SDUST2020MGCR: a global marine gravity change rate model determined from multi-satellite altimeter data

Zhu, Fengshun; Guo, Jinyun; Zhang, Huiying; Huang, Lingyong; Sun, Heping; Liu, Xin

doi:https://doi.org/10.5194/essd-2023-498

Preprints

https://doi.org/10.5194/essd-2023-498

Preprints

11 Dec 2023

| 11 Dec 2023

Status: a revised version of this preprint was accepted for the journal ESSD and is expected to appear here in due course.

SDUST2020MGCR: a global marine gravity change rate model determined from multi-satellite altimeter data

Fengshun Zhu, Jinyun Guo, Huiying Zhang, Lingyong Huang, Heping Sun, and Xin Liu

Abstract. Investigating global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data. However, satellite gravity data exhibits low spatial resolution and signal distortion. The satellite altimetry is an important technique for observing global ocean, providing continuous multi-year data that enables the study of high-resolution time-varying marine gravity. This study aims to construct a high- resolution marine gravity change rate (MGCR) model using multi-satellite altimetry data. Initially, multi-satellite altimetry data and ocean temperature-salinity data from 1993 to 2019 are utilized to estimate the altimetry sea level change rate (SLCR) and steric SLCR, respectively. Subsequently, the mass-term SLCR is calculated. Finally, based on mass-term SLCR, we construct the global MGCR model on 5′×5′ grids (SDUST2020MGCR) applying the spherical harmonic function method and mass load theory. Comparisons and analyses are conducted between SDUST2020MGCR and GRACE2020MGCR resolved from GRACE/GRACE-FO gravity data. The spatial distribution characteristics of SDUST2020MGCR and GRACE2020MGCR are similar in the sea areas where gravity changes significantly, such as the seas near some ocean currents, the western seas of Nicobar Islands, and the southern seas of Greenland. The statistical mean values of SDUST2020MGCR and GRACE2020MGCR in global and local oceans are all positive, indicating that MGCR is rising. Nonetheless, differences in spatial distribution and statistical results exist spatial resolution disparities among altimetry data, ocean temperature-salinity data, between SDUST2020MGCR and GRACE2020MGCR, primarily attributable to and GRACE/GRACE-FO data. Compared with GRACE2020MGCR, SDUST2020MGCR has higher spatial resolution and excludes stripe noise and leakage errors. The high-resolution MGCR model constructed using altimetry data can reflect the long-term marine gravity change in more detail, which is helpful to study Earth mass migration. The SDUST2020MGCR model data is available at https://zenodo.org/records/10098524 (Zhu et al., 2023b).

Received: 30 Nov 2023 – Discussion started: 11 Dec 2023

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Fengshun Zhu, Jinyun Guo, Huiying Zhang, Lingyong Huang, Heping Sun, and Xin Liu

Status: closed

RC1:
'Reviewer Comment on essd-2023-498', Anonymous Referee #1, 07 Jan 2024

I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
(1) Mass-trends from GRACE are usually meant to reflect only the water-related mass anomalies, whereas signals from the solid like glacial isostatic adjustment (GIA) or co- and postseismic deformations are typically removed from the Level-3 GRACE products. In your Figure 6, strong residual signals from earthquakes are clearly visible, and I also suspect some residual GIA signals particularly in the North Atlantic. I doubt that many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects. I suggest to further clarify your intented users, or attempt to further separate those signals.
(2) The variations in barystatic sea-level can be very well explained with the sea-level equation (see Tamisiea et al., 0.1029/2009JC005687). Figure 6a shows features around Greenland that appear to be consistent with the sea-level equation, but it would be nice to see a corresponding figure 6c of the mass trends predicted by the sea-level equation to compare with the results from GRACE and altimetry.
(3) Many of the small-scale features of Figure 6a are not related to mass trends, but rather to steric sea-level changes associated with meso-scale eddies that were not sampled by the just 4,000 ARGO floats currently operating in the world's oceans. Please try to assess those signals, maybe by splitting the altimetry record in half and by comparing the trends from both periods. Where trends differ substantially, the altimetry results are much less reliable. Those regions need to be conveyed in an appropriate manner to the potential users of your data-set.

Citation: https://doi.org/10.5194/essd-2023-498-RC1
- AC1: 'Reply on RC1', Jinyun Guo, 25 Feb 2024
  
  Comment: I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
  Reply: Thanks for your suggestions and comments. Your opinions are reasonable, greatly helping me improve my article. The response to the comments is as follows.
  Comment1: Mass-trends from GRACE are usually meant to reflect only the water-related mass anomalies, whereas signals from the solid like glacial isostatic adjustment (GIA) or co- and postseismic deformations are typically removed from the Level-3 GRACE products. In your Figure 6, strong residual signals from earthquakes are clearly visible, and I also suspect some residual GIA signals particularly in the North Atlantic. I doubt that many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects. I suggest to further clarify your intented users, or attempt to further separate those signals.
  Reply1: Thank you for your thoughtful comments. The Mascon product do not require any post-processing, they exclude the leakage errors caused by filtering, and remove the GIA effects and seismic deformations. However, the application and evaluation of the Mascon product is still an open question, and there is no clear and unified understanding of the GRACE Mascon product yet. GRACE observation data are mainly given in the form of spherical harmonic coefficients. The GRACE time-varying gravity signals only as a comparison of this paper, so we use the spherical harmonic coefficients product to obtain GRACE time-varying gravity. The GRACE preprocessing includes low-degree term supplementation and replacement, north-south strip noise removal, leakage error correction, GAD model addition and GIA correction. After the above preprocessing, there may be some error residuals in the GRACE time-varying gravity signals, which we add more explanation in the paper. In this study, the GIA effect is deducted as a known factor, and thus the marine gravity change rate is investigated for other factors. Indeed, many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects (GIA effects and seismic deformations). Therefore, we have updated the model product (SDUST2020MGCR) to provide data that include the separated signals (the netCDF4 grid file contains the solved altimetry MGCR and GIA MGCR). The user can sum the altimetry MGCR with the GIA MGCR to obtain a full-signal MGCR. And we have added model descriptions to make it more user-friendly.
  Comment2: The variations in barystatic sea-level can be very well explained with the sea-level equation (see Tamisiea et al., 0.1029/2009JC005687). Figure 6a shows features around Greenland that appear to be consistent with the sea-level equation, but it would be nice to see a corresponding figure 6c of the mass trends predicted by the sea-level equation to compare with the results from GRACE and altimetry.
  Reply2: Thank you for your valuable comments. The variation of water stored on land, which is unevenly distributed in space. This unevenly variation of mass will in turn load the Earth and cause sea level change, these effects are termed self‐attraction and loading (SAL) (Tamisiea et al., 2010). Based on the method proposed by Sun et al (2018), the GRACE/GRACE-FO data and the fingerprints of mass redistributions (fingerprint is base function associated with a particular spatial mass distribution) is used, the sea level equation on an elastic Earth is solved. The SAL effect is estimated, and the result is shown in Fig. 6(c). Comparing Fig. 6 (a), (b), (c), the results show that there is a correlation between mass-term sea level decline in the southern Greenland and a reduction in Greenland terrestrial water storage.
  Figure 6. The long-term mass-term SLCR. (a) SDUST_Mass_SLCR, (b) GRACE_Mass_SLCR. . (c) The SLCR caused by self‐attraction and loading effect
  Tamisiea, M. E.; Hill, E. M.; Ponte, R. M.; Davis, J. L.; Velicogna, I.; Vinogradova, N. T. (2010). Impact of self-attraction and loading on the annual cycle in sea level. Journal of Geophysical Research, 115(C7). doi:10.1029/2009jc005687
  Sun, Y; Riva, R; Ditmar, P; Rietbroek, R. (2019). Using GRACE to explain variations in the Earth's oblateness. Geophysical Research Letters, 2019, 46(1), 158-168.  doi:10.1029/2018GL080607
  Comment3: Many of the small-scale features of Figure 6a are not related to mass trends, but rather to steric sea-level changes associated with meso-scale eddies that were not sampled by the just 4,000 ARGO floats currently operating in the world's oceans. Please try to assess those signals, maybe by splitting the altimetry record in half and by comparing the trends from both periods. Where trends differ substantially, the altimetry results are much less reliable. Those regions need to be conveyed in an appropriate manner to the potential users of your data-set.
  Reply3: Thank you very much for your good comments. In this study, the 19-year moving window method was used to divide the altimetry data between 1993 and 2019 into nine groups (groups: 1993-2011, 1994-2012, 1995-2013, 1996-2014, 1997-2015, 1998-2016, 1999-2017, 2000-2018, 2001-2019), and nine mean sea level models were constructed, which in turn estimated the altimetry sea level change rate (SLCR). Following your comment, we split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions will be lower. In the revised paper, we describe the approach used to test the reliability of the SLCR, and point out that the reliability of the results will be lower in the ocean current area. It is worth noting that the 19-year moving window method was used to calculate the SLCR, which can reduce the influence of ocean currents.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC1
- AC4: 'Reply on RC1', Jinyun Guo, 27 Feb 2024
  
