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.

Very well crafted paper, the topic is without a doubt relevant to the sea ice modeling and simulation community. I recommend acceptance of the manuscript. I have pointed out a few typos on the manuscript and some very minor details that would benefit from an extra round of clarification (see attached PDF). Also, considering that https://doi.org/10.1029/2023MS003696 has been published, it would make sense to find a place in the manuscript to at least acknowledge its existence.

Congratulations to the authors on a very good paper.