Surveys in Geophysics

, Volume 38, Issue 2, pp 443–477 | Cite as

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

Article

Abstract

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.

Keywords

Height system unification GOCE Gravity forward modeling Rock–Water–Ice (RWI) approach Tesseroids 

References

  1. Amjadiparvar B, Rangelova E, Sideris MG (2016) The GBVP approach for vertical datum unification: recent results in North America. J Geod 90(1):45–63. doi:10.1007/s00190-015-0855-8 CrossRefGoogle Scholar
  2. Amjadiparvar B, Rangelova E, Sideris MG, Véronneau M (2013) North American height datums and their offsets: the effect of GOCE omission errors and systematic levelling effects. J Appl Geod 7(1):39–50. doi:10.1515/jag-2012-0034 Google Scholar
  3. Barzaghi R, Carrion D, Reguzzoni M, Venuti G (2016) A feasibility study on the unification of the Italian height systems using GNSS-Leveling data and global satellite gravity models. In: Rizos C, Willis P (eds) IAG 150 years, International Association of Geodesy Symposia, vol 143. Springer, Berlin, pp 281–288. doi:10.1007/1345_2015_35 Google Scholar
  4. Blackman RB, Tukey JW (1958) The measurement of power spectra from the point of view of communications engineering - Part I. Bell Syst Tech J 37(1):185–282. doi:10.1002/j.1538-7305.1958.tb03874.x CrossRefGoogle Scholar
  5. Blewitt G, Altamimi Z, Davis J, Gross R, Kuo CY, Lemoine FG, Moore AW, Neilan RE, Plag HP, Rothacher M, Shum CK, Sideris MG, Schöne T, Tregoning P, Zerbini S (2010) Geodetic observations and global reference frame contributions to understanding sea-level rise and variability. In: Church JA, Woodworth PL, Aarup T, Wilson WS (eds) Understanding sea-level rise and variability. Wiley, Hoboken, pp 256–284. doi:10.1002/9781444323276.ch9 CrossRefGoogle Scholar
  6. Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh WD (2014) EGM_TIM_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett 41(22):8089–8099. doi:10.1002/2014GL061904 CrossRefGoogle Scholar
  7. Bruinsma SL, Förste C, Abrikosov O, Lemoine JM, Marty JC, Mulet S, Rio MH, Bonvalot S (2014) ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys Res Lett 41(21):7508–7514. doi:10.1002/2014GL062045 CrossRefGoogle Scholar
  8. Colombo OL (1980) A world vertical network. Report 296, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, USAGoogle Scholar
  9. Ekman M (1989) Impacts of geodynamic phenomena on systems for height and gravity. Bull Géod 63(3):281–296. doi:10.1007/BF02520477 CrossRefGoogle Scholar
  10. ESA (1999) The four candidate Earth explorer core missions – Gravity field and steady-state ocean circulation. In: Battrick B (ed) Reports for mission selection, ESA Special Publication, vol 1233(1). ESA Publications Division, ESTEC, Noordwijk, The NetherlandsGoogle Scholar
  11. Ferreira VG, de Freitas SRC (2011) Geopotential numbers from GPS satellite surveying and disturbing potential model: a case study of Parana. Brazil. J Appl Geod 5(3–4):155–162. doi:10.1515/JAG.2011.016 Google Scholar
  12. Ferreira VG, de Freitas SRC, Heck B (2016) Analysis of the discrepancy between the Brazilian vertical reference frame and GOCE-based geopotential models. In: Rizos C, Willis P (eds) IAG 150 years, International Association of Geodesy Symposia, vol 143. Springer, Berlin, pp 227–232. doi:10.1007/1345_2015_20 Google Scholar
  13. Forsberg R, Tscherning CC (1997) Topographic effects in gravity field modelling for BVP. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, Lecture Notes in Earth Sciences, vol 65. Springer, Berlin, pp 239–272. doi:10.1007/BFb0011707 CrossRefGoogle Scholar
