A variational regularization of Abel transform for GPS radio occultation

Wee, Tae-Kwon

doi:https://doi.org/10.5194/amt-11-1947-2018

Articles | Volume 11, issue 4

https://doi.org/10.5194/amt-11-1947-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Special issue:

Observing Atmosphere and Climate with Occultation Techniques...

https://doi.org/10.5194/amt-11-1947-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 11, issue 4

Research article

|

06 Apr 2018

Research article |

| 06 Apr 2018

A variational regularization of Abel transform for GPS radio occultation

Tae-Kwon Wee

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Final revised paper (published on 06 Apr 2018)
Preprint (discussion started on 26 Jul 2017)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'review of amt-2017-228: VR of Abel transform for GPS-RO', Anonymous Referee #1, 24 Sep 2017
- AC1: 'Response to Reviewer #1', Tae-Kwon Wee, 01 Jan 2018
RC2: 'Referee Report', Anonymous Referee #2, 05 Oct 2017
- AC2: 'Response to Reviewer #2', Tae-Kwon Wee, 01 Jan 2018

Peer-review completion

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

AR by Tae-Kwon Wee on behalf of the Authors (01 Jan 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (19 Jan 2018) by Sean Healy

RR by Anonymous Referee #2 (05 Feb 2018)

RR by Anonymous Referee #1 (06 Feb 2018)

Suggestions for revision or reasons for rejection

The manuscript overall presents a case which is the current Abel inversion applied when processing a GPS-RO occultation could be improved by doing a variational regularization, or a 1D-Var in the GPS-RO observation space, to re-retrieve the bending angle and refractivity with both using the refractional radius as the vertical coordinate. A final posterior height determination can then provide both refractivities or bending angles and an associated impact parameter. It is stated that this regularization is now included in a publically available 1D-Var package, and that a stand-alone regularization which shares the background with the data assimilation system may be beneficial. Even though incorporation of these regularized bending angle or refractivity profiles would still suffer from an error-in-variable due to the relatively coarse vertical resolution of the model. Further, the operational weather centers typically do not begin with the full vertical resolution of the GPS-RO sounding. So there are still questions as to how one would apply this work to a typical assimilation procedure with typical input data streams. Ideally, the COSMIC 1D-Var package could take a full vertical resolution occultation and provide regularized bending angles or refractivity at a user specified set of levels for ingestion by the subsequent DA. In summary, I find the manuscript acceptable for publication in its current form after some minor grammatical and typographical corrections.

For this work to make full impact, a path forward can continue to be laid out. Would there be a potential to have this adopted as a procedure to provide GPS-RO occultation processing. Again the typical GPS-RO feed to operational centers is not full vertical resolution, but only at 250-300 impact heights. It is suggested that if that is the starting point, there is little hope to avoid an EIV in any subsequent DA. In the final paragraph of the summary and conclusions, it was eluded that a VR, or 1D-Var retrieving refractivity and using RR as vertical coordinate, could be used. Then followed by potentially another 1D-Var now in the model vertical coordinate, and then the final solve 3D, 4D or ensemble based. But again the practical consideration of what data is typically provided in near real time would need to be revisited? The sooner all of this is brought out in the open, the sooner the community can react. Everyone is interested in getting the best use of this data, and particularly in the lower troposphere.

Please consider these grammatical and typographic corrections:
Page 2, lines 13-15: personally I don’t think the parenthesis are required here.
Page 2, lines 20: … can be as large as …
Page 3, line 8: Readers are referred to (or “The reader is …”)
Page 6, line 12: … RR represents the one for the … ( or the RR is representative at the ray’s … )
Page 9, line 23: .. the tangent point is equal to the …
Page 10, line 1: Due to the imperfect model refractivity, x is not a definite measure of the position, and contains some error. Subsequently, most data assimilation systems consider the RR to be free from error.
Page 10, line 16: In that respect, a short-term forecast from a NWP model is …
Page 10, line 32: … RO observations for a particular impact height …
Page 16, line 28: Namely, a perfect bending angle in IP space is the condition for a perfect …
Page 17, line 18: IMHO, think you can remove the word “suggests” from the first sentence.

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ED: Publish subject to technical corrections (01 Mar 2018) by Sean Healy

Short summary

The refractivity in the radio occultation (RO) is generally obtained from the inverse Abel transform (AI) of measured bending angle. While concise and mathematically exact, AI is susceptible to the error present in the measurement. Aiming to reduce the adverse effects of the measurement error, this study proposes a new method for determining the refractivity through a variational regularization (VR). Verification shows that VR offers a definite advantage over AI in the quality of refractivity.