This article applies several different CH4 retrieval schemes to HySpex imaging spectrometer data from an anthropogenic point source.  It compares a nonlinear algorithm, involving spectrum fitting using a nonlinear radiative transfer model, to various linear schemes.  It also compares several algorithm variants, including pre-clustering data with k means and accounting for the covariance of surface reflectance in the nonlinear model.  

There are some clear and obvious achievements.  The algorithm descriptions are incredibly comprehensive, with enough detail to serve as a reference for investigators coding their own implementations.  The manuscript deals with an important and timely topic, adding to the growing literature on point source GHG detection from coarse-spectral-resolution imaging spectrometers.  It independently validates these approaches, and adds some new data sets to the mix.  

This said, I have some recommendations for how the manuscript might be improved.

My first major recommendation is to clarify the thesis statement. After reading the article, I'm still a bit unclear on the fundamental contribution.  The manuscript focuses mostly on retrofitting the BIERRA algorithm for CH4 point source detection at coarse spectral resolution.  However, by the end of the manuscript it is unclear what advantages this offers beyond the state of practice Matched Filter methods or other very similar nonlinear model-fitting methods in common use (like the Thorpe et al. IMAP-DOAS approach).  The affect of albedo on nonlinear CH4 retrievals is great, but it has been investigated even more thoroughly before - see for example Ayasse et al. 2019 (https://doi.org/10.1016/j.rse.2018.06.018).  I think the authors could do a better job of calling out what is new and significant about the BIERRA approach.

My second major recommendation is to have a quantitative performance comparison.  The current assessment is fairly subjective, related to the quality of the plume image and the visual appearance of background interference.  Couldn't the background variability outside the plume be used to quantify the detection noise for each method?  And couldn't the strength of the plume enhancements then be used to create an SNR score or statistical confidence?  As a part of this effort, it would be great to translate all of the plume maps into similar units.  Currently maps appear variously as ppbv, alpha-CH4, and "enhancement factors," which makes it difficult to inter-compare.  It should be possible to translate any one of the linear detection algorithm results into an equivalent CH4 mass enhancement, and compare the effective plume-to-background detection SNR of each of the algorithms.  

Minor suggestions:

1. Almost all of the prior literature cited on CH4 point source detection, and the vast majority of the imaging spectroscopy community working at these spectral resolutions, plot spectra in wavelength rather than wavenumber. Setting aside the question of which convention is more convenient or appropriate from a technical perspective, it would certainly be easier for the majority of the readership to quickly understand the figures if wavelengths were used.  This would make the instrument sampling evenly-spaced in the horizontal direction.

2. On line 61, are there citations for CarbonMapper or CO2Image missions?  I think the claim that CarbonMapper operates at higher spectral resolution than average land surface imaging spectrometers (5-10nm sampling) could be incorrect.

3. On line 65, in the literature review of airborne CH4 point source campaigns, consider also the studies by Frankenberg et al. 2016 (https://doi.org/10.1073/pnas.1605617113) and Duren et al. 2019 (https://doi.org/10.1038/s41586-019-1720-3) which were earlier and larger.

4. Figure 2 (a) seems to be missing some lines.  "Grass" is misspelled. 

5. On line 183, can you provide any more specifics about the low order polynomial used?  What was its degree and where was it centered?  The details are significant because, as you note, the surface reflectance is often quite complex over these wide spectral ranges. Changes in the reflectance representation can have huge changes on albedo sensitivity.

6.  On line 195, the section comparing different least squares solvers seems ancillary.  Least squares solvers are a commodity 

7. Figure 10.  I'm not sure what this is supposed to show.  Could it be removed?  

8.  On Figure 12, the enhancement within the plume appears completely saturated, which makes it difficult to assess.  Can you rescale the colormap to make it more similar to the other plume images? 

9.  The discussion and conclusion is good, but would be further strengthened by quantitative claims about where and how the different algorithms outperform each other.

The manuscript of Hochstaffl et al. present an intercomparison of different CH4 retrieval approaches for airborne hyperspectral measurements during an overflight of the HySpex instrument over a known CH4 emission source in Poland. Gives a short overview over the different techniques and present the retrieved maps for specific scene which are then discussed. CH4 retrievals from hyperspectral measurements is a quickly evolving field and there is merit in intercomparing different retrieval methods based on real, measured spectra.

