This work describes the development and evaluates the performance of  artificial neural networks (ANNs) to diagnose riming using measurements from vertically-profiling Doppler radars.

This is a useful scientific objective.  From a remote sensing perspective, knowing when and where riming is occurring can help improve estimates of precipitation rates and reduce uncertainties in retrievals based on radar observations.  The work suggests that riming can be diagnosed without using mean Doppler velocity - this is useful because mean Doppler velocity will be perturbed in areas of ascent or descent such as convective cores or atmospheric waves.  Finally, detecting and quantifying riming provides information about the microphysical processing experienced by ice-phase precipitation.

The method for development of the ANNs is sound, as is the testing of the ANNs, but I feel there are some shortcomings in terms of scientific quality.  The analysis of the test results, particularly for the BAECC cases, seems unnecessarily limited and basic.  While several sources of uncertainty are acknowledged, there is only a rudimentary discussion of quantified uncertainties, and there is no quantitative estimate of the propogation of these uncertainties into the results of the study.  Additionally, one critical source of uncertainty is not addressed.

Figures are generally well-made and used well to convey information.  The narrative overall is good, but there is some text that would benefit from better organization.

See my specific comments below for details.  I think it would be worthwhile to provide more quantitative analysis of the BAECC results and make some minor reorganization to the section that is noted below.   I'm recommending this be treated as a "major revision".

Specific comments

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The method for creating the FR values in the BAECC dataset depends on a 

mass-dimension relationship for unrimed snow, and neither the 

uncertainty of this relationship nor its impact on the FR predictions of 

the ANN are assessed.  The mass-dimension relationships for snow 

particles are highly variable.  

The description of the development of the ANN provided in section 2.3.2 

would benefit from some reorganization.  See my comments below about 

some explanations about the hyperparameters and loss function that seem 

to be out of order.

In the discussion of the testing with the TRIPEx-Pol data, there's very 

little in the way of quantitative comparisons between the results for 

ANN #1 vs. #2 and W-band vs. Ka-band.  The description of the data 

(section 2.1.2) indicated that the data were regridded onto a common 

height-time grid.  Wouldn't it be possible to make more quantitative 

comparisons, for example by looking at whether there is a 1:1 

relationship among the four possible combinations?  I think a 

quantitative comparison would be a more convicing demonstration rather 

than the statements that the "predicted riming index is very similar and 

the features are almost identical" (P13, L13-14).

P3. L2-3:  It would be helpful to be clear how "terminal fall velocity" 

is being defined.  Is this the fallspeed (speed at which a particle 

approaches the Earth's surface) or is the terminal speed (or terminal 

"velocity", which is relative to the motion of the fluid)?  Also, in 

almost no case will the speed of a single particle be equal to MDV, 

since MDV is determined by an integration over the Doppler spectrum.

P4, L5:  It is not fully clear to me what is meant by "developed 

models".  Is this referring to the ensemble of ANNs?

P5, L9-10:  Can you describe why these particular days were selected?

P6, L8:  It is not clear here what is meant by "having the same D_max as 

the observed particles".  Since IWC is determined by integration over 

the size distribution, it is not necessary that the sizes of the 

observed and unrimed snow particle be the same.  Do you mean "for 

unrimed snow having the same N(D_max) as the observed particles"?

P6, L9-10:  What was the total number of samples examined, and how many 

of those had FR < 1?

P6, L15-16:  Since air below CBH is subsaturated, is the loss of ice 

mass by sublimation possibly significant?

P6, L18:  Was it necessary to assume that MDV is constant between CBH 

and the surface?  Doesn't the KAZR provide MDV profiles at bins below 

CBH?

P7, L10-15:  Then, how are the impacts of these uncertainties 

quantified?  Is this discussed later in the paper?

P7, L24:  Not just momemts, but also SEW, which is not a moment.

P8, L7:  Is the use of "x" in "max(0,x)" intentional, and does it 

represent time as it did in P6, L16?

P8, L9-10:  Could you provide a more complete description of the error?  

I'm not sure of the meaning of "This error is defined by the loss 

function".  Is this simply a measure of the difference between the 

outputs of the ANN and the actual observed values?  How is it 

calculated?

