Ice core nitrate isotope compositions may be useful to reconstruct atmospheric nitrate isotope compositions in the past with paleoclimate implications. Previous studies have investigated impacts of post-depositional processing on isotope compositions of nitrate preserved in snow and ice. In this work, Jiang et al. revised the TRANSITS model (a one-dimension snow photochemistry model) to calculate atmospheric nitrate deposition flux and isotope compositions based on snow records. Exemplary applications were applied to Summit and Dome C data and the calculated results were compared with measurement data. Although future efforts are needed to further evaluate and improve this model, this work is an important step towards a more precise interpretation of ice core nitrate isotope data. The equation derivation appears correct, and the model logic looks scientifically reasonable to me. However, the writing of this manuscript is too technical to readers outside the small community of post-depositional possessing of nitrate isotopes, and one may need to read all papers written by the authors previously to understand this work. This writing style is not easy for casual readers (especially for atmospheric scientists who do not work in cryospheric sciences and isotopes) to follow. I spent considerable time to digest the manuscript, even though I am kind of familiar with topics discussed in this manuscript. I therefore have some suggestions that aim to improve the clarity of this manuscript.

1. Line 29: Please define Fpri at the very beginning. For readers who did not read the authors’ previous papers, they would not understand what it is.
2. Lines 263-265: Please rewrite this sentence. It is not clear.
3. The definition listed in Table 1 is unclear. For example, I do not understand what “d15N of archived nitrate flux” means. Does a flux have a d15N value? Does it mean d15N of archived nitrate? In my opinion, these definitions make the manuscript difficult to follow.
4. There are 13 input parameters listed in Table 1, but only 6 are described in Table 2. It is difficult for readers to check everything throughout different parts of the manuscript and from different papers.
5. Section 3: It is recommended to explicitly describe what parameters were used to do the calculation and what parameters were used to compare with the model results at each site. For example, it is stated that weekly data from Jiang et al. (2022) were used (Section 3.1). I need to re-read Jiang et al. (2022) to understand what these data are. In addition, I do not fully understand how the authors tested their model results. Did they use the atmospheric nitrate data reported in Jiang et al. (2022) or the surface snow as described in page 12? Where are the data from?
6. Lines 387-389 and 397-398: I would not say that the seasonality of modeled d15N agrees well with observation based on Figure 3. As noted by the authors, the model cannot capture the seasonal variation from September to April.
7. Lines 428-430: Could the authors tune the epsilon value in the model, give a quick estimation what epsilon value may reproduce the observational data, and briefly discuss if this epsilon value is reasonable? This test should be straightforward.
8. Figure 5: I am confused what the results of “inverse model” mean. The inverse model used measured isotope values as input parameters. So I guess the model “results” plotted in this graph are the isotope values of “deposition nitrate” calculated from the model or the model input (calculated averages of measured values?). Please clarify.
9. Figure 6: Is it possible to show a similar figure for Summit so that readers can better understand how the model behaves if we just look at the annual average?
10. The authors may notice the new work by Shi et al. (2023), which is highly relevant to this manuscript and was just published after the submission of this manuscript. Please cite this work during the revision: Shi, G., Buffen, A. M., Hu, Y., Chai, J., Li, Y., Wang, D., & Hastings, M. G. (2023). Modeling the complete nitrogen and oxygen isotopic imprint of nitrate photolysis in snow. Geophysical Research Letters, 50, e2023GL103778

Overall assessment

The paper by Jiang et al. presents for the first time an inverse model (based on the forward model from Erbland et al.) to reconstruct atmospheric nitrate load and its nitrogen AND oxygen isotopic signatures based on snow pack data. In particular, it includes the postdepositional loss/recycling of nitrate by photolysis and nitrate reformation and compares the results from two ice core end members  (Summit, Dome C) with atmospheric information. Overall, the results agree surprisingly well with atmospheric observations and for example support a clear stratospheric origin of the primary nitrate at Dome C. This all justifies the publication of this paper in ACP with minor revisions.

Having said that, the paper is not always easy to follow and I am afraid that especially readers not familiar with the respective background of the mass balance and Rayleigh fractionation equations would need more guidance. I would therefore suggest to expand the Appendix A to give a more detailed derivation. I also felt that the discussion of initial deposition and re-deposition of nitrate produced during photolysis needs somewhat more explanation in the beginning. In the end this process may easily explain, the observed deviations of the atmospheric d15N in observations and model results in certain months. Finally, a comparison with the results by Shi et al. in GRL (10.1029/2023GL103778), who also include oxygen isotopes in a forward model approach, is still missing in the discussion

Apart from this I made several comments and language corrections in the annotated pdf file attached.