the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Jan 2025
GCL-Mascon2024: a novel satellite gravimetry mascon solution using the short-arc approach
Abstract. This paper reports an innovative mass concentration (mascon) solution obtained with the short-arc approach, named “GCL-Mascon2024”, for estimating spatially enhanced mass variations on the Earth's surface by analyzing K-/Ka Band Ranging satellite-to-satellite tracking data collected by the Gravity Recovery And Climate Experiment (GRACE) mission. Compared to contemporary GRACE mascon solutions, this contribution has three notable and distinct features: First, this solution recovery process incorporates frequency-dependent data weighting techniques to reduce the influence of low-frequency noise in observations. Second, this solution uses variable-shaped mascon geometry with physical constraints such as coastline and basin boundary geometries to more accurately capture temporal gravity signals while minimizing signal leakage. Finally, we employ a solution regularization scheme that integrates climate factors and cryospheric elevation models to alleviate the ill-posed nature of the GRACE mascon inversion problem. Our research has led to the following conclusions: (a) the temporal signals from GCL-Mascon2024 exhibit 6.5 %−20.4 % lower residuals over the continental regions, as compared with the (Release) RL06 versions of other contemporary mascon solutions from GSFC, CSR, and JPL; (b) in Greenland and global hydrologic basins, the correlation coefficients of estimated mass changes between GCL-Mascon2024 and other RL06 mascon solutions exceed 95.0 %, with comparable amplitudes; especially over non-humid river basins, the GCL-Mascon2024 suppresses random noise by 36.7 % compared to contemporary mascon products; and (c) in desert regions, the analysis of residuals calculated after removing the climatological components from the mass variations indicates that the GCL-Mascon2024 solution achieves noise reductions of over 28.1 % as compared to the GSFC and CSR RL06 mascon solutions. The GCL-Mascon2024 gravity field solution (Yan and Ran, 2024) is available at https://doi.org/10.5281/zenodo.14008167.
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Status: final response (author comments only)
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RC1: 'Comment on essd-2024-512', Anonymous Referee #1, 04 Mar 2025
Summary
This paper presents a novel satellite gravimetry mascon solution named GCL-Mascon2024 for recovering the mass changes on the Earth's surface, which is the first to implement the short-arc approach for Mascon solution estimation. I commend the authors for their novel approach and encourage them to continue refining and expanding upon this exciting methodology. The research findings are highly innovative and scientifically valuable and are of great significance for the research of the Earth's gravity field and the development of related fields. The paper has a complete structure, clear logic, reasonable experimental design, and detailed data, providing new ideas and methods for follow-up research. However, there is still room for improvement. I would like to recommend minor revisions of the manuscript before publication in Earth System Science Data, according to the comments as follows.
Comments
- I would like to know whether the gradient correction, a well-established component of the classical short-arc approach, was incorporated into the Mascon solution process. If gradient correction was applied, I recommend the authors provide a detailed description of the strategy used. If gradient correction was not applied, the authors should justify this decision. This additional information would enhance the methodological transparency and allow readers to better evaluate the robustness of the proposed approach.
- The noise of GCL-Mascon2024 in the Caspian Sea and northern Australia is very low. This is an intriguing result that warrants further investigation. It is advisable to conduct an in-depth analysis centering around the Caspian Sea, highlighting the performance of your solution and improving the analysis.
- It is recommended to add comparisons of the residuals in the open ocean.
- Please clarify the time interval used for constructing the observation equation, particularly in light of the differing sampling rates between the kinematic orbit (10 seconds) and other L1B data (5 seconds). Specifically, address how these discrepancies in sampling rates are reconciled.
- Kindly provide a detailed explanation of the error assessment strategy employed for the kinematic orbits. This should include the following: -The criteria used to identify and classify errors, -Whether interpolated epochs are incorporated into constructing the observation equation, etc.
Minor comments
- Page 3, Lines 93-95: Section 5 is information on the dataset, and section 6 is the conclusion. These two parts are reversed in the text. Please adjust the order to ensure consistency.
- Page5, Line 157, Table 1: Please explain the similarities and differences between the background force model in the Mascon solution and the spherical harmonic solution.
- Page12, Line 320: annual amplitude -> annual amplitudes
- Page 16, Table 5: The table currently presents with four decimal places. However, such precision does not appear necessary for this study's context. To improve clarity and readability, it is recommended to round the values to 1 decimal place or, at most, 2 decimal places.
- Page 19, Table6: Similar to the above comment. Please revise the table 6 accordingly.
- Page 18, section 4.2.3: Please explain why the climate component needs to be removed from the desert for the Mascon solutions validation and assessment and add the necessary references.