P9, L1-7:  This paragraph begins by identifying the number of hidden 

layers and number of neurons as hyperparameters to be tuned, but the 

following description of k-fold cv says nothing about how these 

hyperparameters are tuned.  Instead, the role of k-fold cv to produce 

multiple models for estimating average and variance is described.  

P9, L16:  Does "layer depth" = number of hidden layers?

P9, L16-19:  This seems to be the content that should follow the first 

sentence of the paragraph starting at P9, L1 (see my comment above).

P9, L17:  The RMSE of what?

P9, L20:  So, is this the definition of the "loss function" (see my 

earlier question) and is the RMSE described above on L17?

P9, L22-24, P10, L1-2:  There are a few point to ask regarding this 

paragraph.  What is meant specifically by "less well represented"?  How 

can high FR cases be "less well represented" but still be "clearly 

separated in the input feature space"?  The RMSE *is* the error, or at 

least it is one way of measuring the error.  It is probably not 

necessary to say that it "basically represents the error".  Is the 

performance of ANN #0 actually "much worse"?  The "test set RMSE" is 

only 0.02 larger than that for ANN #2.  

P10, L2:  Please clarify this.  Why would you change the name for a 

quantity because there are many steps involved in its calculation?

P10, L12-13:  I expect this 1.5 hour period on 21 Feb 2014 was not 

included in the training data.  Is that correct?  Is it part of the 10% 

of data that was retained for the testing phase (see P7, L28-29.

P13, L20-21:  The differences in sensitivity between the W- and Ka-band 

radars have not been discussed previously (section 2.1.2).  I'm not sure 

that I understand this comment about the differences in sensitivity.  

For either the W-band or Ka-band radar, if the backscattering from a 

radar bin is below the minimum detectable signal of the radar, I would 

guess that there is no data for that radar bin and there would be no ANN 

estimate of FR for that radar bin.  How would *sensitivity* influence 

the *accuracy" of the predicted FR?

P13, L24-25:  I think this needs some additional details.  You seem to 

be describing the features of a plot, but it is not clear what is being 

plotted.  Also, regarding "These signatures are attributed to changes in 

the particle density during the riming process", I assume that only 

applies to the riming signature.  Is there an explanation also for the 

"hook-like" signature associated with aggregates? 

P15, L1-2:  I see a (weak) suggestion of a hook-like feature in the 

upper-left panel of Figure 6, but not so much in the other panels.  I 

suggest maybe overplotting a line or an oval to indicate where the 

hook-like features are located in the panels.  

P18, L13-14:  I think it is probably necessary to acknowledge, though, 

that the presence of rimed particles at the surface indicates that 

riming is occurring *somewhere* in the column, but that it isn't strong 

evidence of the correctness of the vertical distribution of FR as 

predicted by the ANNs.

P18, L16:  Are you saying that you are confident you can apply the ANN 

#2 to W-band radar observations and get accurate indications of riming?

P21, L20-25:  It seems to me that application to airborne in situ 

observations (airborne radar plus particle imaging probes) would be a 

natural extension of this work and could help validate the ANN results 

for riming aloft.

Technical corrections

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P1, L1:  SLW has not yet been defined.

P5, L5:  "poiting" should be "pointing".

P5, L13:  I believe "Snofall" should be "Snowfall".

P5, L25:  I believe that "Lee" is not capitalized in this usage.

P7, L18:  This is the first use of the term "fully-connected" (the term 

"fully connected" is used on P8) and the only use of the term "deep 

neural network".  It would be helpful to define them here if they are 

important to this paragraph.

P10, L13:  "17.00" should be "17:00".

P13, L22:  "outruled" is more commonly expressed as "ruled out".

P15, Figure 5:  Note that the righthand panels are mislabelled as 

"W-band".

P15, L7-8:  Since the first sentence refers to findings in the previous 

section, it would be clearer to say "the 19 March 2021 Leipzig case".

P15, L9:  I think the term "instability" would usually be used, rather 

than "lability"?  Is that the intended meaning?

P16, Figure 6:  Please check the arrangement of the panels of the plot.  

According to the caption, W-band should be on top and Ka-band on the 

bottom, but this doesn't seem to be the case.

General comment:

The manuscript developed artificial neural networks to estimate rime degrees within ice precipitating clouds using limited data. It is a novel approach to establish ANNs using vertically-pointing radar data.  The manuscript well written including detailed enough descriptions of the ANN technique, although I have a few questions about the technique and method. The figures are appropriate. I also have a few questions/concerns that should be clarified before considering publication.

