Review of the manuscript entitled, “In-situ estimation of ice crystal properties at the South Pole using LED calibration data from the IceCube Neutrino Observatory” submitted to The Cryosphere

This study discusses propagation patterns of the ~400 ns wavelength light wave (or photons) within a thick ice sheet at South Pole, Antarctica, with a local condition of the crystal preferred orientation (CPO), grain shape and size of polycrystalline ice. The authors (a team of very many people) used ~5000 photomultipliers installed within the ice sheet, as IceCube Neutrino Observatory instruments. Through procedures for calibration of the light emitters and the receivers, the authors discovered unexpected light propagation effect within the ice sheet. The authors described it as “an anisotropic attenuation”. It is orientation-dependent variations of the received light, which has directional dependence of wave propagation along the flow direction of the ice sheet. The authors examined birefringence of ice crystal grains, that is, anisotropic properties of reflections and refractions at ice grain boundaries, birefringent propagation within each crystal grains, as well as additional effects from grain shapes and sizes as possible main causes for the observed effect. The authors examined both orientation dependent scattering effects due to impurity-related inclusions and various effects related optical birefringence of ice. They claimed that they made a model that is quantitatively accurate for optical properties of the IceCube glacial ice. They found an explanation as to why curved light trajectories occur resulting from asymmetric diffusion. To harmonize between simulated effects using their model and the observational data in the field laboratory, the authors raised a possibility that ice crystal may have anisotropic absorption properties and stress-strain induced changes in optical properties, which is still unknown in the research field of ice physics. 

General comments

I put number to each section of comment.

[G1] This is an interesting and informative paper in which the authors examined propagation of light wave (photons) within the thick polar ice sheet, using a local area (~1 km³) of the ice sheet as a field laboratory. Ice has special crystal orientation fabric and undulation of internal layers in the vicinity. To my knowledge, there seems no prior studies who found or explained propagation of light wave within a condition of a particular crystal orientation fabric. Basic investigations that the authors performed seem sound, such as CPO, grain shape and size, and propagation of light wave within polycrystalline ice.

I must confess that for a few sub-sections of the manuscript, I found difficulty to understand.

The study also clarified that there were still many major unknowns, such as anisotropy in imaginary part of the refractive index of ice single crystals (in crystal lattice) or stress/strain induced properties. I must note that there is major uncertainty in the discussions. Possibilities that the authors raised – ice crystal lattice should have both anisotropic absorption properties and stress-strain induced changes in optical properties – may be either correct or incorrect. If it is correct, we must find yet-unexplored physical properties of ice. If the hypothesis is incorrect, there can be major points to reconsider, repair or modify in their models. Questions are open now. My concern is that in this study there are accumulated errors in model simulations, and then possibly false reasons are examined attempting to explain them, without knowing they are errors.

[G2] This paper is useful and important for people who analyze Cherenkov light in the IceCube project. They need to know accurately how light wave have nature of light propagation in glacial ice. In terms of cryospheric sciences, it may provide insights into crystal properties in the ice sheet. What seems robust and new is light propagation within preferred orientation of ice lattice, grain shape and size and grain boundary network. In terms of cryospheric sciences, immediately useful practical applications are not clear at least for me.

[G3] In this paper, many factors that can affect propagation of light wave were discussed. However, I felt that they are not well listed or summarized to be understood comprehensively. The authors tend to list them one by one in different sections within the manuscript. Sometimes they were mentioned only conceptually and vaguely such as “the first-order principles”. I suggest that the authors should provide a table (or tables) as supplementary information, listing items, shape and size of the items, state of presence (or distribution), possible effects in terms of light wave propagation, reference papers, and notes (such as unknown, hypothesized by this work, and so on). Such tables will help better understanding. Possible items that are useful for readers are, for example, as follows.

I. Ice matrix items that can cause effects of reflection, refraction, scattering or absorption.

Anisotropic refractive index (real part) of ice in each crystal grain

Crystal Preferred Orientation

Grain shape and size

Distribution network of grain boundaries in terms of ice fabric, grain shape and size

Distribution of triple junctions of grains in terms of ice fabric, grain shape and size*

*The authors did not mention it. But it is one of major locations for presence of impurities. See Stoll et al. (2021) given in [D19] below.

