Regional assessment of high-degree combined global gravity field model for geoid modelling over Nigeria
Abstract
Given the multitude of global gravity field model (GGMs) at our disposal, evaluating them against independent data is indispensable for delineating their quality and ascertaining their accuracy in Nigeria regions. In this study, we evaluated five combined GGMs (specifically SGG-UGM-2, XGM2019e_2159, GECO, EIGEN-6C4, and EGM2008) over Nigeria. Our evaluation is conducted using geoid undulations (mainly in FCT-Abuja) and free-air gravity anomalies (covering the whole country, Nigeria). The results showed that the differences between observed and GGMs implied geoid undulations at 20 GNSS/levelling points over FCT-Abuja (small area) revealed that XGM2019e_2159 fit better with standard deviation (SD) of 11.9 cm over the study area compared to other four evaluated combined GGMs. On the other hand, SD of the differences between observed and GGMs implied free-air gravity anomalies over Nigeria showed that XGM2019e_2159 performs slightly better than the other four evaluated combined GGMs with an SD of 7.04 mGal. These results further indicate a good prospect for the development of a precise gravimetric geoid model over Nigeria using XGM2019e_2159 model. However, more GNSS/levelling stations will be required for fittings of the gravimetric geoid model to the national vertical datum of Nigeria.
Acknowledgments
The authors would like to thank four anonymous reviewers for their constructive comments and discussions. The authors wish to thank DTU Space for providing the GRAVSOFT packages that was used in the gravity evaluation and MATLAB for the computation. The author is also grateful to the anonymous reviewers whose comments will improved this work.
-
Research ethics: This study adheres to ethical standards in the research.
-
Informed consent: Not applicable.
-
Author contributions: M. B. designed, analyzed the results and wrote the manuscript.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: The authors declare that they have no conflicts of interest.
-
Research funding: Non declared.
-
Data availability: The raw data can be obtained on request from the corresponding author.
References
1. Odumosu, JO, Nnam, VC, Nwadialor, IJ. An assessment of spatial methods for merging terrestrial with GGM-derived gravity anomaly data. J Afr Earth Sci 2021;179:104202. https://doi.org/10.1016/j.jafrearsci.2021.104202.Search in Google Scholar
2. Bako, M, Elsaka, B, Kusche, J, Feboglio-Marc, L. Evaluation of GOC/GRACE and combined global geopotential models using GNSS/levelling data over Nigeria. Studia Geophys Geod 2024;1–21. https://doi.org/10.1007/s11200-023-0804-6.Search in Google Scholar
3. Pavlis, NK, Holmes, SA, Kenyon, SC, Factor, JK. The development and evaluation of the Earth gravitational model 2008 (EGM2008). J Geophys Res 2012;117:1–38. https://doi.org/10.1029/2011jb008916.Search in Google Scholar
4. Moka, EC, Jackson, K, Lawrence, H. Development of a gravimetric geoid model for Nigeria. Niger J Geod 2018;1:1–9.Search in Google Scholar
5. Ince, ES, Barthelmes, F, Reißland, S, Elger, K, Förste, C, Flechtner, F, et al.. ICGEM – 15 years of successful collection and distribution of global gravitational models, associated services and future plans. Earth Syst Sci Data 2019;11:647–74. https://doi.org/10.5194/essd-11-647-2019.Search in Google Scholar
6. Odera, PA. Evaluation of the recent high-degree combined global gravity-field models for geoid modelling over Kenya. Geod Cartogr 2020;46:48–54. https://doi.org/10.3846/gac.2020.10453.Search in Google Scholar
7. Liang, W, Li, J, Xu, X, Zhang, S, Zhao, Y. A high-resolution Earth’s gravity field model SGG-UGM-2 from GOCE, GRACE, satellite altimetry, and EGM2008. Engineering 2020;6:860–78. https://doi.org/10.1016/j.eng.2020.05.008.Search in Google Scholar
8. Zingerle, P, Pail, R, Gruber, T, Oikonomidou, X. The combined global gravity field model XGM2019e. J Geod 2020;94:66. https://doi.org/10.1007/s00190-020-01398-0.Search in Google Scholar
9. Förste, C, Bruinsma, SL, Abrikosov, O, Lemoine, JM, Schaller, T, Gotze, H, et al.. EIGEN-6C4 the latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Serv 2014. https://doi.org/10.5880/icgem.2015.1.Search in Google Scholar
10. Gilardoni, M, Reguzzoni, M, Sampietro, D. GECO: a global gravity model by locally combining GOCE data and EGM2008. Studia Geophys Geod 2016;60:228–47. https://doi.org/10.1007/s11200-015-1114-4.Search in Google Scholar
11. Drinkwater, M, Floberghagen, R, Haagmans, R, Muzi, D, Popescu, A. GOCE: ESA’s first Earth explorer core mission. Space Sci Rev 2003;108:419–32. https://doi.org/10.1007/978-94-017-1333-7_36.Search in Google Scholar
12. Tapley, B, Bettadpur, S, Watkins, M, Reigber, C. The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 2004;31. https://doi.org/10.1029/2004GL019779.Search in Google Scholar
