Assessment of temporal variations of geoid, ellipsoidal and orthometric heights at proposed IHRF sites using space geodetic data
Abstract
The determination of accurate geoid, ellipsoidal and orthometric heights is essential for applications related to surveying engineering, geodetic and geoscience research. The International Association of Geodesy (IAG) defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The realization of the IHRS to establish an International Height Reference Frame (IHRF) and its temporal variations, is an ongoing geodetic task. The objective of this research is to assess temporal variations of geoid, ellipsoidal and orthometric heights at proposed IHRF sites using space geodetic data, namely Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO), Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) and hydrological model. GRACE/GRACE-FO-based and GLDAS-based Global Geopotential Models were utilized to determine temporal variations of geoid height (ΔN) and time-dependent changes of ellipsoidal height (Δh) at proposed IHRF sites. Moreover, Δh at proposed IHRF sites were also obtained from GNSS, VLBI, SLR and DORIS solutions. Temporal variations of orthometric height (ΔH) at proposed IHRF sites were determined by combining ΔN and Δh. Results reveal that ΔN, Δh, and ΔH at proposed IHRF sites are not negligible as they can reach several centimetres in terms of seasonal variations and at the and 1 cm level annually. These ΔN, Δh, and ΔH would be required for the modernization and unification of international/national vertical datums in addition to contemporary requirements for precise height measurements.
Funding source: Narodowe Centrum Nauki
Award Identifier / Grant number: 2021/42/E/ST10/00218
-
Research ethics: Not applicable.
-
Informed consent: Not applicable.
-
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: The author states no conflict of interest.
-
Research funding: This research was funded by the National Science Center (NCN), Poland [grant number 2021/42/E/ST10/00218].
-
Data availability: Not applicable.
References
1. Drewes, H, Kuglitsch, F, Adám, J, Rózsa, S. The geodesist’s handbook 2016. J Geod 2016;90:907–1205. https://doi.org/10.1007/S00190-016-0948-Z.Search in Google Scholar
2. Foroughi, I, Vaníček, P, Kingdon, RW, Goli, M, Sheng, M, Afrasteh, Y, et al.. Sub-centimetre geoid. J Geod 2019;93:849–68. https://doi.org/10.1007/S00190-018-1208-1.Search in Google Scholar
3. Ellmann, A, Märdla, S, Oja, T. The 5 mm geoid model for Estonia computed by the least squares modified Stokes’s formula. Surv Rev 2020;52:352–72. https://doi.org/10.1080/00396265.2019.1583848.Search in Google Scholar
4. Wang, YM, Sánchez, L, Ågren, J, Huang, J, Forsberg, R, Abd-Elmotaal, HA, et al.. Colorado geoid computation experiment: overview and summary. J Geod 2021;95:127. https://doi.org/10.1007/S00190-021-01567-9.Search in Google Scholar
5. Ihde, J, Sánchez, L, Barzaghi, R, Drewes, H, Foerste, C, Gruber, T, et al.. Definition and proposed realization of the international height reference system (IHRS). Surv Geophys 2017;38:549–70. https://doi.org/10.1007/S10712-017-9409-3.Search in Google Scholar
6. Sánchez, L. International height reference system (IHRS): required measurements and expected products. In: GGOS days. Cambridge, MA, USA; 2016.Search in Google Scholar
7. Sánchez, L, Sideris, MG. Vertical datum unification for the international height reference system (IHRS). Geophys J Int 2017;209:570–86. https://doi.org/10.1093/GJI/GGX025.Search in Google Scholar
8. Sanchez, L, Barzaghi, R. Activities and plans of the GGOS focus area unified height system. In: EGU general assembly. Vienna, Austria; 2020.10.5194/egusphere-egu2020-8625Search in Google Scholar
9. Godah, W, Ray, JD, Szelachowska, M, Krynski, J. The use of national CORS networks for determining temporal mass variations within the Earth’s system and for improving GRACE/GRACE-FO solutions. Remote Sens 2020a;12:3359. https://doi.org/10.3390/RS12203359.Search in Google Scholar
