the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Jan 2022
Rigid Sets and Coherent Sets in Realistic Ocean Flows
Abstract. This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new “diffeomorphism-based” criterion to extract “rigid sets”, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.
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Interactive discussion
Status: closed
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RC1: 'Comment on npg-2022-1', Anonymous Referee #1, 01 Feb 2022
This paper studies how to extract Lagrangian Coherent sets from velocity fields. Another one. The paper has two parts: the first is devoted to extract rigid sets based on a diffeomorphism criterion, and the second is oriented to compute coherent sets with operator methods. The authors insist in the novelty of both methologies, but this is not clear all along the paper. There are already so many new methods to study LCS/rigid sets that the focus should be in the applications (even more if NPG is for applications in Geophysics): discuss the advantages of the new method in a particular oceanic example, focus on the physical processes it can describe better than previous methodologies, and stress the computational beneficts of using this particular method. What scientists working in ocean dynamics can learn using this "new" methodology?
I have not seen all this in this manuscript. The paper is difficult to follow, it has too much mathematical discussion (but without any proof), and it has two independent parts with their own definitions and numerical results. Maybe a single scheme with all the theory together in the beginning and then numerics would be better. Moreover, the novelty of the methods when applied to a realistic oceanic velocity field is not clear. The discussion of the results for the Palau Island region is vague. I think the paper (which of course has interesting material, very professional and with potential interest) could be largely improve if the authors reduce the mathematical discussion and enlarge the physical meaning (comparing with the obtained with other methodologies) of their results.
Citation: https://doi.org/10.5194/npg-2022-1-RC1 -
RC2: 'Comment on npg-2022-1', Anonymous Referee #2, 21 Feb 2022
This is another entry in the development of methods to identify Lagrangian coherent structures. There are many mathematical details, which might be better treated in another journal, with significant applications, say, published in NPG. It is somewhat unclear how "diffeomorphism-based" is a new method for discovering LCS. Previous methods are all based on the flow map, \phi, which is a diffeomorphism. So is this a mere re-branding?
There are results on the three text cases, including the Palau island region, but it is unclear what additional clarity is brought to understanding the Lagrangian transport.
Citation: https://doi.org/10.5194/npg-2022-1-RC2
Interactive discussion
Status: closed
-
RC1: 'Comment on npg-2022-1', Anonymous Referee #1, 01 Feb 2022
This paper studies how to extract Lagrangian Coherent sets from velocity fields. Another one. The paper has two parts: the first is devoted to extract rigid sets based on a diffeomorphism criterion, and the second is oriented to compute coherent sets with operator methods. The authors insist in the novelty of both methologies, but this is not clear all along the paper. There are already so many new methods to study LCS/rigid sets that the focus should be in the applications (even more if NPG is for applications in Geophysics): discuss the advantages of the new method in a particular oceanic example, focus on the physical processes it can describe better than previous methodologies, and stress the computational beneficts of using this particular method. What scientists working in ocean dynamics can learn using this "new" methodology?
I have not seen all this in this manuscript. The paper is difficult to follow, it has too much mathematical discussion (but without any proof), and it has two independent parts with their own definitions and numerical results. Maybe a single scheme with all the theory together in the beginning and then numerics would be better. Moreover, the novelty of the methods when applied to a realistic oceanic velocity field is not clear. The discussion of the results for the Palau Island region is vague. I think the paper (which of course has interesting material, very professional and with potential interest) could be largely improve if the authors reduce the mathematical discussion and enlarge the physical meaning (comparing with the obtained with other methodologies) of their results.
Citation: https://doi.org/10.5194/npg-2022-1-RC1 -
RC2: 'Comment on npg-2022-1', Anonymous Referee #2, 21 Feb 2022
This is another entry in the development of methods to identify Lagrangian coherent structures. There are many mathematical details, which might be better treated in another journal, with significant applications, say, published in NPG. It is somewhat unclear how "diffeomorphism-based" is a new method for discovering LCS. Previous methods are all based on the flow map, \phi, which is a diffeomorphism. So is this a mere re-branding?
There are results on the three text cases, including the Palau island region, but it is unclear what additional clarity is brought to understanding the Lagrangian transport.
Citation: https://doi.org/10.5194/npg-2022-1-RC2
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