Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction

An, Zhe; Rey, Daniel; Ye, Jingxin; Abarbanel, Henry D. I.

doi:https://doi.org/10.5194/npg-24-9-2017

Articles | Volume 24, issue 1

https://doi.org/10.5194/npg-24-9-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/npg-24-9-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 24, issue 1

Research article

|

16 Jan 2017

Research article |

| 16 Jan 2017

Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction

Zhe An, Daniel Rey, Jingxin Ye, and Henry D. I. Abarbanel

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Final revised paper (published on 16 Jan 2017)
Preprint (discussion started on 22 Mar 2016)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Reviewer Comments', S.G. Penny, 02 May 2016
- AC1: 'Authors’ Response to Referee, Dr. S.G. Penny', zhe an, 10 May 2016
RC2: 'Revision of manuscript NPGD-2016-22', Anonymous Referee #2, 24 May 2016
- AC2: 'Authors’ Response to Referee', zhe an, 07 Jun 2016

Peer-review completion

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

AR by zhe an on behalf of the Authors (19 Jun 2016) Manuscript

ED: Reconsider after major revisions (further review by Editor and Referees) (30 Jun 2016) by Zoltan Toth

Dear Authors,
Thank you for your original submission and the revised version of your manuscript. We received two very informative reviews. Both reviewers found your work worthy of publication but raised important questions and concerns about your manuscript. Given the substance and extensive nature of these reviews I will ask the two reviewers to look at your manuscript again once the revision is complete.

However, closely inspecting the two reviews and your replies I found that further revisions are necessary before I can request comments from the reviewers again. One concern is the selective and incomplete nature of your response to the reviewers comments. You chose to respond only to a few of the reviewers' comments while leaving most comments unanswered. Furthermore, in the cases where you did give a response in your reply, you did not indicate whether and how you responded to their questions and comments in the manuscript - except in the cases where you stated you chose not to make corresponding changes in the manuscript.

Specific comments related to your reply to Rev. 1's review:
Your item #2 - I agree with Rev. 1 and Rev. 2's related comment #23 and respectfully ask that you put your time-delay extended nudging technique in the context of existing 4-dvar methods. What is functionally common, what is different, how the two approaches differ conceptually and from theoretical considerations. This will enhance your manuscript and make it more accessible to the readers.

Your item #4 - I echo the Rev.'s request for an explicit statement in the manuscript about a limitation of your study, namely that you have not tested the method with more realistic temporally correlated errors.

Your items #6 & #7 - Again, I find Rev. 1's suggestion helpful. A discussion of the relationship of your method and more commonly used approaches in the context of diagonal only vs non-diagonal coupling will be helpful for a proper assessment of the methodology you use.

Your item #8 - The issue of observational errors comes up in several comments from both reviewers. Please carefully respond to each of these points by the Reviewers as this is an important aspect of your experiments.

Other critical items raised by the Revs that you have not addressed in your reply include
1) Requests for a more thorough discussion and interpretation of the results (e.g., Rev 2's comment #17, Rev. 1's comment on Page 9)
2) Portions of the text is unclear and needs significant improvements (e.g., Rev. 2's comments #19, 21
3) The relative (pointed out at several places by both Reviewers) vs absolute nature of information pertaining the percentage of variables that need to be observed (e.g., Rev. comments on p.1, p.2, p.3 l.29, p.7 l.10, p.9 l.20, p14 l.8)

Before I request a second review from the two referees, I respectfully ask that you respond to each and every comment from both reviewers. In your point by point reply, please clearly indicate whether and how you respond to the critical comments and suggestions (i.e., what changes you make in the manuscript). Your replies can be brief but they must clearly indicate your action as to changes you make in the manuscript. If you like, you can copy and paste relevant material from the revised text into your written reply to the Revs' comments.

Once we have your full response to the reviews and my comments, I will ask the reviewers for their evaluation of your revised manuscript.

I am looking forward to receiving your reply and your revised manuscript. Respectfully
Zoltan Toth

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AR by zhe an on behalf of the Authors (10 Jul 2016) Manuscript

ED: Referee Nomination & Report Request started (19 Jul 2016) by Zoltan Toth

RR by Anonymous Referee #2 (22 Jul 2016)

RR by S.G. Penny (08 Aug 2016)

Suggestions for revision or reasons for rejection

The authors have greatly improved the clarity, conciseness, and focus of the manuscript. It reads well and should be considered for publication with minor revisions at detailed below.

As a general technical comment, try to avoid 2-sentence paragraphs.

I think it would be a useful addition to the presentation to have the first figure of the manuscript as an example representation of the model domain, similar to Figure 10, but just showing a snapshot of an example flow and surface height field that is representative of the model’s behavior under the given surface forcing.

p.2, line 3:
I suggest to change the citation format from “ (Abarbanel (2013)).” to “(Abarbanel 2013).” for this and all following similarly-formatted citations for conciseness.

p.2, line 8:
This is a 2-sentence paragraph, the first of which is a run-on sentence. I suggest breaking the first sentence up to be more concise.

p.2, line 10:
Remove “In other words,” since what follows is adding information rather than rephrasing the previous statement.

p.2, line 23:

“These outcomes suggest that time delays may be useful for reducing the number of required observations to meet the practical constraints of operational NWP”

I suppose there is some degree of interpretation here as to what qualifies as a ‘countable’ observation. I would call a single instrument making 10 consecutive measurements at the same point 10 observations. In that sense, the use of time-delay methods could make better use of a fixed number of observations that might currently be ignored.

