the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Feb 2026
HUST-Grace2026s: A high-resolution static gravity field product from GRACE and GRACE-FO observations (2002–2025)
Abstract. HUST-Grace2026s is a GRACE-only static gravity field determined by HUST (Huazhong University of Science and Technology). It’s determined based on more than 20 years’ observation data from GRACE (Gravity Recovery and Climate Experiment) and its successor GRACE-FO. The model provides high spatial resolution (up to degree/order 180) for mass distribution monitoring, complementing temporal series like HUST-Grace2024.
This study presents the motivation and key outcomes behind our new static gravity field model, HUST-Grace2026s: (1) Merely adding current GRACE-FO observations offers limited improvement to existing GRACE-only models, due to GRACE-FO’s current orbital altitude. (2) The application of stochastic model based on postfit residual significantly enhances accuracy, reducing cumulative geoid error by up to 66 % at degree 180 compared to the nominal strategy. (3) The benefit of LRI data on static gravity field determination is strongly tied to the strategy for estimating rate terms. (4) Comprehensive internal and external validation confirms that HUST-Grace2026s achieves higher spatial resolution than unregularized solutions and improves accuracy by over 50 % compared to its predecessor, HUST-Grace2016s. This product serves as a benchmark for long-term mass change studies.
The primary model data consisting of potential coefficients representing Earth’s static gravity field, together with secular and annual variations. This data set is identified with the following DOI: https://doi.org/10.5880/icgem.2026.001 (Zhou et al, 2026).
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Status: open (until 25 Apr 2026)
- CC1: 'Comment on essd-2026-53', Jiahui Zhang, 02 Mar 2026 reply
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RC1: 'Comment on essd-2026-53', Anonymous Referee #1, 20 Mar 2026
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General Comments
This manuscript presents a significant and timely contribution to the field of satellite gravimetry by introducing HUST-Grace2026s, a new static gravity field model that consistently integrates over 20 years of data from both the GRACE and GRACE-FO missions, thereby bridging the gap between these two satellite gravimetry eras. The authors apply advanced processing strategies—including stochastic modeling based on postfit residuals and rate-term estimation—to derive the model, and provide a thorough validation against independent data sources. The work is well-structured, technically sound, and offers valuable insights into the challenges and opportunities of extending static gravity field solutions into the GRACE-FO era. However, several aspects of the manuscript would benefit from clarification and revision to enhance its clarity, consistency, and impact. The following comments are intended to help the authors strengthen the presentation and address a few issues that may affect the interpretation of their results.
Comment on key outcome 1 (P26;)
The first conclusion states that "processing chain refinements can play a more critical role than the simple addition of GRACE-FO data." While this finding is supported by the analysis of the current dataset (GRACE-FO data up to March 2025 at ~500 km altitude), the statement as written lacks the temporal qualifiers that the authors themselves include in the main text (e.g., in Section 3.1.2, they note that GRACE-FO "currently operates at a higher orbital altitude of about 500 km"). To maintain consistency and avoid overgeneralization, it is recommended that the authors explicitly qualify this conclusion in the same manner, noting that it applies to the current orbital phase of GRACE-FO and that this assessment may change as the orbit decays in later mission phases.
Comment on Contribution Matrices (Figures 10 and 11)
The contribution matrices in Figures 10 and 11 are presented as revealing the "relative importance" of each data source. However, these matrices are derived from normal equations that are themselves influenced by the chosen parameterization (e.g., rate-term truncation at degree 60), and VCE weighting. They reflect the modeler's decisions as much as the data's inherent information content. The claim that GRACE-FO LRI data "provides the principal constraint on zonal coefficients" may be an artifact of the specific processing choices rather than a fundamental property of the data. A more cautious interpretation would strengthen the manuscript by acknowledging that these contributions are conditional on the processing framework.
Minor Comments
Minor Comment on Section 3.1.2
In the second paragraph of Section 3.1.2 (Page 16), the authors state that they attribute the limited improvement from GRACE-FO data to "two main factors," but then proceed to list three factors (numbered 1, 2, and 3). This inconsistency should be corrected. Please revise either the introductory phrasing to read "three main factors" or adjust the numbering to match the stated count.
Minor Comment on Section Numbering
In Section 3.1, the subsection titled "Combination with KBR1B data" is numbered as 3.2.2. This appears to be a numbering error, as it should be 3.1.2 to be consistent with the hierarchical structure. Please correct this numbering.
Comment on Figures with Multiple Curves (e.g., Figures 4, 5, 6, 8, 9, 12, 15)
The authors present multiple curves in these figures to compare different models or processing strategies. However, the current color scheme, particularly the use of similar shades of blue and green, makes it difficult to distinguish between curves. This issue is compounded by the fact that many of these curves exhibit only small differences, which are already challenging to visualize. To improve readability and allow readers to better appreciate both the similarities and subtle distinctions among the compared solutions, it is recommended to use a more distinguishable color palette (e.g., colorblind-friendly options from ColorBrewer) and/or incorporate distinct line styles (solid, dashed, dotted). These adjustments will not only enhance clarity but also help convey that certain models are nearly identical in performance.
Citation: https://doi.org/10.5194/essd-2026-53-RC1
Data sets
HUST-Grace2026s: unconstrained GRACE and GRACE Follow-On Static gravity field solution Hao Zhou, Lijun Zheng, Zebing Zhou, and Zhicai Luo https://doi.org/10.5880/icgem.2026.001
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This paper showcases the latest progress of the HUST team in the field of gravity field modeling. HUST-Grace 2026s successfully integrates 23 years of GRACE and GRACE-FO observation data spanning from 2002 to 2025. Both the accuracy and reliability of the model have been significantly enhanced. Incorporating LRI1B data into the static field determination framework is a major highlight of this study, providing a valuable reference for the establishment of cross generational satellite gravity benchmarks.
There may still be room for further exploration regarding the analysis of the LRI contribution. Utilizing the resolution matrix is an effective way to understand the relative contribution of each observation component within the entire solution system. According to the results in Fig. 11, GRACE KBR plays a more dominant role compared to GRACE-FO KBR/LRI for the HUST-Grace 2026s model. This is likely due to the fact that the GRACE KBR data spans 15 years while the GRACE-FO data covers only about 6 years within the timeframe. However, this could easily lead readers to the misconception that the data of GRACE KBR is superior to that of GRACE-FO KBR/LRI. I believe this point needs to be clarified in the text to distinguish between data quantity and data quality. Additionally, I am curious to know what the relative contributions of GRACE-FO KBR and LRI to the static field would be if the calculation timeframe were restricted to the GRACE-FO mission period alone, for example, from January 2019 to June 2023.