the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Jan 2024
Development of a total variation diminishing (TVD) Sea ice transport scheme and its application in an ocean (SCHISM v5.11) and sea ice (Icepack v1.3.4) coupled model on unstructured grids
Abstract. As the demand for increased resolution and complexity in unstructured sea ice models is growing, a more advanced sea ice transport scheme is needed. In this study, we couple the Semi-implicit Cross-scale Hydro-science Integrated System Model (SCHISM) with Icepack, the column physics package of the sea ice model CICE; a key step is to implement a total variation diminishing (TVD) transport scheme for the multi-class sea ice module in the coupled model. Compared with the upwind scheme and a central difference scheme, the TVD transport scheme is found to have better performance for both idealized and realistic cases, and meets the requirements for conservation, accuracy, efficiency (even with very high resolution), and strict monotonicity. The coupled model for the Arctic Ocean successfully reproduces the long-term changes in the sea ice extent, the sea ice boundary and concentration observation from the satellite.
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RC1: 'Comment on gmd-2023-236', Anonymous Referee #1, 24 Jan 2024
The manuscript presents some interesting developments for SCHISM and may be of interest for the respective community, and possibly beyond. I recommend a revision along the following lines. Â
I do not see that the introductory part gives a relevant story, which is: There is a certain model (SCISM) that already has a sea-ice module. This module is further improved by adding the ICEPACK and by adopting the advection scheme proposed in the manuscript. While the need to include ICEPACK does not require much motivation, the need to develop a new advection scheme is not properly explained. In addition to the advection schemes used by the available UG sea-ice models, numerous other advection schemes (including the TVD schemes) have been proposed in the literature for unstructured meshes. In the manuscript, only one is mentioned outside the models, and only at the end (by Casulli). An analysis of the existing approaches is needed, explaining what was missing and why the authors choose to develop the new approach.Â
Secondly, given that the other focus of the manuscript is on the implementation of ICEPACK, I expected to see a demonstration of the changes brought about by ICEPACK, compared to the previous version of the sea ice model. I do not find such a discussion in the manuscript. I also miss the discussion of the computational aspect of the ICEPACK implementation, as well as on the computational aspect of running SCHISM in the Arctic Ocean, which is a remarkable undertaking in itself.Â
Thirdly, much of the material in the discussion of the performance of the new advection scheme is on an almost trivial level: the issues accompanying the first-order upwind or central schemes are well known. There is no point in section 3.1.2, since the finite volume methods are by definition conservative, and the authors have already mentioned this in the manuscript. The 'non-conservation' discussed here is due to clipping for the central differences. No one will use central differences when positivity is required. This section needs to be removed. Compare the new scheme with those used by other models or known from the literature and discuss its advantages. This will give a useful message to a wider community of modellers. Otherwise --- almost any sophisticated scheme will outperform the two used here for the comparison. Therefore, the analysis in 3.1 lacks substance. Â Â
There are many specific points, some minor, but some requiring more attention. These are listed below.
Line 40 and in other places: Gurvan is the name, not the family name. The list of references contains errors, please check and correct (line 485 - non-standard, 527 the list of authors is non-standard and contains a lot of garbage, 544 non-standard).Âline 45 You are talking about implementation of ICEPACK, so the reference should be on the implementation.
line 67 'but is inefficent ...' ??? How do you know? Please provide a reference; line 67 is pure fantasy -- fine meshes can also be used in this case. I do not see that the authors fully know what they are writing about.
71 Again 'Gurvan'
72 'The efficiency ...' These are regular mesh model. Their efficiency has been tested in numerous applications. Nobody is going to apply these models at resolutions going to 10 m. Better remove altogether.
80 Â 'but it cost is linearly increasing' -- but this is the case with all the schemes mentioned above except for incremental remapping, but even in this case there is a significant increase. Â
81 'strict monotonicity comes with a high cost' -- what is meant? FCT is not cheap, but the first order upwind mentioned further is much less accurate. Â Â92 'a new model?' Â I would call it an update of the SCISM for ICEPACK and new advection scheme for the sea ice.
93 Strict monotonicity is not very welcome because the sea-ice velocities have non-zero divergence. Tests carried out in the manuscript do not explore the order.
