the physics (i.e. deviatoric stresses) leading to deformation and COF changes.
Line 346 -yes, in terms of "comprehensive" analysis of the thin sections measurements -this paper is awesome. In terms of interpretation based on stress state, this paper needs work. There have been some other work on temperate glaciers (including some ongoing work on a glacier in Alaska I thinkby Gerbi and others? I'm not sure the status of their publications).
We agree that we have to revise the interpretation part and added a couple of additional details about the stress state in the glacier as derived from the model and further provided information about the strain rates from in situ measurements. These data should simplify the interpretation and allow a better access to the information provided in our paper. We also figured out that there are a couple of presentations from Gerbi at AGU. However, there seems to be no field data published yet.

Dear Peter Hudleston,
We appreciate your constructive and valuable comments to our manuscript tc-2020-133 entitled "Crystallographic analysis of temperate ice on Rhonegletscher, Swiss Alps". We have considered your typographic recommendations and have provided a point-by-point response to your review comments.
If there are further questions, we are happy to answer them and look forward to hearing back from you regarding your decision.
Kind regards, Sebastian Hellmann and the co-authors.

General comments
This paper provides a detailed description and analysis of the crystallographic fabric of ice taken from a core from the surface to bedrock in the central part of the ablation zone of a temperate valley glacier. It finds that multimaxima fabrics of the type commonly found in most valley glaciers, usually just from nearsurface samples, occur at all depths within the glacier, with some systematic changes with depth in orientation of the clusters that constitute the fabric. This is a new finding and deserves to be published on this basis alone. The paper then, importantly, relates the fabric to the stress field derived from numerical modeling and finds a direct relationship between the orientation of the fabric and orientation of the modeled principal stresses. This leads to a possible explanation of these four maxima fabrics. I question parts of the interpretation and don't believe these fabrics are yet fully explained, as discussed in the specific comments below, keyed to lines in the text. I have also corrected a few typographical errors and made some suggestions for language usage.
We considered the typographic recommendations in the most recent version. Based on the reviewer comments, we revised the modelling part and recalculate the values from the model. The new results slightly change our interpretation and also fit better to your explanations. We are going to add the actually derived values for the stress components to the interpretation part to improve the argumentation. Furthermore, we will remove Fig. 9 as it may not fit to the improved results anymore. The recommendations about grammar and language, especially in the first sections are already included (comments like "changed")

Specific suggestions:
Line 9-10. The language here doesn't clearly describe the observed relations, since there are four azimuths and colatitudes that define the fabric and three principal stress directions. It is the centroid of the fabric and the maximum principal stress direction that nearly coincide in orientation.
We changed this sentence: The centroid of the four-maxima patterns of the individual core samples and the coinciding maximum eigenvector align with the compressive stress directions obtained from numerical modelling.
Line 31. The stress and kinematic conditions in valley glaciers are more complex than just combinations of simple and pure shear.
Changed to: In contrast, for ice samples from temperate glaciers, the deformation is dominated by a series of interfering and variable compressional, extensional, and shear stress conditions along the flow in the valley.
Line 94. Although the details of the numerical model need not be given here, the basic form of the flow law should be given, since the value of the flow law parameter A is defined. The value of the power law exponent, n, in the flow law should also be noted.
See our remarks for substantial changes. We added a new section and provide the basic equations for ice flow and the Weertman's friction law. We also define/describe the respective parameters.
Line 117. It is not clear what is meant by fractures here, since there are no actual fractures in this core. This needs clarification. What are the physical manifestation of the 'fractures?" They must be defined by some combination and bubble or grain size distribution.
We changed it to "fracture traces" as recommended in your comment for Line 151. However, in other literature we found the term "fissures". As it seems not to be conclusive, we use both terms.

