Abstract

Inconsistent geoid heights may introduce uncertainties that limit its use in applications. Consequently, the scientific community has been collaborating to determine more rigorous geoid models in order to improve the accuracy of orthometric heights estimated with height transformation from the Global Navigation Satellite System (GNSS) positioning techniques. In this regard, this study evaluated the influence of different parameters (such as mass density, topographic models, geopotential models, and Stokes kernel modifications) used in the determination of a gravimetric geoid model through the remove-compute-restore (RCR) technique to contribute to these efforts. As a result of the analyses, it was determined that the Stokes kernel modification type and the global geopotential model selection significantly influence the improvement of geoid models in the study area (state of São Paulo, Brazil). However, the resolution of digital terrain models and the values of the lateral topographic density have less of an impact on the model’s accuracy when determining the geoid. In order to acquire findings that are consistent with geoid heights estimated by each determination technique, it is necessary to conduct a rigorous study of the employed data and computation parameters as a preliminary process.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models and code used during the study were provided by a third party and direct requests for those materials may be made to the provider as indicated in the Acknowledgments. Some of those materials are available in online repositories, such as: terrestrial gravity data (https://www.ibge.gov.br/); global geopotential models (http://icgem.gfz-potsdam.de/); topographic models (https://earthexplorer.usgs.gov/); lateral topographic density model for Brazil (https://zenodo.org/record/5601931); and marine gravity data (https://www.space.dtu.dk/). The GRAVTool package used during the study might be available, with restrictions, by the corresponding author.

Acknowledgments

The authors thank the National Institute of Science and Technology for Tectonic Studies - INCTET (465613/2014-4), Foundation for Research Support of the Federal District, Brazil - FAPDF (00193.00001526/2021-93), and Coordination for the Improvement of Higher Education Personnel - CAPES (Finance Code 001), for the technical and financial support for carrying out the research. G.S.M. would like to thank the National Council for Scientific and Technological Development - CNPq (PQ-2, 308270/2022-3) for financial support. The authors thank IBGE and ANP, ICGEM, USGS, and DTU for providing, respectively, the terrestrial gravity data, the global geopotential models, the topographic models and the marine gravity data used in this research. The authors thank Medeiros et al. (2021) for providing the lateral topographic density model for Brazil, and Featherstone (2003) for providing the MODKERN.f code.

