Journal of Geodesy

, Volume 90, Issue 2, pp 105–127 | Cite as

A new degree-2190 (10 km resolution) gravity field model for Antarctica developed from GRACE, GOCE and Bedmap2 data

  • Christian HirtEmail author
  • Moritz Rexer
  • Mirko Scheinert
  • Roland Pail
  • Sten Claessens
  • Simon Holmes
Original Article


The current high-degree global geopotential models EGM2008 and EIGEN-6C4 resolve gravity field structures to \(\sim \)10 km spatial scales over most parts of the of Earth’s surface. However, a notable exception is continental Antarctica, where the gravity information in these and other recent models is based on satellite gravimetry observations only, and thus limited to about \(\sim \)80–120 km spatial scales. Here, we present a new degree-2190 global gravity model (GGM) that for the first time improves the spatial resolution of the gravity field over the whole of continental Antarctica to \(\sim \)10 km spatial scales. The new model called SatGravRET2014 is a combination of recent Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite gravimetry with gravitational signals derived from the 2013 Bedmap2 topography/ice thickness/bedrock model with gravity forward modelling in ellipsoidal approximation. Bedmap2 is a significantly improved description of the topographic mass distribution over the Antarctic region based on a multitude of topographic surveys, and a well-suited source for modelling short-scale gravity signals as we show in our study. We describe the development of SatGravRET2014 which entirely relies on spherical harmonic modelling techniques. Details are provided on the least-squares combination procedures and on the conversion of topography to implied gravitational potential. The main outcome of our work is the SatGravRET2014 spherical harmonic series expansion to degree 2190, and derived high-resolution grids of 3D-synthesized gravity and quasigeoid effects over the whole of Antarctica. For validation, six data sets from the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) database were used comprising a total of 1,092,981 airborne gravimetric observations. All subsets consistently show that the Bedmap2-based short-scale gravity modelling improves the agreement over satellite-only data considerably (improvement rates ranging between 9 and 75 % with standard deviations from residuals between SatGravRET2014 and AntGG gravity ranging between 8 and 25 mGal). For comparison purposes, a degree-2190 GGM was generated based on the year-2001 Bedmap1 (using the ETOPO1 topography) instead of 2013 Bedmap2 topography product. Comparison of both GGMs against AntGG consistently reveals a closer fit over all test areas when Bedmap2 is used. This experiment provides evidence for clear improvements in Bedmap2 topographic information over Bedmap1 at spatial scales of \(\sim \)80–10 km, obtained from independent gravity data used as validation tool. As a general conclusion, our modelling effort fills—in approximation—some gaps in short-scale gravity knowledge over Antarctica and demonstrates the value of the Bedmap2 topography data for short-scale gravity refinement in GGMs. SatGravRET2014 can be used, e.g. as a reference model for future gravity modelling efforts over Antarctica, e.g. as foundation for a combination with the AntGG data set to obtain further improved gravity information.


GRACE GOCE Geopotential model Gravity Topography Bedmap2 Forward gravity modelling Antarctica 



