Adjoint-Based Simultaneous State and Parameter Estimation in an Arctic Sea Ice-Ocean Model using MITgcm (c63m)

Lyu, Guokun; Mu, Longjiang; Koehl, Armin; Lei, Ruibo; Liang, Xi; Liu, Chuanyu

doi:https://doi.org/10.5194/gmd-2024-189

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https://doi.org/10.5194/gmd-2024-189

Preprints

Submitted as: development and technical paper

30 Apr 2025

Submitted as: development and technical paper |

| 30 Apr 2025

Status: a revised version of this preprint is currently under review for the journal GMD.

Adjoint-Based Simultaneous State and Parameter Estimation in an Arctic Sea Ice-Ocean Model using MITgcm (c63m)

Guokun Lyu, Longjiang Mu, Armin Koehl, Ruibo Lei, Xi Liang, and Chuanyu Liu

Abstract. Parameters in sea ice-ocean coupled models greatly affect the simulated ocean and sea ice evolution, and are normally tunned to bring the model state close to the observations. Using an adjoint method, spatiotemporally varying parameters of Arctic sea ice-ocean coupled model are optimized simultaneously with the initial condition and the atmospheric forcing by assimilating satellite and in-situ observations. The assimilation results show that the joint state and parameter estimation (SPE) substantially improves the sea ice concentration simulation. Particularly in October when the ocean surface starts to refreeze, SPE reduces the lead closing parameter H_o, which determines the minimum ice thickness formed in the open water, to increase the lateral sea ice growth and facilitate the seasonal rapid sea ice recovery in the Pacific sector. Comparisons with sea ice thickness observations from the moored upward looking sonars and Ice Mass Balance buoys demonstrate that the inclusion of model parameters in the optimization also leads to better sea ice thickness estimation. Overall, the adjoint-based SPE scheme has the potential to better reproduce the Arctic ocean and sea ice state and will be applied to reproduce a new Arctic sea ice-ocean reanalysis.

Received: 10 Oct 2024 – Discussion started: 30 Apr 2025

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Guokun Lyu, Longjiang Mu, Armin Koehl, Ruibo Lei, Xi Liang, and Chuanyu Liu

Status: final response (author comments only)

RC1:
'Comment on gmd-2024-189', Anonymous Referee #1, 15 May 2025
This study potentially contributes significantly to the sea ice model optimisation problem by employing an adjoint method that, for the first time, simultaneously optimises both the model state and a set of its parameters. Therefore, the study topic is valuable and suitable for GMD, so its publication after a careful revision is recommended.
A major issue is that the study is based on the very exceptional year 2011/2012 in the Arctic. However, the authors make general claims about the physical importance of sea ice model parameters. A question arises: Is one year enough to reach such conclusions, and are the results robust when tested for other years?
There is an issue of reproducibility, as the adjoint model is only available to the editors and reviewers for review via the submission system, and the study may not comply with the FAIR principles (https://www.nature.com/articles/sdata201618).
The discussion section is very brief, and what is crucially missing from it is comparing the study results with others, which would importantly put them in the context of broader research. Such a comparison would also help assess the results' robustness and novelty. Also, English is poor in places, with many writing mistakes and misspelled words. There is a need to check English grammar.
Finally, I have multiple minor points and editorial suggestions that I hope the authors will consider:
line 18: tuned

line 28: The end of Abstract mentions new Arctic reanalysis, but the manuscript does not provide any substantial information on that. I suggest you add such information, or delete the mention from Abstract.

Introduction is missing to cite the relevant-looking paper by Xiying Liu and Lujun Zhang "Study on Optimization of Sea Ice Concentration with Adjoint Method," Journal of Coastal Research 84(sp1), 44-50, (1 June 2018). https://doi.org/10.2112/SI84-006.1

as they optimised MITgcm initial conditions. I suggest you add the citation.

In introduction machine learning studies are mentioned. A potentially relevant study by Nie Y, Li C, Vancoppenolle M, et al (2023) Sensitivity of NEMO4.0-SI3 model parameters on sea ice budgets in the Southern Ocean. Geoscientific Model Development 16:1395–1425. https://doi.org/10.5194/gmd-16-1395-2023, is missing. I suggest considering adding it.

line 72: What are 'intermediate coupled models'? Do you mean intermediate complexity. Seems a word is missing here.

line 98: 'z-levels ranging', again a word seems missing here. Do you mean z-level thicknesses?

lines 108-114: This paragraph is hard to grasp. Could you clarify it e.g. by adding a sketch or a diagram illustrating a simple example?

Table 1 lists the parameters selected for optimisation. Why these parameters were selected has not been explained.

line 165 and possibly elsewhere: Numbers and units have a space between them. '48h' -> '48 h'.

Table 2. The first column lists observational variables. Would be useful to explain in the caption what these acronyms mean. They are in text but caption seems more appropriate. In general, table and figure captions are quite brief and do not explain the figure and table contents very well.

line 171: 'include' -> 'includes'

line 182: Does 'long measurement' mean long measurement period? It is not sure whether the IMB deployments on thick ice ensure the spatial representativeness, if the surrounding ice is thinner.

line 184: perhaps delete word 'fully'.

line 219: 'parameters' -> 'parameter'

line 219: 'H0and evaluate' -> 'H0 and evaluate'

lines 221-222: Are equations (2) and (3) representing a tangent linear model?

line 231: Why does the model not reproduce positive SIC changes well?

line 278: Could you justify why October is important for Arctic sea ice?

line 280: 'most prounced over the Arctic Ocean.' -> 'most pronounced.'

