Review of “Implementation of a brittle sea-ice rheology in an Eulerian, finite-difference, C-grid modeling framework: Impact on the simulated deformation of sea-ice in the Arctic” by Brodeau et al,  (MS gmd-2023-231) 

The manuscript describes the Brittle Bingham-Maxwell (BBM) rheology of Olason et al (2022) and its implementation into SI3, the sea ice component of NEMO. Particular emphasis is placed on the implementation of a staggered C-grid. A few simulations serve to evaluate the implementation relative to statistics of observations and the default VP-rheology with an aEVP solver. The structure of the text ist mostly clear. 

Clearly this is important work that will make it possible for a large community sea-ice/ocean/climate models to use the BBM model in their simulations. The manuscript, however, requires major revisions to turn this into a scientific paper.

Major issues

The main problem with the manuscript is that the statements in the introduction, discussion and conclusion are often not backed by the presented work. Instead, the reader gets the impression that this is a text that tries to “sell” this implementation, where a scientific paper should describe the work and provide objective statements about the value of the work in the context of the scientific discussion. Here, most of the text implies that one should only use the current sea ice model with BBM, because everyone else is getting it work. I am exaggerating a little. Because is a general “impression” after reading the text, it is  very hard to pinpoint individual issues, because the phrasing etc is scattered throughout the manuscript. Here are some more prominent example, and I have listed many places where I found the wording or phrasing to fit for scientific paper. For example:

- The statement about heterogeneity and coupled model in lines 17-20 is too strong. It should be clear that the heat fluxes are very strong in leads and that this is important, but it not as clear how important the transition from parameterising this (i.e. in terms of fraction ice cover) to resolving the leads is. As long as the atmosphere does not resolve the heterogeneity of the high resolution surface fields (typically in coupled system, atmosphere models have a much lower resolution than the ocean/sea ice system, because the characteristic eddy scale is so much larger), it is not clear if this heterogeneity has any impact on the atmosphere, because one needs to average over it anyway.

- Already in the model description section (2.3, page 7), the authors come to the conclusion that (l180) “using the C-grid is not the most appropriate choice”. Then (l183) “The spatial staggering between the point definition of the normal (diagonal) and shear (off-diagonal) elements of these tensors becomes an issue whenever the parameterization of the constitutive law requires e12 or sig12 to be known at a T-point.” 

These are unbacked statement. It may be the result of the work presented here, but cannot be the starting point. It’s clear that the spatial staggering is not good for all terms. One may argue that the stress tensor divergence is the leading term in the momentum balance. But it is not clear, why this is worse for sea ice models than for ocean models, where the dominant geostrophic balance also suffers from the velocity staggering on C-grids. That’s why early ocean models were implemented on B-grids with co-located velocities. The C-grid model has been shown to violate wave dispersion relationships and the Coriolis terms leads to numerical noise. But this noise has been found to be less problematic than the issues of the B-grid, so that now ocean models (e.g. NEMO) mostly use the C-grid in spite of problematic discretisation of the main balance in the ocean (geostrophy).

Since this manuscript stresses the staggering issue so much, it should become clear to the reader, why it is worse for the stress tensor than for velocity vector to not be collocated at one grid point.

- Interpretation of figures, e.g.

— l372 “power-law tail (in Fig7)”

Power laws lead to a straight line in a loglog plot (as the reference with -3 shows). None of the curves, not even the RGPS curve show that. Clearly the aEVP solution differs more from the RGPS solution than the BBM solution. But I think that this metric does not allow any strong conclusions (such as “suggests the advantage of BBM over aEVP”). Further the aEVP model is not tuned to give high deformation events. It is possible to do so (see Bouchat et al 2022 and Bouchat and Tremblay 2017), so this comparison does not “demonstrate higher skills” of the BBM model, but only the difference between two simulations with default parameters. I think that the authors need to tone down their conclusions.

— l389 “As illustrated in figure 8, …”

Same as before, clearly the agreement of the BBM simulation with RGPS is better, but the specific aEVP solution has not been tuned to give high deformation, so that designing a metric that emphasises high deformation (for which the brittle model family was designed) is a self-fullfilling prophecy and of little value.

What’s intersting is that the aEVP solution is not always worse than the BBM-solution (e.g. 03-15 to 04-01). It would be interesting to understand, why BBM, from which we always expect higher deformation, underestimates the high deformation events here.

