Strategy for Connecting to the IHRF: Case Study for the Tide Gauge of Cananeia-SP
DOI:
https://doi.org/10.11137/1982-3908_2021_44_41104Keywords:
Helmert orthometric height, Normal height, Local reference systemAbstract
In July 2018, IBGE launched the new heights of the Brazilian Geodetic System (BGS), the normal height, which has associated gravity. These new heights are replacing the old normal-orthometric ones, in which there was only the non-parallelism correction. The IBGE informs that the values farther from the origin, have less accuracy. This lower accuracy may interfere in the future, the connection of the local tide gauges to IHRF (International Reference Frame Height). Thus, this paper proposes the integration of the local tide gauge of Cananeia-SP to the IHRF. In order to validate the methodology, the normal, Helmert, and rigorous orthometric heights using two distinct references: the Imbituba-SC tide gauge, as the origin of the BGS and the Cananeia-SP tide gauge, as a local tide gauge to be integrated into the IHRF. Calculating the three heights through these two origins, we analyzed the discrepancies in comparison to the heights calculated by IBGE. Numerical tests indicate that there was an improvement in terms of a mean and standard deviation when using the Cananeia gauge as origin in the calculation of normal, Helmert, and rigorous heights. In the congruence analysis, the calculations indicate that the highest standard deviation is presented when using IBGE normal heights. Thus, we have a new origin that is reliable and functional, can be integrated with the IHRF, where the Helmert and rigorous orthometric heights have the best statistical results.
References
Albarici, F.L., Guimarães, G.N., Foroughi, I., Santos, M. & Trabanco, J.A. 2018, ‘Separação Entre Geoide e Quase-Geoide: Análise das Diferenças Entre as Altitudes Normal-Ortométrica e Ortométrica Rigorosa’, Anuário do Instituto de Geociências, vol. 41, no. 3, pp. 71-81. https://doi.org/10.11137/2018_3_71_81.
Albarici, F.L., Foroughi, I., Guimarães, G.N., Santos, M. & Trabanco, J.A. 2019, ‘New Perspective for Physical Heights in Brazil’, Bulletin of Geodetic Sciences, vol. 25, no 1, pp. 1-20. https://doi.org/10.1590/s1982-21702019000100001.
Dalazoana, R. & de Freitas, S.R.C. 2020, ‘Sistemas Geodésicos de Referência: Rumo ao GGRS/GGRF’, Revista Brasileira De Cartografia, vol. 72. no. Special, pp. 962-82. https://doi.org/10.14393/revbrascartogr.
Ekman, M. 1989, ‘Impacts of Geodynamic Phenomena’, Bulletin Géodésique, vol. 63, pp 281-96. https://doi.org/10.1007/BF02520477.
Ellmann, A. and Vaníček, P. 2007, UNB application of Stokes-Helmert's approach to geoid computation, Journal of Geodynamics, vol. 43, no. 2, pp. 200–13. https://doi.org/10.1016/j.jog.2006.09.019.
Foroughi, I., Vaníček, P., Sheng, M., Kingdon, R.W. & Santos, M.C. 2017, ‘In defense of the classical height system’, Geophysical Journal International, vol. 211, no. 2, pp 1176-83. https://doi.org/10.1093/gji/ggx366.
Förste, C., Bruinsma, S.L., Abrykosov, O., Lemoine, J.M., Marty, J.C., Flechtner, F., Balmino, G., Barthelmes, F. & Biancale, R. 2014, ‘EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse’, 5th GOCE USER WORKSHOP, GFZ Data Services, Paris, GFZ, p. 25–8. https://doi.org/10.5880/icgem.2015.1.
Gilardoni, M., Reguzzoni, M. & Sampietro, D. 2016, ‘GECO: a global gravity model by locally combining GOCE data and EGM2008’, Studia Geophysica et Geodaetica, vol. 60, pp. 228-47. https://doi.org/10.1007/s11200-015-1114-4.
Heiskanen, W.A. & Moritz, H. 1967, Physical Geodesy, Freeman and Company, San Francisco.
Hofmann-Wellenhof, B. & Moritz, H. 2006, Physical Geodesy, Springer-Verlag, Berlin.
IBGE - see Instituto Brasileiro de Geografia e Estatística.
Instituto Brasileiro de Geografia e Estatística 2018, Relatório Reajustamento da Rede Altimétrica com Números Geopotenciais REALT-2018, Rio de Janeiro, viewed 3 January 2019,<ftp://geoftp.ibge.gov.br/informacoes_sobre_posicionamento_geodesico/rede_altimetrica/relatorio/relatorio_REALT_2018.pdf>.
