General comments

This study present an innovative method for estimating total column methane (XCH₄) using a Lagrangian Particle Dispersion Model (LPDM), FLEXPART, and way to assimilate the data in an atmospheric inverse model, FLEXINVERT. The case study is carried out for Siberia for 2022. The comparison against the “traditional” ground-based inversion showed broad agreement with the inversion using TROPOMI data, and consequently reliability and a good potential in the presented method for estimation of regional CH₄ fluxes. The method sounds applicable for other LPDMs, and could contribute significantly to the atmospheric inverse modelling community with new ways to infer greenhouse gas flux information from satellite data. The fact that LPDMs can be run in much higher resolution than Eulerian transport models will be an advantage for incorporating information from future satellites with much higher spatial resolution. Therefore, this paper is worth of prompt publication after considering a few points below.

• The authors found large differences in modelled XCH₄ depending on background initial mixing ratios. The boundary conditions were optimised to somewhat discriminate the “errors”, but how can it be sure that the signals within the domain is not over constrained by the background? In L280, it is said that the correction of modelled XCH₄ was “largely due to the improvement to the background estimate”, and the posterior fluxes from the TROPOMI inversion did not change much from the prior. I suppose that with less uncertainty in the background, the fluxes would change more. How do you know what is a good balance?
• High northern latitudes are challenging regions such that satellite retrievals are associated with various biases, especially those related to seasonal variations may plan an significant role. I wonder how much of the differences between the ground-based and TROPOMI inversions were due to these biases. Please discuss.
• The inverse model results are associated with various uncertainties. You have discussed and did sensitivity tests on background mixing ratios, but other optimization setups, such as choice of retrieval products, pre-processing methods of the satellite data, prior fluxes and prior uncertainties for observations and fluxes are also important. As this paper do not present variety of sensitivity tests, the conclusion of the paper about CH₄ flux estimates should be presented carefully that the results may change significantly depending on the setups.

Specific comments

L160: Why do you use area-weighed averages? I understand it is somewhat reasonable for mixing ratios, but for averaging kernels and presser weighting, I do not fully understand how the area would be affected. Could you also explain how did you take into account differences in number of observations within the aggregated cells?

Section 3: Did you include temporal correlation of the state vectors? Please add information somewhere.

L195: Could you add a figure on spatial resolution? Where were lowest and highest resolutions? Were the resolutions same for the TROPOMI and ground-based inversions, despite the fact that they would have differences in “how strongly the fluxes influence the observations” due to differences in locations and quantity (surface vs total column) of the observations? Please clarify.

L209-213: In later sections, it is said that the background mixing ratios were also optimised. What were the uncertainties in the boundary conditions?

L218: Why did you chose the grid cell sizes of 0.25° and 0.5°? FLEXPART is run at 0.5° and smallest optimisation spatial resolution is also 0.5°, so why did you chose to have observations at higher spatial resolutions? Can FLEXPART resolve differences well (or what is done) if there are more than one observations within a 0.5° x 0.5° grid cell?

L223: I suppose number of observation vary a lot within the study period. Please add information about number of observations also perhaps in 14-days temporal resolution, which is your flux optimisation resolution. I would also like to see for both TROPOMI and ground-based observations.

L225-232:

• The source information for JR-STATIONS are available in Data availability section, but how about other ground-based data?
• Did you process/filter these data at all?
• For the TROPOMI data, you mentioned that the observation uncertainties were 14-20 ppb. How about for these ground-based observations?

Section 3.1.3:

• Did all the prior fluxes had estimates for 2020? If not, what did you do? What were the original resolution of the prior fluxes? Did you do any interpolation when original resolution was lower than 0.5°?
• Do I understand it correctly that you include ocean emissions, but do not optimise them? How large were the contribution of ocean fluxes to the total fluxes of this domain?

Section 3.2: I understand that you only optimise total fluxes, but as you find some spatial differences in the flux increments between the TROPOMI and ground-based inversions, can you speculate whether emissions from oil and gas sources have different seasonal patters in the two inversions?

L286, L306: Could you add uncertainty estimates as well?

L295-299: Are the number of TROPOMI observations less than those from the ground-based stations? Do you argue that number of the observations was persistent for all months? I suppose flux uncertainties are larger in summer (as a whole domain) due to contribution of wetlands (although it is not so clear from Figure 6)? How would the retrieval biases possibly play a role that were discussed in e.g. Lindqvist et al. (2024)?