  Comment: I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
  Reply: Thanks for your comments. We further clarify this data record as follows:
  In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy, the GRACE and altimetry results are difficult to verify each other (Willis et al., 2008; Feng et al., 2014; Zhang and Wang 2015). Therefore, it is difficult to use GRACE results to assess the uncertainty of altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals. And strip noise, leakage errors and their residuals affect the true physical signal, so the GRACE time-varying marine gravity used for comparison is not precise. In the process of solving the mean sea level using the along-track altimetry data, the altimetry data were preprocessed (such as 19-year moving grouping, collinear adjustment, space-time objective analysis interpolation, and crossover adjustment) to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.
  Although it is not possible to use the GRACE MGCR to evaluate the reliability of the altimetry MGCR, we have added a reliability analysis based on your comments. We split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions may be lower. The true results of marine gravity changes at ocean currents remain to be verified and analyzed by future gravity satellite programs that provide global gravity field results with higher spatiotemporal resolution. The use of altimetry data can maximize the opportunity to construct a high-resolution, high-precision MGCR model. Although the altimetry MGCR may be less reliable at ocean current areas, the construction of altimetry MGCR fills the data gap compared to inability of GRACE to detect small-scale marine gravity changes caused by ocean currents, which is already an improvement.
  The marine gravity changes are mainly caused by the seawater mass changes: (1) global warming leads to melting of glacier and ice sheet, sea level rise and seawater mass increase, which in turn affects the global marine gravity field. (2) the climate warming leads to change of ocean dynamics, such as increase in the intensity and number of tropical cyclones and enhancement of ocean circulation, which causes changes in the seawater mass distribution, and then affects the marine gravity field. (3) The variation of terrestrial water storage is unevenly distributed in space, this unevenly variation of mass will in turn load the Earth, named as self-attraction and loading effect, which causes changes in seawater mass distribution, and consequently changes in marine gravity. In conclusion, SDUST2020MGCR has higher spatial resolution and excludes stripe noise and leakage errors, it can more realistically reflect the long-term marine gravity change in more detail, which is meaningful for the study of seawater mass migration and its associated geophysical processes.
  Willis, J.K., Chambers, D.P. and Nerem, R.S.: Assessing the globally averaged sea level budget on seasonal to interannual timescales, J. Geophys. Res. Oceans, 113 (C6), https://doi.org/10.1029/2007JC004517, 2008.
  Feng, W., Zhong, M. and Xu, H.: Global sea level changes estimated from satellite altimetry, satellite gravimetry and Argo data during 2005-2013, Prog. Geophys., 29 (2), 471–477, doi:10.6038/pg20140201, 2014.
  Zhang, B. & Wang, Z.: Global sea level variations estimated from satellite altimetry, GRACE and oceanographic data, Geomat. Inform. Sci. Wuhan Univ., 40 (11), 1453–1459. doi:10.13203/j.whugis20150230, 2015.
  Chen, J., Li, J., Zhang, Z., & Ni, S.: Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007, 2014.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC4
RC2:
'Comment on essd-2023-498', Anonymous Referee #2, 02 Feb 2024

The objective of this study is to construct a high-resolution global marine gravity change rate (MGCR) model using multi-satellite altimetry data. Many academic institutions have constructed global static marine gravity fields based on altimetry data, but there are few studies of time-varying marine gravity and no high-resolution model products. Nowadays, time-varying marine gravity studies using GRACE satellite gravity data have some problems: the spatial resolution is low, and the true geophysical signal is affected by strip noise, signal leakage error and their residuals. Therefore, the study of high-resolution time-varying marine gravity based on altimetry data is a very meaningful work. It is worth saying that the SWOT altimetry mission has been implemented in December 2022, and the SWOT wide-swath mode can obtain the sea surface height covering global in a short period, and when SWOT accumulates many years of data, more time-varying marine gravity studies will appear in the future. In general, I think the manuscript is valuable to be published. My suggestion is for minor revision, and there are some points that can be improved to make the work presentation better:
1、Check the presentation to make the content clearer:
① In the data introduction section, the purpose of using the data should be clearly indicated (for example, L2P product data and AVISO monthly sea level anomaly data are both altimetry data, while in the flowchart of Fig. 3, the authors did not indicate which altimetry data was used to construct the SDUST2020MGCR model), which makes the paper more reader-friendly. ② In studies related to ocean and climate change, the GIA effect is usually deducted. While the purpose of this paper is to study marine gravity field change, the author needs to explain the reasons for subtracting the GIA effect. ③ The spherical harmonic coefficient degree of GIA model is fully expanded to 256, while the degree of altimetry model is expanded to 2160, and the GRACE model is expanded to 60, the degree of models are inconsistent, and the author need to describe clearly the calculation here. ④ The English language is sometimes not so fluent, and some English words are not specialized vocabulary, and this doesn't help the readability of the paper (at least in my remember, the expression "seawater volume change" is rarely used).
2、Add explanations to improve the reliability of the results:
Investigating global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data, but strip noise, leakage errors and their processed residuals, which affect the true physical signal, and this is a major problem in the study of time-varying marine gravity using GRACE. In the results and analysis section, I would ask the author to give some explanations/comments after describing the results of altimetry and GRACE (for example, highlighting the advantages of altimetry and introducing the problems of GRACE). ① The lines 426 and 463 of manuscript both mention that the STD of the altimetry result is less than the GRACE result, I think that a discussion about uncertainties, in the GRACE MGCR and altimetry MGCR, could improve the paper by giving more reliability to the results. ② Author needs to read the manuscript carefully and consider the appropriate references that could be added (for example, the lines 423 and 449).
3、Standardize the display of figures and formulas:
①In mathematical formulas, the use of the division sign, multiplication sign, and brackets should be consistent. ② Please check equation 7, I think the bracket can be removed. ③ In my version, formulas 3, 5, and 9 look strange, Please check and correct if needed. ④ Please check the font size of the formula symbols in the sentence on line 312. ⑤ The statistical histogram of Figure 8, the histogram can be plotted densely and continuously if needed. ⑥ The figures (1, 4, 5, 6, 7) in the manuscript are blurry, please increase the resolution.