Line 135. Surely this is mm2 not µm2
Indeed, this must be mm2, changed.
Line 151. Here is some information about the fractures. Presumably these patterns are in the form of linear traces in thin section. Following Hambrey I like the term 'fracture traces' for these likely healed fractures.
We changed it to "fracture traces" as a much better name for these features that could be observed in some core depths. However, they are sometimes called fissures. Therefore, we mention both names.
Line 157. You use the term centroid here for the maximum eigenvector on these plots, and state that these are equivalent in the caption to Table 1. Yet in Figure  7 the two are represented and plotted as separate entities. The usage needs to be consistent. In this case how is centroid defined?
We revised the usage of centroid and centre (i.e. midpoint) between the clusters. The midpoint (red dots in Fig. 7) is defined as geometric point between the four maxima (independent of number of grains per cluster). The centroid is affected by the particular distribution of grains and those maxima with a larger grain number attract the centroid. Therefore, midpoint and centroid differ slightly. When calculating the opening angle we considered the midpoint as symmetry point of the multi-maxima pattern.
Line 173-174. It should be noted that Kamb, Hooke and others have discussed the issue of accounting for complex and branching shapes of large grains when making c-axis plots.
We added the recommended references and furthermore two papers that also show images for a better visualisation: Therefore, two-dimensional cuts through large, branched grains may let them appear as several individual grains within the same section. Kamb (1959) and Hooke (1969) have already discussed the statistical relevance of these branched grains. The sketches in Hooke (1980), Fig. 6 and more recently in Monz (2020), Fig. 3, further illustrate this issue that could result in over-represented clusters in the superimposed stereo plots from the different sub-samples. Changed.
Line 192. The c-axis fabric has orthorhombic (and perhaps close to axial) symmetry, but is this also true of the stresses? What about the other two principal stresses. Are they consistent with plane strain or plane stress, as appears to be assumed in Fig. 9? Are the principal stresses and strain rates in this section of the glacier near the surface parallel to the flow direction (σ1), vertical ( σ3) and horizontal (σ2), with the lateral strain rate close to zero, as one would expect for a valley of constant width. One would expect the maximum principal stress to become inclined deeper into the ice as shear stress parallel to the base increases, which the modeled stress shows a tendency to do.
We added the requested components to Figs 5 (eigenvectors) + 7 (stresses). The eigenvalues are named with \lambda_1 -\lambda_3 and the stress axes with \ sigma_1 to \sigma_3 in decending order. The symbol size decreases respectively in both Figures.
We assume, that the eigenvectors are aligned with the strain rates (i.e. deformation). Due to the non-coaxial relation for simple shear, the eigenvectors could differ from the stress principal axes by up to 45°. Under this assumption, the largest eigenvector in 79 m is perfectly aligned with the strain rate direction for dominating simple shear. Figure 9 was removed due to speculative parts (see substancial changes).
Line 200-204. This is a possible explanation, but I prefer the misorientation of the sample as the explanation, which as you state, fits very nicely when a 60o azimuthal 'correction' is made. A preserved fabric from earlier in the flow path is less likely at high temperatures when rapid recrystallization is expected.
We removed this immature hypothesis, especially as we cannot see a smaller deviatoric stress in the uppermost parts.
Lines 210-213. With this explanation you would expect σ1 to be vertical to explain the fabric at 79m depth and not as given by the numerical model. Although the vertical normal stress increases with depth, it is the deviatoric stress that controls deformation, not absolute stress values, and this likely does not change greatly with depth. I think the main thing that changes with depth is not the vertical effective compression (σ1 -σmean) but the increasing addition of base parallel shear stress, that in general terms increases linearly with depth.
Our mistake was to consider a (hydrostatic) overburden pressure. However, this hydrostatic pressure does not contribute to the deviatoric stress that drives the caxis orientation (via strain rates). We revised this part accordingly. As you say, the c-axis orientation (i.e. the centroid) in the deepest part is in alignment with shear stress: Base-parallel shear stress lead to a base-parallel orientation of the basal planes and thus a more vertical c-axis. The model shows that the shear stress component σ d xz (which we will add to the results section) is the most dominant stress and the in-flow compressional component σ d xx is much smaller in this depth (similar to σ d yy ).
Line 217. There is almost certainly some dependence of fabric on strain, which may not be great with fast recrystallization.
We revised the details about recrystallization. Now, we consider, that straininduced grain boundary migration with nucleation of new grains is the driving force. Then we do not have to assume any "fast" or "complete" recrystallization.
Line 213-214. In simple shear the directions of principal stress are only aligned with those of principal strain for infinitesimal strains. The divergence grows as strain increases.
We assume that strain rate (and the strain) and stress direction form an angle of ~45°. Therefore, the principal stress direction (governed by the simple shear component) in the deepest part of ~48° and the actual centroid (~2°) would fit under such an assumption. The MM cluster is aligned with the strain rate direction in that depth and not with stress as stress and strain diverge for simple shear.
Line 238 I don't believe Cuffey and Paterson really explain why there should be four maxima when the stress deviates from unconfined compression. This is more of an observation than an explanation.
No, they only provide a description and mention different stresses are required for multi-maxima. In the revised version there is no need to cite them. We considered the more specific literature.
Lines 244-245. This is unclear. A change in direction of glacier flow could be associated with either an increase or decrease in strain rate and thus decrease or increase in recrystallized grain size. Why just a decrease? This is correct, it could be an increase as well. In our detailed description for SIBM-N and SIBM-O we discuss in detail, how the grain size evolves under different conditions. We added a supplementary figure (Fig. 8, revised version) and median and 6 different grain size classes to Table 2 (now Table 4).

