Thank you for the thorough and constructive review, and for the positive remarks on the methodology and overall quality of the manuscript. We have carefully considered each comment, in particular the concerns about the interpretation of the 4DvarNet results. We now address each point individually below.

l41-l42: Provide references for "recent studies" or rephrase. Aha: The next 3 sentences provide these references.

Thank you for noting this. As noted, the studies are cited in the immediately following sentences. We have nevertheless re‑read the passage to ensure the flow is clear and find the current sequence to be natural.

l119: Not sure what an "event-based perspective" could refer to.

We acknowledge the ambiguity. By “event‑based perspective” we meant the qualitative examination of individual eddy case studies presented later in Section 4. To avoid confusion, we have changed the wording to “case‑study perspective” and clarified the sentence accordingly.

l406: The word "captures" implies that these strain structures are realistic. I think a better word is "contains" since the realism of the structures is unknown.

We agree with the referee's suggestion and have replaced “captures” with “contains” in the description of the FSLE filamentary patterns. The revised wording avoids implying that the strain structures are fully realistic. At the same time, we wish to clarify that the original use of “captures” was intended to convey a narrower, observation‑based point: for the SME case presented (Case 3), 4DvarNet was the only product that reproduced a closed SSH contour and an identifiable eddy core consistent with SWOT L3, thereby “capturing” the existence of the eddy where the other products did not. We have therefore retained “captures” in the part of the discussion that refers directly to the SSH‑based eddy identification, while adopting “contains” for the unvalidated FSLE diagnostics.

l421: 4DvarNET "better preserves fine-scale spatial organization" is totally speculative. A more justified or balanced statement could be, "4DvarNET generates spurious small-scale flow features which look realistic, but which are not supported by any validation data. Hence, dynamical inferences from this product should be avoided."

We accept the referee’s assessment and agree that the suggested statement more objectively describes 4DvarNet’s performance and its potential issues. We have therefore adopted the referee’s wording in the revised manuscript.

l438: How do you know that 4DvarNET exhibits "enhanced sensitivity to fine-scale variability"? Could this not simply be due to spurious structures in the training data or mis-tuning of the assumed noise level?

We appreciate the referee’s caution. In the original text we used “enhanced sensitivity” merely to describe the larger Rossby number magnitudes and sharper gradients produced by 4DvarNet, not as a claim of physical superiority. However, the wording was easily misinterpreted. We have now clarified that this property could equally reflect noise or artifacts, and that the origin of the variance amplification remains unresolved.

l495-l496: omit "as it better preserves ..."

We agree with the referee that the original phrasing was not sufficiently cautious, particularly regarding strain organization, whose physical realism cannot be assessed with the available validation data. However, the sharpness of SSH gradients was directly compared with SWOT L3 in the case studies (Case 3), where 4DvarNet more closely reproduced the observed gradient magnitudes than the other products. We have therefore retained a qualified reference to SSH gradient sharpness while removing the unsupported claim about strain organization, and have added a note urging caution in the interpretation of these features.

l502: Why does inclusion of the neural networks "appear particularly promising"? Your results appear to show the opposite is true.

We thank the referee for this valid criticism. We have adjusted the original text to better separate the current performance of the 4DvarNet product from its conditional future potential, rather than implying that the method is inherently superior based on the present results. In particular, we have clarified that the “promising” aspect refers to a longer‑term methodological perspective, not to the overall skill of the current experimental product.

We would like to explain our cautiously positive view of 4DvarNet based on the following considerations. First, observational data for submesoscale processes remain relatively scarce, which means that the training and validation of neural‑network‑based methods still have considerable room for improvement. For instance, 4DvarNet was the only product able to detect a coherent ~10 km eddy clearly visible in SWOT L3, suggesting that data‑driven variational methods can extract fine‑scale information that other approaches currently miss; with more high‑resolution observations and high‑quality model outputs, this capability could be further strengthened. Second, the current 4DvarNet implementation does not incorporate explicit physical constraints, and its spatial discontinuity is amplified in Lagrangian diagnostics, which are particularly sensitive to small‑scale velocity inconsistencies. This does not negate the potential of the methodology; rather, it highlights that the present configuration is not yet fully optimized. If such limitations are addressed—for example, by integrating dynamical regularization or improving spatial coherence—data‑driven variational methods could complement physics‑based approaches in resolving fine‑scale dynamics. We have therefore adjusted the original passage to reflect this more balanced view, while emphasizing that any advancement of such methods must be accompanied by rigorous validation.