References

Abbak, R. A., B. Erol, and U. Ustun. 2012. “Comparison of the KTH and remove–compute–restore techniques to geoid modelling in a mountainous area.” Comput. Geosci. 48 (Nov): 31–40. https://doi.org/10.1016/j.cageo.2012.05.019.
Albarici, F. L., I. Foroughi, G. N. Guimarães, M. Santos, and J. Trabanco. 2019. “A new perspective for physical heights in Brazil.” Boletim de Ciências Geodésicas 25 (1): e2019001. https://doi.org/10.1590/s1982-21702019000100001.
Andersen, O. B., and P. Knudsen. 2019. “The DTU17 global marine gravity field: First validation results.” In Proc., Int. Association of Geodesy Symposia, Fiducial Reference Measurements for Altimetry, edited by S. Mertikas and R. Pail, 150. Cham, Switzerland: Springer. https://doi.org/10.1007/1345_2019_65.
Ayhan, M. E. 1993. “Geoid determination in Turkey (TG-91).” Bull. Geod. 67 (1): 10–22. https://doi.org/10.1007/BF00807293.
Blitzkow, D., A. C. O. C. de Matos, J. D. Fairhead, M. C. Pacino, M. C. B. Lobianco, and I. O. Campos. 2012. “The progress of the geoid model for south America under GRACE and EGM2008.” In Proc., Int. Association of Geodesy Symposia, Geodesy for Planet Earth, edited by S. Kenyon, M. Pacino, and U. Marti, 136. Berlin: Springer. https://doi.org/10.1007/978-3-642-20338-1_112.
Ellmann, A. 2001. Least squares modification of Stokes formula with applications to the Estonian geoid. Stockholm, Sweden: Royal Institute of Technology.
Erol, B. 2007. “Investigations on local geoid for geodetic applications.” Ph.D. dissertation, Dept. of Geodesy and Photogrammetry, Istanbul Technical Univ.
Farr, T. G., P. A. Rosen, E. Caro, R. Crippen, R. Duren, S. Hensley, M. Kobrick, M. Paller, E. Rodriguez, and L. Roth. 2007. “The shuttle radar topography mission.” Rev. Geophys. 45 (2): RG2004. https://doi.org/10.1029/2005RG000183.
Featherstone, W., J. Evans, and J. Olliver. 1998. “A Meissl-modified Vaníček and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations.” J. Geod. 72 (3): 154–160. https://doi.org/10.1007/s001900050157.
Featherstone, W. E. 2003. “Software for computing five existing types of deterministically modified integration kernel for gravimetric geoid determination.” Comput. Geosci. 29 (2): 183–193. https://doi.org/10.1016/S0098-3004(02)00074-2.
Featherstone, W. E., and M. C. Dentith. 1997. “A geodetic approach to gravity reduction for geophysics.” Comp. Geosc. 23 (10): 1063–1070. https://doi.org/10.1016/S0098-3004(97)00092-7.
Förste, C., S. Bruinsma, O. Abrykosov, J. M. Lemoine, J. C. Marty, F. Flechtner, G. Balmino, F. Barthelmes, and R. Biancale. 2014. “IGEN-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. https://doi.org/10.5880/icgem.2015.1.
Heck, B., and W. Grüninger. 1987. “Modification of Stokes’s integral formula by combining two classical approaches.” In Vol. 2 of Proc., 19th General Assembly of the Int. Union of Geodesy and Geophysics, 309–337. Vancouver, BC, Canada: Univ. of British Columbia.
Heiskanen, W. A., and H. Moritz. 1985. Geodesia física, 369. Madrid, Spain: Instituto Geográfico Nacional.
Hinze, W. J. 2003. “Bouguer reduction density, Why 2.67?” Geophysics 68 (5): 1559–1560. https://doi.org/10.1190/1.1620629.
Hirt, C. 2011. “Mean kernels to improve gravimetric geoid determination based on modified Stokes’s integration.” Comput. Geosci. 37 (11): 1836–1842. https://doi.org/10.1016/j.cageo.2011.01.005.
Hofmann-Wellenhof, B., and H. Moritz. 2006. Physical geodesy. Wien: Springer.
Huang, J., P. Vaníček, S. Pagiatakis, and W. Brink. 2001. “Effect of topographical density on geoid in the Canadian Rocky Mountains.” J. Geod. 74 (11–12): 805–815. https://doi.org/10.1007/s001900000145.
ICGEM (International Center for Global Earth Models). 2023. “International centre for global earth models.” Accessed January 5, 2023. http://icgem.gfz-potsdam.de/home.
Kiamehr, R. 2006. “The impact of lateral density variation model in the determination of precise gravimetric geoid in mountainous areas: A case study of Yran.” Geophys. J. Int. 167 (2): 521–527. https://doi.org/10.1111/j.1365-246X.2006.03143.x.
Kim, K. B., H. S. Yun, and H. J. Choi. 2020. “Accuracy evaluation of geoid heights in the national control points of south Korea using high-degree geopotential model.” Appl. Sci. 10 (4): 1466. https://doi.org/10.3390/app10041466.
Kirby, J. F., and W. E. Featherstone. 1997. “A study of zero- and first-degree terms in geopotential models.” Geom. Res. Australas. 66: 93–108.
Kuroishi, Y. 1995. “Precise determination of geoid in the vicinity of Japan.” Bul. Geographical Surv. Inst. 41: 1–94.
León, J. G., A. V. Fernández, V. Sánchez, J. P. Salvatierra, R. W. Kingdon, and O. H. Lücke. 2020. “A regional Stokes-Helmert geoid determination for Costa Rica (GCR-RSH-2020): Computation and evaluation.” Contrib. Geophys. Geod. 50 (2): 223–247. https://doi.org/10.31577/congeo.2020.50.2.3.
Li, X., and Y. Wang. 2011. “Comparisons of geoid models over Alaska computed with different Stokes’ kernel modifications.” J. Geodetic Sci. 1 (2): 136–142. https://doi.org/10.2478/v10156-010-0016-1.
Liang, W., J. Li, X. Xu, S. Zhang, and Y. Zhao. 2020. “A high-resolution earth’s gravity field model SGG-UGM-2 from GOCE, GRACE, satellite altimetry, and EGM2008.” Engineering 6 (8): 860–878. https://doi.org/10.1016/j.eng.2020.05.008.
Lücke, O. H., A. Vega Fernández, M. Varela Sánchez, L. A. Barbosa, and J. G. León. 2021. “The improvements of the Costa Rican ground-based gravity dataset as a result of a comprehensive attribute and spatial assessment of the historical databases.” Appl. Geomat. 13 (3): 401–413. https://doi.org/10.1007/s12518-021-00356-5.
Marotta, G. S., Y. M. Almeida, and M. L. Chuerubim. 2019. “Análise da Influência do Valor de Densidade na Estimativa do Modelo Geoidal Local para o Distrito Federal, Brasil” [Analysis of the influence of the density value on the estimation of the local geoid model for the Federal District, Brazil]. [In Portuguese.] Rev. Bras. de Cartografia 71 (4): 1089–1113. https://doi.org/10.14393/rbcv71n4-49274.
Marotta, G. S., and R. M. Vidotti. 2017. “Development of a local geoid model at the Federal District, Brazil, patch by the remove-compute-restore technique, following Helmert’s condensation method.” Bol. Cienc. Geod. 23 (3): 524–540. https://doi.org/10.1590/S1982-21702017000300035.
Martinec, Z., P. Vaníček, A. Mainville, and M. Véronneau. 1995. “The effect of lake water on geoidal height.” Manuscr. Geod. 20 (3): 193–203.
Medeiros, D. F., G. S. Marotta, C. A. M. Chaves, and G. S. L. A. França. 2022. “Orthometric, normal and geoid heights in the context of the Brazilian altimetric network.” Bol. Cienc. Geod. 28 (1): e2022003. https://doi.org/10.1590/s1982-21702022000100003.
Medeiros, D. F., G. S. Marotta, E. Yokoyama, I. B. Franz, and R. A. Fuck. 2021. “Developing a lateral topographic density model for Brazil.” J. South Am. Earth Sci. 110 (Mar): 103425. https://doi.org/10.1016/j.jsames.2021.103425.
Molodensky, M. S., V. F. Eremeev, and M. I. Yurkina. 1962. Methods for study of the external gravitational field and figure of the earth, 248. Jerusalem, Israel: Translation of Scientific Publications.
Moritz, H. 1984. “Geodetic reference system 1980.” Bull. Géodésique 58 (Sep): 388–398. https://doi.org/10.1007/BF02519014.
Mouratidis, A., G. Karadimou, and A. Dimitrios. 2017. “Extraction and validation of geomorphological features from EU-DEM in the Vicinty of the Mygdonia Basin, Northern Greece.” IOP Conf. Ser.: Earth Environ. Sci. 95 (Feb): 032009. https://doi.org/10.1088/1755-1315/95/3/032009.
Nash, J. E., and J. V. Sutcliffe. 1970. “River flow forecasting through conceptual models part I—A discussion of principles.” J. Hydrol. 10 (3): 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Nicacio, E., R. Dalazoana, and S. R. C. Freitas. 2018. “Evaluation of recent combined global geopotential models in Brazil.” J. Geodetic Sci. 8 (1): 72–82. https://doi.org/10.1515/jogs-2018-0008.
Odera, P. A., and Y. Fukuda. 2014. “Improvement of the geoid model over Japan using integral formulae and combination of GGMs.” Earth Planets Space 66 (1): 22. https://doi.org/10.1186/1880-5981-66-22.
Orlando, F. C., E. S. Bias, and A. Cereda Jr. 2022. “SRTM: Para uma melhor Utilização—Conhecendo um pouco mais da qualidade planialtimétrica, da influência da resolução espacial e dos modelos de superfície equipotenciais de referência” [SRTM: For a better user—Knowing a little more about planialtimetric quality, the influence of spatial resolution and reference equipotential surface models]. Rev. Bras. de Geografia Física 15 (2): 1153–1168. https://doi.org/10.26848/rbgf.v15.2.p1153-1168.
Petit, G., and B. Luzum. 2010. IERS conventions (2010). Frankfurt, Germany: Verlag des Bundesamts für Kartographie und Geodäsie.
Piñón, D. A., K. Zhang, S. Wu, and S. R. Cimbaro. 2017. “A new Argentinean gravimetric geoid model: Geoidear.” In Proc., Int. Symp. on Earth and Environmental Sciences for Future Generations, edited by J. T. Freymueller and L. Sánchez, 147. Cham, Switzerland: Springer. https://doi.org/10.1007/1345_2017_267.
Rózsa, S. 2002. “Local geoid determination using surface densities.” Period. Polytech. Civ. Eng. 46 (2): 205–212.
Sampietro, D., M. Capponi, and D. Triglione. 2016. “GTE: A new software for gravitational terrain effect computation: Theory and performances.” Pure Appl. Geophys. 173 (7): 2435–2453. https://doi.org/10.1007/s00024-016-1265-4.
Sansò, F., and M. G. Sideris. 2013. Geoid determination: Theory and methods. Berlin: Springer.
Schwarz, K. P., M. G. Sideris, and R. Forsberg. 1987. “Orthometric heights without leveling.” J. Surv. Eng. 113 (1): 28–40. https://doi.org/10.1061/(ASCE)0733-9453(1987)113:1(28).
Schwarz, K. P., M. G. Sideris, and R. Forsberg. 1990. “The use of FFT techniques in physical geodesy.” Geophys. J. Int. 100 (3): 485–514. https://doi.org/10.1111/j.1365-246X.1990.tb00701.x.
Sheng, M. B., C. Shaw, P. Vaníček, R. W. Kingdon, M. Santos, and I. Foroughi. 2019. “Formulation and validation of a global laterally varying topographical density model.” Tectonophysics 762 (Apr): 45–60. https://doi.org/10.1016/j.tecto.2019.04.005.
Silva, M. A., D. Blitzkow, and M. C. B. Lobianco. 2003. “A case study of different modified kernel applications in quasi-geoid determination.” In Proc., 3rd Meeting of the Int. Gravity and Geoid Commission, 138–143. Thessaloniki, Greece: Ziti Edittions.
Silva, V. C., F. Almeida, D. Blitzkow, and A. C. Matos. 2021. “The geoid and quasigeoid of São Paulo state using the updated gravimetric data and the 2018 BVRF.” Bull. Geodetic Sci. 27 (2): e2021018. https://doi.org/10.1590/1982-2170-2020-0061.
Sjöberg, L. E. 2003. “A computational scheme to model the geoid by the modified Stokes formula without gravity reductions.” J. Geod. 77 (7–8): 423–432. https://doi.org/10.1007/s00190-003-0338-1.
Sjöberg, L. E. 2004. “The effect on the geoid of lateral density variations.” J. Geod. 78 (Apr): 34–39. https://doi.org/10.1007/s00190-003-0363-0.
Smith, D. A. 1998. “There is no such thing as The EGM96 geoid: Subtle points on the use of a global geopotential model.” IGeS Bull. 8: 17–28.
Stokes, G. G. 1849. “On the variation of gravity at the surface of the earth.” Trans. Cambridge Philos. Soc. 8: 672–695.
Tenzer, R., and P. Vaníček. 2009. “Correction to Helmert’s orthometric height due to actual lateral variation of topographical density.” Rev. Bras. de Cartografia 55 (2): 44–47. https://doi.org/10.14393/rbcv55n2-43494.
Tziavos, I. N., and W. E. Featherstone. 2001. “First results of using digital density data in gravimetric geoid computation in Australia.” In Proc., Gravity, Geoid and Geodynamics 2000, edited by M. G. Sideris, 123. Berlin: Springer. https://doi.org/10.1007/978-3-662-04827-6_56.
Tziavos, I. N., G. S. Vergos, and V. N. Grigoriadis. 2010. “Investigation of topographic reductions and aliasing effects on gravity and the geoid over Greece based on various digital terrain models.” Surv. Geophys. 31 (1): 23. https://doi.org/10.1007/s10712-009-9085-z.
Vaníček, P., and A. Kleusberg. 1987. “The Canadian geoid—Stokesian approach.” Manuscr. Geod. 12 (2): 86–98.
Vaníček, P., and L. E. Sjoberg. 1991. “Reformulation of Stokes’s theory for higher than second-degree reference field and modification of integration kernels.” J. Geophys. Res. Solid Earth 96 (B4): 6529–6539. https://doi.org/10.1029/90JB02782.
Wong, L., and R. Gore. 1969. “Accuracy of geoid heights from modified Stokes kernels.” Geophys. J. Int. 18 (Jun): 81–91. https://doi.org/10.1111/j.1365-246X.1969.tb00264.x.
Yakubu, C. I., V. G. Ferreira, and C. Y. Asante. 2017. “Towards the selection of an optimal global geopotential model for the computation of the long-wavelength contribution: A case study of Ghana.” Geosciences 7 (4): 113. https://doi.org/10.3390/geosciences7040113.
Zhang, K., W. Featherstone, M. Stewart, and A. Dodson. 1998. “A new gravimetric geoid for Austria.” In Proc., 2nd Continental Workshop on the Geoid. Reports of the Finnish Geodetic Institute, 225–233. Kirkkonummi, Finland: Finnish Geodetic Institute.
Zingerle, P., R. Pail, T. Gruber, and X. Oikonomidou. 2020. “The combined global gravity field model XGM2019e.” J. Geod. 94 (7): 66. https://doi.org/10.1007/s00190-020-01398-0.

