Geopotential-number estimation based on regional and global geoid models towards vertical datum modernization in India
-
Ana Isela Vidal-Vega
, Manuel E. Trejo-Soto, Karan Nayak
, Manuel Trejo-Echeagaray , Aníbal I. Arana Medina and Tiojari D. Guzman Galindo
Abstract
This study focuses on the analysis of the dataset currently available over the Indian subcontinent for the calculation of geopotential numbers and orthometric heights, mainly the performance of regional and global geoid models across diverse topographic conditions. Using Global Navigation Satellite System (GNSS) observations from 17 Asia Pacific Regional Geodetic Project (APRGP) stations distributed across plains, plateaus, coastal areas, and complex mountainous regions, we compared six geoid models: three global (EIGEN-6C4, xGM2019e_2159, SGG-UGM-2) and three regionals (IndGG-SH2021, IndGG-CUT2021, and IndGG-LSMSA2021). Interpolated gravity values, geoidal heights, and geodetic coordinates were utilized to derive geopotential numbers, which were further analyzed to estimate orthometric heights and quantify the discrepancies obtained using currently available data. Our results indicate that recent global geoid models, particularly XGM2019e_2159 and SGG-UGM-2, have improved and have consistency with respect to regional geoid models, mainly with IndGG-SH2021 in terms of accuracy and reliability. Stations located in moderate terrain zones such as Bangalore, Delhi, and Hyderabad showed minimal variations (<±15 cm) in orthometric heights, However, significant discrepancies were observed in mountainous regions like Kashmir, where orthometric height differences exceeded ±25 cm, especially with the IndGG-CUT2021 model. Based on these findings, it is strongly recommended to use gravimetric geoid models derived from satellite missions to analyze the strength of regional models that allow to observation of the trend of the results in each model to verify its consistency. Furthermore, obtain absolute gravity data for India’s vertical datum modernization.
Acknowledgments
The authors thank the International Center for Global Earth Models (ICGM) for geoidal height and gravimetric data. This work was carried out with the support (CVU: 915661) of the Secretariat of Science, Humanities, Technology and Innovation (SECIHTI).
-
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: All other authors state no conflict of interest.
-
Research funding: This work was carried out with the support (CVU: 915661) of the Secretariat of Science, Humanities, Technology and Innovation (SECIHTI).
-
Data availability: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
1. Vanicek, P, Krakiwsky, EJ. Geodesy: the concepts, 2nd ed. Amsterdam, North-Holland: Elsevier Science Publishers B.V.; 1986.Search in Google Scholar
2. Bosch, W. Geodetic application of satellite altimetry. In: Hwang, C, Shum, CK, Li, J, editors. Satellite altimetry for geodesy, geophysics and oceanography. Berlin, Heidelberg: Springer; 2003:3–21 pp.10.1007/978-3-642-18861-9_1Search in Google Scholar
3. Ihde, J, Barzaghi, R, Marti, U, Sánchez, L, Sideris, M, Drewes, H, et al.. Report of the Ad-hoc group on an International Height Reference System (IHRS). In: Drewes, H, Hornik, H, editors. Travaux de l’AIG 39, IAG reports 2011–2015; 2015.Search in Google Scholar
4. Rummel, R. Height unification using GOCE. J Geod Sci 2012;2:355–62. https://doi.org/10.2478/v10156-011-0047-2.Search in Google Scholar
5. Janjić, T, Schröter, J, Savcenko, R, Bosch, W, Albertella, A, Rummel, R, et al.. Impact of combining GRACE and GOCE gravity data on ocean circulation estimates. Ocean Sci 2012;8:65–79. https://doi.org/10.5194/os-8-65-2012.Search in Google Scholar
6. Dahle, C, Murböck, M, Flechtner, F, Dobslaw, H, Michalak, G, Neumayer, KH, et al.. The GFZ GRACE RL06 monthly gravity field time series: processing details and quality assessment. Remote Sens (Basel). 2019;11:2116. https://doi.org/10.3390/rs11182116.Search in Google Scholar
7. Förste, C, Bruinsma, SL, Abrikosov, O, Lemoine, JM, Schaller, T, Götze, HJ, et al.. The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ potsdam and GRGS Toulouse. Potsdam, Germany and Toulouse, France: GFZ; 2014, vol 11.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. 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
10. Amjadiparvar, B, Rangelova, EV, Sideris, MG, Véronneau, M. North American height datums and their offsets: the effect of GOCE omission errors and systematic levelling effects. J Appl Geodesy 2013;7:39–50. https://doi.org/10.1515/jag-2012-0034.Search in Google Scholar
11. Sánchez, L, Ågren, J, Huang, J, Wang, YM, Mäkinen, J, Pail, R, et al.. Strategy for the realisation of the International Height Reference System (IHRS). J Geod 2021;95:33. https://doi.org/10.1007/s00190-021-01481-0.Search in Google Scholar
12. Barzaghi, R, Carrion, D, Reguzzoni, M, Venuti, G. A feasibility study on the unification of the italian height systems using GNSS-leveling data and global satellite gravity models. In: International association of geodesy symposia. Springer Verlag; 2015:281–8 pp.10.1007/1345_2015_35Search in Google Scholar
13. Sánchez, L. Strategy to establish a global vertical reference system. In: International association of geodesy symposia; 2009:273–8 pp.10.1007/978-3-642-00860-3_42Search in Google Scholar
14. 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
15. Sánchez, L, Sideris, MG. Vertical datum unification for the International Height Reference System (IHRS). Geophys J Int 2017;209:570–86.10.1093/gji/ggx025Search in Google Scholar
16. Guimarães, GN, Blitzkow, D. Guía 04 Selección de Estaciones IHRF. Bogotá, Colombia: Guías técnicas. SIRGAS; 2025.Search in Google Scholar
17. Vergos, G, Sánchez, L, Barzaghi, R, IHRF Team. Current activities of the newly established IAG/IGFS IHRF coordination center for the realization and maintenance of the IHRS/IHRF [presentation]. In: IAG workshop 2024 on Asia Pacific gravity, geoid and vertical datums. Manila, Philippines: IAG; 2024.Search in Google Scholar
18. Singh, SK. Towards the modernization of Indian vertical datum. In: FIG congress 2018 embracing our smart world where the continents connect: enhancing the geospatial maturity of societies Istanbul. Turkey; 2018.Search in Google Scholar
19. Emery, KO, Aubrey, DG. Tide gauges of India. J Coast Res 1989;5:489–501.Search in Google Scholar
20. Amos, MJ, Featherstone, WE. Unification of New Zealand’s local vertical datums: iterative gravimetric quasigeoid computations. J Geod 2009;83:57–68. https://doi.org/10.1007/s00190-008-0232-y.Search in Google Scholar
21. Imakiire, T, Hakoiwa, E. JGD2000 (vertical) – the new height system of Japan. Bull Geogr Surv Inst 2004;51:31–51.Search in Google Scholar
22. Jekeli, C, Yang, HJ, Kwon, JH. The offset of the South Korean vertical datum from a global geoid. KSCE J Civ Eng 2012;16:816–21. https://doi.org/10.1007/s12205-012-1320-3.Search in Google Scholar
23. Kasenda, A, Kearsley, AHW. Offsets between some local height datums in the South East Asia region. In: 3rd meeting of the international gravity and geoid commission. Thessaloniki: Ziti Editions; 2003:384–8 pp.Search in Google Scholar
24. Nyoka, CJ, Din, AHM, Pa’suya, MF, Omar, AH. A combined regional geopotential model using optimized global gravity field solutions. IOP Conf Ser Earth Environ Sci 2022;1051:012001.10.1088/1755-1315/1051/1/012001Search in Google Scholar
25. Vidal-Vega, AI, Trejo-Soto, ME, Tocho, CN, Romero-Andrade, R, Nayak, K. Assessment of geoid models for geopotential values determination in Mexico’S continuous monitoring network. J South Am Earth Sci 2024:148.10.1016/j.jsames.2024.105192Search in Google Scholar
26. Srinivas, N, Tiwari, VM. Gravity and geodetic studies in India: historical observations and advances during the past decade. Proc Indian Natl Sci Acad 2019;85:343–61.Search in Google Scholar
27. Goyal, R. The Indian gravimetric geoid model based on the Stokes-Helmert approach with Vaníček-Kleusberg modification of the Stokes kernel: IndGG-SH2021. Kanpur and Perth: Indian Institute of Technology Kanpur and Curtin University of Technology; 2022.Search in Google Scholar
28. Hu, G. Report on the analysis of the Asia Pacific Regional Geodetic Project (APRGP) GPS campaign 2023. GA Record 2024/27. Canberra, AU: Commonwealth of Australia (Geoscience Australia); 2024.Search in Google Scholar