Line 251 and
Line 255-266. I'm not sure how much information is given by the air bubbles, except they do provide excellent evidence of active recrystallization by grain boundary migration. Bubbles are found both within grains and along grain boundaries both in temperate ice and in cold ice experiencing dynamic recrystallization, although the recrystallization mechanism may differ.
As we found a better way to explain the recrystallization processes, we removed this Fig. 8 Line 269. Hooke and Hudleston were concerned with polar, not temperate ice. The study was made on the Barnes Ice Cap.
Thank you, again a valuable hint. We will change it: They were observed in early studies on temperate glaciers (e.g., Rigsby, 1951;Kamb, 1959;Rigsby, 1960), ice capes with ice temperatures above -10°C (Hooke and Hudleston, 1980), and also in the bottom ice of Byrd Station and Cape Folger in Antarctica (Gow and Williamson, 1976;Thwaites et al., 1984). They are often referred as "diamond-shape" pattern or fabrics.
Line 276. Whether the multimaxima fabrics are a result of unrepresentative sampling is still arguable in some circumstances, although the case you have here for these being true multimaxima fabrics is a strong one.
Line 290-291. I think more data is needed to support this conclusion. The cores taken by Tison and Hubbard were in a different regime within the glacieraccumulation zone where perhaps there is longitudinal extension rather than compression, and close to the lateral margin of the glacier rather than in the center. This must lead to a more complex stress regime.
Actually, some cores were drilled in the ablation zone and in these cores they found multi-maxima at the bottom. However, it is true that they are drilled at the margin and therefore they could significantly differ from our core close to the centre flow line of the glacier. This could complicate a direct comparison.
Line 298-299. The combination of compression plus simple shear as applied in these experiments makes sense for much of your core, but not for the highest one where the shear component is minimal, nor for the lowest one, where the σ1 direction lies well outside the small-circle girdle of maxima. Some other explanation must hold in these places.
Our revised interpretation assumes that the multi-maxima pattern clusters around the dominant strain rate direction, which is the one of base-parallel simple shear for this depth. The eigenvector is aligned with the expected strain rate direction (as you also describe). Due to recrystallization, we observe the clustering of four maxima around this axis.

Line 300-301. I'm not sure if I'm properly interpreting what you are saying here, but the planes of maximum shearing stress in Duval's combined compressionsimple shear experiments are not vertical and horizontal in his experiments, but inclined by an amount that depends on the relative amounts of normal compression and simple shear.
This is exactly, what we wanted to cite here. His experiments show a multimaximum pattern that is aligned with the compressional axis and two of these maxima are also aligned with the poles of the two shear planes as the angle between the maxima and the principal direction is roughly This part has been removed. We cite Llorens to discuss potential localisation effects. However, Qi et al. are not providing any additional information useful for our interpretation. Fig. 9. The stress state shown in Fig. 9 is almost that of simple shear (no baseparallel longitudinal compression) with the shear plane (taken as the glacier bed) horizontal and σ1 inclined at 45o to the shear plane. If it is simple shear, there will be no horizontal compression and thus no shortening in the glacier flow direction, which is incompatible with your data. If horizontal glacier flow-parallel compression is added σ1 will move closer to horizontal than it would be for simple shear alone. This looks like being the case for much of the glacier from the stresses shown in Fig. 7. I would expect the inclination of σ1 to be near zero at the surface and something less than 45o close to bedrock, the amount depending on the amount of horizontal compression. Although not a smooth change, the σ1 directions in Fig. 7 are consistent with this. The plot in Fig. 9 does not correspond to any of the plots in Fig. 7, all of which have σ1 at a shallower inclination than 45o and thus have associated planes of maximum shearing stress that are neither vertical or horizontal, unlike the situation in Fig. 9. The one closest to horizontal thus cannot be considered a plane of simple shear. The 'shear plane' must always be the presumably sub-horizontal glacier bed.
This Figure cannot hold a substantial revision. Therefore, we removed it and all parts in the text.

