Study on The Error Structure of Radar Reflectivity Using The Symmetric Rainrate Predictor

Huyan, Lidou; Gao, Yudong; Wu, Zheng; Liu, Bojun

doi:https://doi.org/10.5194/amt-2023-72

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https://doi.org/10.5194/amt-2023-72

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06 Jun 2023

| 06 Jun 2023

Status: this preprint has been withdrawn by the authors.

Study on The Error Structure of Radar Reflectivity Using The Symmetric Rainrate Predictor

Lidou Huyan, Yudong Gao, Zheng Wu, and Bojun Liu

Abstract. Given that the Gaussianity of observation error distribution is the fundamental principle of most current modern data assimilation methods, the error structure of radar reflectivity becomes increasingly important with the development of reflectivity assimilation in convection-allowing numerical weather prediction. This study examines the error distribution of radar reflectivity and discusses what give rise to the non-Gaussian error distribution by using 6 month reflectivity departures between observations and simulations in the Southwest China. By following the symmetric error model in all-sky satellite radiance assimilation, we unveil the error structure of radar reflectivity as a function of symmetric rainrates, which is the average of observed and simulated rainrates. Unlike satellite radiance, the reflectivity error shows a sharper slope in light precipitations than moderate precipitations. Thus, a three-piecewise fitting function is more suitable for radar reflectivity than a two-piecewise fitting function. The probability distribution functions of reflectivity departures normalized by symmetric rainrates become more Gaussian in comparison with the raw probability distribution function. Moreover, the possibility of using third-party predictor to construct the symmetric error model are also discussed in this study. According to the Jensen-Shannon divergence, a more linear predictor, the logarithmic transformation of rainrate, can provide the most Gaussian error distribution.

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Received: 08 Apr 2023 – Discussion started: 06 Jun 2023

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Lidou Huyan et al.

Interactive discussion

Status: closed

RC1:
'Comment on amt-2023-72', Anonymous Referee #1, 25 Jun 2023

The current work attempts to use "symmetric rainrate predictor" to study the error structure of radar reflectivity observations. Due to the following major concerns, I do not consider it for publication:
1. The English and scientific writing is very poor. There are too many unclear phrases and grammar mistakes, and the language is absolutely not concise.
2. For radar data assimilation, the volume-scan radar data are commonly used. However, the current study is based on radar reflectivity composites. One may wonder its practical value.
3. In radar data assimilation, it is often to use a low threshold value that is set for both simulated and observed reflectivities. It is unusual to remove data wherever they are missing either in simulations or in observations. Nevertheless, in the context of data assimilation, it is nowadays much more interesting to develop more advanced algorithms to deal with non-Gaussianity, instead of making observation error distribution more Gaussian.
4. Authors should give more efforts to clarify the concept of "symmetric rainrate predictor", e.g., what does "symmetric" mean? What is advantage of it over the other methods? Throughtout the manuscript, the interpretation of results strongly rely on Geer and Bauer (2011), which considerably reduces the relevance of this study.

Citation: https://doi.org/10.5194/amt-2023-72-RC1
- AC1: 'Reply on RC1', Yudong Gao, 28 Jun 2023
  
