the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A flexible z-coordinate approach for the accurate representation of free surface flows in a coastal ocean model (SHYFEM v. 7_5_71)
Christian Ferrarin
Marco Bajo
Georg Umgiesser
Abstract. We propose a z-coordinate algorithm for ocean models which, thanks to the insertion and removal of surface layers, can deal with an arbitrarily large tidal oscillation independently of the vertical resolution. The algorithm is based on a classical two steps procedure used in numerical simulations with moving boundaries (grid movement followed by a grid topology change, that is insertion/removal of surface layers) which leads to a stable and accurate numerical discretization. With ad-hoc treatment of advection terms at non-conformal edges that may appear due to insertion/removal operations, mass conservation and tracer constancy are preserved. This algorithm, called z-surface-adaptive, can be reverted, as a particular case when all layers are moving, to other z-surface-following coordinates, such as z-star or quasi-z. With simple analysis and realistic numerical experiments, we compare the surface-adaptive-z coordinate against z-star and we show that it can be used to simulate effectively coastal flows with wetting and drying.
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Luca Arpaia et al.
Status: final response (author comments only)
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RC1: 'Comment on gmd-2023-13', L. Bonaventura, 08 Mar 2023
The preprint presents a potentially interesting contribution to numerical modelling of coastal and oceanic flows. The overview of the literature is broad (even though it could be further improved) and the level of detail in the description of the proposed numerical procedure is appropriate for the scope of GMD. The proposed technique could be very useful for the improvement of the results of coastal and oceanic simulations and deserves to be made available to the community doing research on numerical models for coastal flows, along with a comprehensive assessment of its performance.
However, the detailed description of the numerical method is strongly affected by a number of unclear statements, undefined symbols and imprecise definitions. This makes the paper hard to read in its present form and its real value difficult to assess even for an experienced reader. The authors claim that the method they propose has superior stability properties with respect to those available in the literature, but no stability analysis is provided. The authors' attempt at generality in considering apparently several z-coordinate approaches in the same framework unfortunately ends up making the preprint more obscure, since it is often unclear whether the whole approach has general validity or whether parts of it only apply to some specific z-coordinate formulation. Finally, the truncation error analysis of the vertical discretization appears to be only marginally related to the main topic of the preprint and is affected by several mathematical inconsistencies. The authors may consider removing this part from the revised version of the preprint.
The preprint can be considered for publication after major revisions, that are detailed in the attached file.
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AC1: 'Reply on RC1', Luca Arpaia, 04 Apr 2023
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-13/gmd-2023-13-AC1-supplement.pdf
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RC2: 'Reply on AC1', L. Bonaventura, 06 Apr 2023
I am generally satisfied with the authors' replies and the proposed changes. Concerning point 6 in the replies, the problem is not so much that the ratio A/H is not small enough for linearization (it is small enough). Rather, A=O(1) means that an O(1) mean velocity U must be assumed, while in the preprint the authors linearized around U=0, which I find physically inconsistent with the regime being studied.
Citation: https://doi.org/10.5194/gmd-2023-13-RC2 -
AC2: 'Reply on RC2', Luca Arpaia, 06 Apr 2023
We have finally understood the reason of the inconsistency. Thank you for the explanation and, in general, for the preciseness of the comments.
Citation: https://doi.org/10.5194/gmd-2023-13-AC2
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AC2: 'Reply on RC2', Luca Arpaia, 06 Apr 2023
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RC2: 'Reply on AC1', L. Bonaventura, 06 Apr 2023
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AC1: 'Reply on RC1', Luca Arpaia, 04 Apr 2023
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RC3: 'Comment on gmd-2023-13', Giacomo Capodaglio, 11 May 2023
The authors present a novel alternative to existing z-coordinate type models for the simulation of multi layer shallow water systems. The main novelty is given by the use of a feature that allows the insertion and removal of vertical layers. The paper is interesting and the algorithm well developed. Extra significance is provided by the ability of the proposed method to recover other types of z-coordinate models by appropriately tuning some of the parameters of the novel method.
I recommend the paper be accepted after the authors have properly complied with the following requests (I have attached a PDF with inline comments, this PDF will be referenced next).
Major points:
1. The paper is currently suffering from a lack of mathematical rigor and the presentation is sometimes confused. The notation is often unnecessarily complex and some definitions are missing. Please refer to the comments in the attached PDF document and revise the presentation (especially in Section 2).
2. The authors are doing a good job in the numerical results with showing that the proposed method is well behaved and that it does not perform worse than z-star. Although it is my opinion that additional results are missing to show that the extra hassle of introducing or removing layers is actually beneficial for some application. The authors should include at least one additional test case to show that their method enables simulations that are currently not possible with other existing z-type coordinate models. If this is deemed unfeasible, please show at least that there exists one relevant test case for which your model clearly outperforms existing z-coordinate models.
3. The computational peformance of the method is relegated to the last 4 lines of the numerical results section. Parallel performance is clearly of paramount interest for your readers so a more detailed analysis should be included in the paper. Currently, in the serial runs reported, the overhead of the present method is 8% over z-star. Would that get worse in parallel? If so, what are possible avenues for mitigation?
Minor comments:
Please see the attached PDF. NOTE: I do not expect the authors to supply a point by point response to all the comments in the PDF as that would take too long. As far as I am concerned, it is enough for them to provide a written answer to just the three major points above. However, I expect to see amendments in the revised manuscript addressing all points mentioned in the PDF. In case there is something the authors do not agree with, please include your comment in the written response along with the response to the major points. Thank you.
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AC3: 'Reply on RC3', Luca Arpaia, 19 May 2023
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-13/gmd-2023-13-AC3-supplement.pdf
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AC3: 'Reply on RC3', Luca Arpaia, 19 May 2023
Luca Arpaia et al.
Model code and software
SHYFEM version with z-surface-adaptive coordinates Luca Arpaia https://doi.org/10.5281/zenodo.7528682
Luca Arpaia et al.
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