The manuscript under consideration by Hachmeister et al. investigates the impact of polar vortex dynamics on XCH4 retrievals from TCCON. This is a very relevant topic for high-latitude sites and I recommend publication after minor revisions.

Specific comments:

I agree one would expect the variations of the CH4 a-priori profile to be a profound disturbance of CH4 retrievals under vortex conditions. However, the disappointingly low Pearson correlation of the results shown in Fig. 4 and the huge scatter of airmass dependence as fct of XGF shown in Figs. 10, 11, 12, 13, and 14 seem to indicate further mechanisms of action being involved. There is only a very short discussion on this problem (lines 145 ff). I think this aspect would deserve a more systematic investigation. Specifically, I would find it interesting to show the typical scatter of XCH4 airmass dependence for a midlatitude background site. This would provide a benchmark and help to decide whether this large scatter is related to some additional mechanism affecting polar sites.

Overall, it would preferrable to perform a more consistent investigation across all TCCON sites (the model prior is investigated for Ny-Alesund only, why?).

On several occurences (section on detection of polar vortex, use of model prior, relation between observation and vortex edge, ...) the reader wonders whether the slanted line-of-sight of the FTIR measurement is taken into account. Given the low SZA angles during relevant periods, the lateral displacement of LOS coordinates as function of altitude can be quite pronounced. Please detail on this aspect.

My main critics of the current manuscript is related to section 7.4, the AirCore comparison. In my impression, the study falls short at this point. A single AirCore is used for illustrating the effects on a TCCON observation. I would expect a systematic investigation in this section which makes use of all available in-vortex AirCore launches and compares these profiles with standard TCCON a-prioris for estimating the expected disturbance on TCCON XCH4 results. Note that this only requires TCCON sensitivities, not actual colocated TCCON observations. Next, the static prior (using the option of a vortex mask) and the model prior could undergo the same kind of investigation.

Minor / technical comments:

Abstract: "In the Arctic .. polar nights .. prevent solar absorption measurements for half of the year". This is not true.

Abstract: "These effects can be explained by the fact that TCCON uses a profile scaling retrieval". This would indicate that application of a profile retrieval would altogether cure the problem. This is not true, as a constrained profile retrieval still has imperfect column sensitivity (although improved over a scaling retrieval).

Appendix B and C:

Why are these rather ad-hoc profile correction schemes used? A correction describing a downwelling of the original undisturbed profile would better correspond to the underlying processes?

In this manuscript, Hachmeister et al. propose a methodology to improve the ability of the ginput algorithm to generate accurate methane a priori profiles in locations influenced by the polar vortex. They show that the current version of ginput produces a priori profiles that overestimate the CH4 in the 20 to 40 km altitude range compared to data from ACE-FTS solar occultation retrievals, NDACC direct-sun retrievals, and the limited number of AirCore in situ profiles taken at Sodankyla when the air over that site was in the polar vortex.

They propose two main methods to improve the priors. The first is a "static" correction derived from tests conducted using data from the Ny-Alesund TCCON site that imposes the same modification to the priors for any profile inside the polar vortex. The second is a "dynamic" correction that varies the magnitude of the modification to the prior based on the retrieved XHF amount. This method relies on enhanced XHF being an indicator of polar vortex influence due to the chemistry that produces HF in the stratosphere. They also consider modeled priors, but only for one site.

The authors evaluate the results in several ways. First, they show that the SZA-dependence of the retrieved XCH4 is reduced with the modified priors. They argue that an incorrect prior can produce this SZA-dependence because of the correlation between high XHF values (indicating an likely incorrect profile shape) and the SZA-dependence and argue for a physical reason based on the XCH4 averaging kernels. Second, they show that the modified priors result in smaller spectral residuals. Third, they compare the retrieved XCH4 using the different priors to the sole AirCore profile available for validation during the polar vortex.