- Page 20, section 6: I recommend including the access dates for all datasets, which ensures readers and future researchers can trace the exact versions of the data used in the study.
- P25, Lines 794-796: The manuscript generally maintains a high referencing standard; however, I noticed inconsistencies in the formatting of author names in the reference list. e.g., in Line 794, the author is cited as "Wiese, D.," while in Line 796, the same author is cited as "Wiese, D. N.". I recommend carefully reviewing the entire reference list and standardizing the formatting of author names.
Citation: https://doi.org/10.5194/essd-2024-512-RC1 -
CC1: 'Comment on essd-2024-512', Yaozong Li, 10 Mar 2025
This paper presents some novel work for a new mascon result, particularly in the design of regularization matrix.
I woud like to know the underlying considerations behind different resolutions for ocean and land regions ( 400×400 km vs. 300×300 km).
The design of the MVRCN matrix lacks specific explanation for oceanic regions, and similarly, analysis of the results.
Figure 8, Panel (b): y-axis label may be corrected from “mE/Hz1/2” to "m/Hz1/2"; Panel (d): to "m/s/Hz1/2".
Citation: https://doi.org/10.5194/essd-2024-512-CC1 -
RC2: 'Comment on essd-2024-512', Anonymous Referee #2, 06 Apr 2025
The manuscript provides a new approach to estimate a mascon-based GRACE product. The manuscript is well organized and the technical details are clearly presented. It has a high potential to contribute to this field and to raise widespread interest. However, the results have some unique features that deviate from the previous mascon products and I am curious about their reliability.
1) the seemingly high spatial resolution of the product in this study (GCL-mascon2024) apparently comes from the regularization constraint shown in Fig. 3. This strong and time-invariant a priori information could lead to several problems. First, the distribution of the regularization agrees well with the seasonality in mass changes, but deviates from the long-term trends, implying that the trend will be less constrained. It is strange that the authors didn’t provide a comparison of the trend maps. Second, the oceans are not constrained, and the authors didn’t provide the results in oceans either. I suspect that the results in oceans may not be as good as on land. Third, I don’t get the rationale for placing a topographic constraint on ice sheets.
2) The results of this study seem to be always smaller than the other mascons (Fig. 9, 10). I feel a stronger regularization is imposed in this study. How about the series of total mass changes in Greenland and Antarctica?
3) The comparison in Apr. 2008 (Fig. 6) looks like GCL-mascon2024 could provide more details, .e.g, in the tropical Africa, Bangladesh and Amazon. But some signals seem to be removed, e.g., in Caspian and Madagascar. Please add more regional comparisons and use hydrological models to evaluate the differences. Comparison for more epochs is also recommended.
The comparison in Annual amplitude (Fig. 7) also raises some interesting phenomenon. Again, GCL-mascon2024 shows are details, but also numerous speckles, in the south of the Sahara Desert, in the U.S, and in south China. Some signals are missing, like, in California, Caspian (I feel the authors directly attribute zero to this region), areas surrounding the Gulf of Carpentaria. Some signals are newly revealed, like, in eastern Europe.
4) there should be comparison in the time series of ocean mass and a check on the mass conservation at the global scale.
5) The figures are of poor quality. The maps are too small and the time series are blurred. This seriously affects the correct assessment of the quality of the results.
--- other comments
L76, it should be explained the potential advantage of using short-arc.
Equ(1) rho_i is not explained
L130, I could not see basin boundaries play a role in Fig. 1.
L133, “no signal correlation between basins”, I am curious to see whether it is physically true. Have the authors carried out numerical experiments based on models to confirm this? Besides, where did the authors apply this non-correlation criterion in the inversion?
Fig. 1, the polar regions are distorted. Add plots using polar projection to better show these regions.
Equ(4) \epsilon_0 is not explained.
Equ (5), there is no regularization factor in front of C_M?
Fig. 3, I feel this map will be upscaled to the mascon-size resolution. If so, please also provide this map.
It should be explained how the values in oceans are derived.
L240, I don’t get why there should be a constraint based on topography in ice sheets.
L244, why in equ (5) does the L-curve take an effect? I suppose there is a regularization factor. Besides, is the regularization factor different month by month? If so, please show it. Third, please give some examples illustrating the sensitivity of results to different regularization factors.
Citation: https://doi.org/10.5194/essd-2024-512-RC2
Data sets
GCL-Mascon2024: a novel satellite gravimetry Mascon solution using the short-arc approach Zhengwen Yan and Jiangjun Ran https://doi.org/10.5281/zenodo.14008167
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