132 and many cases below: change 'Where' to 'where'Â
140-142 One needs a positive scheme. The enforcement of monotonicity is an error in the context of sea-ice modeling. The statement made by the authors is strange and throws doubts   on the entire paper. Please explain in detail how a monotone scheme can be made appropriate in a converging or diverging velocity field. Note that the first order upwind scheme will is only positive in divergent flows provided time step limitations.
151 approximate
Eq. (10) Is similar limiting applied to thicknesses and enthalpies? Please carefully explain.
195 The discussion is inconsistent: first strict monotonicity is mentioned, second (200) new extrema are mentioned.Â
197 The limiter was already mentioned. It is van Leer (not Van-leer)
199 Is this reference related to the situation on unstructured grids? There are many flux contributions, and the velocity field is divergent.
200-202: Please demonstrate this, the non-negativeness is not obvious from what has been written in the manuscript, and I do not necessarily see how this statement will hold for a divergent flow.Â
203 Â Results
220 outline? Â shape or form
230 'minor' -- they are rather large and quite noticeable.
237 The discussion here is too trivial to be included in the manuscript
 Figure 4. I was not able to guess what is shown in this figure. I am also unable to understand what is the intension of this section. Monotonicity for the first order upwind is well known, as well as non-monotonicity for the central differences.
286-287 Was there any doubt? Better remove this sentence.
299 Why is this related to the increase of cost?
308-309 from the upwind -- in the upwind
than from the TVD -- than in the TVD.311. You demonstrate that model works in realistic application, there was no doubt on cross-scale, for Zhang et al. 2023 already showed this.
318 The time step is too small for the resolution mentioned.
328 hydro-model  -- sounds strange in this case -- it is ocean model
398-339 The CD representation is much more resolving even on coarse meshes (according to the cited paper).
400 Which oscillations are meant?
404 How can the central scheme to be similar? It is not clear what the authors are willing to say here, and furthermore, they are even not certain what the advection scheme in Gao et al. 2013 does precisely. Either remove or explain properly with accurate statements.
410 Casulli's scheme appears all of a suddenÂ
Citation: https://doi.org/10.5194/gmd-2023-236-RC1 - AC1: 'Reply on RC1', Qian Wang, 11 Apr 2024
-
RC2: 'Comment on gmd-2023-236', Anonymous Referee #2, 10 Feb 2024
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-236/gmd-2023-236-RC2-supplement.pdf
- AC2: 'Reply on RC2', Qian Wang, 11 Apr 2024
Status: closed
-
RC1: 'Comment on gmd-2023-236', Anonymous Referee #1, 24 Jan 2024
The manuscript presents some interesting developments for SCHISM and may be of interest for the respective community, and possibly beyond. I recommend a revision along the following lines. Â
I do not see that the introductory part gives a relevant story, which is: There is a certain model (SCISM) that already has a sea-ice module. This module is further improved by adding the ICEPACK and by adopting the advection scheme proposed in the manuscript. While the need to include ICEPACK does not require much motivation, the need to develop a new advection scheme is not properly explained. In addition to the advection schemes used by the available UG sea-ice models, numerous other advection schemes (including the TVD schemes) have been proposed in the literature for unstructured meshes. In the manuscript, only one is mentioned outside the models, and only at the end (by Casulli). An analysis of the existing approaches is needed, explaining what was missing and why the authors choose to develop the new approach.Â
Secondly, given that the other focus of the manuscript is on the implementation of ICEPACK, I expected to see a demonstration of the changes brought about by ICEPACK, compared to the previous version of the sea ice model. I do not find such a discussion in the manuscript. I also miss the discussion of the computational aspect of the ICEPACK implementation, as well as on the computational aspect of running SCHISM in the Arctic Ocean, which is a remarkable undertaking in itself.Â
Thirdly, much of the material in the discussion of the performance of the new advection scheme is on an almost trivial level: the issues accompanying the first-order upwind or central schemes are well known. There is no point in section 3.1.2, since the finite volume methods are by definition conservative, and the authors have already mentioned this in the manuscript. The 'non-conservation' discussed here is due to clipping for the central differences. No one will use central differences when positivity is required. This section needs to be removed. Compare the new scheme with those used by other models or known from the literature and discuss its advantages. This will give a useful message to a wider community of modellers. Otherwise --- almost any sophisticated scheme will outperform the two used here for the comparison. Therefore, the analysis in 3.1 lacks substance. Â Â
There are many specific points, some minor, but some requiring more attention. These are listed below.
