the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Sep 2026
Quantifying area-source methane fluxes with path-averaged laser beam concentration measurements and Bayesian inversion
Abstract. Accurate quantification of diffuse, area-source methane emissions remains a key challenge in closing the gap between bottom-up and top-down estimates of the global methane budget. Existing measurement approaches are limited by spatial coverage and ability to interrogate diffuse sources in the presence of a time-varying background concentration. Here, we present a framework combining kilometer-scale path-averaged laser beam concentration measurements with an analytical Bayesian inverse modeling approach to simultaneously retrieve spatially distributed area-source methane fluxes and a time-varying background concentration, without requiring direct background subtraction. We evaluate the system through an Observing System Simulation Experiment (OSSE) using real meteorological data, realistic instrument and transport model error, and a representative laser beam geometry observing three distinct but diffuse area sources. The inversion framework accurately retrieves weekly average emission rates across a wide range of flux magnitudes, with well-constrained estimates achievable for near-beam sources at median concentration enhancements as low as 1 ppb above background. We demonstrate the utility of running an ensemble of inversions to provide more robust emission estimates in the presence of uncertain prior flux distribution parameters. The system maintains accuracy within 10 % flux sources characterized in the prior even when a nearby emitting source is not represented in the prior estimate. This framework expands the conditions over which path-averaged laser concentration measurements can be used for area-source emission quantification and provides a pathway for optimizing future real-world deployments.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-3516', Anonymous Referee #1, 18 Oct 2026
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RC2: 'Comment on egusphere-2026-3516', Anonymous Referee #2, 27 Oct 2026
This paper numerically investigates the ability of open-path concentration measurements to constrain area sources using a Bayesian inversion approach. Several OSSEs were performed across a range of source strengths. In general, the inversion approach performed well was able to accurately determine flux and no flux regions. While the approach is not necessarily "novel" in that the Bayesian inversion is regularly used with point measurements, there has not been a full study of an inversion with open-path measurements. Thus, the results are of interest and provide a framework for future work. Overall, the paper is well written, and I would recommend publication after some modification.
Major points:
- I have some questions about how the model uncertainty was treated.
- Were the same footprints used to generate the enhancements as well as to run the inversion? It would be better to have these be uncorrelated, which would add some treatment of model uncertainty.
- It sounds like L (Obukhov length) was constant, is this correct? If so, this does not mimic reality and could add challenges to the inversion. Have you tried with variable L?
- In addition, was the 20% uncorrelated between temporal steps? This also is not necessarily physically realistic. Have you tried including a correlation time in this error? Can you try to use a ensemble approach with met uncertainty (including L as mentioned above)?
- While there are many additional OSSEs that could be run, it is of course not possible to do all of them. However, one that would be helpful I think would be to have the source regions set to different emissions rates within the uncertainty range of the prior to make sure the inversion converges to the correct values.
Minor questions/comments:
- Line 192: How was the 50 m resolution chosen?
- Line 193: Were the paths all measured simultaneously or sequentially? If sequentially, what was the dwell time per path?
- Line 257: Did you try other numbers of segments per beam path?
- Line 339: If the correlation length for source regions is 1500 m, does this mean that there is an enforced correlation between source regions? Or is that just within a single source region?
- Line 389: Does this mean that the correlation and error covariance for region 2 is also that of a non-source region?
- Line 490: Consider rewording "mean 0.2393 for all background concentration averaging kernel averaged through time"
- Figure 5: Can you add an indicator line or similar for what the experiment 1 run was?
- Line 544: "receives incomplete constraint". I would suggest that an aggregated averaging kernel of 0.026 is basically unconstrained, not incomplete constraint
- Line 555: I don't understand how the aggregated averaging kernel is >= 0.98. In Figure 4 (which I think is the same flux value), the averaging kernel seems to be around 0.2 on average.
- Line 597: typo "in the fluxes of are"
- Line 612: add "the" between "prior, prior"
Citation: https://doi.org/10.5194/egusphere-2026-3516-RC2
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The manuscript presents a synthetic study on the information content of path averaged concentration measurements close to the ground with respect to area emissions. The authors chose a Bayesian framework to perform an Observing System Simulation Experiment (OSSE) on a network of kilometre long paths, fanning out from a central point – a common setup for this type of remote sensing system. While this type of inversion framework or study is not new to the remote sensing world, its application to the quantification of area sources using path averaged concentration measurements is a seldom covered niche and major real-world issues, like a varying background or unknown source regions, are addressed. Hence, this is a valuable study that fits the scope of AMT, and I recommend it for publication after minor revisions, which should clarify some important technical details and sharpen the relevance for real world deployment.