Line 340. I disagree with the statement here (see comments for lines 210-213). Although the absolute value of the vertical normal stress increases with depth, the deviatoric vertical normal stress changes much less. It is the increase in base-parallel shear stress combined with the horizontal compressive stress (σxx if you like) that causes σ1 to rotate from near horizontal at the surface to inclined at some angle of less than 45° at the base.
Indeed, the vertical stress σ d zz is not responsible and actually decreases in our revised model with increasing depth. We will change this conclusion accordingly and agree with your suggestion that the orientation is driven by σ d xz and σ d xx Line 342. The second part (ii) of the explanation for multimaxima fabrics given here makes no sense by itself. All states of stress that are non isotropic involve shear stresses. If the multimaxima fabric depended solely on the state of stressthat is with instantaneous adjustment of the c-axis fabric as the stress field changes -then there should be a constant relationship between the positions of the maxima and the principal stress directions. This clearly is not the case as the relationship in the deepest sample shows. There is, however, as you note, a consistent relationship between the fabric and the σ1 direction through most of the glacier and in all cases, with small deviations, the centroid of the COF fabric and the σ1 direction lie in the vertical plane that contains the flow direction. This is a key relationship that I believe you have only partly explained.
We also put a larger emphasis on the fact that the general COF pattern is aligned with the flow direction (with an exception in 79 m).

Substantial Changes:
Introduction: Here we flipped two paragraphs as it improves the readability of the manuscript. Furthermore we changed the quickly changing simple and pure shear interfering and changing compressional, extensional, and shear stress conditions along the valley in combination with Data acquisition: We moved the modelling part to an individual section and corrected some writing errors.
Ice flow modelling We moved the details of the model to a new individual section. We provide more details and additional basic equations (Glens flow law and Weertman's friction law) for a better understanding. Furthermore, we got some information about the basal velocities. We used these information to further constrain our model. We also include details about sensitivity studies and explain more in detail why we use the respective parameters.

Crystal Orientation Fabric Analysis
We removed the details about the LASM measurements as they are no longer needed (see changes in Discussion).

Results
We added some more details about the eigenvectors (vaules and ranges) and a more precise distinction between mid-point and centroid. Furthermore, we considered literature recommendations from the reviewers.

Interpretation
Here, we added a general description about the stress conditions in the glacier and highlighted the dominant elements of the stress tensor. Furthermore, we calculate the strain rates and provide all modelled stress and strain rate components in tables. The strain rates cannot be derived directly from our model as we ran it in stationary fashion. Therefore, we calculated the strain rates via Glen's flow law. We described more precisely the correlations between glacier flow and c-axes orientations for the observed azimuthal and co-latitudinal variations. For this, we used the previously defined deviatoric stress components as references and to enhance the readability.
Especially in subsection 6.3 we removed the imprecise and speculative parts as criticised by both reviewers. Instead, we provide a detailed description about the recrystallization mechanisms that we believe are most important for our observations. Based on this RX-mechanism we provide an interpretation for the formation of the observed multi-maxima. We also added further details to the results shown in Table 4 (previously Table 2). These classifications are more useful for our interpretation than the previously employed LASM scans. Therefore, we removed these LASM-scans and the information about them.

Discussion
In our discussion, we mainly revised the parts about recrystallization and restructured this section. Fat first, we compare our findings with other field studies, then with laboratory experiments and afterwards we describe in detail the recrystallisation. We explain in detail, why we follow the approach of Faria et al (2014) and explain the difference to previous studies. Based on these findings we discuss the formation of the multi-maxima pattern. We also consider additional hypotheses and mention them in the discussion. However, we removed the speculative part in conjunction with Fig. 9. This part cannot sustain in a thorough review.