Anisotropic refractive index (imaginary part) of ice in each crystal grain

II. Clathrate hydrate inclusions

Number density, size distribution and possible localization within ice matrix.

III. Various inclusions

Dust (Number density, size distribution and possible localization within ice matrix).

Salt particles (Number density, size distribution and possible localization within ice matrix).

Acids (State of presence and possible localization at triple junctions)

Soot (Number density, size distribution and possible localization within ice matrix)

Volcanic ash (Number density, size distribution and possible localization within ice matrix)

Possible alignment of these items along some orientations

Possible effects from stress/strains or pressures

Also, the authors cited an old textbook by Hobbs published in 1960s. Rather than citing such old very thick textbook, I suggest the authors to cite responsible original papers which really addressed points. For readers it is hard to find out points of discussions in thick textbooks. Also, similar situation occurs when citation is PhD thesis.

[G4] As for citations for the glaciology-based information, there are points that seems necessary to be updated, or more proper papers should be cited. In detailed comments, I will comment one by one.

[G5] My concern as for the structure of the paper is sequential order of Section 4.3 and Section 5. Section 4.3 discusses early empirical modelling, given just after the observational results (Sections 4.1 and 4.2). When we think about glacial ice as a media of light propagation, it seems natural that light diffusion in birefringent polycrystals should be taken as one of substantial bases. This phenomenon should have priority to be discussed. And then, empirical modelling related to absorption should be provided as the item with secondary priority because in this aspect modelling attempt does not seem very successful to explain observations. In addition, assumptions for directional dependence for absorption seem to be suffered from lack of observational evidence.

For readers, they need to be informed, with an order of importance. Present order will tend to confuse readers, as I felt so.

[G6] Length of the manuscript

Main text alone has 14,000 words. The paper is very long. For a better readability, this can be more concise, by sending some parts to supplementary information.

Detailed comments

[D1] Abstract, Lines 4-5:

I suggest that “Birefringent light propagation has been examined” can be modified as “Birefringent light propagation through networks of ice grain boundaries has been examined” (or something like this) to stress substantial points, medium of propagation, in this study. It seems that birefringence is one of components in the model. But it seems that grain boundary network closely related to ice fabric is also one of essential conditions. The authors termed as “birefringence model”. My concern is adequacy of this vague wording. Please choose more concrete terms.

[D2] Abstract in general:

Readers of this paper will wonder if this paper discusses polycrystalline properties, ice lattice properties within single crystal, or both. Indeed, this paper discusses both. Please consider a possibility that the authors already mention these key points in the abstract. It seems fairer then.

[D3] Abstract, Lines 6-8:

Only polycrystalline properties are given. How about lattice properties?

[D4] Citations in general:

It seems to me that several citations require "e.g.," because they are not unique choice of possible citations. In the introduction, Cuffey, McConnel, Faria, and Alley papers (books) are such examples. Cuffey citation is a textbook where established knowledge is reviewed. McConnel is a very old paper. Anisotropy in plastic deformation of ice was reviewed in many textbooks of ice, such as Hobbs, Petrenko&Whitworth etc. Rather than giving only one, the most original paper, it is beneficial for readers to find recent textbooks as well. Alley 1988 is one of papers in which the measurement method was applied. I suggest that useful method papers for readers include, as follows.

Langway, C. C. J. (1958), Ice fabrics and the universal stage., SIPRE Tech. Rep., 62.

Wilen, L., C. L. DiPrinzio, R. B. Alley, and N. Azuma (2003), Development, principles and applications of automated ice fabric analyzers, Microscopy Research and Technique.

[D5] Lines 20-21:

The authors mention only a case of growth of vertical girdle fabric here. At this stage of this paper, the authors should assume that readers do not know how special the cases of the vertical girdle fabric are. The authors need to specify type of strain, compression, extension, or shear. If the authors express c-axes orthogonal to the strain, it is response to the extensional strain or convergent ice flow.

[D6] Lines 22-23

This statement is wrong: vertical girdle fabric is typical only at ice divides and in convergent flow. They are rather limited zone in the ice sheet. It will not occur in divergent flow or simple laminar flow.

