Reply on RC2

General comment 1: How general are the observed correlations? From the perspective of a potential user whose aim is to retrieve characteristic sizes from dual-frequency radar measurements, some information may be missing. It would be relevant to include more information on the data that were collected. For example, how many data points were included how long were the time periods used (after the preprocessing steps which include e.g. removing mixed-phase conditions) to compute the coefficients of Fig 6? What were the flight conditions like, in terms of (for example) altitude, temperature, total water content...? Similarly, the authors mention the presence of various particle habits, but this could be expanded (e.g. indicate the classes of particles present in the entire dataset used, mention the presence of riming if any...). All this could help the reader get an idea of how general the derived relations are, and how they might hold in various environments.


General comment 2. Could a little more be said about the vertical beam results?
The authors point out that the DWR-Dv relations are more robust when using the horizontal beams. Unfortunately, most long-term radar observations are either spaceborne or ground based and thus rely on vertical beams; hence, I wonder if a little more could be said on the DWR-Dv relations with vertical beams. Is the spread completely "random", or perhaps could it be easily related to varying particle habits, aspect ratios...? for example a suggestion could be to color-code the scatter plot e.g. on Fig. 4 with particle type or aspect ratio.
Response: As suggested, a color-coding was added in Fig. 4. The spread in DWR-Dv points around the best fit for the horizontal radar beam is smaller than that for the vertical beam regardless of the predominant habit, even though large dendritic crystals (Fig. 4) often (but not always) produced higher DWR values.