Conclusion
Based on the changes in our discussion, we also rewrote parts of the conclusion. We mainly included the effects of SIBM-N and removed the (obvious and useless) statements that simple shear and compression are the main driving forces.
The ice of temperate glaciers is comparable with a metamorphic rock close to its melting point (Hambrey and Milnes, 1977) that has been exposed to a long series of deformation processes along the valley. This deformation is caused by various shear 45 and compressional stresses that have been applied to the ice. These stress regimes produce heterogeneously distributed dislocations, which cause dynamic recrystallisation by rearrangement of these dislocations or ::: and : by internal strain energy reduction.
In this study, we analyse ice core samples from a temperate alpine glacier. We describe and compare our findings with studies from the last century and provide a hypothesis for the resulting COF in terms of given stress and temperature conditions. We analyse the stress regime in the vicinity of the ice core, using additional borehole measurements and discuss recrystallisation processes and grain growth in temperate ice. For selected examples we take a closer look at the development of new ice crystals 70 under the current stress regime of the glacier. The microstructural results of this study serve as a basis for geophysical experiments on ice core samples , which will be discussed in an accompanying paper, and they can ::: also be compared with results from larger scale geophysical experiments.

Field Site and Data Acquisition
The field work was carried out on Rhonegletscher, located in the Central Swiss Alps (Fig. 1). This glacier currently covers an 75 area of about 15.5 km 2 and is flowing in a : southern direction from 3600 m a.s.l. down to 2200 m a.s.l. It is a medium-sized valley glacier, easily accessible, and therefore investigations were ::: had :::: been : carried out already in the last two centuries and continuously since 2006 .
In August 2017, the ice core was drilled ::: we ::::: drilled ::: an ::: ice :::: core in the ablation area of the glacier (Fig. 1), approximately 500 m north of its current terminus. Here, the ice was flowing with an average surface velocity of 16.2 m a −1 in the season 2017/18 80 according to GNSS measurements. This location was selected, because the glacier surface forms a relatively even plateau with only 5 m elevation change over a distance of 40 m and is free of crevasses. Further up-glacier there is a steep and crevassed area. An analysis of the bedrock with ground-penetrating radar measurements also confirmed a transition from a steep to a more flat zone of the valley  at the ice core location.
As the ice is just at the pressure melting point, :: we :::: used : a thermal drilling technique (Schwikowski et al., 2014)was used.

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Although hot-water drillings, performed in the vicinity of the ice core location, showed a mean ice thickness of 110 m, the drilling was stopped :: we ::::::: stopped ::::::: drilling at 80 m, when hitting some gravel, which . :::: This :::::: gravel blocked the cutter head. An ::: We ::::::: retrieved ::: an 80 m long ice core, with a gap between 46 and 50 m due to technical issues, was retrieved. Due to the thermal drilling technique, which did not apply a rotational force onto the ice core segments, an oriented retrieval of the segments was possible. A freshly drilled segment was manually connected to the previous one, which worked out well 90 for most of the segments. Additional measurements of the Earth's magnetic field, while drilling, could be used in some cases to reconstruct the orientation within a range of ±10 • when matching of neighbouring segments was not possible.