13. Gruber, T. Evaluation of the EGM2008 gravity field using GPS-levelling and sea surface topography solutions; external evaluation reports of EGM2008. Newton’s Bull 2009;4:3–17.Search in Google Scholar
14. Hirt, C, Gruber, T, Featherstone, WE. Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights. J Geod 2011;85:723–40. https://doi.org/10.1007/s00190-011-0482-y.Search in Google Scholar
15. Apeh, OI, Moka, EC, Uzodinma, VN. Evaluation of gravity data derived from global gravity field models using terrestrial gravity data in Enugu State, Nigeria. J Geod Sci 2018;8:145–53. https://doi.org/10.1515/jogs-2018-0015.Search in Google Scholar
16. Apeh, OI, Tenzer, R. Selection of an optimum global gravitational model for geological mapping of Afikpo and Anambra Basins in Nigeria. Geod Cartogr 2022;48:92–106. https://doi.org/10.3846/gac.2022.14551.Search in Google Scholar
17. Bako, M, Kusche, J. Evaluation and homogenization of a marine gravity database from shipborne and satellite altimetry-derived gravity data over the coastal region of Nigeria. J Appl Geodesy 2024;19:175–89. https://doi.org/10.1515/jag-2024-0059.Search in Google Scholar
18. Yılmaz, M, Kozlu, B. The comparison of gravity anomalies based on recent high-degree global models. Afy Kocatepe Üni 2018;18:981–90. https://doi.org/10.5578/fmbd.67502.Search in Google Scholar
19. Nyoka, CJ, Din, AHM, Pa’suya, MF, Omar, AH. Rigorous evaluation of global geopotential models for geoid modelling: a case study in Kenya. J Afr Earth Sci 2022;194:104612. https://doi.org/10.1016/j.jafrearsci.2022.104612.Search in Google Scholar
20. Kvas, A, Brockmann, JM, Krauss, S, Schubert, T, Gruber, T, Meyer, U, et al.. GOCO06s–a satellite-only global gravity field model. Earth Syst Sci Data Discuss 2021;13:1–31. https://doi.org/10.5194/essd-13-99-2021.Search in Google Scholar
21. Andersen, OB, Knudsen, P, Kenyon, S, Factor, J, Holmes, S. The DTU13 global marine gravity field-first evaluation. In: Ocean surface topography science team meeting. Boulder, Colorado; 2013.Search in Google Scholar
22. Mayer-Gürr, T, Eicker, A, Kurtenbach, E, Ilk, K-H. ITG-GRACE: global static and temporal gravity field models from GRACE data. In: Flechtner, F, editor. System earth via geodetic-geophysical space techniques. Advanced technologies in earth sciences (2190-1643). Berlin, Heidelberg: Springer; 2010:159–68 pp.10.1007/978-3-642-10228-8_13Search in Google Scholar
23. Andersen, OB, Knudsen, P. Global marine gravity field from the ERS-1 and the Geosat geodetic mission altimetry. J Geophys Res: Oceans 1998;103:8129–37. https://doi.org/10.1029/97jc02198.Search in Google Scholar
24. Bako, M, Ojigi, LM, Dodo, JD. An evaluation of different GNSS orbit solutions for precise point positioning in the federal capital territory, Abuja. J Geoinf Earth Sci 2019;1:1–8.Search in Google Scholar
25. Okiemute, ES, Ono, MN, Oluyori, PD. Comparison of two polynomial geoid models of GNSS/leveling geoid development for orthometric heights in FCT, Abuja. Int J Eng Res Adv Technol 2018;4:1–9. https://doi.org/10.31695/ijerat.2018.3330.Search in Google Scholar
26. Bruinsma, SL, Forste, C, Abrikosov, O, Marty, JC, Rio, MH, Mulet, S, et al.. The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett 2013;40:3607–12. https://doi.org/10.1002/gri.50716.Search in Google Scholar
27. Wenzel, HG. Global models of the gravity field of high and ultrahigh resolution. Budapest, Hungary: International School for the Determination and use of the Geoid; 2005.Search in Google Scholar
28. Heiskanen, WA, Moritz, H. Physical geodesy. San Francisco: W. H. Freeman; 1967.10.1007/BF02525647Search in Google Scholar
29. Barthelmes, F. Definition of functionals of the geopotential and their calculation from spherical harmonic models. In: Theory and formulas used by the calculation service of the international centre for global Earth models (ICGEM); 2013, Scientific Technical Report SRT09/02.Search in Google Scholar
30. Forsberg, R, Tscherning, CC. An overview manual for the GRAVSOFT geodetic gravity field modelling programs. DRAFT 1 ed. Copenhagen; 2008, Contract Report for JUPEM.Search in Google Scholar
31. Forsberg, R. A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Columbus: Department of Geodetic Science and Surveying, Ohio State University; 1984, Report 355.10.21236/ADA150788Search in Google Scholar
32. USGS. Shuttle radar topography mission; 2017. Available from: https://earthexplorer.usgs.gov.Search in Google Scholar
33. Forsberg, R. Gravity field terrain effect computations by FFT. Bull Geod 1985;59:342–60. https://doi.org/10.1007/BF02521068.Search in Google Scholar
34. Kotsakis, C, Sideris, MG. On the adjustment of combined GPS/levelling/geoid networks. J Geod 1999;73:412–21. https://doi.org/10.1007/s001900050261.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