[D7] Line 23 “aforementioned scenario”

Despite these words, it was not mentioned before in this manuscript. It seems that this manuscript takes the girdle fabric as a basis. Please inform non-specialist readers of more general aspects, such as relations between type of strains and consequent preferred orientations of the c axes.

[D8] Lines 29-30, citation of Linow

Linow et al. (2012) discuss a very special case of firn, and not ice-depths below pore close-off. In ordinary ice cores using X-ray CT, we will not observe presence of grain boundaries, grain volume or grain elongation. Please rewrite and repair this part of description. Please do not mislead readers. In addition, X-ray CT is available even for whole cylinder of ice cores. Please look at Freitag 2013 paper indicated below for example. Thus, "these techniques further restrict the sampling volume" is not correct as a general statement.

Freitag, J., S. Kipfstuhl, and T. Laepple (2013), Core-scale radioscopic imaging: a new method reveals density–calcium link in Antarctic firn, J. Glaciol., 59(218), 1009 - 1014, doi:10.3189/2013JoG13J028.

[D9] Lines 30-31:

It is sudden that the authors mention thin slices here. It is nothing to do with previous sentences.

[D10] Around lines 32-33:

I suggest that a method described in papers below is available for detection of ice fabric using thick volume of ice core using radio-wave birefringent nature of polycrystalline glacial ice. Because your context is on limitations of earlier methods, these seem necessary citations.

Saruya, T., S. Fujita, and R. Inoue (2022), Dielectric anisotropy as indicator of crystal orientation fabric in Dome Fuji ice core: method and initial results, J. Glaciol., 68(267), 65-76, doi:10.1017/jog.2021.73.

Saruya, T., Fujita, S., Iizuka, Y., Miyamoto, A., Ohno, H., Hori, A., Shigeyama, W., Hirabayashi, M., and Goto-Azuma, K.: Development of crystal orientation fabric in the Dome Fuji ice core in East Antarctica: implications for the deformation regime in ice sheets, The Cryosphere, 16, 2985–3003, https://doi.org/10.5194/tc-16-2985-2022, 2022.

[D11] Lines 33-34:

I did not understand a relation between "can not only be imaged in ice cores" and the rest of this sentence. As for meaning, I did not find good link.

[D12] Line 41: Optical anisotropy

Term is vague. Please specify as optical anisotropy of polycrystalline glacial ice, single crystal, or both.

[D13] Lines 42-46: “The effect was originally modelled as a direction-dependent modification to Mie scattering quantities, either through a modification of the scattering function as proposed by Chirkin (2013d) or through the introduction of a direction-dependent absorption as introduced by Rongen (2019). As also shown by Rongen (2019), both parameterizations lack a thorough theoretical justification and resulted in an incomplete description of the IceCube data.”

Please specify, at least, how these authors assumed sources of scattering or absorption. Otherwise, readers do not easily understand what kinds of studies they have done before unless they visit these papers and read closely. Also, it is hard for readers to explore someone’s PhD thesis.

[D14] Line 47: grain size

Please specify size range, to provide not only concept but also range of quantity.

[D15] Line 48: grain boundary properties

What kind of properties? Please specify to readers, to provide not only concept but also concrete physical basis.

[D16] Lines 53-54:

Please explain to readers about physical mechanisms responsible for the scenario of the diffusion. Things are explained rather conceptually around this part of the paper.

[D17] Line 110

Bubble – clathrate hydrate transition occurs as a thick zone ranging several hundred meters. Please let readers know it.

[D18] Lines 137 – 138

When you express as “ice”, please specify whether it is polycrystalline glacial ice or intrinsic nature of single crystal of ice. Otherwise, it will be one of sources of confusion for readers. When you discuss nature of absorption or scattering, we need to know, if nature under discussion is polycrystalline ice with grain boundary network or not. Also, we need to know if nature is for ice that include various kinds of impurities/inclusions or not. Please be careful on this point throughout this manuscript.

Specifically at lines 137-138, please clarify if Warren and Brandt assessed nature of ice sheet ice or not.

[D19] Lines 139-141, “The impurity constituents are believed by He and Price (1998) to be dominated by mineral dust, marine salt and acid droplets as well as (volcanic) soot.”

