We sincerely thank the reviewer for the detailed and constructive feedback. We greatly appreciate the time and effort devoted to evaluating our work. Please find our point-by-point responses below.

Questions

Q1: Line 106: what does $\mathbf{x}$ contain here? Is it just the $\theta$ and $\phi$ ?

Response: Yes, $\mathbf{x}$ refers only to latitude and longitude: $\theta$ and $\phi$. We will revise Lines 90–91 to clarify this as follows: "..., parameterized by latitude–longitude coordinates $\mathbf{x} = (\theta, \phi) \in \Omega = [-\frac{\pi}{2}, \frac{\pi}{2}] \times [-\pi, \pi]$."

Q2: Figure 2: does the source module implement both the source term and the conservation loss?

Response: Thank you for raising this helpful point. The source module handles the source term exclusively, while the mass conservation loss is implemented separately by computing (1) the inter-frame change in $\bar{\varphi}$ and (2) the frame-wise difference between the coarse nutrient field $\bar{\varphi}$ and the refined field $\hat{\varphi}$. We agree that Figure 2 may be misleading in this regard, and we will revise it by removing the mass conservation block to avoid potential confusion.

Q3: Line 130: could the authors show why the perturbation term scales with $\Vert \delta \Vert$ ?

Response: Thank you for the insightful question. Let us write the velocity perturbation as $\delta = \|\delta\| \cdot \hat{\delta}$, where $\|\delta\|$ is a spatially varying scalar field and $\hat{\delta}$ is a unit vector field. Applying the product rule:

This decomposition shows that the second term in the perturbation scale linearly with $\|\delta\|$. We will clarify this point in the revised text.

Q4: Line 145 - 146: the authors state "The initializer is trained to be robust to flow perturbations ...". How exactly is this done?

Response: Thank you for this thoughtful question. To enhance robustness to flow perturbations, we apply a Fourier filter in the coarse module to remove high-frequency eddy components from the flow field before passing it to the initializer. This ensures that the initializer operates on the large-scale, stable part of the flow and is less sensitive to high-frequency variability. The original phrasing "is trained to be robust" reflects that all components of NUTS are trained jointly. To more accurately convey this architectural intent, we will revise Lines 145-146 to read: "The initializer is designed to operate on filtered, low-frequency flow fields, ensuring robustness to high-frequency perturbations...".

Q5: Line 163: is it this loss that is driving the updates for all the learnable parameters in Figure 2?

Response: Yes. All learnable parameters in Figure 2 are optimized via the total objective $\mathcal{L}_{\text{total}}$.

For clarity, we will revise the sentence to: The final training objective is "The final training objective is $\mathcal{L}_{\text{total}}=...,$ which governs the optimization of all learnable components in NUTS.", which governs the optimization of all learnable components in NUTS.

We hope this revision makes it clearer that $\mathcal{L}_{\text{total}}$ governs the training of all learnable components in the model.

Q6: Line 260 - 261: could the authors write out the formula being used for computing the NRMSE?

Response: Thank you for raising this point. We provide the full formula for computing NRMSE below and refer the reviewer to Appendix D.2 of the supplementary material for a detailed explanation. Let $y_{thw}$ represents the ground-truth value at a give time $t$, latitude $h$ and longitude $w$, and $u_{thw}$ is the corresponding reconstructed value, the RMSE is calculated as follow:

where $\alpha(h)=cos(h)/(\frac{1}{H}\sum_{h'}cos(h'))$ is the latitude weight. The NRMSE is calculated by normalizing RMSE with the mean of the ground-truth values:

NRMSE quantifies the relative reconstruction error normalized by the mean nutrient concentration, providing a scale-independent measure of accuracy. We hope this clarification is helpful, and please refer to Appendix D.2 of the supplementary materials for further details.

Q7: Are the numbers after the $\pm$ in Table 3 standard errors? Or something else? Please clarify.

Response: Yes, the numbers following the $\pm$ symbol in Table 3 are standard errors computed over 3 trials. We will revise the caption in the final version to explicitly state this for improved clarity.

Q8: Figure 4: it's not super clear what P and N in the legend are without the context in the surrounding text. Maybe these can just be written out into phosphate and nitrate for improved readability.

Response: Thank you for your suggestion. We use abbreviations "P" for phosphate and "N" for nitrate due to space limitations. We totally agree that writing out the full terms would improve clarity. We will update the legend accordingly in final version, where space limitations are less restrictive.

Q9: While lines 312 - 315 state that naive-B suffers large errors because it directly propagates the full velocity field without filtering, it seems from Figure 5 that NUTS suffers (relatively) equally for gamma tending towards -1. Could the authors comment on this?

Response: Thank you for your insightful observation. In our experiments, the perturbation level is defined as $\delta = \gamma \mathbf{v}^\*$, where $\gamma < 0$ corresponds to removing a portion of the eddy components from the flow. For instance, setting $\gamma = -1$ yields a modified flow $\mathbf{w}^* = \bar{\mathbf{w}} + \frac{1}{\epsilon}(1 + \gamma)\mathbf{v}^* = \bar{\mathbf{w}}$, effectively eliminating the eddy-driven information. This removal leads to degraded performance across models, including NUTS, as the fine-scale variability essential for accurate reconstruction is lost.

Q10: The paragraph starting on Line 332 doesn't make any reference to Table 4 even though it's the results in Table 4 that are under discussion. Maybe the authors could add an explicit reference in the same way they do it in the next paragraph?

Response: Thank you for raising this point. We agree that the reference to Table 4 should be made explicit in the paragraph discussing Obs. 5. We will revise Line 334-336 to "Among several options, the Fourier filter achieves the lowest NRMSE on both daily (0.136) and monthly (0.151) tasks, outperforming wavelet, Gaussian, and moving average filters (Table 4a)." and Line 339-340 to "Lower ratios—removing more unresolved eddy components—consistently improve reconstruction accuracy, while higher ratios degrade performance (Table 4b)", including direct reference to Table 4.

Q11: Table 6: it seems there is result tables for a - f but the caption only has explanations for a - e (some of which don't match their respective table, I think). Please fix.

Response: Thank you for your suggestion. In the caption of Table 6, we merged the explanations for Tables 6(b) and 6(c) under caption (b), which may have caused confusion. We will revise the caption to " ...(b) Analysis of model depth in the coarse module; (c) Analysis of model depth in the refinement module; (d) Evaluation of source and conservation loss terms; (e) Quantification of the impact of auxiliary input variables; (f) Assessment of sensitivity to temporal interval length... " in the final version, avoiding potential confusion.

Q12: Table 6 (f): what are the units of the interval length? And is this the length of the prediction or the length of the context? Also, why are the short intervals worse than the intermediate ones? This feels counterintuitive.

Response: Thank you for your thoughtful question. The interval length is measured in days for the Daily dataset and in months for the Monthly dataset. This interval length represents the length of the context used by the model. We observe performance peaks at a moderate interval length. Short contexts provide insufficient temporal information for the initializer to capture temporal dependencies, while long contexts introduce noise and uncorrelated information which may hinder model performance.

Q13: Line 260: change "obatained" to "obtained"

Response: We appreciate your careful review, and we will revise the grammar in the final version.

Thank you once again for your valuable feedback. We hope our responses address your concerns, and we would be happy to clarify further if needed. We look forward to your thoughts.

We sincerely thank the reviewer for the professional and valuable feedback. Please find our detailed responses below.

Weakness

W1: No uncertainty quantification.

Response: Thank you for raising this point. While NUTS does not explicitly model uncertainty, it is designed to handle key sources of variability—such as eddy-induced perturbations—through architectural decomposition and robust refinement. This makes it practically valuable in scenarios where accurate, physically consistent reconstruction is prioritized over full posterior characterization. That said, we agree that uncertainty quantification is an important next step, and NUTS provides a natural foundation for future extensions via ensemble or variational methods. We will clarify this perspective in the revised manuscript.

During the rebuttal phase, we conducted a preliminary uncertainty analysis using a simple ensemble approach. Specifically, we perturbed the initializer output with Gaussian noise—analogous to injecting variability into the initial condition—where the noise at each grid point was scaled to 20% of the local temporal standard deviation of ground-truth nitrate concentrations from the {Monthly} dataset. We generated 10 ensemble members and computed the relative error in total nutrient mass between NUTS and the ground truth across four representative years. The "$\pm$" values in Table T1 denote the one-sigma spread across ensemble samples.

While intentionally simple, this time-based perturbation reveals that NUTS can model meaningful initialization-driven uncertainties. As shown in Table T1, the relative errors remain low across years and months, while the ensemble spread is moderate—capturing plausible variability without overestimating uncertainty. This suggests that NUTS offers a credible starting point for uncertainty modeling. Future work will incorporate more structured perturbations—such as spatially coherent modes via EOFs—to better reflect dynamically consistent variability.

Table T1: Relative error (%) between total nutrient mass from NUTS and ground truth across four years. The $\pm$ indicates the one-sigma confidence interval.

W2: Insufficient qualitative results. The single output example in Figure 2 looks overly smooth and does not seem challenging. In Figure 3, I am concerned that the model performance is biased toward larger values, resulting in a loss of fine-scale structure despite yielding small field errors.

Response: Thank you for raising this point. We agree that qualitative evaluation adds valuable context beyond metrics. In the final version, we will include additional qualitative analysis in the supplementary material, including: (1) NRMSE maps for NUTS and baselines to show spatial reconstruction accuracy, and (2) regional time series in dynamically complex zones such as the North Pacific and Southern Ocean.

Figure 2 appears smooth due to the coarse color scale and the use of a simple example meant to illustrate model structure. We will clarify this in the caption to avoid confusion.

For Figure 3, we appreciate the concern. The figure is meant to illustrate spatial variability in nutrient dynamics—not reconstruction quality—and helps explain why phosphate is more challenging to recover. While we agree that visual support would help, we are unable to add new figures due to this year’s rebuttal policy. However, we will include additional qualitative discussion (e.g., error trends in high-variability regions) to demonstrate that NUTS preserves fine-scale structure even when coefficient values span several orders of magnitude.

W3: High model complexity vs. baselines.

Response: We thank the reviewer for highlighting this concern. We acknowledge the model size: NUTS has 125.6M parameters versus 0.3M in 4DVarNet. However, this does not translate to significantly higher cost. On matched hardware (two RTX 6000 Ada GPUs, batch size 8), NUTS trains in 92s/epoch and infers in 58s—comparable to 4DVarNet’s 94s and 46s, respectively (Appendix D.6, Table 15). The reason is that 4DVarNet relies on iterative variational optimization, which is difficult to parallelize. NUTS uses batched, multi-step rollouts with efficient GPU utilization. In addition, NUTS delivers lower error (NRMSE: 0.035 $\pm$ 0.002) and comparable runtime, despite having 400 $\times$ more parameters. For context, NUTS is also 10--20 $\times$ smaller than foundation-scale models like Prithvi (2.3B) and AtmoRep (0.7B), while being both faster and more accurate. We believe this reflects a favorable tradeoff between expressiveness and efficiency.

Questions

Q1: In Figure 2, the boxes are colored in yellow, red, and green. Please explain what each color represents and why those specific colors were chosen, if it is intentional.

Response: Thank you for pointing this out. The colors in Figure 2 are used to group components by function: yellow indicates physics-based operations within the coarse module, red denotes intermediate variables passed between modules, and green highlights trainable components in the refinement stage. The gray initializer is also trainable and grouped under the coarse module. The color scheme was chosen for clarity rather than strict semantic coding. We will add a legend and clarify the color conventions in the final version.

Q2: Have the authors employed higher‑order finite‑difference methods in their computations, and how does the approximation error vary with the order of the numerical methods?

Response: Thank you for the suggestion. During the rebuttal phase, we experimented with fourth-order central and second-order upwind differences for discretizing the advection–diffusion equation. On the Monthly nitrate dataset, this led to degraded performance: NRMSE increased from 0.151 to 0.166. We suspect this is due to numerical instability introduced by higher-order schemes, which may amplify noise in sparse observational settings.

Thank you once again for your valuable feedback. We hope our responses have addressed your concerns. Please feel free to reach out if any further clarification is needed. We look forward to your continued thoughts.

Dear Reviewer TCj8,

We hope this message finds you well. As the discussion period is nearing its end, we want to ensure that we have addressed all your concerns satisfactorily. If there are any additional questions or feedback you'd like us to consider, please let us know. Your comments are valuable to improve our work.

Thank you for your time and effort in reviewing our paper.

We sincerely appreciate the time and effort you dedicated to reviewing our paper, as well as the thoughtful and constructive comments provided. Please find our responses to your questions below.

Weakness

W1: Potential Time Drift: The design isolates the refinement module. It acts as a spatial correction but as a post-processing step only. It does not appear to feed its corrected field back into the PDE solver. This creates a risk of drifts over time, leading to poor detail in the long term rollouts. It is not clear if the learned diffusion model is consistent with the refinement module.

