A Gaussian mixture method for specific differential phase retrieval at X-band frequency

Wen, Guang; Fox, Neil I.; Market, Patrick S.

doi:https://doi.org/10.5194/amt-12-5613-2019

Articles | Volume 12, issue 10

https://doi.org/10.5194/amt-12-5613-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/amt-12-5613-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 12, issue 10

Research article

|

23 Oct 2019

Research article |

| 23 Oct 2019

A Gaussian mixture method for specific differential phase retrieval at X-band frequency

Guang Wen, Neil I. Fox, and Patrick S. Market

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Final revised paper (published on 23 Oct 2019)
Preprint (discussion started on 13 May 2019)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'weather radar', Anonymous Referee #1, 08 Jul 2019
- AC1: 'Responses for review #1', Guang Wen, 19 Jul 2019
- AC4: 'revised paper', Guang Wen, 19 Jul 2019
- AC2: 'responses for review #2', Guang Wen, 19 Jul 2019
RC2: 'KDP retrieval with GMR', Anonymous Referee #2, 10 Jul 2019
- AC2: 'responses for review #2', Guang Wen, 19 Jul 2019
- AC4: 'revised paper', Guang Wen, 19 Jul 2019
RC3: 'Gaussian Mixture Method for Kdp estimation', Anonymous Referee #3, 16 Jul 2019
- AC3: 'responses for review #3', Guang Wen, 19 Jul 2019
- AC4: 'revised paper', Guang Wen, 19 Jul 2019

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Guang Wen on behalf of the Authors (19 Jul 2019) Manuscript

ED: Referee Nomination & Report Request started (22 Jul 2019) by Gianfranco Vulpiani

RR by Anonymous Referee #3 (12 Aug 2019)

Suggestions for revision or reasons for rejection

With respect to the AMT discussion paper, an important improvement is the adoption of different for the propagation differential phase and the total differential phase, which includes the differential phase upon backscattering. The other important addition is the estimate of the computing time, that an important factor for the acceptance of the method by the community. Of course making sw implementation available is good mean to achieve that goal. I welcome and support any attempts to improve Kdp estimation, which is still an important and totally solved aspect of radar meteorology. In my previous revision I noticed an insufficient discussion of results, while granting authors attenuating circumstances based on the impossibility of providing an ultimate proof and also. Authors replied that validation will be presented in a series of new papers. Based on this reply, I cannot change my recommendation to the editor based on authors’ justifications, because I would like more convincing validation results here.

Specific issues (numbers corespond to replies to reviewer; pages and number are referred to the manuscript explicitly showing changes):

Reply 2.2: When figures about computation time are given, the computing environment must be specified in the text.

Reply 2.3: What I asked was to separate Kdp estimation methods based on dp profile derivative from methods based on self-consistency with Zh and , which is valid only in rain. In addition in the introduction, “A linear regression model has been developed to derive Kdp from the slope of the range profile of dp for S-band radars. In Hubbert et al. (1993), ….”. Methods described in Hubbert’s papers from 1990s were evaluated using the POLDIRAD, a C-band radar of DLR (Germany). Following my (and maybe other reviewers’ comments), a couple of sentences were added. According to those sentences, Vulpiani et al’. s method is just applicable to C-band, in Italy, and in complex terrain (actually it is a general method and can be found in published studies at X-band, non necessarily in complex orography regions). About Gorgucci et al (1999) authors say “that the nonuniform rainfall path produces large errors in the Kdp estimates, while the errors increase as the radar reflectivity varies in dimensions.” I do not understand this sentence.

Reply 2.4. I suggested the need to justify the importance of providing the standard deviation of Kdp estimate. At the moment, I am not aware of applications that require this quantity as input. Authors insert a sentence for this: “it can be used to calculate the variances of ZH and ZDR and rain rate, and to study the streamflow trends in the hydrological model”. Exploiting authors wording in replies and in conclusion, a more convincing justification can be found. I recommend to use those words here. I understand that standard deviation of Kdp is useful in modelling error in Kdp-based QPE and attenuation/specific attenuation estimation. I am not sure about the application to hydrological modelling.

Reply 2.5. I think there is a fundamental misunderstanding about the supposed constancy of variance of dp. The formulas summarized in Bringi and Chandrasekar (2001) that were developed in previous studies conducted in 1990s, were actually a-priori models to highlight the dependency of the standard deviation of dp estimates on different characteristics of observed precipitation phenomenon and on the processing parameters, such as the number of samples. They answered to questions like: what is the expected accuracy of the estimates ? how many samples should we use to achieve it? In developing these models, a number of assumptions were made, such as, SNR high, TX phase stability and uniform beam filling. It is a common experience to verify that error is of some degrees higher and that, say at far distances, where SNR (and hv) is likely low, error on dp is higher than predicted by those models. You may discuss the adequacy of the old style a-priori models, and conclude that your model give a better characterization of the error based on measurements, but a sentence like “2(dp) is stable in LR” is wrong.

Reply 3.9. Figure 4 is still without x-label. I requested a justification of the interpretation ofco based on Zdr, but authors prefer to eliminate Zdr (It sounds like hiding the dust under the carpet).

Reply 3.10. Ho do authors know that non-uniform beam filling is not relevant here ? Actually it is an important source of error that is neglected by “old” models but affect your variance estimates.

Reply 3.12. I do think that presenting performance on unfolding is important. You may say that that 100% of unfording are detected with 0% false alarm.

Reply 3.18. Radome attenuation should not determine underestimation in Kdp, unless SNR drops significantly due to attenuation. I disagree with authors’interpretation

Appendix A: What the goal of this section ? The final formula is already available in literature.

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ED: Reconsider after major revisions (12 Aug 2019) by Gianfranco Vulpiani

AR by Guang Wen on behalf of the Authors (27 Aug 2019) Manuscript

ED: Referee Nomination & Report Request started (27 Aug 2019) by Gianfranco Vulpiani

RR by Anonymous Referee #3 (21 Sep 2019)

ED: Publish subject to technical corrections (21 Sep 2019) by Gianfranco Vulpiani

AR by Guang Wen on behalf of the Authors (23 Sep 2019) Author's response Manuscript

Short summary

In this study, we propose a probabilistic method based on the Gaussian mixture model to estimate the slope of a data profile. The Gaussian mixture method (GMM) not only obtains the expected value of the slope by differentiating the conditional expectation of the data, but also yields the variance of the slope regarding the errors in the calculation of the first derivative.