Validation of a tailored gravity field model for precise quasigeoid modelling over selected sites in Cameroon and South Africa
-
Patroba Achola Odera
,
Ojima Isaac Apeh
,
Loudi Yap
und
Matthews Siphiwe Mphuthi
Abstract
In this study, a tailored gravity-field model is developed to fit and recover local terrestrial gravity data by integrating gravity from global gravity-field models, residual gravity derived from topographic data and observed terrestrial gravity over two study sites in Africa (Cameroon and South Africa). During the modelling phase, two-thirds of the terrestrial gravity data is utilised, reserving the remaining one-third for validation purposes. Additionally, an independent validation is conducted by comparing computed quasigeoid models (derived from tailored gravity data) with height anomalies from GPS/levelling data over the two study sites. The accuracy of the tailored gravity model in reproducing observed gravity data is noteworthy, with a ±8.9 mGal accuracy for the study site in South Africa at 2867 test points and a ±10.4 mGal accuracy for the study site in Cameroon at 637 test points. Comparing height anomalies from GPS/levelling with the SATGQG quasigeoid model (developed from tailored gravity data) and the recent CDSM09A quasigeoid model at 11 GPS/levelling data points reveals comparable accuracies of ±0.10 m and ±0.05 m, for SATGQG and CDSM09A, respectively for the site in South Africa. For the Cameroon site, the differences between height anomalies from GPS/levelling and the CTGQG quasigeoid model (developed from tailored gravity data), along with the recent CGM20 quasigeoid model at 38 GPS/levelling data points, show practically equal accuracies of ±0.15 m for CTGQG and ±0.11 m for CGM20. These findings underscore the potential of tailored gravity-field model in developing accurate quasigeoid models, particularly in regions with limited gravity data coverage. This approach holds promise for gravity recovery and precise geoid modelling in developing countries and regions with insufficient coverage of terrestrial gravity data.
Acknowledgments
We are grateful to the following organisations for directly providing or making relevant data freely available on their websites: South Africa’s National Geo-Spatial Information and National Institute of Cartography of Cameroon (GPS/levelling); South Africa’s Council for Geoscience, Bureau Gravimétrique International and National Institute of Cartography of Cameroon (terrestrial gravity); United States Geological Survey (global digital elevation models). International Centre for Global Gravity Field Models (static gravity-field models).
-
Research ethics: Not applicable.
-
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Competing interests: The authors state no conflict of interest.
-
Research funding: None declared.
-
Data availability: Not applicable.
References
1. Saadon, A, El-Ashquer, M, Elsaka, B, El-Fiky, G. Determination of local gravimetric geoid model over Egypt using LSC and FFT estimation techniques based on different satellite-and ground-based datasets. Surv Rev 2022;54:263–73. https://doi.org/10.1080/00396265.2021.1932148.Suche in Google Scholar
2. El-Ashquer, M, Elsaka, B, El-Fiky, G. EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements. Arabian J Geosci 2017;10:1–10. https://doi.org/10.1007/s12517-017-3042-9.Suche in Google Scholar
3. Belay, EY, Godah, W, Szelachowska, M, Tenzer, R. ETH–GM21: a new gravimetric geoid model of Ethiopia developed using the least-squares collocation method. J Afr Earth Sci 2021;183:104313. https://doi.org/10.1016/j.jafrearsci.2021.104313.Suche in Google Scholar
4. Belay, EY, Godah, W, Szelachowska, M, Tenzer, R. ETH-GQS: an estimation of geoid-to-quasigeoid separation over Ethiopia. Geodesy Geodyn 2022;13:31–7. https://doi.org/10.1016/j.geog.2021.09.006.Suche in Google Scholar
5. Merry, CL. DEM-induced errors in developing a quasi-geoid model for Africa. J Geodesy 2003;77:537–42. https://doi.org/10.1007/s00190-003-0353-2.Suche in Google Scholar
6. Merry, CL. Evaluation of global geopotential models in determining the quasigeoid for Southern Africa. Surv Rev 2007;39:180–92. https://doi.org/10.1179/003962607X165159.Suche in Google Scholar
7. Abd-Elmotaal, H, Kühtreiber, N, Seitz, K, Heck, B. A precise geoid model for Africa: AFRgeo2019. In: International association of geodesy symposia; 2020.10.1007/1345_2020_122Suche in Google Scholar
8. Lemoine, FG, Kenyon, SC, Factor, JK, Trimmer, RG, Pavlis, NK, Chmn, DS, et al.. The development of the joint NASA GSFC and the national imagery and mapping agency (NIMA) geopotential model EGM96. Technical Report NASA/TP-1998206861. NASA Greenbelt; 1998:575 p.Suche in Google Scholar
9. Pavlis, NK, Holmes, SA, Kenyon, SC, Factor, JK. The development and evaluation of the earth gravitational model (EGM2008). J Geophys Res 2012;117:1–38. https://doi.org/10.1029/2011JB008916.Suche in Google Scholar
10. Yi, W, Rummel, R. A comparison of GOCE gravitational models with EGM2008. J Geodyn 2014;73:14–22. https://doi.org/10.1016/j.jog.2013.10.004.Suche in Google Scholar
11. Cheng, M, Ries, JC. Evaluation of GOCE gravity models with SLR orbit tests. Newton’s Bull 2015;5:187–92.Suche in Google Scholar
12. Godah, W, Krynski, J, Szelachowska, M. Accuracy assessment of GOCE-based geopotential models and their use for modelling the gravimetric quasigeoid – a case study for Poland. Adv Geodesy Geoinf 2014;63:3–24. https://doi.org/10.2478/geocart-2014-0001.Suche in Google Scholar
13. Hirt, C, Rexer, M, Claessens, S. Topographic evaluation of fifth generation GOCE gravity field models globally and regionally. Newton’s Bull 2015;5:163–86.Suche in Google Scholar
14. Huang, J, Véronneau, M. Assessments of recent GRACE and GOCE release 5 global geopotential models in Canada. Newton’s Bull 2015;5:127–48.Suche in Google Scholar
15. Abd-Elmotaal, HA. Validation of GOCE models in Africa. Newton’s Bull 2015;5:149–62.Suche in Google Scholar
16. Alothman, A, Godah, W, Elsaka, B. Gravity field anomalies from recent GOCE satellite-based geopotential models and terrestrial gravity data: a comparative study over Saudi Arabia. Arabian J Geosci 2016;9:356. https://doi.org/10.1007/s12517-016-2393-y.Suche in Google Scholar
17. Odera, PA, Fukuda, Y. Evaluation of GOCE-based global gravity field models over Japan after the full mission using free-air gravity anomalies and geoid undulations. Earth Planets Space 2017;69:1–7. https://doi.org/10.1186/s40623-017-0716-1.Suche in Google Scholar
18. Odera, PA. Assessment of the latest GOCE-based global gravity field models using height and free-air gravity anomalies over South Africa. Arabian J Geosci 2019;12:1–7. https://doi.org/10.1007/s12517-019-4337-9.Suche in Google Scholar
19. Odera, PA. Evaluation of the recent high-degree combined global gravity-field models for geoid modelling over Kenya. Geodesy Cartogr 2020;46:48–54. https://doi.org/10.3846/gac.2020.10453.Suche in Google Scholar
20. Förste, C, Bruinsma, SL, Abrikosov, O, Lemoine, JM, Marty, JC, Flechtner, F, 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. Germany: GFZ Data Services; 2014.Suche in Google Scholar
21. 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.Suche in Google Scholar
22. Liang, W, Xu, X, Li, J, Zhu, G. The determination of an ultra-high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data. Acta Geod Cartogr Sinica 2018;47:425–34. https://doi.org/10.11947/j.AGCS.2018.20170269.Suche in Google Scholar
23. 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.Suche in Google Scholar
24. Zingerle, P, Pail, R, Gruber, T, Oikonomidou, X. The experimental gravity field model XGM2019e. Germany: GFZ Data Servicer; 2019.10.1007/s00190-020-01398-0Suche in Google Scholar
25. Andersen, O, Knudsen, P, Stenseng, L. The DTU13 MSS (mean sea surface) and MDT (mean dynamic topography) from 20 years of satellite altimetry. In: IGFS; 2015:111–21 pp.10.1007/1345_2015_182Suche in Google Scholar
26. Kande, L, Kamguia, J, Yap, L, Foyang, L. Reference ellipsoid parameters of Cameroon from GPS data. Int J Geosci 2016;7:1049–56. https://doi.org/10.4236/ijg.2016.78079.Suche in Google Scholar
27. Carme, JL. Le nouveau réseau géodésique national du Cameroun. Revue XYZ 2012;131:37–46.Suche in Google Scholar
28. Apeh, OI, Tenzer, R. Development of tailored gravity model based on global gravitational and topographic models and terrestrial gravity data for geophysical exploration of southern benue trough in Southeast Nigeria. J Appl Geophys 2022;198:104561. https://doi.org/10.1016/j.jappgeo.2022.104561.Suche in Google Scholar
29. Yamazaki, D, Ikeshima, D, Tawatari, R, Yamaguchi, T, O’Loughlin, F, Neal, JC, et al.. A high-accuracy map of global terrain elevations. Geophys Res Lett 2017;44:5844–53. https://doi.org/10.1002/2017GL072874.Suche in Google Scholar
30. Ebinne, ES, Apeh, OI, Moka, EC, Abah, EJ. Comparative analysis of freely available digital elevation models for applications in multi-criteria environmental modelling over data limited regions. Remote Sens Appl Soc Environ 2022;27:100795. https://doi.org/10.1016/j.rsase.2022.100795.Suche in Google Scholar
31. Hirt, C, Yang, M, Kuhn, M, Bucha, B, Kurzmann, A, Pail, R. SRTM2gravity: an ultrahigh resolution global model of gravimetric terrain corrections. Geophys Res Lett 2019;46:4618–27. https://doi.org/10.1029/2019GL082521.Suche in Google Scholar
32. Apeh, OI, Tenzer, R. Selection of an optimum global gravitational model for geological mapping of Afikpo and Anambra Basins in Nigeria. Geodesy Cartogr 2022;48:92–106. https://doi.org/10.3846/gac.2022.14551.Suche in Google Scholar