Overall, the authors have done a good job demonstrating the impact of their proposed improvement to the priors. By testing with the current high-latitude TCCON sites, they have characterized the positive and negative changes to the retrievals at the relevant locations. I recommend publication after the comments below are addressed.

Major comment:

My only major comment is that, as the person most likely to be responsible for implementing this operationally, there are some details around the practical implementation of the dynamic priors that would help guide operational development if included.

First, the dynamic approach multiplies each prior by a shifted normal distribution that is a function of the XHF value. The manuscript says that "each prior" is multiplied by this; however, the TCCON retrievals use the same prior for all spectra in a 3 hour-long block. This reduces the number of times that absorption coefficients must be calculated. Going to per-spectrum priors would either entail (a) a large increase in the computational time for the algorithm or (b) reworking of the retrieval code to distinguish between changes in priors the require recalculating the absorption coefficients from those that do not. Please indicate whether the dynamic approach truly introduces a new prior for each spectrum or uses some average XHF value throughout the 3 hour block to modify the prior for a common set of spectra. If the former, it would be very helpful to see how the results change when switching to the latter - at least plots of the differences in the modified profiles between the per-spectrum and per-3 hour block approach, if not the full evaluation on the retrieval results.

Second, I am very curious if the dynamic method must use column average XHF, or if the vertical column density of HF is sufficient. This is because a practical implementation would require running retrievals twice: once to get the HF quantity used to drive the modification to the profile and then again to produce the final L2 products. Ideally, we want that first retrieval to be as quick as possible. If this method can use the HF vertical columns, then we need only run the retrieval for the narrow spectral window used for HF (which will be relatively fast). However, if XHF is needed, then we will also have to run the wide (and slow) O2 window. Thus, if we can use HF vertical column densities, we can minimize the run time before performing the final L2 retrievals. As with the first point, I would like to see at least the difference in the dynamically modified priors using HF column density as the predictor, if redoing the evaluation of the retrievals is not practical.

Minor comments:

- Section 1: the introduction is a bit thin on why it is important to improve the retrievals for the relatively small number of arctic sites. I suggest pointing out that the planned Canadian AIM-North mission will need reliable XCH4 validation in the arctic (https://www.asc-csa.gc.ca/eng/blog/2023/07/26/the-arctic-observing-mission-monitoring-the-arctic-in-new-and-profound-ways.asp) as well as to various papers in the literature that discuss the potential "tipping point" of arctic methane release (e.g., https://doi.org/10.1007/s13280-011-0221-x).

- Lines 78-80: "Trace gas measurements using remote sensing techniques based on solar absorption spectroscopy (like TCCON or various satellites) are expected to be affected by the polar vortex only in (early) spring, when sufficient light again becomes available to conduct measurements, as the vortex needs time to fully form during the autumn." This is true for sites above the arctic circle, but the fact that you include ETL in this study shows that there is also concern about vortex filaments reaching sites outside the arctic circle, and those sites would be affected throughout their winter season. Recommend making this statement more general to capture more of the relevant cases.

- Sect. 3.1.1: The TCCON retrievals use GEOS FP-IT or GEOS IT data. While those are not easily accessible, GEOS FP is, and that is a more similar product to the standard TCCON meteorological inputs. It includes Ertel's potential vorticity and wind variables, so a note on why you chose ERA5 data over GEOS FP would be helpful. (Perhaps because GEOS FP does not cover the full operational time span for Ny Alesund?) Again, from the perspective of making this operational, we would need to know whether there is a compelling reason to investigate ERA5 met data as an alternative for future algorithm versions.

- Lines 120-122: "AMDs can be caused by uncertainties in spectroscopy, by instrument alignment, by non-linearity problems and by the use of the wrong measurement time. TCCON data are corrected during post-processing using an airmass-dependent correction factor..." To be specific, the airmass correction is intended to correct an airmass dependence that is consistent across all sites (which should come from errors in the spectroscopy). Issues of non-linearity and timing errors should be corrected by individual sites earlier in the retrieval process, and severely mis-aligned spectra should be flagged out. Please rephrase this to clarify that the airmass correction is targeted at the spectroscopically-driven airmass dependences only, and the other factors should be handled with their own correction procedures.

