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The Potential Application of the GNSS Leveling Method in Local Areas by Means of Sector Analysis
Corresponding Author(s) : Alina Fedorchuk
Geomatics and Environmental Engineering,
Vol. 16 No. 3 (2022): Geomatics and Environmental Engineering
Abstract
The purpose of this work is to perform the comparison of heights of global geoid models EGM08, EIGEN-6C4, GECO, and XGM2019e based on sector analysis that are obtained relative to the ellipsoid WGS84 and GRS80 in order to implement the method of GNSS leveling in local areas. The heights of the global geoid models determined from the ellipsoid WGS84 should be reduced by −41 cm ("œzero-degree term") in order to scale them to the calculated geoid by GNSS leveling. Heights determined from the ellipsoid GRS80 should be increased by +52 cm. Spatial analysis of the heights of geoid models in the relative system for the northern territory shows that the standard deviation of the heights of geoid models is 13.6 cm, and for the southern territory it is 36.5 cm. The elevation errors of the geoid models in the relative system were estimated to be standard deviations of 2.9 cm within the northern area and 2.3 cm within the southern one. The root mean square values of initial errors of the models EGM08, EIGEN-6C4, GECO, and XGM2019e are 8.6 cm, 4.6 cm, 4.4 cm, and 3.8 cm, respectively, and standard deviation values are 2.0 cm, 2.2 cm, 3.2 cm, and 2.4 cm. The paper also performs a sector analysis of the geoid model errors in order to correct them for the application of the GNSS leveling method within the research area. The standard deviations of the residual error of the corrected model heights are 1.8 cm, 1.9 cm, 2.5 cm, and 2.0 cm for EGM08, EIGEN-6C4, GECO, and XGM2019e. The root mean square values of these residual errors for the geoid models are 1.9 cm, 2.0 cm, 2.5 cm, and 2.0 cm, respectively.
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- Barthelmes F.: Global models. [in:] Grafarend E. (ed.), Encyclopedia of Geodesy, Springer, Cham 2014, pp. 1–9. https://doi.org/10.1007/978-3-319-02370-0_43-1.
- ICGEM: International Centre for Global Earth Models (ICGEM). http://icgem.gfz-potsdam.de/ [access: 3.01.2021].
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- Pavlis N.K., Holmes S.A., Factor J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, vol 117, 2012, B04406. https://doi.org/10.1029/2011JB008916.
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- Kryński J., Kloch-Główka G.: Evaluation of the Performance of the New EGM2008 Global Geopotential Model over Poland. Geoinformation Issues, vol. 1, no. 1, 2009, pp. 7–17.
- Ellmann A., Kaminskis J., Parseliunas E., Jürgenson H., Oja T.: Evaluation results of the Earth Gravitational Model EGM08 over the Baltic countries. Newton’s Bulletin, vol. 4, 2009, pp. 110–121.
- Kostelecký J., Klokocnik J., Bucha B., Bezdek A., Foerste C.: Evaluation of gravity field model EIGEN-6C4 by means of various functions of gravity potential, and by GNSS/levelling. Geoinformatics FCE CTU, vol. 14, no. 1, 2015, pp. 7–28. https://doi.org/10.14311/gi.14.1.1.
- Reķe I., Celms A., Rusiņš J.: Latvian normal height system testing using GNSS measurements. Research for Rural Development, vol. 1, 2016, pp. 164–169.
- Wu Y., Luo Z., Mei X., Lu J.: Normal Height Connection across Seas by the Geopotential-Difference Method: Case Study in Qiongzhou Strait, China. Journal of Surveying Engineering, vol. 143(2), 2016, 05016011. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000203.
- Gruber T., Zingerle P., Pail R., Oikonomidou X.: High resolution gravity field models as global reference surface for heights. SIRGAS 2019, Rio de Janeiro, 12.11.2019 [conference presentation].
- Hofmann-Wellenhof B., Lichtenegger H., Wasle E.: GNSS – Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and more. Springer Wien New York, 2008.
- Seeber G.: Height Determination. [in:] Seeber G., Satellite Geodesy: 2nd completely revised and extended edition, Walter de Gruyter, Berlin – New York 2003, pp. 366–368.
- Kim K.B., Yun H.S., Choi H.J.: Accuracy Evaluation of Geoid Heights in the National Control Points of South Korea Using High-Degree Geopotential Model. Applied Sciences, vol. 10(4), 2020, 1466. https://doi.org/10.3390/app10041466.
- Odumosu J.O., Onuigbo I.C., Nwadialor I.J., Olurotimi K., Elegbede D., Kemiki O.A.: Analysis of some factors that affect accuracy in long wavelength geoid determination using GrafLab. Nigerian Journal of Geodesy, vol. 1(1), 2017, pp. 91–103. http://repository.futminna.edu.ng:8080/jspui/handle/123456789/10381 [access: 22.01.2021].
- National Geospatial-Intelligence Agency (NGA): EGM2008-WGS84 Version. https://www.nga.mil/index.html [access: 22.01.2021].
- Fedorchuk A.: Previous analysis of developments determination of normal heights from GNSS-observations on the city of Lviv and followed territories. [in:] International Conference of Young Scientists “GeoTerrace-2018”, December 13–15, 2018 Lviv, Ukraine, Lviv Polytechnic Publishing House, Lviv, pp. 33–36 [Федорчук А.: Попередній аналіз похибок визначення нормальних висот із GNSS-спостережень на територію міста Львова та його околиць. [в:] Міжнародна Науково-Технічна Конференція Молодих Вчених «GeoTerrace-2018», 13–15 грудня 2018, Львів, Україна, Видавництво Львівської політехніки, Львів].