Major points
A common argument for path averaged measurements and their inherently averaging nature is that they should be less prone to errors resulting from small scale spatial structure in the emissions not captured by the prior. Is there a way to represent emission heterogeneity instead of just a factor on the enhancement for your simulated observation errors (2.3.5) or later your large scale unknown source? A demonstration of a reduction of the transport model error or a lower sensitivity to a wrong emission structure in the prior would elevate the impact substantially. It might be too much to ask within the revisions of this manuscript, but I would like to encourage the authors to consider whether their setup can provide such insights in a meaningful way.
Regarding your a priori constraints on source and non-emitting regions: Even with relative uncertainties of up to 200%, in absolute terms your non-source regions are quite strongly regularized to zero. Similarly, your spatial correlation length difference between non-source and source pixels seems to enforce a very strong boundary between source and non-emitting regions (do they even influence each other?). As a result, you seem to enforce an unrealistic heterogeneity, size, and shape of your different regions. I fear this only works because your synthetic setup is in itself structured like this (rectangular source, uniform strength, etc.). In my opinion it remains mostly unclear how your results relate to a real world application, especially without a demonstration of how errors in these structural elements of the prior propagate. I would ask the authors to strengthen this link to real world applications.
Related to the previous point, some key details of the most relevant experiment (source region 2, which is not known a priori) remain unclear in the manuscript and require a more precise explanation. Some key statements in this context are also pointed out in the line-by-line comments.
Line by line comments
Line 195ff: In most of these works the path is quite a bit higher than 2 m above ground, which is often simply required by topography on horizontal scales of 1000 m and more. Can you comment on how this impacts the results/analysis?
Line 206: Could you elaborate (if of interest) on the necessity of the buffer zone region 5? In its current form I don’t understand it.
Table 2: Alignment of the numbers in the second column should be the same for all.
Line 237f: Do you have evidence from data that this two-component approach for the noise resembles real world data?
Line 257: How did you decide on the spatial resolution?
Line 258: Which exact BLS model/implementation did you use? Or is it home grown? Maybe you mentioned it somewhere, but I couldn’t find it.
Table 3: In absolute terms your non-emitting regions are quite heavily constrained (even with the 100%-200% uncertainty)
Line 330ff: This relates to major point 2. It is quite instructive to see how a priori assumptions on the (spatial) structure enter the off-diagonal elements of the covariance matrix. But to me it is currently not 100% clear how the correlations across the boundaries between non-emitting and emitting regions are handled and what the respective results are.
Line 353f: Why 20%?
Line 389f: Again related to major point 2. Does that mean that the correlation length is treated for region 2 as for non-emitting regions?
Figure 4: Could you please give the spatial resolution of the inversion pixels in the caption? Also, if it is a single instance, could you show the (synoptic) wind speed in the plots?
Line 476: I am missing a description of how you arrive at the matrix in Fig. S4, since you are inverting on a pixel grid and not just these 7 parameters. Maybe add that to the supplement.
Line 499ff: The statement (“For those reasons [..]”) is not clear to me.
Line 575f: Maybe related again to previous points, but I don’t understand whether region 2 does not even exist or is simply set to the same prior/correlation lengths, etc.
Figure 6: Something like Fig. 4 would be useful here, especially the posterior fluxes for a high median enhancement.
Line 595f: The statement “This increase […]” might miss what is actually happening. As I understand it, the non-source regions in Fig. 6 are summed over the whole respective region. Since you retrieve pixel by pixel, the sharpness of the boundary for region 2 (see Fig. 4) would actually be unexpected if not for the fact that you enforce a certain homogeneity across a predefined domain with your spatial correlations. So if you dropped this form of top-down definition of sources the boundary should get fuzzy and you should also see similar enhancements in the actual non-source regions close to it. The very small errors in the inset of Fig. 6 could then also result from the fact that the domains are substantially larger than region 2. I think that it would be clearer what happens with a spatially resolved plot of the posterior fluxes as proposed in my comment on Fig. 6.
Line 597: “uncertainty in the fluxes of are” – language?
Line 607ff: again, something like Fig. 4 would help here.
Line 611ff: Priors are of course always imperfect. I think the narrative of this final paragraph could be improved.
Line 621ff: It should be clearer in the conclusion that this is a synthetic study.
Line 637ff: Since this is a synthetic study, I don't consider this an issue here. The more relevant question is whether you would want to replace the BLS with something else for field deployment.
Line 648ff: While I agree that end-to-end simulations are desirable, you seem to skip the important step of analysing the impacts of actual terrain and a more heterogeneous/realistic environment in your outlook.
Please note that I used an AI tool for minor language touch ups.