L318-321: Related to questions above, why do you think that the flux were not as well constrained in the TROPOMI inversions? Satellite data are suppose to have good spatial coverage compared to ground-based data, and with much large number of data, it should, in principal, constrain the fluxes better than the ground-based data. But it is not the case here. Is this a general feature or something specific to high northern latitudes?

Technical comments

Introduction: Please add information about focus/simulation years

L67: Please add references to FLEXPART.

Equations: Please use bold fonts for vectors and matrices.

L210: ...ERA5 at 0.5° x 0.5° and… ?

Table 1. What are the altitudes here? Elevation of the site or height from which FLEXPART trajectories were calculated?

Figure 2: Are these of super-observations? Please clarify.

Figure 4:

• You could perhaps consider adding number of observations here?
• Could you also consider adding ranges?

Please consider combining Figures 5 and 8, and Figures 7 and 9. It would be easy to compare between TROPOMI-based and ground-based inversions that way.

References

Lindqvist, H., et al.: Evaluation of Sentinel-5P TROPOMI Methane Observations at Northern High Latitudes, Remote Sensing, 16, 2979, https://doi.org/10.3390/rs16162979, 2024.

Review of ‘Efficient use of a Lagrangian Particle Dispersion Model for atmospheric inversions using satellite observations of column mixing ratios’ by Thompson et al.

This work documents an interesting case study in which a Lagrangian Particle Dispersion Model (LPDM) is used together with high-resolution satellite data in an inversion. The paper describes an efficient method for producing SRR ‘footprints’ using an LPDM from a large number of satellite retrievals, which would ordinarily be resource-intensive and time-consuming. The new method is applied to a northern high-latitude region and results are compared to an inversion using ground-based observations within the same region. The authors found that the satellite-based inversion produced posterior fluxes which were very close to the prior, and put forward suggestions for why this was the case.

Overall this is an interesting study and a nice documentation of a method that will likely become more and more important as satellite resolution continues to increase. The method is well-described on the whole and the figures are OK. I have some comments and suggestions regarding some aspects of the method and the presentation, but I am happy to recommend publication of the manuscript after these are addressed.

Major comment

Throughout the document, the authors correctly refer to the fact that LPDMs are not usually used for this type of satellite-based inversion – e.g. ‘LPDMs have not been used to any significant extent with satellite observations’ (line 48).

However, I do think some discussion of any previous satellite-based LDPM inversions is merited. It should be made clear exactly what exactly the novel parts of this new methodology are. For example, Ganesan et al. (2017) performed a GOSAT-based inversion over India using a different LDPM. There should be some discussion of how your method differs to and updates theirs, as is necessary due to the increased volume of data available from TROPOMI compared to GOSAT. The novel aspects of your method should be highlighted more explicitly (e.g. the use of P_n = Pa_nw_n, in Eqn. 7, which is nice).

Specific comments

Line 85: ‘SRRs have only been calculated for point observations …’. For FLEXPART, although this is not true of other Lagrangian models.

Line 101: How exactly might chemical loss be represented during the backward simulation? Via an assumed fixed lifetime, or via actual representation of OH concentration and chemical loss rates? Is there likely any effect from not including this here?

Line 195: Is it possible to include a map of the variable resolution of the optimised flux grid?

Line 255: Can you provide a measure of the chi-square value for the various retrievals to test the convergence?

Line 295: I am a little surprised at the limited posterior uncertainty reduction. You say that this is to be expected due to limited observational coverage due to cloud cover and other issues, but you say earlier that there are over 3500 super observations per day, with TROPOMI having good sensitivity down toward the surface. Is the satellite coverage quite heterogeneous? Perhaps a figure showing the super observation coverage density by the satellite over the region for the spring and summer periods would be useful (perhaps alongside the SRR map in Figure S6).

Line 295: If you were expecting such poor satellite coverage over a difficult-to-observe region, why did you choose this region for your case study?

Figure 10: I think there are some data points falling outside of the boundary of the Taylor diagram (around NSD = 2.5; R = 0.5). These are easily missed by the reader and the Taylor diagram should be expanded to include them if possible. Also please include a label on the angular axis.

Supplementary Figure: I’d be interested to see a plot showing ‘posterior – prior’ XCH4 for the results shown in Figure 2. Is there any spatial variability in the change to XCH4 produced by the inversion in this case or is it simply a homogeneous addition/subtraction of background CH₄ within that latitude band?

Please see the attached file.