The scope of the paper is clear and the idea of proposing an ESM for raindrops at W-band for polarimetric variables is very original. The consequences of using an ESM instead of the standard spheroidal approximation are also thoroughly discussed. The topic is very relevant for precipitation research and characterization of rain microphysics.

There is room for improving the manuscript according to the following suggestions.

• Unclear what is the take home message in the remark at the end of Sect 4.2
• Line 304: “because of smaller concentration of these drops and attenuation by liquid

and gas” I disagree on the second reason, attenuation acts uniformly across the spectrum.

• Line 310-312: I have never noticed this secondary minimum. I would doubt these is due to non spherical effects, I would be more in favor of considering DSD effects only (unless we really disproof Mie)  

• Not sure why Figure 9 comes before figure 8. Anyhow to me Fig9 is repetitive (you could include the red model lines in the left panels of fig.8

• 3: do we really need an artificial neural network? To me it just adds confusion. I would stick with a LUT based on Fig.8. Not sure what you add more than that.

• Sect 6.1: I see the differences between integrated ZDR and delta when using your ESM. Maybe it is worth comparing these differences with typical errors of such variable (you mention errors in delta, maybe it is worth also mentioning errors in zdr).

• 11: what are the blue dots all exactly at 6 dB Z offset?

Minor corrections:

• Line 47 A compactness è The compactness
• Line 48: “A large number of cloud radars are capable of polarimetric measurements” (well there are few in the world, I would attenuate the statement.
• Also statements at line 54-56 ( a bit vague, e.g. what do you mean with strong rain, I would rephrase them)
• “an oscillatory behavior at drop sizes roughly proportional to half of the radar wavelength”, there are multiple oscillations occurring at multiple size, rephrase
• “In real rain measurements, however, we do see Zdr considerably exceeding 0.12 dB”. It looks like a sentence out of the blue, not corroborated by any data or a reference. You need to explain more here or skip it. Also could that signal be caused by differential attenuation?
• Line 118-120. The radar actually provides spectra as a function of the radial velocity (V_k) not of v_k. A different thing is how you reprocess the data.
• Line 124: high è higher and lowè lower
• “still include observations in rain affected by strong attenuation”, not sure how you can do that if Z<5 dBZ are excluded, or you need to specify what you mean with strong attenuation
• “all lines with SNR below 30 dB” è all spectral signal with ….. The term “lines” sounds a little bit ambiguous to me. Check its use.
• Line 339: delete “a”
• Line 413: add spheroidal (before approximations)

The manuscript focuses on analyzing radar data from relatively quiet rain areas by applying data constraints. Three radar variables are analyzed: the fall velocity of raindrops, ZDR, and scattering differential phase δ. The authors’ data on the fall velocity (Fig. 6a) repeat the known dependence of the velocity on droplet size (D). The authors' ZDR(D) and δ(D) dependencies deviate from those obtained from the T matrix method (Fig. 9).

The following questions about the collected radar data should be clarified to use the authors' results for microphysical studies.    

• The authors select radar returns with strong SNRs (section 3.1) produced by significant rain. The range of radar observations can be longer than 1 km. An estimation of differential attenuation in rain would be desirable in analyzing the dual-pol variables. Differential attenuation decreases measured ZDR and δ values that could cause the decrease in these variables in Fig. 9.
• To my knowledge, the radar has an antenna radome. The radar measurements were taken in rain when the radome was wet. Water on radome affects dual-polarization measurements. If the authors have data on differential attenuation caused by a wet radome, they should be included in the manuscript.
• The authors compare radar data with data obtained from the Thies disdrometer located within 10 m of the radar (p. 5, Ln. 144). At a slant distance of radar observation of 1000 m (Table 2) and 30 deg of antenna elevation, the height of radar resolution volume is 500 m above the radar position and about 860 m in the horizontal direction. That is, an assumption of the uniformity of rain at those distances is made. Justification is needed.
• The authors indicate that their constraints are meant to avoid turbulent areas (section 3). Rain frequently suppresses turbulence, but the horizontal wind shear can be significant. The effectiveness of raindrops as wind tracers depends on their sizes. The horizontal wind shear reshuffles raindrops and its impact on radar spectra can be significant. Therefore, information on possible wind shears would be informative. Such information can be obtained from the collected radar data by analyzing the Doppler velocity along the radials.    

I am curious why eq. (3) has the tanh(.) functions? Is there any reason for that? The curve in Fig 6a is quite smooth to be approximated with a simple polynomial function as it is typically done.