the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 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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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-3857', Anonymous Referee #1, 07 Nov 2025
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AC1: 'Reply on RC1', Kao-Shen Chung, 18 Dec 2025
We sincerely appreciate the reviewer’s considerate comments regarding the inherent issues identified in previous studies, as well as for the valuable suggestions pointing to potential new research directions. To the best of our knowledge, however, the limitations of the power-law fitting approach—particularly the issue of unreasonable negative ZDR—have not been explicitly addressed in the existing literature. Despite this deficiency, power-law fitting–based operators continue to be employed in recent studies (e.g., Kabasawa et al., 2018; Lee et al., 2026). Since the bias of the background directly leads to physically unreasonable outcomes after data assimilation, it is essential to highlight such systematic biases and to ensure that their limitations are well recognized by the research community. Although the polynomial fitting method addressed by Zhuang et al. (2021) can alleviate the negative ZDR, it still exhibits uncertainties in representing ZDR, particularly for wet snow and for extreme value in the real case simulation. Furthermore, since the polynomial fitting is applied after numerical integration, it is needed to first evaluate whether the integration-form operator provides sufficient accuracy under the meteorological conditions in Taiwan before applying the polynomial fitting. While we acknowledge the importance of systematically comparing different operators and discussing their respective strengths and weaknesses, we believe that explicitly identifying significant biases and preventing potential misuse of existing approaches is both necessary and timely. By clarifying these issues, our study aims to provide guidance toward more appropriate choices and to improve the physical consistency of observation operators. Consequently, the background simulations and associated error structures can be made more reliable prior to data assimilation.
For the points by points responses, please see the attached. Thank you for your comments and suggestion.
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AC1: 'Reply on RC1', Kao-Shen Chung, 18 Dec 2025
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RC2: 'Comment on egusphere-2025-3857', Anonymous Referee #2, 20 Nov 2025
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.
Citation: https://doi.org/10.5194/egusphere-2025-3857-RC2 -
AC2: 'Reply on RC2', Kao-Shen Chung, 18 Dec 2025
We sincerely appreciate the reviewer’s considerate comments regarding the insufficiency of the Introduction, and we have revised this section to substantially improve its completeness. As the primary objective of this research is to validate and point out the unavoidable biases associated with two types of observation operators, the revised Introduction now focuses more explicitly on studies related to dual-polarization radar observation operators. In addition, key references on the LETKF framework, including comparisons between LETKF and other EnKF-based systems, are now briefly introduced for context. Since the biases of simulated observed variables in the background leads to unreasonable error covariance degrading data assimilation performance, it is needed to validate the behavior of the observation operator itself. The added value of this study is explicitly identifying the unavoidable negative ZDR associated with small raindrops. We believe that by depicting these issues could guide future researchers toward more appropriate operator choices and make the simulation more reasonable.
For the points by points responses, please see the attached. Thank you for your comments and suggestion.
- In some parts, the article is difficult to read as it does not follow a logical sequence in its descriptions and explanations.
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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.