I understand that He and Price (1998) paper summarized possible materials that can interact with light, with their knowledge in 1998. However, there are advancement of science in cryospheric sciences.

I suggest that the authors to consider providing updated knowledge, rather than drawing attentions of readers to old belief of 24 years ago.

Just as an example, I provide one of possible statements.

The impurity constituents are dominated by insoluble mineral dust, salt components, liquid phase acids, soot and volcanic glass (e.g., Arienzo et al., 2017; Barnes et al., 2003; Narcisi et al., 2005; Sakurai et al., 2011; Stoll et al., 2021).

Points: Belief by He and Price seems old to cite here now in 2022. Chemical reactions related to salts are much more understood nowadays. Various chemical reactions occur in the atmosphere during transport of aerosols and in snow and firn to general salts and acids in ice. In addition, soot is not related to volcanic eruptions (though there may be exceptions). Droplet does not seem proper wording. Acids sometimes exist at grain boundaries as liquid depending on components, temperature, and chemical reactions. Particles that come from volcano is glass shards.

Here, possible citations are as follows. There are much more choices.

Arienzo, M. M., McConnell, J. R., Murphy, L. N., Chellman, N., Das, S., Kipfstuhl, S., and Mulvaney, R. (2017), Holocene black carbon in Antarctica paralleled Southern Hemisphere climate, J. Geophys. Res. Atmos., 122, 6713– 6728, doi:10.1002/2017JD026599.

Barnes, P. R. F., E. W. Wolff, H. M. Mader, R. Udisti, E. Castellano, and R. Röthlisberger (2003), Evolution of chemical peak shapes in the Dome C, Antarctica, ice core, Journal of Geophysical Research-Atmospheres, 108(D3), doi:412610.1029/2002jd002538.

Narcisi, B., J. R. Petit, B. Delmonte, I. Basile-Doelsch, and V. Maggi (2005), Characteristics and sources of tephra layers in the EPICA-Dome C ice record (East Antarctica): Implications for past atmospheric circulation and ice core stratigraphic correlations, Earth and Planetary Science Letters, 239(3-4), 253-265, doi:10.1016/j.epsl.2005.09.005.

Sakurai, T., Ohno, H., Horikawa, S., Iizuka, Y., Uchida, T., Hirakawa, K., & Hondoh, T. (2011). The chemical forms of water-soluble microparticles preserved in the Antarctic ice sheet during Termination I. Journal of Glaciology, 57(206), 1027-1032. doi:10.3189/002214311798843403

Stoll, N., J. Eichler, M. Hörhold, W. Shigeyama, and I. Weikusat (2021), A Review of the Microstructural Location of Impurities in Polar Ice and Their Impacts on Deformation, 8, doi:10.3389/feart.2020.615613.

In addition, as for clathrate hydrate crystals, a paper below seems informative for examination of light wave propagation, even if the authors evaluate possible effects are negligibly small. In the present paper, you are discussing weak changes in refractive index. There is huge amount of clathrate hydrate crystals in the ice sheet. Thus, readers need to know this presence is properly assessed by the authors.

Uchida, T., A. Miyamoto, A. Shin’yama, and T. Hondoh (2011), Crystal growth of air hydrates over 720 ka in Dome Fuji (Antarctica) ice cores: microscopic observations of morphological changes below 2000 m depth, Journal of Glaciology, 57(206), 1017-1026, doi:10.3189/002214311798843296.

[D20] Line 145:

I suggest that “climatological conditions” can be “climatological conditions such as dusts and aerosols in the atmosphere in the past” to be more concrete.

[D21] Lines 170-171:

The authors wrote as “The limited volume of the ice cores does thus not allow for a direct measurement of optical properties, even though they are able to inform on the impurity constituents and their size distributions.”

It seems a vague and subjective statement. There should be many methods to directly measure “optical properties” of ice. You state generally as optical properties; it seems impossible to provide a statement like this. You mention propagation through distance of 100-400m. If we can prepare proper experimental setting, we may be able to detect it.