Response: Thank you for highlighting this concern. While the refinement module operates independently at each time step and does not explicitly feed back into the PDE solver, we address potential temporal drift via a mass conservation loss (Eqs.162-163) applied during training. This loss penalizes tracer mass discrepancies between the coarse and refined outputs, coupling the refinement and diffusion modules and enforcing physical consistency over time.

To empirically validate this design, we conducted an additional experiment during the rebuttal phase. We computed the monthly variation rate of total nutrient mass—relative to January—for two representative years (2014 and 2020). As shown in Table T1, the refinement module maintains variation within $\pm$ 0.04% throughout the year, effectively flat. In contrast, NUTS—produced by summing the refined state and predicted source—exhibits substantial drift, with deviations up to 10.6% in 2014 and 16.1% in 2020, tracking ground-truth dynamics. This confirms that our refinement strategy avoids cumulative error and preserves long-term stability despite its non-recurrent design. We will clarify this mechanism and its empirical support in the final version.

Table T1: Monthly variation rates (%) of total nutrient mass from Refinement Module, NUTS and ground-truth (G-T) across two years. The variation rate is defined as the ratio of each month’s total nutrient mass to that of January within the same year. We report the NRMSE between the variation rates over the interval.

W2: Not Scalable for Long-Term Forecasting: The model excels at reconstruction in short term intervals, but it is not shown to work for long forecasting rollouts. Since spatio-temporal transformer is used for long range effects, it may not scale well to increased time rollouts.

Response: Thank you for this thoughtful comment. We would like to clarify that NUTS is designed for spatio-temporal reconstruction, not long-horizon forecasting. Forecasting aims to extrapolate future states—often benefiting from longer rollouts—whereas reconstruction targets missing data within a fixed historical window. In this setting, the interval length is a tunable design choice. As shown in Figure 6(f), performance degrades as the interval grows too long, reflecting a tradeoff in reconstruction fidelity—not a failure to generalize in time.

We agree that long-term forecasting is a challenging and valuable direction, but it differs fundamentally in both objective and constraints. We will clarify this distinction in the final version to avoid confusion, and we consider extending NUTS to forecasting as an exciting direction for future work.

Question

Q1: Why is it that mesoscale eddies carry more energy than the mean flow? In typical eddy simulation models, or reduced order models, the large-scale flow carries the majority of the energy. Is this affected by the choice of the threshold to separate scales that is typically used in multiscale ocean flow?

Response: Thank you for this thoughtful observation. We agree that at the global scale, the mean flow typically carries more energy. Our intention was to emphasize that in localized regions—such as western boundary currents and eddy-active zones—mesoscale eddies often exhibit higher local speed than the mean flow, which strongly influences nutrient transport.

To clarify this, we will revise Lines 125--126 to: "Mesoscale eddies are small-scale (10--100 km), high-energy structures that can dominate local transport processes." and Lines 130--131 to: "...which can be large, as mesoscale eddies often exhibit higher local speed than the mean flow (Figure 2)."

Q2: As I understood, the learned diffusion term, which models the effect of the eddy components, is not coupled with the refinement module. Wouldn't the output of the refinement module directly affect the diffusion term due to the eddy components? Did you consider adding a constraint or loss term in the architecture? For instance, it seems plausible that over a long time rollout the diffusion term may drift out of sync with the refined details.

Response: Thank you for the follow-up question. We address this concern in our response to W1: while the refinement module does not explicitly feed back into the diffusion term, we impose a mass conservation loss (Eq. 162–163) that couples the coarse and refined fields during training. This constraint ensures consistency between the diffusion dynamics and the refined output, effectively mitigating drift and preserving physical coherence over time. We will clarify this interaction in the final version.

Q3: In Table 3, since NUTS has 125M params v/s the closest baseline, the U-Net which has 31M params, why not make the U-Net larger to make the number of params in both methods similar?

Response: Thank you for raising this point. During the rebuttal phase, we try scaling U-Net to 150M parameters and conduct experiments on the Monthly dataset, with nitrate being the target nutrient. We find that the reconstruction NRMSE drops from 0.187 to 0.171, achieving comparable results with NUTS, which is 0.151.

Q4: Could you report for training and inference times for the baseline methods, at least the U-Net and the 4D-VarNet?