Citation: https://doi.org/10.5194/essd-2023-498-RC2
- AC2: 'Reply on RC2', Jinyun Guo, 25 Feb 2024
  
  Comment: The objective of this study is to construct a high-resolution global marine gravity change rate (MGCR) model using multi-satellite altimetry data. Many academic institutions have constructed global static marine gravity fields based on altimetry data, but there are few studies of time-varying marine gravity and no relevant global model products. Nowadays, time-varying marine gravity studies using GRACE satellite gravity data have some problems: the spatial resolution is low, and the true geophysical signal is affected by strip noise, signal leakage error and their residuals. Therefore, the study of high-resolution time-varying marine gravity based on altimetry data is a very meaningful work. It is worth saying that the SWOT altimetry mission has been implemented in December 2022, and the SWOT wide-swath mode can obtain the sea surface height covering global in a short period, and when SWOT accumulates many years of data, more time-varying marine gravity studies will appear in the future. In general, I think the manuscript is valuable to be published. My suggestion is for minor revision, and there are some points that can be improved to make the work presentation better:
  Reply: Thanks for your suggestions and comments. The response to the comments is as follows.
  Comment1: Check the presentation to make the content clearer:
  ① In the data introduction section, the purpose of using the data should be clearly indicated (for example, L2P product data and AVISO monthly sea level anomaly data are both altimetry data, while in the flowchart of Fig. 3, the authors did not indicate which altimetry data was used to construct the SDUST2020MGCR model), which makes the paper more reader-friendly. ② In studies related to ocean and climate change, the GIA effect is usually deducted. While the purpose of this paper is to study marine gravity field change, the author needs to explain the reasons for subtracting the GIA effect. ③ The spherical harmonic coefficient degree of GIA model is fully expanded to 256, while the degree of altimetry model is expanded to 2160, and the GRACE model is expanded to 60, the degree of models are inconsistent, and the author need to describe clearly the calculation here. ④ The English language is sometimes not so fluent, and some English words are not specialized vocabulary, and this doesn't help the readability of the paper (at least in my remember, the expression "seawater volume change" is rarely used).
  Reply1: Thank you for your valuable comments.
  ① Two types of altimetry data were used in this study, including L2P product data and AVISO monthly sea level anomaly data. Figure 3 shows the flowchart for constructing the SDUST2020 MGCR model using altimetry data, but it is not labelled which altimetry data is used, which gives the reader a wrong understanding. So we modified Figure 3 to indicate that the altimetry data used to construct the SDUST MGCR is the L2P product data.
  ② In this study, the GIA effect is deducted as a known factor, and thus the marine gravity change rate is investigated for other factors. Indeed, many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects (GIA effects and seismic deformations). Therefore, we have updated the model product (SDUST2020MGCR) to provide data that include the separated signals (the netCDF4 grid file contains the solved altimetry MGCR and GIA MGCR). The user can sum the altimetry MGCR with the GIA MGCR to obtain a full-signal MGCR.
  ③ The GIA, GRACE and altimetry models do not have the same degree of spherical harmonic expansion. We truncate the degree of the GIA model to the 60, both the GRACE and altimetry models remove the 60 degree GIA model, which we add more explanation in the paper.
  ④ We apologize for our English language of the previous manuscript. We have carefully checked and improved the English writing in the revised manuscript. We have asked an English professional teacher to polish our paper to improve the readability. We have also requested a native English speaker with a PhD in geodesy to review the manuscript and offer suggestions.
  Comment2: Add explanations to improve the reliability of the results:
  Investigating global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data, but strip noise, leakage errors and their processed residuals, which affect the true physical signal. The GRACE time-varying marine gravity used for comparison is not precise. In the results and analysis section, I would ask the author to give some explanations/comments after describing the results of altimetry and GRACE. ① The lines 426 and 463 of manuscript both mention that the STD of the altimetry result is less than the GRACE result, I think that a discussion about uncertainties, in the GRACE MGCR and altimetry MGCR, could improve the paper by giving more reliability to the results. ② Author needs to read the manuscript carefully and consider the appropriate references that could be added (for example, the lines 423 and 449).
  Reply2: Thanks for your suggestions and comments.
  ① We have added some explanations: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), and the large STD of GRACE MGCR may be related to these error residuals. In the process of solving the mean sea level using the along-track altimetry data, we preprocess the altimetry data to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.”
  ② We have added some explanations and references:
  “The statistical results of SDUST_Altimetry_SLCR and AVISO_Altimetry_SLCR are basically consistent, and the mean value of altimetry SLCR in the global ocean is all about 3.2 mm/year. The results of previous studies show that the mean value of global SLCR is about 3 mm/year (Leuliette and Miller, 2009; Cazenave et al., 2014), which is further confirmed by the SLCR results of this study.”
  Based on comments of you and another reviewer, in the revised paper, we have added the description: “In the seas near the West Wind Drift and the Brazilian Warm Current, both SDUST2020MGCR and GRACE2020MGCR reveal that the high-frequency signals of marine gravity changes are relatively significant, which reflects the influence of ocean currents on the marine gravity field, and the reliability of the result will be lower in the ocean current area.”
  The added references are listed below:
  Chen, J., Li, J., Zhang, Z., & Ni, S., 2014. Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007
  Leuliette E W, Miller L. Closing the sea level rise budget with altimetry, Argo, and GRACE [J]. Geophysical Research Letters, 2009, 36: L04608.
  Cazenave A, Dieng H, Meyssignac B, et al. The rate of sea-level rise [J]. Nature Climate Change, 2014, 4(5): 358-361.
  Comment3: Standardize the display of figures and formulas:
  ①In mathematical formulas, the use of the division sign, multiplication sign, and parentheses should be consistent. ② Please check equation (7), I think the bracket can be removed. ③ In my version, formulas (3) (5) (9) look strange, Please check and correct if needed. ④ Please check the font size of the formula symbols in the sentence on line 312. ⑤ The statistical histogram of Figure 8, the histogram can be plotted densely and continuously. ⑥ The figures in the manuscript are blurry, please increase the resolution.
  Reply3: Thanks for your suggestions. The use of consistent figures and formulas helps to improve the standardization of the paper. Based on your suggestions, we have checked and revised the formulas and figures in the manuscript.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC2
CC1:
'Comment on essd-2023-498', Xiaoyun Wan, 18 Feb 2024

This study derived global marine time-varying gravity field model using altimetry data. In this field, we all know that GRACE/GRACE Follow On has played a great role. However, the spatial resolution of the gravity satellite products is low. This study presents an attempts to use high resolution data of satellite altimetry data to derive time-varying marine gravity field signals. The innovation is clear. I think the manuscript is valuable to be published. Detail comments are as follows,
(1)Main concern: How to validate the results?As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.

