General comments:

This study by Kimura and Hasumi introduces a new approach to estimate Arctic sea ice thickness by reconstructing its thermodynamic growth history from satellite-derived motion and concentration data. Virtual ice particles were tracked backward in time using AMSR-E and AMSR2 observations, and surface heat budget calculations were applied along their drift paths to model daily growth, which was then scaled against ULS measurements. The authors demonstrate that satellite-based ice age/backtrajectories in combination with a thermodynamic model can be used to reliably capture sea ice thickness (and annual and interannual variability).

At present, there are very few sea ice age and thickness products available, so the attempt to address this gap in this innovative and new way is highly welcome. The authors make use of a somewhat less commonly applied motion dataset, which renders the resulting ice age product independent of existing products, a very important aspect for any future cross-validation efforts of sea ice age datasets. The method is described with sufficient detail, and overall the paper is very well written and structured. I recommend publication, though I would encourage the authors to expand the validation section somewhat further and make data publicly avaibale.

Here are my two more general comments:

I believe that the validation is currently limited to the Beaufort Sea, which raises the question of whether the admittedly very good results can reasonably be transferred to the entire Arctic. I would encourage the authors to invest some additional effort here. There are a number of alternative data products available, in particular airborne measurements in the central Arctic, which are by no means inhomogeneous but rather represent local conditions very well as well as additional ULS datasets from other Arctic regions (e.g., Belter et al.). I believe the additional effort required would be relatively modest and would help to better justify the chosen correction factor. Furthermore, I would recommend that the authors consider dispensing with the correction factor altogether and instead frame this as an error inherent in the data. Such an error characterization should ideally also be included in the abstract, at least with a few key figures.

Another point that I personally find very important is that the presented dataset has not yet been made available. The manuscript states that it will at some point be accessible via a website. However, I believe that the availability of such datasets is a fundamental prerequisite for publication, as otherwise reviewers have no opportunity to directly examine the presented results and data. I am not sure whether this is also an explicit requirement of The Cryosphere, but before publication it should be ensured that the dataset is accessible and well documented. In addition, the motion dataset underlying the ice age product should also be made available. At present, only a link to a main webpage is provided, but not to the actual dataset itself

Minor issues:

Title: “Arctic themodynamic? Sea ice thickness?

Line 19 and 29: References are somewhat outdated. The most recent one listed is some 11 years old 😊

Line 66: obtained from sea ice motion data derived from passive microwave….

Line 69: along each trajectory using XY

Line 77: thermodynamic model combined with

Line 98: Provide number (error)

Line 104-110: I’m not entirely sure here: Wouldn’t it be important for the comparison later to derive the modal value of the ULS observations? At the moment, the mean is being used, but the mean includes deformed ice, which is then compared against a thermodynamic model.

Line 119: …according to changes in sea ice extent: What is meant by this?

Fig 2: Is it possible to zoom in or enlarge the fig?

Caption Fig. 2: Held stationary or stopped?

Line 130: Why limited to 4 years? From my own experience (and looking at the past 2 years) there is lots of ice around that is older then 4 years?

Line 138: This confirms https://www.nature.com/articles/s41598-019-41456-y

Fig. 3 plus caption: I really like this form of presentation, as it makes the effect that ice concentration has on the distribution of ice age at the end visible. Perhaps the different periods mentioned in the figure caption could be displayed as a legend.

Fig 4: Same as for Fig. 3. Please add a legend. Red is not displayed.

Line 200 – 205: Very interesting. Fun to read.

Line 216: May be some more up to date reference would be nice

Line 230: The phrase ‘it may also implicitly capture’ sounds rather vague to me, and it is unclear why, in addition to thermodynamic growth, dynamic growth would be considered here. I think, in order for the sentence to remain as it is, the effect would need to be shown and that part expanded considerably.

Fig. 8: I would directly include error assumptions, significance level, etc. in Fig. 8. It would also be nice to indicate the observation period, for example through a color coding of the figure.

Line  279: Smoothing is generally fine, but in this case I don’t see the necessity or the rationale for choosing, for example, a two-week time window. I would either elaborate on this part or leave the sentence out entirely.

General comment on validation: At present, the validation is strongly limited to the Beaufort Sea, which naturally makes the transferability of the results to the rest of the Arctic somewhat difficult. I would generally recommend that the authors broaden the validation. From my perspective, ship-based observations can equally be used for validation, as well as data from numerous airborne campaigns, some of which are publicly available. In addition, in the Russian Arctic or in regions primarily dominated by FYI, there are moorings that can serve validation purposes (e.g. https://tc.copernicus.org/articles/14/2189/2020/). In particular, since a correction factor is applied that is then used across the entire Arctic, a more comprehensive validation is required. I therefore recommend expanding this aspect, either through airborne data (e.g. EM-Bird data) or through additional ULSs.

Line 285: Can you provide more detail on how it was derived? For Fig. 7 its kind of clear how this is done… but how comes Fig. 6 into play?

Another point concerns the temporal validity of such a correction factor. The authors derive ice age for a period that clearly exceeds the coverage of the validation dataset on which the correction factor was ultimately developed. I wonder whether it might not be better to omit the correction factor altogether and instead simply acknowledge that the chosen approach overestimates the actually observed values by about 25%.

Line 315: I would avoid terms like “reasonably accurate” in particularly after applying a correction factor.

Line 325: I disagree with this statemtent. In particular, EM data cover large areas that have remained unconsidered in the validation and are generally very homogeneous, apart from the data in Fram Strait. Since the data were apparently already considered for use, it would be very interesting to present this comparison here as well, as otherwise it might give the impression of a somewhat selective use of data.

Last chapter / Fig. 111/12: The quality of the agreement in Fig. 11/12 (Fram Strait) is somewhat surprising to me. I would have expected a considerably poorer comparison, and in the end the good performance here is quite convincing.

The authors may wish to elaborate further on the limitations of the low-resolution data (both here and elsewhere in the manuscript), in particular the strong underestimation of drift speeds in the Fram Strait that may prefent from resolving daily to subdaily variability.

Regarding structure, it might be worth considering integrating the Fram Strait validation into the preceding chapter, as the separate treatment in the final chapter feels somewhat unusual.

Line 407: It is very encouraging to hear about these plans. I believe that providing an additional ice age and ice thickness product, which employs different approaches and methods than those already existing, will represent a highly valuable contribution to the scientific community. Many thanks for this excellent work — it was a genuine pleasure to read the paper.

Data availability: Please provide a direct link to the motion dataset that is used in this study.

Please ensure that the sea ice age, mean sea ice age and sea ice thickness is pubilcy available prior publication