{"title":"Estimation of regional ice mass trends in Greenland using a global inversion of level-2 satellite gravimetry data","authors":"Pavel Ditmar","doi":"10.1007/s00190-025-02028-3","DOIUrl":"https://doi.org/10.1007/s00190-025-02028-3","url":null,"abstract":"A methodology has been developed for an accurate estimation of mass anomalies in the Earth system using level-2 data products from satellite gravimetry GRACE and GRACE Follow-On (GFO) missions. Its key elements are: (i) direct inversion of Spherical Harmonic Coefficients (SHCs)—or SHC trends—into a global distribution of mass anomalies (or their trends); (ii) Spatially-varying regularization that takes into account available information about the behavior of mass anomalies; and (iii) rigorous optimization of the data processing consistently with the target estimates. The methodology is applied to quantify the mass balance of the Greenland Ice Sheet and its individual Drainage Systems (DSs) in Apr. 2002–Aug. 2023 on the basis of GRACE/GFO monthly solutions from the Institute of Geodesy at Graz University of Technology (ITSG). It is found that the rate of the total mass loss in Greenland was <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$271 pm 10$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>271</mml:mn> <mml:mo>±</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> Gt/yr. It varied between <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$19 pm 4$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>19</mml:mn> <mml:mo>±</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> Gt/yr in northeast DS and <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$77 pm 7$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>77</mml:mn> <mml:mo>±</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> Gt/yr in southeast DS. In average, the mass balance of individual DSs is estimated with an accuracy better than 5 Gt/yr. As a consequence, the obtained estimates show a sufficiently high signal-to-noise ratio (between 5 in the northeast DS and 42 in the northwest DS). This opens the door, among other, for using GRACE/GFO data for a comparison, validation, and calibration of physical models describing mass changes in Greenland, including its surface mass balance, at the scale of individual DSs.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Schroth, T. Forbriger, M. Westerhaus, M. Müller, J. Saynisch-Wagner, B. K. Arbic, K. Drach, M. Thomas, U. Gräwe, J. F. Shriver, A. Mehra
{"title":"The annual variation of the M2 gravimetric tidal parameters investigated with nonlinear, time-stepping ocean models","authors":"E. Schroth, T. Forbriger, M. Westerhaus, M. Müller, J. Saynisch-Wagner, B. K. Arbic, K. Drach, M. Thomas, U. Gräwe, J. F. Shriver, A. Mehra","doi":"10.1007/s00190-025-02013-w","DOIUrl":"https://doi.org/10.1007/s00190-025-02013-w","url":null,"abstract":"Temporal variations of the M2 tidal parameters in gravity are observed at all superconducting gravimeter stations. We specifically investigate the annual variation of M2 tidal parameters. A similar variation is observed for the parameters from sea surface heights which is larger than expected from astronomical forcing alone. This leads to the hypothesis that the variations of the gravimetric tidal parameters are caused by the loading of the annual variation of M2 in the oceans. Only nonlinear, time-stepping ocean models are able to describe such variations. We use sea surface heights from three global and two regional models of this kind to calculate the loading. The loading time series is then added to synthetic body tides and analyzed by a moving window tidal analysis with ETERNA in the same way as the measured data. We compare the resulting variations of the M2 tidal parameters for synthetic gravity with those observed from measurements. Three of the five ocean models show an annual variation of a similar order of magnitude which supports our hypothesis. The other two ocean models produce smaller or no clear annual variation of the M2 tidal parameters. In the ocean the annual variation of M2 has large amplitudes in shelf areas and small amplitudes in the open ocean. Large areas with small amplitude might contribute to the gravity loading as much as small areas with large amplitudes do. We investigate this with the global Hycom model at three SG stations. The investigation shows that not only close shelf areas but also distant ocean regions, including open ocean areas, contribute significantly to the annual variation of the M2 tidal parameters at the superconducting gravimeter stations.