the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Jul 2025
WIce-FOAM 1.0: Coupled dynamic and thermodynamic modelling of heterogeneous sea ice and waves using OpenFOAM-v2306
Abstract. We present WIce-FOAM 1.0, a numerical model built on OpenFOAM that couples the dynamics and thermodynamics of heterogeneous sea ice to analyse waves’ response in marginal ice zone regions composed of consolidated ice floes and interstitial grease ice. The model represents prototypical conditions on the 5-kilometre scale, where each 10-metre grid cell classified as ice floe or grease ice may contain both ice types, but are predominantly occupied by one. Our model aims to study the mean shear viscosity of heterogeneous sea ice to bridge the gap with larger-scale ocean-sea ice models in which sub-grid details and wave effects are neglected. We tested the model in the Southern Ocean using a realistic sea-ice field from a SAR satellite image and complemented our analysis by idealised simulations. The thermodynamic model was coupled online to optimize the stiffness of the process scales and to explicitly account for the distinct characteristics of different ice types. We first investigated the dynamic response of sea ice to one-way wave forcing across a range of wave periods and directions. The results show that the domain-averaged sea-ice viscosity is scale invariant from approximately 800 m to 5 km and is primarily governed by the relative proportion of ice floes to grease ice, with less sensitivity to wave periods and directions. While the wave direction affects the local strain rate and viscosity, and the presence and orientation of narrow connections between the larger ice floes significantly influence the mean viscosity, these effects do not break the observed scale invariance. Finally, we demonstrate that, despite the different time scales, the mean viscosity responds nonlinearly to the inclusion of thermodynamic sea-ice growth. This model represents a first step towards a mechanistic understanding and description of heterogeneous sea ice, which is common in the Antarctic and is increasing in the warming Arctic. It can be used to design field experiments and to derive parametrisations of waves-in-ice response for large-scale sea-ice models.
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CEC1: 'Comment on egusphere-2025-2184 - No compliance with the policy of the journal', Juan Antonio Añel, 28 Jul 2025
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AC1: 'Reply on CEC1', Rutger Marquart, 01 Aug 2025
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Dear Executive editor,
We would like to confirm that all the necessary code to reproduce the simulations was included in our original submission. We understand that the difficulty in accessing the code and the README file may have caused some confusion.
We have now transferred the release used in this work to the Zenodo repository: https://doi.org/10.5281/zenodo.16681435 (DOI: 10.5281/zenodo.16681435)
For clarity, we have converted the README.docx to a README.md file and uploaded it separately on Zenodo. Additionally, we appropriately included the GPL 3.0 license and added a copyright notice at the beginning of each solver source file to ensure compliance with the OpenFOAM license.
We have updated the 'Code and Data Availability' section to include the link to the code and data on Zenodo, and will incorporate this update in the revised manuscript.
Kind regards,
Rutger Marquart
Citation: https://doi.org/10.5194/egusphere-2025-2184-AC1 -
CEC2: 'Reply on AC1', Juan Antonio Añel, 01 Aug 2025
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Dear authors,
Many thanks for addressing the mentioned issues with your manuscript so quickly. We can consider now your manuscript in compliance with the Code and Data policy of the journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-2184-CEC2
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CEC2: 'Reply on AC1', Juan Antonio Añel, 01 Aug 2025
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AC1: 'Reply on CEC1', Rutger Marquart, 01 Aug 2025
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RC1: 'Comment on egusphere-2025-2184', Anonymous Referee #1, 11 Aug 2025
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This paper presents a novel sea ice model that represents the mixed phase between grease ice and consolidated ice floes, including both dynamic and thermodynamic components. The work investigates the response of this model to idealized wave forcing for a sea ice configuration derived from SAR imagery. Simpler configurations are also considered as sensitivity experiments. The key diagnostics are the mean viscosity and local strain rate as a function of wave properties and ice floe concentration relative to grease ice.
This work represents a useful advance in modelling sea ice within marginal ice zones and its response to wave forcing. My specific comments are listed below.
Eq. 6: Does the vertical component of wave velocity play a role in these simulations? The rheology seems to be described for a 2-D simulation only (section 2.1.2).
