On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models

Xu, S.; Wang, B.; Liu, J.

doi:https://doi.org/10.5194/gmd-8-3471-2015

Articles | Volume 8, issue 10

https://doi.org/10.5194/gmd-8-3471-2015

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

https://doi.org/10.5194/gmd-8-3471-2015

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

Articles | Volume 8, issue 10

Development and technical paper

|

29 Oct 2015

Development and technical paper |

| 29 Oct 2015

On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models

S. Xu, B. Wang, and J. Liu

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Final revised paper (published on 29 Oct 2015)
Supplement to the final revised paper
Preprint (discussion started on 13 Feb 2015)

Interactive discussion

Status: closed

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

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- Supplement

RC C354: 'Review comments for gmd-2014-242', Anonymous Referee #1, 03 Apr 2015
- AC C600: 'Reply to RC C354: 'Review comments for gmd-2014-242' by Anonymous Referee #1', Shiming Xu, 03 May 2015
RC C869: 'Comment on “On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models”, by S. Xu, B. Wang, and J. Liu', Anonymous Referee #2, 25 May 2015
- AC C1432: 'Reply to RC C869 by referee #2', Shiming Xu, 21 Jul 2015

Peer-review completion

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

AR by Shiming Xu on behalf of the Authors (31 Jul 2015)

ED: Referee Nomination & Report Request started (10 Aug 2015) by David Ham

RR by Anonymous Referee #2 (30 Sep 2015)

Suggestions for revision or reasons for rejection

This revised manuscript demonstrates the application of conformal mapping techniques to generate orthogonal grids for global ocean models. Many commonly used large-scale ocean models assume the use of an orthogonal coordinate system (specifically, these models use discretizations that do not differentiate between co-variant and contravariant derivatives), so techniques such as that described here could have great value in expanding these models’ versatility. The description of the techniques is now easier to follow, although the poor English grammar and word choice are still significant obstacles that the reader must work hard to overcome. This is moving toward an acceptable form, but there are still several issues that I think need to be addressed before this manuscript should be published in Geoscientific Model Development.

Major comments:

1. The English in this manuscript is very difficult to read, with incorrect words in almost every paragraph. I would strongly urge the authors to find a native (or at least fluent) English speaker and have them go through this document thoroughly and correct this problem. The value of this paper is greatly diminished by this problem.

2. The metric for the limit on the timesteps is not based on the minimum grid spacing, but rather it is the highest resolved wavenumber, which is diagonal to the grid and is a 2 grid-point wave in each of the two grid directions. That is, whereas min(\Delta x, \Delta y) is used on p. 13, p. 15 and the time-step count panels of figures 10 and 14, it needs to be replaced by sqrt(1 / (1 / \Delta x^2 + 1 / \Delta y^2)) or equivalently sqrt (\Delta x^2 \Delta y^2 / (\Delta x^2 + \Delta y^2)). This result comes from the basic stability analysis of gravity waves, the discrete form of the gravity wave dispersion relation \omega^2 = g H (k^2 + l^2), where \omega is the wave frequency, and k and l are the wavenumbers in the x and y directions. This is basic numerical analysis, and must be corrected in this paper.

3. My first reaction to the thumbnail depictions of the ocean simulation (Figures 10 and 14) is that there must be something seriously wrong with these simulations, since they appear to have no Antarctic Circumpolar current or ocean gyres, but this is most Iikely the consequence of showing the surface speed (a scalar – velocities are vectors) and a heavily damped sea surface temperature. If the authors were to choose just a single picture to illustrate an ocean-like simulation, the sea surface height (or dynamic surface pressure in a rigid-lid model) would be vastly easier for an oceanographically oriented reader to meaningfully interpret.

4. The case for aligning the grid with the large-scale coastlines is still grossly overstated in this manuscript. The authors did thoughtfully respond to this concern in their reply to my previous comment, but they did not actually modify the manuscript itself accordingly.

Specific comments:

There were scores of places where I replaced incorrect words in my copy of the manuscript, but such detailed editing goes well beyond my responsibility as a reviewer. The specific comments below cite places where I thought the substance of the paper (as I could understand it) needs correction.

1. On p. 4, lines 12-13, it is stated that “a majority of OGCMs utilize finite difference[s] in [the] spatial and temporal domain[s], …”. This is not true. Most modern OGCMs use finite volume methods for many of their discrete expressions. It would be true to say that “many OGCMs use a mixture of finite difference and finite volume spatial and temporal discretizations, …”. The comment about the assumption of grid orthogonality is correct.

2. On p. 5, point 4: Ease of analysis is _not_ the same as using a latitude-longitude grid. Arctic ocean simulations routinely use a polar stereographic projection to facilitate analysis and avoid the polar singularity with a latitude-longitude grid, and a tripolar cap is actually very convenient for the analysis of the Arctic Ocean because it looks very much like a local Cartesian grid.

3. P. 13, line 16: It is true that “the control of anisotropy indtroduces more meridional steps, but has no effect on the zonal edge size.” is true. However then next sentence, “Therefore it does not further decrease the maximum time step size that is allows for the simulation” is simply wrong. (Please see major point #2 above for the right metric to use in evaluating this statement and therefore an explanation for why this statement is incorrect.)

4. Pp 18-19, lines 28-29: The phrase “close to or over 60%” is unnecessarily vague. Which is it? Is it close to 60% or is it over 60%?

5. P. 23, line 21: The statement that the 93.8% covered by a regular latitude-longitude grid “is higher than conventional … tripolar grids” is inconsistent with the earlier statement on p. 14 that 96% of the area with a tripolar grid is covered with a latitude-longitude grid when the transition occurs at 66 N, as is common in such CMIP5 models as those from NOAA/GFDL or the Australian ACCESS models. A more accurate phrase would be “… is higher than for conventional dipolar grids and comparable to commonly used tripolar grids.”

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ED: Publish subject to minor revisions (Editor review) (06 Oct 2015) by David Ham

AR by Shiming Xu on behalf of the Authors (16 Oct 2015) Author's response Manuscript

ED: Publish as is (20 Oct 2015) by David Ham

AR by Shiming Xu on behalf of the Authors (21 Oct 2015) Manuscript

Short summary

This article applies Schwarz-Christoffel (SC) conformal mappings for single-connected and multiple-connected regions to the generation of general orthogonal grids for OGCMs, to achieve 1) the enlarged lat-lon proportion, 2) the removal of landmass and easier load balancing, 3) better spatial resolution on continental boundaries, and 4) alignment of grid lines to large-scale coastlines. The generated grids could be readily utilized by the majority of OGCMs that support general orthogonal grids.