— l416/Fig9: “ … but seems to break for scales larger than about 300 km”

Hutter et al 2018, doi:10.1002/2017JC013119 found that the scaling for VP models breaks down at around 10 times the grid spacing, marking the effective resolution of grid-point model where the VP model dynamics are resolved (i.e. you need 5-10 grid points to represent a sharp transition without inflicting numerical issues). With dx=10km in this simulation, it means that anything **below** 100km should be considered as unusable, i.e. the fit should be applied to the 3 points above 100km, which would lead to larger slopes. Brittle models scale down the grid scale, as they are designed to produce heterogeneity at the grid scale. The interpretation of the fig9 hence needs to be revised.

- In the conclusions we read (l520) “Based on our results, we conclude that the ability of a continuous sea-ice model to simulate the complex sea-ice dynamics across scales, as observed from satellites, depends primarily on the type of rheology used rather than on the type of modeling formalism chosen (i.e. Eulerian versus Lagrangian).”

It is very likely that this is the case, but the statement is way too strong. I think, one can conclude that the difference between neXtSIM and SI3-BBM is smaller than between the SI3-BBM and aEVP implementation (although no direct comparison with neXtSIM was made here, only indirectly), in particular in the observed statistics that are attributed to “complex dynamics” of deformation. There are no large scale comparisons about sea-ice distribution, thickness etc. so that the concluding statement can only be about the deformation properties.

Cited literature is quoted only where it fits the story of superior brittle models, but the same literature is not used to discuss the pros and cons, e.g.

- l32: “poses a fundamental and major challenge (e.g. Bouchat et al., 2022; Hutter et al., 2022)”.

Interestingly, “challenge” appears only once in Hutter et al, and never in Bouchat et al. Instead, both papers point to the ambiguity of scaling metrics and multi-fractality as a metric for evaluation different sea ice model. These references do not seem support the statement in this paragraph.

Instead, I think that Bouchat and Hutter especially highlight the need for more than one MEB model to compare to and introduce more and different comparison and evaluation tools. This manuscript introduces an additional brittle model implementation, but uses the scaling analysis that was shown by Bouchat and Hutter to be not sensitive enough to discriminate between models.

- Plante et al. 2020 is probably the first implementation of MEB on a C-grid; it’s not BBM, so the author’s can claim that their implementation is the first BBM model the C-grid, but as far as I understand the differences between MEB and BBM (limit the maximum allowed compressive strength P), the C-grid plays no role in this so we can assume that Plante et al have experienced the same issues with the C-grid report here. It is true that (l63) “The idealized nature of these simulations prevented their results from being assessed against observations of sea-ice drift and deformation.”, but equally one could say that avoiding idealised configurations makes it impossible to detect (small) implementation errors, that would, e.g., break symmetry etc. In l70, it is written that “[spatial interpolation the C-grid] is not well-suited for brittle rheologies”, but it is not mentioned that Plante et al (2020) did find a solution to obtain stable solutions by a mix of double defined variable akin to the E-grid solution presented here and averaging. In line 196, Plante et al is cited to have observed checkerboard (not chessboard) instabilities, but the authors fail to write, that these patterns never appear in the presented solution, because Plante et al designed (and described) a the numerical scheme to avoid them. Instead, the manuscript gives the impression that their E-grid solution is the only way to solve this, thereby neglecting previous successful methods.

It is also not discussed that in Plante’s model, the heterogeneity does not appear to be as chaotic and noisy as in the neXtSIM publications. Maybe it makes sense to actually try to reproduce Plante’s results?

“Cross-nudging” is a new filter introduced in the MS and this seems to be a crucial part of the E-grid it requires more attention. The authors (l263)) “conclude that the right compromise is achieved when gamma_C typically lies between 1 and 3, with 2 being the value used in our experiments”.