- Line 132: "We define the AMD as the slope of the linear function fitted to the XCH4-SZA data within a day." Please indicate if you use the 82 deg maximum SZA limit typically applied to TCCON data. If not, it might be worth addressing why you use SZA instead of airmass as the predictor, since at very large SZAs, the relationship between the two becomes more non-linear, and airmass should have the more direct physical relationship to the deviation in XCH4.

- Line 143: "A clear tendency of higher AMD for higher XHF (and hence inside-vortex air) can be seen..." Perhaps qualify that this is clearest at the high latitude sites (NYA, EUR, SOD), with ETL being more ambiguous.

- Lines 147-150: "This can be explained by a) other effects causing AMD, which have not been corrected by the airmass-dependent correction factor and are not considered here, b) the existing prior not being consistently wrong (the difference between prior and true profile shape can vary) or c) true changes in diurnal XCH4 caused by local emissions or changes in atmospheric transport." (c) is why the procedure to derive the airmass corrections for the TCCON retrieval fit basis functions that are both symmetrical and asymmetrical with respect to solar noon. It is not perfect, but could address this issue. A note explaining why you did not use the standard TCCON fitting approach would be appropriate.

- Fig. 4 and 22: it is very difficult to distinguish the two series of points by size alone. Please consider using different marker types (e.g., + and o).

- Fig. 4: I assume "rho" in the legend is the coefficient represented by "R" in other literature, i.e., a value of 1 is perfect correlation and -1 is perfect anticorrelation? If so, please use "R" rather than "rho"; "rho" is too easily confused with "p" as in the p-statistic referenced in statements like "the slope is significant at the p = 0.05 confidence level".

- Lines 190-192: "To enable direct comparison between NDACC profiles and TCCON priors (see Sec. 5.4), the closest TCCON measurement within a day was collocated to each NDACC measurement." Please provide a scatter plot (in an SI or appendix would be fine) showing the NDACC vs. TCCON observation times that were matched. This would allow the reader to understand how close in time these values are if, e.g., a site does NDACC measurements in the morning and TCCON measurements in the afternoon.

- Figs. 6 and 7: Please make the lines in the legend thicker; it is difficult to see the line colors in the legend clearly with such thin lines. Also recommend moving the legend outside of the figure and increasing the font size.

- Sect. 6.3: Why was the model prior only tested for Ny-Alesund? It would be helpful to know if this model is an option for other arctic sites.

- Lines 266-268: "Retrievals using modified priors were performed for NYA, SOD, ETL and EUR. Retrievals using the static priors were performed for NYA, SOD and ETL. Retrievals using the dynamic prior were performed for all three stations. The model prior was only tested for NYA." From results later in the paper, it looks like the dynamic prior was tested on Eureka data, but these three sentences make it sound like the dynamic prior was only tested on NYA, SOD, and ETL. It would also be worth mentioning why EUR did not test the static priors.

- Lines 277-278: "The static prior was especially designed for inside-vortex measurements and thus yields a significant bias for high-XHF measurements..." Should "significant bias" be "significant bias reduction"? More generally, I suggest avoiding the use of "bias" here; that implies knowledge of the systematic difference between the retrieved and true XCH4. While the reduction in airmass dependence is a good indicator that the retrievals will be more accurate, it is only an indirect metric. Perhaps instead you might say a "significant reduction in AMD" (and note the first time that this likely indicates a more accurate retrieval).

- Line 280: "...and leads to an overall improvement with values below μ = 1.06 ppb deg−1." Do you mean "leads to a lower mean AMD of μ = 1.06 ppb deg−1 for values with XHF < 100 ppt"?