10. Szelachowska, M, Godah, W, Krynski, J. Contribution of GRACE satellite mission to the determination of orthometric/normal heights corrected for their dynamics—a case study of Poland. Remote Sens 2022;14:4271. https://doi.org/10.3390/RS14174271.Search in Google Scholar
11. van Dam, T, Wahr, J, Lavallée, D. A comparison of annual vertical crustal displacements from GPS and gravity recovery and climate experiment (GRACE) over Europe. J Geophys Res Solid Earth 2007;112:B03404. https://doi.org/10.1029/2006JB004335.Search in Google Scholar
12. Eriksson, D, MacMillan, DS. Continental hydrology loading observed by VLBI measurements. J Geod 2014;88:675–90. https://doi.org/10.1007/S00190-014-0713-0.Search in Google Scholar
13. Rangelova, E, Sideris, MG. Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America. J Geodyn 2008;46:131–43. https://doi.org/10.1016/J.JOG.2008.03.006.Search in Google Scholar
14. Rangelova, E, Fotopoulos, G, Sideris, MG. Implementing a dynamic geoid as a vertical datum for orthometric heights in Canada. In: International association of geodesy symposia; 2010.10.1007/978-3-642-10634-7_38Search in Google Scholar
15. Krynski, J, Kloch-Glowka, G, Szelachowska, M. Analysis of time variations of the gravity field over Europe obtained from GRACE data in terms of geoid height and mass variation. In: International association of geodesy symposia; 2014.10.1007/978-3-642-37222-3_48Search in Google Scholar
16. Godah, W, Szelachowska, M, Krynski, J. On the analysis of temporal geoid height variations obtained from GRACE-based GGMs over the area of Poland. Acta Geophys 2017a;65:713–25. https://doi.org/10.1007/S11600-017-0064-3.Search in Google Scholar
17. Godah, W, Szelachowska, M, Krynski, J. On the estimation of physical height changes using GRACE satellite mission data – a case study of Central Europe. Geod Cartogr 2017b;66:211–26. https://doi.org/10.1515/geocart-2017-0013.Search in Google Scholar
18. Godah, W, Szelachowska, M, Krynski, J. Application of the PCA/EOF method for the analysis and modelling of temporal variations of geoid heights over Poland. Acta Geod Geophys 2018a;53:93–105. https://doi.org/10.1007/s40328-017-0206-8.Search in Google Scholar
19. Godah, W. IGiK–TVGMF: a MATLAB package for computing and analysing temporal variations of gravity/mass functionals from GRACE satellite based global geopotential models. Comput Geosci 2019;123:47–58. https://doi.org/10.1016/J.CAGEO.2018.11.008.Search in Google Scholar
20. Purkhauser, AF, Pail, R. Next generation gravity missions: near-real time gravity field retrieval strategy. Geophys J Int 2019;217:1314–33. https://doi.org/10.1093/gji/ggz084.Search in Google Scholar
21. Godah, W, Szelachowska, M, Zeray Öztürk, E, Krynski, J. On the contribution of physical height changes estimated with the use of GRACE satellite mission data to the modernization of a national vertical system. In: AGU fall meeting. Washington, D.C., USA; 2018.Search in Google Scholar
22. Zeray Öztürk, E, Godah, W, Abbak, RA. Estimation of physical height changes from GRACE satellite mission data and WGHM over Turkey. Acta Geod Geophys 2020;55:301–17. https://doi.org/10.1007/S40328-020-00294-5.Search in Google Scholar
23. Yadeta, SM, Godah, W, Szelachowska, M, Fotopoulos, G. Assessment of temporal variations of orthometric/normal heights at proposed international height reference frame sites using GRACE/GRACE-FO. Surv Rev 2024;56:489–99. https://doi.org/10.1080/00396265.2023.2293367.Search in Google Scholar
24. Zhang, S, Guo, J, Shi, T, Chang, X, Zhu, G, Huang, L, et al.. Height variations in the Mississippi River basin from daily time-varying satellite gravity data and hydrological model. IEEE J Sel Top Appl Earth Obs Remote Sens 2024;17:9846–57. https://doi.org/10.1109/JSTARS.2024.3397620.Search in Google Scholar