This is a central issue. In order to avoid the staggering issues of the C-grid, a new issue is introduced: the E-grid solutions diverge and need to be coupled explicitly. The coupling parameter is found by trial and error (fine with me), but there is no reference as to which metric is used other than “the right compromise [between smoothing and coupling]”, which is somehow related to Fig5. What is this “right compromise”? I need to know if I want to, as suggested, reject the C-grid (without attempting to fix the issues on it) in favour of an E-grid with different issues that need to be fixed. “spatial consistency”, “smoothness” (or rather the absence of it) are more soft metrics, which I cannot evaluate. I do not see a qualitative difference between 5b and 5c, but 5d appears even smoother hence it is rejected. The structure in 5a (no cross nudging) shows the checkerboard like patterns that Plante describe, but I don’t see a figure with gamma_C below 1 (but >0), where the solution is supposed to become increasingly noisy/

For choosing gamma_C, I only see the possibility of generating some reference (observational data? NextSIM output?) and somehow define a “goodness of fit” to this reference data when you tune the cross-nudging parameter. It would be very interesting to see, if one couldn’t achieve something similar with a C-grid and some averaging as done in Plante et al (2020).

There are many judgemental statements that support the general “salesman” tone of the manuscript, for example,

- l204: “To avoid the problems related to the staggering of the C-grid”

- l234: “Thanks to” 

that suggest that something is problematic, or better or worse, without any support in the text (or proof).

The language is often sloppy, there are many unnecessary repetitions. Often it sounds like listening to an informal talk about the subject (where the language would be OK to my mind). There are a few grammar problems, and many places where the formulations could be made much more concise (by removing unnecessary words and phrases).

Smaller problems, typos, technical issues:

Abstract:

page 1

l2 new spatial discretisation framework

The E-grid is only new to NEMO, rephrase

l3 well adapted to solve the equations of sea-ice dynamics

What is “well adapted” in this context. Can be removed 

l3: the numerical issues posed by the use of the staggered C-grid.

What are these issues?

l6: "when using the newly-implemented BBM rheology and when" 

grammar? Main clause is missing

l8: "the relevance of the use of this newly-implemented rheology for future modeling": Awkward, rephrase, no need to emphasise the usefulness of the present work.

l10: "This includes, in particular, coupled climate simulations performed with CMIP-class Earth System Models at coarse to moderate spatial resolution.": There is no information in this sentence.

Introduction: 

l14 Sea-ice is one of the most important physical interfaces

Not sure if sea-ice can be reduced to an “interface” (especially since this “interfaces” uses about 50% of the computer time, Table 3)

page 2

l24: "the abundance ...": Please add some references

l34: "Following the work of Girard et al.": I do not think that we need the history of brittle models again.

l45: These two constraints have proved to be impossible to respect with MEB because of an incomplete treatment of the convergence of highly damaged sea-ice, which results in unrealistic sea-ice thicknesses after a couple of years of model integration.

Does that mean, that MEB, while always being superior to other models (according to cited references), cannot even get the fundamentals right? Also, how much of this can be attributed to MEB, and how much to the specific implementation in neXtSIM?

l49: pure -> purely

l56: "excellent": What does make the scalability “excellent”? Reference? I think the use of superlative adjectives needs to be re-considered.

page 3

l60: double “))”

l74: In this paper, we propose a solution to this problem and provide a detailed description of the implementation of BBM into 75 an Eulerian, finite-difference, staggered-grid modeling framework; namely that of SI3, the sea-ice component of the NEMO modeling system.

There is a lot of repetition of previous paragraphs in this paragraph. It may be worth it to try to streamline the introduction to avoid unnecessary repetitions.

l84: some important aspects

It’s always good to “discuss some important aspects”, but what are they? Rewrite to be more specific.

page 4

eq(1) sign error in Coriolis term? Unless \vec{k} points downward.

l91: Appendix A1

It is tedious, but I think the notation needs to be introduced where it appears (on top of Appendix A1, to which I do not always want to refer, when reading the manuscript)

l92: writes -> is written as

l98: where the underbar notation indicates that the tensors are expressed in their pseudovector form, and K is the elastic stiffness tensor

I guess “K” is also in its pseudovector form? Why no underbar? The pseudo vector form is also called Voigt notation, maybe add to make it clearer to more readers.

l109: I don’t think it “happens to differentiate”, but it 

differentiates, also since it is specific to BBM, this is a bit of repetition. Please rewrite.

page 5

l110: the excessive convergence of ice when damaged

I am sure that the physical motivation for the form of this term (eq8) is described at length in Olason et al. Still it would be a courtesy to the reader to repeat the reasoning here, because it appears to be so fundamental to BBM. Otherwise it just appears to be a quick fix to solve a severe MEB problem.

l114: Ólason et al. (2022) follow Dansereau et al. (2016)

That’s nice of Ólason et al., but what do you do in this paper?

