the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 May 2026
MSR v1.0: A High-Resolution Ocean Parameterization Approach via Multiphysics Super-Resolution
Abstract. High-resolution reconstruction of ocean dynamics is challenging because spectral bias and the neglect of cross-variable couplings in existing super-resolution (SR) methods often lead to over-smoothed, physically inconsistent outputs, limiting their utility for eddy parameterizations. To overcome these limitations, we present a Multiphysics Super-Resolution version 1.0 (MSR v1.0) framework that jointly reconstructs eight closure-relevant diagnostics—vorticity, deformation measures, stress tensor components, and subgrid momentum forcing terms—directly from low-resolution (LR) velocity fields, consistency is maintained under a filtering scale that aligns with the definition of subgrid tendencies. Our approach integrates three key components: (1) a Dynamic Enhancement Feature (DEF) module to prioritize dynamically active regions; (2) a High-Frequency Enhancement (HFE) module that fuses spatial and spectral operators via learned gating to restore suppressed fine-scale structures such as fronts and eddy rims; and (3) a Physical Consistency Loss that aligns derivative-level structures and algebraic couplings across diagnostics. Experiments on an eddy-resolving simulation dataset across multiple ocean basins and downscaling factors show that MSR consistently outperforms strong SR baselines, yielding sharper reconstructions with improved high-wavenumber spectra and cross-variable consistency. The MSR-reconstructed diagnostics are closure-ready for low-resolution ocean models and can inform or constrain eddy parameterizations, providing a practical, spectrally selective, scale-aware surrogate for high-fidelity multiphysics diagnostics.
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Status: open (until 01 Jul 2026)
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RC1: 'Comment on egusphere-2026-691', Anonymous Referee #1, 05 Jun 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-691/egusphere-2026-691-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/egusphere-2026-691-RC1 -
AC1: 'Reply on RC1', Fuhua Zhu, 05 Jun 2026
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Dear Reviewer,
Thank you again for the detailed and constructive comments. Since the public discussion is still ongoing, we will carefully consider all comments together before preparing the revised manuscript. At this stage, we would like to clarify several points and indicate how we plan to address them.
First, regarding the scope of “parameterization”, we understand the reviewer’s concern that the current wording may overstate the sense in which MSR is a parameterization. Our intention was not to claim that the current model is already a fully online parameterization scheme directly coupled to a low-resolution ocean model. Rather, we view the proposed model as a deep-learning surrogate or approximation for parameterization-related diagnostic computation, where high-resolution diagnostic fields and subgrid-forcing-related quantities are reconstructed from low-resolution velocity inputs. In the revised manuscript, we will refine the title and related wording to make this scope clearer and avoid giving the impression that the present work demonstrates a complete online ocean parameterization.
Second, we agree that the term “generalization” in Experiment 2 requires clarification. In the current manuscript, Experiment 2 mainly presents multi-region performance under the same architecture and experimental protocol, and the wording may have conflated regional robustness with stricter out-of-distribution generalization. We acknowledge that, in geoscientific applications, a stronger test of generalization is to train the model in one region and evaluate it directly in another region without retraining. We have conducted such cross-region experiments, but they were not presented clearly in the current manuscript. In the revised manuscript, we will add these results as a separate OOD evaluation and clearly distinguish them from the existing multi-region robustness experiment. We will also explicitly state which experiments involve retraining in each region and which experiments use fixed trained weights for cross-region testing.
Third, we agree that the motivation for the selected prediction targets should be explained more explicitly. Some of this motivation is already present in the current manuscript, where vorticity, deformation, stress-tensor components, and subgrid momentum-forcing terms are derived from the velocity field and are used to characterize dynamically relevant mesoscale structures. However, we agree that this discussion should be reorganized and strengthened. In the revised manuscript, we will add a clearer explanation of the physical connections among these variables and their roles in parameterization-related diagnosis, while also distinguishing these derived diagnostics from prognostic ocean-state variables such as velocity, sea surface height, temperature, and salinity.
Fourth, regarding the EDSR baseline, we respectfully note that our own experiments do not support the expectation that simple hyperparameter tuning of EDSR can achieve a similar improvement for this ocean-diagnostic reconstruction problem. We tested several EDSR configurations, including changes in depth, width, learning rate, residual scaling, and training settings, but these adjustments did not close the performance gap in our setting. We agree that this point should be documented more clearly, and in the revised manuscript we will describe the baseline tuning protocol and report the tuned EDSR results more transparently.
