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EIGEN-5 activities in GFZ and GRGS R. Biancale , J.-M. Lemoine, S. Bruinsma, S. Loyer*

EIGEN-5 activities in GFZ and GRGS R. Biancale , J.-M. Lemoine, S. Bruinsma, S. Loyer* CNES/GRGS Toulouse, France * Noveltis, Ramonville Saint-Agne, France Ch. Förste, F. Flechtner, R. Schmidt GeoForschungsZentrum Potsdam, Germany. EIGEN statistics. GFZ.

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EIGEN-5 activities in GFZ and GRGS R. Biancale , J.-M. Lemoine, S. Bruinsma, S. Loyer*

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  1. EIGEN-5 activities in GFZ and GRGS R. Biancale, J.-M. Lemoine, S. Bruinsma, S. Loyer* CNES/GRGS Toulouse, France * Noveltis, Ramonville Saint-Agne, France Ch. Förste,F. Flechtner, R. Schmidt GeoForschungsZentrum Potsdam, Germany

  2. EIGEN statistics GFZ • Mean Time-variable (monthly solutions) • EIGEN-GRACE01S 39 days • EIGEN-GRACE02S 110 days 9 (04/2002-11/2003) • EIGEN-GRACE03S 376 days 16 (02/2003-07/2004) • EIGEN-GRACE04S 430 days 46 (02/2003-12/2006) • EIGEN-GRACE05S not yet 45 (02/2003-11/2006) GRGS • Mean Time-variable (10-day solutions) • EIGEN-GL04S over 2 full years 86 (07/2002-03/2005) • EIGEN-GL05S not yet 146 (07/2002-12/2006) Common • EIGEN-GL04S1/-GL04C (2006) expanded in s.h. up to 150/360 • EIGEN-5S/-5C (mid/end 2007) expanded in s.h. up to 150/360

  3. Gain in spectral accuracy of EIGEN models • Further investigations : • adjusting tides (S2,...) • using KBR data • destriping geoid models

  4. EIGEN Standards • Major updates in EIGEN-GRACE05S: • Static background gravity model: EIGEN-GL04C (150x150). • Updated K2 and included M4 tide in FES2004 ocean tides. • Usage of ocean pole tide model (Desai 2002). • Usage of new atmospheric/oceanic de-aliasing product AOD1B-RL04 (mass- conserving baroclinic OMCT ocean model). • Relativity extended by Lense-Thirring & de Sitter effects (IERS Conventions 2003). • IERS 2003 nutation and precession model. • Tidal and nutational corrections to EOP (local spline interpolation). • Az/El dependent phase center corrections for GPS-SST of GRACE-A/B (JPL) • Major differences of EIGEN-GL04S wrt. EIGEN-GRACE05S : • MOG2D (LEGOS/CLS) instead of OMCT • Az/El dependent phase center corrections for GPS-SST of GRACE-A/B (GRGS) • KBRR data (GRGS’ derivation of Level-1B KBR data) • KBRR empirical parameterization

  5. .11628 10-10 /y EIGEN-GL04C GGM2C C20 normalized coefficient series from LAGEOS only (in red),GRACE+LAGEOS (in blue), empirical model (in green)

  6. Ways of taking into account time variations • Adjusting bias + drift + annual + semi-annual terms for all coefficients up to degree 40; keeping the static field for higher degrees. • Computing « gravitological months » : averaging each month over 4 years. • Assimilating GRACE results into hydrological models (i.e. WGHM).

  7. POD Results for GRACE 31 mm 30 mm 29 mm 30 mm 7.4 mm 7.2 mm 7.1 mm 6.4 mm 19 μm 12 μm 11 μm 12 μm .18 μm/s .14 μm/s .14 μm/s .14 μm/s

  8. POD Results for JASON 12.7 mm 12.2 mm 11.9 mm 11.5 mm .3219 mm/s .3185 mm/s .3185 mm/s .3181 mm/s 54.7 mm 54.6 mm 54.6 mm 54.3 mm

  9. Jason radial orbit comparison over 10 days using a 10-day model vs. EIGEN-GL04S March 2005 – radial rms = 5 mm

  10. Degree 1 coefficients Until now degree 1 coefficients were not delivered in the 10-day models (i.e. the origin of EIGEN models is the Earth centre of mass). They are adjusted only through Lageos data. Nevertheless they could be delivered for altimetric purposes. In summary for the next “satellite” EIGEN-5S model we can propose delivering optional annual and semi-annual sine and cosine terms from degree 1 to 40 (and some drifts as well).