         We thank Referee 1 for some vital comments. However, Referee 1 seems misunderstood the main purpose of this study. To avoid further misunderstandings, we iterate the goal of this study here. This study is only related to analysis of observation. we think this study may fall better in the scope of Atmospheric Measurement Techniques. We used the symmetric error model, which is widely used in all-sky satellite radiance assimilation, to unveil the heteroscedasticity of composite reflectivity. The results showed the symmetric error model make a more Gaussian distribution of composite reflectivity, which accords with the most current data assimilation principles. It demonstrated that the symmetric method is an effective method to attack the non-Gaussian problem of radar reflectivity. Although the heteroscedasticity of composite reflectivity is not exactly identical to that of reflectivity, both heteroscedasticities of composite reflectivity and reflectivity are related to the location, shape and intensity of convective systems. How to apply the symmetric error model on reflectivity assimilation will be reported in another study.
        We responded all major concerns of Referee 1 in the following context.
  1. The English and scientific writing is very poor. There are too many unclear phrases and grammar mistakes, and the language is absolutely not concise.
  Response:
        This manuscript is a resubmission. We revised our original manuscript according to a number of comments from different reviewers. Owing to our limited writing skill, the presentation become wordy and ambiguous after several rounds. We can hire a wordsmith to help us if this study does not have any scientific issue.
  2. For radar data assimilation, the volume-scan radar data are commonly used. However, the current study is based on radar reflectivity composites. One may wonder its practical value.
  Response:
        As in the title, this study is about “the error structure of radar reflectivity using the symmetric rainrate predictor”, does not include how to use the error structure in reflectivity assimilation to improve the numerical weather prediction. In general, we used the rainrate predictor to describe the heteroscedasticity of composite reflectivity. We found that the Gaussianity of error distribution of composite reflectivity is improved, which is consistent with the principle of most current data assimilation methods. Thus, we recommend that using the rainrate-dependent error model, especially for the logarithmic transformation, can improve the reflectivity assimilation.
        We are aware of the differences between standard deviations of two-dimensional composite reflectivity and three-dimensional reflectivity. However, both composite reflectivity and reflectivity are good indicators of convective storms. The intensities and distributions of composite reflectivity and reflectivity are associated with the variation of convective systems. Thus, the heteroscedasticities of composite reflectivity and reflectivity are associated with the location and intensity of convective systems, which is indicated by the rainrate in this study. The variation of composite reflectivity could be similar to the variation of reflectivity for a precipitating weather system. The fitting functions could be used to inflate the reflectivity errors in data assimilation. It is worthy to discuss how to put the fitting function into a data assimilation system in another study because some fundamental parameters could be very sensitive.
        As the first in-depth study to unveil the error structure by using the symmetric predictor, we hope this study can inspire other scientists who are more familiar with radar measurements to propose other reliable predictors for radar reflectivity.
  3. In radar data assimilation, it is often to use a low threshold value that is set for both simulated and observed reflectivities. It is unusual to remove data wherever they are missing either in simulations or in observations. Nevertheless, in the context of data assimilation, it is nowadays much more interesting to develop more advanced algorithms to deal with non-Gaussianity, instead of making observation error distribution more Gaussian.
  Response:
        In this study we only use ‘both-reflectivity’ scenario to illustrate what give rise to the non-Gaussian error distribution of radar reflectivity, do not remove the misses and false simulations in data assimilation. The ‘both-reflectivity’ scenario is only used as a benchmark to illustrate the non-Gaussian issue of reflectivity assimilation. The Fig. 3 and Fig. 4 illustrate that the bimodal distribution of reflectivity errors comes from the misses and false simulations. The effects of more or less accurate observations and the logarithm transformation on the symmetric error model are presented by Fig. 7, Fig. 9 and Fig. 11.
        The observation error model and advanced non-Gaussian algorithm are both effective ways to attack the non-Gaussian issue in data assimilation. The former method, such as bias correction, is already used in satellite radiance assimilation, especially in most operational centers, as cited in this manuscript. Thus, we attempt to construct an error model for radar reflectivity and hope to use it in operation soon. Because a few non-Gaussian algorithms are used in current operational systems.
  4. Authors should give more efforts to clarify the concept of "symmetric rainrate predictor", e.g., what does "symmetric" mean? What is advantage of it over the other methods? Throughtout the manuscript, the interpretation of results strongly rely on Geer and Bauer (2011, hereafter GB2011), which considerably reduces the relevance of this study.
  Response:
        The ‘symmetric predictor’, computed by the average of simulations and observations, can normalize the probability distribution function (PDF) of reflectivity error more Gaussian. In this study, the ‘symmetric rainrate predictor’ is the average of simulated and observed rainrates. According to Fig. 6 in GB2011, if the background cloud amount was used to build the error model, the PDF was skewness, showing that the background cloud amount was a bias predictor.
        The construction of symmetric error model for radar reflectivity is inspired by the achievements of symmetric error model in all-sky satellite assimilation. Using a ‘symmetric predictor’ to build an error model is a common method in all-sky satellite assimilation. Considering the symmetric error model was introduced by GB2011, the interpretation of results following GB2011 can give a better explanation.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC1
- AC3: 'Reply on RC1', Yudong Gao, 24 Aug 2023
  
