Global Mean Gravity Field Models from Combination of Satellite Mission and Altimetry/Gravimetry Surface Data

Transcription

1 Global Mean Gravity Field Models from Combination of Satellite Mission and Altimetry/Gravimetry Surface Data Christoph Förste (1), Frank Flechtner (2), Roland Schmidt (2), Rolf König (2), Ulrich Meyer (2), Richard Stubenvoll (1), Markus Rothacher (1), Franz Barthelmes (1), Hans Neumayer (2), Richard Biancale (3), Sean Bruinsma (3), Jean-Michel Lemoine (3) and Sylvain Loyer (3) (1) GeoForschungsZentrum Potsdam, Telegrafenberg A17, D Potsdam, Germany (2) GeoForschungsZentrum Potsdam, c/o DLR Oberpfaffenhofen, D Wessling, Germany (3) Groupe de Recherche de Geodesie Spaciale, 18, avenue Edouard Belin, F Toulouse, France

2 Background Global high-resolution gravity field models can be derived 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. The combination of the different data sets is made on the basis of normal equations. This presentation will give a report on the current status of the EIGEN processing at GFZ Potsdam and GRGS Toulouse about: Currently used data sets, Details in strategy of combination; The latest results in comparison to earlier EIGEN- and other models. * EIGEN = European Improved Gravity model of the Earth by New techniques

3 Overview over the GFZ Gravity field solutions released during the last years EIGEN-CG01C EIGEN-CG03C EIGEN-GL04C EIGEN-GL05Cp released: May 2004 March 2005 March 2006 preliminary Resolution: 360 x x x x 360 Main differences: Satellite data: CHAMP 33 months: 10/ / GRACE 200 days: 04/ / months: 02/ / months: 02/ / months: 02/ /2006 LAGEOS months: 02/ / months: 02/ /2005 Ocean data (direct altimetry) CLS01 sea surface heights GFZ mean sea surface heights Max. degree of the the full normal matrix Overlapping range [deg] between satellite and terrestrial data: using constraints Terrestrial data: Grid size for the full normal equations 1 x 1 1 x 1 30 x x 30 Remarks: including the latest ArcGP data (Forsberg 2006)

4 GRACE and LAGEOS satellite data for EIGEN-GL04C and EIGEN-GL05Cp Data Period: CNES (for GRACE and LAGEOS): February 2003 February 2005 GFZ (for GRACE): February July 2005 (without January 2004) [ for EIGEN-GL04C ] GFZ (for GRACE): February Febr (without January 2004) [ for EIGEN-GL05Cp ] Arc Length: LAGEOS: 7d GRACE: 1d Dynamical Parametrization: LAGEOS: emp. Coefficients, along-track polygon with 4d spacing, GRACE: along-track and cross-track emp. 1/rev coefficients changing every 4 d K-band empirical coefficients, accelerometer 3D scaling factors and biases at begin and end of the arc Processing Standards: Gravity Field: EIGEN-CG03C (150x150) Ocean Tides: FES2004 (80x80) Earth Tides: IERS2003 Solid Earth Pole Tide: IERS2003 De-aliasing: AOD1B RL03 (ECMWF, OMCT) Ocean Pole Tide: Desai 2002 (80x80)

5 Surface data sets for EIGEN-GL05Cp Arctic Gravity Project (ArcGP). Gravity anomalies for regions of latitude > 64 (Forsberg, Kenyon 2004 & 2006) Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data.

6 Surface data sets for EIGEN-GL05Cp NRCan gravity anomalies covering North America. (Véronneau 2003, personal communication) Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data.

7 Surface data sets for EIGEN-GL05Cp LDO and AWI gravity anomalies. Small areas over Antarctica and adjacent sea ice. Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set (LDO: Bell et al., 1999; AWI:Studinger 1988) 7) over water depths less than 2000 m; white areas are not covered with surface data.

8 Surface data sets for EIGEN-GL05Cp Geoid undulations over the oceans: GFZ-MSSH minus ECCO-SSTop. (GFZ: T. Schöne and S. Esselborn 2005, personal communication); Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over ECCO: water Stammer depths less et al., than 2002), 2000 m; white areas are not covered with surface data.

9 Surface data sets for EIGEN-GL05Cp NIMA altimetric gravity anomalies over the ocean if not covered by GFZ-geoid (including standard deviations) Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data.

10 Surface data sets for EIGEN-GL05Cp NIMA terrestrial gravity anomalies (including standard deviations), almost worldwide continental coverage, except for Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data. Antarctica and some smaller data gaps.

11 Surface data sets for EIGEN-GL05Cp NIMA ship-borne gravity anomalies over water depths less than 2000 m. (white contourline) Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data.

12 Surface data sets for EIGEN-GL05Cp Data gaps filled with GRACE03S-solution. Coverage of surface data sets 1 through 6; white lines mark used ship gravimetry data (data set 7) over water depths less than 2000 m; white areas are not covered with surface data.

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

14 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: LAGEOS 30 overlapping Integration GRACE surface, full surface, block diagonal degree/order **) constraints (pseudo observations), applied between degree 90 and 150: C/ m, LAG. Sn, m, Surface C/ Sn, GRACE + = 0±σ σ= e l

15 EIGEN-GL05Cp gravity anomaly Δg, 0.5 x 0.5 [mgal] 3rd International GOCE User Workshop, ESA/ESRIN Frascati, 6-8 November 2006

16 EIGEN-GL05Cp minus EGM96: LONG wavelengths (n,m= ) wrms=4.22 mgal Δg = EIGEN-GL05Cp EGM96 [mgal]

17 EIGEN-GL05Cp minus EGM96: LONG wavelengths (n,m= ) without EGM96 data gaps!!l wrms=3.03 mgal Δg = EIGEN-GL05Cp EGM96 [mgal]

18 EIGEN-GL05Cp minus EGM96: SHORT wavelengths (n,m= ) wrms=3.53 mgal Δg = EIGEN-GL05Cp EGM96 [mgal]

19 EIGEN-GL05Cp minus EGM96: SHORT wavelengths (n,m= ) without EGM96 data gaps!!l wrms=2.54 mgal Δg = EIGEN-GL05Cp EGM96 [mgal]

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

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

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

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

24 Comparison with independent data sets (1) 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. gravity field model altimetry based data set Filterlength EGM96 GGM02C EIGEN- CG01C EIGEN- CG03C EIGEN- GL04C EIGEN- GL05Cp NIMA *) [mgal] CLS-ECCO **) [m] 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)

25 Comparison with independent data sets (2) Comparison with geoid heights determined point-wise by GPS positioning and levelling: Root mean square (cm) about mean of GPS-Levelling minus model-derived geoid heights (number of points in brackes). EGM96 GGM02C/ E I G E N EGM96* CG01C CG03C GL04C GL05Cp Europe (186) Germany (675) Canada (1930) USA (669) Used GPS/Levelling data sets: - USA (Milbert, 1998) - Canada (Véronneau, personal communication 2003, Natural Resources Canada) - Europe/Germany (Ihde et al., 2002). * GGM02C up to n=m=200; EGM96 for n,m > 200

26 Comparison of Orbit adjustment tests (1) Mean RMS: SLR and PRARE in cm, PRARE-Doppler and DORIS in mm/sec All gravity fields truncated to 120x120 Satellite Data (#arcs) DATA Typ GGM02C EIGEN- CG01C EIGEN- CG03C EIGEN- GL04C EIGEN- GL05Cp GFZ-1 5 x 3 days SLR STELLA 5 x 3 days SLR STARLETTE 5 x 3 days SLR AJISAI 5 x 3 days SLR LAGEOS-1 5 x 6 days SLR LAGEOS-2 5 x 6 days SLR ERS-2 6 x 6 days SLR PRARE PRARE- Doppler ENVISAT 7 x days SLR DORIS WESTPAC 5 x 6 days SLR

27 Comparison of Orbit adjustment tests (2) RMS: SLR and GPS-Code in cm, GPS-Phase in cm Used Data: one 1.5 day arc gravity fields truncated to: (1) 120 x 120 (2) 150 x 150 Satellite Data Typ GGM02C EIGEN-CG01C EIGEN-CG03C EIGEN-GL04C EIGEN- GL05Cp (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) CHAMP SLR GPS P-Code GPS Phase GRACE SLR K-Band-RR GPS P-Code GPS Phase

28 Improvement of the marine geoid in satellite-only models Geostrophic surface currents from comparison with GFZ Mean Sea Surface data EGM96S EIGEN-GRACE03S All major ocean currents can be identified in the right figure, whereas noise and systematic errors dominate the picture in the left figure.

29 Summary and Outlook The quality of the EIGEN-GL04C model was recently appreciated by adopting it as a standard for the reprocessing of the Jason and TOPEX/Poseidon data, The EIGEN-GL04C coefficients are available for download at the ICGEM* data base at GFZ Potsdam: Further improvements of the current EIGEN-GL05Cp model are planned for the upcoming EIGEN-05 gravity field model: - reprocessing (new release) of all GRACE (and CHAMP) data - inclusion of CHAMP - extension of the full ground data based normal equations to higher degrees (n,m=250) - usage of new/updated ground data sets The upcoming combined EIGEN-05 model could be a candidate for a standard for the future GOCE data processing *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

30 T H E E N D