General

The manuscript discusses a new lidar approach to estimate CCN concentrations. It is a useful contribution to the lidar literature. However, since a new lidar method is introduced and the manuscript deals with all details of this method including an uncertainty analysis, AMT would be more appropriate.

Minor revisions are necessary.

Detailed comments:

p3, l97: Why do we need to know the particle size distribution? CCN is just the overall particle number concentration (integral over all sizes)!

Regarding aerosol type, to my opinion the separation into dust and non-dust is sufficient. Size plays a strong role, but chemical composition a minor role…? Maybe discuss that a bit more.

What I learned from all these complex lidar inversion papers since Mueller et al. (1999) and Veseolovskii et al. (2002) is….  that it is impossible to retrieve the particle size distribution with good accuracy, even from a set of 3 backscatter and 3 extinction coefficients. Furthermore, the retrieved particle number concentration always shows the largest uncertainty (close to 100%). Now you use Look Up Tables. How can you have uncertainties < 50% when using a much more simple approach than these sophisticated inversion techniques? Please comment on that in the manuscript!

P3, l101: Why do you mention the Rosenfeld et al (2016) method in this lidar paper?

P4, l125: In addition to Burton et al. (2016) I think one should cite the original papers of Mueller et al., 1999, 2005 and of Veselovskii et al., 2002, 2004, 2012.

P4, l131: to my opinion, you have just a 2+2 lidar because the 1064 nm BSC is always a problem and the solutions are rather uncertain, because clear air  calibration is very difficult and a good calibration is only possible in the presence of ice clouds.

P4, l147: Are you sure that the assumption of spheroidal dust particles is ok to obtain trustworthy dust lidar ratios at all three wavelengths? You may check the recent paper of Haarig et al. (2022).

Haarig et al., First triple-wavelength lidar observations of depolarization and extinction-to-backscatter ratios of Saharan dust, Atmos. Chem. Phys., 22, 355–369, https://doi.org/10.5194/acp-22-355-2022, 2022.

P6-9, section 2.2: The main questions I had after reading section 2.2:

How do you handle all kinds of external mixtures, e.g., marine and dust, pollution and dust, smoke and dust, etc.  The LUTs only include pure aerosol type information, right? So this is an open point that should be better explained in the manuscript.

Relative humidity has a strong influence on all the retrievals. Are the growth or enhancement factors for all three wavelengths the same? Please provide more information. Just references are not sufficient. What about enhancement factors for internally mixed sulfate-BC-OC particles, or sulfate coated dust? What about growth factors for mixture of fine mode (urban haze) and coarse mode dust. The enhancement factor will then be clearly wavelength dependent, because 355 nm is very sensitive to hygroscopic small particles, and 1064 nm will be very sensitive to the hydrophobic dust particles. Is it possible to consider all these complex items?

Final point, RH values are at all obtained from models?  Absolute uncertainties of plus-minus 20% have always to be kept in mind…. in many cases even 50% is my long-term experience.  Are there papers that provide clear statements on modelled RH uncertainty?

P9, l301: I am not sure, but is the critical radius not defined as the radius for which 50% of particles are activated….

P9, l307: The critical radius can be as low as 25 nm for high super saturations of 0.8 to 1%.   The lidar backscatter and extinction is only sensitive to particles with radius of 50 nm and larger…. How can you then derive a critical radius of 25 nm? Please clarify and explain that in the manuscript!

Probably you make use of  Eq.(8), but that is then an  assumption you use here… and causes an uncertainty. What about the impact of new particle formation on the actual Aitken mode (contributing to the CCN concentration)? This is an important uncertainty source, I could imagine!

Results:

p10, l317 and p11, l358:  To my understanding, ECLiAP is not an inversion method. It is just an LUT approach. One should not mix that.

The relative humidity is a crucial input parameter. Uncertainties of 10-20% can never be excluded. So, resulting CCN retrieval uncertainties must be visualized up to RH plus minus 20%.

P13, l461: The HSRL does not measure directly the 1064 nm extinction! ..is stated in line 461. This statement comes much too late. It must be clear from the beginning that HSRL is a typical 3+2 lidar instrument. You even do not know the 1064 nm lidar ratio. Please provide the lidar ratio! It is an important quantity! but not mentioned. May be you assumed 40 sr at 1064 nm, and in reality it is  80-100 sr, what are the consequences of such a bad assumption on the CCN retrieval? Please comment on that in the manuscript.

P13, l471: That is my basic question: How do you handle mixtures: dust, marine, and smoke…. in your retrieval…

P15, l506-511: I have no idea what you mean here…. because CALIOP is a 2+0 lidar, or even a 1+0 lidar. Please explain better …!

P15, l512-526: Again,I have no idea what you did? Did you apply the depolarization-ratio-based method to separate dust and non-dust components? And then what did you do in the next steps? Must be clear in the manuscript.

P16, l548: Again, there is a mixture of dust and continental pollution. What are the different steps of the retrieval. Please explain in detail!

P16, l573: What does that mean… a more realistic LUT-based approach using the 3+3 wavelength technique? You do not have any good information about the 1064 nm lidar ratio!

