DTRF2020 is the latest realization of the International Terrestrial Reference System (ITRS) by DGFI-TUM and is based on the same input data as ITRF2020. It is generated using the DGFI-TUM two-step combination approach, combining cumulative normal equations from the individual techniques GNSS, SLR, VLBI and DORIS. DTRF2020 introduces three key innovations: (1) it is the first secular ITRS realization with scale determined jointly from VLBI and GNSS; (2) it applies non-tidal loading corrections from atmospheric, oceanic, and hydrological models; and (3) it models post-seismic deformation using logarithmic and exponential functions. In addition to SINEX and EOP files, DTRF2020 provides all information required to compute instantaneous station positions: non-tidal loading reductions, post-seismic deformation models, residual and translations time series. Non-tidal loading corrections reduce GNSS height RMS for 99% of stations and significantly decrease annual signals in translation and scale. DTRF2020 agrees well with DTRF2014. Compared to ITRF2020, transformation differences reach up to 3.1 mm in position and 0.13 mm/yr in velocity for GNSS, VLBI, and SLR, and below 4.6 mm and 0.27 mm/yr for DORIS. Height velocities are consistent with GIA and CMR-based models, with regional differences within ± 3 mm/yr.
{"title":"DTRF2020: The ITRS 2020 realization of DGFI-TUM","authors":"Manuela Seitz, Mathis Bloßfeld, Matthias Glomsda, Detlef Angermann, Sergei Rudenko, Julian Zeitlhöfler, Florian Seitz","doi":"10.1007/s00190-026-02032-1","DOIUrl":"https://doi.org/10.1007/s00190-026-02032-1","url":null,"abstract":"DTRF2020 is the latest realization of the International Terrestrial Reference System (ITRS) by DGFI-TUM and is based on the same input data as ITRF2020. It is generated using the DGFI-TUM two-step combination approach, combining cumulative normal equations from the individual techniques GNSS, SLR, VLBI and DORIS. DTRF2020 introduces three key innovations: (1) it is the first secular ITRS realization with scale determined jointly from VLBI and GNSS; (2) it applies non-tidal loading corrections from atmospheric, oceanic, and hydrological models; and (3) it models post-seismic deformation using logarithmic and exponential functions. In addition to SINEX and EOP files, DTRF2020 provides all information required to compute instantaneous station positions: non-tidal loading reductions, post-seismic deformation models, residual and translations time series. Non-tidal loading corrections reduce GNSS height RMS for 99% of stations and significantly decrease annual signals in translation and scale. DTRF2020 agrees well with DTRF2014. Compared to ITRF2020, transformation differences reach up to 3.1 mm in position and 0.13 mm/yr in velocity for GNSS, VLBI, and SLR, and below 4.6 mm and 0.27 mm/yr for DORIS. Height velocities are consistent with GIA and CMR-based models, with regional differences within ± 3 mm/yr.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"12 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146138716","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}
Pub Date : 2026-02-05DOI: 10.1007/s00190-026-02034-z
Jia-Chun Guo, Nico Sneeuw, Shao-Feng Bian, Yi Liu
{"title":"Analytic definitions of the Gauss–Krüger projection: a review and two new formulations","authors":"Jia-Chun Guo, Nico Sneeuw, Shao-Feng Bian, Yi Liu","doi":"10.1007/s00190-026-02034-z","DOIUrl":"https://doi.org/10.1007/s00190-026-02034-z","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"45 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146138719","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}
Pub Date : 2026-02-01DOI: 10.1007/s00190-026-02031-2
Fei Lin, Yu Sun, Natthachet Tangdamrongsub, Shuo Zheng, Bao Zhang
{"title":"Implications of phase information from GPS and GRACE(FO) for identifying GPS stations influenced by poroelastic deformation","authors":"Fei Lin, Yu Sun, Natthachet Tangdamrongsub, Shuo Zheng, Bao Zhang","doi":"10.1007/s00190-026-02031-2","DOIUrl":"https://doi.org/10.1007/s00190-026-02031-2","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"30 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146101867","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}
Pub Date : 2026-01-26DOI: 10.1007/s00190-025-02027-4
Zemin Wu, Shaofeng Bian
{"title":"Applications of GNSS BIE-ECDs theory to the least-squares estimator of the integer ambiguity","authors":"Zemin Wu, Shaofeng Bian","doi":"10.1007/s00190-025-02027-4","DOIUrl":"https://doi.org/10.1007/s00190-025-02027-4","url":null,"abstract":"","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"15 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048448","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}
Pub Date : 2026-01-23DOI: 10.1007/s00190-025-02028-3
Pavel Ditmar
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 $$271 pm 10$$271±10 Gt/yr. It varied between $$19 pm 4$$19±4 Gt/yr in northeast DS and $$77 pm 7$$77±7 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.
{"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}
Pub Date : 2026-01-22DOI: 10.1007/s00190-025-02013-w
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
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.
{"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}
Pub Date : 2026-01-17DOI: 10.1007/s00190-025-02017-6
Tao Jiang, Zejie Tu, Jiancheng Li
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.
{"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}
Pub Date : 2026-01-17DOI: 10.1007/s00190-025-02029-2
Huacan Hu, Haiqiang Fu, JianJun Zhu, Yanzhou Xie, Qijin Han, Aichun Wang, Mingxia Zhang, Jun Hu
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.
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：