25. Guo, J, Shi, T, Jin, X, Liu, X, Zhao, B, Qiao, X. Geodetic analysis of orthometric height variations in mainland China using GRACE, hydrological models, and GPS data. IEEE Trans Geosci Rem Sens 2024;62:4504815–5. https://doi.org/10.1109/TGRS.2024.3386879.Search in Google Scholar
26. Kusche, J, Schmidt, R, Petrovic, S, Rietbroek, R. Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. J Geod 2009;83:903–13. https://doi.org/10.1007/s00190-009-0308-3.Search in Google Scholar
27. Landerer, F. CSR TELLUS GRACE-FO level-3 monthly ocean bottom pressure anomaly release 6.2 version 04. Ver. RL06.2v04. CA, USA: PO.DAAC; 2023.Search in Google Scholar
28. Cheng, M, Ries, J. C20 and C30 variations from SLR for GRACE/GRACE-FO science applications. J Geophys Res Solid Earth 2023;128:e2022JB025459. https://doi.org/10.1029/2022JB025459.Search in Google Scholar
29. SOPAC and CSRC. GARNER GPS archive; 2024. http://garner.ucsd.edu/pub/measuresESESES_products/Timeseries/Global/ [Accessed 5 Oct 2024].Search in Google Scholar
30. NGL. Nevada geodetic laboratory; 2024. http://geodesy.unr.edu/ [Accessed 5 Oct 2024].Search in Google Scholar
31. Blewitt, G, Hammond, WC, Kreemer, C. Harnessing the GPS data explosion for interdisciplinary science. Eos 2018;99. https://doi.org/10.1029/2018eo104623.Search in Google Scholar
32. Villiger, A, Dach, R. International GNSS service technical report 2016 (IGS annual report). IGS Central Bureau and University of Bern; 2017. Available from: https://boris-portal.unibe.ch/handle/20.500.12422/152377.Search in Google Scholar
33. Altamimi, Z, Rebischung, P, Métivier, L, Collilieux, X. ITRF2014: a new release of the international terrestrial reference frame modeling nonlinear station motions. J Geophys Res Solid Earth 2016;121:6109–31. https://doi.org/10.1002/2016JB013098.Search in Google Scholar
34. Bock, Y, Moore, AW, Argus, D, Fang, P, Golriz, D, Guns, K, et al.. Extended solid Earth science ESDR system (ES3): algorithm theoretical basis document. NASA MEaSUREs Project #NNH17ZDA001N; 2021. http://garner.ucsd.edu/pub/measuresESESES_products/ATBD/ESESES-ATBD.pdf [Accessed 27 Mar 2025].Search in Google Scholar
35. Araszkiewicz, A, Figurski, M, Jarosiński, M. Erroneous GNSS strain rate patterns and their application to investigate the tectonic credibility of GNSS velocities. Acta Geophys 2016;64:1412–29. https://doi.org/10.1515/acgeo-2016-0057.Search in Google Scholar
36. Wu, D, Yan, H, Shen, Y. TSAnalyzer, a GNSS time series analysis software. GPS Solut 2017;21:1389–94. https://doi.org/10.1007/s10291-017-0637-2.Search in Google Scholar
37. Amiri-Simkooei, AR, Hosseini-Asl, M, Asgari, J, Zangeneh-Nejad, F. Offset detection in GPS position time series using multivariate analysis. GPS Solut 2019;23:13. https://doi.org/10.1007/s10291-018-0805-z.Search in Google Scholar
38. Bruyninx, C, Legrand, J, Fabian, A, Pottiaux, E. GNSS metadata and data validation in the EUREF permanent network. GPS Solut 2019;23:106. https://doi.org/10.1007/s10291-019-0880-9.Search in Google Scholar
39. Khazraei, SM, Amiri-Simkooei, AR. Improving offset detection algorithm of GNSS position time-series using spline function theory. Geophys J Int 2021;224:257–70. https://doi.org/10.1093/gji/ggaa453.Search in Google Scholar
40. Lahtinen, S, Jivall, L, Häkli, P, Nordman, M. Updated GNSS velocity solution in the Nordic and Baltic countries with a semi-automatic offset detection method. GPS Solut 2022;26:9. https://doi.org/10.1007/s10291-021-01194-z.Search in Google Scholar
41. Magyar, B, Kenyeres, A, Tóth, S, Hajdu, I, Horváth, R. Spatial outlier detection on discrete GNSS velocity fields using robust Mahalanobis-distance-based unsupervised classification. GPS Solut 2022;26:145. https://doi.org/10.1007/s10291-022-01323-2.Search in Google Scholar
42. Willis, P, Lemoine, FG, Moreaux, G, Soudarin, L, Ferrage, P, Ries, J, et al.. The international DORIS service (IDS): recent developments in preparation for ITRF2013. In: International association of geodesy symposia; 2015.10.1007/1345_2015_164Search in Google Scholar