The manuscript is in principle relevant and suitable for Atmos. Meas. Tech. but there are several shortcoming that limit its value. The manuscript is somewhat dominated by the method section while the discussion could be more detailed. In this section, a lot of material is squeezed in which makes it hard to read and I am not sure how much the reader gets out of it, especially since variables are not always well defined or used in consistent manner. The presented analysis is purely qualitative, very brief and limited to a single scene. The lack of ground truthing means that it is not possible to tell which method is best and thus the study is limited to comparisons against each other which then should be done more rigorously.

My main comments are:

• Several figures need to be improved and labelled consistently (see detailed comments below). Especially the map of retrieved methane should be shown for the same number of cross and along track pixels so that results can be compared. Also, give results in CH4 for all methods and not as scalding factors.
• The analysis should be more quantitative. In the discussion, you state that the MF method can be used as reference, so lets also do this. You can apply simple methods to identify a plume (eg thresholding) which will then allow you do contrast inferred plume shapes. Also, I would like to see correlation plots of CH4 enhancements between different methods for example for pixels within the plume (eg defined according to the the MF method).
• Also, check all equations and ensure that all variables are fully defined and used consistently. For example, beta is used to describe 3 different variables.

Specific comments:

Page 2, line25: important greenhouse gas -> important anthropogenic greenhouse gas

Page 2 line 32: fossile -> fossil

Page 2 line 38: besides satellites, there are the global in-situ surface networks

Page 2 , line 55: smaller emitting area. This does not refer to IR so it is reflecting rather than emitting.

Page 3, line 61: add reference for CHIME, eg. Rast et al., IEEE, 2021

Page 3, lines 60-63: add MethaneSat for completeness

Page 3, line 75: slowly varying part is also from scattering

Page 3, line 81: This study compares various retrieval schemes ….  -> please add the the goal of study

Page 4, section 2.1: I suggest to add a table with the key instrument parameters for the HySpex instrument

Page 4, line 96: in detail in (IMF) -> missing reference ?

Page 4, figure 1b: The fonts on the figure are too small and can not be read in a hardcopy.

Page 4, line 97: in the following chapters -> in the following sections

Page 4, line 101: …and if so how accurate… -> I don’t think that this is addressed in this manuscript ?

Page 4, line 108: seen in Image 1a, -> Figure 1a

Page 5, line 109: wind data for the USCB area -> This needs to be defined separately to the definition in the abstract. However, I don t see the need to introduce this acronym as it is not used anywhere else.

Page 5, line 119: 967–2496 nm (4005–10338cm−1). Throughout the manuscript at some places wavelength and and at other wavenumber is used. Since wavenumber is primarily used, I suggest to use consistently wavenumber throughout the manuscript and give everything in wavenumber and not wavelength.

Page 6, figure 2: a) please make fonts larger and lines thicker. In a hardcopy this figure is hard to read.  Also, can you give a reference for the albedo data

b) Use either ‘wavenumber’ or ‘wavenumbers’ for the x-axis. Use either round or square brackets to give units. Label the y-axis with the shown parameter (not only units).

Remove the 2 extra digits on the x-axis labels.

Caption: CH4 -> CH₄

I don’t think that adding the vertical lines to indicate spectral pixels adds value and neither does overplotting all spectra into the figure. I suggest to remove the lines and show a mean spectrum and a standard deviation. You could add the one spectrum with the outlier.  

Page 6, line 131, see absorption from methane’s 2ν3 band around 6000cm−1 -> where do I see this. Can you label this in the figure ?

Page 7, line 136: under clear sky conditions (cloud free) -> also scattering free in general

Page 7, eq. 1: ds needs to be removed in the sum of the first equation. define all variables including tau, nu, p, T, s and m

Page 7, lines 145-150: I don’t see how the extract on aerosol optical properties is relevant. I suggest to remove this and simply refer to a textbook. The use of wavenumber of wavelength in this section is unnecessary. K_aer: give units.

Page 7, line 153: composed by pure -> composed of pure

Page7 , lines 154-155: define z, also I don’t see the need to use zmol, zsc  instead of simply z.

Page 7, eq.5, define tau_bg and tau_pl. What is alpha here ?