References
Barthelmes F.: Global models. [in:] Grafarend E. (ed.), Encyclopedia of Geodesy, Springer, Cham 2014, pp. 1–9. https://doi.org/10.1007/978-3-319-02370-0_43-1.
ICGEM: International Centre for Global Earth Models (ICGEM). http://icgem.gfz-potsdam.de/ [access: 3.01.2021].
Barthelmes D.F.: International Centre for Global Earth Models (ICGEM). [in:] Drewes H., Hornik H. (eds.), Travaux: Volume 39: Reports 2011–2015: Edited for the IUGG General Assembly Prague, Czech Republic June 22 – July 2, 2015, International Association of Geodesy IAG, 2015, pp. 427–434.
Ince E.S., Barthelmes F., Reißland S., Elger K., Foerste C., Flechtner F., Schuh H.: ICGEM – 15 years of successful collection and distribution of global gravitational models, associated services, and future plans. Earth System Science Data, vol. 11, 2019, pp. 647–674. https://doi.org/10.5194/essd-11-647-2019.
Pavlis N.K., Holmes S.A., Factor J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, vol 117, 2012, B04406. https://doi.org/10.1029/2011JB008916.
Förste Ch., Bruinsma S.L., Abrikosov O., Lemoine J.-M., Schaller T., Götze H.-J., Ebbing J., Marty J.C., Flechtner F., Balmino G., Barthelmes F., Biancale R.: EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. Geophysical Research Abstracts, vol. 16, EGU2014-3707, EGU General Assembly 2014. https://doi.org/10.5880/icgem.2015.1.
Gilardoni M., Reguzzoni M., Sampietro D.: GECO: a global gravity model by locally combining GOCE data and EGM2008. Studia Geophysica et Geodaetica, vol. 60(2), 2016, pp. 228–247. https://doi.org/10.1007/s11200-015-1114-4.
Zingerle P., Pail R., Gruber T., Oikonomidou X.: The combined global gravity field model XGM2019e. Journal of Geodesy, vol. 94, 2020, 66. https://doi.org/10.1007/s00190-020-01398-0.
Kryński J., Kloch-Główka G.: Evaluation of the Performance of the New EGM2008 Global Geopotential Model over Poland. Geoinformation Issues, vol. 1, no. 1, 2009, pp. 7–17.
Ellmann A., Kaminskis J., Parseliunas E., Jürgenson H., Oja T.: Evaluation results of the Earth Gravitational Model EGM08 over the Baltic countries. Newton’s Bulletin, vol. 4, 2009, pp. 110–121.
Kostelecký J., Klokocnik J., Bucha B., Bezdek A., Foerste C.: Evaluation of gravity field model EIGEN-6C4 by means of various functions of gravity potential, and by GNSS/levelling. Geoinformatics FCE CTU, vol. 14, no. 1, 2015, pp. 7–28. https://doi.org/10.14311/gi.14.1.1.
Reķe I., Celms A., Rusiņš J.: Latvian normal height system testing using GNSS measurements. Research for Rural Development, vol. 1, 2016, pp. 164–169.
Wu Y., Luo Z., Mei X., Lu J.: Normal Height Connection across Seas by the Geopotential-Difference Method: Case Study in Qiongzhou Strait, China. Journal of Surveying Engineering, vol. 143(2), 2016, 05016011. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000203.
Gruber T., Zingerle P., Pail R., Oikonomidou X.: High resolution gravity field models as global reference surface for heights. SIRGAS 2019, Rio de Janeiro, 12.11.2019 [conference presentation].
Hofmann-Wellenhof B., Lichtenegger H., Wasle E.: GNSS – Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and more. Springer Wien New York, 2008.
Seeber G.: Height Determination. [in:] Seeber G., Satellite Geodesy: 2nd completely revised and extended edition, Walter de Gruyter, Berlin – New York 2003, pp. 366–368.
Kim K.B., Yun H.S., Choi H.J.: Accuracy Evaluation of Geoid Heights in the National Control Points of South Korea Using High-Degree Geopotential Model. Applied Sciences, vol. 10(4), 2020, 1466. https://doi.org/10.3390/app10041466.
Odumosu J.O., Onuigbo I.C., Nwadialor I.J., Olurotimi K., Elegbede D., Kemiki O.A.: Analysis of some factors that affect accuracy in long wavelength geoid determination using GrafLab. Nigerian Journal of Geodesy, vol. 1(1), 2017, pp. 91–103. http://repository.futminna.edu.ng:8080/jspui/handle/123456789/10381 [access: 22.01.2021].
National Geospatial-Intelligence Agency (NGA): EGM2008-WGS84 Version. https://www.nga.mil/index.html [access: 22.01.2021].
Fedorchuk A.: Previous analysis of developments determination of normal heights from GNSS-observations on the city of Lviv and followed territories. [in:] International Conference of Young Scientists “GeoTerrace-2018”, December 13–15, 2018 Lviv, Ukraine, Lviv Polytechnic Publishing House, Lviv, pp. 33–36 [Федорчук А.: Попередній аналіз похибок визначення нормальних висот із GNSS-спостережень на територію міста Львова та його околиць. [в:] Міжнародна Науково-Технічна Конференція Молодих Вчених «GeoTerrace-2018», 13–15 грудня 2018, Львів, Україна, Видавництво Львівської політехніки, Львів].