Combined Gravity Field Model EIGEN-5C


The combined gravity field model EIGEN-5C is an upgrade of EIGEN-GL04C. The model is a combination of GRACE and LAGEOS mission data plus 0.5 x 0.5 degrees gravimetry and altimetry surface data. The combination of the satellite and surface data has been done by the combination of normal equations, which are obtained from observation equations for the spherical harmonic coefficients.

The satellite data have been processed by GFZ Potsdam (GRACE for February 2003 - January 2007) and GRGS Toulouse (GRACE for August 2002 - January 2007 and LAGEOS for January 2002 - December 2006). The satellite data processing has been done in accordance to the GRACE GFZ Level-2 Processing Standards Release 4 (see GRACE GFZ Level-2 Processing Standards Document for Product Release 04, available at ISDC or PO.DAAC). This comprises for instance arc lengths of 1 day for GRACE and 10 days for LAGEOS and the usage of EIGEN-GL04C as a-priori gravity field. The GRGS standards are nearly identical.

The used surface data are identical to EIGEN-GL04C except of new gravity anomaly data sets for Europe (H. Denker, IfE Hannover, 2007, personal communication), the latest Arctic Gravity Project gravity anomaly data (Forsberg, Kenyon 2006) and newer Australian gravity anomalies (A. Murray, Geosciences Australia, 2001). As the precursor joint GFZ/GRGS combined gravity field models, EIGEN-5C is complete to degree and order 360 in terms of spherical harmonic coefficients which corresponds to a spatial resolution of 55 km on the Earth's surface. Again, a special band-limited normal equation combination method has been applied in order to preserve the high accuracy from the satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high frequency information coming from the surface data. EIGEN-5C and its associated satellite only model EIGEN-5S has been selected as standard for ESA's official data processing of the upcoming gradiometer satellite mission GOCE.


The improvement with respect to precursor EIGEN models is reflected in different comparisons and tests.

1.) Independent comparisons with geoid heights determined point-wise by GPS positioning and GPS levelling are shown for EIGEN-CG01C, -CG03C, -GL04C and -5C using GPS levelling data from the US (Milbert, 1998), Canada (Veronneau, National Ressources Canada, personal communication 2003), Australia (G. Johnston, Geoscience Australia and W. Featherstone, Curtin University of Technology, personal communication 2007), Germany (Ihde et al., 2002) and Europe (Ihde, personal communication, 2008) in Table 1.

Gravity Model

Table 1: Root mean square (rms) about mean of GPS-levelling minus gravity field model derived geoid heights [cm] (number of points in brackets).

2.) The unrealistic meridional striping patterns over the oceans in the precursor EIGEN models could be much reduced (see figure 1 for the North Atlantic and figure 2 for a global view). This is mainly a result of improvements in the GRACE satellite-only models and refinements in the combination of the individual normal equations.

EIGEN-CG03C North Atlantic Geoid Height
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EIGEN-GL04C North Atlantic Geoid Height
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EIGEN-5C North Atlantic Geoid Height
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Figure 1: North Atlantic geoid heights [m] of EIGEN-CG03C (left), EIGEN-GL04C (middle) and EIGEN-5C (right) after subtraction of a surface gravity data based geoid.

EIGEN-CG03C Global Geoid Height
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EIGEN-GL04C Global Geoid Height
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EIGEN-5C Global Geoid Height
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Figure 2: Global residual ocean geoid [m] of EIGEN-CG03C (left), EIGEN-GL04C (middle) and EIGEN-5C (right) after the subtraction of an ocean geoid based on altimetry (= GFZ Mean Sea Surface Heights minus ECCO Dynamic Ocean Topography). Note the disappearance of the unrealistic ringing pattern around New Zeeland.

3.) The satellite-only models, on which the combined models are based, contain unrealistic meridional stripes also over the continents. Figure 3 shows, how these stripes disappear during the combination with the surface data for Europe/West Asia.

Gravity Anomalies Tibet
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Figure 3: Gravity anomaly plots for the satellite-only models EIGEN-GL04S1 and EIGEN-5S in comparison with the combined model EIGEN-5C. Note the disappearance of the unrealistic stripes over West Siberia and the highlands of Tibet.


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EIGEN-5C has been presented at the EGU general assembly in Vienna: Foerste, C.; Flechtner, F.; Schmidt, R.; Stubenvoll, R.; Rothacher, M.; Kusche, J.; Neumayer, K.-H.; Biancale, R.; Lemoine, J.-M.; Barthelmes, F.; Bruinsma, J.; Koenig, R.; Meyer, U. (2008), EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation, General Assembly European Geosciences Union (Vienna, Austria 2008), Geophysical Research Abstracts, Vol. 10, Abstract No. EGU2008-A-06944, 2008

The presentation held in Vienna can be downloaded here (3.4 Mb).

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Originator: Ch.Foerste, F. Flechtner
September 29, 2008, webadmin S. Magnussen