Fifth, we understand the concern that the manuscript currently describes many small architectural components. Our intention was to make the implementation easier to understand and reproduce, rather than to claim that each component is an independent major contribution. Nevertheless, we agree that the current presentation may obscure the main idea. In the revised manuscript, we will simplify the method section, emphasize the most important components supported by ablation evidence, and move or shorten secondary implementation details where appropriate.
We also appreciate the reviewer’s comment that some methodological ideas appear repetitive. In the revised manuscript, we will clarify the distinct roles of derivative-based input features, feature-space high-frequency enhancement, and output-level physical consistency constraints. We will also merge or shorten descriptions where similar ideas are currently repeated, for example in the discussion of derivative operators, wavelet/Fourier-based enhancement, and loss-level spectral or physical constraints.
Sixth, regarding the HighResUNet baseline, we agree that its role should be clarified. HighResUNet was included only as an HR-input reference, indicating what can be achieved when high-resolution input information is available. It is not intended as a deployable LR-to-HR baseline. This is also why later experiments focus on models driven by low-resolution inputs, since the main application scenario considered in this work is precisely that high-resolution inputs are limited while low-resolution fields are more commonly available. We will make this distinction explicit in the revised manuscript.
Seventh, regarding noise sensitivity, we agree that this is an important issue. The proposed model includes a coarse/residual pathway to preserve the large-scale state and reduce over-reliance on high-frequency amplification. However, we also agree that this design does not by itself prove robustness to noisy inputs. Figure 6 illustrates the intended enhancement of medium- and high-frequency features in clean simulation data, but controlled-noise experiments would provide more direct evidence. In the revised manuscript, we will either add such controlled-noise tests or discuss this limitation more explicitly, especially with respect to potential applications involving observational data.
Eighth, regarding the evaluation metrics, we agree that repeatedly showing MSE, RMSE, and R² leads to redundancy. We originally used these metrics for consistency across experiments, but we agree that the ablation study, especially for the loss terms, should include validation metrics beyond standard reconstruction errors. In the revised manuscript, we will keep one primary accuracy metric in the main text, most likely RMSE or normalized RMSE, and replace some redundant panels with additional spectral or physical-consistency metrics. This will allow the effect of the loss terms and architectural components to be evaluated more directly, rather than relying only on MSE-type reconstruction errors.
Regarding Minor Comment 2, we have checked the visually strange regions in Fig. 7. These regions are not valid ocean areas. They arise from the plotting procedure: the original plotted domain has a roughly parallelogram-like shape, and the surrounding area was filled for visualization convenience. These filled regions should not be interpreted as physical structures or model outputs over valid ocean points. We will revise the figure or caption to make the valid mask clearer, for example by explicitly showing or masking out the invalid filled regions.
Regarding Minor Comment 3, we agree that the legend in Fig. 12 obscures part of the results. We will revise the figure by reducing the legend size or moving it outside the plotting area.
We appreciate these comments, as they help us clarify the scope of the work.
Citation: https://doi.org/10.5194/egusphere-2026-691-AC1
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AC1: 'Reply on RC1', Fuhua Zhu, 05 Jun 2026
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RC2: 'Comment on egusphere-2026-691', Anonymous Referee #2, 08 Jun 2026
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This paper presents a super-resolution approach as a general framework applied to ocean simulation data, although the title is confusing. The contribution here is based on the multiple components (DEF, HFE and physical constistency loss) used to extract important features found in ocean dynamics and several experiments are performed to try to assess the quality of the proposed methodology. The paper is however lacking important motivations, justifications and requires substantial reorganization before being considered for GMD. I can therefore not recommand publication of the manuscript in this current state.
Major comments:
1. Overall motivation of the paper. Among important tasks in computational oceanography, subgrid parameterization consists in predicting subgrid tendencies from coarse-resolution states, which amounts to predict the subgrid forcing (see Eq. 1 from Zanna and Bolton, 2020 for example), or some approximation such as the one introduced by Zanna and Bolton, 2020 for a barotropic or baroclinic model. The task of super-resolution is better related to state estimation, from which you try to improve on the current representation of the states of the system (either because these are lacking details—under-resolved—or because they are sparse and/or noisy). If you can estimate the states of the system (generally velocity components u, v, not derived quantities such as vorticity, strain, etc), it means that you are now able to compute the subgrid-term from them. I don't see here the added benefit of predicting subgrid terms since they can be computed analytically from the other predicted quantities; which also makes the physical consistency loss unnecessary.
