Behavior of the iterative ensemble-based variational method in nonlinear problems

Nakano, Shin'ya

doi:https://doi.org/10.5194/npg-28-93-2021

Articles | Volume 28, issue 1

https://doi.org/10.5194/npg-28-93-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-28-93-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 28, issue 1

Research article

|

08 Feb 2021

Research article |

| 08 Feb 2021

Behavior of the iterative ensemble-based variational method in nonlinear problems

Shin'ya Nakano

Download

Final revised paper (published on 08 Feb 2021)
Preprint (discussion started on 17 Apr 2020)

Interactive discussion

Status: closed

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

- Printer-friendly version

- Supplement

RC1: 'Review comments', Anonymous Referee #1, 18 May 2020
- AC1: 'Reply to the comments by Referee 1', Shinya Nakano, 03 Aug 2020
RC2: 'Review comments', Anonymous Referee #2, 16 Jun 2020
- AC2: 'Reply to the comments by Referee 2', Shinya Nakano, 03 Aug 2020

Peer-review completion

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

AR by Shinya Nakano on behalf of the Authors (31 Aug 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (19 Oct 2020) by Amit Apte

RR by Anonymous Referee #3 (20 Oct 2020)

Suggestions for revision or reasons for rejection

The paper adequately documents the 4DEnVar method, which essentially uses an ensemble of runs to approximate the model Jacobians required in typical 4DVar implementations. The allure of such an approach is clear, as it means that one does not need to modify an existing code in order to calculate said Jacobians. They have demonstrated the approach functions, and the sensitivity of convergence to certain parameters, with application to the toy Lorenz 96 (L96) problem with the largest tested state vector being 400 elements long. The presentation of the results, however, in section 7 is somewhat lacking. I would suggest they give the reader more of an impression of what the algorithm is attempting to do by presenting for a specific state times series of the truth, overlaid by the observed and estimated values. They may also wish to present a time series of the error between the true and estimated states. At present the convergence of the objective function J with iteration is somewhat too abstract.

Additionally, I don’t think the author can state that they have shown that the approach is applicable to high dimensional geophysical systems. It may well be, but one cannot say as such given the suit of presented experiments. Whilst L96 has been applied many times in the literature for such problems it does not have many of the properties that are intrinsic and essential to high dimensional geophysical systems. Specifically: there is no notion of physical space and hence no spatial error correlation; it does not have long lived serial temporal error correlations; and perhaps most importantly it is not multi-scale. The author either needs to convince me that this 4DEnVar method will also perform well in multi-scale systems, or significantly tone down their claims. Note, I would not class the two level subgrid version of L96 mutli-scale either, it is dual scale.

Hide

RR by Anonymous Referee #2 (13 Nov 2020)

ED: Publish subject to minor revisions (review by editor) (21 Dec 2020) by Amit Apte

AR by Shinya Nakano on behalf of the Authors (29 Dec 2020) Author's response Manuscript

ED: Publish as is (05 Jan 2021) by Amit Apte

AR by Shinya Nakano on behalf of the Authors (06 Jan 2021) Manuscript

Short summary

The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.