In the summary and conclusion section one could discuss: How large is the chance that there will be an airborne or spaceborne  3+3 HSRL in the near future (within the next 10 years).

P20, l684, the depol value  of 0.31 holds for 532 nm only!

Tables 1 and 2: If the numbers are so small, do we really have to show this?

Figure 6 triggered my basic question: How are aerosol mixtures handled in the entire retrieval procedure?

Figure 8: I have no idea how you got all the shown information and how you could estimate CCN at the end. And who can evaluate the quality of the products? We have just to believe.

The paper by Patel et al. presents a methodology to infer the concentration of cloud condensation nuclei (N_CCN) from multiwavelength Raman or high spectral resolution lidar observations. This outline of the paper’s content shows that the title is not at all in line with what is actually presented. The technical nature of the work suggests that it should have been submitted to AMT rather than ACP. Below, I am providing a list of some of the many issues with this contribution that lead me to recommend rejection of this work for publication in ACP (and AMT in case it is deferred there). 

1. Originality: It is very hard to assess the originality of this work. Entire sections and figures seem to be copied from earlier publication (in particular Lv et al., 2018; Tan et al., 2019; and Choudhury and Tesche, 2022a) without bothering to even reformulate or redesign. This is also witnessed by the unusually high similarity index of 20%. The authors should state more clearly as is currently the case that they are following the methodology of earlier publications and emphasise in which form they are improving upon the earlier methods. They currently fail to properly acknowledge alternative efforts to infer global height-resolved and aerosol-type specific CCN concentrations from spaceborne CALIPSO lidar observations as described in Choudhury and Tesche (2022a; b) and Choudhury et al. (2022).
2. Reproducibility: The (data and) methodology section is incomplete and doesn’t provide the necessary information that would allow a reproduction of the authors’ work. Also, not a single instrument whose data are considered later in the study is introduced in this section. Here are some specific issues:
   1. The authors are not particularly accurate regarding their methodology. It is certainly not an inversion, as the particle size distribution is described. It is more of an optimisation in which the produced look-up tables serve as reference. In that context, whenever the authors refer to the 3+2 or 3+3 techniques, they actually just want to state that they are using this particular combination of parameters, i.e. 3 backscatter coefficients and 2 or 3 extinction coefficients. If they were to use the actual 3+2/3+3 technique, they would use these parameters as input to a real lidar inversion (suitable references would be Müller et al. (1998, 2001, 2016) and Veselovskii et al. (2002, 2010)) – which they are not. Consequently, the mentioning of 3+2/3+3 (inversion) techniques is misleading.
   2. It is not at all clear how the look-up tables have been created. We don’t know how the considered particle size distributions have been obtained. Okay, they are from AERONET. But for which sites? And why should they be representative for the different aerosol types? How do the authors compensate for the lack of large particles in AERONET size distributions that are particularly important for obtaining parameters that are measured with lidar? What are the ranges of complex refractive indices used in the creation of the look-up tables? How are non-spherical particles treated exactly? At which size parameter do the authors switch from T-matrix to geometric optics? These questions offer material for multiple in-depth studies and shouldn’t be dismissed.
   3. Why do we have to learn about HSRL-2, the ORACLE in-situ instruments, or CALIPSO in the results section? This should be part of the section that describes data and methods so that readers get an impression were the work is headed. It would also be good to point out from the outset that the authors don’t actually work with 3+3 input data as HSRL-2 doesn’t give independent backscatter and extinction coefficients at 1064 nm. This leads to the question why they are developing the method for 3+3 input data? Is there any lidar in existence that can provide 6 independent input parameters? Is it developed anywhere? This reviewers knows that the likelihood for such instruments becoming a common occurrence is negligible. But readers might not and, thus, should be informed about this.
3. Error analysis: While it is laudable that the authors put quite some emphasis on error analysis, there are serious issues with the way errors are treated in this work:
   1. The authors fail to address an obvious error source: How representative are the selected size distributions (see point 2b) and what happens when reality provides size distributions that differ from what is assumed? While it seems that some variation is considered, the authors don’t account for potential changes in the mode radii. Choudhury and Tesche (2022a) show that this has quite some effect on the CCN retrieval.
   2. As someone with a background in lidar measurements, I am astonished that the authors put so much emphasis on systematic errors. Any decent lidar operator will see the reduction of systematic errors as their utmost concern. Today, there is quite an arsenal of methods for addressing and reducing systematic errors including instrument simulators, calibration measurements, and instrument comparisons. This Special Issue in AMT provides a glimpse into the efforts taken to reduce systematic measurement errors: https://amt.copernicus.org/articles/special_issue70.html
   3. The findings of the sensitivity analysis with error-free data show surprisingly small errors. Are the authors certain that they are indeed using an independent approach? Errors of 0% strongly suggest that circular thinking is involved. The authors don’t describe where their error-free lidar measurements come from (add this to 2b) so I presume they were forward calculated based on the considered size distributions and (unknown) refractive indices? In that case, it’s no surprise that the retrieval finds a match in the look-up table with negligible error.
   4. The authors should consider realistic error estimated for atmospheric aerosol lidar measurements. Generally, those are on the order of 5% to 15% for backscatter coefficients and 15% to 30% for extinction coefficients. These errors increase with decreasing signal-to-noise ratio.
   5. It is incomprehensible to me who a retrieval that uses up to seven input parameters (3+3+RH) with a (currently far too low) random error estimate of at most 10% each can give an output with an error that is below that of any input parameter! Simple error propagation (\sqrt(7*0.1^2)) would suggest that the error should be at least 26%. How straightforward is it really to apply the retrieval to fewer input parameters than the 3+3 it has been designed for? Reducing the number of input parameters should lead to a larger number of matches and, thus, increase the overall error.
4. Application to atmospheric measurements:
   1. The authors have an excellent data set for assessing the quality of their retrieval at their disposal. However, it’s hard to comment on the comparison due to the lack of information regarding the retrieval itself (as outlined to some degree above). Looking at Figure 6, it is not clear what is meant with estimated extinction coefficients. How are they part of the retrieval? Also, can AERONET-derived size distributions produce spectral extinction coefficients as shown between 1 and 2 km height? What about real-life aerosol mixtures? Those could not be addressed with the retrieval but will certainly be present in the ORACLES data. I would also recommend to use the colour coding commonly applied to lidar data, i.e. 355 in blue, 532 in green, and 1064 in red.
   2. I am astonishing by the authors’ audacity of presenting an application of their retrieval to CALIPSO measurements without addressing obvious issues or providing any form of independent validation. How can their method be directly applied to CALIPSO observations when the available number of input parameters (2+0) is far lower then what the retrieval has been designed for (3+3)? Also, the selection of used size distributions should have quite some effect if they are not the same as in the CALIPSO aerosol model. Finally, there is no verification of their findings with independent measurements even though they have the in-situ measurements from multiple ORACLES campaigns at their disposal. There certainly must have been CALIPSO overpasses during these campaigns. The application to CALIPSO observations should not be part of the paper without addressing these issues.

