Numerical models for simulating ocean physics

Bell, Michael J.; Schiller, Andreas; Ciliberti, Stefania

doi:https://doi.org/10.5194/sp-5-opsr-10-2025

Articles | Volume 5-opsr

https://doi.org/10.5194/sp-5-opsr-10-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

Report:

Ocean prediction: present status and state of the art (OPSR)

https://doi.org/10.5194/sp-5-opsr-10-2025

© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 5-opsr

02 Jun 2025

| OPSR | Chapter 5.1

| 02 Jun 2025 | OPSR | Chapter 5.1

Numerical models for simulating ocean physics

Michael J. Bell, Andreas Schiller, and Stefania Ciliberti

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Final revised paper (published on 02 Jun 2025)
Preprint (discussion started on 07 Oct 2024)

Interactive discussion

Status: closed

RC1:
'Comment on sp-2024-41', Anonymous Referee #1, 11 Oct 2024

It is a daunting task to summarize ocean numerical model physics in a few pages. My comments are as follows:
1. Contrast between Sections 2 and 3: Section 2 is written at an elementary level with no references while Section 3 is technical with many references. While this is announced in the abstract, the transition is too abrupt. It is almost as if it was written by two different contributors. I suggest that the authors slightly rewrite both sections for a better flow/continuity.
2. The paper is lacking a summary section. I suggest discussing the current state of the art and where numerical models might be 20 years from now. An example can be found in the introductory encyclopedia paper of Chassignet et al. (2019) (https://www.coaps.fsu.edu/pub/eric/papers_html/Chassignet_et_al_19.pdf) which also aims at reaching a broad audience.
3. As in Chassignet et al. (2019), I suggest adding a "Further Reading" section for the readers that interested in more details.
4. Minor comment: In the Introduction, on line 20, you introduce Section 4 of Wan et al. It is a bit awkward as it follows the description of Section 3 of your paper and you do not have a Section 4. I assume Wan et al. is part of the same issue - I suggest rephrasing the sentence to make it clear that it is complementary to this paper.

Citation: https://doi.org/10.5194/sp-2024-41-RC1
- AC1: 'Reply on RC1', Mike Bell, 12 Nov 2024
  
  Please see attached file
  
  Citation: https://doi.org/10.5194/sp-2024-41-AC1
RC2:
'Comment on sp-2024-41', Anonymous Referee #2, 01 Nov 2024

This is a very short, elementary overview of ocean modeling, targeting mainly "large-scale" simulations of the ocean circulation. Given the limited space, the manuscript is necessarily subjective, especially in the choice of references, which is fine. Several in-depth review papers (and reference texts) are cited, which is good. I think the manuscript is a useful short introduction. I do have a few comments which should be addressed prior to publication.

Around line 45:
In addition to the 7 equations, it might be useful to also mentioning the surface, bottom, and lateral boundary conditions (the surface being the most relevant one)

line 45-51:
A distinction between "resolution" and "grid" spacing might be appropriate. The two aren't the same but are treated as such. It takes multiple (at least 4) grid spacings to "resolve" a process, such that for a given grid spacing dx, we may begin to resolve a processes of size 4*dx.

line 50:
You mention that parameterizations are inevitably limited. Please spend one sentence as to why? (Structural and parametric uncertainty, lack of calibration, discretization errors).

line 60 on MOC:
It is not only convective mixing in high lats, it is also boundary mixing, as revealed in the OSNAP East measurements.
Furthermore, closure of the global MOC is also through a range of mixing processes.

line 62 on boundary currents:
Those have nothing to do with the MOC, i.e., they exist regardless of the MOC. Please remove "MOC" mention here (westward intensification goes back to the models by Stommel (1948) and Munk (1950)).

line 70:
I think you mean "mass balance", not "heat balance".

line 75-78:
You could reference papers here on data assimilation and sea ice modeling that will appear in the same issue as part of OceanPrediction.

line 90:
"...the elliptical geoid of the Earth’s bulge follows a spherical surface"
This is a bit obscure. The geoid proper deviates from the reference ellipsoid (by about +-80 metres).
I think what you mean is that the centrifugal term is absorbed in the gravitational term by means of a geopotential).
It would be good to clarify your sentence.

Citation: https://doi.org/10.5194/sp-2024-41-RC2
- AC2: 'Reply on RC2', Mike Bell, 12 Nov 2024
  
  please see attached file
  
  Citation: https://doi.org/10.5194/sp-2024-41-AC2

Peer review completion

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

ED: Publish subject to minor revisions (review by editor) (12 Dec 2024) by Enrique Álvarez Fanjul

AR by Mike Bell on behalf of the Authors (13 Dec 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (13 Dec 2024) by Enrique Álvarez Fanjul

AR by Mike Bell on behalf of the Authors (24 Dec 2024) Author's response Manuscript

Short summary

We provide an introduction to physical ocean models, at elementary and intermediate levels, describing the properties they represent, the principles and equations they use to evolve these properties, the physical phenomena they simulate, and the wider context and prospects for their further development. We also outline, at a more technical level, the methods and approximations that they use and the difficulties that limit their accuracy or reliability.