General comments:

This study evaluates the simulation of radar variables (ZH and ZDR) by the polarimetric radar observation operator of Jung et al. (2008) using the power-law fitting and direct integration methods for scattering calculations. This study is interesting for the polarimetric radar data assimilation. However, both the fitting and direct integration methods presented in this manuscript have their own inherent problems, which have already been addressed or improved by Jung et al. (2010), Dawson et al. (2014), Putnam et al. (2019), and Zhang et al. (2021). In short, the fitting method fails to accurately simulate the polarimetric radar signatures, as demonstrated in the manuscript results. Based on the operator of Jung et al. (2008), Jung et al. (2010) developed more accurate and generalized operators using the direct integration method for both rain and ice hydrometeors. Nevertheless, these operators are complex and require computationally expensive numerical integration over the particle size distribution. Subsequently, Putnam et al. (2019) modified the operators of Jung et al. (2010), introducing precomputed lookup tables to increase computational efficiency with some sacrifice to accuracy, and demonstrated their application in assimilating real ZDR (Putnam et al. 2021). However, the operators modified by Putnam et al. (2019) are still computationally expensive and difficult to use in data assimilation, especially in variational assimilation. Zhang et al. (2021) developed a set of parameterized operators based on the numerical integration of the scattering weighted by the particle size distribution. It is challenging to balance the computational efficiency and accuracy of the observation operator within data assimilation systems.

I really appreciate the authors’ efforts in exploring a challenging path toward the effective assimilation of polarimetric radar observations. However, I would strongly encourage the authors to find new avenues rather than retreading ground that has already been explored.

Major comments:

(1) Introduction: I suggest that the authors systematically review the development of polarimetric radar observation operators, highlighting the respective strengths and weaknesses of different operators in both simulation and assimilation.  

(2) Methodology: The manuscript appears to employ the direct integration method only for the raindrop. It is unclear how the manuscript handles ice-phase particles (snow and graupel/hail) and mixed-phase particles (wet snow and wet graupel/hail). A fair comparison should use the same method for all hydrometeor species. Additionally, the sacrifice of accuracy in the fitting method is unavoidable. Therefore, the authors need to clarify the computational advantages of this approach. If the fitting method provides neither improved efficiency nor adequate accuracy, then what is the rationale for using it instead of the direct integration method?

(3) Results: The authors need to present the spatial distribution of the polarimetric radar variables simulated by different methods, including both horizontal and vertical cross-sections. In section 5.3, the authors used the fitted Dmr from the radar variables as a reference “observation” for comparison. However, it is unclear what the purpose of such a comparison is when the “observations” themselves do not represent the truth. Why are the radar variables not compared directly?

Reference:

Dawson, D. T., E. R. Mansell, Y. Jung, L. J. Wicker, M. R. Kumjian, and M. Xue (2014), Low-Level Z_DR Signatures in Supercell Forward Flanks: The Role of Size Sorting and Melting of Hail, Journal of the Atmospheric Sciences, 71(1), 276-299, doi:10.1175/jas-d-13-0118.1.

Jung, Y., G. Zhang, and M. Xue (2008), Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part I: Observation Operators for Reflectivity and Polarimetric Variables, Monthly Weather Review, 136(6), 2228-2245, doi:10.1175/2007mwr2083.1.

Jung, Y., M. Xue, and G. Zhang (2010), Simulations of Polarimetric Radar Signatures of a Supercell Storm Using a Two-Moment Bulk Microphysics Scheme, Journal of Applied Meteorology and Climatology, 49(1), 146-163, doi:10.1175/2009jamc2178.1.

Putnam, B., M. Xue, Y. Jung, N. Snook, and G. Zhang (2019), Ensemble Kalman Filter Assimilation of Polarimetric Radar Observations for the 20 May 2013 Oklahoma Tornadic Supercell Case, Monthly Weather Review, 147(7), 2511-2533, doi:10.1175/mwr-d-18-0251.1.

Putnam, B., Y. Jung, N. Yussouf, D. Stratman, T. A. Supinie, M. Xue, C. Kuster, and J. Labriola (2021), The Impact of Assimilating Z_DR Observations on Storm-Scale Ensemble Forecasts of the 31 May 2013 Oklahoma Storm Event, Monthly Weather Review, 149(6), 1919-1942, doi:https://doi.org/10.1175/MWR-D-20-0261.1.

Zhang, G., J. Gao, and M. Du (2021), Parameterized Forward Operators for Simulation and Assimilation of Polarimetric Radar Data with Numerical Weather Predictions, Advances in Atmospheric Sciences, 38(5), 737-754, doi:10.1007/s00376-021-0289-6.

General comment:

The topic is of great interest and relevance. The direct assimilation of radar data, and in particular polarimetric variables, represents a challenge in data assimilation. 

The article refers to various types of radar data assimilation (variational and LEFTK), but does not describe in detail the different methodologies used for the assimilation of such data. For example, with regard to LEFTK, the EMOVRADO operator was developed within the ICON limited area modelling framework, which also has a specific component for “polarimetric data assimilation”.

The introductory part of the article should provide an in-depth overview of this, following a logical path from the definition of the observables to be assimilated, the methodologies already in use, the limitations and strengths of the methodologies. In this context, it is unclear what added value the proposed methodology offers over current methods, considering the results obtained.  

Specific comments:

• In some parts, the article is difficult to read as it does not follow a logical sequence in its descriptions and explanations.
  
  For example, Section 2 introduces the LETKF system without ever having explained what it consists of (there is a brief mention of the ETKF). Moreover, it is unclear what it means that the WLTAS system is a deterministic ENKF.
• From the introduction, it is unclear whether this study is conducted for all types of hydrometeors or whether, as it appears to be, it is conducted only for raindrops. If it is a choice, the reason must be given.
• In section 3, it would be preferable to first describe the types of data used and then the selected case studies
• In section 4, in the part concerning model configuration, it is assumed that the reader is already familiar with the specifications of the model used.