  Authors upload their responses again in the attached PDF file.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC3
RC2:
'Comment on amt-2023-72', Anonymous Referee #2, 06 Aug 2023

The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-72/amt-2023-72-RC2-supplement.pdf

Citation: https://doi.org/10.5194/amt-2023-72-RC2
- AC2: 'Reply on RC2', Yudong Gao, 21 Aug 2023
  
  Please find our responses in the attachment.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC2
CC1:
'Comment on amt-2023-72', Shizhang Wang, 23 Aug 2023

It is an interesting study introducing a method designed for satellite data to estimate radar data errors. However, there are some statements that need clarification.
1. According to the abstract, the purpose of this work is unclear. Did the author aim to estimate the reflectivity error or rainrate error? What is the innovation of the present work? Will the present work provide referential information for data assimilation (DA)? All of these points should be stated explicitly.
2. The statement "The error of equivalent reflectivity can change as a function of precipitation" raises the question if the precipitation mentioned involves ice phase hydrometers. If it does, why is rainrate used in the abstract instead of reflectivity? Additionally, why should the error be symmetric? No related context is provided before this.
3. How can we exclude the impact of ice phase particles when estimating rainrate using radar reflectivity in terms of the Z-I relationship?
4. Again, in the introduction, I understand what the authors planned to do, but I'm unclear about the purpose. The motivation should have been clearer.
5. In this study, according to the symmetric error model constructed by the rainrate predictor, the standard deviations of reflectivity could range from about 12 to 35 dBZ. Should we believe the authors' claims that the error is indeed so large?"

Citation: https://doi.org/10.5194/amt-2023-72-CC1
- AC4: 'Reply on CC1', Yudong Gao, 24 Aug 2023
  
  Authors upload their responses in the attached PDF file.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC4
RC3:
'Comment on amt-2023-72', Anonymous Referee #3, 24 Aug 2023

The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-72/amt-2023-72-RC3-supplement.pdf

Citation: https://doi.org/10.5194/amt-2023-72-RC3
- AC5: 'Reply on RC3', Yudong Gao, 30 Sep 2023
  
  The attached file is the responses to Referee 3.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC5

Interactive discussion

Status: closed

RC1:
'Comment on amt-2023-72', Anonymous Referee #1, 25 Jun 2023

The current work attempts to use "symmetric rainrate predictor" to study the error structure of radar reflectivity observations. Due to the following major concerns, I do not consider it for publication:
1. The English and scientific writing is very poor. There are too many unclear phrases and grammar mistakes, and the language is absolutely not concise.
2. For radar data assimilation, the volume-scan radar data are commonly used. However, the current study is based on radar reflectivity composites. One may wonder its practical value.
3. In radar data assimilation, it is often to use a low threshold value that is set for both simulated and observed reflectivities. It is unusual to remove data wherever they are missing either in simulations or in observations. Nevertheless, in the context of data assimilation, it is nowadays much more interesting to develop more advanced algorithms to deal with non-Gaussianity, instead of making observation error distribution more Gaussian.
4. Authors should give more efforts to clarify the concept of "symmetric rainrate predictor", e.g., what does "symmetric" mean? What is advantage of it over the other methods? Throughtout the manuscript, the interpretation of results strongly rely on Geer and Bauer (2011), which considerably reduces the relevance of this study.

