This is a very solid and well written paper describing the optimal estimation (OE) algorithm for retrieval of microphysical characteristics of ice using combined polarimetric and dual-frequency radar measurements. The algorithm was tested on the data collected during the ICE-POP 2018 experiment in Korea. Although certain microphysical features of ice / snow are well captured, an overall quality of the algorithm performance is quite modest which might be possibly or partially attributed to the instrumental biases of the radar measurements (and the dual-wavelength ratio DWR in particular).

A fundamental question this study raises regards the feasibility of utilizing a very complicated and computationally intense OE methodology to solve multiparameter problems with large uncertainties in the state and observed vectors. I do not exclude that combining more simplistic retrieval methods with careful data quality control might be more efficient under such scenario.

Here is a list of more concrete comments and suggestions,

• The authors avoid using specific differential phase K_DP in their formalism and resort to the total differential phase instead. Radial dependencies of Φ_DP in Fig. 4 and temporal plots of K_DP in Fig. 8 (bottom panels) show that K_DP can be quite reliably estimated at both Ku and Ka bands. K_DP is very sensitive to a lower end of the particle spectrum and the results of this and similar studies indicate that K_DP is strongly correlated with the total concentration of smaller-size ice. In other words, K_DP has very strong informative content and is immune to attenuation, resonance scattering effects (even at Ka band), and radar miscalibration.
• Since the D3R radar was able to do genuine RHIs during the ICE-POP experiment, would it be possible to display composite RHIs of Z, Z_DR, and K_DP and generate vertical profiles of the radar variables (at Ku and Ka bands) over the PIP location in a height vs time format? This would give a better idea about the vertical microphysical structure of the storm and possible problems in the radar – PIP comparison which are mentioned in the manuscript such as enhanced vertical gradients of Z likely responsible for underestimation of snow rate and size.
• Captions to Figs. 4 and 5 are the same.
• Correct the reference the Ryzhkov et al. (2016) paper. It is not in press.

Title: Snow Microphysical Retrieval from the NASA D3R Radar During ICE-POP 2018

Manuscript summary:

The manuscript introduces an algorithm retrieving the particle size distribution and various microphysical properties of snow from dual-wavelength dual-polarization radar via optimization estimation. These estimations include characteristic particle size, shape parameter of the size distribution, rime fraction, mean aspect ratio, orientation distribution and snowfall rate (volumetric and water equivalent). The results are verified with the ground instrument during ICE-POP 2018. Most of the comparisons indicate high biases but with high correlation coefficients.

The major concern of the algorithm is trying to estimate various parameters (Eq. 13, 9 parameters at each gate) at the same time, yet the information for retrieval is limited (EQ. 12, 5 measurements). The validation indicates high biases. The manuscript needs substantial revision. Major revision is recommended.

Major comments:

1. Considering the number of variables (nine) is higher than measurements (five), it’s highly possible the final retrievals are mostly from the “background” value (e.g., Prior in Table 5). The manuscript did not compare the PPI (or RHI )simulated measurements from “Prior” and “last iteration”. This is important to ensure the retrieval is not mostly from “background” term (2^nd term of RHS in Eq. 11). Figure 4 is the only figure to show that the final simulated measurements from optimal estimation. Yet, a ray data is not convincing. Please do show the PPI or RHI simulated measurements for all of the experiments including Hu-only, DWR-only, Ku-pol and All-obs.
2. Since the observational information is limited, fixing the value of some parameters (e.g., axis-weighted ellipse ratio, riming fraction). Figure 10 and 11 indicate that the effective density and ellipse ration has little change compared to other variables. Has author considered to reduce retrieved variables?
3. Three cases are show for validation. Two of the cases (9 Jan. and 28 Feb.) has pronounced bias between radar measurement and PIP simulation (Fig. 8). Later, the retrieval bias can also be noticed among those two cases (Figs. 9 and 10). In terms of snowfall rate, author can consider perform more comprehensive validation by including more Pluvio data.
4. Overall, the validation is rather disappointing. The bias and MAR are around +/- 30% in snowfall rate, nearly 40% in volume-weighted diameter (Dp), 40% in area-weighted ellipse and box aspect ratio. It’s a good sign that the correlation coefficient is high. Moreover, there is no PPI or RHI retrieval to ensure that the retrievals are consistent in spatial domain.

Minor comments:

Figure 4, please change the color of simulated measurements of the last iteration to red color for clarity.  

Figure 9, please show the snow fall rate from “background” simulation.