43. Moreaux, G, Lemoine, FG, Capdeville, H, Otten, M, Štěpánek, P, Saunier, J, et al.. The international DORIS service contribution to ITRF2020. Adv Space Res 2023;72:65–91. https://doi.org/10.1016/J.ASR.2022.07.012.Search in Google Scholar
44. CDDIS. Crustal dynamics data information system; 2024. https://urs.earthdata.nasa.gov/ [Accessed 5 Oct 2024].Search in Google Scholar
45. JPL. JTRF2014 solution; 2024. https://www.jpl.nasa.gov/site/jsgt/jtrf/solutions/jtrf2014/ [Accessed 21 Oct 2024].Search in Google Scholar
46. Schlüter, W, Behrend, D. The international VLBI service for geodesy and astrometry (IVS): current capabilities and future prospects. J Geod 2007;81:379–87. https://doi.org/10.1007/S00190-006-0131-Z.Search in Google Scholar
47. Vennebusch, M, Böckmann, S, Nothnagel, A. The contribution of very long baseline interferometry to ITRF2005. J Geod 2007;81:553–64. https://doi.org/10.1007/S00190-006-0117-X.Search in Google Scholar
48. Bachmann, S, Messerschmitt, L, Thaller, D. IVS contribution to ITRF2014. In: van Dam, T, editor. REFAG 2014, international association of geodesy symposia. Cham: Springer International Publishing; 2017, vol 146:47–52 pp.10.1007/1345_2015_136Search in Google Scholar
49. Pearlman, MR, Degnan, JJ, Bosworth, JM. The international laser ranging service. Adv Space Res 2002;30:135–43. https://doi.org/10.1016/S0273-1177(02)00277-6.Search in Google Scholar
50. Luceri, V, Pavlis, E. The ILRS contribution to ITRF2014. https://itrf.ign.fr/docs/solutions/itrf2014/ILRS-ITRF2014-description.pdf [Accessed 19 Apr 2025].Search in Google Scholar
51. Rodell, M, Houser, PR, Jambor, U, Gottschalck, J, Mitchell, K, Meng, CJ, et al.. The global land data assimilation system. Bull Am Meteorol Soc 2004;85:381–94. https://doi.org/10.1175/BAMS-85-3-381.Search in Google Scholar
52. GGFC. The IERS special bureau for hydrology. Global Geophysical Fluids Center; 2024. https://www2.csr.utexas.edu/research/ggfc/ [Accessed 5 Oct 2024].Search in Google Scholar
53. Müller Schmied, H, Caceres, D, Eisner, S, Flörke, M, Herbert, C, Niemann, C, et al.. The global water resources and use model WaterGAP v2.2d: model description and evaluation. Geosci Model Dev (GMD) 2021;14:1037–79. https://doi.org/10.5194/gmd-14-1037-2021.Search in Google Scholar
54. Rodell, M, Houser, PR, Jambor, U, Gottschalck, J, Mitchell, K, Meng, C-J. TELLUS_GLDAS-NOAH-3.3_TWS-ANOMALY_MONTHLY. Ver. 3.3. USA: PO.DAAC, CA; 2020. https://doi.org/10.5067/GGDAS-3NH33 [Accessed 03 Jan 2025].Search in Google Scholar
55. Richard Peltier, W, Argus, DF, Drummond, R. Comment on “an assessment of the ICE-6G_C (VM5a) glacial isostatic adjustment model” by purcell et al. J Geophys Res Solid Earth 2018;123:2019–28. https://doi.org/10.1002/2016JB013844.Search in Google Scholar
56. Zhang, X, Jin, S, Lu, X. Global surface mass variations from continuous GPS observations and satellite altimetry data. Remote Sens 2017;9:1000. https://doi.org/10.3390/RS9101000.Search in Google Scholar
57. Dziewonski, AM, Anderson, DL. Preliminary reference Earth model. Phys Earth Planet Inter 1981;25:297–356. https://doi.org/10.1016/0031-9201(81)90046-7.Search in Google Scholar
58. Heiskanen, WA, Moritz, H. Physical geodesy. San Francisco: W. H. Freeman; 1967.10.1007/BF02525647Search in Google Scholar
59. Barthelmes, F. Definition of functionals of the geopotential and their calculation from spherical harmonic models: theory and formulas used by the calculation service of the international centre for global Earth models (ICGEM). Potsdam, Germany: GFZ German Research Centre for Geosciences; 2013:32 p.Search in Google Scholar
60. Makridakis, S, Wheelwright, SC, Hyndman, RJ. Forecasting: methods and applications, 3rd ed. New York: Wiley; 1998.Search in Google Scholar