We thank three anonymous reviewers for their comments on this manuscript. This study received support from the Australian Research Council (ARC, grant DP120102441) and Curtin University’s Office of Research and Development. Further, it was created with the support of the Technische Universität München—Institute for Advanced Study, funded by the German Excellence Initiative. Christian Hirt is the recipient of an ARC Discovery Outstanding Researcher Award and of a Hans-Fischer Fellowship by IAS. Parts of the computations were carried out with resources provided by the Leibniz Rechenzentrum München. We thank Jan-Martin Brockmann for providing GOCE data sets and Thomas Fecher for providing routines for solving of normal equations. The topographic potential model dV_ELL_RET2014 and combined SatGravRET2014 model will be delivered to IAG’s ICGEM service ( Our models are also available via The topographic input data sets used in this study can be downloaded from


  1. Amante C, Eakins BW (2009) ETOPO1 1 arc-minute global relief model: procedures, data sources and analysis. In: NOAA Technical Memorandum NESDIS NGDC-24, p 19Google Scholar
  2. Balmino G, Vales N, Bonvalot S, Briais A (2012) Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. J Geod 86(7):499–520. doi: 10.1007/s00190-011-0533-4 CrossRefGoogle Scholar
  3. Bamber JL, Griggs JA, Hurkmans RT et al (2013) A new bed elevation data set for Greenland. Cryosphere 7:499–510CrossRefGoogle Scholar
  4. Becker JJ, Sandwell DT, Smith WHF et al (2009) Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Mar Geod 32(4):355–371CrossRefGoogle Scholar
  5. Bell RE, Childers VA, Arko RA, Blankenship DD, Brozena JM (1999) Airborne gravity and precise positioning for geologic applications. J Geophys Res 104(B7):15281–15292. doi: 10.1029/1999JB900122 CrossRefGoogle Scholar
  6. Bonvalot S, Balmino G, Briais A, Kuhn M, Peyrefitte A, Vales N (2012) World Gravity Map, 1:50,000,000 map, Eds. BGI-CGMW-CNES-IRD. ParisGoogle Scholar
  7. Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh W-D (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
  8. Bucha B, Janák J (2014) A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders: efficient computation at irregular surfaces. Comput Geosci 66:219–227. doi: 10.1016/j.cageo.2014.02.005 CrossRefGoogle Scholar
  9. Claessens SJ (2006) Solutions to ellipsoidal boundary value problems for gravity field modelling. PhD thesis, Curtin University of Technology, Perth, Western AustraliaGoogle Scholar
  10. Claessens SJ (2005) New relations among associated Legendre functions and spherical harmonics. J Geod 79(6–7):398–406. doi: 10.1007/s00190-005-0483-9 CrossRefGoogle Scholar
  11. Claessens SJ, Hirt C (2013) Ellipsoidal topographic potential—new solutions for spectral forward gravity modelling of topography with respect to a reference ellipsoid. J Geophys Res Solid Earth 118(15):5991–6002. doi: 10.1002/2013JB010457 CrossRefGoogle Scholar
  12. Davis M (2001) Subglacial morphology and structural geology in the Southern Transantarctic Mountains from airborne geophysics. M.S. Thesis, University of Texas, p 133Google Scholar
  13. Diehl T, Holt J, Blankenship D, Young D, Jordan T, Ferraccioli F (2008) First airborne gravity results over the Thwaites Glacier catchment, West Antarctica. Geochem Geophys Geosyst 9(4):Q04011. doi: 10.1029/2007GC001878 CrossRefGoogle Scholar
  14. Fecher T, Pail R, Gruber T (2015) Global gravity field modeling based on GOCE and complementary gravity data. Int J Appl Earth Obs Geoinformation 35:120–127. doi: 10.1016/j.jag.2013.10.005 CrossRefGoogle Scholar
  15. Flury J, Rummel R (2005) Future satellite gravimetry for geodesy. Earth Moon Planets 94:13–29. doi: 10.1007/s11038-005-3756-7 CrossRefGoogle Scholar
  16. Forsberg R (1984a) Local covariance functions and density distribution. OSU Report 356, Department of Geodetic Science and Surveying, Ohio State University, ColumbusGoogle Scholar
  17. Forsberg R (1984b) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. OSU Report 355. Department of Geodetic Science and Surveying, Ohio State University, ColumbusGoogle Scholar
  18. Forsberg R, Olesen AV, Yildiz H, Tscherning CC (2011) Polar gravity fields from GOCE and airborne gravity. In: Proc of 4th international GOCE user workshop, ESA SP-696. MunichGoogle Scholar