  11. GFZ/GRGS activities on combined gravity field models Task • Computation of global high-resolution gravity field models in terms of spherical harmonic coefficients from the combination of satellite data and surface gravity data. • At GFZ Potsdam and GRGS Toulouse, such global gravity models are routinely produced in the framework of the EIGEN* processing activities. Combined data sets Satellite data: • GRACE GPS/SST and K-Band data • CHAMP GPS/SST data • LAGEOS Satellite Laser Ranging measurements Ground data: • Gravity anomaly data over land (based on classical and air-born gravimetry) • Ocean geoid height and ocean gravity anomaly data (based on altimetry and ship gravimetry) The ground data presently available for GFZ/GRGS allow a global grid coverage of 0.5° x 0.5° resolution, corresponding to a maximum degree of 360 for the spherical harmonic coefficients of a global gravity field model obtained from it. * EIGEN = European Improved Gravity model of the Earth by New techniques

  12. LAGEOS 30 200 150 overlapping Integration GRACE GRACE surface, full surface, block diagonal 70 70 90 2 degree/order degree/order 155 360 359 359 Combination scheme of EIGEN-GL05Cp contribution to the solution, full normal matrix: kept separately and bound together with the surface data using constraints**): kept separately (reduced from the full normal matrix): not used: contribution to the solution, block diagonal matrix: contribution to the solution, numerical integration: **) constraints (pseudo observations), applied between degree 90 and 150 :

  13. EIGEN-GL05Cp gravity anomaly Resolution: 0.5° x 0.5° [mgal]

  14. EIGEN-GL05Cp Geoid height differences vs. a global ground data only solution EIGEN-GL04C EIGEN-CG03C -1.0 0.0 1.0 [meter] -1.0 0.0 1.0 [meter] -2.0 0.0 2.0 [meter] Improvement of combined EIGEN-models (1) Δζ, 0.5° x 0.5° →Reduction of the meridional stripes !

  15. Geoid height differences vs. a global ground data only solution Improvement of combined EIGEN-models (2) Δζ, 0.5° x 0.5° EIGEN-GL05Cp EIGEN-GL04C [meter] →Reduction of the meridional stripes ! EIGEN-CG03C

  16. EIGEN-GL05Cp: Geoid Degree Amplitudes (1) EGM 96 yellow: EIGEN-CG01C vs. GGM02C light blue: EIGEN-CG03C vs. GGM02C brown: EIGEN-GL04C vs. GGM02C green EIGEN-GL05Cp vs. GGM02C

  17. EIGEN-GL04C EGM96 EIGEN-GL05Cp EIGEN-CG01C vs. GGM02C EIGEN-CG03C vs. GGM02C EIGEN-GL04C vs. GGM02C EIGEN-GL05Cp vs. GGM02C EIGEN-GL05Cp: Geoid Degree Amplitudes

  18. gravity field model altimetry based data set Filter- length EGM96 GGM02C EIGEN-CG01C EIGEN-CG03C EIGEN- GL04C EIGEN-GL05Cp NIMA*) [mgal] 3° 4.165 4.256 4.261 4.191 4.109 5° 1.008 1.107 1.105 1.027 1.000 10° 0.313 0.313 0.313 0.313 0.313 CLS-ECCO **) [m] 3° 0.176 0.171 0.182 0.183 0.174 0.169 5° 0.131 0.129 0.133 0.133 0.129 0.128 10° 0.115 0.117 0.116 0.119 0.117 0.117 Comparison with independent ocean gravity data Latitude-weighted root mean square of geoid- and gravity anomaly differences between gravity field models and altimetry based data sets, formed on 1° x 1° grids of the compared data sets, after filtering with different filter lengths. Altimetry based data sets for comparison *) NIMA altimetric gravity anomalies over the ocean (Kenyon, Pavlis 1997) **)Geoid undulations over the oceans derived from CLS01 altimetric Sea Surface Heights (Hernandez et al., 2001) and ECCO simulated sea surface topography (Stammer et al., 2002)

  19. GFZ/GRGS activities on combined gravity field models Status and Future plans: The current published combined model is EIGEN-GL04C. It’s coefficient set is available for download at theICGEM*data base at GFZ Potsdam: http://icgem.gfz-potsdam.de/ICGEM/ICGEM.html Further improvements of the preliminary EIGEN-GL05Cp model are planned for the upcoming EIGEN-05C gravity field model: - based on EIGEN-GRACE05S (GFZ) and EIGEN-GL05S (GRGS) models - inclusion of CHAMP data - extension of the full ground data based normal equations to higher degrees (n,m=250 or more) - usage of new/updated ground data sets *ICGEM =TheInternational Center of Global Earth Models at GFZ Potsdam is one of the six data centers of the International Gravity Field Service (IGFS) of the IAG

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