Page 8, line 161: The CH4 background as well as the CO2 initial guesses -> The CH4 background profile as well as the CO2 initial guess profiles

Page 8, figure 3: BoA, TOA -> BOA, TOA

Al least for CO2 and CH4, a mixing ratio profile would be more meaningful

Page 9,line 186: is SRF different to ISRF ? This are examples for the many acronyms introduce but not used in the manuscript.

Page 10, figure 4: remove unnecessary digits on x label. Thicker lines in panel b would be helpful

Page 10, line 194: Jacobian matrix -> define Jacobian

Page 11, Figure 5: give the definition of alpha and r in caption . Remove unnecessary digits

Page 11, line 202: the converged spectrum->  the converged spectrum I

Page 11, line 206: from the diagonal elements -> from the square root of the diagonal elements

Page 12: beta is already used as Angstrom coefficient on page 7. Please use another variable name here.

Page 12, eq. 11: define meaning of y hat.

Page 13, define alpha tilde is.

Page 13, line 231: What is a scene average scaling factor. I don’t believe that the given references apply such a scene average scaling factor.

Page 13, eq. 12: usually the CH4 to Co2 ratio is multplied by a ‘known’ CO2 profile. If you use the co2 scaling factor directly as a correction for light path modificatiins then you assume that the CO2 profile is perfect and that alpha is 1 in absence of scattering.

Page 14, line 256: the (saturated, see…  -> the saturated (see…

Page 14: eq 14: what is the meaning of the up and down arrows in the optical depth. Why is there a beta factor in the Taylor expansion why is not in the exp function. Also, how is beta defined. Note that beta is used already twice with other meanings.

Page 14, lines 261-261: M and N is now used in capital but was used before in small letters m and n (page 11)

Page 14, line 269, condition number of 885 -> Please put this in some context. Which condition number is sufficient and which not.

Page 15, eq. 16: isn’t (J – mu) the target spectrum t . If so, then use t in equation.

P15, l284: here tau and beta is defined which would already be needed with eq. 14

P 15, eq. 18: is t here now the Jacobian. Jacibas so far is called J while t has been used as target spectrum in section 2.5.1.

Page 16, figure 7: What does stand. rad. mean? State in caption that u1-u4 are singular vectors ?

Page 17, eq. 21: meaning of beta ?  I assume this is again different to the 3 previously define beta’s?

Page 17, line 343: retrieal’s -> retrieval’s

Page 18: lines 348: changing the resolution will typically also change the SNR

Page 18, table 1: condition numbers need to be put into context.

Page 18, line 351: The state vector x = (3m,3r) was found to be robust toward low SNR… -> what do you mean by robust?

Page 18, lines 354: use wavenumber here and not wavelength so that it is consistent

Page 20: figure 8: can you add figure with retrieved surface reflectivity.

Page 21, Figure 9 : make figure the same along track and across track range as figure 8. Please make all the plume figures the same range for comparability. Also, give CH4 on maps and not the scaling factors (figure 13 and 14, 15).

Page 22, figure 10: Hard to see anything. I suggest to plot only lines instead of lines+symbols.

Page 26, lines 424: The relative enhancement is slightly better represented in Fig. 14a.-> I don’t think you can tell what is better as you don’t know the truth.

Page 27: The method yields consistent results for both spectral intervals. -> results shown in Figure 16 are very different. In which way are they consistent ?

Page 28, line 444, should Figure 16 have 3 rows for zero, 1 and second order ?

Page 29, Figure 16: can you use same colour scale and format to increase the comparability ?

Page 30: A validation from independent measurements is hence outside the scope of this study -> A validation from independent measurements is outside the scope of this study

Page 30, lines 461: the results from the well established MF method can be considered

some sort of verification -> what is the justification for this. Is there a reference that can be used in support ? Also, the results from MF are not used as reference for the analysis.

Page 30, line 463: and the results agreed well with ≈ 3%. -> where is this shown ?

Page 30, line 467: was found to be the most sensitive method for the detection of enhanced methane -> how is this conclusion drawn ?  

Page 30,line 478: and potentially quantified from HySpex -> you have not shown this. 

Page 31: line 494: agree well on the plume’s shape. -> this is not shown in the manuscript

Page 30, conclusion: can you discuss if the findings from this study are only applicable to Hyspex or also to wider range of hyperspectral sensors for example on satellites,

Review

Title: Methane retrieval from airborne HySpex observations in the short-wave infrared

Author(s): Philipp Hochstaffl et al.