  19. Förste C, Bruinsma SL, Abrikosov O, Lemoine J-M, Schaller T, Götze H-J, Ebbing J, Marty JC, Flechtner F, Balmino G, 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. In: Presented at the 5th GOCE user workshop. ParisGoogle Scholar
  20. Fretwell P, Pritchard HD, Vaughan DG, Bamber JL et al (2013) Bedmap2: improved ice bed, surface and thickness data sets for Antarctica. The Cryosphere 7:375–393CrossRefGoogle Scholar
  21. 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
  22. Hirt C (2012) Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth’s surface using the gradient approach. J Geod 86(13):729–744. doi: 10.1007/s00190-012-0550-y CrossRefGoogle Scholar
  23. Hirt C, Claessens SJ, Kuhn M, Featherstone WE (2012) Indirect evaluation of Mars gravity model 2011 using a replication experiment on Earth. Stud Geophys Geodetica 56(2012):957–975. doi: 10.1007/s11200-011-0468-5 CrossRefGoogle Scholar
  24. Hirt C, Claessens SJ, Fecher T, Kuhn M, Pail R, Rexer M (2013) New ultra-high resolution picture of Earth’s gravity field. Geophys Res Lett 40(16):4279–4283. doi: 10.1002/grl.50838 CrossRefGoogle Scholar
  25. Hirt C (2014) GOCE’s view below the ice of Antarctica: satellite gravimetry confirms improvements in Bedmap2 bedrock knowledge. Geophys Res Lett 41(18):5021–5028. doi: 10.1002/2014GL060636 CrossRefGoogle Scholar
  26. Hirt C, Kuhn M, Claessens SJ, Pail R, Seitz K, Gruber T (2014) Study of the Earth’s short-scale gravity field using the ERTM2160 gravity model. Comput Geosci 73:71–80. doi: 10.1016/j.cageo.2014.09.00 CrossRefGoogle Scholar
  27. Hirt C, Kuhn M (2014) Band-limited topographic mass distribution generates a full-spectrum gravity field—gravity forward modelling in the spectral and spatial domain revisited. J Geophys Res Solid Earth 119(4):3646–3661. doi: 10.1002/2013JB010900 CrossRefGoogle Scholar
  28. 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 Geoinformation 39:103–112. doi: 10.1016/j.jag.2015.03.001 CrossRefGoogle Scholar
  29. Hirt C, Rexer M, Claessens SJ (2015) Topographic evaluation of fifth-generation GOCE gravity field models—globally and regionally. In: Special issue on validation of GOCE gravity fields. Newton’s Bulletin, vol 5, pp 163–186Google Scholar
  30. Holmes SA (2003) High degree spherical harmonic synthesis for simulated earth gravity modelling. PhD Thesis, Department of Spatial Sciences, Curtin University of Technology, Perth, Western AustraliaGoogle Scholar
  31. Holmes SA, Pavlis NK (2007) Some aspects of harmonic analysis of data gridded on the ellipsoid. In: Proceedings of the 1st international symposium of the international gravity field service (IGFS). Istanbul, pp 151–156Google Scholar
  32. Holmes SA, Roman D (2010) The application of high-degree gravitational models to processing airborne gravity collected under the NGS GRAV-D project. In: Paper presented at FIG Congress 2010. Facing the Challenges—Building the Capacity, SydneyGoogle Scholar
  33. Holmes SA, Featherstone WE (2002) A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalized associated Legendre functions. J Geod 76(5):279–299. doi: 10.1007/s00190-002-0216-2 CrossRefGoogle Scholar
  34. Holt J, Richter T, Kempf S, Morse D, Blankenship D (2006) Airborne gravity over Lake Vostok and adjacent highlands of East Antarctica. Geochem Geophys Geosyst 7(15):Q11012. doi: 10.1029/2005GC001177 Google Scholar
  35. Jarvis A, Reuter HI, Nelson A, Guevara E (2008) Hole-filled SRTM for the globe v4.1. Available from the CGIAR-SXI SRTM 90m database at:
  36. Jekeli C (2010) Correlation modeling of the gravity field in classical geodesy. In: Freeden W, Nashed MZ, Sonar T (eds), Handbook of geomathematics, pp 833–866. doi: 10.1007/978-3-642-01546-5_28
  37. Jekeli C (1988) The exact transformation between ellipsoidal and spherical expansions. Manuscr Geodaetica 13:106–113Google Scholar