Also, what is a “two-step approach” in this context? I guess this follows in after l115, but it’s not clear from this sentence.

Don’t get me wrong, I am fine with omitting details and referring to previous papers for them, but here the mix is strange: Many (all?) details of the equations of the model are repeated, but some steps in the solution method are omitted. As a reader, I would be fine with saying: The BBM model is described in Olason et al, we do everything in the same way, please refer to Olason et al. Or put all or most of this into the appendix, as it is not new. The only information that I need as a reader is the stress tensor and its discretisation (according to the introduction and abstract).

l127: "In the case of the BBM framework, Ólason et al. (2022) and the damage criterion shown in Fig. 1 and dcrit expresses as follows"

Something is wrong with this sentence, please fix

l132: "for the healing the ice": for the healing of ice OR for healing the ice

l132: which is associated with refreezing within open leads and which is therefore based on a rate of decrease of the damage that depends on the temperature of the ice.

Please rewrite to disentangle the various relative clauses and the not always correct usage of “which” and “that”.

page 6

l145: "which" Start a new sentence, too many relative clauses

l146: "In non-regularized frameworks" Not clear what this means in this context. What is a regularised framework, in contrast?

l150: tend to exhibit very sharp gradients, or "near-discontinuities"

It needs to be shown that this is specific to brittle models. The neXtSIM MEB papers always imply this, but e.g. the fields in Plante et al (2020) are generally much smoother. Also these “near-discontinues” also appear in high-resolution VP simulations (e.g. Ringeisen et al 2019, 2021).

L152 remove the “,”

l159: "In BBM ..."

This seems to be a specific issue with the specific BBM implementation of Olason. In theory (Dansereau et al 2016 describe an iterative procedure with a tolerance, their page 1350, rhs column, Plante et al update damage, E, \lambda during an iteration), it should be possible to iterate the “two-step approach” until convergence.

This discussion about details of the timestepping and convergence is a little akin to the EVP evolution, where the somewhat naive iterative process lead to a (noisy) solution that was not intended, until papers like Lemieux et al 2012, Boullion et al 2013, Kimmritz et al 2016 came up with a solution for this (revised, modified, adaptive EVP).

page 8

l204: To avoid the problems related to the staggering of the C-grid, namely the interpolation

I strongly suggest avoiding this type of judgemental phrasing here and elsewhere, write instead: To avoid the interpolation of … due to the staggering of the C-grid …

I am pretty sure that the E-grid is not without issues, and I am waiting for similar statements about the “problems related to the E-grid”.

l209: Arakawa E-grid

BTW, there was a successful ocean model that used the E-grid: The Hamburg Large-Scale Geostrophic (LSG) model (by Ernst Maier-Reimer). Here, the E-grid was chosen, because the dominant balance (geostrophy) can be expressed more accurately and without noise while retaining some of the “nice” properties of the C-grid (representation of divergence). Maybe that’s an analogy worth mentioning.

page 9

L234 “Thanks to” -> “With”

Again this is judgemental, this time in the “positive” sense. Statements like these set a certain tone that appears biased and scientifically non-objective.

l237 “and no interpolation is needed to solve the equations” But this advantage comes with the disadvantage of the cross-nudging

l248: upper-convected time derivative

Later this term is introduced properly (l289), maybe do it here already. Or just use “advection” for simplicity here and introduce the upper-convected time derivative later.

L259 and eq16: denoted by interpF@T and interpT@F,

As this is a math expression, why not use more “math-like” symbols to denote the interpolation, e.g. \overline{\hat{\sigma}_{11}}^T, where \overline{…}^T means interpolation to T points, etc.

page 10

l264: Don’t refer to figure 5 before figure 4?

l266: horizontally and vertically aligned with the grid cells. -> aligned with the grid

There is no “vertical” in a 2D horizontal grid.

L289 upper-convected time derivative

It would be good to add a reference here, as this terminology of complex fluids is probably not common knowledge of the GMD reader.