Citation: https://doi.org/10.5194/amt-2023-72-RC1
- AC1: 'Reply on RC1', Yudong Gao, 28 Jun 2023
  
         We thank Referee 1 for some vital comments. However, Referee 1 seems misunderstood the main purpose of this study. To avoid further misunderstandings, we iterate the goal of this study here. This study is only related to analysis of observation. we think this study may fall better in the scope of Atmospheric Measurement Techniques. We used the symmetric error model, which is widely used in all-sky satellite radiance assimilation, to unveil the heteroscedasticity of composite reflectivity. The results showed the symmetric error model make a more Gaussian distribution of composite reflectivity, which accords with the most current data assimilation principles. It demonstrated that the symmetric method is an effective method to attack the non-Gaussian problem of radar reflectivity. Although the heteroscedasticity of composite reflectivity is not exactly identical to that of reflectivity, both heteroscedasticities of composite reflectivity and reflectivity are related to the location, shape and intensity of convective systems. How to apply the symmetric error model on reflectivity assimilation will be reported in another study.
        We responded all major concerns of Referee 1 in the following context.
  1. The English and scientific writing is very poor. There are too many unclear phrases and grammar mistakes, and the language is absolutely not concise.
  Response:
        This manuscript is a resubmission. We revised our original manuscript according to a number of comments from different reviewers. Owing to our limited writing skill, the presentation become wordy and ambiguous after several rounds. We can hire a wordsmith to help us if this study does not have any scientific issue.
  2. For radar data assimilation, the volume-scan radar data are commonly used. However, the current study is based on radar reflectivity composites. One may wonder its practical value.
  Response:
        As in the title, this study is about “the error structure of radar reflectivity using the symmetric rainrate predictor”, does not include how to use the error structure in reflectivity assimilation to improve the numerical weather prediction. In general, we used the rainrate predictor to describe the heteroscedasticity of composite reflectivity. We found that the Gaussianity of error distribution of composite reflectivity is improved, which is consistent with the principle of most current data assimilation methods. Thus, we recommend that using the rainrate-dependent error model, especially for the logarithmic transformation, can improve the reflectivity assimilation.
        We are aware of the differences between standard deviations of two-dimensional composite reflectivity and three-dimensional reflectivity. However, both composite reflectivity and reflectivity are good indicators of convective storms. The intensities and distributions of composite reflectivity and reflectivity are associated with the variation of convective systems. Thus, the heteroscedasticities of composite reflectivity and reflectivity are associated with the location and intensity of convective systems, which is indicated by the rainrate in this study. The variation of composite reflectivity could be similar to the variation of reflectivity for a precipitating weather system. The fitting functions could be used to inflate the reflectivity errors in data assimilation. It is worthy to discuss how to put the fitting function into a data assimilation system in another study because some fundamental parameters could be very sensitive.
        As the first in-depth study to unveil the error structure by using the symmetric predictor, we hope this study can inspire other scientists who are more familiar with radar measurements to propose other reliable predictors for radar reflectivity.
  3. In radar data assimilation, it is often to use a low threshold value that is set for both simulated and observed reflectivities. It is unusual to remove data wherever they are missing either in simulations or in observations. Nevertheless, in the context of data assimilation, it is nowadays much more interesting to develop more advanced algorithms to deal with non-Gaussianity, instead of making observation error distribution more Gaussian.
  Response:
        In this study we only use ‘both-reflectivity’ scenario to illustrate what give rise to the non-Gaussian error distribution of radar reflectivity, do not remove the misses and false simulations in data assimilation. The ‘both-reflectivity’ scenario is only used as a benchmark to illustrate the non-Gaussian issue of reflectivity assimilation. The Fig. 3 and Fig. 4 illustrate that the bimodal distribution of reflectivity errors comes from the misses and false simulations. The effects of more or less accurate observations and the logarithm transformation on the symmetric error model are presented by Fig. 7, Fig. 9 and Fig. 11.
        The observation error model and advanced non-Gaussian algorithm are both effective ways to attack the non-Gaussian issue in data assimilation. The former method, such as bias correction, is already used in satellite radiance assimilation, especially in most operational centers, as cited in this manuscript. Thus, we attempt to construct an error model for radar reflectivity and hope to use it in operation soon. Because a few non-Gaussian algorithms are used in current operational systems.
  4. Authors should give more efforts to clarify the concept of "symmetric rainrate predictor", e.g., what does "symmetric" mean? What is advantage of it over the other methods? Throughtout the manuscript, the interpretation of results strongly rely on Geer and Bauer (2011, hereafter GB2011), which considerably reduces the relevance of this study.
  Response:
        The ‘symmetric predictor’, computed by the average of simulations and observations, can normalize the probability distribution function (PDF) of reflectivity error more Gaussian. In this study, the ‘symmetric rainrate predictor’ is the average of simulated and observed rainrates. According to Fig. 6 in GB2011, if the background cloud amount was used to build the error model, the PDF was skewness, showing that the background cloud amount was a bias predictor.
        The construction of symmetric error model for radar reflectivity is inspired by the achievements of symmetric error model in all-sky satellite assimilation. Using a ‘symmetric predictor’ to build an error model is a common method in all-sky satellite assimilation. Considering the symmetric error model was introduced by GB2011, the interpretation of results following GB2011 can give a better explanation.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC1
- AC3: 'Reply on RC1', Yudong Gao, 24 Aug 2023
  