L138: What does ‘apical plane’ mean?
Table 1: Can you describe how these values were chosen?
L238: Why can we expect a higher growth rate for frazil ice? Is it because it is thinner than the floes?
Fig 2: Why is there not much happening in the first and last parts of the curves in Fig 2a and the first part of Fig 2b?
Fig 2: What are the radiative and snow forcings used to obtain these plots? And what is used for the simulations presented in the results section?
L306-307: How was the thickness of ice determined in the SAR image?
L307: The minimum threshold for what exactly?
L312: If I understand correctly, the sub-domains are defined for diagnosis purpose only. Mentioning them here caused some confusion for me, as not much information was provided about what they represented. One solution could be to not mention them here, but describe them later in the context of Fig 8.
L317: ‘that gradually increase in thickness’. This could be misinterpreted as an increase in time. I suggest rephrasing.
Fig 5: Could you please explain the motivation behind the configurations shown in panels b-e, including the wiggles in panel e?
L338-339: ‘The viscosity is locally affected by the propagating wave, since the rheology of the grease ice and ice floes is described as a function of thickness (Eq. (15) and (18)).’ I don't understand how the first part of the sentence follows from the second part. Could you please explain in more detail?
L361-364: ‘Figure 8(e) and (f) illustrate the relative difference in shear viscosity between the highest and lowest wave periods. The viscosity values in the case with waves from the west are significantly higher than those from the south, indicating a greater response to wave periods.’ I don’t understand how this indicates a greater response to wave periods. Could you clarify?
L369-370: The north-south orientation of what?
L370: Can this linear relationship be derived analytically? If so, this may be another useful output of the paper regarding parameterization of these effects in climate models.
L376-377: ‘Based on the linear relationship presented in Fig. 9, we assume that the model resolves the smaller scales of the heterogeneous field, allowing us to extract properties at larger scales.’ How does the linear relationship allow you to make this assumption?
L380-381: ‘Therefore, we considered subdomain groups of increasing size from 1 to 6, with the latter corresponding to the full domain (see Fig. 8(a))’. This is not entirely clear to me. What are the sizes of these groups and how are they chosen spatially? What units does ‘1 to 6’ have in the above sentence and what does it represent exactly? Perhaps a diagram would help?
L382: ‘The results are presented in Table 3, showing a strong scale invariance from 800 m up to 5 km. The 800 m scale is already sufficient to capture the heterogeneity of the ice cover, and variations in ice type patterns do not affect the mechanical response at the larger scales up to 5 km.’ Where do the numbers 500 m and 5 km come from? I am guessing they result from the size of each group, but this is hard to infer from just Table 3. Also, for clarity, please state explicitly what is invariant with scale.
L497: ‘in the dynamic model by 3% in t = 24h’. Should it be ‘at t = 24h’?
L507-508: ‘degree of heterogeneity’ is a bit ambiguous to me. I think ice floe percentage relative to grease ice would be clearer.
Citation: https://doi.org/10.5194/egusphere-2025-2184-RC1 -
AC2: 'Reply on RC1', Rutger Marquart, 19 Aug 2025
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Please find attached a PDF file containing the authors' responses to all comments from Referee #1.
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AC2: 'Reply on RC1', Rutger Marquart, 19 Aug 2025
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Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived your code on GitHub. However, GitHub is not a suitable repository for scientific publication. GitHub itself instructs authors to use other long-term archival and publishing alternatives, such as Zenodo. Additionally, you have stored in the Git site only the solvers, not the full code of your model (including OpenFOAM). You must publish all the code and data necessary to replicate your work.
Therefore, the current situation with your manuscript is irregular. Please, publish your code in one of the appropriate repositories and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy. Also, please include the relevant primary input/output data to replicate your work.
Also, in the Git site, for the code that you have shared, no license is listed. This is illegal. As you are using OpenFOAM, which is released under the GPLv3, when distributing any code that interacts with OpenFOAM, you must release it under the GPLv3 too. If you do not include a license the code remains your property, and nobody can use it.
Finally, you must include a modified 'Code and Data Availability' section in a potentially reviewed manuscript, containing the information of the new repositories.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in our journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor