{"title":"Jacobi’s solution for geodesics on a triaxial ellipsoid","authors":"Charles F. F. Karney","doi":"10.1007/s00190-026-02030-3","DOIUrl":"https://doi.org/10.1007/s00190-026-02030-3","url":null,"abstract":"On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of this solution is described. This entails accurately evaluating the integrals and solving the resulting coupled system of equations. The inverse problem, finding the shortest path between two points on the ellipsoid, can then be solved using a similar method as for biaxial ellipsoids.","PeriodicalId":54822,"journal":{"name":"Journal of Geodesy","volume":"94 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2026-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146205318","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":"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}
{"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}
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}
{"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}
{"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}