After reading up on this (in a book about polymer flow!) it is not even clear, why we have to use the upper-convected time derivative, and not the lower-convected time derivative or a linear combination of the two. In Danserau et al (2016) something similar is called the Gordon-Schowalter derivative (it’s not the same but some linear combination of the upper and lower convected derivative), and obviously it is not entirely clear what is the correct form to use, as any frame-invariant time derivative is formally allowed. So some discussion with appropriate reference seems in place here.

Eq17 and 18 do not describe the upper-convected time derivative. WIth L in eq18 and a plus-sign in Eq17, this would be LOWER convected time derivative. 

The component form (eq19) is correct (and consistent with the form of L =  (\nabla\vec{u})^T \cdot \sigma + \sigma\cdot\nabla\vec{u}) for the upper convected time derivative)

Eq18 would give components with \partial_y U and \partial_x V exchanged (w.r.t eq19).

page 11

l299: Then, the tensor-specific contribution −L is added.

Is this done successively, I.e. use the sigmas after advection with the material derivative D/DT to compute L (i.e. some sort of split operator method), or do you use the sigmas before applying D/DT? Please be more precise.

l305: It largely inherits from LIM3 Rousset et al. (2015), to which it succeeds

Please simplify and fix in-line citations.

What are “significant inclusions”? Are they important for this manuscript? If not I wouldn’t mention that (again, we do need a full history of the model components), if important, then we need more information.

page 12

l324: “We carried out a twin coupled ocean/sea-ice hindcast,”

That is a lot of words for just saying “we compared two simulations”

l329: “while”, wrong connector, -> and

l331: For the second spin-up segment, 

Why does SI3 need this “re-initialisation”? The model should be more or less in balance with the ocean state.

Also the initialisation is short. In my experience, a sea ice model needs some 2-3 years to spin-up (the ocean model much longer, but that’s not really necessary for this paper).

l333: were extracted from a coupled OCE-neXtSIM simulation

Why do you need the solution from a different simulation to restart the model?

l335: a duration sufficiently long for the coupled system to recover from the ad-hoc reinitialization.

I doubt, that this is long enough. The fast waves will have left the domain, but everything else …?

l339: the tuning of SI3 is kept as close as possible to the default namelist

rewrite: tuning is a process and you cannot kept a process close to a namelist.

l340: "thermodynamics features";  Grammar?

L343 :Table A1 in appendix C.

There are many problems: Why is called A1 if it belongs to section C? Section C1 is one sentence, and is not needed. Table A1 does not contain any parameter values, only descriptions; according to SI standards, units should not be in brackets “[]”; especially in this context the brackets make no sense (same for Table A5). 

Paragraph l339 to l347 could much clearer, including the extra information, supposedly in tables in the appendix. The tables could be in the main text, so that the reader does not have to flip back and forth in the paper (from here to appendix C, then back to Table A1, etc.). Since the time-splitting was already introduced, no need for phrases like “As mentioned in … “ (better: For the time-splitting approach (Section 2.2), we use a small timestep of …)

Section 3.3 should be part of a data and methods section. Now it is strangely split between the model evaluation section and the appendix. It would be much nicer for the reader to have everything in one place. 

L351 “(RGPS hereafter)” Unnecessary; it’s enough to introduce the abbreviation RGPS earlier in the line.

• Highlight, page 13

l358: "(see the Code and data availability section." Closing “)” is missing

L366 in the literature

I guess it’s fair to cite Ron Kwok’s paper about this.

L367 quite realistic

What’s the meaning of “quite” in this context?

L368 very smooth fields of deformation with no such localized features

Definitely true, but the figures, where the quadrilateral data is plotted on triangles with gaps in between makes it very hard to read the figures. For example, the aEVP solution seems to be noisy, but I cannot tell if this is an effect of the plotting. Convergence is an issue with aEVP (it’s very slow) and one can only expect “smooth” fields at all times if the aEVP parameters are tuned properly, see Kimmritz et al 2016. The smoother the solution, the slower the convergence.

L369 consistent

I am not sure, if you can say that, because there are also “coarse” (ie. 10km) runs in Bouchat et al 2022 the have quite some LKFs (their Fig10, the McGill model with smaller e). EVP models tend to have fewer LKFs in that paper (see previous comment about convergence), there’s even a comment about EVP models, convergence and deformation rates in Bouchat et al (their section 4.1.1)

page 15

L429 “A critical requirement for the consistent implementation of the brittle rheology”

This is phrased as a well known fact, whereas this is just what the authors find. An ill-meaning reader could conclude: The authors did not manage to succeed in stabilising the model on a C-grid. Please tone down these statements.

