Global geoid adjustment on local area for GIS applications using GNSS permanent station coordinates
Abstract
Orthometric heights, useful for many engineering and geoscience applications, can be obtained by GPS (Global Positioning System) surveys only when an accurate geoid undulation model (that supplies the vertical separation between the geoid and WGS84 ellipsoid) is available for the considered topic area. Global geoid height models (i.e., EGM2008), deriving from satellite gravity measurements suitably integrated with other data are free available on web, but their accuracy is often not sufficient for the user’s purposes. More accurate local models can nevertheless be acquired, but often only for a fee. GPS/levelling surveys are suitable for determining a local, accurate geoid model, but may be too expensive. This paper aims to demonstrate that GNSS (Global Navigation Satellite System) Permanent Station documents (monographs), freely available on the web and supplying orthometric and ellipsoidal heights, permit to calculate precise geoidal undulations useful to perform global geoid modelling on a local area. In fact, in this study 25 GNSS Permanent Stations (GNSS PS), located in North-Western Italy are considered: the differences between GNSS PS geoidal heights and the corresponding EGM2008 1′ × 1′ ones are used as a starting dataset for Ordinary Kriging applications. The resulting model is summed to the EGM2008 1′ × 1′, obtaining a better-performed model of the interest area. The accuracy tests demonstrate that the resulting model is better than EGM2008 grids to produce contours from a GPS dataset for large-scale mapping.
Keyword : Geoid, EGM2008, GNSS Permanent Stations, spatial interpolation, Ordinary Kriging, GIS
How to Cite
Falchi, U., Parente, C., & Prezioso, G. (2018). Global geoid adjustment on local area for GIS applications using GNSS permanent station coordinates. Geodesy and Cartography, 44(3), 80-88. https://doi.org/10.3846/gac.2018.4356
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Alothman, A., Bouman, J., Gruber, T., Lieb, V., Alsubaei, M., Alomar, A., Fuchs, M., & Schmidt, M. (2014). Validation of Regional geoid models for Saudi Arabia using GPS/levelling data and GOCE models. Gravity, Geoid and Height Systems, IAG Symposia, 141, 193-199.
Angulo-Martínez, M., Lopez-Vicente, M., Vicente-Serrano, S. M., & Beguería, S. (2009). Mapping rainfall erosivity at a regional scale: a comparison of interpolation methods in the Ebro Basin (NE Spain). Hydrology and Earth System Sciences, 13(10), 1907-1920. https://doi.org/10.5194/hess-13-1907-2009
Barzaghi, R., Borghi, A., Carrion, D., & Sona, G. (2007). Refining the estimate of the Italian quasigeoid. Bollettino di Geodesia e Scienze Affini, 3, 145-160.
Barzaghi, R., Carrion, D., Pepe, M., & Prezioso, G. (2016). Computing the deflection of the vertical for improving aerial surveys: a comparison between EGM2008 and ITALGEO05 estimates. Sensors, 16(8), 1168. https://doi.org/10.3390/s16081168
Belfiore, O. R., & Parente, C. (2016). Comparison of different algorithms to orthorectify WorldView-2 satellite imagery. Algorithms, 9(4), 67. https://doi.org/10.3390/a9040067
Biagi, L., Caldera, S., Capra, A., Castagnetti, C., & Sansò, F. (2008). Densification of IGS/EPN by local permanent networks: sensitivity of results with respect to the adjustment choices. In Bulletin of Geodesy and Geomatics. Istituto Geografico Militare, Firenze (Italy).
Das, R. K., Samanta, S., Jana, S. K., & Rosa, R. (2017). Polynomial interpolation methods in development of local geoid model. The Egyptian Journal of Remote Sensing and Space Science. https://doi.org/10.1016/j.ejrs.2017.03.002
Dashtpagerdi, M. M., Vagharfard, H., & Honarbakhsh, A. (2013). Application of cross-validation technique for zoning of groundwaterlevels in Shahrekord plain. Agricultural Sciences, 4(7), 329-333. https://doi.org/10.4236/as.2013.47047
Dawod, G. M., Mohamed, H. F., & Ismail, S. S. (2009). Evaluation and adaptation of the EGM2008 geopotential model along the Northern Nile Valley, Egypt: Case study. Journal of Surveying Engineering, 136(1), 36-40. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000002
Di Pasquale, A., Nico, G., Pitullo, A., & Prezioso, G. (2018). Monitoring strategies of earth dams by ground-based radar interferometry: how to extract useful information for seismic risk assessment. Sensors, 18(1), 244. https://doi.org/10.3390/s18010244
El-Hallaq, M. A. (2012). Development of a local GPS-leveling geoid model for the Gaza Strip area. International Journal of Emerging Technology and Advanced Engineering, 2, 268-273.