29. Hofmann-Wellenhof, B, Moritz, H. Physical geodesy. Vienna: Springer; 2005.Search in Google Scholar
30. Moritz, H. Geodetic reference system 1980. Bull Geod 1980;54:395–405. https://doi.org/10.1007/bf02521480.Search in Google Scholar
31. Tozer, B, Sandwell, DT, Smith, WHF, Olson, C, Beale, JR, Wessel, P. Global bathymetry and topography at 15 Arc Sec: SRTM15+. Earth Space Sci 2019;6:1847–64. https://doi.org/10.1029/2019ea000658.Search in Google Scholar
32. Barthelmes, F. Definition of functionals of the geopotential and their calculation from spherical harmonic models [Internet]; 2013. Available from: http://icgem.gfz-potsdam.de/ICGEM/.Search in Google Scholar
33. Bureau Gravimétrique International. IGSN71 reference stations [Internet]. Toulouse, FR: Bureau Gravimétrique International; 2025. Available from: https://bgi.obs-mip.fr/data-products/gravity-databases/igsn71-reference-stations/#/.Search in Google Scholar
34. Goyal, R. The Indian gravimetric geoid model based on the curtin university approach with Featherstone-Evans-Olliver modification of the stokes kernel: IndGG-CUT2021. Kanpur and Perth: Indian Institute of Technology Kanpur and Curtin University of Technology; 2022.Search in Google Scholar
35. Goyal, R. The Indian gravimetric geoid model based on the KTH method of least squares modification of the stokes formula with additive corrections: IndGG-LSMSA2021. Kanpur and Perth: Indian Institute of Technology Kanpur and Curtin University of Technology; 2022.Search in Google Scholar
36. Goyal, R. Towards a gravimetric geoid model for the mainland India. Australia: School of Earth and Planetary Sciences; 2022.Search in Google Scholar
37. ICGEM. Root mean square (rms) about mean of GNSS/levelling minus gravity field model derived geoid heights; 2025. Available from: https://icgem.gfz-potsdam.de/tom_gpslev.Search in Google Scholar
38. Tocho, CN, Antokoletz, ED, Piñón, DA. Towards the realization of the International Height Reference Frame (IHRF) in Argentina. In: International association of geodesy symposia. Springer Science and Business Media Deutschland GmbH; 2020:11–20 pp.10.1007/1345_2020_93Search in Google Scholar
39. Sánchez, L, Čunderlík, R, Dayoub, N, Mikula, K, Minarechová, Z, Šíma, Z, et al.. A conventional value for the geoid reference potential W0. J Geod 2016;90:815–35. https://doi.org/10.1007/s00190-016-0913-x.Search in Google Scholar
40. Guimarães, GDN, Blitzkow, D, de Matos, ACOC, Silva, VC, Inoue, MEB. The establishment of the IHRF in Brazil: current situation and future perspectives. Rev Bras Cartogr 2022;74:651–70. https://doi.org/10.14393/rbcv74n3-64949.Search in Google Scholar
41. Heiskanen, W, Moritz, H. Physical geodesy. San Francisco: W. H. Freeman and Company; 1967.10.1007/BF02525647Search in Google Scholar
42. Mäkinen, J. The permanent tide and the International Height Reference Frame IHRF. J Geod 2021;95:106. https://doi.org/10.1007/s00190-021-01541-5.Search in Google Scholar
43. Guimarães, GN, Tocho, C, Subiza Piña, WH, Oliveira Cancoro de Matos, AC, Gómez, A, Antokoletz ED, et al. Guía. In: Directrices para El Cálculo De Los Valores de Potencial de Gravedad en las Estaciones IHRF de la Región SIRGAS. Bogotá, Colombia: Guías técnicas. SIRGAS; 2024:06.Search in Google Scholar
44. Torge, W. Geodesy, 3rd ed. Berlin: Gruyter, Editor; 2001.10.1515/9783110879957Search in Google Scholar
45. Banković, T, Brajković, L, Banko, A, Pavasović, M. The impact of gravity on different height systems: a case study on Mt. Medvednica. Appl Sci (Switz) 2025;15:5680. https://doi.org/10.3390/app15105680.Search in Google Scholar
46. Carrión, J, Flores, F, Rodríguez, F, Pozo, M. Global geopotential models assessment in ecuador based on geoid heights and geopotential values. J Geod Sci 2023;13:20220165. https://doi.org/10.1515/jogs-2022-0165.Search in Google Scholar
47. Gerlach, C, Rummel, R. Benefit of classical leveling for geoid-based vertical reference frames. J Geod 2024;98:64. https://doi.org/10.1007/s00190-024-01849-y.Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston