The satellite-only gravity field model GOCO2025s

Öhlinger, Felix; Mayer-Gürr, Torsten; Krauss, Sandro; Dumitraschkewitz, Patrick; Strasser, Andreas; Süsser-Rechberger, Barbara; Brockmann, Jan Martin; Niedermaier, Josef

doi:10.5194/essd-2026-639

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https://doi.org/10.5194/essd-2026-639

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29 Sep 2026

| 29 Sep 2026

Status: this preprint is currently under review for the journal ESSD.

The satellite-only gravity field model GOCO2025s

Felix Öhlinger, Torsten Mayer-Gürr, Sandro Krauss, Patrick Dumitraschkewitz, Andreas Strasser, Barbara Süsser-Rechberger, Jan Martin Brockmann, and Josef Niedermaier

Abstract. GOCO2025s is a global gravity field model represented by spherical harmonic coefficients up to degree and order 300, with constrained secular, annual, and semi-annual variations up to degree and order 200. It is derived from 23 years of satellite data, incorporating observations from the dedicated gravity field missions Gravity field and steady-state Ocean Circulation Explorer (GOCE), Gravity Recovery and Climate Experiment (GRACE), and GRACE Follow-On (GRACE-FO), as well as kinematic orbits of 18 low Earth orbit satellites and satellite laser ranging observations to 9 passive geodetic satellites. The complementary measurement principles of the different satellite missions and their strengths in determining specific parts of the spherical harmonic spectrum were exploited by combining the data at the normal equation level, with emphasis on the stochastic modeling of each contribution. Particular focus was placed on the inclusion of GRACE-FO laser ranging interferometer (LRI) data, which provided the dominant contribution to the estimation of the spherical harmonic coefficients between degrees 70 and 200. All processing steps, except for the determination of the GOCE normal equations, were carried out at the Institute of Geodesy at Graz University of Technology (TUG) employing up-to-date background models. The consistent in-house processing of nearly all satellite data, using the Gravity Recovery Object Oriented Programming System (GROOPS) software package, minimized errors arising from inconsistencies of different algorithms or models being applied.

The individual files of the GOCO2025s model (Öhlinger et al., 2025) are available at the TUG repository and identified with the following DOI: 10.3217/f48p8-8h651. They comprise the static and time-dependent gravity field coefficients and their respective uncertainty information, all parts of the normal equation system of the static gravity field, and the gravitational potential of non-tidal atmospheric and ocean masses already included in GOCO2025s.

Received: 10 Aug 2026 – Discussion started: 29 Sep 2026

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Felix Öhlinger, Torsten Mayer-Gürr, Sandro Krauss, Patrick Dumitraschkewitz, Andreas Strasser, Barbara Süsser-Rechberger, Jan Martin Brockmann, and Josef Niedermaier

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'Comment on essd-2026-639', Anonymous Referee #1, 26 Oct 2026 reply
This manuscript presents GOCO2025s, a publicly available satellite-only gravity field model developed by combining different types of satellite observations at the normal-equation level. Compared to GOCO06s, the new model incorporates GRACE-FO observations and data from additional low Earth orbit satellites, uses updated background and stochastic modeling strategies, and extends the temporal parameterization. The model provides a useful basis for further satellite gravity field studies and data combinations. However, several aspects of the methodology and the interpretation of the results require further clarification or additional analysis:

In Section 2.2, GOCO2025s is described as including semi-annual terms in addition to the trend and annual terms used in GOCO06s. Although the inclusion of semi-annual terms may improve the representation of periodic gravity field variations, it also increases the number of parameters to be estimated, which may strengthen correlations with the static coefficients, trends, and annual terms, and allow some residual modeling errors to be absorbed. While the manuscript describes the regionally varying prior constraints applied to the semi-annual terms, it does not assess their necessity or their influence on the other parameters to be estimated. Please explain the motivation for introducing these terms and consider comparing solutions with and without them using the same observations and processing settings. In particular, how does their inclusion affect the static gravity field coefficients, trends, and annual terms? Have the authors also examined the correlations between the semi-annual terms and other parameters, as well as the possibility that these terms may absorb residual errors arising from non-gravitational force modeling or background models?

