1. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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. OSTST Meeting, Hobart, Australia, March 12-15, 2007 EIGEN statistics MeanTime-variable (monthly solutions) EIGEN-GRACE01S 39 days EIGEN-GRACE02S110 days 9 (04/2002-11/2003) EIGEN-GRACE03S376 days16 (02/2003-07/2004) EIGEN-GRACE04S430 days46 (02/2003-12/2006) EIGEN-GRACE05Snot yet45 (02/2003-11/2006) MeanTime-variable (10-day solutions) EIGEN-GL04Sover 2 full years 86 (07/2002-03/2005) EIGEN-GL05Snot yet146 (07/2002-12/2006) 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. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Gain in spectral accuracy of EIGEN models Further investigations : adjusting tides (S2,...) using KBR data destriping geoid models

4. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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. OSTST Meeting, Hobart, Australia, March 12-15, 2007 C 20 normalized coefficient series from LAGEOS only (in red), GRACE+LAGEOS (in blue), empirical model (in green) GGM2C EIGEN-GL04C.11628 10 -10 /y

6. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Adjustment of 6 parameters for all coefficients : Bias Drift COS(annual) SIN(annual) COS(semi-annual) SIN(semi-annual) Proposal : Additional periodic coefficients could be delivered as well with the EIGEN-5 models C 21 /S 21 normalized coefficient series

7. OSTST Meeting, Hobart, Australia, March 12-15, 2007 1.Adjusting bias + drift + annual + semi-annual terms for all coefficients up to degree 40; keeping the static field for higher degrees. 2.Computing « gravitological months » : averaging each month over 4 years. 3.Assimilating GRACE results into hydrological models (i.e. WGHM). Ways of taking into account time variations

8. OSTST Meeting, Hobart, Australia, March 12-15, 2007 POD Results for GRACE 19 μm 12 μm 11 μm 12 μm.18 μm/s.14 μm/s 7.4 mm 7.2 mm 7.1 mm 6.4 mm 31 mm 30 mm 29 mm 30 mm

9. OSTST Meeting, Hobart, Australia, March 12-15, 2007 POD Results for JASON 54.7 mm 54.6 mm 54.3 mm.3219 mm/s.3185 mm/s.3181 mm/s 12.7 mm 12.2 mm 11.9 mm 11.5 mm

10. OSTST Meeting, Hobart, Australia, March 12-15, 2007 over 10 days using a 10-day model vs. EIGEN-GL04S March 2005 – radial rms = 5 mm Jason radial orbit comparison

11. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Example of selected GFZ RL04 and WGHM coefficients GFZ RL04 monthly coefficients and fitted periodic signal WGHM (Water GAP Global Hydrology Model, Döll et al., 2003) monthly coefficients and fitted periodic signal

12. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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. Degree 1 coefficients 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).

13. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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 GFZ/GRGS activities on combined gravity field models

14. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Surface Data Unfiltered data Filtered data for avoiding of truncation errors (n,m >179 filtered) Blockdiagonal normal equ. (n=m=0,359) & Integration ( n=m=360) Complete normal equ. (n=m=1,200) COMBINATION COMPLETE GRAVITY FIELD SOLUTION (n=m=360) Preprocessing Combined Satellite normal equ. GPS ground data GRACE GPS-SST GRACE K-band range rate Strategy for Combination of Satellite and Surface Data Filtering for highest frequ. (n,m >360 filtered) LAGEOS SLR data GPS orbits and clocks GRACE orbits and observation equations LAGEOS orbits & normal equations (n=m=1,30) GRACE normal equations (n=m=1,150) COMBINATION

15. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Algorithms The combination of the different data sets is made on the basis of normal equations: Up to degree of 200 (presently):  Computation of full normal equation matrices: LAGEOS data, until degree 30 GRACE data, until degree 150 Ground data, until degree 200, one normal equation matrix for each individual data set  Accumulation of the individual normal equation matrices  Solution of the combined normal equation matrix by inversion incl. computation of the full variance/covariance matrix From degree 200 up to 360: Forming and solution of a block-diagonal normal equation matrix from the global gravity anomaly ground data GFZ/GRGS activities on combined gravity field models

16. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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: 70 GRACE degree/order 359 360 Integration overlapping surface, full 70 GRACE 155 surface, block diagonal degree/order 359 30 LAGEOS 150 200 2 90 **) constraints (pseudo observations), applied between degree 90 and 150 : Combination scheme of EIGEN-GL05Cp

17. OSTST Meeting, Hobart, Australia, March 12-15, 2007 GFZ/GRGS combined Gravity field solutions released during the last years Terrestrial data: Grid size for the full normal equations Satellite data:------- 33 months: 10/2000 - 06/2003 CHAMP 34 months: 02/2003 - 02/2006 30 months: 02/2003 - 07/2005 16 months: 02/2003 - 07/2004 200 days: 04/2002 - 11/2003 GRACE Main differences: 30‘ x 30‘ 1° x 1° 70... 150 using constraints 70.. 11570... 12070... 109Overlapping range [deg] between satellite and terrestrial data: 200179140 Max. degree of the the full normal matrix GFZ mean sea surface heightsCLS01 sea surface heightsOcean data (direct altimetry) 24 months: 02/2003 - 02/2005 24 months: 02/2003 - 02/2005 ---- LAGEOS 360 x 360 preliminaryMarch 2006March 2005May 2004 released: Resolution: EIGEN-GL05CpEIGEN-GL04CEIGEN-CG03CEIGEN-CG01C

18. OSTST Meeting, Hobart, Australia, March 12-15, 2007 EIGEN-GL05Cp gravity anomaly Resolution: 0.5° x 0.5° [mgal]

19. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Δζ, 0.5° x 0.5° Geoid height differences vs. a global ground data only solution EIGEN-CG03C -2.0 0.0 2.0 [meter] EIGEN-GL04C -1.0 0.0 1.0 [meter] EIGEN-GL05Cp -1.0 0.0 1.0 [meter] Improvement of combined EIGEN-models (1) → Reduction of the meridional stripes !

20. OSTST Meeting, Hobart, Australia, March 12-15, 2007 EIGEN-CG03C EIGEN-GL04C [meter] EIGEN-GL05Cp → Reduction of the meridional stripes ! Improvement of combined EIGEN-models (2) Δζ, 0.5° x 0.5° Geoid height differences vs. a global ground data only solution

21. OSTST Meeting, Hobart, Australia, March 12-15, 2007 EIGEN-GL05Cp: Geoid Degree Amplitudes (1) yellow: EIGEN-CG01C vs. GGM02C light blue:EIGEN-CG03C vs. GGM02C brown:EIGEN-GL04C vs. GGM02C greenEIGEN-GL05Cp vs. GGM02C EGM 96

22. OSTST Meeting, Hobart, Australia, March 12-15, 2007 EIGEN-GL05Cp: Geoid Degree Amplitudes EIGEN-GL04C EGM96 EIGEN-GL05Cp EIGEN-CG01C vs. GGM02C EIGEN-CG03C vs. GGM02C EIGEN-GL04C vs. GGM02C EIGEN-GL05Cp vs. GGM02C

23. OSTST Meeting, Hobart, Australia, March 12-15, 2007 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) 0.117 0.1190.1160.1170.11510° 0.1280.1290.133 0.1290.1315° 0.1690.1740.1830.1820.1710.1763°CLS-ECCO **) [m] 0.313 10° 1.0001.0271.1051.1071.0085° 4.1094.1914.2614.2564.1653°NIMA *) [mgal] EIGEN- GL05Cp EIGEN- GL04C EIGEN- CG03C EIGEN- CG01C GGM02CEGM96 Filter- length gravity field model altimetry based data set

24. OSTST Meeting, Hobart, Australia, March 12-15, 2007 Status and Future plans: The current published combined model is EIGEN-GL04C. It’s coefficient set is available for download at the ICGEM* 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 = The International 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 GFZ/GRGS activities on combined gravity field models