L434 The “Leap Frog scheme” may be a good analogy, but by the same analogy, the leap frog scheme is very much outdated and more stable schemes are commonly used in general circulation models nowadays (e.g. 2nd or 3rd order Adams-Bashforth in FESOM, MITgcm, ROMS, 2nd order Runge-Kutta in MOM6). I am surprised to learn that NEMO still uses a Leap Frog scheme. 

In this light, introducing yet another filter like the Asselin filter does not “serve[] a useful purpose” (l441)

page 16

l462: that -> which

l464: When SI3 is coupled to OCE, however, the cost increase is somehow dissolved by the overwhelming cost of OCE and falls below 30%.

It is interesting to note that other groups find that the sea ice dynamics, especially at high resolution, can become the most expensive part of a sea ice-ocean model (e.g. Koldunov et al 2019,  doi:10.1029/2018MS001485). I do not share the relief, that the sea ice model does not get “that much” more expensive when coupled to an ocean model. The cost increase definitely does not “dissolve”.

The numbers in Table 3 tell me that the ocean model uses 157/159 cpu h in this configuration (not sure where the difference of 2h between the setups comes from), the sea ice model 139 or 223 cpu h, so that with BBM, the sea ice model already uses more than 50% of the total time. Even the 139 cpu h of aEVE appear long in this context (47% of the total run time). That’s where Koldunov start to worry about overall performance. I think that this needs to be discussed in more general terms, i.e. how much time to allocate to a small part of our coupled model.

L472 “an insufficient number of iterations”

aEVP was designed to lead to smooth solution even when the solver is not fully converged. If there are checkerboard patterns in the solutions, then the choice of aEVP parameters is poor and should be improved  (“In practice, the value of $c$ depends on forcing, geometry of boundaries and on resolution and has to be selected experimentally”, Kimmritz et al 2016).

l477: like for instance about the Arctic sea-ice thickness distribution.

Please rephrase. Also, what are “promising results”? I think it would serve the manuscript, if this were formulated more concisely.

If this were my manuscript, I’d rewrite the entire parargraph along these lines:

Large-scale realistic sea-ice simulations with a model using the BBM rheology showed encouraging agreement of, for instance, the Artic sea-ice thickness distribution with observations (see also, Ólason et al., 2022; Boutin et al., 2023). Yet, deformation in convergence and sub grid-scale processes related to sea-ice ridging are not represented by BBM with the same degree of accuracy. The model overestimates the number of converging events with magnitudes of about 1 to 5% per day, and underestimates, although not as much as the aEVP solution, the most extreme events (Fig 7c, and Ólason et al. (2022). So far, parameter tuning, in particular the BBM-specific ridging threshold parameter $P_{max}$, did not help to improve agreement with observed convergence PDFs (not shown), so that we conclude that some fundamental processes need to be reconsidered in BBM (and aEVP) [ or now some other educated guess/speculation about the BBM (and maybe aEVP) equations that makes it impossible in principle, to get the convergence right ].

page 17

L488 “are doing better in this particular matter” , Rephrase: “agree better with observations” or similar.

l490: best -> most likely (and remove the following “likely”)

L491 “as these steps are absent”

Rephrase, “numerical dispersion and diffusion” are not “steps”. 

Also you could test that by using other, more diffusive/less dispersive advection schemes.

But what about the cross-nudging process? That was not part of neXtSIM either and could very well be a likely candidate for differences.

L495 “relevant” not the right word here. -> promising?

Conclusions:

In general, I don't think that the tone of the conclusions is appropriate (see main points). As if there is only this solution and everything else is wrong from the beginning. Many conclusions are drawn from trial and errors (as described here and in the text). I think it is good to show and discuss failures, so that others do not stumble into the same problems again, but there needs to be a more systematic list of things that did not work and why. The way this manuscript is written, I get the impression, we are presented with the result of something that finally works in spite of all the hardships encountered along the way, told by the fireside.

L501 The use of the Arakawa C-grid, as used in SI3, has proven to be poorly fitted for brittle rheologies.

