| 28 Aug 2025
Evaluate the Impact of Power-Law Scattering Amplitude Fitting on Dual-Polarization Radar Data Assimilation—Summertime Cases Study
Abstract. Different configurations within the observation operator cause dual-polarization radar parameters to exhibit various characteristics, which affect the structure of background error covariance as well as the results of data assimilation. Through real case data assimilation experiments, this study evaluates the raindrop-contributed term in the simulated reflectivity (ZHH) and differential reflectivity (ZDR) to describe the effect of different calculation methods within the operator: the fitting and direct integration methods. In the fitting method, dual-polarization variables are calculated using an analytic function, which assumes a gamma-shaped drop size distribution and fits the relationship between the scattering amplitude (SA) and drop size. In the direct integration method, the quantities of the hydrometeor species and SA are integrated with respect to drop size during the calculation. The results indicate that the fitting method effectively simulates the ZHH. However, the limitations of the fitting function may impact the accuracy when represents the structure of ZDR. By contrast, the direct integration method effectively simulates polarimetric variables. Validation of the raindrop mass-weighted mean diameter (Dmr) indicates that assimilation of dual-polarization radar data into the model results in adjustment of the raindrop size distribution regardless of which configuration is used. However, the Dmr- ZDR structure is closer to the observed structure, and the ZDR structure is more reasonable when the direct integration method is employed. In summary, different configurations within the operator directly affect the results of data assimilation, and the direct integration method has more reasonable performance with respect to simulating dual-polarization radar variables.
Competing interests: Dr. Gyuwon Lee and I have one paper published in Atmoshperic Research which I am third author, and Dr. Lee is the sixth author. Dr. Ya-Chien Feng and I have one paper published in QJRMS which I am the second author, and Dr. Feng is the third author. For the rest of referee, I declare that the neither I nor my co-authors have any competing interests.
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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 ZDR 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 ZDR 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.