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Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights

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Abstract

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.

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References

  • Andersen OA, Knudsen P, Berry PAM (2010) The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J Geod 84(3): 191–199. doi:10.1007/s00190-009-0355-9

    Article  Google Scholar 

  • Bürki B, Somieski, AE, Sorber P, Kahle HG, Hirt C (2007) The digital astronomical deflection measuring system DIADEM. Swiss National Rep. on the Geodetic Activities in the Years 2003–2007, Presented to the XXIV General Assembly of the IUGG in Perugia, Italy, Swiss Geodetic Commission, pp 143–144

  • Bruinsma SL, Marty JC, Balmino G, Biancale R, Förste C, Abrikosov O, Neumayer H (2010) GOCE Gravity Field Recovery by Means of the Direct Numerical Method. Presented at the ESA Living Planet Symposium 2010, Bergen, June 27–July 2 Bergen, Norway

  • Drinkwater MR, Floberghagen R, Haagmans R, Muzi D, Popescu A (2003) GOCE: ESA’s first Earth Explorer Core mission. In: Beutler GB, Drinkwater MR, Rummel R, von Steiger R (eds) Earth gravity field from space—from sensors to earth sciences. In the Space Sciences Series of ISSI, vol 18, Kluwer Academic Publishers, Dordrecht, pp 419–432. ISBN: 1-4020-1408-2/

  • EGM Development Team (2009) Description of files containing propagated error estimates from EGM2008 on global 5′ × 5′ Grids, US National Geospatial Intelligence Agency (NGA). Available at: http://earth-info.nga.mil/GandG/wgs84/gravitymod/

  • Featherstone WE (2007) Augmentation of AUSGeoid98 with GRACE satellite gravity data. J Spatial Sci 52(2): 75–86

    Article  Google Scholar 

  • Featherstone WE, Morgan L (2007) Validation of the AUSGeoid98 model in Western Australia using historic astrogeodetically observed deviations of the vertical. J R Soc West Aust 90(3): 143–149

    Google Scholar 

  • Featherstone WE, Lichti DD (2009) Fitting gravimetric geoid models to vertical deflections. J Geod 83(6): 583–589. doi:10.1007/s00190-008-0263-4

    Article  Google Scholar 

  • Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown NJ, Hu H, Johnston GM (2011) The AUSGeoid09 model of the Australian height datum. J Geod 85(3): 133–150. doi:10.1007/s00190-010-0422-2

    Article  Google Scholar 

  • Forsberg R, Tscherning CC (1981) The use of height data in gravity field approximation by collocation. J Geophys Res 86(B9): 7843–7854

    Article  Google Scholar 

  • Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Report 355, Department of Geodetic Science and Surveying, Ohio State University, Columbus

  • GOCO Consortium (2010) The satellite-only global gravity field model GOCO01S derived from GOCE and GRACE. http://inas.tugraz.at/GOCO/ and http://icgem.gfz-potsdam.de/ICGEM/ICGEM.html

  • Gruber T (2004) Validation concepts for gravity field models from satellite missions. In: Lacoste H (ed) Proceedings of the 2nd International GOCE User Workshop “GOCE, The Geoid and Oceanography”, ESA SP-569, ESA

  • Gruber T (2008) The GOCE gravity field space mission as an important step for the exploration of our planet. In: Proceedings of INCOSE2008—Systems Engineering for the Planet, International Council of System Engineering (INCOSE), pp 14

  • Gruber T (2009) Evaluation of the EGM2008 gravity field by means of GPS-levelling and sea surface topography solutions. External quality evaluation reports of EGM08, Newton’s Bulletin. Bureau Gravimétrique International (BGI)/International Geoid Service (IGeS) 4: 3–17

    Google Scholar 

  • 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 (submitted)

  • Hirt C, Flury J (2008) Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. J Geod 82(4–5): 231–248. doi:10.1007/s00190-007-0173

    Article  Google Scholar 

  • Hirt C, Seeber G (2008) Accuracy analysis of vertical deflection data observed with the Hannover Digital Zenith Camera System TZK2-D. J Geod 82(6): 347–356. doi:10.1007/s00190-007-0184-7

    Article  Google Scholar 

  • Hirt C (2010) Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data. J Geod 84(3): 179–190. doi:10.1007/s00190-009-0354-x

    Article  Google Scholar 

  • Hirt C, Marti U, Bürki B, Featherstone WE (2010a) Assessment of EGM2008 in Europe using accurate astrogeodetic vertical deflections and omission error estimates from SRTM/DTM2006.0 residual terrain model data. J Geophys Res Solid Earth 115: B10404. doi:10.1029/2009JB007057

    Article  Google Scholar 

  • Hirt C, Featherstone WE, Marti U (2010b) 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

    Article  Google Scholar 

  • Hirt C, Bürki B, Somieski A, Seeber G (2010c) Modern determination of vertical deflections using digital zenith cameras. J Surv Eng 136(1): 1–12. doi:10.1061/_ASCE_SU.1943-5428.0000009

    Article  Google Scholar 

  • Holmes SA, Pavlis NK (2008) Spherical harmonic synthesis software harmonic_synth. http://earth-info.nga.mil/GandG/wgs84/gravitymod/new_egm/new_egm.html

  • Ihde J, Wilmes H, Müller J, Denker H, Voigt C, Hosse M (2010) Validation of satellite gravity field models by regional terrestrial data sets. In: System Earth via geodetic-geophysical space techniques advanced technologies in Earth sciences, Part 3, pp 277–296

  • Jarvis A, Reuter HI, Nelson A, Guevara E (2008) Hole-filled SRTM for the globe Version 4, Available from the CGIAR-SXI SRTM 90m database: http://srtm.csi.cgiar.org

  • Jekeli C (1999) An analysis of vertical deflections derived from high-degree spherical harmonic models. J Geod 73(1): 10–22. doi:10.1007/s001900050213

    Article  Google Scholar 

  • Kaula WM (1966) Theory of satellite geodesy. Blaisdel, Waltham

    Google Scholar 

  • Marti U (2004) High-precision combined geoid determination in Switzerland. Presented at gravity, geoid and space missions (GGSM) 2004 Symposium, Porto, Aug 30–Sep 03 2004, Porto, Portugal

  • Mayer-Gürr T (2007) ITG-Grace03s: the latest GRACE gravity field solution computed in Bonn. Joint Int. GSTM and SPP Symposium, 15–17 Oct. 2007, Potsdam, Germany. http://www.geod.uni-bonn.de/itg-grace03.html

  • Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010

  • Metzler B, Pail R (2005) GOCE data processing: the spherical cap regularization approach. Stud Geophys Geod 49: 441–462. doi:10.1007/s11200-005-0021-5

    Article  Google Scholar 

  • Migliaccio F, Reguzzoni M, Sanso F, Tscherning CC, Veicherts M (2010) GOCE data analysis: the space-wise approach and the first space-wise gravity field model. Presented at the ESA Living Planet Symposium 2010, Bergen, June 27–July 2, Bergen, Norway

  • Murray AS (1997) The Australian national gravity database. AGSO J Aust Geol Geophys 17: 145–155

    Google Scholar 

  • Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geod 74(7–8):552–560. doi:10.1007/s001900000116. Erratum in J Geod 76(8):475. doi:10.1007/s00190-002-0264-7

    Google Scholar 

  • Newton’s Bulletin (2009) External quality evaluation reports of EGM08. Issue 4, Bureau Gravimétrique International (BGI)/ International Geoid Service (IGeS)

  • Pail R, Goiginger H, Schuh WD, Höck E, Brockmann JM, Fecher T, Gruber T, Mayer-Gürr T, Kusche J, Jäggi A, Rieser D (2010a) Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys Res Lett 37: L20314. doi:10.1029/2010GL044906

    Article  Google Scholar 

  • Pail R, Goiginger H, Mayrhofer R, Schuh W-D, Brockmann JM, Krasbutter I, Höck E, Fecher T (2010b) Global gravity field model derived from orbit and gradiometry data applying the time-wise method. Presented at the ESA Living Planet Symposium 2010, Bergen, June 27–July 2, Bergen, Norway

  • Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh W-D, 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 (submitted)

  • Pavlis NK, Saleh J et al (2004) Error propagation with geographic specifity for very high degree geopotential models. In: Jekeli C (eds) Proceedings of GGSM 2004 IAG International Symposium Porto, Portugal. Springer, Heidelberg, pp 149–154

    Google Scholar 

  • Pavlis NK, Factor JK, Holmes SA (2007) Terrain-related gravimetric quantities computed for the next EGM. In: Proceedings of the 1st International Symposium of the International Gravity Field Service (IGFS), Istanbul, pp 318–323

  • Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2160: EGM2008. Presented at the 2008 General Assembly of the European Geoscience Union, Vienna, Austria, April 13–18, 2008

  • Reigber C, Balmino G, Schwintzer P, Biancale R, Bode A, Lemoine JM, König R, Loyer S, Neumayer H, Marty JC, Barthelmes F, Perosanz F, Zhu SY (2002) A high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophys Res Lett 29(14). doi:10.1029/2002GL015064

  • Reigber C, Schmidt R, Flechtner F, König R, Meyer U, Neumayer KH, Schwintzer P, Zhu SY (2005) An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J Geodyn 39(1): 1–10

    Article  Google Scholar 

  • Rummel R, Balmino G, Johannessen J, Visser P, Woodworth P (2002) Dedicated gravity field missions—principles and aims. J Geodyn 33(1–2): 3–20

    Article  Google Scholar 

  • Rummel R, Gruber T, Koop R (2004) High level processing facility for GOCE: products and processing strategy. In: Lacoste H (ed) Proceedings of the 2nd International GOCE User Workshop. GOCE, The Geoid and Oceanography, ESA SP-569

  • Rummel R (2005) Geoid and gravity in earth sciences—an overview. Workshop on Enabling Observation Techniques for Future Solid Earth Missions, Jan 30–Feb 01, 2003, Int Space Sci Inst Bern Switzerland, Earth Moon and Planets 94(1–2): 3–11

    Google Scholar 

  • Rummel R, Gruber T, Flury J, Schlicht A (2009) ESA’s gravity field and steady-state ocean circulation explorer GOCE. Zeitschrift für Vermessungswesen 3: 125–130

    Google Scholar 

  • Schwarz KP (1985) Data types and their spectral properties. UCSE Report Nr. 60003. Division of Surveying Engineering, University of Calgary, Calgary, Alberta, Canada

  • Tapley B, Ries J, Bettadpur S, Chambers D, Cheng M, Condi F, Gunter B, Kang Z, Nagel P, Pastor R, Pekker T, Poole S, Wang F (2005) GGM02—an improved Earth gravity field model from GRACE. J Geod 79(8): 467–478. doi:10.1007/s00190-005-0480-z

    Article  Google Scholar 

  • Tapley B, Ries J, Bettadpur S, Chambers D, Cheng M, Condi F, Poole S (2007) The GGM03 mean Earth gravity model from GRACE. Eos Trans. AGU 88(52), Fall Meeting of American Geophysical Union 2007, Abstract G42A-03

  • Torge W (2001) Geodesy, 3rd edn. de Gruyter, New York

    Book  Google Scholar 

  • Visser PNAM, Rummel R, Balmino G, Sünkel H, Johannessen J, Aguirre M, Woodworth PL, Le Provest C, Tscherning CC, Sabadini R (2002) The European Earth explorer mission GOCE: impact for the geosciences. Ice Sheets, Sea Level and the Dynamic Earth 29: 95–107

    Article  Google Scholar 

  • Voigt C, Denker H, Hirt C (2009) Regional astrogeodetic validation of GPS/levelling data and quasigeoid models. In: Sideris MG (eds) Observing our changing Earth. Springer, New York, pp 413–420

    Google Scholar 

  • Wessel P, Smith WHF (1998) New, improved version of the generic mapping tools released. EOS Trans AGU 79: 579

    Article  Google Scholar 

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Hirt, C., Gruber, T. & Featherstone, W.E. Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights. J Geod 85, 723–740 (2011). https://doi.org/10.1007/s00190-011-0482-y

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