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"67 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Physics-informed neural networks for geoid modeling","authors":"Tao Jiang, Zejie Tu, Jiancheng Li","doi":"10.1007/s00190-025-02017-6","DOIUrl":"https://doi.org/10.1007/s00190-025-02017-6","url":null,"abstract":"The accurate modeling of the Earth gravity field and geoid is critical for geodesy, yet traditional methods face limitations in handling the growing complexity and heterogeneity of modern geodetic data. To address these challenges, this study proposes a physics-informed neural network (PINN) framework for high-precision geoid modeling. The PINN employs convolutional neural networks (CNNs) to extract multi-scale features from terrestrial and airborne gravity data, which are then processed by a multilayer perceptron (MLP) to establish an accurate mapping between these features and the disturbing potential. Physical constraints, including Laplace’s equation and differential equations governing gravity anomaly and gravity disturbance, are embedded into the loss function to enhance both accuracy and interpretability. The proposed method is applied to the Colorado 1 cm geoid experiment. Compared to GNSS/leveling data of the Geoid Slope Validation Survey 2017 (GSVS17), the PINN-derived geoid model achieves a standard deviation (STD) of 2.1 cm. This represents a 12.5%–27.6% improvement over traditional methods and purely data-driven networks (DDNs). The PINN exhibits strong generalization under sparse data conditions, achieving 28.5% higher accuracy than the DDN with only 500 samples. Furthermore, analysis of geoid slopes and physical constraint contributions demonstrates that PINN’s dual physical constraints effectively balance global characteristics and localized fidelity of the geoid. This study establishes the PINN as a robust, physically interpretable machine learning approach for geoid modeling, outperforming classical methods and offering a promising pathway for gravity field estimation in regions with sparse or heterogeneous data. By bridging purely data-driven machine learning with fundamental geodetic principles, this work paves the way for future advancements in physics-informed machine learning-based geodetic modeling.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"45 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Huacan Hu, Haiqiang Fu, JianJun Zhu, Yanzhou Xie, Qijin Han, Aichun Wang, Mingxia Zhang, Jun Hu
{"title":"Sub-canopy topography estimation based on sub-aperture decomposition and least-squares collocation from LuTan-1 InSAR data","authors":"Huacan Hu, Haiqiang Fu, JianJun Zhu, Yanzhou Xie, Qijin Han, Aichun Wang, Mingxia Zhang, Jun Hu","doi":"10.1007/s00190-025-02029-2","DOIUrl":"https://doi.org/10.1007/s00190-025-02029-2","url":null,"abstract":"LuTan-1 (LT-1) provides unprecedented L-band bistatic interferometric synthetic aperture radar (InSAR) data for terrain mapping. In forested areas, although the L-band exhibits strong penetration capability, the phase center is still located above the bare ground due to forest volume scattering. Furthermore, the bistatic acquisition provides only single-baseline, single-polarization data, leading to an underdetermined issue for existing scattering models in sub-canopy topography inversion. To address these issues, this study proposes a sub-canopy topography estimation framework based on sub-aperture decomposition and the least-squares collocation (LSC) method. The contributions of this study are: 1) assessing the feasibility of sub-aperture decomposition under LT-1’s small azimuth observation angles; 2) using sub-aperture coherence to provide additional observations and address the underdetermination issue of InSAR inversion; and 3) developing an LSC-based method to separate and calibrate LT-1 orbital and scattering model errors, with the latter arising from complex terrain, forest property variations, and model solution. The proposed framework was tested and validated using LT-1 InSAR data acquired over coniferous, evergreen broadleaf, and tropical forests. The estimated sub-canopy topography achieved a root mean square error (RMSE) between 1.22 and 3.85 m, representing an average improvement of over 60% compared to the InSAR DEM and an improvement of over 30% compared to the initial terrain that did not account for scattering model errors. Moreover, the results indicate that the proposed method also exhibits superior performance under varying terrain and forest conditions, further demonstrating its effectiveness and robustness.