  38. Luyendyk B, Wilson D, Siddoway C (2003) Eastern margin of the Ross Sea Rift in western Marie Byrd Land, Antarctica: crustal structure and tectonic development. Geochem Geophys Geosyst 4(14):1090. doi: 10.1029/2002GC000462 Google Scholar
  39. Lythe, MB, Vaughan DG, and the Bedmap Consortium (2001) BEDMAP: a new ice thickness and subglacial topography model of Antarctica. J Geoph Res 106(B6):11335–11351. doi: 10.1029/2000JB900449
  40. Mayer-Gürr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010: the new GRACE gravity field release computed in Bonn. In: Paper presented at European Geosciences Union General Assembly 2010, Geophys. Res. Abstr., vol 12, EGU2010-2446. ViennaGoogle Scholar
  41. Mayer-Gürr T, Rieser D, Höck E, Brockmann JM, Schuh W-D, Krasbutter I, Kusche J, Maier A, Krauss S, Hausleitner W, Baur O, Jäggi A, Meyer U, Prange L, Pail R, Fecher T, Gruber T (2012) The new combined satellite only model GOCO03s. Abstract at GGHS2012, Venice (Poster)Google Scholar
  42. McKenzie D, Yi W, Rummel R (2015) Estimates of Te for continental regions using GOCE gravity. Earth Planet Sci Lett 399:116–127. doi: 10.1016/j.epsl.2014.05.003 CrossRefGoogle Scholar
  43. Morgan PJ, Featherstone WE (2009) Evaluating EGM2008 over East Antarctica. Newton’s Bull 4:317–331Google Scholar
  44. O’Donnell JP, Nyblade AA (2014) Antarctica’s hypsometry and crustal thickness: implications for the origin of anomalous topography in Antarctica. Earth Plan Sci Lett 388:143–155. doi: 10.1016/j.epsl.2013.11.051 CrossRefGoogle Scholar
  45. 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 85(15):819–843. doi: 10.1007/s00190-011-0467-x CrossRefGoogle Scholar
  46. 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 318–323Google Scholar
  47. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth gravitational model 2008 (EGM2008). J Geophys Res 117(B4):B04406Google Scholar
  48. Rapp RH (1997) Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. J Geod 71(5):282–289CrossRefGoogle Scholar
  49. Rexer M, Hirt C (2015) Spectral analysis of the Earth’s topographic potential via 2D-DFT—a new data-based degree variance model to degree 90,000. J Geod 89(9):887–909. doi: 10.1007/s00190-015-0822-4
  50. Rummel R, Horwath M, Yi W, Albertella A, Bosch W, Haagmans R (2011) GOCE, satellite gravimetry and antarctic mass transports. Surv Geophy 32(4–5):643–657. doi: 10.1007/s10712-011-9115-5 CrossRefGoogle Scholar
  51. Rummel R (2013) Height unification using GOCE. J Geod Sci 2(4):355–362. doi: 10.2478/v10156-011-0047-2 Google Scholar
  52. Rummel R, Rapp RH, Sünkel H, Tscherning CC (1988) Comparisons of global topographic/isostatic models to the Earth’s observed gravity field. Report No 388, Dep, Geodetic Sci. Surv., Ohio State University, Columbus, OhioGoogle Scholar
  53. Scheinert M (2012) Progress and prospects of the Antarctic Geoid Project (Commission Project 2.4), in Geodesy for Planet Earth. In: IAG Conf. Series, vol. 136. Springer, Berlin, pp 451–456Google Scholar
  54. Scheinert, M, Ferraccioli F, Schwabe J, Bell R, Studinger M, Damaske D, Jokat W, Aleshkova N, Jordan T, Leichenkov G, Blankenship DD, Damiani TM, Young D (2015) New Antarctic gravity anomaly grid for enhanced geodetic and geophysical studies in Antarctica. Geophys Res Lett. (post-revision)Google Scholar
  55. Scheinert M, Müller J, Dietrich R, Damaske D, Damm V (2008) Regional geoid determination in Antarctica utilizing airborne gravity and topography data. J Geod 82(7):403–414. doi: 10.1007/s00190-007-0189-2 CrossRefGoogle Scholar
  56. Schwabe, J, Scheinert M, Dietrich R, Ferracccioli F, Jordan T (2012) Regional geoid improvement over the Antarctic Peninsula utilizing airborne gravity data. In: Geodesy for Planet Earth, IAG Conf. Series, vol 136. Springer, Berlin, pp 457–464Google Scholar