Specific comments:

1. It was not clear to me why the authors employed the ANN technique rather than a standard technique that explicitly estimates empirical equations e.g. FR(Ze, MDV, SEW, skewness), FR(Ze, SEW, skewness) as Kneifel and Moisseev (2020) derived FR(MDV). I think that deriving such empirical equations is not so hard. Please clarify the advantage of using ANN techniques compared to others.  
2. A major concern is that this study lacks quantitative evaluations of the established ANNs. The evaluations of the results from the applied ANNs presented in this manuscript are all qualitative, and only a few of short periods near the surface are picked up to compare the results with the in-situ measurements. I understand that the qualitative evaluation of the selected short periods is valuable, but quantitative evaluations, including the entire periods of the application cases, should also be more valuable.
3. It was not clear why the authors used SEW instead of Doppler spectrum width. What micriohysical/dynamical processes does SEW represent? How do those processes impact the ANNs? What is the advantage over the Doppler spectrum width? Doppler spectrum width is a standard moment parameter, which is available for even radars that do not collect Doppler spectra, whereas SEW requires Doppler spectrum data, which are expensive for many radars.
4. As the authors pointed near the end of the manuscript, SEW can be strongly influenced by turbulence broadening. Why did the authors use SEW in both ANN1 and ANN2? My specific questions are:
   • For the significant turbulence cases, if SEW was not used in an ANN, could the result be more reasonable?
   • Can you quantify the uncertainty attributed to the turbulence broadening in the ANN-based rime degree estimate?
   • Can you train the ANNs to minimize the turbulence broadening effect?
   • SEW depends on sensitivity. Do the ANNs work with different systems that have different sensitivity?
5. The manuscript needs descriptions about how to deal with attenuation effects.

• Were the radar data corrected for attenuations? The attenuations affect not only reflectivity but also MDV and SEW. Especially, SEW might strongly be affected by the attenuation.
• Do the attenuations for hydrometeors and gases affect the prediction and the accuracy of the established ANNs?
• Especially the Fig.4’s case includes many regions of rain, so the attenuation must be significant. Does the attenuation influence the riming prediction above the melting layer?
• One of the findings of this study is that the ANNs can be applied at a different cloud radar frequency. Do the attenuation effects influence this?

6. Section 2.2: When I first read this paragraph, it was not clear whether those processes described in this section were applied to all datasets from all sites or only the BAECC datasets. I suppose that they were applied to the BAECC datasets, which were used as training datasets, correct? Please clarify here.
7. 9 line 24: Please describe why the performance of the ANN #0 is much worse than for the others.
8. 10 lines 1-2: Please explain more why “riming index” is used instead of FR. What is the relationship between riming index and FR? Please explain more why the output from the training process is different from FR for readers that do not have expertise in ANN.
9. Section 3.2: Most of this case seems to have a melting layer, meaning rain near the surface. Which height/time was characterized as "aggregation" or "riming"?
10. Figure 6: Many data points with higher riming index > 0.7 are deviated from the pink line. Are they accurate predictions? I think that adding the same plots but with color scales with FR will be useful.
11. 21 line 19: In cases where MDV is not available due to orographic effects, SEW could also be impacted by a turbulence.

Technical comments:

1. 4, line 10: SEW is first used here.
2. Table 1: Please give the total time of the datasets used. This would also be useful.
3. 9 line2: I am not sure if five folds are enough for the validation process. Could you evaluate/explain that the number is appropriate?
4. P10 line 18: What is the unit of 0.7 and 0.9?
5. Figure 2: Please add temperature contours similar to Fig. 5.
6. Figure 3: Please add time series of FR estimated from the in-situ measurements and compare it with the riming index from the ANNs.
7. Were DWRs corrected for attenuations?
8. 13 line 15: When is the riming period?
9. 4d: Please use appropriate color scale.
10. Figure 5: Is it possible to have riming with T<-40C (0.4 riming index)?
11. Legends on Figs. 5a-5d present all “W band.”
12. Figure 6: I think that the four panels in this figure used the same dataset, and the distribution of the data points should be same. Why is the distribution in the plots in the left column and the right column different?
13. Figure 8: Could you add time series of FR estimated from the in-situ measurements or similar parameter from the image analysis?