- Lines 296-297: "Overall, the dynamic prior reduces the average AMD for most data for all four stations. For NYA, the dynamic prior shows the best results, while for SOD and ETL over corrections are visible for the range 140 >XHF≥ 120 ppt." But this might be because you fit Ny-Alesund data to calculate the dynamic correction, yes? How much do the dynamic method's coefficients change if you fit data from the other stations? Does the station from which you derive the coefficients always have the best results? How might we think about ensuring the most representative correction for all arctic and subarctic sites if the coefficients vary too much depending on which sites' data are fit?

- Sect 7.2: It would be helpful to include a figure, table, or discussion of whether the RMS/CL values for spectra that the XHF method classifies as in-vortex are actually out-vortex according to the EPV and wind mask, or vice versa (from the discussion around Fig. 2). This would be important to know, because if those false positives and negatives are the ones with the largest increase in RMS/CL, then that suggests that an operational implementation of this approach would benefit from including the vortex mask as a binary criterion on top of the XHF dependence modification.

- Lines 307-308, Figs. 15-18: "Positive values of ΔR constitute an improvement of the fit (lower RMS/CL), negative values an increase in RMS/CL compared to the reference retrieval." This seems backwards to me, (new - current)/current would be more intuitive so that negative values match up with a decrease in RMS/CL.  Later, you use the (new - current)/current convention for the AKs, so being consistent would help the readers interpret the various plots more easily.

- Line 324-325: "Improvements are between roughly 53% and 72% for the different fit windows and thus smaller than for NYA." Meaning between 53% and 72% of the spectra have improved RMS/CL values? If so, please say that more explicitly.

- Lines 355-356: "where ΔAi is the relative change of the AK. This yields differences up to 10 ppb in magnitude and a mean difference of roughly 3.5 ppb." It is worth putting this in the context of the TCCON error budget: since that is 4 to 4.5 ppb for XCH4, the mean is within our standard uncertainty. How common are the differences above the error budget? And what is the shape of the example profile used here?

- Line 358: "Previous results were confined to the analysis of relative improvements between different versions of the TCCON retrieval." Recommend rephrasing, as this sounds like comparisons were done between major versions of the TCCON retrieval (e.g., GGG2014 vs. GGG2020) and possibly results in other papers. Perhaps instead: "The results in the previous sections were confined to the differences among retrievals using different a priori CH4 profiles."

- Line 364: Was the AirCore integration done with a pressure weighting method? Please provide a reference or equation.

- Fig. 19 caption: "...the standard TCCON CH4 retrieval for NYA." Perhaps clearer to say "using the standard prior" to be consistent with the language elsewhere in the paper.

- Lines 416-417: "Nonetheless, (i)–(iii) prove that improvements to the TCCON retrieval are possible using relatively simple modifications to the prior profile, which don’t depend on external data." Please acknowledge that the dynamic method, in particular, adds a new back-dependency between the retrieved quantities and a priori profiles, which will require careful implementation to avoid poor quality HF retrievals from degrading the CH4 priors. That is, the method is conceptually simple, but does involve a more complex operational implementation.

- Figs. 19 & 20: these might be better combined into a single figure so that a reader can compare the standard AKs and the changes without having to switch pages.

- Line 431: "In summary, we want to highlight that the prior shape has a significant impact on the retrieval..." Here again quantifying this relative to the TCCON error budget would be useful: changes on the order of twice the error budget are statistically significant and worth reducing, but do not mean that the current approach has a critical flaw.

- Fig. 22: is the difference dynamic minus standard or vice versa? Dynamic minus standard would follow the same (new - current) convention discussed previously and is my preference, and in either case, the sign convention should be stated.

- Code and data availability: Thank you for including a notebook to walk through the calculation of the vortex mask. I would also like to see at least the code used to derive and apply the static and dynamic modifications be included as well, so that it is archived in case we need to redo this analysis in the future for updated base CH4 profiles. It would also be good practice to include a requirements.txt, pyproject.toml, or environment.yml file alongside the code to identify the versions of Python packages used here.