This study introduces an online Lagrangian tracking module implemented in the CICE under the coupled model system of CESM to enhance Lagrangian diagnostics in sea ice models. The authors validated their module through numerical experiments focusing on sea ice deformations and kinematics. These experiments revealed multi-fractal characteristics in both spatial and temporal domains, as well as spatial-temporal coupling. The novelty of this work lies in the development of the Lagrangian tracking module and its emphasis on the importance of the Lagrangian perspective. This contributes significantly to the field of sea ice research. While the work is of sufficient quality and depth for publication, I have a few minor inquiries that I would like to discuss:

1. The authors outline the general structure of Lagrangian tracking within the time step of CICE. Lagrangian tracking was conducted prior to ridging and rafting. However, in these phenomena, multiple Lagrangian points may overlap or intersect. It would be helpful to clarify whether, in cases of strong ridging or rafting, these overlapping or intersecting Lagrangian points were considered as a single point or if they were treated separately in the tracking process. Could you elaborate more about ridging and rafting?
2. The authors discuss the climatology of Lagrangian points under NYF (figure 6), supplemented with video. This discussion is valuable for understanding the functionality of Largrangian tracking module and visualizing sea ice export and melting. While direct comparison to observations is constrained, it would be beneficial to discuss the convergence of results concerning the number of Lagrangian points. In addition, exploring sea ice transport using non-uniform or localized distributions of Lagrangian points could provide further insights into sea ice dynamics. Understanding how variations in Lagrangian point distribution influence sea ice transport patterns would enhance the comprehensiveness of the study's findings.
3. The authors compare the model track with buoy track (figure 7) and evaluate differences between the model points and the corresponding buoys (figure 8). While three possible reasons for the tracking uncertainties are outlined, additional details on each factor would enhance the understanding of their impact. For example, the authors could explore the effects of spatial resolution by conducting sensitivity analyses with varying resolutions and comparing results for different cases. The authors could try to quantify the effects of uncertainty in atmospheric forcing on tracking, if possible. Can you also increase the size of ‘+’ markers on the map? It is hard to see in the printed version.
4. The authors used convex structure functions to fit sea ice deformation trends. While referencing observed multi-fractal deformations is valuable, further discussion on the selection of this specific form of function would enhance clarity.
5. In the discussion of spatial scaling around Dec. 20th and Feb. 6th for four different temporal scales (figures 10 and 11), the 3-day and 10-day cases exhibit a larger difference in beta compared to the 1-day and 30-day cases for both dates. Could you provide the reason for this?
6. In appendix B detailing the calculation of sea ice deformation, it is important to consider scenarios where the grid becomes highly deformed, akin to figure B1.C. I am curious whether the patch is redrawn at every time step. If not, how could sea ice deformation be calculated in the case of highly deformed grids?
7. The figure numbers in lines 94 and 96 on page 4 are typos. Figure 1 should be there.
8. In line 101, there is a typo: “the cell the point” needs correction.

This manuscript is technically sound, offers a new code likely to be of wide interest within the sea ice modeling community, and presents compelling results to clear up an unresolved question in previous sea ice model intercomparison projects.   There were a number of issues left hanging, for example, in the works of Bouchat et al. (2022) and Hutter et al. (2022) for the Sea Ice Rheology Experiment (SIREx).  One of the issues was the somewhat nebulous role of the ocean in the modeled sea ice deformation statistics.  That remains unresolved in this work, since a simple mixed layer ocean has been used to generate sea ice deformation statistics. The second unresolved issue was the difficulty in consistently accounting for deformation across Lagrangian and Eulerian models, which is a problem this paper addresses.   The scientific results are excellent and worthy of publication.  The issues I found amount to relatively minor edits and additions: 1) English in this paper needs a thorough proofing; 2) Some math notation should be aligned with existing sea ice literature; 3) I suggest editing the methods section so there can be no doubt this paper concerns a diagnostic tool rather than one influencing the physics of CICE; 4) In the presentation of results, please give consideration to a figure that would convey key climatological circulation features of the Arctic to help provide visual proof that your tool works correctly; and finally 5) perhaps most importantly for GMD, please make sure the Zenodo code base provides everything needed in CICE to reproduce results documented in this paper.   I provide further details here:

Lexicon:

Here are examples of the issues I noticed in my reading with English grammar and notation:

• Sea ice deformation should not be pluralized (i.e. deformation not deformations)
• Change: “Since they drift with the sea ice, their locations are also representative of the sea ice floe they are attached to” to “Since they drift with the sea ice, their locations are also representative of the sea ice floe to which they are attached”. (line 30)
• Pluralize “sea ice dynamic” to “sea ice dynamics”.
• Instead of denoting deformation rates as ’s, please use the correct mathematical expression for these rates to be consistent with existing sea ice rheological literature.
• Change “…are capable to reproduce certain…” to “…are capable of reproducing certain…”. (line 55)
• “It is worth to note…” should be changed to “It is worth noting…” (line 155)

Please carefully proof the entire document to address similar English grammar issues.

Methods:

The methods section is well explained, and I suggest only needs minor edits:

• For section 2.2.1, please consider a section title more useful than “Basic Support”. “Software implementation” may be more descriptive.
• In Figure 3, the “Lagrangian Tracking” box would suggest that somehow the tracking is instrumental in the physics of your version of CICE, when it’s actually a diagnostic but not prognostic tool. I suggest the “Lagrangian Tracking” box should be shifted to the side of and outside of the step_dynamics box so that there can be no confusion on this point.

Results:

There are a number of issues that should be addressed in the graphical presentation of your results:

• The color scale in Figure 5 is smooth to the point of deception. It appears that there is a significant problem with your thickness field in that you have near zero thickness in patches surrounding the North Pole.  I may have missed it, but you appear to have omitted any comment about this problem.  The problem does not preclude publication, and is almost certainly an artifact of your forcing, but please comment on the cause of this.
• You have a wonderful Lagrangian tracking tool, but at no point in the manuscript do you make use of it to show streamlines exceeding two weeks in length. Rather than just a novelty, it is essential to show at least seasonal tracks for proof that your tracking system is able to perceive the most basic of circulation features of the Arctic: the Beaufort Gyre and the Transpolar drift.   I recommend including a separate figure accompanying Figure 6 with seasonal breakdowns of a less dense sub-selection of the tracer points in that figure.  Without this, it is very difficult to make sense of, for example, Figure 6(b).

Code and Model Specifics relevant to GMD:

Information provided in Appendix A offers far from an exhaustive list of model parameters in CICE, and it’s difficult to understand why only some default constants and parameters are listed.  Either make the table exhaustive of the model parameter space, or only show parameters you have changed from the default CESM version 2 code base, and state so.  Please ensure, that a namelist for the model is available, or make it clear that the CICE namelist remains unchanged from CESM.

It appears that in the Zenodo link you have provided, only the subroutines needed to be switched out in the CESM code are given.  However, the CESM code is a GitHub release, and therefore subject to change.  My understanding is that GMD, like other journals, now requires a stable and orphaned code base rather than a link subject to institutional change.  As your Zenodo link currently stands, one could not take that code and preproduce the results in this paper without reliance on NCAR. That needs to be fixed.

References

Bouchat, A., Hutter, N., Chanut, J., Dupont, F., Dukhovskoy, D., Garric, G., et al. (2022). Sea Ice Rheology Experiment (SIREx): 1. Scaling and statistical properties of sea-ice deformation fields. Journal of Geophysical Research: Oceans, 127, e2021JC017667. https://doi.org/10.1029/2021JC017667

Hutter, N., Bouchat, A., Dupont, F., Dukhovskoy, D., Koldunov, N., Lee, Y. J., et al. (2022). Sea Ice Rheology Experiment (SIREx): 2. Evaluating linear kinematic features in high-resolution sea ice simulations. Journal of Geophysical Research: Oceans, 127, e2021JC017666. https://doi.org/10.1029/2021JC017666