2. Interpretability. The paper describes many complex components one by one, with unclear motivations. For example, it is said that "SFE is essential for capturing dynamical ocean features such as fronts and eddy rims" and a few paragraphs later that HFE is essential for the exact same purpose. I appreciate the ablation study at in Experiment 5.4 that gives some insight on the impact of each individual component, but this is not done properly. It also seems that some components are not improving much and could be removed to improve clarity of the manuscript.
3. Unclear numerical setup. The problem is applied to ocean states but samples shown in e.g. Fig.2 seems to only represent zoomed-in versions which makes it difficult to see how they relate to real ocean data. Experiment 5.2 in particular is said to be applied on three different domains with given coordinates. Please, provide a map with insets of the choosen regions. Also, it is not clear from the beginning what is the target ratio used between HR and LR. We can guess at L 176 that the "default" factor is equal to 2 because LR fields are defined such that X_{LR} \in R^{2 \times H/2 \times W/2}. Please use generic ratio throughout the methodology, or clearly define that the ratio is equal to 2; since this can lead to largely different results as you pointed out in Experiment 5.3Minor comments:
- L 139: The reference is incorrectly given as BZ2019 instead of ZB2020.
- Fig 5: We can't see anything in the "initial" row. Is it possible to increase its value or narrow down the colorbar?
- L 290: Rename the "After" and "Before" curves to "F_0'" and "F_hfe".
- L 305-306: ASPP and RRDB acronymes introduced before full definition.
- L 349: remove comma after "high-frequency details".
- L 363: definition of rho is already given in Eq. 28.
- It is not clear how HighResUNet is different from the LowRes. At L 436, it is written that the former is trained on HR inputs, but since the goal is to predict HR outputs, does it mean that this model is not doing super-resolution at all? Clarifications are required.
- Figs 9-11: please remove MSE as it is redundant with RMSE. Instead, using a statistical metric such as a Wasserstein distance could be interesting.
- Fig 12: It is difficult to read because the legend overlap with some important bars. Consider moving the legends outside of the plots.
- L 486: it is not clear that the gap increases with resolutions. This claim needs more evidence.
- L 511: not near-best. but always best.
- L 512: it looks like the largest reductions are for D, S_u and S_v.
- L 532: to me, it is more degraded for T_11, T_22 and T_12.
- L 534: contradicts the previous sentence concerning the removal of the Phy loss contribution.
- L 565: what is BH-FDR?Citation: https://doi.org/10.5194/egusphere-2026-691-RC2 -
AC2: 'Reply on RC2', Fuhua Zhu, 09 Jun 2026
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We sincerely thank the reviewer for the careful and constructive comments. We agree that the current manuscript does not sufficiently clarify the distinction between super-resolution, state estimation, and subgrid parameterization, and that the motivation and organization need to be substantially improved.
In the revised manuscript, we will revise the title, abstract, introduction, and method description to clarify that the proposed MSR framework is primarily a dynamics-aware super-resolution approach for reconstructing high-resolution, closure-relevant ocean diagnostics from low-resolution velocity fields, rather than a complete online subgrid parameterization scheme. We will also clarify why direct reconstruction of closure-relevant diagnostics is considered here, how it differs from reconstructing high-resolution velocity states followed by analytical diagnostic computation, and better justify the role of the physical consistency loss as a constraint on the algebraic and derivative-level consistency among the jointly reconstructed diagnostics.
We will further reorganize the description of the model components to clearly distinguish the roles of DEF, SFE, HFE, and the physical consistency loss. We will also strengthen the ablation discussion and reconsider the necessity of components with marginal contributions to improve the clarity and interpretability of the framework.
In addition, we will improve the numerical setup section by explicitly defining the downscaling factors, clarifying the LR–HR construction, adding a map with the selected regions, and improving the figures, metrics, baselines, and terminology as suggested. In particular, we will clarify the role of the HighResUNet baseline and avoid presenting it as a standard super-resolution model if it uses HR inputs.
All minor comments will also be addressed carefully in the revised manuscript, including reference corrections, acronym definitions, figure readability, redundant metrics, terminology, and statistical notation.
Citation: https://doi.org/10.5194/egusphere-2026-691-AC2
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AC2: 'Reply on RC2', Fuhua Zhu, 09 Jun 2026
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