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"63 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The gravitational potential inside, on, and outside of a homogeneous tetrahedron","authors":"Thunendran Periyandy, Michael Bevis","doi":"10.1007/s00190-025-02024-7","DOIUrl":"https://doi.org/10.1007/s00190-025-02024-7","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"11 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145770606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recent disappearing and re-excited Earth’s Chandler wobble: contributions from GRACE/GFO hydrological and cryospheric mass changes","authors":"Qiqi Shi, Yonghong Zhou, Jianli Chen, Xueqing Xu","doi":"10.1007/s00190-025-02021-w","DOIUrl":"https://doi.org/10.1007/s00190-025-02021-w","url":null,"abstract":"Geophysical sources and processes that excite the Earth’s Chandler wobble (CW) have long been debated. Significant discrepancies remain at times between geophysical fluid models, especially regarding inaccurate hydrological and cryospheric estimates, and observed CW series. Recently, the CW experienced anomalous behavior after 2015, with a disappearance and a re-excitation. Understanding hydrological and cryospheric effects on the CW and their contributions to this anomaly requires urgent investigation. Utilizing the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) measurements, we reconstruct the CW series contributed from the hydrology and cryosphere for the GRACE period (April 2002 to December 2015) and GFO period (June 2018 to December 2024), respectively. We find that GRACE/GFO measurements can capture more accurate hydrological and cryospheric forcing CW signals than models. For the first time, our reconstructed results successfully account for the recent observed disappearing and re-excited CW phenomenon. Considering global mass conservation associated with barystatic sea-level changes, the GRACE/GFO-derived hydrological and cryospheric effects agree well with geodetic CW observations. The absence of hydrological and cryospheric contributions on the reconstructed CW would lead to the unmanifested CW re-excitation phenomenon. Additionally, the relative contributions of the hydrology and cryosphere to CW amplitudes exhibit temporal variability, with ratios of approximately 3 to 1 and 2 to 1 during the GRACE and GFO periods, respectively. These findings improve our understanding of the Earth’s rotational dynamics under climate change in relation to the effects of hydrological and cryospheric processes.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"14 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalizing linear combination-based GNSS PPP-RTK network processing: geometry-free, ionosphere-free, and geometry- and ionosphere-free","authors":"Hans Daniel Platz","doi":"10.1007/s00190-025-02020-x","DOIUrl":"https://doi.org/10.1007/s00190-025-02020-x","url":null,"abstract":"Traditionally, global navigation satellite system (GNSS) observations in precise point positioning were processed using geometric ionosphere-free (GIF) code and phase linear combinations (LC). With multi-frequency observations of modernized GNSS, the processing of undifferenced and uncombined (UDUC) observations has gained popularity, often attributed to its increased flexibility and generality. Building on the theoretical foundation of UDUC processing, this work derives an equivalent LC-based network processing approach that maintains the full generality of the UDUC approach while offering some practical advantages. The approach makes use of the following types of LCs: (1) geometry-free and ionosphere free (GFIF), (2) geometric ionosphere-free (GIF), and (3) ionospheric geometry-free (IGF). When processing the GFIF LCs, biases and ambiguities can be estimated. The GFIF model enables compact modeling by reducing continuous observation arcs to a single observation and supports (extra-) wide-lane ambiguity resolution. To obtain the ionosphere-free model, i.e., an equivalent reformulation of the UDUC approach where epoch-wise and line of sight specific ionospheric delays are assumed, exactly one GIF LC per line-of-sight and epoch is added to the GFIF LCs. To obtain the geometry-free model, commonly used for ionospheric modeling, exactly one IGF LC is added to the GFIF LCs per line-of-sight and epoch. Adding both the GIF and IGF LCs to the GFIF LCs yields an exact reformulation of the UDUC with no implicit assumptions regarding ionospheric or geometric parameters. Finally, a brief runtime analysis of LC-based models shows case-dependent efficiency gains over UDUC implementations.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"29 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Agustín R. Gómez, Claudia N. Tocho, Ezequiel D. Antokoletz, Sergio R. Cimbaro
{"title":"Local quasigeoid modeling at Argentinean stations of the International Height Reference Frame (IHRF)","authors":"Agustín R. Gómez, Claudia N. Tocho, Ezequiel D. Antokoletz, Sergio R. Cimbaro","doi":"10.1007/s00190-025-02018-5","DOIUrl":"https://doi.org/10.1007/s00190-025-02018-5","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"107 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145593536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}