（2）The presentation can be improved. For example,
There are many sentences which indeed are two sentences, such as lines 63~64, 364-365, etc.
Line 161, “provides”-provide.
Line 452, “may contains”->may contain
Please also check other parts of the manuscript.
（3）The literature on Equation (1) should be cited, because it would be difficult for readers to know how the formulas are derived.
（4）Lines 333`334. The time period is from 1993 to 2019. If the time interval is 1 year, 18 mean sea level models can be derived, but not 9 models. It seems that the interval should be 2 year. Please check it.
（5）Lines 374-375, How to process the land effect on the recovery of spherical harmonic coefficients? Is the impact of land large, since there is no data?

Citation: https://doi.org/10.5194/essd-2023-498-CC1
- AC3: 'Reply on CC1', Jinyun Guo, 25 Feb 2024
  
  Comment: This study derived global marine time-varying gravity field model using altimetry data. In this field, we all know that GRACE/GRACE Follow On has played a great role. However, the spatial resolution of the gravity satellite products is low. This study presents an attempts to use high resolution data of satellite altimetry data to derive time-varying marine gravity field signals. The innovation is clear. I think the manuscript is valuable to be published. Detail comments are as follows.
  Reply: Thanks for your suggestions and comments. Your opinions are reasonable, greatly helping me improve my article. The response to the comments is as follows.
  Comment1: Main concern: How to validate the results? As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.
  Reply1: Thank you for your valuable and thoughtful comments. We apologize for the missing of detailed explanations in the previous manuscript. In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy. Therefore, it is difficult to compare the uncertainty of GRACE results and altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The GRACE time-varying marine gravity used for comparison is not precise. The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals, and strip noise, leakage errors and their residuals affect the true physical signal. In the process of solving the mean sea level using the along-track altimetry data, we preprocess the altimetry data to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.”
  Chen, J., Li, J., Zhang, Z., & Ni, S., 2014. Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007
  Comment2: The presentation can be improved. For example,
  There are many sentences which indeed are two sentences, such as lines 63~64, 364-365, etc.
  Line 161, “provides”-provide.
  Line 452, “may contains”->may contain
  Please also check other parts of the manuscript.
  Reply2: Thanks for your comments. We apologize for our English language of the previous manuscript. We have carefully checked and improved the English writing. We have asked an English professional teacher to polish our paper to improve the readability. We have also asked a PhD in Geodesy, a native English speaker, to read through the paper and give some advice.
  Comment3: The literature on Equation (1) should be cited, because it would be difficult for readers to know how the formulas are derived.
  Reply3: Thank you for your suggestion. We apologize for the missing of clear explanations in the previous manuscript. We checked Equation (1) and added some descriptions: The spherical harmonic coefficients in the ICE-6G model correspond to the inter-annual trend, and we need to compute the monthly trend and compute the GIA effect for each month. Finally, the monthly GIA effect is subtracted from the GRACE monthly spherical harmonic coefficients.
  Comment4: Lines 333-334. The time period is from 1993 to 2019. If the time interval is 1 year, 18 mean sea level models can be derived, but not 9 models. It seems that the interval should be 2 year. Please check it.
  Reply4: Thanks very much for your comments. We apologize for the missing of detailed explanations of some manipulations in the previous manuscript. In this study, the 19-year moving window method was used to divide the altimetry data between 1993 and 2019 into nine groups (1993-2011, 1994-2012, 1995-2013, 1996-2014, 1997-2015, 1998-2016, 1999-2017, 2000-2018, 2001-2019, respectively), and nine mean sea level models were constructed, which in turn estimated the altimetry sea level change rate (SLCR).
  Comment5: Lines 374-375, How to process the land effect on therecovery of spherical harmonic coefficients? Is the impact of land large, since there is no data?
  Reply5: Thank you for your valuable suggestions. Since the land time-varying gravity observation data are insufficient, the data on land are set to 0 in this study. The MGCR (Fig. 7(a)) is calculated using the SLCR (Fig. 6(a)) by applying the spherical harmonic function method. Comparing Figures 6(a) and 7(a), it can be seen that the data on land set to 0 does not have a significant effect on the results. In the future, the time-varying gravity observation data on land can be used as a supplement to construct a global-scale gravity change model.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC3
- AC5: 'Reply on CC1', Jinyun Guo, 27 Feb 2024
  
  Comment1: Main concern: How to validate the results? As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.
  Reply1: Thank you for your valuable comments. Our modification and additions are as follows:
  Modification of figure 9: We checked the Figure 9 and found an error. During the previous power spectral density analysis, the geospatial ranges of GRACE2020MGCR and SDUST2020MGCR were not exactly the same, hence the erroneous results shown in Figure 9. We repeated the power spectral density analysis, and the geospatial ranges of both GRACE2020MGCR and SDUST2020MGCR are -70S~70°N and 0~360°E, and the result of the power spectral density analysis is shown in the following figure. This figure shows that the signal strengths in the long wavelength of GRACE2020MGCR and SDUST2020MGCR are basically the same, while the signal strength in the short-medium wavelength of SDUST2020MGCR is greater than GRACE2020MGCR. This result is more consistent with reality.
  Addition of more explanations and analyses: In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy, the GRACE and altimetry results are difficult to verify each other (Willis et al., 2008; Feng et al., 2014; Zhang and Wang 2015). Therefore, it is difficult to use GRACE results to assess the uncertainty of altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals. And strip noise, leakage errors and their residuals affect the true physical signal, so the GRACE time-varying marine gravity used for comparison is not precise. In the process of solving the mean sea level using the along-track altimetry data, the altimetry data were preprocessed (such as 19-year moving grouping, collinear adjustment, space-time objective analysis interpolation, and crossover adjustment) to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.
  Addition of other validation: Although it is not possible to use the GRACE MGCR to evaluate the reliability of the altimetry MGCR, we have added a reliability analysis based on comments of anonymous referee #1. We split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions may be lower. The true results of marine gravity changes at ocean currents remain to be verified and analyzed by future gravity satellite programs that provide global gravity field results with higher spatiotemporal resolution. The use of altimetry data can maximize the opportunity to construct a high-resolution, high-precision MGCR model. Although the altimetry MGCR may be less reliable at ocean current areas, the construction of altimetry MGCR fills the data gap compared to inability of GRACE to detect small-scale marine gravity changes caused by ocean currents, which is already an improvement.
  Willis, J.K., Chambers, D.P. and Nerem, R.S.: Assessing the globally averaged sea level budget on seasonal to interannual timescales, J. Geophys. Res. Oceans, 113 (C6), https://doi.org/10.1029/2007JC004517, 2008.
  Feng, W., Zhong, M. and Xu, H.: Global sea level changes estimated from satellite altimetry, satellite gravimetry and Argo data during 2005-2013, Prog. Geophys., 29 (2), 471–477, doi:10.6038/pg20140201, 2014.
  Zhang, B. & Wang, Z.: Global sea level variations estimated from satellite altimetry, GRACE and oceanographic data, Geomat. Inform. Sci. Wuhan Univ., 40 (11), 1453–1459. doi:10.13203/j.whugis20150230, 2015.
  Chen, J., Li, J., Zhang, Z., & Ni, S.: Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007, 2014.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC5

