the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
CD-type discretization for sea ice dynamics in FESOM version 2
Sergey Danilov
Carolin Mehlmann
Dmitry Sidorenko
Qiang Wang
Abstract. Two recently proposed variants of CD-type discretizations of sea-ice dynamics on triangular meshes are implemented in the Finite volumE Sea ice – Ocean Model (FESOM version 2). The implementations employ the finite element method in spherical geometry using longitude-latitude coordinates. Both of them rely on the edge-based sea-ice velocity vectors, but differ in basis functions used to represent velocities. The first one uses nonconforming linear (Crouzeix–Raviart) basis functions, and the second one uses continuous linear basis functions on subtriangles obtained by splitting parent triangles into four smaller triangles. Test simulations are used to show how the performance of the new discretizations compares with the A-grid discretization using linear basis functions. Both the CD discretizations are found to simulate a finer structure of linear kinematic features (LKFs). Only the first CD variant demonstrates some sensitivity to the representation of scalar fields (sea-ice concentration and thickness), simulating a finer structure of LKFs with the cell-based scalars than with the vertex-based scalars.
Sergey Danilov et al.
Status: open (until 29 Jun 2023)
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RC1: 'Comment on gmd-2023-37', Anonymous Referee #1, 04 Jun 2023
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Review of “CD-type discretization for sea ice dynamics in FESOM version 2”
The authors create and test two variants of CD-type discretizations for sea ice. Both are edge-based methods, but differ in the basis functions used. The first uses Crouzeix–Raviart basis functions, and the second one uses continuous linear basis functions on subtriangles.
The introduction provides a detailed overview of the state of other sea ice models and the methods they use. The following two sections derive each of the two methods. A Fourier analysis then compares the accuracy of the linearized form of these methods with A-grid and B-grid methods. Finally, a comparison of performance using numerical simulations is presented by comparing the numerical efficiency and ability to represent linear kinematic features.
This paper is well-written, with a clear presentation of the mathematical derivations of the methods. The analysis shows that the two methods both work in the functional sense, and provides insight into the differences between them. The paper will be useful to sea ice modelers who are also considering these discretizations, and it is appropriate for the larger GMD audience. I have no requests for revisions, but have the following minor comments.
110: it would be helpful to say that the colon (:) is a tensor product.
164: dirscretization -> discretization
242: rectangular triangles – is that correct?
253 or fig. 3: would be good to remind the reader here what delta is.
Citation: https://doi.org/10.5194/gmd-2023-37-RC1
Sergey Danilov et al.
Sergey Danilov et al.
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