MS No.: amt-2022-271

MS type: Research article

Special Issue: CoMet: a mission to improve our understanding and to better quantify the carbon dioxide and methane cycles (AMT/ACP/GMD inter-journal SI)

This work study the performance of methane retrievals deduced by non-linear and linear methodologies from data obtained by airborne HySpex observations. Methods are applied in several spectral ranges in the SWIR, where methane absorption features are located.

Within non-linear methods we find the Nonlinear Least Squares, the Separable Least Squares and the Generalized Least Squares and within the linear methods we find the Linear Least Squares, the Matched Filter, the Single Value Decomposition, and the

Spectral Signature Detection. While non-linear methods are more time-consuming and get a best estimate, linear methods are faster and can be more suitable for real-time onboard measurements.

This study is helpful in order to understand the limitations of HySpex in detecting methane emissions with several methods. A good understanding of these limitations can establish a strategy to get optimal methane concentration maps on real time and after the flight.

The results introduced in this work are of remarkable interest and a great amount of work must have been involved. Methane retrieval and methane retrieval error figures are very self-explanatory and visual. Moreover, there are a great diversity of methodologies that

have been explored, which is a decision that helps to determine more thoroughly the limitations of Hyspex for methane mapping.

I find high value in the objectives of this paper and the figures, but I see strong shortcomings that make me decide to accept this paper with ‘major revisions’.

Major revisions

- The paper is hard to read: there are very long sentences that are difficult to understand, and I find a strong lack of coherence and consistency in writing. I would recommend a rewriting that makes the work easier to read.

- Figures are not exploited. Although the figure can be mentioned in the text, there is little feedback between text and figures. This happens with Fig. 3, Fig. 4, Fig. 6, Fig. 7. I doubt if these figures are necessary. Besides, I find information that does not contribute to the paper, such as a lot of details about the in the aircraft measurements, determining the nature of absorption features (vibrational transition), etc. Altogether, the paper could be shorter and preserve the important information at the same time.

- Methods are not clearly introduced. Some parameters are not explained and some formulas appear without a previous justification or citation. As a consequence, the reader could doubt about the theoretical basis of the diverse methods. There is also a lack of consistency in nomenclature: some variables are written in different ways along the study, which makes it difficult to keep up with the paper.

- Results are nor exposed nor discussed in a consistent manner. For example, methane retrievals are showed in both single spectral intervals and also the multi-interval in the NLS, but the multi-interval is not shown in GLS. Besides, I think a more thorough discussion would have been appropriate. A table gathering statistic information about the performance of every method could be an adequate manner to do it.

- Conclusions about the different methods are not clear. Which are then the best methods? Which is the best strategy to map methane in real-time flight and after the flight? Maybe this could be clearer with the table that I commented previously.

Minor revisions

Line 33: Fossil fuel exploitation is responsible for 30-42% of all anthropogenic CH4

emissions (Saunoise, 2020).

Line 40: the absorption spectral ranges are not correct.

Line 54-57: example of too long sentence.

Line 75: moderate spectral resolution is defined as ‘>1nm’. And what about the coarse spectral resolution?

Line 77: I think you can make a more thorough distinction between data-driven methods and physically based methods (see Guanter, 2021).

Line 96: ‘a VNIR-1600 and a SWIR-320m-e’. I supposed the former can measure VNIR radiation and the latter SWIR radiation, but this is not explicitly explained.

Line 112: I think ‘0955 UTC’ is not a valid timestamp format.

Line 156: ‘methane enhancement’ instead of ‘Gaussian plume’. The gaussian plume would be the result of the methane enhanced pixels close to an emitting source.

Line 166: ‘BIRRA level 2 processor’ could be in italics.

Line 166: DLR initials are already explained.

Line 319: interpolated band ratio (CIBR) from Green et al.(1989)…

Line 344: retrieval.

Line 399-400: ‘The algorithm employs the inverse of a scene’s covariance structure to account for backgorund statistics in the retrieval’. This was already stated in ‘Methodology’.

Line 445: What is (a,d,g), (b,e,h), and (c,f,i)? It is not clear.

Line 469: However.

Line 474: So far, only narrow…