Status: closed

RC1:
'Reviewer Comment on essd-2023-498', Anonymous Referee #1, 07 Jan 2024

I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
(1) Mass-trends from GRACE are usually meant to reflect only the water-related mass anomalies, whereas signals from the solid like glacial isostatic adjustment (GIA) or co- and postseismic deformations are typically removed from the Level-3 GRACE products. In your Figure 6, strong residual signals from earthquakes are clearly visible, and I also suspect some residual GIA signals particularly in the North Atlantic. I doubt that many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects. I suggest to further clarify your intented users, or attempt to further separate those signals.
(2) The variations in barystatic sea-level can be very well explained with the sea-level equation (see Tamisiea et al., 0.1029/2009JC005687). Figure 6a shows features around Greenland that appear to be consistent with the sea-level equation, but it would be nice to see a corresponding figure 6c of the mass trends predicted by the sea-level equation to compare with the results from GRACE and altimetry.
(3) Many of the small-scale features of Figure 6a are not related to mass trends, but rather to steric sea-level changes associated with meso-scale eddies that were not sampled by the just 4,000 ARGO floats currently operating in the world's oceans. Please try to assess those signals, maybe by splitting the altimetry record in half and by comparing the trends from both periods. Where trends differ substantially, the altimetry results are much less reliable. Those regions need to be conveyed in an appropriate manner to the potential users of your data-set.

Citation: https://doi.org/10.5194/essd-2023-498-RC1
- AC1: 'Reply on RC1', Jinyun Guo, 25 Feb 2024
  
  Comment: I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
  Reply: Thanks for your suggestions and comments. Your opinions are reasonable, greatly helping me improve my article. The response to the comments is as follows.
  Comment1: Mass-trends from GRACE are usually meant to reflect only the water-related mass anomalies, whereas signals from the solid like glacial isostatic adjustment (GIA) or co- and postseismic deformations are typically removed from the Level-3 GRACE products. In your Figure 6, strong residual signals from earthquakes are clearly visible, and I also suspect some residual GIA signals particularly in the North Atlantic. I doubt that many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects. I suggest to further clarify your intented users, or attempt to further separate those signals.
  Reply1: Thank you for your thoughtful comments. The Mascon product do not require any post-processing, they exclude the leakage errors caused by filtering, and remove the GIA effects and seismic deformations. However, the application and evaluation of the Mascon product is still an open question, and there is no clear and unified understanding of the GRACE Mascon product yet. GRACE observation data are mainly given in the form of spherical harmonic coefficients. The GRACE time-varying gravity signals only as a comparison of this paper, so we use the spherical harmonic coefficients product to obtain GRACE time-varying gravity. The GRACE preprocessing includes low-degree term supplementation and replacement, north-south strip noise removal, leakage error correction, GAD model addition and GIA correction. After the above preprocessing, there may be some error residuals in the GRACE time-varying gravity signals, which we add more explanation in the paper. In this study, the GIA effect is deducted as a known factor, and thus the marine gravity change rate is investigated for other factors. Indeed, many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects (GIA effects and seismic deformations). Therefore, we have updated the model product (SDUST2020MGCR) to provide data that include the separated signals (the netCDF4 grid file contains the solved altimetry MGCR and GIA MGCR). The user can sum the altimetry MGCR with the GIA MGCR to obtain a full-signal MGCR. And we have added model descriptions to make it more user-friendly.
  Comment2: The variations in barystatic sea-level can be very well explained with the sea-level equation (see Tamisiea et al., 0.1029/2009JC005687). Figure 6a shows features around Greenland that appear to be consistent with the sea-level equation, but it would be nice to see a corresponding figure 6c of the mass trends predicted by the sea-level equation to compare with the results from GRACE and altimetry.
  Reply2: Thank you for your valuable comments. The variation of water stored on land, which is unevenly distributed in space. This unevenly variation of mass will in turn load the Earth and cause sea level change, these effects are termed self‐attraction and loading (SAL) (Tamisiea et al., 2010). Based on the method proposed by Sun et al (2018), the GRACE/GRACE-FO data and the fingerprints of mass redistributions (fingerprint is base function associated with a particular spatial mass distribution) is used, the sea level equation on an elastic Earth is solved. The SAL effect is estimated, and the result is shown in Fig. 6(c). Comparing Fig. 6 (a), (b), (c), the results show that there is a correlation between mass-term sea level decline in the southern Greenland and a reduction in Greenland terrestrial water storage.
  Figure 6. The long-term mass-term SLCR. (a) SDUST_Mass_SLCR, (b) GRACE_Mass_SLCR. . (c) The SLCR caused by self‐attraction and loading effect
  Tamisiea, M. E.; Hill, E. M.; Ponte, R. M.; Davis, J. L.; Velicogna, I.; Vinogradova, N. T. (2010). Impact of self-attraction and loading on the annual cycle in sea level. Journal of Geophysical Research, 115(C7). doi:10.1029/2009jc005687
  Sun, Y; Riva, R; Ditmar, P; Rietbroek, R. (2019). Using GRACE to explain variations in the Earth's oblateness. Geophysical Research Letters, 2019, 46(1), 158-168.  doi:10.1029/2018GL080607
  Comment3: Many of the small-scale features of Figure 6a are not related to mass trends, but rather to steric sea-level changes associated with meso-scale eddies that were not sampled by the just 4,000 ARGO floats currently operating in the world's oceans. Please try to assess those signals, maybe by splitting the altimetry record in half and by comparing the trends from both periods. Where trends differ substantially, the altimetry results are much less reliable. Those regions need to be conveyed in an appropriate manner to the potential users of your data-set.
  Reply3: Thank you very much for your good comments. In this study, the 19-year moving window method was used to divide the altimetry data between 1993 and 2019 into nine groups (groups: 1993-2011, 1994-2012, 1995-2013, 1996-2014, 1997-2015, 1998-2016, 1999-2017, 2000-2018, 2001-2019), and nine mean sea level models were constructed, which in turn estimated the altimetry sea level change rate (SLCR). Following your comment, we split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions will be lower. In the revised paper, we describe the approach used to test the reliability of the SLCR, and point out that the reliability of the results will be lower in the ocean current area. It is worth noting that the 19-year moving window method was used to calculate the SLCR, which can reduce the influence of ocean currents.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC1
- AC4: 'Reply on RC1', Jinyun Guo, 27 Feb 2024
  
