Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

Ruggiero, G. A.; Ourmières, Y.; Cosme, E.; Blum, J.; Auroux, D.; Verron, J.

doi:https://doi.org/10.5194/npg-22-233-2015

Articles | Volume 22, issue 2

https://doi.org/10.5194/npg-22-233-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/npg-22-233-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 22, issue 2

Research article

|

29 Apr 2015

Research article |

| 29 Apr 2015

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

G. A. Ruggiero, Y. Ourmières, E. Cosme, J. Blum, D. Auroux, and J. Verron

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Final revised paper (published on 29 Apr 2015)
Preprint (discussion started on 16 Jul 2014)

Interactive discussion

Status: closed

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

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- Supplement

RC C373: 'Referee comment', Anonymous Referee #1, 08 Aug 2014
- AC C571: 'comments for the first reviewer', Giovanni Ruggiero, 23 Oct 2014
RC C379: 'Referee Comment', Anonymous Referee #2, 19 Aug 2014
- AC C572: 'comments for the second reviewer', Giovanni Ruggiero, 23 Oct 2014
EC C515: 'Editor's response', Olivier Talagrand, 21 Sep 2014

Peer-review completion

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

AR by Giovanni Ruggiero on behalf of the Authors (23 Oct 2014) Author's response Manuscript

ED: Referee Nomination & Report Request started (27 Oct 2014) by Olivier Talagrand

RR by Anonymous Referee #2 (11 Nov 2014)

Suggestions for revision or reasons for rejection

Dear Editor,

I have read the manuscript Data assimilation Experiments using the
Diffusive Back and Forth Nudging for the NEMO ocean model by Ruggiero
et al.

I think that the authors only partially answered to my questions and
moreover I think the theoretical basis of the manuscript is still
unclear and not sound enough.

Let us start from the main point, namely Eq.(6) and (7). The algebraic
derivation is now clear but the mathematical intepretation is
completely unclear. Let us examine Eq.(7). This Eq. refers to all
variables calculated at the same time t fulfilling 0<t<T, so this is a
standard Poisson equation with a source term depending on the
measurements. This can be solved in a unique way given the boundary
condition on x_{\infty}. This solution DOES not depend on the dynamics
but only on the measurements.

Eq.(6) on the other hand says that x_{\infty} is a trajectory
fulfilling the actual dynamics that does not depend on the
measurements. I find very strange that these two equations may lead to
the same solution so I still find not sound the theoretical basis of
the method and I am not sure that the iterations of the DBFN converges
to a solution satisfying both Eq. 6 and 7.

The other doubt is on the form of K. I asked the authors to explain
the form used in the assimilation experiments. In the present version
of the manuscript there is a sentence:

"In this study the matrix K is composed by the two operations:".

K is a matrix so what the reader needs is an equation stating K=....
Reading Sec. 5.1 I understand that \Theta is probably the diagonal
part of K for measured variables while B^{PLS} seems to refer to
non-measured components. The problem that I face is that Eq.(15)-(16)
etc. look like analysis equations like those of the Kalman filter and
not the Nudging term of Eq. 3. Only in the introduction the authors
write down K = k H^T R^-1, but only in the answer to the referees they
comment this expression.

The choice of the inflation \gamma is quite misterious. Authors state:

"We note that the minimum error for the DBFN is
reached after 9 iterations. This is quite consistent with our choice
gamma = 18, since theoretically it allows the use of the same set of
observations for 18 times."

that is completely unclear to me.

Aside from the details, the main message I found in Sec.5.1 is that
the forecast/background covariance is estimated in a statistical way
and so it does not adapt to the dynamical state of the system.
Consequently I find very surprising that the DBFN should perform
better than 4DVar.

A final remark on the sentence of Sec. 5.4 "Therefore, the problem is
undetermined, since the observations represent only a 4% of the total
state space." For chaotic system like the one under examination the
issue of determinacy is very subtle. One can also measure all
variables but if the time distance between measurements is larger than
the leading Lyapunov time, i.e. the fastest time of error growth, then
the data assimilation algorithm is not able to control the system. On
the contrary if the unstable structure are stronly correlated in the
spatial dimension, then a small number of high frequency measurements
is able to avoid filter divergence. For these reason I think that the
naive interpretation given by the authors, also induced by the comment
of one of the referees, is quite misleading.

As a conclusion I think that the paper is not suitable for
publication. I did not find any theoretical reason to justify why the
DBFN should perform better than or as good as other techniques like
4DVar. The authors present some cases where they find that it is so
but the lack of theoretical justification suggests, in my opinion,
that this is not a general behavior. Morevoer the manuscript is still
unclear and somewhere confusing.

Hide

RR by Anonymous Referee #1 (23 Nov 2014)

ED: Reconsider after major revisions (further review by Editor and Referees) (24 Nov 2014) by Olivier Talagrand

AR by Giovanni Ruggiero on behalf of the Authors (12 Jan 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (04 Feb 2015) by Olivier Talagrand

RR by Anonymous Referee #1 (17 Feb 2015)

ED: Publish subject to minor revisions (further review by Editor) (19 Feb 2015) by Olivier Talagrand

AR by Giovanni Ruggiero on behalf of the Authors (08 Mar 2015) Author's response Manuscript

ED: Publish subject to technical corrections (26 Mar 2015) by Olivier Talagrand

AR by Giovanni Ruggiero on behalf of the Authors (03 Apr 2015) Author's response Manuscript