Short summary

The authors derive relations between radar reflectivity (Ze) and ice water content (IWC), as well as Ze and snowfall rate (SR). Compared to existing relations, they take into account the normalized rime mass (M) into their relations. The relations are trained on data from one field site and evaluated on data from three other field campaigns. Additionally, since M is often unknown, they also provide relations based on liquid water path (LWP). Those relations could be applied to space-borne measurements.

General Comment

I think the manuscript is generally well written and addresses a relevant scientific question within the scope of the journal. Therefore, it is likely worth of publication after all comments are addressed.

I like that the authors train their relations based on data from one site and then test the performance at three other locations on very different latitudes. This greatly increases the credibility into the universality and robustness of the method.

The only issue I see is the following: The relations are established as a fit of a polynomial function between Ze and IWC. However, IWC can not be observed directly. Since the in situ imager can only measure the particle size distribution N(D), we need an estimate of the snowflake mass. This mass information depends on estimates of the normalized rime mass M, which in turn is derived from N(D) and Ze. Therefore, in the training, the "labels" (IWC) are not independent from the "features" (Ze)!

This is the case for the train and test sites. The only truly independent evaluation, if I am correct, is coming from the SR gauge. 

I think one has to discuss carefully what this double use of Ze implies. Would a bias in Ze go unnoticed, since it affects both sides of the fit equation equally? Can it explain the weaker correlation with gauge measurements?

Generally, for me, it seems like the retrievals of IWC and M face a similar problem: In both cases, Ze, which depends on number and mass, has not enough information to fully constrain the values of interest. For IWC, we need additional information about the mass or density (like M). 

For the retrieval of M, we need information about the particle number, which is coming from the particle imager N(D). Then, a forward operator in combination with an optimal estimation approach is used to find the M, which matches the observed Ze best.

So why not using the same approach directly for the retrieval of IWC? I.e., given N(D), using a forward operator and vary IWC until it matches the observed Ze?

Otherwise, an interesting study on a unique dataset!



Other Comments

- line 36-42: I believe error cancellation happens if the relations are trained on enough data to capture the full snowfall climatology with all its diversity in shape, habit, etc. Then, a relation can be wrong in a single case, but the overall average might be correct.  However, if the relations themselves differ by about one order of magnitude, why would you assume that the error cancels out on seasonal time scales? If one relation is systematically higher than another (compare e.g. in Fig. 5 i) ), it will also lead to systematically higher results  for any reflectivity time series!

- Line 205: Why not discarding NaN cases? (Would it reduce the number of data points too much?)

- Sec. 3.4, Equations 6,7,8,9: Can you motivate, why you chose exactly this functional form as a basis for the regression?  For example, when I look at the measurement data in Fig. 4a+c, it seems like the cone of data points is getting more narrow towards the right (the spread of IWC and SR is becoming less with higher Ze). This is not visible in your fit functions in Fig. 4b+d. Why not including a coefficient in the fit function which would allow for this flexibility?

- Line 224: Why not using the SAIL-derived 2.25 dB as offset for the viewing angle correction, instead of the 2.29 dB derived from inter-site comparison (line 218)? That way, the data evaluation from the validation sites would be completely independent from the training site.

- Fig. 3 caption: I thought the offset between SAIL and HYY+NYA is 2.29 dB +-0.39?

- Line 276: Does this mean the relations become uncertain/invalid beyond 20 dBZ? I would recommend to plot only the range where data points are available, or at least indicate the range where the relations are based on extrapolation.

- Line 289: "based on in situ data" -> not only (see main comment)

- Line 307: Site specific effects -> what could those be?

- Sec. 4.2.2.: You trained the retrieval based on air temperature measurements and, if I understand correctly, also use air temperature in your "simulated" satellite retrieval (+-2K uncertainty). For the case of a real satellite, which temperature would you use? Would it be valid to use brightness temperature? Would this limit the retrieval to cloud top?

- Line 325: Interesting. I would have assumed, since the inclusion of LWP (as proxy for M) is the main improvement over existing relations, the influence of LWP would be bigger. What are the other error sources you mention?

- Fig. 7: Instead of SAIL vs All sites, I would probably split SAIL vs Other sites (clear Train vs Test distinction). Also in other figures.

- Line 352: A positive bias increases the NRMSE, a negative has no effect. Why is this asymmetry?

- Fig. 11, 12: It is interesting to see that the gauge error (R2, RMSE, ME) seems to be generally less for HYY than for SAIL, even though the relations are developed on SAIL data.

- Conclusion 1 (line 376 following): Since the viewing angle offset was derived for  unrimed particles, high and low IWC situations are mainly different in number concentration and particle size, I assume. Since riming is a main point of this study, it is interesting to ask what happens for riming. Intuitively, at least for strong riming, I would expect the particles to become rounder and therefore, the offset between vertical and slanted observations to become smaller?



Technical Comments

- Line 42: "cancel partly out" -> "cancel out partly"

- Line 166: "Windows corresponds"-> Windows correspond

- Line 218: "between the vertically pointing" -> remove?

- Line 221: "when they when" -> when they where

- Line 298: there -> their

- Figure 4, panel b): What is the black dashed line? Add a legend.

- Figure 6: Even though histogram units are often w.r.t. density or similar, a colorbar would be nice.

- Fig. 11 & 12 could optionally be combined into one figure, like Fig. 9.

- Line 414, last sentence: incomplete?

Please see the attached comments.