The abstract and conclusions emphasize the contribution of LRI observations, whereas Figure 2 in Section 4.1 shows the relative contribution of the GRACE-FO normal equations as a whole, including KBR, LRI and kinematic orbit information. Moreover, LRI observations were not available for all GRACE-FO months. Therefore, the figure illustrates the overall contribution of GRACE-FO but does not directly quantify the improvement attributable to LRI. Please compare KBR-only and combined KBR+LRI solutions over the same periods when both ranging datasets are available. Differences in the spherical harmonic coefficients between degrees 70 and 200, together with corresponding validation results, would provide more direct evidence of the contribution of LRI observations.

In Section 3.2, The authors estimate the stochastic model from residuals from an adjustment truncated at degree and order 96 and subsequently apply it to gravity field recovery up to degree 230 or 250. The computational advantage of this approach is understandable, but it is unclear whether degree 96 is sufficient to characterize the observation noise for the higher-degree solutions. How is the gravity field signal above degree 96 treated during the preliminary adjustment? Have the authors investigated whether using a higher truncation degree in the preliminary adjustment affect the estimated stochastic model or the final gravity field solution?

In Eq. (10) of Section 3.3, the authors use 0.5 times the LISFLOOD signal as a proxy for hydrological background-model error because LISFLOOD uncertainty information was unavailable. While this explains the need for an approximation, the reason for choosing a scaling factor of 0.5 remains unclear. Was this value based on previous studies, selected through preliminary tests, or adopted as an empirical assumption? Please clarify the basis for this choice. It would also be useful to examine the sensitivity of the results to other plausible scaling factors.

In Sections 2.2 and 2.3, the temporal gravity field parameters for GRACE and GRACE-FO are estimated up to degree and order 150, whereas the final GOCO2025s model provides temporal coefficients up to degree and order 200, with regionalized regularization applied as described in Section 4. Could the authors clarify how the temporal coefficients of degrees 151–200 are determined, particularly the roles of observational information and the regionalized prior covariance in their estimation, and to what extent these higher-degree coefficients depend on the prior constraints?

There are also some expressions in the text that need to be confirmed:

(a) L381: "radial directions The" -> "radial directions. The"?
(b) L391: The statement “As expected, ITSG operational yields the lowest RMS values” is not entirely consistent with the results in Table 3, particularly for Swarm B. Please also ensure that the satellite names in Table 3 are consistent with those used in the main text.
(c) Specify the physical unit of the three-dimensional orbit RMS values in the caption；
(d) Figure 5 caption "GOCO2025s-dervied" -> "GOCO2025s-derived"?
(e) L472: "AOD1B_RL0X_included_in_GOCO22025s.gfc" -> "AOD1B_RL0X_included_in_GOCO2025s.gfc"?
(f) L516: "https://doi.org/https://doi.org/10.5880/ICGEM.2019.003, 2019." -> "https://doi.org/10.5880/ICGEM.2019.003, 2019."?

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Citation: https://doi.org/10.5194/essd-2026-639-RC1

Felix Öhlinger, Torsten Mayer-Gürr, Sandro Krauss, Patrick Dumitraschkewitz, Andreas Strasser, Barbara Süsser-Rechberger, Jan Martin Brockmann, and Josef Niedermaier

Data sets

The satellite-only gravity field model GOCO2025s Öhlinger, Felix; Mayer-Gürr, Torsten; Krauss, Sandro; Dumitraschkewitz, Patrick; Süsser-Rechberger, Barbara; Strasser, Andreas; Tieber-Hubmann, Cornelia; Brockmann, Jan Martin https://doi.org/10.3217/f48p8-8h651

Felix Öhlinger, Torsten Mayer-Gürr, Sandro Krauss, Patrick Dumitraschkewitz, Andreas Strasser, Barbara Süsser-Rechberger, Jan Martin Brockmann, and Josef Niedermaier

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Short summary

GOCO2025s is a global gravity field model derived from satellite observations collected over a period of 23 years. By combining complementary measurement principles from different satellite missions, it provides a highly accurate representation of the Earth’s gravity field. This information is crucial for investigating the dynamics and ongoing changes of our planet.


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