  14. Gatti A, Reguzzoni M, Venuti G (2013) The height datum problem and the role of satellite gravity models. J Geod 87(1):15–22. doi:10.1007/s00190-012-0574-3 CrossRefGoogle Scholar
  15. Gerlach C, Fecher T (2012) Approximations of the GOCE error variance-covariance matrix for least-squares estimation of height datum offsets. J Geod Sci 2(4):247–256. doi:10.2478/v10156-011-0049-0 Google Scholar
  16. Gerlach C, Rummel R (2013) Global height system unification with GOCE: a simulation study on the indirect bias term in the GBVP approach. J Geod 87(1):57–67. doi:10.1007/s00190-012-0579-y CrossRefGoogle Scholar
  17. Gomez ME, Pereira RAD, Ferreira VG, Cogliano DD, Luz RT, de Freitas SRC, Farias C, Perdomo R, Tocho C, Lauria E, Cimbaro S (2016) Analysis of the discrepancies between the vertical reference frames of Argentina and Brazil. In: Rizos C, Willis P (eds) IAG 150 years, International Association of Geodesy Symposia, vol 143. Springer, Berlin, pp 289–295. doi:10.1007/1345_2015_75 Google Scholar
  18. Grombein T, Luo X, Seitz K, Heck B (2014) A wavelet-based assessment of topographic-isostatic reductions for GOCE gravity gradients. Surv Geophys 35(4):959–982. doi:10.1007/s10712-014-9283-1 CrossRefGoogle Scholar
  19. Grombein T, Seitz K, Heck B (2013) Optimized formulas for the gravitational field of a tesseroid. J Geod 87(7):645–660. doi:10.1007/s00190-013-0636-1 CrossRefGoogle Scholar
  20. Grombein T, Seitz K, Heck B (2016a) The Rock-Water-Ice topographic gravity field model RWI_TOPO_2015 and its comparison to a conventional rock-equivalent version. Surv Geophys 37(5):937–976. doi:10.1007/s10712-016-9376-0 CrossRefGoogle Scholar
  21. Grombein T, Seitz K, Heck B (2016b) Height system unification based on the fixed GBVP approach. In: Rizos C, Willis P (eds) IAG 150 years, International Association of Geodesy Symposia, vol 143. Springer, Berlin, pp 305–311. doi:10.1007/1345_2015_104 Google Scholar
  22. Gruber T, Gerlach C, Haagmans R (2012) Intercontinental height datum connection with GOCE and GPS-levelling data. J Geod Sci 2(4):270–280. doi:10.2478/v10156-012-0001-y Google Scholar
  23. Gruber T, Visser PNAM, Ackermann C, Hosse M (2011) Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons. J Geod 85(11):845–860. doi:10.1007/s00190-011-0486-7 CrossRefGoogle Scholar
  24. Haagmans RHN, van Gelderen M (1991) Error variances-covariances of GEM-T1: their characteristics and implications in geoid computation. J Geophys Res 96(B12):20011–20022. doi:10.1029/91JB01971 CrossRefGoogle Scholar
  25. Heck B (1981) Der Einfluß einzelner Beobachtungen auf das Ergebnis einer Ausgleichung und die Suche nach Ausreißern in den Beobachtungen. Allg Vermes Nachr 88(1981):17–34Google Scholar
  26. Heck B (1990) An evaluation of some systematic error sources affecting terrestrial gravity anomalies. Bull Géod 64(1):88–108. doi:10.1007/BF02530617 CrossRefGoogle Scholar
  27. Heck B (2004) Problems in the definition of vertical reference frames. In: Sansò F (ed) V Hotine-Marussi symposium on mathematical geodesy, International Association of Geodesy Symposia, vol 127. Springer, Berlin, pp 164–173. doi:10.1007/978-3-662-10735-5_22 CrossRefGoogle Scholar
  28. Heck B, Rummel R (1990) Strategies for solving the vertical datum problem using terrestrial and satellite geodetic data. In: Sünkel H, Baker T (eds) Sea surface topography and the geoid, International Association of Geodesy Symposia, vol 104. Springer, Berlin, pp 116–128. doi:10.1007/978-1-4684-7098-7_14 CrossRefGoogle Scholar
  29. Heck B, Seitz K (2007) A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling. J Geod 81(2):121–136. doi:10.1007/s00190-006-0094-0 CrossRefGoogle Scholar
  30. Heiskanen WA, Moritz H (1967) Physical geodesy. W. H Freeman & Co, San Francisco, USAGoogle Scholar
  31. Hirt C (2013) RTM gravity forward-modeling using topography/bathymetry data to improve high-degree global geopotential models in the coastal zone. Mar Geod 36(2):183–202. doi:10.1080/01490419.2013.779334 CrossRefGoogle Scholar
  32. Hirt C, Featherstone WE, Marti U (2010) Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data. J Geod 84(9):557–567. doi:10.1007/s00190-010-0395-1 CrossRefGoogle Scholar
  33. Hirt C, Kuhn M (2014) Band-limited topographic mass distribution generates full-spectrum gravity field: gravity forward modeling in the spectral and spatial domains revisited. J Geophys Res 119(4):3646–3661. doi:10.1002/2013JB010900 CrossRefGoogle Scholar
  34. Hirt C, Rexer M (2015) Earth 2014: 1 arc-min shape, topography, bedrock and ice-sheet models - available as gridded data and degree-10,800 spherical harmonics. Int J Appl Earth Obs Geoinform 39:103–112. doi:10.1016/j.jag.2015.03.001, http://ddfe.curtin.edu.au/models/Earth2014
  35. Höggerl N (1986) Die Ausgleichung des österreichischen Präzisionsnivellementnetzes. Österreichische Z Vermess und Photogramm 74(4):216–249Google Scholar
  36. Höggerl N, Ruess D (2004) The new orthometric height system in Austria. In: Proceedings of the EUREF 2003 Symposium, no. 13 in EUREF Publication, Mitteilungen des Bundesamtes für Kartographie und Geodäsie, vol. 33, pp 202–206Google Scholar
  37. Holmes SA, Pavlis NK (2006) Spherical harmonic synthesis software harmonic_synth_v02.f. http://earth-info.nga.mil/GandG/wgs84/gravitymod/new_egm/new_egm.html
  38. Huang J, Véronneau M (2013) Canadian gravimetric geoid model 2010. J Geod 87(8):771–790. doi:10.1007/s00190-013-0645-0 CrossRefGoogle Scholar
  39. IAG Resolutions (2015) IAG resolution (No. 1) for the definition and realization of an International Height Reference System (IHRS). International Association of Geodesy, http://iag.dgfi.tum.de/fileadmin/IAG-docs/IAG_Resolutions_2015
  40. IERS Conventions (2010) In: Petit G, Luzum B (eds) IERS Technical Note, no. 36, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, GermanyGoogle Scholar
  41. Ihde J (1995) Geoid determination by GPS and levelling. In: Sünkel H, Marson I (eds) Gravity and geoid, International Association of Geodesy Symposia, vol 113. Springer, Berlin, pp 519–528. doi:10.1007/978-3-642-79721-7_55 Google Scholar
  42. Ihde J, Sánchez L (2005) A unified global height reference system as a basis for IGGOS. J Geodyn 40(4–5):400–413. doi:10.1016/j.jog.2005.06.015 CrossRefGoogle Scholar
  43. Klokočník J, Wagner CA, Kostelecký J, Bezděk A, Novák P, McAdoo D (2008) Variations in the accuracy of gravity recovery due to ground track variability: GRACE, CHAMP, and GOCE. J Geod 82(12):917–927. doi:10.1007/s00190-008-0222-0 CrossRefGoogle Scholar
  44. Kotsakis C, Katsambalos K, Ampatzidis D (2012) Estimation of the zero-height geopotential level \(W_0^\text{ LVD }\) in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands. J Geod 86(6):423–439. doi:10.1007/s00190-011-0530-7 CrossRefGoogle Scholar
  45. Kutterer H, Neilan R (2016) Global geodetic observing system (GGOS). The Geodesists Handbook 2016. J Geod 90(10):1079–1094. doi:10.1007/s00190-016-0948-z Google Scholar
  46. Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. Technical report 1998-206861, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. http://ntrs.nasa.gov/search.jsp?R=19980218814