Response: Thank you for the suggestion. We report training/inference time and VRAM usage for NUTS and all baselines—including U-Net and 4D-VarNet—in Table T2. To ensure fair comparison, all models were benchmarked under the same hardware: two RTX 6000 Ada GPUs with identical batch size (8), as detailed in Appendix D.6 (Table 15).

Despite having more parameters, NUTS achieves the lowest NRMSE while maintaining competitive runtime and memory usage. Notably, 4D-VarNet is over 400 $\times$ smaller than NUTS in parameter count, yet its training (94s/epoch) and inference (46s) times are comparable. This is due to its iterative variational optimization, which requires repeated PDE solves and limits parallelism. In contrast, NUTS uses batched multi-step rollouts with data-driven initialization, making it more GPU-efficient despite its larger size.

Table T2: Parameter, efficiency and Phosphate (sampling ratio=0.1%) reconstruction performance comparison of different models on the WOD (Daily) dataset.

Thank you again for your insightful feedback. We hope our responses have addressed your concerns. Please do not hesitate to contact us if further clarification is needed. We look forward to your continued input.

Dear Reviewer hsCa,

We hope this message finds you well. As the discussion period is nearing its end, we want to ensure that we have addressed all your concerns satisfactorily. If there are any additional questions or feedback you'd like us to consider, please let us know. Your comments are valuable to improve our work.

Thank you for your time and effort in reviewing our paper.

Thank you for taking the time to review our paper and provide your thoughtful feedback. We are glad that our rebuttal has addressed your concerns.

We sincerely thank the reviewer for the valuable feedback. Below, we provide a point-by-point response and hope the response can effectively address your concerns.

Weaknesses

W1: The learnable source/sink module (for biological processes) lacks detailed evaluation. Its impact on long-term nutrient cycling is not quantified beyond ablation (Table 6d).

Response: Thank you for your insightful comment. To quantitatively evaluate its long-term effect, we added an additional analysis during the rebuttal phase: we compute the monthly variation rate of total nutrient mass, defined as the ratio of each month's total mass to that of January in the same year, across four distinct years. As shown in Table T1, the refinement module maintains variation rates within $\pm 0.4$%, adhering to the mass conservation constraint. Moreover, by introducing the source module, NUTS closely follows the ground-truth (G-T) variation trends. Since the final output of NUTS is defined as the sum of the learned source contribution and the refinement correction, this result highlights the source module’s ability to capture seasonally varying source–sink dynamics and maintain physically consistent nutrient cycling over time. Experiments are conducted on the Monthly dataset with nitrate as the target nutrient.

Table T1: Monthly variation rates (%) of total nutrient mass from Refinement Module, NUTS and ground-truth (G-T) across two years. The variation rate is defined as the ratio of each month’s total nutrient mass to that of January within the same year.

W2: NUTS contains 125.6M parameters compared to 0.3M in 4DVarNet, leading to higher model, computational, and time complexity.

Response: Thank you for raising this concern. While NUTS has 125.6M parameters—significantly larger than 4DVarNet (0.3M)—it achieves a markedly lower reconstruction error on phosphate (NRMSE: 0.035 $\pm$ 0.002) and demonstrates comparable computational efficiency under matched hardware settings. To ensure fair comparison, we report training and inference times in Appendix D.6 of the supplementary materials (Table 15), where all models were trained and evaluated on two RTX 6000 Ada GPUs with identical batch size (8). Under this setup, NUTS trains in 92s/epoch and infers in 58s/epoch, closely matching 4DVarNet's training and inference times (94s/epoch and 46s/epoch, respectively), despite having over 400 $\times$ more parameters.

This underscores a key point: efficiency is not solely determined by parameter size. 4DVarNet incurs high cost due to its iterative variational optimization, requiring repeated forward–adjoint PDE solves and offering limited parallelism. In contrast, NUTS employs batched, multi-step PDE rollouts with data-driven initialization, enabling efficient GPU acceleration and scalable inference.

Furthermore, compared to foundation-scale models like Prithvi (2.3B) and AtmoRep (0.7B), NUTS is 10-20 $\times$ smaller, faster to train and deploy, and more accurate. It thus strikes a practical balance: accurate and efficient relative to both lightweight and large-scale baselines. Pretrained checkpoints and evaluation scripts are provided to support ease of use.

W3: Fourier filtering with strict cutoff ratio may lead to over-smoothing in dynamically complex regions such as boundary currents.

Response: We thank the reviewer for this thoughtful observation. While Fourier filtering may suppress high-frequency features in complex regions such as boundary currents, NUTS explicitly addresses this by reintroducing the normalized filtered component in the refinement module to recover eddy-driven variability. To ensure physical coherence, we further impose a mass conservation loss during refinement, preventing artificial changes in total tracer mass. This design allows NUTS to restore fine-scale detail while maintaining global consistency.

Questions

Q1: The refinement module may overlook temporal eddy dependencies, limiting long-term coherence.

Response: We thank the reviewer for this valuable point. Although the refinement module operates independently at each time step, we impose a mass conservation loss (Eq. 162–163) to ensure no artificial tracer mass is introduced. Since the homogenized PDE preserves mass at the coarse level, this constraint enforces consistency during refinement and introduces an implicit temporal linkage across the refined predictions.

We agree that capturing temporal dependencies in the eddy component could be beneficial. To test this, during the rebuttal phase, we implemented a spatio-temporal transformer that integrates 4 frames of eddy components into the refinement stage. However, performance worsened—NRMSE on nitrate increased from 0.151 to 0.162 on the Monthly dataset—and computation rose from 990 to 1215 GFLOPs. We suspect accumulated truncation errors in the coarse fields disrupt temporal attention, offsetting potential gains.

Q2.1: Figure 2 makes NUTS appear overly complex, with many inter-module connections that may hinder readability.

Response: Thank you for raising this point. In the final version, we will simplify the figure to enhance readability. Specifically, we will merge functionally related components--for example, merging the two "Coarse Nutrient Field" boxes into a single box labeled "Coarse Nutrient Field $\bar{\varphi}(\mathbf{x}_k, t)$". Additionally, we will streamline the data flow by removing some elements, such as the "Mass Conservation Loss" box, to reduce visual clutter and overlapping connections.

Q2.2: Is there over-modeling in NUTS?

Response: We thank the reviewer for this thoughtful question. We believe each component in NUTS is functionally necessary, as confirmed by extensive ablation studies. (1) In the coarse module, spatio-temporal architectures outperform static baselines, and transformer-based models consistently surpass CNNs due to superior capacity (Table 6(a)). (2) In the refinement module, a moderately deep network is essential to recover fine-scale nutrient structure from eddy flows (Figure 5, Table 6(c)). (3) The source module and conservation loss both contribute measurable gains (Table 6(d)), with the conservation loss further enforcing mass conservation (Appendix E.2 of the supplementary materials). These empirical results underscore the necessity of the proposed model components.

Q3: I would like to see the model, computational, and time complexity of the full model and each module.

Response: We thank the reviewer for highlighting this important point. Table T2 provides a detailed breakdown of parameter count, computation (GFLOPs), and runtime per forward pass (batch size = 8) for each component of NUTS. While the PDE solver has negligible parameter count (0.04M), its compute (181 GFLOPs) and runtime (75ms) are comparable to the coarse and refinement modules due to the cost of multi-step integration. The coarse and refinement modules account for most of the complexity (328 and 300 GFLOPs), yielding a total of 125.6M parameters, 990 GFLOPs, and 413ms per batch. We also refer the reviewer to Appendix D.6 of the supplementary materials (Table 15) for full comparisons against other models. Despite its larger size, NUTS achieves state-of-the-art accuracy while maintaining competitive training and inference efficiency under matched hardware settings.

Table T2: Number of parameters, computation complexity and time complexity of NUTS and its components.

Q4: Will the code be open-sourced, and if so, to what extent?

Response: Thank you for raising this point. We open-sourced the code for training and testing our NUTS, as well as the Daily and Monthly datasets. While we are prohibited to provide external links according to the guidelines, the URL in Sec 4.1 directs to the anonymous code repository containing the code and datasets.

Thanks again for your valuable reviews and we hope our response can resolve your concerns. Please don't hesitate to contact us if you have further questions. Looking forward to hearing from you.

Dear Reviewer 9Xop,

We hope this message finds you well. As the discussion period is nearing its end, we want to ensure that we have addressed all your concerns satisfactorily. If there are any additional questions or feedback you'd like us to consider, please let us know. Your comments are valuable to improve our work.

Thank you for your time and effort in reviewing our paper.