Line 40 and in other places: Gurvan is the name, not the family name. The list of references contains errors, please check and correct (line 485 - non-standard, 527 the list of authors is non-standard and contains a lot of garbage, 544 non-standard).Âline 45 You are talking about implementation of ICEPACK, so the reference should be on the implementation.
line 67 'but is inefficent ...' ??? How do you know? Please provide a reference; line 67 is pure fantasy -- fine meshes can also be used in this case. I do not see that the authors fully know what they are writing about.
71 Again 'Gurvan'
72 'The efficiency ...' These are regular mesh model. Their efficiency has been tested in numerous applications. Nobody is going to apply these models at resolutions going to 10 m. Better remove altogether.
80 Â 'but it cost is linearly increasing' -- but this is the case with all the schemes mentioned above except for incremental remapping, but even in this case there is a significant increase. Â
81 'strict monotonicity comes with a high cost' -- what is meant? FCT is not cheap, but the first order upwind mentioned further is much less accurate. Â Â92 'a new model?' Â I would call it an update of the SCISM for ICEPACK and new advection scheme for the sea ice.
93 Strict monotonicity is not very welcome because the sea-ice velocities have non-zero divergence. Tests carried out in the manuscript do not explore the order.
132 and many cases below: change 'Where' to 'where'Â
140-142 One needs a positive scheme. The enforcement of monotonicity is an error in the context of sea-ice modeling. The statement made by the authors is strange and throws doubts   on the entire paper. Please explain in detail how a monotone scheme can be made appropriate in a converging or diverging velocity field. Note that the first order upwind scheme will is only positive in divergent flows provided time step limitations.
151 approximate
Eq. (10) Is similar limiting applied to thicknesses and enthalpies? Please carefully explain.
195 The discussion is inconsistent: first strict monotonicity is mentioned, second (200) new extrema are mentioned.Â
197 The limiter was already mentioned. It is van Leer (not Van-leer)
199 Is this reference related to the situation on unstructured grids? There are many flux contributions, and the velocity field is divergent.
200-202: Please demonstrate this, the non-negativeness is not obvious from what has been written in the manuscript, and I do not necessarily see how this statement will hold for a divergent flow.Â
203 Â Results
220 outline? Â shape or form
230 'minor' -- they are rather large and quite noticeable.
237 The discussion here is too trivial to be included in the manuscript
 Figure 4. I was not able to guess what is shown in this figure. I am also unable to understand what is the intension of this section. Monotonicity for the first order upwind is well known, as well as non-monotonicity for the central differences.
286-287 Was there any doubt? Better remove this sentence.
299 Why is this related to the increase of cost?
308-309 from the upwind -- in the upwind
than from the TVD -- than in the TVD.311. You demonstrate that model works in realistic application, there was no doubt on cross-scale, for Zhang et al. 2023 already showed this.
318 The time step is too small for the resolution mentioned.
328 hydro-model  -- sounds strange in this case -- it is ocean model
398-339 The CD representation is much more resolving even on coarse meshes (according to the cited paper).
400 Which oscillations are meant?
404 How can the central scheme to be similar? It is not clear what the authors are willing to say here, and furthermore, they are even not certain what the advection scheme in Gao et al. 2013 does precisely. Either remove or explain properly with accurate statements.
410 Casulli's scheme appears all of a suddenÂ
Citation: https://doi.org/10.5194/gmd-2023-236-RC1 - AC1: 'Reply on RC1', Qian Wang, 11 Apr 2024
-
RC2: 'Comment on gmd-2023-236', Anonymous Referee #2, 10 Feb 2024
The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2023-236/gmd-2023-236-RC2-supplement.pdf
- AC2: 'Reply on RC2', Qian Wang, 11 Apr 2024
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