  47. Luz RT, Bosch W, de Freitas SRC, Heck B, Dalazoana R (2009a) Evaluating the Brazilian vertical datum through improved coastal satellite altimetry data. In: Sideris MG (ed) Observing our changing Earth, International Association of Geodesy Symposia, vol 133. Springer, Berlin, pp 735–741. doi:10.1007/978-3-540-85426-5_84 CrossRefGoogle Scholar
  48. Luz RT, de Freitas SRC, Heck B, Bosch W (2009b) Challenges and first results towards the realization of a consistent height system in Brazil. In: Drewes H (ed) Geodetic reference frames, International Association of Geodesy Symposia, vol 134. Springer, Berlin, pp 291–296. doi:10.1007/978-3-642-00860-3_45 CrossRefGoogle Scholar
  49. Luz RT, Guimarães VM, Rodrigues AC, Correia JD (2002) Brazilian first order levelling network. In: Drewes H, Dodson AH, Fortes LPS, Sánchez L, Sandoval P (eds) Vertical reference systems, International Association of Geodesy Symposia, vol 124. Springer, Berlin, pp 20–22. doi:10.1007/978-3-662-04683-8_5 Google Scholar
  50. Mäkinen J, Ihde J (2009) The permanent tide in height systems. In: Sideris MG (ed) Observing our changing Earth, International Association of Geodesy Symposia, vol 133. Springer, Berlin, pp 81–87. doi:10.1007/978-3-540-85426-5_10 CrossRefGoogle Scholar
  51. Mayer-Gürr T, Zehentner N, Klinger B, Kvas A (2014) ITSG-Grace2014: a new GRACE gravity field release computed in Graz. https://pure.tugraz.at/portal/files/3412370/2014-09-30_mayer-guerr_etal_ITG-Grace2014_GSTM_Potsdam
  52. Mayer-Gürr T, Pail R, Gruber T, Fecher T, Rexer M, Schuh WD, Kusche J, Brockmann JM, Rieser D, Zehentner N, Kvas A, Klinger B, O B, Höck E, Krauss S, Jäggi A (2015) The combined satellite gravity field model GOCO05s. Geophysical Research Abstracts, vol 17, EGU2015-12364Google Scholar
  53. Montecino HD, de Freitas SRC (2014) Strategies for connecting Imbituba and Santana Brazilian datums based on satellite gravimetry and residual terrain model. In: Rizos C, Willis P (eds) Earth on the edge: science for a sustainable planet, International Association of Geodesy Symposia, vol 139. Springer, Berlin, pp 543–549. doi:10.1007/978-3-642-37222-3_72 CrossRefGoogle Scholar
  54. Moritz H (1980) Geodetic reference system 1980. Bull Géod 54(3):395–405. doi:10.1007/BF02521480 CrossRefGoogle Scholar
  55. Pail R, Bruinsma SL, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geod 85(11):819–843. doi:10.1007/s00190-011-0467-x CrossRefGoogle Scholar
  56. Pail R, Goiginger H, Schuh WD, Höck E, Brockmann JM, Fecher T, Gruber T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D (2010) Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett 37(20):L20314. doi:10.1029/2010GL044906 CrossRefGoogle Scholar
  57. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008. J Geophys Res 117:B04406. doi:10.1029/2011JB008916 CrossRefGoogle Scholar
  58. Rapp RH (1983) The need and prospects for a world vertical datum. In: Proceedings of the 18th IAG General Assembly, International Association of Geodesy Symposia, vol 2, pp 432–445Google Scholar
  59. Rapp RH, Nerem RS, Shum C, Klosko SM, Williamson RG (1991) Consideration of permanent tidal deformation in the orbit determination and data analysis for the Topex/Poseidon mission. Technical report NASA-TM-100775, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. http://ntrs.nasa.gov/search.jsp?R=19910021305
  60. Ruess D, Mitterschiffthaler P (2015) Rezente Höhenänderungen in Österreich abgeleitet aus geodätischen Wiederholungsmessungen. In: Hanke K, Weinold T (eds) 19. Internationale Woche. Wichmann-Verlag, Heidelberg, pp 111–123Google Scholar
  61. Rülke A, Liebsch G, Sacher M, Schäfer U, Schirmer U, Ihde J (2012) Unification of European height system realizations. J Geod Sci 2(4):343–354. doi:10.2478/v10156-011-0048-1 Google Scholar