International Association of Geodesy 2015, International Height Reference System (IHRS). viewed 15 January 2021, <https://iag.dgfi.tum.de/fileadmin/IAG- docs/IAG_Resolutions _2015.pdf>.
Heikkinen, M. 1978, On the tide-generating forces. Finnish Geodetic Institute, Helsinki, Finland.
Jekeli, C. 2000, Heights, the Geopotential, and Vertical Datums. Report 459. Ohio, Department of Civil and Environmental Engineering and Geodetic Science, viewed 04 January 2021, <https://kb.osu.edu/bitstream/handle/1811/78667/SES_GeodeticScience_Report_459.pdf?sequence=1> .
Kingdon, R., Vaníček, P., Santos, M.C., Ellmann, A., Tenzer. R. 2005, ‘Toward an improved orthometric height system for Canada’, Geomatica, vol. 59, no. 3, pp. 241–50 (Errata: Figure 4 on Geomatica, vol. 60, no, 1, pp. 101).
Kingdon, R. 2012, ‘Advances in Gravity based Height Systems’, Ph.D. Thesis, Department of Geodesy and Geomatics Engineering, University of New Brunswick. http://www2.unb.ca/gge/Pubs/TR292.pdf.
Kotsakis, C., Katsambalos, K. & Ampatzidis, D. 2012, ‘Estimation of the zero-height geopotential level W0LVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands’, Journal of Geodesy, vol. 86, no. 6, pp. 423-39. https://doi.org/10.1007/s00190-011-0530-7.
Molodensky, M. 1945, ‘Fundamental Problems of Geodetic Gravimetry’, TRUDY Technical Report No. 42, Geodezizdat Novosibirskiy Institut Inzhenerov Geodezii, Aerofotos yemki i Kartografii (NIIGAiK), Moscow.
Molodensky, M., Eremeev, V. & Yurkina, M. 1962, Methods for the study of the external gravitational field and figure of the Earth’, Israel Program for Scientific Translations, Jerusalem.
Moritz, H. 1980, ‘Geodetic reference system 1980’, Bull. Géodésique, vol. 54, no. 3, pp. 395–405. https://doi.org/10.1007/BF02521480.
Rapp, R. 1989, ‘The treatment of permanent tidal effects in the analysis of satellite altimetry data for sea surface topography’, Manuscripta geodaetica, vol. 14, pp. 368–72.
Roman, D. & Smith, D. 2002, ‘Recent investigations toward achieving a one-centimeter geoid. Gravity, Geoid and Geodynamics 2000’, International Association of Geodesy Symposia, vol. 123, Springer, New York, pp. 285–90.
Santos, M.C., Vaníček, P., Featherstone, W.E., Kingdon, R., Ellmann, A., Martin, B. -A., Kuhn, M. & Tenzer. R. 2006, ‘The relation between Rigorous and Helmert’s definition of orthometric heights’, Journal Geodesy, vol. 80, pp. 691–704. https://doi.org/10.1007/s00190-006-0086-0.
Sánchez, L. 2013, ‘Towards a vertical datum standardisation under the umbrella of Global Geodetic Observing System’, Journal of Geodetic Science, vol. 2, no. 4, pp. 325-342. https://doi.org/10.2478/v10156-012-0002-x.
Sánchez, L., Čunderlík, R., Dayoub, N., Mikula, K., Minarechová, Z., Šíma, Z., Vatrt, V. & Vojtíšková, M. 2016, ‘A conventional value for the geoid reference potential W0’, Journal Geodesy, vol. 90, no. 9, pp. 815–35. https://doi.org/10.1007/s00190-016-0913-x.
Sánchez, L. & Sideris, M.G. 2017, ‘Vertical datum unification for the International Height Reference System (IHRS)’, Geophysical Journal International, vol. 209, no. 2, pp 570– 86. https://doi.org/10.1093/gji/ggx025.
Sansò, F. & Rummel, R. 1997, ‘Geodetic Boundary Value Problems in View of the One Centimeter Geoid’. Springer, New York, U.S.A.
Sistema de Referência Geocêntrico para as Américas 2020, Geocentric Reference System for the Americas, viewed 28 December 2020, <http://www.sirgas.org/en/sirgas-definition/>.
Tenzer, R., Vaníček, P., Santos, M., Featherstone, W.E. & Kuhn, M. 2005, ‘The rigorous determination of orthometric heights’, Journal of Geodesy, vol. 79, pp. 82-92. https://doi.org/10.1007/s00190-005-0445-2.
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