33. Kamguia, J, Tabod, CT, Nouayou, R, Tadjou, JM, Manguelle-Dicoum, E, Kande, HL. The local geoid model of Cameroon: CGM05. Nordic J Survey Real Estate Res 2007;4:7–23.Suche in Google Scholar
34. Tapley, B, Ries, J, Bettadpur, S, Chambers, D, Cheng, M, Condi, F, et al.. GGM02 – an improved earth gravity field model from GRACE. J Geodesy 2005;79:467–78. https://doi.org/10.1007/s00190-005-0480-z.Suche in Google Scholar
35. Barzaghi, R, Carrion, D, Kamguia, J, Kande, LH, Yap, Y, Betti, B. Estimating gravity field and quasi-geoid in Cameroon (CGM20). J Afr Earth Sci 2021;184:104377. https://doi.org/10.1016/j.jafrearsci.2021.104377.Suche in Google Scholar
36. Chandler, G, Merry, CL. The South African geoid 2010: SAGEOID10. In: PositionIT; 2010:29–33 pp.Suche in Google Scholar
37. Barthelmes, F, Köhler, W. International centre for global earth models (ICGEM). In: Drewes, H, Kuglitsch, F, Adám, J, Rózsa, S, editors. The geodesists handbook 2012, J Geodesy. Germany: Springer; 2012, vol. 86:932–4 pp. https://doi.org/10.1007/s00190-012-0584-1 Suche in Google Scholar
38. 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.Suche in Google Scholar
39. 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). Scientific Technical Report STR09/02, Revised Edition 2013.Suche in Google Scholar
40. Heiskanen, WA, Moritz, H. Physical geodesy. Bull Geod 1967;86:491–2. https://doi.org/10.1007/bf02525647.Suche in Google Scholar
41. Morelli, C, Gantar, C, McConnell, RK, Szabo, B, Uotila, U. The international gravity standardization net 1971 (IGSN 71). Italy: Osservatorio Geofisico Sperimentale Trieste (Italy); 1972.Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Ionospheric TEC modeling using COSMIC-2 GNSS radio occultation and artificial neural networks over Egypt
- Regional GPS orbit determination using code-based pseudorange measurement with residual correction model
- Analysis of different combinations of gravity data types in gravimetric geoid determination over Bali
- Assessment of satellite images terrestrial surface temperature and WVP using GNSS radio occultation data
- GNSS positioning accuracy performance assessments on 1st and 2nd generation SBAS signals in Thailand
- Differential synthetic aperture radar (SAR) interferometry for detection land subsidence in Derna City, Libya
- Advanced topographic-geodetic surveys and GNSS methodologies in urban planning
- Detection of GNSS ionospheric scintillations in multiple directions over a low latitude station
- Spatiotemporal postseismic due to the 2018 Lombok earthquake based on insar revealed multi mechanisms with long duration afterslip
- Practical implications in the interpolation methods for constructing the regional mean sea surface model in the eastern Mediterranean Sea
- Validation of a tailored gravity field model for precise quasigeoid modelling over selected sites in Cameroon and South Africa
- Evaluation of ML-based classification algorithms for GNSS signals in ocean environment
- Development of a hybrid geoid model using a global gravity field model over Sri Lanka
- Implementation of GAGAN augmentation on smart mobile devices and development of a cooperative positioning architecture
- On the GPS signal multipath at ASG-EUPOS stations
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Ionospheric TEC modeling using COSMIC-2 GNSS radio occultation and artificial neural networks over Egypt
- Regional GPS orbit determination using code-based pseudorange measurement with residual correction model
- Analysis of different combinations of gravity data types in gravimetric geoid determination over Bali
- Assessment of satellite images terrestrial surface temperature and WVP using GNSS radio occultation data
- GNSS positioning accuracy performance assessments on 1st and 2nd generation SBAS signals in Thailand
- Differential synthetic aperture radar (SAR) interferometry for detection land subsidence in Derna City, Libya
- Advanced topographic-geodetic surveys and GNSS methodologies in urban planning
- Detection of GNSS ionospheric scintillations in multiple directions over a low latitude station
- Spatiotemporal postseismic due to the 2018 Lombok earthquake based on insar revealed multi mechanisms with long duration afterslip
- Practical implications in the interpolation methods for constructing the regional mean sea surface model in the eastern Mediterranean Sea
- Validation of a tailored gravity field model for precise quasigeoid modelling over selected sites in Cameroon and South Africa
- Evaluation of ML-based classification algorithms for GNSS signals in ocean environment
- Development of a hybrid geoid model using a global gravity field model over Sri Lanka
- Implementation of GAGAN augmentation on smart mobile devices and development of a cooperative positioning architecture
- On the GPS signal multipath at ASG-EUPOS stations