  Comment: I reviewed the manuscript "SDUST2020MGCR: a global marine gravity change rate model" submitted for possible publication in ESSD. The article describes an attempt to derive mass change trends over the oceans out of data from satellite altimetry. I do agree wholeheartedly that it is a very good idea to create (and publish) such a data-set, but I feel somewhat uneasy about the maturity of the current version of the product In view of my detailed comments given below, it might be better to wait with a publication in ESSD a little longer to further clarify the scope of this data record.
  Reply: Thanks for your comments. We further clarify this data record as follows:
  In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy, the GRACE and altimetry results are difficult to verify each other (Willis et al., 2008; Feng et al., 2014; Zhang and Wang 2015). Therefore, it is difficult to use GRACE results to assess the uncertainty of altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals. And strip noise, leakage errors and their residuals affect the true physical signal, so the GRACE time-varying marine gravity used for comparison is not precise. In the process of solving the mean sea level using the along-track altimetry data, the altimetry data were preprocessed (such as 19-year moving grouping, collinear adjustment, space-time objective analysis interpolation, and crossover adjustment) to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.
  Although it is not possible to use the GRACE MGCR to evaluate the reliability of the altimetry MGCR, we have added a reliability analysis based on your comments. We split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions may be lower. The true results of marine gravity changes at ocean currents remain to be verified and analyzed by future gravity satellite programs that provide global gravity field results with higher spatiotemporal resolution. The use of altimetry data can maximize the opportunity to construct a high-resolution, high-precision MGCR model. Although the altimetry MGCR may be less reliable at ocean current areas, the construction of altimetry MGCR fills the data gap compared to inability of GRACE to detect small-scale marine gravity changes caused by ocean currents, which is already an improvement.
  The marine gravity changes are mainly caused by the seawater mass changes: (1) global warming leads to melting of glacier and ice sheet, sea level rise and seawater mass increase, which in turn affects the global marine gravity field. (2) the climate warming leads to change of ocean dynamics, such as increase in the intensity and number of tropical cyclones and enhancement of ocean circulation, which causes changes in the seawater mass distribution, and then affects the marine gravity field. (3) The variation of terrestrial water storage is unevenly distributed in space, this unevenly variation of mass will in turn load the Earth, named as self-attraction and loading effect, which causes changes in seawater mass distribution, and consequently changes in marine gravity. In conclusion, SDUST2020MGCR has higher spatial resolution and excludes stripe noise and leakage errors, it can more realistically reflect the long-term marine gravity change in more detail, which is meaningful for the study of seawater mass migration and its associated geophysical processes.
  Willis, J.K., Chambers, D.P. and Nerem, R.S.: Assessing the globally averaged sea level budget on seasonal to interannual timescales, J. Geophys. Res. Oceans, 113 (C6), https://doi.org/10.1029/2007JC004517, 2008.
  Feng, W., Zhong, M. and Xu, H.: Global sea level changes estimated from satellite altimetry, satellite gravimetry and Argo data during 2005-2013, Prog. Geophys., 29 (2), 471–477, doi:10.6038/pg20140201, 2014.
  Zhang, B. & Wang, Z.: Global sea level variations estimated from satellite altimetry, GRACE and oceanographic data, Geomat. Inform. Sci. Wuhan Univ., 40 (11), 1453–1459. doi:10.13203/j.whugis20150230, 2015.
  Chen, J., Li, J., Zhang, Z., & Ni, S.: Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007, 2014.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC4
RC2:
'Comment on essd-2023-498', Anonymous Referee #2, 02 Feb 2024

The objective of this study is to construct a high-resolution global marine gravity change rate (MGCR) model using multi-satellite altimetry data. Many academic institutions have constructed global static marine gravity fields based on altimetry data, but there are few studies of time-varying marine gravity and no high-resolution model products. Nowadays, time-varying marine gravity studies using GRACE satellite gravity data have some problems: the spatial resolution is low, and the true geophysical signal is affected by strip noise, signal leakage error and their residuals. Therefore, the study of high-resolution time-varying marine gravity based on altimetry data is a very meaningful work. It is worth saying that the SWOT altimetry mission has been implemented in December 2022, and the SWOT wide-swath mode can obtain the sea surface height covering global in a short period, and when SWOT accumulates many years of data, more time-varying marine gravity studies will appear in the future. In general, I think the manuscript is valuable to be published. My suggestion is for minor revision, and there are some points that can be improved to make the work presentation better:
1、Check the presentation to make the content clearer:
① In the data introduction section, the purpose of using the data should be clearly indicated (for example, L2P product data and AVISO monthly sea level anomaly data are both altimetry data, while in the flowchart of Fig. 3, the authors did not indicate which altimetry data was used to construct the SDUST2020MGCR model), which makes the paper more reader-friendly. ② In studies related to ocean and climate change, the GIA effect is usually deducted. While the purpose of this paper is to study marine gravity field change, the author needs to explain the reasons for subtracting the GIA effect. ③ The spherical harmonic coefficient degree of GIA model is fully expanded to 256, while the degree of altimetry model is expanded to 2160, and the GRACE model is expanded to 60, the degree of models are inconsistent, and the author need to describe clearly the calculation here. ④ The English language is sometimes not so fluent, and some English words are not specialized vocabulary, and this doesn't help the readability of the paper (at least in my remember, the expression "seawater volume change" is rarely used).
2、Add explanations to improve the reliability of the results:
Investigating global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data, but strip noise, leakage errors and their processed residuals, which affect the true physical signal, and this is a major problem in the study of time-varying marine gravity using GRACE. In the results and analysis section, I would ask the author to give some explanations/comments after describing the results of altimetry and GRACE (for example, highlighting the advantages of altimetry and introducing the problems of GRACE). ① The lines 426 and 463 of manuscript both mention that the STD of the altimetry result is less than the GRACE result, I think that a discussion about uncertainties, in the GRACE MGCR and altimetry MGCR, could improve the paper by giving more reliability to the results. ② Author needs to read the manuscript carefully and consider the appropriate references that could be added (for example, the lines 423 and 449).
3、Standardize the display of figures and formulas:
①In mathematical formulas, the use of the division sign, multiplication sign, and brackets should be consistent. ② Please check equation 7, I think the bracket can be removed. ③ In my version, formulas 3, 5, and 9 look strange, Please check and correct if needed. ④ Please check the font size of the formula symbols in the sentence on line 312. ⑤ The statistical histogram of Figure 8, the histogram can be plotted densely and continuously if needed. ⑥ The figures (1, 4, 5, 6, 7) in the manuscript are blurry, please increase the resolution.

Citation: https://doi.org/10.5194/essd-2023-498-RC2
- AC2: 'Reply on RC2', Jinyun Guo, 25 Feb 2024
  
