The authors have addressed many of my comments since the first review, and the manuscript is definitely improved. However, I still have some significant concerns that need to be addressed before the paper can be published.
--Major Comments:
(1) My biggest concern is with the uncertainty. The highly structured reflectivity curve of the mirrors significantly limits the accuracy of the Rayleigh scattering cross sections in this study and therefore limits the conclusions that can be drawn from this work. The unfortunate reality is that the very thing that is newest about this paper (the very broad wavelength mirrors) is the thing that seems to cause the most problems.
The limitations on accuracy due to the structured reflectivity is abundantly clear in Figure 9. The Pink data simply cannot be used to provide any constraint on distinguishing the green (previous work) and black (this study) fit lines, especially for SF6 and CH4. Perhaps the green and black fit lines are different enough for N2O to warrant producing a new dispersion relation. But for SF6 and CH4, the results of this study can only be used to say that they validate the existing n-based expressions.
Moreover, as now detailed in lines 254-259 of the revised manuscript, there are additional uncertainties beyond those treated in the paper that the authors cannot quantify and did not even attempt to estimate. Because the uncertainty of the N2 reference cross section is unknown at wavelengths greater than 468 nm and because the mirror reflectivity is highly structured, the authors do not know their true uncertainties, and the values in the paper represent a lower limit. Indeed, because N2 is used to determine the pathlength, all of the Rayleigh scattering cross sections reported in this study have unknown uncertainties >468 nm.
For these reasons, I would state even more strongly than in my previous review that there is no point in publishing new dispersion relationships in this paper that are indistinguishable within uncertainty from the dispersion relationships already in the literature. The authors take this approach for CO2, opting not to report a new dispersion relationship, and they should take a consistent approach with SF6 and CH4, given that the uncertainties are too large to say anything other than the SF6 and CH4 measurements in this study agree with the dispersion relationships currently in the literature.
2) On Line 457, it is stated that the average deviations in the dispersion relationships between the literature and this study for SF6 and CH4 are 0.1% for both gases. On first read, this level of agreement would seem to be almost impossibly close given the large uncertainties in the present data set. But upon closer inspection, this remarkable agreement in reality is simply due to the fact that the authors are just repeating the method of Wilmouth and Sayres (2020) for determining the dispersion relations and adding in their data from this study. Therefore, the 0.1% agreement essentially just means that one gets the same dispersion relation using the Wilmouth and Sayres (2020) method for SF6 and CH4 regardless of whether or not the data from the present study is included in the fit. Again, there is no justification here for providing new dispersion relationships for SF6 and CH4.
(3) The authors have a new approach from their previous manuscript of presenting the differences between their Rayleigh scattering cross sections and the n-based values as x +/- y%, as in lines 22-23 of the Abstract and in several places in the text. For example, for CO2, the difference is listed at 0.37 +/- 1.24%. Some explicit discussion when this approach is first presented (around line 306) regarding why the standard deviation is so much larger than the mean would be helpful. There are also too many significant figures being used in this approach. I recommend at most 2 significant figures rather than 3, e.g., with CO2, it should be listed at 0.4 +/- 1.2%.
(4) Based on lines 241-247, the authors appear to be using their precision as if it were their accuracy. The variation in the temperature and pressure over the 150 scans is the precision, not the accuracy. This new text now makes it clear why the pressure uncertainty is listed at the unrealistic value of +/-0.01%, as I noted in the previous review. I would be extremely surprised if the pressure gauge used in this study were capable of 0.01% accuracy. Please update the uncertainties with reasonable estimates for accuracy, not using the precision.
(5) As stated in (2) above, the dispersion relationships for SF6 and CH4 in this study appear to have been calculated using the exact same method and data sets as Wilmouth and Sayres (2020) except that the data from the present study were included in the fit, and “all sets of data were weighted equally” according to the text. This latter point is stated as if it were important, but it is never actually explained in the text what weighting the data sets equally means.
Does weighting the data sets equally mean that the points from all of the data sets were combined, and then the fit obtained? If so, then the data set with the most points will have far more weight than the ones with fewer points, such that they will not be truly weighted equally. More specifically, with this approach, the Vukovic, Watson, and Cuthbertson studies will be mostly irrelevant in the fits because the BBCES studies have so many more data points.
Alternatively, weighting them equally could mean that each data set was normalized according to how many points were in the data set, such that each study got equal weight. The downside of this approach is that the older Watson and Cuthbertson studies are probably less accurate, but they would be given equal weight with the newer studies.
Either way, it should be clearly stated what was done. Or alternatively, as strongly recommended above, delete the dispersion relationship calculations altogether for the reasons outlined in points (1) and (2).
--Additional Comments/Corrections:
Line 72 and many other Lines in the manuscript: I mentioned this in my previous review, but the problem persists. The authors use “BBCES” as if it were the name of their experimental setup. If the sentence doesn’t make sense with “Broadband Cavity Enhanced Spectroscopy” substituted in place of “BBCES”, the sentence should be edited. In general, anywhere in the paper that the expression “the BBCES” or “our BBCES” is written, it is incorrect. For example, “the BBCES setup” or “our BBCES instrument” could be stated instead.
Lines 282-284. These values are not the “1-sigma uncertainty” as stated in the text. They appear to be from a root sum of squares calculation that includes the N2 reference cross section with the precision of the temperature, precision of the pressure, and precision of the test gas spectra. The true 1-sigma uncertainty is much large than the numbers presented in this sentence.
Line 429 and Line 438: Saying “for 288.15K and 1013.25 hPa” is ambiguous as written in these sentences, as it sounds like the measurements were made at these conditions. These T and P values should appear a bit later with the dispersion relationships to be clear that n is being defined at 288.15K and 1013.25 hPa in order to be consistent with past studies.
Line 430: Delete “better” and Line 431: Delete “alternative”. This is the standard form of the fit; it is not better or alternative to what has been done before.
Line 447: To avoid ambiguity, replace “their refractive index” with “Sneep and Ubachs (2005)”.
Line 475: Please repeat the list of gases in order before “respectively”. As it is, this sentence is referencing a gas list from two sentences prior.
Table 1: The He equation is still incorrect. There is a missing decimal in 1.8102.
Figure 5b: Missing right parenthesis in figure caption
Figure 9, panel (c): Is the green fit line plotted for CH4? It is not visible on the plot.
--Minor Corrections:
Line 80: Change “is” to “are”
Line 84: Add “applicable” after “CH4” and change “264” to “250”
Lines 135-136: Delete the sentence beginning “In this study…” as it simply repeats what was just stated on Lines 126-127.
Lines 273-275: The sentence beginning “The mean uncertainty…” could be deleted as it repeats what was already stated on Lines 246-247.
Line 292: Change “listed” to “lists”
Line 299: Add “, 2020” after “2019”
Line 301: Change “calculation” to “calculations”
Line 309: Define variables in the equation
Line 310: Change “fitted” to “fit”
Line 359: Change “slops” to slopes
--Note
A few of the changes indicated in the authors’ response to the previous review were never actually made in the revised manuscript.
--Final Suggestion
If someone were to summarize what’s new about this paper in a single statement, it would be that the measurements were made with such broad mirrors. I think some perspective text at the end of the paper discussing pros and cons of using mirrors like these would be appropriate. It seems clear that there is a tradeoff one must make here between speed (acquiring a broad wavelength range quickly) and accuracy (the structured reflectivity curve is limiting). |
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