Response to Reviewer Comments

Dear Editor and Reviewer,

We sincerely thank the reviewers and editors for their constructive feedback and thoughtful suggestions on our manuscript. We have carefully addressed each comment and made corresponding revisions to enhance the clarity, consistency, and overall quality of the manuscript. Below, we provide a detailed point-by-point response to each comment. All changes have been highlighted in the revised manuscript for ease of reference.

_____________________________________________

Point-by-Point Responses

1.    P1, l10: Replace "actual ocean environment" with "real ocean environment."

Response: We have replaced "actual ocean environment" with "real ocean environment" to better reflect the terminology commonly used in geophysical studies, as suggested by the reviewer.

2.    P1, l12-13: Rephrase for clarity: "The comparison between the VGGA and the SIO V32.1 model shows a residual mean of -0.08 Eötvös (E) and an RMS of 8.50 E, demonstrating high consistency on a global scale."

Response: The sentence has been rephrased for clarity and improved readability. The updated version maintains the original meaning while enhancing the flow.

3.    P1, l16: Consider using "multidirectional" instead of "multi-directional" for a more modern and streamlined expression.

Response: We have updated "multi-directional" to "multidirectional," as this is the more modern and concise form, in line with current scientific writing conventions.

4.    P2, l29: Specify that the paper used VXX, VYY, and VZZ.

Response: We have provided further clarification that the study specifically utilized the gradients of gravity from the GOCE satellite, including the components VXX, VYY, and VZZ, to avoid any ambiguity and provide more specific details about the data.

5.    P2, l44: Maintain consistency in terminology. Since "gradients of gravity" was used earlier, ensure it is used consistently instead of "gravity gradients."

Response: We have ensured that the term "gradients of gravity" is used consistently throughout the manuscript to maintain uniformity and avoid confusion.

6.    P3, l86: Replace "mean sea surface" with its abbreviation MSS after first defining it. Refer to the https://www.earth-system-science-data.net/submission.html#reference for consistency.

Response: We have defined "mean sea surface" (MSS) at first mention and used the abbreviation consistently thereafter, adhering to the recommended formatting for clarity and consistency.

7.    P4, l118: Clarify that only the "curv" dataset of SIO V32.1 was used, rather than the entire dataset. Update Figure 4 accordingly.

Response: We have clarified that only the "curv" dataset of the SIO V32.1 model was used in the analysis. Additionally, we have updated Figure 4 to accurately reflect this change.

8.    P5, l128: The model's name, SDUST2023VGGA, is acceptable; however, inconsistent use of VGGA throughout the text creates confusion. Ensure a clear distinction is made.

Response: We have revised the manuscript to use the model name "SDUSTVGGA" consistently throughout, ensuring clarity and avoiding any confusion between different references to the model.

9.    P6, Fig 1: While Arial font is acceptable, the latitude/longitude labels and partition indices lack clarity and should be improved. For Fig 2, the title should include "example," as seen in Fig 3, to account for the partition changes beyond 60° latitude.

Response: We have improved the clarity of the latitude/longitude labels and partition indices in Figure 1 for better readability. We have also updated the title of Figure 2 to include the word "example," aligning it with Figure 3, to reflect the partition changes correctly beyond 60° latitude.

10.    P6, l155: Resolve the inconsistency between VGGA and SDUST2023VGGA to avoid reader confusion.

Response: Inconsistencies between "VGGA" and "SDUST2023VGGA" have been resolved, and "SDUSTVGGA" is now used consistently throughout.

11.    P7, l161: Address grammatical issues in this line.

Response: The grammatical issues in the specified line have been corrected to enhance readability and ensure accurate communication of the intended meaning.

12.    P7, l175: Reorganize the language to improve clarity and readability.

Response: The language has been reorganized to improve both clarity and readability, ensuring a more coherent presentation.

13.    P7, l184: Use "geoid" instead of "geoid structure," and enhance the explanation of Equation (6).

Response: The term "geoid structure" has been replaced with "geoid" to align with standard geophysical terminology. Additionally, we have expanded the explanation of Equation (6), providing more detailed descriptions of the symbols and wavelengths involved.

14.    P8, Fig 3: The use of bold Arial font enhances visibility. Apply this style to Fig 1 for consistency.

Response: We have applied the bold Arial font style to the labels and text in Figure 1 to ensure consistency with the style used in Figure 3, improving the overall visual clarity.

15.    P8, l186: Replace "multiple directions" with "multidirectional," and revise Equation (10) to align with the weighted least squares method described earlier.

Response: The phrase "multiple directions" has been replaced with "multidirectional," as it is more precise. We have also revised Equation (10) to ensure it aligns with the weighted least squares method described earlier in the manuscript.

16.    P8, l189: Consider replacing "formula" with "equation," as it is more commonly used in technical writing.

Response: "Formula" has been replaced with "equation" to adhere to more conventional technical writing terminology, which enhances the manuscript’s consistency.

17.    P8, l198: The formatting of equations is acceptable and aligns with journal requirements.

Response: No changes were needed, as the formatting of the equations already complies with the journal's requirements.

18.    P9, l203: Replace "directions" with "components" for technical accuracy.

Response: "Directions" has been replaced with "components" to reflect more accurate technical language in line with the terminology used in the field.

19.    P9, l207: Ensure matrices are consistently printed in boldface.

Response: All matrices have been reviewed and consistently formatted in boldface throughout the manuscript, as per the journal's guidelines.

20.    P10, Fig 4: The handling of overlapping partitions is explained in Fig 4 but is not adequately addressed in the text. Add a clear explanation.

Response: We have added a detailed explanation in the manuscript regarding the handling of overlapping partitions, clarifying the trimming and merging processes. Figure 4 has been updated to better illustrate these steps.

21.    P9, l217: State the degree and order of XGM2019e used in model construction.

Response: We have clearly stated that the XGM2019e model was used up to degree and order 2190, providing more transparency on the model's configuration.

22.    P9, l218: There seems to be an extraneous “)” that might be a typographical error. Additionally, the term "estimated" could be replaced with a more precise term. Reorganizing this paragraph would enhance readability and clarity.

Response: The typographical error has been corrected, and the term "estimated" has been replaced with more precise language. The paragraph has also been reorganized for better readability and clearer communication.

23.    P12–13: Review references and ensure consistent use of latitude/longitude.

Response: We have reviewed and ensured the consistent use of latitude/longitude throughout the manuscript, removing any tangential references that could confuse the reader.

24.    P14, l305: The term "additional" might not accurately describe the filtering process. It would be clearer to specify that the three-sigma criterion filters 1.41% of the data.

Response: The description of the filtering process has been clarified to specify that the three-sigma criterion filters out 1.41% of the data.

25.    P15, Fig 7: Correct discrepancies in labels and data in the top-right corner of the figure.

Response: Discrepancies in labels and data in the top-right corner of Figure 7 have been corrected to match the corresponding data in the manuscript.

26.    P15, l330: Remove repeated text caused by potential copy-paste errors.

Response: Repeated text has been removed to streamline the manuscript and ensure that the content flows logically without redundancy.

27.    P18, l354: Simplify "residual values" to "residuals" per the https://www.earth-system-science-data.net/submission.html.

Response: "Residual values" has been simplified to "residuals," in accordance with the journal's submission guidelines.

28.    P19, l379: Correct noun errors in this line.

Response: Noun errors in the specified line have been corrected to ensure clarity and proper grammatical structure.

29.    P19, l389: Merge "The modeling results in different regions are shown in Figure 10." with the previous paragraph for better flow.

Response: he sentence has been merged with the preceding paragraph to improve the flow of the text and create a more cohesive structure.

30.    P20, Fig 9: While the color scheme is visually appealing, bolden the text to improve clarity.

Response: The text in Figure 9 has been boldened to enhance its visibility and readability.

31.    P21, Fig 10: Thicken the axis lines for better readability.

Response: The axis lines in Figure 10 have been thickened to improve readability, ensuring that the figure is clearer and easier to interpret.

32.    P22, Section 5: To improve the organization and readability of the manuscript, I recommend that this section be moved to a separate subsection under Section 5. Additionally, while the results presented here reflect an initial attempt by the authors, and the manuscript appropriately acknowledges their limitations, these results still offer some level of validation for the accuracy of the model.

Response: A new subsection under Section 5 has been created to improve organization.

33.    P22, l429: Use the format "hereafter referred to as SDUSTVGGA" consistently throughout the text for clarity.

Response: The format "hereafter referred to as SDUSTVGGA" has been applied consistently throughout the manuscript for clarity and to avoid ambiguity.

34.    P23, Fig 11: Consider splitting this figure into two for better presentation.

Response: Figure 11 has been split into two separate figures to improve clarity and presentation.

35.    P24, l480: Rewrite the conclusion to remove redundant expressions and incorporate specific details from the results and analysis.

Response: The conclusion has been rewritten to eliminate redundancy and incorporate more specific details drawn from the results and analysis, ensuring a more concise and impactful summary.

36.    P28, l594: The citation of Kim et al. does not convincingly support the manuscript's findings and should be removed.

Response: The citation of Kim et al. has been removed as it was not directly relevant to the manuscript’s findings, thereby improving the focus and relevance of the references.

We hope the revised version meets your expectations and are grateful for the opportunity to improve our work based on your valuable input. Should you have further questions or suggestions, we would be happy to address them.

Best regards,

Jinyun Guo

Dear Reviewer,

Thank you for your valuable feedback and constructive suggestions on our manuscript. We have carefully reviewed and incorporated the comments from both reviewers to improve the experimental procedures and result analysis. These revisions have significantly enhanced the quality of our work.

As the interactive discussion platform does not support the submission of the full manuscript, we have uploaded the updated figures reflecting the changes based on your recommendations and those of the other reviewer. The complete revised manuscript, which addresses all the feedback, will be submitted through the journal's formal submission system.

We appreciate your time and effort in reviewing our work and hope that the revised version addresses all your concerns.

Best regards,

Jinyun Guo

Dear Reviewer,

We sincerely thank the reviewers for their time, effort, and thoughtful comments on our manuscript. Your valuable feedback has played a crucial role in improving the quality of our work. Below, we provide a point-by-point response to address each of your comments in detail. We have carefully considered all suggestions, and where appropriate, revised the manuscript accordingly to clarify our methods and enhance the overall presentation of the study.

Please note that, due to the limitations of the current online review system, we are unable to attach the updated manuscript directly within this response. However, all suggested revisions have been incorporated, and additional adjustments have been made to further strengthen the manuscript.

Point-by-Point Responses：

1.    P1L8: The order of the gravity field model should be clearly specified. Additionally, the term "original geoid" is used incorrectly and should be corrected for accuracy.

Response: We have clarified the degree and order of the gravity field model in the manuscript and corrected "original geoid" to "full-wavelength geoid" to ensure accuracy.2.    P1L18: The term "SDUST2023VGGA model" should be used consistently throughout the text instead of alternating with "dataset" to avoid confusion.

Response:  We have ensured consistent use of the term "SDUST2023VGGA model" throughout the manuscript and replaced all instances of "dataset" to prevent confusion.

3.    P1L20: FYI, the SWOT-derived VGG has been released by SIO using wide-swath data, the first evaluation suggested that this dataset was much better than that derived solely from nadir altimetry (1 year SWOT was better than 30 years of nadir altimetry). The authors may include the SWOT information in deriving the global VGG.

Response: Thank you for highlighting the potential of SWOT-derived VGG data. In our study, we utilized multi-year mean sea level (MSS) data for the following reasons:

a. The currently available SWOT data spans approximately one year, which is insufficient for developing multi-year averages required for stable long-term trends.

b. Multi-year MSS data helps reduce the influence of transient ocean phenomena, leading to a more reliable VGGA model.

c. SWOT data lacks directly usable MSS models, limiting its immediate applicability to our methodology.

We recognize SWOT's value and plan to incorporate it in future studies to refine and validate the VGGA model further.

4.    P3L55-L64: The language in this section should be restructured to enhance clarity and readability.

Response: We have restructured this section to improve clarity and enhance readability.

5.    P3L64: Why not use observed SSHs from multi-satellite missions, why used an existing MSS model for deriving the VGG? The authors may include the possible reasons.

Response: Thank you for this thoughtful question. We chose to use the DTU21MSS model instead of directly using observed Sea Surface Heights (SSH) from multiple satellite missions for the following reasons:

a. The DTU21MSS model provides long-term stable sea level data, optimized and validated over multiple years, ensuring consistent trends. In contrast, multi-satellite SSH data may introduce inconsistencies due to differences in satellite missions and processing methods.

b. The DTU21MSS model effectively mitigates oceanic phenomena (e.g., tides, wind waves), ensuring reliable data. Using raw multi-satellite SSH data would require additional processing, which is not yet fully integrated into our current methodology.

c. Integrating SSH data from various satellites involves complex calibration to ensure consistency and accuracy, whereas the DTU21MSS model offers a validated, streamlined data pipeline that meets our requirements.

By using the DTU21MSS model, we ensure that the VGGA derivation is based on reliable and well-processed data, crucial for capturing long-term sea level trends.

6.    P3L65: It appears that only the vertical gravity gradient anomaly has been modeled. Consequently, the study's objectives should be revised to accurately reflect this specific focus.

Response: Thank you for your observation. We have revised the study's objectives to explicitly state that the focus is on modeling the vertical gravity gradient anomaly, aligning the objectives with the study's scope.

7.    P3L86: There are multiple instances of inconsistent abbreviation usage throughout the manuscript. Please ensure that all abbreviations are defined upon their first occurrence and maintained consistently throughout the text.

Response: All abbreviations have been defined at their first occurrence, and we have ensured consistency in their usage throughout the manuscript.

8.    P4: While the CNES-CLS22 MDT is mentioned as having increased resolution, the original resolution of the model is not specified and should be included. Additionally, the order of the XGM2019e model is not mentioned and should be provided for completeness.

Response: Thank you for your feedback. We have updated the manuscript to specify the resolution of the CNES-CLS22 MDT as 7.5′. Additionally, we have included the order of the XGM2019e model for completeness. These additions enhance the clarity and accuracy of the model descriptions.

9.    P5L129: The term "reference data" is inappropriate in this context and should be revised to a more suitable term.

Response: We have revised the text to clarify the specific objectives of using the GEBCO model: first, to assess the performance of SDUST2023VGGA in different seafloor topographies, and second, to examine the correlation between SDUST2023VGGA and the GEBCO model, particularly in terms of vertical gravity gradient anomalies and their ability to explain seafloor topography. This revision directly addresses the study's aims without the use of the term "reference data."

10.    P5L139-155: Several uncommon terms are used in this section. Consider replacing "several" with "multiple" and "set to" with "defined as" to adopt a more formal tone. Additionally, substituting "Clip" with "Crop" would improve clarity and understanding.

Response: Thank you for these helpful suggestions. We have implemented the following changes to improve clarity and formality:

a. We have replaced "several" with "multiple" to adopt a more formal tone.

b. We have replaced "set to" with "defined as" for better precision and consistency.

However, we have retained the term "Clip" instead of substituting it with "Crop," as "Clip" is widely recognized in geospatial analysis for describing the exclusion of data beyond a defined boundary. Using "Crop" could introduce ambiguity by implying a visual adjustment rather than a computational operation. We appreciate your understanding of this decision and your valuable input.