Later at lines ~290, you showed directional dependence of the signal was double for propagation of 125 m. If assume that directional dependence of the signal was 3dB / 100m as approximation, for diameter of an ice core (0.1m), it is 0.0003dB/0.1m. It is far better if the authors provide size of numbers that is necessary for a scale of ice core measurements.

[D22] Line 184:

Please clarify meaning of “ice realizations” to the readers of TC. I did not understand what was meant. My concern is that the same problem happens to many readers of TC.

[D23] Line 187:

c_ice is not defined anywhere. I imagine it is speed of light in ice. I wonder if it is an expression commonly used in physics.

[D24] Lines 187-189:

I did not find definition of scattering coefficient in the equation. Did you simply rephrase “diffusion coefficient” as “scattering coefficient”? If it is so, please make it clear to readers.

[D25] Lines 190-191:

I was confused at multiple points. Please let us understand why this is inaccurate. Please let us know why an assumption of clear and layered ice causes problem? What do you mean with a word “layered”? Do you mean layers caused by deposition layering? Alternatively, do you assume presence of layered propagation paths?

From here, please note that my understanding after section 3.2 was bad, even after reading the paper many times. I ask the editor to find a reviewer who can fairly evaluate these sections.

[D26] Section 3.2 in general

I did not understand how your Photon Propagation Code (PPC) was used. Please let readers know how you assumed many physical properties of ice and inclusions, in your PPC calculations.

[D27] Sections 3.2 and 3.3 in general

It was hard for me to understand this part of the paper. Possibly, some scientists can understand these sections without difficulties.

[D28] Figure 5:

I did not understand the authors’ purpose of showing this figure. I wonder why mixtures of data from various origins were given here.

[D29] Sections 3.4

I did not understand the model “South Pole Ice Model”. It seems again vague words. What kind of model to analyze what? What are the parameters? If you call it as Ice model, again it seems vague as a term. Can it be ice flow model, light wave propagation model in ice, or ice sheet model related to absorption and scattering? Do you mean profiles in Figure 5 as layering model?

[D30] Line 274:

I did not understand meaning of “footprint of IceCube”. Is it related to footprint of the radar beam pattern in IceCube experiment area? Is it area and depth ranges where you covered by IceCube experiment? If true, why was a term footprint used?

[D31] Line 276 “laminar flow as described by Aartsen et al. (2013a)”

Are you describing flow regime of the ice sheet? Please state more in detail to make it understandable to readers. Also, the vertical girdle fabric should develop under conditions of convergent ice flow. If it is simple laminar flow, presence of the vertical girdle fabric should not be explained. Please provide a brief statement as to how this ice fabric developed within the ice sheet with laminar flow dominated by simple shear strains. Simple shear will give single pole fabric.

[D32] Line 281:

Please word “ice model” (again vague) as ice sheet flow model or something like this to make it understandable. By choices of terms, I was often confused.

[D33] Lines 284 and 290:

“Ice optical anisotropy” does not seem proper term in physics because main topic in this paper is for the polycrystalline ice within the ice sheet. If wording is ice optical anisotropy, it is vague; not a few readers will first think about optical properties of single crystal ice. Wording something like “anisotropy in optical properties within the ice sheet” or “optical anisotropy in polycrystalline glacial ice “ seem better. Please consider.

[D34] Lines 305-311:

I did not understand statements related to elevation angle. My concern is that not a few readers will experience the same. Similarly, I did not understand a situation why this is a parameter which is hard to accurately obtain from ice core data. Please make it understandable.

[D35] Figure 8:

I was again confused with reasons below.

• Photon counting perpendicular flow axis is larger than that along flow axis. It does not seem in agreement with Figure 6.
• On the left panel, a peak for the scatter case is at a timing smaller than a peak for the absorption case. I do not understand this timing difference. 　

[D36] Lines 329-330:

I felt that the context became unreliable to read two lines here. If the impurity particles are aligned due to stress/strain conditions, it should have been observed by ice core scientists. Is it along grain boundaries, along triple junctions, along dislocations or along crystal lattice? What kind of particles do you assume? Rather, how about alignment of triple junctions of grains along the normal axis of the vertical girdle plane (axis of tensile strain and grain elongation)?

[D37] Lines 357-386:

There is no subsection title only in this part of the manuscript. Please define what you would like to let readers know by providing proper subsection title.

[D38] Line 455:

I was not able to find Woodcock parameters in several reference papers given here. Please clarify.

[D39] Line 460:

I visited data set of Voigt (2017). Data are stored separately folder by folder; it was hard to grasp wide view in terms of depth dependence. The same situation will occur for many readers. For a better understanding, it would be nice that you prepare an appendix in which readers can browse crystal fabric pattern. It would be even more nice that Woodcock parameters are given together. Just examples from several depths will help.

[D40] A paragraph from line 462 to 475:

We can observe ice fabric, grain shape and size in Alley et al, 2021. Readers will wonder if your assumption of grain shapes agrees with reality. It is something difficult to evaluate only by reading this manuscript.

[D41] Line 477:

When you denote orientation as “tilt direction”, glacier researchers will be more familiar to a term “transverse direction”.

[D42] Figure 11:

Please explain in more detail what asymmetry of the distribution in the second and the 3^rd from the left figures mean.

[D43] Figure 11 and Figure 12 right panel:

I believe that the special case “90 degrees to flow” will attenuate to zero at the end because of scatter at randomly oriented grain boundaries. Perhaps readers should know it if my understanding is correct.

[D44] Figure 13:

It would be useful for readers if you add materials as below.

(i) Elongation 1.0 case, that is, no grain shape effects and only fabric effects

(ii) In (S2/S3) 0.0 case, that is no fabric effects and only grain shape effects

[D45] Figure 13:

Please note to readers that the scales of the ordinate are different depending on rows.

[D46] Lines 583-584:

Elongation fixed to 1.4 does not seem the same as elongation given in Alley et al. (2021). In their slide at page 10, the maximum value is 1.24.

[D47] Lines 596: absorption anisotropy by a factor of 2.45

I find no reason to support or not because there are many items of unknown. 

[D48] Line 601:

Cleaner seems a strange word. Even in case you intended to mean “more transparent”, it is not the case in the ice sheet. Degree of transparency depend on inclusions.

[D49] Lines 601-602:

In two citations, both indicate much larger grain size. Thus, quantitative much seem questionable.

Review of “In-situ estimation of ice crystal properties at the South Pole using LED calibration data from the IceCube Neutrino Observatory” by Abbasi et al.

This paper presents observations of an anisotropic effect in the calibration data from the IceCube detector near South Pole. Photons are deflected from paths that would be expected from scattering and absorption alone. Previous work has shown that this effect can only be approximated poorly using anisotropic absorption and scattering, and these effects are not on firm physical grounds anyway. In the present work, the authors consider the effect of birefringence. They essentially run simulations of the propagation of light (both ordinary and extraordinary waves) through 1000 crystals, and look at the effect of refraction and reflection as a function of the crystal shape and orientation. From this, they parameterize a relatively simple function of how the birefringence affects propagation, and include that function in the original model of absorption and scattering. They find a much better fit to observations, although this fit is still improved with non-physical anisotropic scattering/absorption effects. In addition to describing this work, there is a lot of history and background of IceCube and of other attempts to model the observations.

I must admit that it has been a long time since I had to deal with derivations directly from Maxwell’s equations such as those presented in the paper. While I was fully able to follow the arguments and derivation, I do not think I would have been able to spot an error; hopefully other reviewer(s) have that knowledge. For the portions that I can evaluate, I think the work is nearly publishable (with the exception of the second general comment), though the presentation could use significant improvement to be really digestible. I do not object to long papers, but only when it is justified by the content; here I think the paper needs to be shortened so that the point is not lost in all the other material (see first general comment). I think this will be a very nice contribution when these issues are addressed—the observations are fascinating, and I think the explanation is compelling. While there may not be wide applications, this paper describes very basic information about the properties of ice, and thus deserves to be published.