Please proofread the references list more carefully. I note some problems in Le Guillou 2025 with a quick spot-check, for example.

We thank the referee for this observation. We have carefully proofread the entire reference list and corrected several formatting inconsistencies. In particular, we have fixed the title, spacing, and journal name entry to accurately reflect the published version. All other references have also been checked for correctness and consistency with the journal style.

The careful and constructive review is sincerely appreciated—it has meaningfully improved the rigour and clarity of the paper. The revised text will provide a more balanced, evidence‑based assessment of the three products.

We thank the referee for the constructive and encouraging assessment, and for the valuable suggestions to strengthen the manuscript. We have carefully considered all comments and have revised the manuscript accordingly. Below we provide a point-by-point response.

(l. 15) typo: mprediction -> prediction. I did not find any other obvious typos in the main text but maybe good to double check.

Thank you for catching this. The typo has been corrected, and we have re-checked the whole manuscript for similar errors.

(l. 49-59): there are a couple of other studies the authors can cite wrt the ongoing efforts to understand the SWOT noise / effective resolution and extract velocities from the SWOT data. These include: Archer et al., 2025, Carli et. al., 2025, Wang et al., 2025, and Tranchant et al., 2025.

We thank the referee for pointing out these relevant studies. We have added the suggested references to the introduction and discussion where appropriate, notably in the paragraphs concerning SWOT noise characteristics, effective resolution, and velocity extraction methods. The new citations strengthen the context for the L4 product evaluation.

(l. 95-109): Can the author provide some context about how the various schemes treat small-scale SSH variability? Are unbalanced motions implicitly filtered out of MIOST and 4DvarQG? A short discussion here could help provide context for the later results.

We agree that this context is important for interpreting the later dynamical diagnostics, and we have added a short paragraph in Section 2.1 to clarify how each scheme handles small-scale and unbalanced variability. The three approaches differ fundamentally in this respect. MIOST does not filter unbalanced motions through an explicit dynamical constraint; instead, it represents a prescribed set of variability modes—geostrophic mesoscale, barotropic, and equatorial wave components—in a reduced wavelet basis with mode-specific covariances. Variability that lies outside these modeled modes is not reconstructed and is effectively damped by the scale-dependent covariance regularization. 4DvarQG, by contrast, imposes quasi-geostrophic balance as an explicit dynamical constraint, so ageostrophic motions are filtered out by construction. 4DvarNet is trained end-to-end on 1/60° NATL60 simulations that contain submesoscale and ageostrophic variability, and because its learned prior is not restricted to geostrophic balance, it has in principle the capacity to represent such signals. We also note, however, that the available validation data cannot establish whether the additional small-scale features produced by 4DvarNet correspond to true ageostrophic motions or to amplified noise; this caution is now stated in the revised text.

(l. 115-120): Small quibble with the SWOT L3 version - could the author specify whether they are using the “Smoothed” or “Unsmoothed” version of the v2.0.1 SWOT SSH data?

We have clarified this in the revised manuscript. In the original analysis we used the Expert sub-product of the SWOT L3_LR_SSH v2.0.1 dataset, which is provided on the 2-km grid rather than the 250-m native-grid Unsmoothed sub-product. We note that “Expert” refers to the extended content of the product (additional layers such as sigma0, MSS, absolute geostrophic currents, quality flags, and corrections) and is not itself a filtering designation; the SSH field was used at its delivered 2-km resolution without any additional spatial smoothing.

(l. 115-120): Release v3.0 of the L3 data includes SSH gradients calculated on spline-filtered fields ... Presumably the authors used v2.0.1 for consistency with the various L4 products, but I’m curious if the using the v3.0 filtered fields improves the agreement in Section 4. Could be worth it to take a look at this (for example Figures 9-12) and make a note of any difference or lack thereof in the text.

Thank you for this suggestion. We confirm that v2.0.1 was selected to maintain consistency with the L4 products (the input SWOT L3 data for these products is v1.0), as the referee anticipated. We have additionally examined the v3.0 spline-filtered fields and found that they lead to noticeable changes in the inferred flow structures (Figure R1 of reply). We will therefore add an appendix section in the revised manuscript to briefly discuss these differences, rather than modifying the main analysis.