We appreciate your understanding and thank you again for your valuable feedback.

11.    P6L155: The use of "initially" creates confusion and hinders readability. This phrasing should be revised for greater clarity.

Response: Thank you for pointing this out. We have removed the term "initially" to eliminate potential confusion, resulting in a clearer and more straightforward explanation of the model's construction.

12.    P7L164: The variable "h" in Equation 1 is not defined. Please provide a clear definition or description of this variable.

Response: We thank the reviewer for identifying the omission of the definition for the variable h in Equation (1). Clearly defining all variables is essential for the manuscript's clarity and comprehensibility.

13.    P7L170: Since ∇²U = 0, the vertical component can be expressed using the two horizontal components. Therefore, the original phrasing is unsatisfactory and needs to be improved to accurately convey this relationship.

Response: Thank you for your observation. We have revised the phrasing to clearly explain how the Laplace equation constrains the vertical gravity gradient anomaly in terms of the geoid and its horizontal derivatives. The revised text explicitly describes the relationship between the vertical and horizontal components, ensuring accurate communication of this concept.

14.    P7L175: The rationale behind increasing the resolution should be explained to justify this methodological choice.

Response: We appreciate the reviewer’s comment. We have added an explanation in the manuscript to justify the increase in resolution, emphasizing its importance in enhancing the spatial detail and accuracy of the modeled vertical gravity gradient anomaly. This addition clarifies the reasoning behind our methodological choice.

15.    P7L181: Replace "original" with "full wavelength" to enhance the reader's understanding of the "remove-restore" process.

Response: Thank you for the suggestion. We have replaced "original" with "full-wavelength" in the manuscript to clarify the remove-restore process and improve the overall accuracy of the description.

16.    P8L193: Please verify the accuracy of this citation, as the manuscript does not appear to include any analysis regarding the calculation of window size and its impact on the computation.

Response: We appreciate the reviewer pointing this out. After reviewing the manuscript, we confirmed that it does not include an analysis of window size calculation or its computational impact. As such, we have removed the citation to maintain accuracy and relevance.

17.    P9L203: We recommend referring to it as "component" rather than "direction" to maintain consistency and precision in terminology.

Response: Thank you for the recommendation. We have revised the manuscript to replace "direction" with "component" to ensure consistency and precision, aligning with standard geophysical terminology..

18.    P9L205: Based on your description, the process at this point should involve calculating the residual geoid rather than the geoid. Please verify and correct this accordingly.

Response: You are correct that at this stage in the process, we should be calculating the residual geoid rather than the geoid itself. We have reviewed the manuscript and corrected the relevant section to reflect the calculation of the residual geoid. We have updated the manuscript accordingly to ensure accuracy and consistency with the described process.

19.    P9L207: The variable "l" still needs to be defined. Additionally, the restore process should be clarified. The explanation of the remove-restore process in other sections is more detailed than in the methods section, which is inconsistent and needs to be addressed.

Response: Thank you for highlighting these points. We have made the following revisions:

a. Defined l as the horizontal distance between two points in the calculation.

b. Clarified the restore process to align with the detailed explanation provided in other sections, ensuring consistency and precision in describing the remove-restore methodology.

20.    P9L218: The original text refers to the second-order partial derivative of the MSS data. It should clarify whether this pertains to the second-order partial derivative of the geoid or the residual geoid.

Response: Thank you for identifying this ambiguity. The calculation pertains to the geoid height, not the MSS or residual geoid directly. We have revised the text to clarify this, ensuring it accurately reflects the process of computing geoid height and its second-order partial derivatives.

21.    P10 Fig 4: Does "mean" in the flowchart refer to the operation on the overlap section? Additionally, please provide a clear definition of "overlap" within the manuscript to ensure clarity.

Response: We have added a detailed explanation of the trimming and merging processes for overlapping partitions in the manuscript. Figure 4 has also been updated to clarify the use of "mean" in relation to the overlap section.

22.    P14: The author applied two rounds of filtering to the residuals for data analysis. It should be clarified whether the filtered data were used in subsequent comparisons and processing to Response: understand the impact of this filtering on the results.

Thank you for pointing this out. We have updated the manuscript to explicitly clarify the purpose of the filtered data and its role in subsequent comparisons and analyses. This differentiation ensures the impact of the filtering process on the results is well understood.

23.    P15, “Discussion”. The SIO has released SWOT refined VGG data, the authors can compare your own data with the SIO’s product. I suggest the authors to add these results regarding the comparisons with SWOT-derived VGG.

Response: Thank you for this insightful suggestion. In response, we have added a comparison between our results and the SWOT-derived vertical gravity gradient (VGG) data from SIO in the “Discussion” section. This comparison validates our data and highlights key similarities and differences. Additionally, we have extended the discussion by incorporating an analysis of the relationship between our results and GEBCO bathymetry.

24.    P15L324-356: The discussion is overly verbose, which impacts readability. The text should be reorganized for clarity and conciseness, focusing on the most relevant points and eliminating redundant information.

Response: Thank you for the valuable feedback. We have reorganized the discussion section to enhance clarity and readability. Redundant information has been removed, and the revised text focuses on the most relevant points, ensuring a concise and precise presentation of the results and their implications.

25.    P19L375-379: The results appear to be correct; however, there is a concern that when the slope is below 1%, the STD and RMS values appear to be somewhat larger. Please provide possible explanations for this observation.

Response: Thank you for your insightful comment. In low-slope areas, the residual geoid model is more sensitive to noise and systematic errors in the input data. This heightened sensitivity may lead to slightly larger STD and RMS values, even though these areas are typically expected to exhibit higher model stability. We have revised the manuscript to include this explanation.

26.    P20: For Region C in Fig. 9, was land data included in the calculation? The color bar suggests that this region has complex terrain and areas extending above sea level, which could affect the calculation results. If land data was used, the analysis in this section should be revisited to account for these factors.

Response: Thank you for the observation. Land data was not included in the calculation. All experimental data were processed using GMT to remove land areas before the analysis. This ensures the results are based solely on oceanic regions. Additionally, the analysis across different regions confirms consistency and excludes any interference from land areas.

27.    P22L444-L449: The relationship between VGGA and seabed topography is not linear. Consider removing the Linear Regression analysis unless it is included for comparison with other methods. Please evaluate the primary purpose of this analysis when making your decision.

Response: Thank you for your feedback. After reconsidering the role of linear regression, we acknowledge its limitations in capturing the nonlinear relationship between the GEBCO data and the VGGA model. However, we have retained it as a baseline comparison to highlight the inadequacies of simpler models. The revised manuscript emphasizes the superior performance of non-linear methods, such as SVR and MLP, which better capture the complex relationships between the VGGA model and bathymetric data.

28.    P25: The conclusion section lacks depth, and some analyses, such as those of SVR and MLP, are not well summarized. Expanding this section to include a comprehensive summary of all key findings would strengthen the manuscript.

Response: We have revised the conclusion section to provide a more comprehensive summary of key findings, including specific results from the SVR and MLP analyses. This revision eliminates redundancy and strengthens the synthesis of the study’s findings, offering a robust and concise conclusion.

29.    P27: The format of the References needs to be standardized. Please ensure that all references adhere to the journal's formatting guidelines for consistency and professionalism.

Response: The references have been revised to adhere to the journal's formatting guidelines, ensuring consistency and professionalism throughout. Additionally, some less relevant references have been removed to maintain the focus and relevance of the cited literature.

Once again, we sincerely thank the reviewers for their constructive comments and insightful suggestions. We believe these revisions have significantly improved the manuscript, and we look forward to receiving your further feedback.

Best regards,

Jinyun Guo