  62. Rülke A, Liebsch G, Sacher M, Schäfer U, Ihde J, Woodworth PL (2016) Practical aspects of the unification of height system realizations in Europe. In: Rizos C, Willis P (eds) IAG 150 years, International Association of Geodesy Symposia, vol 143. Springer, Berlin, pp 367–373. doi:10.1007/1345_2015_168 Google Scholar
  63. Rummel R (2002) Global unification of height systems and GOCE. In: Sideris MG (ed) Gravity, geoid and geodynamics 2000, International Association of Geodesy Symposia, vol 123. Springer, Berlin, pp 13–20. doi:10.1007/978-3-662-04827-6_3 CrossRefGoogle Scholar
  64. Rummel R, Teunissen P (1988) Height datum definition, height datum connection and the role of the geodetic boundary value problem. Bull Géod 62(4):477–498. doi:10.1007/BF02520239 CrossRefGoogle Scholar
  65. Rummel R, Yi W, Stummer C (2011) GOCE gravitational gradiometry. J Geod 85(11):777–790. doi:10.1007/s00190-011-0500-0 CrossRefGoogle Scholar
  66. Sacher M, Ihde J, Liebsch G, Mäkinen J (2009) EVRF2007 as realization of the European vertical reference system. Bollett di Geod Sci Affin 68(1):35–50Google Scholar
  67. Sánchez L (2009) Strategy to establish a global vertical reference system. In: Drewes H (ed) Geodetic reference frames, International Association of Geodesy Symposia, vol 134. Springer, Berlin, pp 273–278. doi:10.1007/978-3-642-00860-3_42 CrossRefGoogle Scholar
  68. Sánchez L (2015) Ein einheitliches vertikales Referenzsystem für Südamerika im Rahmen eines globalen Höhensystems. Deutsche Geodätische Kommission, Reihe C, no. 748. Verlag der Bayerischen Akademie der Wissenschaften in Kommission beim Verlag C. H. Beck. http://www.dgk.badw.de.devweb.mwn.de/fileadmin/docs/c-748.pdf
  69. Sansò F, Venuti G (2002) The height datum/geodetic datum problem. Geophys J Int 149(3):768–775. doi:10.1046/j.1365-246X.2002.01680.x Google Scholar
  70. Sjöberg L (2011) On the definition and realization of a global vertical datum. J Geod Sci 1(2):154–157. doi:10.2478/v10156-010-0018-z Google Scholar
  71. Šprlák M, Gerlach C, Pettersen BR (2015) Validation of GOCE global gravitational field models in Norway. In: Huang J, Reguzzoni M, Gruber T (eds) Assessment of GOCE geopotential models, Newton’s Bulletin, no. 5. International Association of Geodesy and International Gravity Field Service, pp 13–24. http://www.isgeoid.polimi.it/Newton/Newton_5/03_Sprlak_13_24.html
  72. Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins MM (2004) GRACE measurements of mass variability in the Earth system. Science 305(5683):503–505. doi:10.1126/science.1099192 CrossRefGoogle Scholar
  73. Voigt C, Denker H (2015) Validation of GOCE gravity field models in Germany. In: Huang J, Reguzzoni M, Gruber T (eds) Assessment of GOCE geopotential models, Newton’s Bulletin, no. 5. International Association of Geodesy and International Gravity Field Service, pp 37–48. http://www.isgeoid.polimi.it/Newton/Newton_5/05_Voigt_37_48.html
  74. Weber D (1994) Das neue gesamtdeutsche Haupthöhennetz DHHN 92. Allg Vermess Nachr 101(5):179–193Google Scholar
  75. Wolf H (1974) Über die Einführung von Normalhöhen. Z Vermess 99:1–5Google Scholar
  76. Woodworth PL, Hughes CW, Bingham RJ, Gruber T (2012) Towards worldwide height system unification using ocean information. J Geod Sci 2(4):302–318. doi:10.2478/v10156-012-0004-8 Google Scholar
  77. Xu P (1992) A quality investigation of global vertical datum connection. Geophys J Int 110(2):361–370. doi:10.1111/j.1365-246X.1992.tb00880.x CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Geodetic InstituteKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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