Information & Authors

Information

Published In

Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 150Issue 2May 2024

History

Received: Feb 13, 2023
Accepted: Nov 9, 2023
Published online: Jan 19, 2024
Published in print: May 1, 2024
Discussion open until: Jun 19, 2024

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Professor, Seismological Observatory, Institute of Geosciences, Univ. of Brasília, Prédio SG 13—Campus Darcy Ribeiro, Asa Norte, Brasília, DF 70910-900, Brazil (corresponding author). ORCID: https://orcid.org/0000-0003-1073-0683. Email: [email protected]
Danilo Fernandes de Medeiros, Ph.D. [email protected]
Seismological Observatory, Institute of Geosciences, Univ. of Brasília, Prédio SG 13—Campus Darcy Ribeiro, Asa Norte, Brasília, DF 70910-900, Brazil. Email: [email protected]
Professor, Faculty of Civil Engineering, Federal Univ. of Uberlândia, Av. João Naves de Ávila, 2121, Uberlandia, MG 38408-100, Brazil. ORCID: https://orcid.org/0000-0003-4380-4650. Email: [email protected]
Professor, Dept. of Geomatics Engineering, Faculty of Civil Engineering, Istanbul Technical Univ., Maslak, Istanbul 34469, Turkey. ORCID: https://orcid.org/0000-0003-0854-788X. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share