Crystal Orientation Fabric Analysis
For detailed structural investigations of the temperate glacier ice, :: we ::::::::: performed : a COF analysis was performed in the laboratories of the Alfred-Wegener-Institute Helmholtz Centre for Polar and Marine Research (AWI). The ::: We :::::::: measured ::: the orientation of the c-axes of the ice grainswere analysed to determine the orientation of the crystals. The c-axis is the symmetry axis perpendicular to the basal plane of a hexagonal crystal. Along the c-axis, the physical properties , such as bulk and shear modulus, differ significantly from any direction parallel to the basal plane (the a-axes). The elastic parameters of the ice, such as bulk or Paterson, 2010, chapter 3). This results in anisotropy effects, which lead, for instance, :::: leads : to different velocities for acoustic waves travelling through the ice (e.g. Diez and Eisen, 2015).
From the ice core extracted from the central borehole BH00 (Fig. 2), seven samples at depths of 2, 22, 33, 45, 52, 65 and 79 m were considered. Due to technical problems during the core retrieval, the azimuthal orientations of the samples at 2 and 45 m depth are subject to some uncertainties. Their azimuthal orientations were thus obtained from extrapolations from adjacent 145 measurements.
Each of the seven samples consisted of an ice core segment of about 50 cm length. Up to four 11 cm long adjacent sub-samples ( Fig. 4) were prepared from each of these segments. Each sub-sample was then further dissected into a horizontal and two vertical cuts, all three . ::: All :::: three :::: cuts ::: are : perpendicular to each other (Fig 4). This resulted in a horizontal circular slice and two vertical slices with SN-and EW-orientations from which thin sections were prepared. Between :: We :::::::: measured :::::::: between 8 and 150 12 thin sections per sample and 77 thin sections in totalwere measured. This procedure enabled a more comprehensive analysis of the large crystals existing in temperate glacier ice (e.g. Kamb, 1959;Rigsby, 1960) and fractures : a :::::: tracing ::: of :::::: fissures ::::: (also During the preparation of the ice thin sections, large-area scanning macroscope (LASM) images (Binder et al., 2013;Krischke et al., 2015) were taken from the polished surface of the 1 thick ice samples. As discussed later, these images provide important information on the grain boundary network as well as the air bubble distribution, since light from the active camera is backscattered to a great extend by the evenly polished ice surfaces. Uneven parts, such as air bubbles or grain boundaries, reduce the amount of 160 backscattered light and appear darker in the image.All sections were analysed using polarised :::::::::::: cross-polarised : light Peternell et al., 2009). The :: We ::::: used ::: the automatic fabric analyser G50 from Russell-Head Instruments  was used to measure the orientation of the c-axis on a predefined mesh grid with a pixel resolution of 20x20 µm 2 .
The eigenvectors of the polycrystalline orientation tensor were calculated for each depth, and they are also shown in the stereo plots (blue dots in Fig. 5). For an enhanced visibility, the normal plane for :::: plane :::::: normal :: to : the eigenvector associated with the largest eigenvalue :: λ 1 is indicated with a dashed blue line. This eigenvector is plotting in the centre of the four-point-maximum.

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To check the consistency of the individual orientations, the c-axis distribution for each sub-section (horizontal, east-west and south-north) was analysed separately. Figure 6 shows the results for the sample at 33 m depth. All three sub-sections show a similar pattern. The individual maxima appear in all sections and are not a result of stitching differently orientated sections together. However, due to the afore-mentioned reasons, the actual grain size is difficult to determine. Individual analyses for the other depths showed similarly consistent results (not shown).
To aid :::::: support : the interpretation, the stereo plots in Fig. 5 are shown again in Fig. 7 with adjustments as a result of the following 255 interpretation. Here, only the colour-coded c-axis :::::: density : distributions are plotted, superimposed by additional information obtained from accompanying analyses.
The uppermost sample (2 m) does not fit into this interpretation. Although the magnetometer data are consistent, the onset 270 ::: core :::::: break between two segments at 10 m was unclear and we cannot fully exclude a misorientation between the segments in 2 and 22 m. As shown in Fig. 7 an azimuthal correction of -60 • would lead to a perfect alignment of this sample with all other observation ::::::::::: observations and the modelling results for the particular location. Therefore, we assume a misorientation of the core segments. However, the orientation of the pattern in 2 is in alignment with the glacier flow about 800-1000 up-glacier ( Fig. 1). As the absolute stress and strain rates are lower at the surface, the pattern close to the surface might not be reshaped in 275 the last 1000 of ice flow and thus show the remnant orientation further up-glacier when the ice was buried deeper in the glacier and thus exposed to higher absolute stress and strain rates.
A possible explanation of this observation includes ::: The :::: most ::::: likely :::::: reason ::: for ::: this :::::::::: observation :::::::: involves recrystallisation pro-310 cesses. As described in Duval and Castelnau (1995) and Schulson and Duval (2009, chapter 6), it can be distinguished between rotation recrystallisation, which is observed primarily in cold ice (e.g. Lipenkov et al., 1989), and migration recrystallisation, which seems to be the dominant mechanism in temperate ice near the pressure melting point (e.g. Gow and Williamson, 1976; . In a more recent work ::: For ::: our ::::::::::: interpretation ::: we :::::: follow ::: the ::::::: approach : of Faria et al. (2014b), these processes are no longer just attributed to temperature, but to temperature in combination with cumulative strain and the term dynamic recrystallisation is 315 used. In any case, dynamic grain growth and the formation of new nuclei are dependent on temperature, as the grain boundary mobility depends on the general energy state of the system, and strain rate due to dislocations being formed during deformation.
Under constant strain rates, higher temperatures cause an increased grain growth (Schulson and Duval, 2009, chapter 6) and a faster recrystallisationin case of inadequately oriented grains and heterogeneous distribution of dislocations in neighbouring grains (Weikusat et al., 2009b, Fig. 8). As explained in Cuffey and Paterson (2010, chapter 3), c-axis orientations, resulting 320 from migration recrystallisation tend to deviate from the principle compressive stress direction (σ 1 ), as observed in Fig. 7.
If the recrystallisation would be the result of an unconfined compression only, one should observe a continuous distribution of the c-axes along the small circle girdle (black circles in Fig. 7). Instead, the orientations typically cluster around four maxima lying on these circles. As shown in Figure 3.7 in Cuffey and Paterson (2010, chapter 3), this can be explained by a combination of compressional and shear stresses. The modelled stress tensor provides hints for increasing shear stresses 325 (τ xz )with depth, and also borehole inclination measurements provide some evidence for the occurrence of shear stresses.