  Comment: The objective of this study is to construct a high-resolution global marine gravity change rate (MGCR) model using multi-satellite altimetry data. Many academic institutions have constructed global static marine gravity fields based on altimetry data, but there are few studies of time-varying marine gravity and no relevant global model products. Nowadays, time-varying marine gravity studies using GRACE satellite gravity data have some problems: the spatial resolution is low, and the true geophysical signal is affected by strip noise, signal leakage error and their residuals. Therefore, the study of high-resolution time-varying marine gravity based on altimetry data is a very meaningful work. It is worth saying that the SWOT altimetry mission has been implemented in December 2022, and the SWOT wide-swath mode can obtain the sea surface height covering global in a short period, and when SWOT accumulates many years of data, more time-varying marine gravity studies will appear in the future. In general, I think the manuscript is valuable to be published. My suggestion is for minor revision, and there are some points that can be improved to make the work presentation better:
  Reply: Thanks for your suggestions and comments. The response to the comments is as follows.
  Comment1: Check the presentation to make the content clearer:
  ① In the data introduction section, the purpose of using the data should be clearly indicated (for example, L2P product data and AVISO monthly sea level anomaly data are both altimetry data, while in the flowchart of Fig. 3, the authors did not indicate which altimetry data was used to construct the SDUST2020MGCR model), which makes the paper more reader-friendly. ② In studies related to ocean and climate change, the GIA effect is usually deducted. While the purpose of this paper is to study marine gravity field change, the author needs to explain the reasons for subtracting the GIA effect. ③ The spherical harmonic coefficient degree of GIA model is fully expanded to 256, while the degree of altimetry model is expanded to 2160, and the GRACE model is expanded to 60, the degree of models are inconsistent, and the author need to describe clearly the calculation here. ④ The English language is sometimes not so fluent, and some English words are not specialized vocabulary, and this doesn't help the readability of the paper (at least in my remember, the expression "seawater volume change" is rarely used).
  Reply1: Thank you for your valuable comments.
  ① Two types of altimetry data were used in this study, including L2P product data and AVISO monthly sea level anomaly data. Figure 3 shows the flowchart for constructing the SDUST2020 MGCR model using altimetry data, but it is not labelled which altimetry data is used, which gives the reader a wrong understanding. So we modified Figure 3 to indicate that the altimetry data used to construct the SDUST MGCR is the L2P product data.
  ② In this study, the GIA effect is deducted as a known factor, and thus the marine gravity change rate is investigated for other factors. Indeed, many science applications that require mass change trends over the oceans would require both ocean mass signals and solid Earth effects (GIA effects and seismic deformations). Therefore, we have updated the model product (SDUST2020MGCR) to provide data that include the separated signals (the netCDF4 grid file contains the solved altimetry MGCR and GIA MGCR). The user can sum the altimetry MGCR with the GIA MGCR to obtain a full-signal MGCR.
  ③ The GIA, GRACE and altimetry models do not have the same degree of spherical harmonic expansion. We truncate the degree of the GIA model to the 60, both the GRACE and altimetry models remove the 60 degree GIA model, which we add more explanation in the paper.
  ④ We apologize for our English language of the previous manuscript. We have carefully checked and improved the English writing in the revised manuscript. We have asked an English professional teacher to polish our paper to improve the readability. We have also requested a native English speaker with a PhD in geodesy to review the manuscript and offer suggestions.
  Comment2: Add explanations to improve the reliability of the results:
  Investigating global time-varying gravity field mainly depends on GRACE/GRACE-FO gravity data, but strip noise, leakage errors and their processed residuals, which affect the true physical signal. The GRACE time-varying marine gravity used for comparison is not precise. In the results and analysis section, I would ask the author to give some explanations/comments after describing the results of altimetry and GRACE. ① The lines 426 and 463 of manuscript both mention that the STD of the altimetry result is less than the GRACE result, I think that a discussion about uncertainties, in the GRACE MGCR and altimetry MGCR, could improve the paper by giving more reliability to the results. ② Author needs to read the manuscript carefully and consider the appropriate references that could be added (for example, the lines 423 and 449).
  Reply2: Thanks for your suggestions and comments.
  ① We have added some explanations: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), and the large STD of GRACE MGCR may be related to these error residuals. In the process of solving the mean sea level using the along-track altimetry data, we preprocess the altimetry data to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.”
  ② We have added some explanations and references:
  “The statistical results of SDUST_Altimetry_SLCR and AVISO_Altimetry_SLCR are basically consistent, and the mean value of altimetry SLCR in the global ocean is all about 3.2 mm/year. The results of previous studies show that the mean value of global SLCR is about 3 mm/year (Leuliette and Miller, 2009; Cazenave et al., 2014), which is further confirmed by the SLCR results of this study.”
  Based on comments of you and another reviewer, in the revised paper, we have added the description: “In the seas near the West Wind Drift and the Brazilian Warm Current, both SDUST2020MGCR and GRACE2020MGCR reveal that the high-frequency signals of marine gravity changes are relatively significant, which reflects the influence of ocean currents on the marine gravity field, and the reliability of the result will be lower in the ocean current area.”
  The added references are listed below:
  Chen, J., Li, J., Zhang, Z., & Ni, S., 2014. Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007
  Leuliette E W, Miller L. Closing the sea level rise budget with altimetry, Argo, and GRACE [J]. Geophysical Research Letters, 2009, 36: L04608.
  Cazenave A, Dieng H, Meyssignac B, et al. The rate of sea-level rise [J]. Nature Climate Change, 2014, 4(5): 358-361.
  Comment3: Standardize the display of figures and formulas:
  ①In mathematical formulas, the use of the division sign, multiplication sign, and parentheses should be consistent. ② Please check equation (7), I think the bracket can be removed. ③ In my version, formulas (3) (5) (9) look strange, Please check and correct if needed. ④ Please check the font size of the formula symbols in the sentence on line 312. ⑤ The statistical histogram of Figure 8, the histogram can be plotted densely and continuously. ⑥ The figures in the manuscript are blurry, please increase the resolution.
  Reply3: Thanks for your suggestions. The use of consistent figures and formulas helps to improve the standardization of the paper. Based on your suggestions, we have checked and revised the formulas and figures in the manuscript.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC2
CC1:
'Comment on essd-2023-498', Xiaoyun Wan, 18 Feb 2024

This study derived global marine time-varying gravity field model using altimetry data. In this field, we all know that GRACE/GRACE Follow On has played a great role. However, the spatial resolution of the gravity satellite products is low. This study presents an attempts to use high resolution data of satellite altimetry data to derive time-varying marine gravity field signals. The innovation is clear. I think the manuscript is valuable to be published. Detail comments are as follows,
(1)Main concern: How to validate the results?As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.

（2）The presentation can be improved. For example,
There are many sentences which indeed are two sentences, such as lines 63~64, 364-365, etc.
Line 161, “provides”-provide.
Line 452, “may contains”->may contain
Please also check other parts of the manuscript.
（3）The literature on Equation (1) should be cited, because it would be difficult for readers to know how the formulas are derived.
（4）Lines 333`334. The time period is from 1993 to 2019. If the time interval is 1 year, 18 mean sea level models can be derived, but not 9 models. It seems that the interval should be 2 year. Please check it.
（5）Lines 374-375, How to process the land effect on the recovery of spherical harmonic coefficients? Is the impact of land large, since there is no data?

Citation: https://doi.org/10.5194/essd-2023-498-CC1
- AC3: 'Reply on CC1', Jinyun Guo, 25 Feb 2024
  