References:

Choudhury, G. and Tesche, M.: Estimating cloud condensation nuclei concentrations from CALIPSO lidar measurements, Atmos. Meas. Tech., 15, 639-654, https://doi.org/10.5194/amt-15-639-2022, 2022a.

Choudhury, G. and Tesche, M.: Assessment of CALIOP-Derived CCN Concentrations by In Situ Surface Measurements, Remote Sens. 2022, 14(14), 3342, https://doi.org/10.3390/rs14143342, 2022b.

Choudhury, G., Ansmann, A., and Tesche, M.: Evaluation of aerosol number concentrations from CALIPSO with ATom airborne in situ measurements, Atmos. Chem. Phys., 22, 7143-7161, https://doi.org/10.5194/acp-22-7143-2022, 2022.

Lv, M., Wang, Z., Li, Z., Luo, T., Ferrare, R., Liu, D., Wu, D., Mao, J., Wan, B., Zhang, F., and Wang, Y.: Retrieval of cloud condensation nuclei number concentration profiles from lidar extinction and backscatter data, J. Geophys. Res.: Atmos., 123, 6082-6098, https://doi.org/10.1029/2017JD028102, 2018.

Müller, D., Wandinger, U., Althausen, D., Mattis, I., and Ansmann, A.: Retrieval of physical particle properties from lidar observations of extinction and backscatter at multiple wavelengths, Appl. Opt., 37, 2260-2263, 1998.

Müller, D., Wandinger, U., Althausen, D., and Fiebig, M.: Comprehensive particle characterization from three-wavelength Raman-lidar observations, Appl. Opt., 40, 4863-4869, 2001.

Müller, D., Böckmann, C., Kolgotin, A., Schneidenbach, L., Chemyakin, E., Rosemann, J., Znak, P., and Romanov, A.: Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET, Atmos. Meas. Tech., 9, 5007-5035, https://doi.org/10.5194/amt-9-5007-2016, 2016.

Tan, W., Zhao, G., Yu, Y., Li, C., Li, J., Kang, L., Zhu, T., and Zhao, C.: Method to retrieve cloud condensation nuclei number concentrations using lidar measurements, Atmos. Meas. Tech., 12, 3825-3839, https://doi.org/10.5194/amt-12-3825-2019, 2019.

Veselovskii, I., Kolgotin, A., Griaznov, V., Müller, D., Wandinger, U., and Whiteman, D.: Inversion with regularization for the retrieval of tropospheric aerosol parameters from multi-wavelength lidar sounding, Appl. Opt., 41, 3685-3699, 2002.

Veselovskii, I., Dubovik, O., Kolgotin, A., Lapyonok, T., Di Girolamo, P., Summa, D., Whiteman, D. N., Mishchenko, M., and Tanré, D.: Application of randomly oriented spheroids for retrieval of dust particle parameters from multiwavelength lidar measurements, J. Geophys. Res., 115, D21203, https://doi.org/10.1029/2010JD014139, 2010.