General comments:

1. The paper is very well written at the sentence level, but the larger structure leaves gaps at some points and provides overly much detail at others. I think a large part of the issue could be alleviated with a more normal paper structure describing a problem and the work to address it rather than the meandering path of the last 10 years (more on this in the next paragraph). One example of a gap is how this work fits into the context of known birefringent effects in ice (I’m thinking of birefringence at frequencies used for radar); this is addressed in Section 5.3, but that is an odd place for the reader to get the context—it would be much more at home in the introduction. As another example, Section 6 jumps in with no intro—I assume that it is there because it is computationally necessary not to explicitly model the birefringence effects in individual crystals during the simulations, but it would help if that were stated clearly. In terms of excess details, this is an extremely long manuscript; it can take a really long time to get to the explanation of how the pieces fit together, by which point the reader is already lost. For example, section (3) describing what is essentially an isotropic model of the optical properties of the detector, is not really motivated and so comes as a distraction/reads as history until much later when I understood how the parameterization from the anisotropic model was then used in the isotropic one. Some of the figures, which appear to be reproduced from elsewhere and are not particularly necessary for the present work, could be cut to streamline things; in my view, Figures 2, 3, 4, and 16 should all be cut. At a number of places, avenues that were pursued but proved fruitless are described in great detail—I would suggest cutting these down for readability.

The paper would benefit greatly from a more clear description of the observations that imply anisotropy early in the paper (like we get along with figure 8), and a description of what the goal of the paper is. The introduction perhaps attempts to do this, but it reads more like a history of IceCube optical modeling than a problem statement--perhaps this was the goal, but it appears that both the other reviewer and I found this to be challenging to read as-is. Much of the second half of the intro in some way gives what the structure of the paper will be (e.g. describing the isotropic model fitting, etc.), but it was phrased in such a way that it was unclear that these would be expanded upon and would be critical components of the present work. In my view, the abstract does an excellent job of presenting what the paper is about, but the structure of the rest of the paper then does not follow the outline laid out in the abstract. For example, it would be very helpful for the reader to know that you are going to develop a grain-resolving anisotropic optical model, from that parameterize a diffusion function, and then input that into the previous ice model.

2. Overall, I think the consideration of possible fabrics is a bit simplistic—this is fine considering the computational expense, but as of now some statements are simply incorrect. For example in Appendix A, the authors write “Woodcock (1977) realized that all possible fabric states can be visualized in a 2D plot,” which is not at all true—only a rotated form of the second order fabric can be visualized in this way. In addition to correcting mistakes like this, we need some consideration of the implications. The question that I am particularly interested in is whether the higher-order moments of the fabric have any effect on the process of interest here; in radar, only the second-order moments control the effects, but I am not sure that the arguments carry over. For example, do circumpolar hoop fabrics and other complicated fabrics which are observed in glacial ice (see, e.g. the Faria paper cited in the text for examples), behave identically to single maxima in terms of this birefringence, or do they produce some other effect? If the latter or if it cannot be determined, then the text should make clear that what was considered was only a subset of the fabrics that have a give pair of Woodcock parameters.

3. We need a better description of how the layering fits into the modeling. I think my confusion stems from a difference in how I think of layers (generally packets of ice deposited at the same time or radar reflections depending on context) and how this paper uses layers (as best I can tell, these are packets at specific depths, but I am unclear how they vary spatially and what the “IceCube coordinate system is”). This ambiguity clouds the results to a certain extent—for example, is a girdle in this coordinate system truly a vertical girdle, or is it tilted by the layer slope? While I list this as a major comment, it is only because I think it is important to address, not because it requires a lot of work—just a clear description of layers at line 148 when then first come up would satisfy me (section 3.4.1 comes late). In addition, this paragraph should make clear the extent to which the tilt is included in the model compared to being a source of error.

Specific comments and technical corrections:

20-21: The sentence ending on line 20 and the one beginning there are both incorrect. While ice is indeed mechanically anisotropic, and bulk anisotropy results from anisotropy of the grains, the development of fabric is not related to this anisotropy in such a simple way. Sometimes fabrics orient favorably to the strain direction, but for some of the most common fabrics observed in ice sheets the opposite is true; beneath divides, where the stress state is uniaxial compression in the vertical, vertical single maxima form, but compression is thought to be harder parallel to the c axis than perpendicular to it. This statement perhaps belies a misunderstanding of the multiple processes contributing to fabric development, among which on migration recrystallization is thought to have the effect described here—and migration recrystallization does not dominate fabric development everywhere (or even most places). Moreover, it is unclear what “c-axes orthogonal to the strain” means, given that strain can act in multiple directions—in the case of compression, as already mentioned, the c-axes tend to orient parallel to the direction of maximum compression.

