|Review for “Metrics for evaluating the “quality” in linear atmospheric inverse problems: a case study of a trace gas inversion”|
The manuscript presents some very interesting analyses on evaluating inversions. I think the author’s have tried to address most previous reviewers’ concerns and I agree with the authors’ decision to submit this as a technical note. The authors have also provided additional details to improve the manuscript compared to the first version. I appreciated the IAOMI and can see the value of this in satellite-based inversions, given the much higher potential for overlapping information. I was surprised that the authors didn’t mention this, given their affiliations.
However, In its current form this manuscript is extremely difficult to read. I recommend this being published in GMD, if the authors are able to make this manuscript more coherent and expand on the discussion of the figures presented in Figs.4 -6. Finally, there are several typographical errors in the manuscript, which is somewhat common while providing a revised version. I have highlighted a couple, but I trust a proofread to fix any remaining errors. Below I provide some suggestions to help improve the manuscript.
1. Lines 31-41: this paragraph comes off as jargon heavy and assumed that readers know what all the terms that are mentioned are (e.g., polynomial Chas expansion, Sobol’s method etc). The authors should provide some clarifications or delete this paragraph.
2. Line 46: Define “analytical closed form solutions”
3. Eq 2: define what the summation is over. For instance, it could be space, time or both. This information is somewhat implicit, but I would appreciate if the authors would state this.
4. Line 129. IAOMI not IOAMI right? The authors use IOAMI several times in the manuscript.
5. Line 139: More jargon. You could rephrase as “Jaccard similarity index which describes… “ Similarly for the Ruzicka index.
6. Line 185: This is an example of how this could be particularly useful for satellite data.
7. Lines 198-208: The authors do a good job at describing the terms in eq 9 and 10 but I think could a line or two about interpreting it. For instance, in both eqs the first term describes the observational constraint while the second term describes prior info (in eq 9) and information about fluxes (through X in eq 10). Also mention why we need the second terms in both equations.
8. Line 215: Reads a little awkward. I’m guessing they are saying Beta needs to be estimated? Clarify.
9. Line 225: What does “entry” mean?
10. Line 319: a great time to remind your readers what GSA means (even if it has been defined earlier).
11. Line 328: Define DGSM
12. Line 375: missing word “for” between accounted and through?
13. Fig 3. This is an interesting figure but perhaps also misleading. Obviously all gridcells in the shaded region for a given observation don’t contain equal information. I would request the authors to provide a complimentary figure showing the footprints.
14. Fig 4. This figure and the caption really need to be improved. The caption currently is not very helpful. I had to refer to Table 1 to interpret it, and it still left me a little puzzled. For eg., if USC is the least sensitive observation to s_hat (according to Table 1) then why are their maxima around other observations? Also panel D shows a footprint for BND, which according to Table 1 is not the least important obs, but is stated to be the least important in line 463.
15. Lines 471-476: This section needs some more clarifications. For instance, how are quantities “grouped”. Not very clear currently.
16. Fig 5. Again not well explained or discussed at all. I would want the authors to expand on this figure and tell the readers exactly what they are seeing. The map of ds/dz shows that there is more sensitivity where there is an observation but if GRA is constraining the fluxes most, I would have expected it to stand out compared to the other sites. Similarly, if BND(?) is constraining the fluxes least I would have expected that site to “merge” with the background color of the map. I also didn’t understand the map of ds_hat/dR or how to interpret the information in that map. In the plot of ds/dQ why is there an increase in sensitivity around observations? Expanding this information would help readers understand what you are learning by computing these partial derivates and prompt other inverse modelers to calculate these for their inversions. Finally, this figure needs sub panels.
17. Fig 6. This figure needs the most help. No information (statistics) on the fits is provided and very little is explained. I would suggest the authors to either remove this figure entirely or discuss each scatter plot and how to interpret.