  Authors upload their responses again in the attached PDF file.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC3
RC2:
'Comment on amt-2023-72', Anonymous Referee #2, 06 Aug 2023

The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-72/amt-2023-72-RC2-supplement.pdf

Citation: https://doi.org/10.5194/amt-2023-72-RC2
- AC2: 'Reply on RC2', Yudong Gao, 21 Aug 2023
  
  Please find our responses in the attachment.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC2
CC1:
'Comment on amt-2023-72', Shizhang Wang, 23 Aug 2023

It is an interesting study introducing a method designed for satellite data to estimate radar data errors. However, there are some statements that need clarification.
1. According to the abstract, the purpose of this work is unclear. Did the author aim to estimate the reflectivity error or rainrate error? What is the innovation of the present work? Will the present work provide referential information for data assimilation (DA)? All of these points should be stated explicitly.
2. The statement "The error of equivalent reflectivity can change as a function of precipitation" raises the question if the precipitation mentioned involves ice phase hydrometers. If it does, why is rainrate used in the abstract instead of reflectivity? Additionally, why should the error be symmetric? No related context is provided before this.
3. How can we exclude the impact of ice phase particles when estimating rainrate using radar reflectivity in terms of the Z-I relationship?
4. Again, in the introduction, I understand what the authors planned to do, but I'm unclear about the purpose. The motivation should have been clearer.
5. In this study, according to the symmetric error model constructed by the rainrate predictor, the standard deviations of reflectivity could range from about 12 to 35 dBZ. Should we believe the authors' claims that the error is indeed so large?"

Citation: https://doi.org/10.5194/amt-2023-72-CC1
- AC4: 'Reply on CC1', Yudong Gao, 24 Aug 2023
  
  Authors upload their responses in the attached PDF file.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC4
RC3:
'Comment on amt-2023-72', Anonymous Referee #3, 24 Aug 2023

The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2023-72/amt-2023-72-RC3-supplement.pdf

Citation: https://doi.org/10.5194/amt-2023-72-RC3
- AC5: 'Reply on RC3', Yudong Gao, 30 Sep 2023
  
  The attached file is the responses to Referee 3.
  
  Citation: https://doi.org/10.5194/amt-2023-72-AC5

Lidou Huyan et al.

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Short summary

In order to deal with this non-Gaussian problem, we describe the variation of reflectivity standard deviation as a function of the symmetric rainrate, which is the average of observed and simulated rainrates. The reflectivity error distribution normalized by the rainrate-dependent function becomes more Gaussian. The effects of the accuracy and linearization of symmetric rainrate on the reflectivity error structure are also discussed.


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