the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Oct 2025
Bayesian denoising of satellite images using co-registered NO2 images
Abstract. Accurate emission tracking (e.g., locating and quantifying hot spots) using satellite images requires a good signal-to-noise ratio (SNR) of total column images. Achieving this SNR is challenging for satellite-based trace gas imagers, especially when enhancements are small relative to the background or small relative to retrieval uncertainty. Therefore, some satellites carry additional trace gas imagers with high SNR, such as NO2, which is co-emitted with the trace gas of interest. While NO2 is frequently used qualitatively for plume detection or plume fitting, its potential for quantitative noise reduction remains largely untapped. This paper presents two methods to enhance the SNR of total column images using co-registered NO2 images through minimum mean square error (MMSE) Bayesian denoising, which are a simple form of a Kalman filter or maximum a posteriori estimate. The first ''joint MMSE'' method relies on the presence of plumes in both the low- and co-registered high-SNR NO2 images. The second ''self-similar MMSE'' method utilizes image self-similarity and is based on an existing technique called BM3D. The methods are evaluated using a synthetic dataset (SMARTCARB) of atmospheric CO2 and NO2 concentrations, achieving over +40 decibels improvement in peak SNR. Additionally, the methods are applied to TROPOMI SO2 and NO2 data over South Africa and used to compute a divergence image, demonstrating that an estimated 30–60 % noise reduction is possible. By enhancing the SNR of total column images, these techniques improve the detectability of subtle emission signals, which could benefit atmospheric monitoring applications.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4477', Anonymous Referee #1, 03 Nov 2025
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RC2: 'Comment on egusphere-2025-4477', Anonymous Referee #2, 25 Nov 2025
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.Citation: https://doi.org/10.5194/egusphere-2025-4477-RC2
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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
Specific comments
Technical corrections