61. Schrama, EJO, Visser, PNAM. Accuracy assessment of the monthly GRACE geoids based upon a simulation. J Geod 2007;81:67–80. https://doi.org/10.1007/s00190-006-0085-1.Search in Google Scholar
62. White, AM, Gardner, WP, Borsa, AA, Argus, DF, Martens, HR. A review of GNSS/GPS in hydrogeodesy: hydrologic loading applications and their implications for water resource research. Water Resour Res 2022;58:e2022WR032078. https://doi.org/10.1029/2022WR032078.Search in Google Scholar PubMed PubMed Central
63. Syed, TH, Famiglietti, JS, Rodell, M, Chen, J, Wilson, CR. Analysis of terrestrial water storage changes from GRACE and GLDAS. Water Resour Res 2008;44:W02433. https://doi.org/10.1029/2006WR005779.Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Review
- GNSS interferometric reflectometry as a passive remote sensing method for studying environmental phenomena
- Original Research Articles
- Assessment of orthometric height determination utilizing network of multi-baselines of GNSS Continuously Operating Reference Stations
- An autoregressive adaptive Kalman filter carrier tracking approach for mitigating ionospheric scintillation effects in GNSS receivers
- Intrinsic and extrinsic calibration of a UAV-based multi-sensor system
- Assessment of temporal variations of geoid, ellipsoidal and orthometric heights at proposed IHRF sites using space geodetic data
- Global equatorial F- and E-region ionospheric irregularities from COSMIC-RO and SCINDA-GNSS observations
- Evaluating stochastic models for estimating site velocity from daily and weekly GNSS time series in the stable region of the South American plate
- Regional assessment of high-degree combined global gravity field model for geoid modelling over Nigeria
- Linking persistent scatterers to airborne laser scanning points for identifying real objects reflecting SAR signal
- Statistical analysis of Precipitable Water Vapor and rainfall variability in different geographical conditions of the Indian region
- Assessing ground deformation monitoring techniques in Midvaal, South Africa
- Investigating the preparation phase of volcanic eruptions using Swarm and GPS-TEC satellite data: The case of the 29 May 2024 Iceland-Sundhnúkur volcanic eruption
- Developing Malaysia continuous hydrographic datum (MyCHD) by assimilating tide gauge, satellite altimeter, and global hydrodynamic model
Articles in the same Issue
- Frontmatter
- Review
- GNSS interferometric reflectometry as a passive remote sensing method for studying environmental phenomena
- Original Research Articles
- Assessment of orthometric height determination utilizing network of multi-baselines of GNSS Continuously Operating Reference Stations
- An autoregressive adaptive Kalman filter carrier tracking approach for mitigating ionospheric scintillation effects in GNSS receivers
- Intrinsic and extrinsic calibration of a UAV-based multi-sensor system
- Assessment of temporal variations of geoid, ellipsoidal and orthometric heights at proposed IHRF sites using space geodetic data
- Global equatorial F- and E-region ionospheric irregularities from COSMIC-RO and SCINDA-GNSS observations
- Evaluating stochastic models for estimating site velocity from daily and weekly GNSS time series in the stable region of the South American plate
- Regional assessment of high-degree combined global gravity field model for geoid modelling over Nigeria
- Linking persistent scatterers to airborne laser scanning points for identifying real objects reflecting SAR signal
- Statistical analysis of Precipitable Water Vapor and rainfall variability in different geographical conditions of the Indian region
- Assessing ground deformation monitoring techniques in Midvaal, South Africa
- Investigating the preparation phase of volcanic eruptions using Swarm and GPS-TEC satellite data: The case of the 29 May 2024 Iceland-Sundhnúkur volcanic eruption
- Developing Malaysia continuous hydrographic datum (MyCHD) by assimilating tide gauge, satellite altimeter, and global hydrodynamic model