Figure 5: What are red and green lines in panels (a), (b) and (c). You should explain them in the caption. What is the year in (d). Is it 2012? You should either add it to the caption or figure labels.

line 291: 'and this ocean heat'

line 293: 'less ocean heat is released'

line 294: 'water areas freeze'

line 296: 'improve the SIC evolution'

line 298: Did you look at how much the ocean heat varies between the simulations?

Figure 6: (b) Add the year (2012) in question.

line 314: broke off

line 319: ocean starts to freeze

Figure 7: Add the year (2012) in question.

line 329: SIC and SIC observations.

line 335: explain symbols N and n in the formula.

line 337-338: 'with long records'

line 339: Are these IMBs still functional?

Figure 8: Wouldn't it make more sense to calculate the statistics (mean and CRMSD) against CS-SMOS instead of IMBs. You seem to treat CS-SMOS as a reference.

line 347: Where do the 0.2-0.7 m SIT biases appear? Not in Figure 8.

line 348: It is not clear that opti-SPE is closer to CS2SMOS than other simulations.

line 351: '... IMB measurements usually show 0.5-1.5 m differences compared ...'

line 355: Although IMB buoys are deployed on thick level ice, pressure ridges increase the areal average thickness of drift ice. Would this also increase CS2SMOs SIT?

line 368: 'drifting periods longer than'

Figure 9: Are these trajectories from Jan-Dec 2012?

line 381: 'the drifting buoys do not differ systematically.'

line 383: 'the region with gradually decreasing SIC'

line 392: buoys 16 and 21 do not show reduction from CTRL to opti-SPE. Choose the buoys that do so, instead.

line 399: Common understanding is that the MIZ starts when SIC is around 85% and the internal ice stress becomes unimportant.

line 401: '(Figure 10b-d)'

line 402: I do not understand this claim related to reproduction of the weakening ice field. In contrast, ice physics simulation becomes easier when the internal ice stress is reduced and ice drift becomes free. The RMSE could increase only due to faster SIV which is also more variable.

lines 408-409: Note that you use continuum ice model that can not capture individual ice floes.

line 411: 'the marginal ice zone'.

Figure 10: Is buoy 16 on the left and 21 on the right? Add relevant information in the figure caption.

lines 415-452: English is very bad in this section. I suggest revising and rewriting entirely.

line 416: 'In a coupled sea ice-ocean model' and 'schemes describe'

line 417: 'parameters are major sources'

lines 417-419: This aspect was not addressed in the study, so the last sentence of this paragraph should be removed, or moved to Introduction with proper literature citations added.

line 420: 'estimate the optimal model state and parameter values'

line 425: 'simultaneous'

line 426: 'traditional'

line 429: Note that sea ice does not grow laterally. There could be frazil ice growth that once buoyant enough starts to float on sea surface. Is that what you mean?

line 433: 'the simulated SIT in agreement with CS2CMOS SIT taking into account its prior uncertainties.'

line 438: 'However, '

line 447: 'brought into agreement' and 'efficiently, and also with independent'

line 448: 'Zampieri et al. (2021) demonstrated '

line 450: 'Therefore, sea ice model remains a suitable tool for the Arctic Ocean'

lines 450-451: 'studies. However, we will update'

line 451: Is it computationally significantly more expensive to run the more complex CICE? Have you considered this aspect?

lines 451-452: 'next state to reconstruct'

line 466: 'University of Washington'
Citation: https://doi.org/10.5194/gmd-2024-189-RC1
- AC2: 'Reply on RC1', Guokun Lyu, 29 Jul 2025
  
  Dear reviewer:
  Thanks for your detailed comments and insightful disscussion on our work. we have revised the manuscript based on the reviewers' comments.
  attached is the response to all your comments.
  please let me konw if you have any further concerns
  
  Guokun Lyu on behalf of the authors.
  
  Citation: https://doi.org/10.5194/gmd-2024-189-AC2
- AC3: 'Reply on RC1', Guokun Lyu, 29 Jul 2025
  
  Dear reviewer:
  Thanks for your detailed comments and insightful disscussion on our work. we have revised the manuscript based on the reviewers' comments.
  attached is the response to all your comments.
  please let me konw if you have any further concerns
  
  Guokun Lyu on behalf of the authors.
  
  Citation: https://doi.org/10.5194/gmd-2024-189-AC3
RC2:
'Comment on gmd-2024-189', Francois Massonnet, 28 Jun 2025

The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2024-189/gmd-2024-189-RC2-supplement.pdf

Citation: https://doi.org/10.5194/gmd-2024-189-RC2
- AC1: 'Reply on RC2', Guokun Lyu, 29 Jul 2025
  
  Dear François Massonnet:
  Thanks for the insightful comments. attached is our response to your comments.
  the revised manuscript will likely be posted soon.
  Best
  Guokun Lyu on behalf of the authors
  
  Citation: https://doi.org/10.5194/gmd-2024-189-AC1

Guokun Lyu, Longjiang Mu, Armin Koehl, Ruibo Lei, Xi Liang, and Chuanyu Liu

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Short summary

In the sea ice-ocean models, errors in the parameters and missing spatiotemporal variations contribute to the deviations between the simulations and the observations. We extended an adjoint method to optimize spatiotemporally varying parameters together with the atmosphere forcing and the initial conditions using satellite and in-situ observations. Seasonally, this scheme demonstrates a more prominent advantage in mid-autumn and show great potential for accurately reproducing the Arctic changes.


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