This study examines the relevance of hydrometeor inertia for the accurate simulation of radar Doppler spectra. The authors develop a novel approach to simulate Doppler spectra based on the equations governing the motion of hydrometeors, and compare it with the traditionally used convolution-based approach. They find that the traditional approach tends to overestimate the degree of broadening associated with inertial particles, while it correctly represents the degree of broadening for particles whose inertia is low enough for them to act as tracers. The authors then compare spectra simulated both with their novel approach, and with the traditional approach, with one observed spectrum. The comparison displays a better matching between the observed spectrum and the spectrum simulated with the author’s approach.

I find the research question of the study to be significant for the cloud radar community, and the novel approach developed by the authors to be sound. The figures are polished, and the overall structure of the manuscript is well layed-out, clearly displaying the reasoning process of the authors. However, I find several sentences in the manuscript to lack in clarity or to have been poorly written, and improvements in this regard are needed. See my detailed comments below.

The only major flaw that I found in the study is in the comparison with observations. The comparison was performed only for one observed sample (one Doppler spectrum). In my opinion such a limited validation is not sufficient to prove the accuracy of the approach developed by the authors. The validation with respect to observations needs to be considerably expanded, and should be performed on a statistical basis using a large number of Doppler spectra, if possible recorded during a few separate events.

I do understand that the authors might want to include such an extensive validation in a follow-up study, but if that is the case, the comparison with observations in section 5 should be framed as a simple illustrative exercise, instead of a proper validation analysis. I included below a list of changes that I deem necessary if the authors do not intend to expand the comparison with observations in the current study. I anyhow strongly recommend that such an extensive validation is included in the current manuscript, as it would make the whole study substantially more sound.

In conclusion, I recommend this study for publication in AMT after major revisions: clarity of the text needs to be improved and I recommend either that the comparison with observations is considerably expanded or the text is adjusted so that such comparison is not presented as a complete validation.

Changes needed if the validation is not expanded

• The sentences at lines 19-23 in the abstract (from “Doppler spectra observed …” until “...morphology”) need to be removed. The comparison with observations should not be mentioned in the abstract as it doesn’t have scientific significance.

• The sentence at lines 84-85 (“section 5 uses … simulator”) needs to reflect the fact that the comparison presented in section 5 is not a validation, but a mere illustrative exercise. Additionally the phrasing “real observed Doppler spectra” is not accurate and should read “one real observed Doppler spectrum”.

• The text in section 2 should be moved to section 5 (or an appendix), as it is not relevant for the main topic of the manuscript, which is the approach development. The text could also be condensed.

• The title as well as the text in section 5 should reflect the fact that only one observed spectrum is used in the comparison instead of multiple spectra. The singular “spectrum” should be used instead of the plural “spectra”.

• The sentences at lines 373-377 need to be rephrased in a more careful manner, as the simple analysis shown does not provide enough evidence to support these statements.

• The same applies to lines 410-415, 418-419, 421-422 in the conclusions.

• The conclusions need to clearly state that the new approach needs to be systematically validated against observations, and that the applications suggested at lines 422-427 may only be looked into after the accuracy of the approach is demonstrated against observations.

Further scientific questions/issues

• Throughout the whole text the term “fall velocity” or “droplet velocity” is used as synonym for “still-air terminal velocity” (e.g. at lines 56, 195, 310, ...). This is incorrect and should be adjusted.

• Throughout the whole text the term “quiet air” is used (e.g. lines 63, 211, 243, ...). The term “still air” is far more commonly used and I recommend that this is used instead.

• Throughout the whole text the term “movement” is used as synonym for “motion” (e.g. at lines 82, 102, 105, ...). This is incorrect and should be adjusted.

• Throughout the whole text the verb “resolve” is used when referring to simulated drop velocities (e.g. at lines 106, 215, 265, 270, 400, 418, ...). I find this ambiguous because the actual particle velocity is not observed in any way, but an artificial velocity value is produced and then used to calculate the Doppler spectrum. Therefore I suggest this is adjusted, e.g. by replacing “resolve” with “simulate”.

• References should be given for all formulas in sections 3.1 and 4.1.

• Throughout sections 3.1 and 3.2 it is not stated in the text whether gravity was included in the simulations. I assume it is not since the corresponding term is missing in eq. (1). Its inclusion or omission should be stated explicitly. If it is included, eq. (1) should be adjusted accordingly.

• Lines 160-162: since the calculation of the artificial wind time series is an integral part of the proposed approach, the method by Deodatis (1996) should be briefly summarized here.

• The same applies to the method used for the calculation of the broadening term sigma_t by Borque et al. (2016), mentioned at lines 247-248.

• When citing a book (e.g. Lhermitte 2002) the exact chapter or pages should be indicated.

• Figure 3a: what values were assigned to the initial velocities of the droplets?

• Lines 244-245: a similar comment should be made regarding the time scales involved.

• Eq. (12): the symbol S_t appears here for the first time and it should be introduced.

• Eq. (12) and line 270: if I understand the text correctly, here V_t is the turbulence-affected drop velocity, but the symbol V_t was previously used to indicate the still-air terminal velocity. I believe a new or different symbol should be used here instead.

• Line 271: please clarify what the term “DSD Doppler spectra” means.

• Lines 294-297: this sentence should be split and explanded. First the concept of Mie notch should be introduced. Then the fact that the Mie notch can be used to compare the two approaches should be explained.

• Figures 4 and 5b: the labels to the y axes should indicate the name of the variable (“spectral reflectivity” in this case) in addition to the unit. The unit is also misindicated as “dB(10log(mm6 m-3))”, it should read either “dBZ” or “10log(mm6 m-3)”.

• Section 5: I would like more details on the processing of the observational radar data. Were the data corrected for attenuation? Was de-aliasing performed? Looking at Fig. 5b it seems that the spectrum was shifted to have its left edge at 0 m/s, is this the case? If the comparison with observations is expanded these details need to be included in the text, otherwise it is sufficient if they are only included in the authors’ reply.

• Line 355 reports that the data were collected between 05:44 and 05:45, but line 94 reports a temporal resolution of 4.28 seconds. Were multiple spectra observed over that one minute averaged together? If not please indicate the exact timestamps with hours, minutes, and seconds. If yes, please clearly state it in the text.

Stylistic/technical corrections

• Line 40: I believe the correct phrasing is “...remove clutter and identify hydrometeor signal”.

• Line 44: I find the phrase “improve the microphysical medlin process” to be unclear.

• Lines 49-50: I find the grammar in this sentence to be overall incorrect, and it should be rephrased.

• Lines 53-55: I believe that the phrase “… spectrum is contributed by …” is gramatically incorrect and it should be improved.

• Line 58: I believe the correct phrasing is “… to reduce retrieval uncertainties…”.

• Line 60: I believe the correct phrasing is “Doppler spectrum simulators”.

• Line 61: I believe the correct phrasing is “Doppler spectrum shape”.

• Line 69: “… unlike small doplets”.

• Line 71: “… large uncertainties for retrieval products”.

• Line 75: “How does inertia…”.

• Line 97: “… identify hydrometeor signals”.

• Line 97: “Additionally, an impact disdrometer…”.

• Line 98: “The disdrometer”.

• Line 136: “The values used for … are …”.

• Line 137: I find the phrase “...as a representation of environment…” unclear. I recommend that it is rephrased.

• Line 145: “...cloud droplet, drizzle, …”.

• Line 160: “...a turbulent environment...”.

• Lines 160-161: I find the phrasing “...are equivalently inertia-free…” unclear.

• Line 190: How small? Quantify please.

• Line 202: “...wind field...”.

• Lines 210-212: This sentence is hard to follow and should be rewritten.

• Line 221: “...is only applicable to vertical...”.

• Line 232: “...Doppler spectrum density … Vt is the droplet…”.

• Line 256: “...and its impact on radar Doppler…”.

• Line 274: I believe this line should read “… total number of simulated timesteps...”.

• Line 276: “...where T and f are ...”.

• Lines 287-288: I would rephrase “the values of the intercept parameter N0 and the slope factor Gamma are chosen to be ...”.

• Line 288: “… droplet diameter ranges…”.

• Line 293: “...larger differences between the generated…”.

• Lines 298-300: I find the term “adjusted time” unclear.

• Lines 313-314: this sentence reads wrong and should be adjusted. E.g.: “… a large differences between the right edges of the spectra from the two simulators can be clearly identified.”

• Line 330: “Comparing the three ...”.

• Lines 353 and 371: Marshall is spelled with two l.

• Line 367: “...spectral power compared to ...”.

• Line 370: I believe the sentence should read “… both the simulated Doppler spectrum and the convolution-based Doppler spectrum near the second notch are not consistent ...”.

• Lines 375-376: “… has shown significant improvement in correctly emulating…”.

• Line 387: either “Radar Doppler spectra ...” or “The radar Doppler Spectrum...”.

• Line 392: I would rephrase “...inertial effects are typically neglected…”.

• Lines 397-398: “… velocity field… incapable of following … as small droplets do.”.

• Line 406: “… caution should be taken when applying convolution-based approaches to represent ...”.

• Line 419 “… various potential ...”.

• Line 450: I believe this should read “initial draft”.

• Line 456: It should read either “contribution is” or “contributions are”.

The study suggests a methodology to account for droplets inertia in the calculation of Doppler spectra broadening due to turbulent air motion. The paper is well-written and easy to follow. The manuscript presents one theoretical and one practical experiment to illustrate the rationale of the new methodology and its effectiveness in better representing the broadening of Doppler spectra due to air turbulence. The figures are of good quality and the conclusions follow the results obtained by the aforementioned experiments.

However, I am not completely sure about the formal correctness of the proposed method. It might be that the authors adopted some implicit assumptions that are just not clear to me. It is possible that those assumptions are explicit in Lhermitte (2002), whose framework the authors declared to follow. I, unfortunately, do not have access to the book at the moment, but, in any case, I recommend the authors to provide a concise, but exhaustive description of all the physical assumptions made in the development of their novel modeling technique.

I recommend the article to be published after a major revision. In doing so, I am aware that my concerns might arise from the mere misunderstanding of the assumptions made in the model formulation. If this is the case it is sufficient for the authors to better describe the physics behind the mathematical formula written. On the other hand, from what I was able to understand, I am not entirely sure that the physical model developed is correct. The better matching of the simulated and observed Doppler spectrum might result from compensating errors in the model formulation. In this case, I suggest the authors to take their time to thoroughly review their work and resubmit at a later stage.

My full review is attached as supplement to this text