48: The wavelength belongs in the previous paragraph describing the observation

82-82: “in addition to photons...mostly photons” is very confusing

147: “Ice layers” asks for confusion considering that the ice physically has layers that can exist on similar spatial scales. The terminology should distinguish between these and annual or radar layers. Slices? Packets?

167: This section seems mistitled—or at a minimum the title is not helpful. As I see it, this section just describes inference of isotropic properties of ice as an optical medium—so why not say that?

170: I do not see why this should be true; e.g. for absorption there is no requirement to measure exactly the e-folding distance, rather than calculating it from the absorption over a shorter distance

Figure 2: is this relevant? For this paper, simply saying that you have a photomultplier, LEDs, and associated electronics seems sufficient

184: Ice realization could use more explanation. There is more detail below, but here perhaps just “hypothesized optical properties and ice-crystal orientations”

234: I find the idea of an “error rate” to be confusing here. Does this mean there is one incident photon not related to the LED every 2 ms?

270: Layers here are still poorly defined. I suggest describing them as annual layers and noting that radar reflections result from contrasts in dielectric properties, which are generally assumed to be isochronous (although not necessarily annual).

281: This feels incomplete: I am left unclear as to whether any effect of this tilt is included in the modeling. We need a description of whether this fit into anything above and a preview of where it will become relevant below.

286: Rather than naively, which is vague, just state the assumption (i.e. that the transmission medium has only isotropic dielectric properties).

291: repetitious

310: The elevation angle is not difficult to obtain from thin sections on an ice core; the full 3d orientation of each individual c-axis is automatically analyzed. Perhaps this should say that the tilt axis is difficult to measure in an ice core, due to the uncertain orientation of the core.

Section 4.3: This is almost all repetition of published work, and the level of detail is unecessary—it should be sufficient to show the curves in Figure 8, point out that a factor of 11 is unreasonable for the absorption anisotropy, and say that the fit was mediocre when only modifying the directional scattering and absorption.

318: unclear if this applies only to Chirkin 2013d or the present work as well-defined

385: Add a reference to Petrenko and Whitworth here

454: Usually the glaciological literature refers to a single Woodcock parameter, log(s_1/s_2)/log(s_2/s_3); I assume that these parameters are the numerator and denominator of that fraction, but it would be helpful to state that explicitly

463–475: I am unclear as to how this incorporated in the results, given the lack of data. It becomes clear much later, but we need a preview

Figure 11: I am unclear on whether perpendicular to the picture is the same as perpendicular to the picture. i.e., it would be helpful to say that photons get “emitted” initially into/out of the page. I also think the description of the axes is unclear—as best as I can tell, this is a histogram of the normalized components of the direction vector? Why not use something other than n, considering that it has other meaning elsewhere?

Figure 12: Ice flow direction should be indicated. Perhaps this should come before Figure 11, to give the reader some intuition?

488: missing punctuation and article/noun mismatch

Section 5.3: Except for the directionality of the effect, the rest of this section could come much earlier (even in the introduction) and give the reader useful context.

529: I count 8 parameters—or should Eq 24 be two equations, one for x and one for y

533: Language is odd—update sounds computational but the rest of the sentence sounds physical

Figure 14: Top y-axis label is mission. I guess the panels on the diagonal are actually different than the rest? It is pretty incomprehensible as-is—perhaps some separation between those panels and the others, and something clear in the legend, would help.

573: we need a definition of pre-fits

Section 7: These results are really nice, and so I was surprised that this section was so short. As mentioned above, I think more of a traditional paper structure (where there is less history and these are the results) would be beneficial.

686: The use of such tensors dates at least to Love, 1944 “A Treatise on the Mathematical Theory of Elasticity, 4th ed.” and presumably earlier (it has a long history in elastics and fibers). In glaciology, it dates at least to Castelnau et al., 1996, “Viscoplastic modeling of texture development in polycrystalline ice with a self-consistent approach: Comparison with bound estimates.”

698: This is not true, as implied below by the acknowledgment that you cannot obtain a true c-axis distribution from these two parameters