Summary

Koene et al. present two MMSE-based methods for denoising CO2 plume signals across different spatial scales using high-SNR proxy fields such as NO2 and SO2. These methods are tested and combined on both synthetic CO2M imagery and real TROPOMI data. The results show that the proposed approaches effectively suppress noise while preserving the plume signal. This is promising work; however, the authors should further clarify and propose a general pipeline for applying these methods to multi-scale data, including a strategy for selecting optimal parameters.

General comments

1. Automatic determination of parameter T (L204)
   • How can the threshold value T be determined automatically? Although the authors discuss possible approaches around L255, it would be valuable to propose a general and robust method for future applications. I suggest testing both CO2M and TROPOMI datasets to evaluate whether an optimal solution can be consistently achieved.
2. Combination with mean filtering
   • While the MMSE methods preserve plume structures, the mean filter produces a much clearer image that could be more practical for identifying source locations and masking plumes. It would be useful to discuss the potential of combining the mean filter and MMSE approaches, and to test such a hybrid method on representative cases.

Specific comments

• L20: Please add the typical background and enhancement levels of atmospheric CO2.
• L21: Define all acronyms in full on first use (GOSAT-GW, CO2M, TANGO).
• L31: Include a short paragraph explaining the practical motivation. Why is a “data-only” Bayesian estimator advantageous (e.g., independence from explicit forward models, suitability for on-board or distributed processing)?
• L73: Avoid using uncertain wording such as “maybe” when presenting derived equations.
• L107: Clarify why a factor of 0.5 was chosen for min–max normalization. Have the authors tested other scaling factors, and what effect do they have on performance?
• Figure 3: Add panel numbers for clarity.
• L187: Explain how the +44.4 dB value was obtained.
• L207: Consider showing noise-removal results for the CO2M image as well.
• L215: Please explain why averaging over year’s data increases noise levels.
• L238: Discuss the cause of negative emissions. The authors could generate synthetic TROPOMI data to test whether these negative values reflect true signal variability or arise from the MMSE denoising process.

Technical corrections

• The code listings are long and could be better shown by uploading them to a public repository (e.g., GitHub) and sharing key scripts or notebooks for illustration. Data could also be deposited on Zenodo for reproducibility.
  • For example the code at L313 U.T((0,1,3,2)) is not valid NumPy syntax.
• Consider moving Appendices B–D to the Supplementary Information to make the main text more concise.

The authors present two methods for denoising satellite "images" of CO2 or SO2 based on co-measured NO2 with higher SNR, which works impressively well.

The methods are derived and explained in great detail, and the final algorithm is also provided in form of a python implementation.

The study is of potentially high value for CO2 emission estimates from upcoming satellite instruments and should thus be published, after dealing with the following issues:

1. Impact on emission estimates

The success of the denoising procedures is clearly demonstrated and quantified based on two performance scores (PSNR and SSIM).

However, the eventual goal is the quantification of emissions, and the crucial question is whether the proposed denoising introduces a bias that might then also bias the estimated emissions.

The authors deal with this question in Figs. 6 & 7, where they apply the divergence method to the SO2 maps and derive emissions from spatial integration.

However, the results are hard to interpret, since the true emissions are not known! 

Thus, this question should be investigated based on the *synthetic* data where emissions are known:

- create an ensemble of noisy CO2 images

- apply the proposed denoising

- quantify emissions from divergence method

- whenever a clear peak is appearing in the denoised data, quantify emissions from a plume-based method (e.g. cross-sectional flux)

- compare the resulting ensemble mean emissions to the a-priori truth for the different denoising algorithms.

This may sound like a major task - however, the authors have all the tools needed at hand, and for me this is the most important question after reading this paper.

For future applications, it should not be the goal to create highest PSNR, but to get the most accurate emissions, so the latter needs to be quantified as well and added to the performance scores.

2. Correlated errors

The derivation assumes independent errors (line 60), and equations become simpler by this assumption (line 77).

This is picked up in section 4 (discussion), shortly mentioning "structural noise patterns, such as stripes".

While it remains unclear, what could cause such structural noise patterns, I am more worried by systematic impacts such as ground albedo or clouds - any bias in the input data would cause correlated errors in NO2 and CO2 (or SO2). This unavoidable source of correlated errors and potential impact on the results needs to be discussed in more detail.

3. Datasets

The proposed method is applied to synthetic data as well as to actual satellite measurement. For the latter, details about the data are missing.

Please add a paragraph on the used satellite data, in particular the chosen products and processor versions, plus appropriate references.

In particular for SO2 this information is crucial, since the operational processor was recently switched to the COBRA algorithm with far lower noise levels.

4. Figures

- size/clarity: Some figure (in particular Figs. 3&4) are not very clear. I would propose to use a different colormap, vary the value range, and increase the figures. Zooming in might help as well (a large area north and south from the plumes seem to be irrelevant).

- scaling / aspect ratios: please add a km scale and choose an aspect ratio such that distances in x and y are scaled same.

Additional comments:

Line 11: I find the 40 decibel hard to visualize and would prefer a ratio of SNR here which would be more transparent and common.

Caption Figure 1: I don't understand / see the "high contrast edges" which should be visible in SO2 but not in NO2. 

In Box C, I see far more plumes in NO2 than in SO2. So to which "edges" does this statement refer/what is the message of this section? 

Line 85: Please explain why hereafter it's E(M) instead of E(~M).

Line 165: Please provide information on the resolution/gridding of the SMARTCARB data.

Fig. 3: CO2 colorbar is given for upper row, but applies for left column. NO2 colorbar is given for lower row, but applies for right column.

Line 196 / footnote 3: So what is the benefit of such a coarse AMF correction? Isn't this just an upscaling of the SO2 data? Does it make any difference for the resulting maps and noise scores if this correction is applied or not?

Line 200: Hard to read with multiple negations (large region of low inverse SNR - is this good or bad?).

Line 220: I assume the averaging of the ERA5 winds uses the GNFR-A profile as weights - please clarify.

Fig. 5:

- which filter has been applied for the satellite measurements?

- please use consistent units for columns (molec/cm2 as in Fig. 3 or mol/m^2 as in the TROPOMI products, but then also for the synthetic data).

- add the PSNR/SSIM scores to (e) and (f), as in Fig. 4.