Physically constrained covariance inflation from location uncertainty

Zhen, Yicun; Resseguier, Valentin; Chapron, Bertrand

doi:https://doi.org/10.5194/npg-30-237-2023

Articles | Volume 30, issue 2

https://doi.org/10.5194/npg-30-237-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-30-237-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 30, issue 2

Research article

|

29 Jun 2023

Research article |

| 29 Jun 2023

Physically constrained covariance inflation from location uncertainty

Yicun Zhen, Valentin Resseguier, and Bertrand Chapron

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Final revised paper (published on 29 Jun 2023)
Preprint (discussion started on 09 Mar 2023)

Interactive discussion

Status: closed

RC1: 'Comment on egusphere-2023-416', Daniel Goodair, 09 Apr 2023

My comments are attached, though I should note a further reccommendation that an expert in the field of modelling validates the mathematical analysis prior to publication.

Citation: https://doi.org/10.5194/egusphere-2023-416-RC1
RC2: 'Comment on egusphere-2023-416', Baylor Fox-Kemper, 21 Apr 2023

This paper improves on previous methods for "covariance inflation" to arrive at perturbations of abstract tensor quantities rather than positive definite scalar quantities. This requires the application of optimal transport theory and Brenier's answer to it. This represents an important incremental step in aligning and rectifying the different approaches to including Location Uncertainty (e.g., LU and SALT approaches nicely reviewed in the introduction). I have only minor technical suggestions.

Some of the math developments go by a bit quickly without reference to the underlying concepts. It would strengthen the manuscript to include them, e.g.,
Section 3.1--it would be nice to name the different forms in (13)-(16) for later reference or just to ground the notation.
Section 3.2--Just after (3.2) it would be nice to link to a reference on CFL conditions there.
Just after (75), please state in words what those equations (29, 75) do so the reader doesn't have to scan backwards.
Typo: just before (65) a reference requires parentheses. Same issue on Line 520.

Citation: https://doi.org/10.5194/egusphere-2023-416-RC2
AC1: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023

Dear reviewers,
The first attachement is our point-by-point response to your comments. The second attachment marks the modification of the draft in blue. We greatly appreciate your time and effort.
Best wishes,
Yicun Zhen

Citation: https://doi.org/10.5194/egusphere-2023-416-AC1
AC2: 'Comment on egusphere-2023-416', Yicun Zhen, 13 May 2023

Here is our point-by-point response.

Citation: https://doi.org/10.5194/egusphere-2023-416-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Yicun Zhen on behalf of the Authors (13 May 2023) Author's response Author's tracked changes Manuscript

ED: Publish as is (23 May 2023) by Jinqiao Duan

AR by Yicun Zhen on behalf of the Authors (25 May 2023)

Short summary

This paper provides perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated with the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application of this perspective is the physically constrained covariance inflation scheme proposed in this paper.