  57. Schwabe J, Ewert H, Scheinert M, Dietrich R (2014) Regional geoid modelling in the area of subglacial Lake Vostok, Antarctica. J Geodyn 75:9–21. doi: 10.1016/j.jog.2013.12.002 CrossRefGoogle Scholar
  58. Schwabe J, Scheinert M (2014) Regional geoid of the Weddell Sea, Antarctica, from heterogeneous ground-based gravity data. J Geod 88(13):821–838. doi: 10.1007/s00190-014-0724-x CrossRefGoogle Scholar
  59. Shepherd A, Ivins ER, Geruo A et al (2012) A reconciled estimate of ice sheet mass balance. Science 338:1183–1189. doi: 10.1126/science.1228102 CrossRefGoogle Scholar
  60. Smith DA, Holmes SA, Li X, Guillaume Y, Wang YM, Bürki B, Roman DR, Damiani TM (2013) Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011. J Geod 87(10–12):885–907. doi: 10.1007/s00190-013-0653-0 CrossRefGoogle Scholar
  61. Sneeuw N, van Gelderen M (1997) The polar gap. In: Sanso F, Rummel R (eds) Geodetic boundary value problems in view of the 1 cm geoid. Lecture notes in earth sciences, vol 65. Springer, Berlin, pp 559–568. doi: 10.1007/BFb0011717
  62. Studinger M, Bell R, Finn C, Blankenship D (2002) Mesozoic and Cenozoic extensional tectonics of the West Antarctic Rift System from high-resolution airborne geophysical mapping. R Soc N Z Bull 35:563–569Google Scholar
  63. Studinger M et al (2003a) Ice cover, landscape setting, and geological framework of Lake Vostok, East Antarctica. Earth Planet Sci Lett 205(3–4):195–210. doi: 10.1016/S0012-821X(02)01041-5
  64. Studinger M, Karner G, Bell R, Levin V, Raymond C, Tikku A (2003b) Geophysical models for the tectonic framework of the Lake Vostok region, East Antarctica. Earth Planet Sci Lett 216(4):663–677. doi: 10.1016/S0012-821X(03)00548-X
  65. Studinger M, Bell RE, Roger Buck W, Karner GD, Blankenship DD (2004) Sub-ice geology inland of the Transantarctic Mountains in light of new aerogeophysical data. Earth Planet Sci Lett 220(3–4):391–408. doi: 10.1016/S0012-821X(04)00066-4 CrossRefGoogle Scholar
  66. Studinger M, Bell RE, Fitzgerald PG, Buck WR (2006) Crustal architecture of the Transantarctic Mountains between the Scott and Reedy Glacier region and South Pole from aerogeophysical data. Earth Planet Sci Lett 250(1–2):182–199. doi: 10.1016/j.epsl.2006.07.035 CrossRefGoogle Scholar
  67. Tenzer R, Chen W, Tsoulis D, Bagherbandi M, Sjöberg LE, Novák P, Jin S (2015) Analysis of the refined CRUST1.0 crustal model and its gravity field. Surv Geophys 36:139–165. doi: 10.1007/s10712-014-9299-6 CrossRefGoogle Scholar
  68. Tenzer R, Abdalla A, Vajda P, Hamayun (2010) The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast. Contrib Geophys Geod 40(3):207–223. doi: 10.2478/v10126-010-0009-1
  69. Torge W, Müller J (2012) Geodesy, 4th edn. de Gruyter, BerlinGoogle Scholar
  70. van der Meijde M, Pail R, Bingham R, Floberghagen R (2015) GOCE data, models, and applications: a review. Int J Appl Earth Obs Geoinformation 35:4–15. doi: 10.1016/j.jag.2013.10.001 CrossRefGoogle Scholar
  71. von Frese RRB, Potts LV, Wells SB et al (2009) GRACE gravity evidence for an impact basin in Wilkes Land, Antarctica. Geochem Geophys Geosystems 10(2):1–14. doi: 10.1029/2008GC002149 Google Scholar
  72. Wessel P, Smith WHF, Scharroo R, Luis JF, Wobbe F (2013) Generic mapping tools: improved version released, EOS. Trans AGU 94:409–410CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Christian Hirt
    • 1
    • 2
    Email author
  • Moritz Rexer
    • 2
  • Mirko Scheinert
    • 3
  • Roland Pail
    • 2
  • Sten Claessens
    • 1
  • Simon Holmes
    • 4
  1. 1.Western Australian Geodesy Group, Department of Spatial Sciences, Institute for Geoscience ResearchCurtin UniversityPerthAustralia
  2. 2.Institute for Advanced Study and Institute for Astronomical and Physical GeodesyTechnische Universität MünchenMunichGermany
  3. 3.Institut für Planetare GeodäsieTechnische UniversitätDresdenGermany
  4. 4.SGT Inc.GreenbeltUSA

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