The paper does not show this. It states that there are fundamental issues related to the staggering of grid points (but that is a problem not only for brittle rheologies) and describes a method to overcome noise issues that were not even demonstrated. By no means there is “proof” that it cannot work on a C-grid.

“poorly fitted” -> I don’t think that the C-grid has been “fitted” to anything. 

L505 This approach prevents the numerical schemes at play in the rheology

What “numerical schemes”? A numerical scheme is designed by a person (or soon by AI), but is not “at play in the rheology”. The paper does not present any stability analysis and or show development of noise due to numerical instability, grid staggering or whatever, so all you can say that with your scheme you are able to suppress any noise that may appear.

L512 deformations -> deformation statistics

L513 “with respect to the viscous-plastic rheology”, “the aEVP simulation with admittedly not properly tuned parameters (reported checkboard noise)”.

The sentence should include, that this happens on the same grid, with the same grid spacing etc.

The aEVP solution also has LKFs, just very few.

page 20

L550 “The average of the four surrounding points is used”  What is done near the boundaries?

A1 I would avoid “if \phi @F (@T)”, but instead use superscripts as in A2

page 22

A5 Table of symbols related to the numerical implementation

The text promise values for the parameters but there are none. Remove [] around units

A5: e1t, etc. why not use \delta x ^{U} for this (or similar). This looks like it’s a Fortran variable from SI3. I think this can appear in the paper, but not in the list of symbols, and I would refrain from using the variable names in equations and text (as done in B2), because for a non-NEMO user/developer it makes the expressions impossible to read and check.

page 23

l565: I think that equations, here “(Eq. B5, B6)”, should be introduced before they are referenced. Now I have to read appendix B2, etc before Appendix B1.

age 24

B1 (@T), etc not really necessary, as the notation has defined this already

page 25

B7: it should be pointed out in the text that \bar{h} is used and not \hat{h}

page 26

B12: what is “N”?

Eq B13, t_d is not a free parameter?

elsewhere: (B14) is implied by B13 when d_crit=1

page 28

L645 "The value of the BBM-specific parameters ..."

Unfortunately they are not listed in the table

L660 What are the criteria for “reasonably well shaped”?

page 29

l666: "consistent with the spatial scale of interest," what does that mean here?

L667: “almost identical”?  Aren’t they within a 3day bin anyway? What does this mean in addition?

L678 To prevent computational waste

I don’t think that’s an appropriate term here. “To save computer time/resources” … or similar

L681 “feeds on”

I don’t think that an algorithm can “feed on” something (animals do)

L685 please check the language of the author contributions for grammar, use of vocabulary …

Well crafted and relevant paper by the authors, it was very nice to see how well the BBM rheology compares to the satellite data for the LKFs. The PDF analysis is another good results that shows the BBM does a good job in describing deformations.

However, I am not convinced that the argument has been conducted in a way that is entirely fair for aEVP for these reasons:

1. If the default number of iterations for aEVP is 100 why has that been changed to 180? That is 80% more. You mention it is for "fairness" but is it fair to make the one you are comparing against slower? As far as I understand it, with 180 iterations your framework is 60% slower than aEVP, does that mean that the comparing to the default number of iterations your framework would be around twice as slow?
2. It is also not clear why when coupling with ocean the difference in time decreases. Can you clarify?
3. You make a comment saying that the resolution does not change with your approach, but you are considering more than double the number of degrees of freedom. When discussing accuracy, I think you should have also compared BBM to a case where aEVP has the same degrees of freedom as BBM. 
4. It is great to use satellite data as comparison and the results you show are definitely very good for BBM. I think however that you should also consider a test that has been widely used by other modelers so that your results with BBM can be put into a common context and it would be easier to compare against existing approaches. The test case I am referring to is the one moving anti-cyclone that can be found for instance here:  Simulating Linear Kinematic Features in Viscous-Plastic Sea Ice Models on Quadrilateral and Triangular Grids With Different Variable Staggering, but has been also used for instance here: Simulating Sea-Ice Deformation in Viscous-Plastic Sea-Ice Models With CD-Grids and here: CD-type discretization for sea ice dynamics in FESOM version2.
   
   
   
   
   
   I recommend the authors address the issues I raised here before I can advise for publication.

Please see review in attachment.