|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’.|
- I find that the manuscript is really hard to read because several reasons:
* There are a lot of information that could be removed without affecting to the quality of the manuscript. This information is often irrelevant and difficults the understanding of the essential the points of the manuscript.
* It is long. Shortening the manuscript could make the text more accesible for readers. I would suggest the authors to optimize the content to the truly important data.
* English can improve. Some expressions doesn't sound natural and there are large sentences that are difficult to read.
- The work presents a complexity that is not well developed. I suggest a more plain explanation of certain points. However, if the authors want to explain them with a high level of complexity, it should be better explained.
- Re-check on citing.
L20 - with the passage of time the word 'latest' loses meaning.
L22 - it seems redundant: 1 decade and approximately 9 years. I'd try to unify these 2 concepts
L25 - concentration instead of content. I think is more appropiate.
L25-26: I think this sentence can be removed: 'Observations indicate an increasing trend in atmospheric CH4 content since 2007, the cause of which is still subject to scientific debate'
L29: to foster understanding OF the global methane cycle
L33: method of choice doesn't sound natural. Maybe... 'typically used methods'
L43: point sources (Duren, 2019, Nature) instead of point-like sources
L43: just 'This limitation is due...'
L56-58: I don't think references are well written here. Besides, to cite EnMAP mission it is better to cite Guanter, 2015. And probably also PRISMA mission should be cited with another reference.
L68-69. There is a specification for spectral resolution (>1nm), but there isn't for spatial resolution.
L70-72. Retrievals are the results. Maybe you mean methods to acquire the trace gas retrievals.
L77. Concentration enhancements*
L89 - 'often PRESENT sufficient accuracy'.
L89 - Every nonlinear method are iterative?
L89 - I would reformulate this sentence. Sufficient accuracy seems a good enough accuracy. Then, why nonlinear methods?
L90 - I don't understand this: 'The retrieval methods are tailored to address the issue of albedo-related biases, which arises due to correlations with broad-band absorption features resulting from the instrument’s low spectral resolution.' - I would try a more plain explanation.
Figure1-caption - It is difficult to distinguish between the dashed and solid lines. I would try to improve the figure in this aspect. What is 'a' in 'kt/a'? Besides, I think that there is some irrelevant information here for the study (QGIS, flight overpass time-stamps...)
L96 - conduct or evaluate?
L99 . I think the comma ',' can be removed.
L100 - I think this is not the best way to cite.
L106 - What does observation mean? It is not clear. Is important to know that?
L106 - '320 across-track detector pixels': this is inherent to the Hyspex SWIR spectrometer measurement.
Figure 2-caption - detectors, not pixels. Pixel position?
Figure 2 - there is a lot to improve in this figure. There is overlapping of numbers, the font from labels makes it difficult to read, the mentioned 'center' is at the left side of the figure, there is two horizontal axis in b) (not necessary).
L111 - No need for specifying the equivalence in wavenumbers units.
L115 - not pixel, just detector
L126 - in general?
L129 - molecular m? not clear
L130 - 'Atmosph’erique'
L141 - not pixels
L145-146 - I'd write 'The highest vertical resolution is found in those layers below...'
Figure3-caption - I don't understand 'mid-infrareddle panel'
L163 - the new Python version of BIRRA that is used is based on...
L170 - 'The transmission by aerosols for different Ångstrom exponents according to is depicted in Fig. 3 (center)' - Incomplete sentence?
L174 - What is 'j'?
2.3.1. - Here NLS, SLS, and GLS are introduced. But in L159 only NLS and SLS are mentioned.
L185 - Function 'L' is not defined.
L188 - You say 'separable least squares solver' when you already defined SLS.
L198-L200 - How do you get C? Why the location of the point source and wind data must be known?
Figure4-caption - Panel show S^-1, but the caption says: 'backgorund covariance matrix', i.e., C.
L209 - Jacobian matrix
Eq 12 and 13) I don't understand where they come from
L263 - likelihood
L269 - per pixel doesn't seem possible (maybe per column)
L284 - USVt is not explained
Figure 5 - Fontsize could improve.
L329 - Figure 8b shows
Figure8-caption - here you shouldn't write 'Best results are acquired for GLS setup'.
I don't think the retrieval from averaged data should be showed. They are not so important and can simply be commented in the text.
L341 - but the and as?
4K and 6K retrievals are shown in some methods and not shown in others. Why so?
L344 - to identify
L345 - the lowest
L347-349 - This should not be in this section