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Interestingly, in more recent studies on other temperate glaciers multi-maximum :::::::::::: multi-maxima fabrics in combination with a large grain size were only observed in the deepest parts of the ice cores (e.g. Tison and Hubbard, 2000). However, following the argumentation in Faria et al. (2014b), strain-induced boundary migration (SIBM) and grain growth is not a result of temperature alone. Grain growth and the formation of new grains depends on temperature and strain rate. Most likely, the observed "diamond shape" pattern only develops under strain-induced boundary migration from new grains (SIBM-N) at high strain rates, in 385 contrast to SIBM-O which already takes place at lower strain rates (under similar high temperature conditions) and in which the old grains are still in place (Faria et al., 2014b, Fig.13+14) ::::: drilled :: in ::: the ::::::: ablation :::: zone :::::::::::::::::::::::::: (e.g. Tison and Hubbard, 2000). The conditions for a ""diamond-shape" : " : pattern seem to be suitable in larger :::: large : glaciers like the Rhonegletscher , whereas in smaller and thinner glaciers, such as Glacier de Tsanfleuron investigated in Tison and Hubbard (2000), the strain rates might be smaller due to the lower ice thickness and thus the multi-maxima patterns develop only in the deepest parts with 390 presumably the highest :::: with :::: high : strain rates. In contrast, in polar ice cores the strain rates are expected to be large enough , but ::: too, ::: but :: a :::::::::::: multi-maxima :::::: fabrics ::: has :::: been :::::::: observed : only in the deepest parts also the temperature conditions are fulfilled for multi-maximum fabrics as observed in :: of some Antarctic and Greenlandic cores (Gow and Williamson, 1976;Thwaites et al., 1984;Montagnat et al., 2014). ::::: There, ::: the :::::::::: temperature ::::::::: conditions ::: are ::::::::: similarily :::: high :: as ::: in :::::::: temperate ::::::: glaciers :::: like ::: the ::::::::::::: Rhonegletscher. The results of Thwaites et al. (1984) for the multi-maximum :::::::::::: multi-maxima ice at the base of Cape Folger ice 395 core show the largest similarities (orientation in relation to observed stresses, grain size structure, and the opening angle of the multi-maximum :::::::::::: multi-maxima structure) with our results. To sum up this argumentation, multi-maxima patterns only form under high temperatures and high strain rates (SIBM-N case). Only if a certain strain rate is applied to the ice, the pattern is created in alignment with the deformation. This may explain why the COF at the depth of 2 ( Figure 5) does not align with the current glacier flow. The absolute strain rate close to the surface is expected to be lower than deeper in the ice. Presumably, 400 this strain rate at the current location is too low for a SIBM-N to take place and thus the previous orientation when the ice was buried deeper in the glacier and exposed to higher strain rates is preserved. The orientation fits to the flow about 800 up-glacier.