Erol, B. (2011). An automated height transformation using precise geoid models. Scientific Research and Essays, 6(6), 1351-1363. https://doi.org/10.5897/SRE10.1119
Errico, A., Angelino, C. V., Cicala, L., Podobinski, D. P., Persechino, G., Ferrara, C., Lega, M., Vallario, A., Parente, C., Masi, G., Gaetano, R., Scarpa, G., Amitrano, D., Ruello, G., Verdoliva, L., & Poggi, G. (2014). SAR/multispectral image fusion for the detection of environmental hazards with a GIS. In Proceedings of SPIE – Earth Resources and Environmental Remote Sensing/GIS Applications V, 9245. International Society for Optical Engineering. https://doi.org/10.1117/12.2066476
Falchi, U. (2017). Spatial data: from cartography to geodatabase. Geodesy and Cartography, 43(4), 142-146. https://doi.org/10.3846/20296991.2017.1412613
Fasshauer, G. E., & Zhang, J. G. (2007). On choosing “optimal” shape parameters for RBF approximation. Numerical Algorithms, 45(1-4), 345-368. https://doi.org/10.1007/s11075-007-9072-8
Featherstone, W. E., Dentith, M. C., & Kirby, J. F. (1998). Strategies for the accurate determination of orthometric heights from GPS. Survey Review, 34(267), 278-296. https://doi.org/10.1179/sre.1998.34.267.278
Fotopoulos, G., Kotsakis, C., & Sideris, M. G. (2003). How accurately can we determine orthometric height differences from GPS and geoid data? Journal of Surveying Engineering, 129(1), 1-10. https://doi.org/10.1061/(ASCE)0733-9453(2003)129:1(1)
Johnston, K., Ver Hoef, J. M., Krivoruchko, K., & Lucas, N. (2001). Using ArcGIS™ geostatistical analyst. Redlands: ESRI.
Kaplan, E., & Hegarty, C. (2005). Understanding GPS: principles and applications (p. 683). Artech house.
Karney, C. (2008). Online geoid calculations using the GeoidEval utility. Retrieved from https://geographiclib.sourceforge.io/cgi-bin/GeoidEval
Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection. Proceedings of IJCAI, 14(2), 1137-1145.
Komarov, R. V., Kascheev, R. A., & Zagretdinov, R. V. (2008). Geoid determination by GPS/leveling method in the Republic of Tatarstan. Georesources, 43(2), 43-45.
Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., & Wang, Y. M. (1998). The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96 (Tech nical Report). Retrieved from https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980218814.pdf
Ligas, M., & Kulczycki, M. (2018). Kriging and moving window kriging on a sphere in geometric (GNSS/levelling) geoid modelling. Survey Review, 50(359), 155-162. https://doi.org/10.1080/00396265.2016.1247131
Maglione, P., Parente, C., Santamaria, R., & Vallario, A. (2014). Modelli tematici 3D della copertura del suolo a partire da DTM e immagini telerilevate ad alta risoluzione WorldView-2. Rendiconti Online della Società Geologica Italiana, 30, 33-40 (in Italian). https://doi.org/10.3301/ROL.2014.08
Maglione, P., Parente, C., & Vallario, A. (2018). Accuracy of global geoid height models in local area: tests on campania region (Italy). International Journal of Civil Engineering and Technology, 9(3), 1049-1057.
Marti, U. (2007). Comparison of high precision Geoid Models in Switzerland. Dynamic Planet, IAG Symposia, 130, 377-382. https://doi.org/10.1007/978-3-540-49350-1_55
NGA/NASA. (n.d.). EGM96, N=M=360 Earth Gravitational Model available online. Retrieved from http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html
NGA-Office of Geomatics. (n.d.). NGA/NASA EGM96. Retrieved from http://earth-info.nga.mil/GandG/update/index.php
Oliver, M. A., & Webster, R. (2014). A tutorial guide to Geostatistics: computing and modelling variograms and kriging. Catena, 113, 56-69. https://doi.org/10.1016/j.catena.2013.09.006
Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2008). EGM2008: An overview of its development and evaluation. In IAG International Symposium, GGEO, 2327. National Geospatial-Intelligence Agency, USA.
Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117(B4). https://doi.org/10.1029/2011JB008916
Pepe, M., Prezioso, G., & Santamaria, R. (2015). Impact of vertical deflection on direct georeferencing of airborne images. Survey Review, 47(340), 71-76. https://doi.org/10.1179/1752270614Y.0000000087
Peprah, M. S., Ziggah, Y. Y., & Yakubu, I. (2017). Performance evaluation of the Earth Gravitational Model 2008 (EGM2008) – a case study. South African Journal of Geomatics, 6(1), 47-72. https://doi.org/10.4314/sajg.v6i1.4
Pugh, D. T. (1987). Tides, surges and mean sea-level (p. 486). John Wiley & Sons.
Rapp, R. H., & Wang, Y. M. (1993). Geoid undulation differences between Geopotential models. Surveys in Geophysics, 14(4-5), 373-380. https://doi.org/10.1007/BF00690565
Refaeilzadeh, P., Tang, L., & Liu, H. (2009). Cross-validation. In Encyclopedia of database systems (pp. 532-538). Boston: Springer US.
Shen, W., & Han, J. (2013). Improved geoid determination based on the shallow-layer method: a case study using EGM08 and CRUST2.0 in the Xinjiang and Tibetan Regions. Terrestrial, Atmospheric & Oceanic Sciences, 24(4), 591-604. https://doi.org/10.3319/TAO.2012.11.12.01(TibXS)
Soycan, M. (2013). Analysis of geostatistical surface model for GPS height transformation: a case study in Izmir territory of Turkey. Geodetski Vestnik, 57(4), 702-718. https://doi.org/10.15292/geodetski-vestnik.2013.04.702-718
Soycan, M. E. T. I. N., & Soycan, A. R. Z. U. (2003). Surface modeling for GPS-levelling geoid determination. Newton’s Bulletin, 1, 41-52. Retrieved from http://www.isgeoid.polimi.it/Newton/Newton_1/soycan.pdf
Van der Marel, H. (2014). Reference systems for surveying and mapping. Retrieved from http://gnss1.tudelft.nl/pub/vdmarel/reader/CTB3310_RefSystems_1-2a_print.pdf
Wackernagel, H. (1995). Multivariate Geostatistics: an introduction with applications (p. 307). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-03098-1
Weiss, S. M., & Kulikowski, C. A. (1991). Computer systems that learn: classification and prediction methods from statistics, neural nets, machine learning, and expert systems (p. 223). Morgan Kaufmann.
Xiao, Y., Gu, X., Yin, S., Shao, J., Cui, Y., Zhang, Q., & Niu, Y. (2016). Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, Northwest China. SpringerPlus, 5(1), 425. https://doi.org/10.1186/s40064-016-2073-0
Angulo-Martínez, M., Lopez-Vicente, M., Vicente-Serrano, S. M., & Beguería, S. (2009). Mapping rainfall erosivity at a regional scale: a comparison of interpolation methods in the Ebro Basin (NE Spain). Hydrology and Earth System Sciences, 13(10), 1907-1920. https://doi.org/10.5194/hess-13-1907-2009
Barzaghi, R., Borghi, A., Carrion, D., & Sona, G. (2007). Refining the estimate of the Italian quasigeoid. Bollettino di Geodesia e Scienze Affini, 3, 145-160.
Barzaghi, R., Carrion, D., Pepe, M., & Prezioso, G. (2016). Computing the deflection of the vertical for improving aerial surveys: a comparison between EGM2008 and ITALGEO05 estimates. Sensors, 16(8), 1168. https://doi.org/10.3390/s16081168
Belfiore, O. R., & Parente, C. (2016). Comparison of different algorithms to orthorectify WorldView-2 satellite imagery. Algorithms, 9(4), 67. https://doi.org/10.3390/a9040067
Biagi, L., Caldera, S., Capra, A., Castagnetti, C., & Sansò, F. (2008). Densification of IGS/EPN by local permanent networks: sensitivity of results with respect to the adjustment choices. In Bulletin of Geodesy and Geomatics. Istituto Geografico Militare, Firenze (Italy).
Das, R. K., Samanta, S., Jana, S. K., & Rosa, R. (2017). Polynomial interpolation methods in development of local geoid model. The Egyptian Journal of Remote Sensing and Space Science. https://doi.org/10.1016/j.ejrs.2017.03.002
Dashtpagerdi, M. M., Vagharfard, H., & Honarbakhsh, A. (2013). Application of cross-validation technique for zoning of groundwaterlevels in Shahrekord plain. Agricultural Sciences, 4(7), 329-333. https://doi.org/10.4236/as.2013.47047
Dawod, G. M., Mohamed, H. F., & Ismail, S. S. (2009). Evaluation and adaptation of the EGM2008 geopotential model along the Northern Nile Valley, Egypt: Case study. Journal of Surveying Engineering, 136(1), 36-40. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000002
Di Pasquale, A., Nico, G., Pitullo, A., & Prezioso, G. (2018). Monitoring strategies of earth dams by ground-based radar interferometry: how to extract useful information for seismic risk assessment. Sensors, 18(1), 244. https://doi.org/10.3390/s18010244
El-Hallaq, M. A. (2012). Development of a local GPS-leveling geoid model for the Gaza Strip area. International Journal of Emerging Technology and Advanced Engineering, 2, 268-273.
Erol, B. (2011). An automated height transformation using precise geoid models. Scientific Research and Essays, 6(6), 1351-1363. https://doi.org/10.5897/SRE10.1119
Errico, A., Angelino, C. V., Cicala, L., Podobinski, D. P., Persechino, G., Ferrara, C., Lega, M., Vallario, A., Parente, C., Masi, G., Gaetano, R., Scarpa, G., Amitrano, D., Ruello, G., Verdoliva, L., & Poggi, G. (2014). SAR/multispectral image fusion for the detection of environmental hazards with a GIS. In Proceedings of SPIE – Earth Resources and Environmental Remote Sensing/GIS Applications V, 9245. International Society for Optical Engineering. https://doi.org/10.1117/12.2066476
Falchi, U. (2017). Spatial data: from cartography to geodatabase. Geodesy and Cartography, 43(4), 142-146. https://doi.org/10.3846/20296991.2017.1412613
Fasshauer, G. E., & Zhang, J. G. (2007). On choosing “optimal” shape parameters for RBF approximation. Numerical Algorithms, 45(1-4), 345-368. https://doi.org/10.1007/s11075-007-9072-8
Featherstone, W. E., Dentith, M. C., & Kirby, J. F. (1998). Strategies for the accurate determination of orthometric heights from GPS. Survey Review, 34(267), 278-296. https://doi.org/10.1179/sre.1998.34.267.278
Fotopoulos, G., Kotsakis, C., & Sideris, M. G. (2003). How accurately can we determine orthometric height differences from GPS and geoid data? Journal of Surveying Engineering, 129(1), 1-10. https://doi.org/10.1061/(ASCE)0733-9453(2003)129:1(1)
Johnston, K., Ver Hoef, J. M., Krivoruchko, K., & Lucas, N. (2001). Using ArcGIS™ geostatistical analyst. Redlands: ESRI.
Kaplan, E., & Hegarty, C. (2005). Understanding GPS: principles and applications (p. 683). Artech house.
Karney, C. (2008). Online geoid calculations using the GeoidEval utility. Retrieved from https://geographiclib.sourceforge.io/cgi-bin/GeoidEval
Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection. Proceedings of IJCAI, 14(2), 1137-1145.
Komarov, R. V., Kascheev, R. A., & Zagretdinov, R. V. (2008). Geoid determination by GPS/leveling method in the Republic of Tatarstan. Georesources, 43(2), 43-45.
Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., & Wang, Y. M. (1998). The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96 (Tech nical Report). Retrieved from https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980218814.pdf
Ligas, M., & Kulczycki, M. (2018). Kriging and moving window kriging on a sphere in geometric (GNSS/levelling) geoid modelling. Survey Review, 50(359), 155-162. https://doi.org/10.1080/00396265.2016.1247131
Maglione, P., Parente, C., Santamaria, R., & Vallario, A. (2014). Modelli tematici 3D della copertura del suolo a partire da DTM e immagini telerilevate ad alta risoluzione WorldView-2. Rendiconti Online della Società Geologica Italiana, 30, 33-40 (in Italian). https://doi.org/10.3301/ROL.2014.08
Maglione, P., Parente, C., & Vallario, A. (2018). Accuracy of global geoid height models in local area: tests on campania region (Italy). International Journal of Civil Engineering and Technology, 9(3), 1049-1057.
Marti, U. (2007). Comparison of high precision Geoid Models in Switzerland. Dynamic Planet, IAG Symposia, 130, 377-382. https://doi.org/10.1007/978-3-540-49350-1_55
NGA/NASA. (n.d.). EGM96, N=M=360 Earth Gravitational Model available online. Retrieved from http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/egm96.html
NGA-Office of Geomatics. (n.d.). NGA/NASA EGM96. Retrieved from http://earth-info.nga.mil/GandG/update/index.php
Oliver, M. A., & Webster, R. (2014). A tutorial guide to Geostatistics: computing and modelling variograms and kriging. Catena, 113, 56-69. https://doi.org/10.1016/j.catena.2013.09.006
Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2008). EGM2008: An overview of its development and evaluation. In IAG International Symposium, GGEO, 2327. National Geospatial-Intelligence Agency, USA.
Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117(B4). https://doi.org/10.1029/2011JB008916
Pepe, M., Prezioso, G., & Santamaria, R. (2015). Impact of vertical deflection on direct georeferencing of airborne images. Survey Review, 47(340), 71-76. https://doi.org/10.1179/1752270614Y.0000000087
Peprah, M. S., Ziggah, Y. Y., & Yakubu, I. (2017). Performance evaluation of the Earth Gravitational Model 2008 (EGM2008) – a case study. South African Journal of Geomatics, 6(1), 47-72. https://doi.org/10.4314/sajg.v6i1.4
Pugh, D. T. (1987). Tides, surges and mean sea-level (p. 486). John Wiley & Sons.
Rapp, R. H., & Wang, Y. M. (1993). Geoid undulation differences between Geopotential models. Surveys in Geophysics, 14(4-5), 373-380. https://doi.org/10.1007/BF00690565
Refaeilzadeh, P., Tang, L., & Liu, H. (2009). Cross-validation. In Encyclopedia of database systems (pp. 532-538). Boston: Springer US.
Shen, W., & Han, J. (2013). Improved geoid determination based on the shallow-layer method: a case study using EGM08 and CRUST2.0 in the Xinjiang and Tibetan Regions. Terrestrial, Atmospheric & Oceanic Sciences, 24(4), 591-604. https://doi.org/10.3319/TAO.2012.11.12.01(TibXS)
Soycan, M. (2013). Analysis of geostatistical surface model for GPS height transformation: a case study in Izmir territory of Turkey. Geodetski Vestnik, 57(4), 702-718. https://doi.org/10.15292/geodetski-vestnik.2013.04.702-718
Soycan, M. E. T. I. N., & Soycan, A. R. Z. U. (2003). Surface modeling for GPS-levelling geoid determination. Newton’s Bulletin, 1, 41-52. Retrieved from http://www.isgeoid.polimi.it/Newton/Newton_1/soycan.pdf
Van der Marel, H. (2014). Reference systems for surveying and mapping. Retrieved from http://gnss1.tudelft.nl/pub/vdmarel/reader/CTB3310_RefSystems_1-2a_print.pdf
Wackernagel, H. (1995). Multivariate Geostatistics: an introduction with applications (p. 307). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-03098-1
Weiss, S. M., & Kulikowski, C. A. (1991). Computer systems that learn: classification and prediction methods from statistics, neural nets, machine learning, and expert systems (p. 223). Morgan Kaufmann.
Xiao, Y., Gu, X., Yin, S., Shao, J., Cui, Y., Zhang, Q., & Niu, Y. (2016). Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, Northwest China. SpringerPlus, 5(1), 425. https://doi.org/10.1186/s40064-016-2073-0