  Comment: This study derived global marine time-varying gravity field model using altimetry data. In this field, we all know that GRACE/GRACE Follow On has played a great role. However, the spatial resolution of the gravity satellite products is low. This study presents an attempts to use high resolution data of satellite altimetry data to derive time-varying marine gravity field signals. The innovation is clear. I think the manuscript is valuable to be published. Detail comments are as follows.
  Reply: Thanks for your suggestions and comments. Your opinions are reasonable, greatly helping me improve my article. The response to the comments is as follows.
  Comment1: Main concern: How to validate the results? As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.
  Reply1: Thank you for your valuable and thoughtful comments. We apologize for the missing of detailed explanations in the previous manuscript. In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy. Therefore, it is difficult to compare the uncertainty of GRACE results and altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The GRACE time-varying marine gravity used for comparison is not precise. The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals, and strip noise, leakage errors and their residuals affect the true physical signal. In the process of solving the mean sea level using the along-track altimetry data, we preprocess the altimetry data to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.”
  Chen, J., Li, J., Zhang, Z., & Ni, S., 2014. Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007
  Comment2: The presentation can be improved. For example,
  There are many sentences which indeed are two sentences, such as lines 63~64, 364-365, etc.
  Line 161, “provides”-provide.
  Line 452, “may contains”->may contain
  Please also check other parts of the manuscript.
  Reply2: Thanks for your comments. We apologize for our English language of the previous manuscript. We have carefully checked and improved the English writing. We have asked an English professional teacher to polish our paper to improve the readability. We have also asked a PhD in Geodesy, a native English speaker, to read through the paper and give some advice.
  Comment3: The literature on Equation (1) should be cited, because it would be difficult for readers to know how the formulas are derived.
  Reply3: Thank you for your suggestion. We apologize for the missing of clear explanations in the previous manuscript. We checked Equation (1) and added some descriptions: The spherical harmonic coefficients in the ICE-6G model correspond to the inter-annual trend, and we need to compute the monthly trend and compute the GIA effect for each month. Finally, the monthly GIA effect is subtracted from the GRACE monthly spherical harmonic coefficients.
  Comment4: Lines 333-334. The time period is from 1993 to 2019. If the time interval is 1 year, 18 mean sea level models can be derived, but not 9 models. It seems that the interval should be 2 year. Please check it.
  Reply4: Thanks very much for your comments. We apologize for the missing of detailed explanations of some manipulations in the previous manuscript. In this study, the 19-year moving window method was used to divide the altimetry data between 1993 and 2019 into nine groups (1993-2011, 1994-2012, 1995-2013, 1996-2014, 1997-2015, 1998-2016, 1999-2017, 2000-2018, 2001-2019, respectively), and nine mean sea level models were constructed, which in turn estimated the altimetry sea level change rate (SLCR).
  Comment5: Lines 374-375, How to process the land effect on therecovery of spherical harmonic coefficients? Is the impact of land large, since there is no data?
  Reply5: Thank you for your valuable suggestions. Since the land time-varying gravity observation data are insufficient, the data on land are set to 0 in this study. The MGCR (Fig. 7(a)) is calculated using the SLCR (Fig. 6(a)) by applying the spherical harmonic function method. Comparing Figures 6(a) and 7(a), it can be seen that the data on land set to 0 does not have a significant effect on the results. In the future, the time-varying gravity observation data on land can be used as a supplement to construct a global-scale gravity change model.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC3
- AC5: 'Reply on CC1', Jinyun Guo, 27 Feb 2024
  
  Comment1: Main concern: How to validate the results? As shown in Figure 9, SDUST2020MGCR has large differences with GRACE2020MGCR. Although GRACE derived results has low resolution, the long wavelength signals of them should have high accuracy. The advantage of altimetry results is in short-wavelength part. Therefore, SDUST2020MGCR should be consistent with GRACE2020MGCR in long-wavelength part in Figure 9, to prove the high accuracy of SDUST2020MGCR. Unfortunately, it is not like that in Figure 9. Or other validation could be added. More explanations or analysis can also be added.
  Reply1: Thank you for your valuable comments. Our modification and additions are as follows:
  Modification of figure 9: We checked the Figure 9 and found an error. During the previous power spectral density analysis, the geospatial ranges of GRACE2020MGCR and SDUST2020MGCR were not exactly the same, hence the erroneous results shown in Figure 9. We repeated the power spectral density analysis, and the geospatial ranges of both GRACE2020MGCR and SDUST2020MGCR are -70S~70°N and 0~360°E, and the result of the power spectral density analysis is shown in the following figure. This figure shows that the signal strengths in the long wavelength of GRACE2020MGCR and SDUST2020MGCR are basically the same, while the signal strength in the short-medium wavelength of SDUST2020MGCR is greater than GRACE2020MGCR. This result is more consistent with reality.
  Addition of more explanations and analyses: In many previous studies, there is a problem that the independent observations of GRACE satellite and altimetry satellite do not match well in terms of spatial resolution and observation accuracy, the GRACE and altimetry results are difficult to verify each other (Willis et al., 2008; Feng et al., 2014; Zhang and Wang 2015). Therefore, it is difficult to use GRACE results to assess the uncertainty of altimetry results. In this study, our modeling statistics show that: the GRACE results have a larger STD than the altimetry results. We have added some explanations and analysis: “The processed GRACE data still have strip noise residuals and signal leakage error residuals (Chen et al., 2014), the large STD of GRACE MGCR may be related to these error residuals. And strip noise, leakage errors and their residuals affect the true physical signal, so the GRACE time-varying marine gravity used for comparison is not precise. In the process of solving the mean sea level using the along-track altimetry data, the altimetry data were preprocessed (such as 19-year moving grouping, collinear adjustment, space-time objective analysis interpolation, and crossover adjustment) to eliminate the influence of anomalous ocean variability and some residuals, meanwhile, the high-frequency signal is also attenuated, so that the STD of the SDUST MGCR is smaller.
  Addition of other validation: Although it is not possible to use the GRACE MGCR to evaluate the reliability of the altimetry MGCR, we have added a reliability analysis based on comments of anonymous referee #1. We split the altimetry data in half, use data groups 1-5 to estimate SLCR1 and data groups 5-9 to estimate SLCR2, and then calculate the difference between the two SLCR. The regions with large SLCR differences mainly correspond to the ocean current areas, and the reliability of altimetry SLCR in these regions may be lower. The true results of marine gravity changes at ocean currents remain to be verified and analyzed by future gravity satellite programs that provide global gravity field results with higher spatiotemporal resolution. The use of altimetry data can maximize the opportunity to construct a high-resolution, high-precision MGCR model. Although the altimetry MGCR may be less reliable at ocean current areas, the construction of altimetry MGCR fills the data gap compared to inability of GRACE to detect small-scale marine gravity changes caused by ocean currents, which is already an improvement.
  Willis, J.K., Chambers, D.P. and Nerem, R.S.: Assessing the globally averaged sea level budget on seasonal to interannual timescales, J. Geophys. Res. Oceans, 113 (C6), https://doi.org/10.1029/2007JC004517, 2008.
  Feng, W., Zhong, M. and Xu, H.: Global sea level changes estimated from satellite altimetry, satellite gravimetry and Argo data during 2005-2013, Prog. Geophys., 29 (2), 471–477, doi:10.6038/pg20140201, 2014.
  Zhang, B. & Wang, Z.: Global sea level variations estimated from satellite altimetry, GRACE and oceanographic data, Geomat. Inform. Sci. Wuhan Univ., 40 (11), 1453–1459. doi:10.13203/j.whugis20150230, 2015.
  Chen, J., Li, J., Zhang, Z., & Ni, S.: Long term groundwater variations in Northwest India from satellite gravity measurements. Global and Planetary Change, 116, 130-138. https://doi.org/10.1016/j.gloplacha.2014.02.007, 2014.
  
  Citation: https://doi.org/10.5194/essd-2023-498-AC5

Fengshun Zhu, Jinyun Guo, Huiying Zhang, Lingyong Huang, Heping Sun, and Xin Liu

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SDUST2020MGCR: a global marine gravity change rate model determined from multi-satellite altimeter data Zhu Fengshun, Guo Jinyun, Zhang Huiying, Huang Lingyong, Sun Heping, Liu Xin https://doi.org/10.5281/zenodo.10096803

Fengshun Zhu, Jinyun Guo, Huiying Zhang, Lingyong Huang, Heping Sun, and Xin Liu

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We used multi-satellite altimeter data to construct a high-resolution marine gravity change rate (MGCR) model on 5′×5′ grids, named SDUST2020MGCR. The spatial distribution of SDUST2020MGCR and GRACE MGCR are similar, such as eastern seas of Japan (dipole), western seas of the Nicobar Islands (rising), and southern seas of Greenland (falling). In particular, the SDUST2020MGCR can provide a detailed view of long-term marine gravity change, which will help to study the Earth's mass migration.


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