What needs clarification is whether L refers to the number of distinct observation locations, or the total number of distinct measurements in a time window? Please make sure this is clear.

p. 2, line 27:
Connect line 27 into the paragraph on the next line.

p.3, line 25:
Is capital Phi the state transition matrix in this context? Could you state its role in this case?

p. 4, line 29:
eq 4: Do you intend for tau to be negative so that adding increasing multiples of tau goes backwards in time? It may be more clear to assume tau is positive and subtract multiples of tau to illustrate the delay aspect of the approach. If not, you may want to make it clear immediately that your time ‘delays’ are actually forward in time given your indexing framework.

p.4, eqns 4, 5:
Thanks, this is much clearer than the previous presentation.

p. 5, line 20:
It may be helpful to clarify the definition of ‘delay’ when the delay is first mentioned.

p. 6, line 2:
Change “nudging [using] truncated” to “nudging [uses] truncated”

p.6, line 14:
This isn’t a complete sentence: “Namely, the shallow water equations.”

p.6, line 18:
“data is taken” to “data are taken”

p. 7, line 24:

“by measuring the average growth rate of random perturbations.”

I think a little more detail is needed here. Are you using a ‘bred vector’ type method? If so, the scales captured are determined by the magnitude of the random perturbations, the rescaling interval, and the norm used. These parameters impact the scales of the instabilities that are amplified and identified by the algorithm. Please provide more detail, as it is difficult to interpret this description.

For bred vectors, e.g., see Toth and Kalnay (1997)
http://journals.ametsoc.org/doi/full/10.1175/1520-0493(1997)125%3C3297%3AEFANAT%3E2.0.CO%3B2

p. 8, table 1:
Could you clarify - is the spacing delta X and delta Y consistent across all resolution experiments {16,32,64}, or is the total domain size constant?

p. 8, table 1:
The authors list the Coriolis parameter f0 and the Rossby parameter (meridional derivative). Please also list the corresponding latitude for this f value (e.g. at the center of the model domain).

p.9, lines 18-24:
Please mention that the results with D_M=7 reached high accuracy in some cases, dependent on initial conditions. These ‘boundary’ cases are interesting to identify for future study.

p. 10, line 30:

Change “The same [striking] improvement” to “The same improvement”

The use of extreme adjectives of this type does not enhance the presentation. The results speak for themselves and the readers can determine whether or not they find them ‘striking’.

p. 10, line 25:

I’d like to see one case additional where the noise is large enough to break the synchronization.

p. 11, line 10:

“The dynamics of drifters are described as two-dimensional fluid parcel motion on the surface of the water layer”

Technically, wouldn’t the drifters modeled in these equations be representative of the vertically integrated layer velocity? This may be a better interpretation anyway, since in reality drifters are usually representative of a given depth. For example, the GDP drifters are drogued at 15m. Surface floating drifters may be adversely impacted by winds and thus not accurately represent the near surface currents.

p. 11, line 14:

“Hybrid measurements are incorporated into the time delay nudging method by combining the grid variables and the collective drifter positions”

Is it the drifter position you are appending, or is it really the drifter id and dimension label as a type of coordinate space for the drifter data? The position data should be analogous to the velocity and height measurements, while drifter id’s are analogous to the model grid points.

p. 11, line 16:
As a warning, the boldface capital R is typically used in DA to represent the observation error covariance matrix, and so the choice to use it in this context may cause unnecessary confusion.

p. 12, line 4-9:
I’d like to see one more case where the approach to forming the initial conditions matching the previous cases is used, and sufficient drifters are added to achieve synchronization. This would make it easier to compare the findings in this section with results from earlier sections.

Page 12, line 21:

Please change:
“when the model is [wrong]” to “when the model is [imperfect]”

If the model is ‘wrong’ in practice then it cannot not be used for forecasting or data assimilation. It must be reasonably accurate to produce any reliable forecast skill.

page 12, line 22:

“this methodology provides some idea as to whether the model is at fault, or whether more observations are needed.”

I suppose I need more explanation for how the methodology provides this information. I understand that it indicates for a given model you can identify how many observations should be sufficient for synchronization. So are the authors extrapolating that then if the model does not synchronize when using real data then the model is to blame? There are subtleties in this process that make this statement seem like an oversimplification, particularly regarding the assimilation of satellite data.

Figures 4,5,6:
It may just be my pdf rendering, but I see two plots on the top row but only one plot in the center of the bottom row. It appears that one is missing. Please double check to make sure there are reproduced as intended.

Figure 10:

It appears your domain is very close to the equator since there is no geostrophic-type flow due to the inclusion of the Coriolis term. Instead it appears you have a down-gradient flow, without the effects of rotation. In the future, I’d suggest focusing on a domain that is shifted more from the equator so there are significant contributions from both the geostrophic and ageostrophic components in your flow field.

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ED: Publish subject to minor revisions (further review by Editor) (22 Aug 2016) by Zoltan Toth

AR by zhe an on behalf of the Authors (01 Sep 2016) Manuscript

ED: Publish subject to technical corrections (23 Sep 2016) by Zoltan Toth

AR by zhe an on behalf of the Authors (28 Sep 2016) Manuscript