Summary:

The submitted draft examines the effect of laser rod temperature on the accuracy of rotational Raman lidar temperature measurements. The authors consider the scenario where they cannot perfectly control the output laser spectrum of a Raman laser system and how that affects the measured Raman spectra, and by extension the systematic error in measured temperature. The authors assume that a seeded laser provides laser output that is effectively a delta function, whereas an unseeded laser will output a Gaussian distribution with some finite width. The laser output spectrum is convolved with the ideal Raman spectrum and passed through ideal optical filters and the difference between calibration curves of the seeded and unseeded lasers are compared. It appears that the authors use real Raman lidar systems as a basis for the specifications presented for this analysis, but that all data presented are of a theoretical nature.

To my knowledge, the above topic has not been published previously and would be of interest to lidar designers (in my understanding because lacking a requirement for a seed laser, the laser system for a Raman lidar can be made cheaper). Furthermore, it is well within the scope of AMT in my opinion. While within scope and not previously published, the results are relatively unsurprising, because the result of the analysis is that the lines of the Raman spectrum are slightly broadened; they don’t go missing or move uncontrollably.  My comments below expand upon this evaluation, but the results presented are also somewhat limited in their applicability to other lidar designs.

In general, I believe this paper should be published after revisions to make the analysis more general and robust.

Major Comments:

1. The prime concern I have is that the authors seem to have picked a confined problem and analyzed it, but that that analysis is somewhat unportable. It seems that the results are specific to a set of interference filters that have a known center location and full width at half maximum. Most Raman lidar systems have slight variations in this parameter and thus the broader applicability is reduced. Not being able to broaden the results from the single system analysis seems to dramatically limit the impacts of this work. Some specific questions are:
   1. What about different passband filters? If you took the same filter center wavelengths and changed the width of the filters, are your results (i.e. the finding that you need approximately 1C temperature stability in your laser rod) robust?
   2. What about filters are different center wavelengths? If you took the same filter set and simply tilted them, their wavelengths would shift to the blue. Alternatively, if you picked different center wavelengths for different temperature sensitivity, the analysis here would need to be altered. Again are your results robust with reasonably different center wavelengths?
   3. What does the laser output wavelength do to the Cabannes line and at what width do you start to worry about contamination into your filters? Said differently, if you use the same filters and start to alter the laser rod temperature (or lack control enough that the Cabannes line widens significantly), at what point does the issue become lack of stability of the laser and more that the contamination for elastic scattering is unavoidable?
   4. What about 532nm vs 355nm? Because all the analysis is basically done in cm^-1, it seems like a relatively simple exercise to, at minimum, comment on the same style Raman lidar system using the 2^nd harmonic of an Nd:YAG laser.

In general, I am imagining a set of contour figures that would allow the filter properties to change slightly, where the contour is the maximum temperature deviation allowable for the laser rod for a set observational temperature error and the axes are widths or center wavelengths of each filter.

1. The subject nature of this paper somewhat naturally uses different units that mean basically the same thing. However, the authors jump between the two rather freely, which is somewhat difficult to follow in my opinion.
   1. For units used to described wavelengths and wavelength changes, I would show both set of units (cm^-1 and nm) simultaneously to aide the reader that is not comfortable jumping between the two. For example, I tend to think of laser spectral output characteristics in units of MHz. This is well done in Table 1 but could be replicated in the text.
   2. Same comment for Figure 4.
   3. I see both Kelvin and Celsius (lines 185-186 for example). I would pick one and stick with it.
2. Figures 2/3/5/6: I note several issues with these figures:
   1. You specify that there are plotted widened and unwidened lines in Figures 2 and 3 but never specify which is dashed and which is solid.
   2. I would move your title to the y-axis as that better illustrates what you are plotting and the units of that.
   3. Using two lines that are almost on top of one another is not really a clear way to present your data. I would suggest using a second y-axis to plot the difference for all four figures. If you choose to do something other, please make sure that it is clear and easy for the interested reader to understand the magnitude of the changes between solid and dashed lines.
3. If I am reading your conclusions correctly, the temperature sensitivity of the interference filters (2-5 pm/C) are at least 33% higher than the laser rod (1.5 pm/C). I recognize that the two will have different thermal management systems, but it does seem like a point that needs to be touched upon. You never mention why you are focused on the laser rod when, ostensibly, the filters are more sensitive.

Minor Comments:

1. Introduction: The authors never really say why one should care about their conclusions. I assume this is because lidar designs that lack a seed laser are cheaper, and if you can get similar performance with cheaper lasers, that makes the technique more useful. However, I suggest the authors state the motivation for using unseeded lasers directly.
2. Lines 23-24: The term “continuous” here requires context. I assume the authors mean on the scale of a few minutes. However, the statement reads (in my opinion) like radiosondes can only be launched during campaigns, which is obviously not true. I suggest adding a numerical definition for the temporal resolution required to be “continuous”.
3. Line 29: “high quantum numbers” should specify “rotational quantum numbers”.
4. Line 68: It is probably worth noting that the wavelengths you specify here are reference to vacuum wavelengths.
5. Figure 1: This figure will be difficult to read for those that are colorblind because you have used both red and green. Suggest modifying colors or including different line styles to be easier to differentiate for such people.
6. Figure 1: The Cabannes line is not part of the pure rotational Raman spectrum because it has no Raman shift. I would either remove the line or not call the presented spectrum the “Pure rotational backscatter Raman spectrum”.
7. Table 1: I am not seeing where “HM” is defined.
8. Lines 94-97: This statement seems experimental in nature, whereas the rest of the manuscript is theoretical. If these are real test results, to what system do they apply?
9. Line 117: The contents of this line are really extensions of the previous line and should not be a separate paragraph.
10. Figure 7/8: I see no clear reason to flip the x and y axis? If there is a good reason, please tell the reader why it is helpful. If not, I would flip it back for consistency.

Comments about References:

1. Line 36: The reference to Hammann et al 2015 is not a seminal reference for calibration of Raman lidar by radiosonde. I would either use an “e.g.” or pick a more original reference.
2. Line 60: In my reading, the citation to Armandillo et al 1997 is not terribly appropriate. The laser presented by Armandillo has a nearly Gaussian profile. This citation seems to indicate however that the Armandillo manuscript is used to suggest that Nd:YAG lasers must have Gaussian profiles. I would find a more fundamental reference here as this assumption is pretty important.
3. Line 70: You have said that the spectrum frequencies from Zenteno-Hernández et al. 2021 relies on previous work from itself. I would remove the second reference at the end of the line.

Typographic Comments:

1. Line 25: “spending” is probably not the word you are looking for here. Perhaps “launching”?
2. Line 29: The antecedent of “has” is “lines”. This should read “…while that of lines with high [rotational] quantum numbers have…”
3. Line 71: There is an extra “)” after Buldakov et al. 1996 that should be removed.
4. Line 92: “atmosphere temperature” should be “atmospheric temperature”.
5. Line 96: “…in spite their higher…” should be “…in spite of their higher…”
6. Line 128: “entrain” is an odd choice of word in my opinion. I would suggest swapping with “include” or “imply”.

Please refer to the attached file for the full review.