(l. 125-128): Have the authors experimented with correcting for the Ekman component as in Tranchant (2025)?

We thank the referee for raising this point. We agree that removing the Ekman component is meaningful for reducing representativeness errors in velocity validation. In the present study, however, the influence of the Ekman contribution on the relative comparison between products is largely eliminated by the way the metric is constructed: the gain/loss ratio is based on the difference between two RMSE values, and the Ekman-related error, which is common to all L4 products under the same drifter observations, is substantially removed during this subtraction step. The relative inter-product comparison is therefore expected to be far less sensitive to the Ekman signal than the absolute RMSE values themselves. We nonetheless acknowledge that the absolute RMSE estimates would benefit from an explicit Ekman correction, and we plan to explore this in future work.

Figures 3-4: (very minor suggestion) it may be useful to include the region boundaries on one or more of the subplots in each figure, if there is a way to do that cleanly.

A good suggestion. We have added the region boundaries to the RMSE and gain/loss maps in Figures 3 and 4 using thin black contours, which does not interfere with the color shading. This makes the spatial interpretation of the regional differences easier.

Section 3.1: it would be helpful to see a plot or plots of the performance changes binned across the different regions that the author is describing verbally in the text. Scatter plots or histograms showing the spread in RMSE or gain/loss ratios over all of the pixels in each region would be interesting. It may be ok to exclude Region 1 here, or push these plots to an appendix or supplement.

We thank the referee for this suggestion. Visualizing the spread of the performance metrics within each region will add useful quantitative support to the regional comparisons described in the text. We will add such plots to the appendix in the revised manuscript. In addition, we have identified some errors in the statistical information presented in Figure 3 of the original manuscript, which we will also correct in the revised version.

(l. 252-289, Figure 5, Figure 6): This is a really interesting section, I’m grateful for the authors contribution here. I wonder if it would be possible to include some discussion of the spread in prediction skill for the various methods across regions and/or seasons (maybe push to a supplement). It would be interesting to see the standard deviation in Gain/Loss ratios for each method overlaid on Figure 6 as shaded envelopes, for example.

We thank the referee for this positive feedback and for the thoughtful suggestion to examine the spread in prediction skill across regions and seasons. We did explore such refinements during the course of the analysis (Figure R2 of reply). Spatially, individual drifter trajectories may cross from one dynamical region to another, which makes a clean region-based attribution of the prediction errors difficult. Temporally, the limited sample sizes in both the Eulerian and Lagrangian error estimates mean that the statistics are highly sensitive to random factors, such as the start or interruption of individual drifter records. Overall, a further breakdown in space and time did not lend itself to a clear causal interpretation, and we therefore chose not to pursue this decomposition of the total error.

(l. 324-329): I think the author should expand on this discussion of the role of the potential role of the training dataset in 4DvarNET’s accuracy either here or in the conclusions. If I recall correctly NATL60 does not include large-scale tidal signals, and seems to underrepresent SSHA signal from fast-moving intertia-gravity waves. Could this deficiency play a role in it’s over-representation of Ro? By eye it seems like the highest gain regions for 4DvarNET are in the more wave-dominated region outside of the Gulf Stream.

We thank the referee for this perceptive remark. The suggestion that the NATL60-based training data may influence 4DvarNet’s tendency to over-represent Rossby number signals is well founded. Indeed, the standard NATL60 configuration does not include explicit tidal forcing, and fast-moving inertia-gravity waves are expected to be only partially represented at the model resolution and sampling timescales relevant here. These deficiencies could plausibly cause the learned mapping to misattribute SSH variance arising from unresolved wave-like variability to vortical structures, which would be consistent with the spatial pattern of the largest 4DvarNet Rossby number enhancements outside the energetic Gulf Stream. We have expanded the discussion in the revised manuscript to present this interpretation, while being careful to frame it as a plausible explanatory hypothesis rather than a demonstrated causal mechanism, because the available independent observations are insufficient to definitively separate balanced and unbalanced contributions at these scales. We have also added a cautionary note to alert potential users of 4DvarNet that Rossby-number-based diagnostics in weakly energetic, wave-influenced regions should be interpreted with particular care.

We are grateful for the thorough review and believe that the manuscript has been substantially improved by addressing these comments. All changes have been incorporated into the revised manuscript.