General comment 3. How do the results compare to model studies?
While I understand and value that the paper's focus is an observational study and not a modeling work, I believe a bridge between the two approaches would be of high interest. Indeed, there have been numerous model-oriented investigations of multi-frequency radar measurements in the past decade (including but not limited to Kneifel 2011, 2015, Leinonen 2012, Ori 2015, Mason 2019, Oue 2021. Even without studying in-depth the accuracy of various models/parameterizations, perhaps some literature results could be used almost as is for comparison (e.g. similar as Matrosov 2019, but with the appropriate frequencies?).
Response: Yes, there have been numerous model-oriented studies of dual-and triple frequency radar ratios. Most of these studies, however, assume random orientations of ice particles. For this assumption, there is no difference between measurements with vertical and horizontal beam pointing. We believe, that one important outcome of our study is providing an observational evidence that there are important DWR signature differences between different geometries of radar beam pointing which can only be explained by the fact that non-spherical particles are preferentially oriented. To a certain extent, a simple oriented spheroidal model can explain the fact that DWR(hor_beam) > DWR(ver_beam). However, given a multitude of different more sophisticated computational models/approaches and a general lack of easily available (in literature) simulated DWRparticle size relations for the W-X band frequency pair, it is not very feasible to provide a meaningful comparison between observational and modeled DWR (from different computational approaches) within a framework of the current study. Such a comparison would be highly desirable in future and it should involve modeler collaborators. We included some thoughts on this in the conclusion section of the revised manuscript.
Specific comment: Sect. 2.1 How were the radars calibrated?
Response: Relative calibration of DWR is achieved by assuming that DWR is 0 dB for the regions of low reflectivity (i.e., small crystals). Absolute calibration is made using clear-air observations of the water surface backscatter cross section (Li et al., 2005). Calibration for other NAWX antennas is done by comparing measurements between antenna ports. More details (and references) on calibration are described by a study of Nguyen et al. (2019), which is referenced in the manuscript.
Specific comment: l. 107 How is the liquid drop mean volume diameter computed (and the LWC)? With the CDP probes?
Response: Liquid versus ice hydrometeor type identification was performed based on the analysis of measurements of a combination of the Rosemount Icing Detector (RID, Mazin et al. 2001), the particle scattering probes (CDP, FCDP), the Cloud Particle Imager (CPI, Lawson et al. 2001) and the 2D-S probe. The choice of the probes was done based on proximity of the LWC measured by the probes to the LWC measured by the RID. The analysis of the RID and scattering probes measurements was primarily used to identify the presence of small liquid cloud droplets. Liquid MVD and LWC values for liquid drop populations were calculated for particles which were identified as liquid drops. We included the relevant explanation in the revised manuscript.
Specific comment: Fig. 2: I recommend the authors re-do this figure. It is 1) very stretched, and 2) the colorbar of the radar data (plots c -f) is not adjusted (it goes down to -20 dBZ but there are no such low values). This makes the reading quite difficult.
Response: We changed the aspect ratio of this figure. Now it looks less starched. To address the reviwer comment, we also attempted different color bars (see the uploaded supplemental file), including -20 dBZ to 44 dBZ (lower frame), -10 dBZ to 44 dBZ (upper frame), and -5 dBZ to 44 dBZ (middle frame). Examples with the use of these color bars are shown in the uploaded supplemental file. We think that the -20 dBZ to 44 dBZ color bar presents a better overall view as it provides a better color coverage for X-band radar data and also it provides an additional yellow hue (compared to other color bars) for the W-band radar data.
Specific comment: l. 156 Which probes were used for the hydrometeor classification? Are all the size ranges included?
Response: The image recognition processing to identify habits of cloud particles (Korolev and Susman, 2000) was applied to the measurements of the OAP-2DC probe (Knollenberg, 1981) which has a 50 μm -1.6 mm size range (with a 50 μm image resolution). Complete and partial images were included in the analysis. Inclusion of partial images in the analysis allowed an extension of the image recognition analysis to particles with sizes up to about 5 mm. This information was included in the revised manuscript.
Specific comment: Fig. 3: Please indicate the scale on the images. It could be relevant to also show the HVPS images at the corresponding time steps: on the right panels, the particles are large and the 2DS images are not very telling.
Response: We included the scale in Fig. 3 following the review comment. However, we consider adding HVPS images redundant here since they do not significantly add to the information on particle habits.
Specific comment: Fig. 8: It would be interesting to also have some results on the observed correlations between DWR and the other characteristic sizes. Is Dv the characteristic size which correlates the best with DWR?
Response: Correlation coefficients between the horizontal radar beam DWR and MVD, D m , D e and D vc are approximately in the 0.82-0.86 range, which is close to the correlation between DWR and D v . DWR and D mean are less correlated (cor≈0.6), which is mostly due to the lower correlation between D mean and other characteristic sizes (Fig. 8c). No meaningful correlation exists between DWR and D eff . The correlation coefficients between the vertical beam DWR and characteristic particle sizes are by about 0.05 smaller compared to those for the horizontal beam DWR. This information was added in the revised manuscript.
Specific comment: l. 289-293. The mass-size relation of ice hydrometeors can vary significantly depending on the particle population (e.g. Mason 2018, Leinonen 2021) . Why was this specific relation chosen? What would be the impact of changing it? Perhaps distinguishing particle types would cause some differences.
Response: The exponent of the m-D relation is the same as in the Brown and Frances (1995) m-D relation which is widely used in the community. The prefactor coefficient in this relation used in our study was found as a result of comparisons of the PSD-to-mass calculations and bulk IWC measured by the isokinetic probe (IKP, Davison et al. 2011). This allowed finding coefficients a and b in the power-law m-D relation (where D is a larger particle projection) that provide best matching of the IWC calculated from PSDs and that measured directly by the IKP. The corresponding explanation is given now in the revised manuscript. Note that the choice of the coefficient in the m-D relation only affects Deff (eq. 9) but not other characteristic sizes considered here. The DWR-Dv relations are not affected by the choice of the m-D relation since the m-D relation is not used for calculations of characteristic sizes other than Deff.
Specific comment: l. 319: Same question -why this relation? was it found appropriate in the ICICLE dataset? Otherwise, would the results differ significantly with another relation? Did the ICICLE payload not include some direct TWC / IWC measurements (perhaps these were not available)?
Response: There were two Nevzorov bulk probes installed during the ICICLE flights. IWC estimates from these probes differ by about 13% on average. We decided to use PSDbased IWC estimates (see the response to the previous comment) for calculating D eff using equation 9 (i.e., this the only equation where IWC is used). This decision was also dictated that by the fact that extinction coefficient in this equation (i.e., α e ) was also estimated using observed PSD. This will result in error compensation and is expected to provide a better estimate of D eff . We make a note in the revised manuscript that D eff values are dependent on the choice of the m-D relations (e.g., D eff is proportional to the prefactor in this relation).
Response: changed as suggested.