Dear authors, please find my review in attachment.

Zheng et al. present the tangent linear and adjoint models for MIPAS-CO2 v7.3 and evaluate the performance of the these new models. In addition, a comparison of adjoint sensitives is performed against CarbonTracker Lagrange. This work is of significant scientific value to the community. I found the manuscript to be well written and concise, and recommend publication after minor revisions. Aside from technical comments below, I would encourage the authors to expand on details of the implementation of the tangent linear model and adjoint in Sec. 3 and 4. For example, I find that Sec. 3.3 and 3.4 of Henze et al. (2007) provide a bit more detail.

Technical Comments

L30: I think better references re-transport error would be:

Schuh et al. On the role of atmospheric model transport uncertainty in estimating the Chinese land carbon sink. Nature 603, E13–E14 (2022). https://doi.org/10.1038/s41586-021-04258-9

Schuh et al. (2019). Quantifying the impact ofatmospheric transport uncertaintyon CO2surface flux estimates. Global Biogeochemical Cycles,33, 484–500.https://doi.org/10.1029/2018GB006086

L100-104: “e” should be defined at first mention.

L249-251: The state vector elements being optimized need to be somewhat coarse, but not the transport model. (e.g.,  https://amt.copernicus.org/articles/14/5521/2021/).

Figure 2 caption: This caption is a bit hard to read, I suggest re-wording to something like:

The (a)-(d) column average (units: ppm/ppm) and (e)-(h) surface sensitivity (units:ppm/μmol m−2 s−1) for CO2 observed  at the WKT tower at 00:00 UTC on March 31 2018. Top-to-bottom shows the sensitivities at 5, 10, 20, and 30 days before the observation. The WKT tower (31.3149oN, 97.3269oW) measurements used here are taken 457m above the ground level and labeled by the red color cross in the figures of the left column.

L274: “The figures show” should be either “The figure shows” or “The figure panels show”

Figure 5: I can’t see the red cross, maybe enlarge?

L300-321: If I understand correctly, Figure 5 and Figure 6 are examining sensitivities for different OCO-2 soundings? Then why not use the same altitudes for both Figures?

L359-379: This feels quite unrelated to the rest of the manuscript. I don’t have an objection to including it, but could it be its own subsection?'

Figure 11: It is hard for me to make sense of the magnitudes on here. Could you show the results with a linear color scale?  Perhaps as a right-hand column