1. ESA Living Planet Symposium, Bergen, 29.6.2010 T. Gruber, C. Ackermann, T. Fecher, M. Heinze Institut für Astronomische und Physikalische Geodäsie (IAPG) Technische Universität München P. Visser Department of Earth Observation and Space Systems (DEOS) Delft University of Technology Validation of GOCE Gravity Field Models and Precise Science Orbits

2. ESA Living Planet Symposium, Bergen, 29.6.2010 What is Validation ? Check Plausibility of Products, Data, Algorithms etc.  Why plausibility and not a real quality check?  We want to determine the quality of something, which is better than everything we ever had before!  For this we need tools to test plausibility. What are such tools? (1)Look on error estimates, (2)Compare solutions, (3)Compare to independent (hopefully better) information. (4)Others

3. ESA Living Planet Symposium, Bergen, 29.6.2010 Example for Plausability – Role of Reference Data

4. ESA Living Planet Symposium, Bergen, 29.6.2010 Outline of Talk 1.GOCE Orbit Validation a)Compare Orbit Positions and Velocities from different Solutions b)Residuals to independent Observations (e.g. SLR) 2.GOCE Gravity Field Validation a)Results of Least-Squares Adjustment: Signals and Errors b)Error Propagation (Variances & Co-variances) c)Orbit Residuals d)Geoid Comparisons e)Sea Surface Topography (Level 3) (not shown here)

5. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Orbit Validation – Product Overview IdentifierDescription SST_PSO_2Precise Science Orbits (reduced dynamic and kinematic):  GOCE precise science orbits final product  Quality report for precise orbits Kinematic OrbitGPS time in [sec] X,Y,Z position in [m] in Earth fixed frame Clock correction Standard deviation of position and clock Variance-covariance matrix for positions (over 9 Epochs) Reduced Dynamic Orbit GPS time in [sec] X,Y,Z position in [m] in Earth fixed frame X,Y,Z velocity in [m/sec] in Earth fixed frame Standard deviation of position and clock Rotation Matrix from EFRF to IRF GPS time in [sec] Quaternions (4) describing rotation angles Detailed Content

6. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Orbit Validation – Compare Orbit Positions Daily RMS of PSO reduced-dynamic vs. PSO kinematic Orbit Positions [mm] Peaks from short, but large outliers in den kinematic orbits in polar regions.

7. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Orbit Validation – SLR Residuals Range residuals between computed range from SLR station to satellite position from reduced-dynamic orbit and observed range with laser system [mm] Statistic: reduced–dynamic orbit: mean = 8.75 mm, RMS = 20.52 mm

8. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Orbit Validation – SLR Residuals Range residuals between computed range from SLR station to satellite position from kinematic orbit and observed range with laser system [mm] Statistic: reduced–dynamic orbit: mean = 8.75 mm, RMS = 20.52 mm kinematic orbit: mean = 8.83 mm, RMS = 22.25 mm

9. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Product Overview IdentifierDescription EGM_GOC_2Gravity Field Model:  Final GOCE Earth gravity field model as spherical harmonic series including error estimates.  Grids of geoid heights, gravity anomalies and deflections of the vertical computed from final GOCE Earth gravity field model.  Grid of propagated geoid height error estimates (variances)  Quality report for GOCE gravity field model EGM_GVC_2Gravity Field Error Structure:  Complete variance-covariance matrix of final GOCE Earth gravity field model

10. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Definition of Models Direct Approach – DIR Start with a state-of-the-art combined gravity field model (GRACE + terrestrial data + altimetry) and use GOCE reduced-dynamic orbits and gradiometry as observation data set. Three independent preliminary GOCE Gravity Field Solutions have been computed from 2 months of data focusing on different approaches & goals ! Time-Wise Approach – TIM Start with zero knowledge and only use GOCE kinematic orbits and gradiometry as observation data set. Space-Wise Approach – SPW Start with a-priori knowledge for long wavelengths and use GOCE kinematic orbits and gradiometry as observation data set.

11. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Signal Signal Degree Variances (Square Root) in Terms of Geoid Height Signal power at high degrees shows Impact of a-priori information depending on what type of information has been used.

12. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Signal & Errors DIR SPW TIM Number of significant Digits: Log10(Signal / Error) Significance up to d/o 170 A-propri information defines mapping of polar gap to spectral bevaviour. A-priori information defines significance for high degrees.

13. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Signal & Errors Significant GOCE contribution between d/o 90 and170. Error Degree Median vs. Mean Signal per Degree:

14. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Errors Cumulative Geoid & Gravity Anomaly Error With 2 months GOCE we can reach between 4 – 7 cm geoid accuracy at d/o 170 (120km spatial resolution) compared to 9 – 10 cm from a combined GRACE model.

15. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Error Propagation Geoid Variances (SQRT) from propagated Variance-Covariance Matrix DIR SPW TIM Polar gaps well recovered. Similar geoid variance structure for all models. Ground track pattern more significant for DIR and TIM. Note different colour bar for DIR.

16. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Orbit Residuals Orbits are recomputed by exchanging gravity field model. Observation residuals to new orbits are computed. Smaller RMS means better suited for a satellite. For altimeter missions in addition radial altimeter crossover differences are computed. Polar Satellites: CHAMP GRACE-A GRACE-B For non-polar Satellites similar results but on a significant lower level.

17. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Orbit Residuals Orbits are recomputed by exchanging gravity field model. Observation residuals to new orbits are computed. Smaller RMS means better suited for a satellite. For altimeter missions in addition radial altimeter crossover differences are computed. Sun-synchronous Satellite: ERS-2 High flying Satellite: LAGEOS-1 ERS-2 Altimetry: Geographical correlated and anti- correlated orbit error

18. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons Principle of Geoid & Sea Surface Topography Comparisons Topography Ellipsoid Geometric Height (1) Evaluate global gravity field model with external & independent data. Here we consider heights on land and on ocean. (2)From GPS positioning and satellite altimetry we get geometric heights on land and sea surface heights on ocean. Mean Ocean Surface Sea Surface Height

19. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons Geoid Geometric Height Physical Height Sea Surface Height Geoid Height Mean Ocean Surface Geoid from Global Model Topography Ellipsoid (3) From levelling we get physical (orthometric) heights on land. (4) From difference between ellipsoidal and physical heights we get geoid heights on land, which can be compared with geoid heights computed from the global model. Principle of Geoid & Sea Surface Topography Comparisons

20. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons Geoid Comparisons – The Problem of Omission spectral domain spatial domain (from zero frequency to infinity – d/o 0 to infinity) (from point values to block mean values) Point observation (e.g. GPS levelling) N=360 ≈ 30'x30' N=60 ≈ 3ºx3º Global Model Solution to D/O 180 - point value Omission Error Global Model Solution to D/O 180 – Point Value N=180 ≈ 2ºx2º N=180 ≈ 10'x10' N=180 ≈ 1°x1°N=180 ≈ 1ºx1º The omission error has to be estimated before comparison of observation and model can be done !

21. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons GPS-Levelling Data Australia 197 points Germany 675 points Canada 430 points (Veronneau, 2007) (Ihde, 2007) (Johnston, 1998) Europe (EUVN-DA) 1233 points (Ihde, 2007) Japan 837 points (Nakagawa, 1999) USA 5168 points (NGS, 1999)

22. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons Geoid Differences Germany 675 Points – Cut off d/o = 60 (top) ; d/o = 120 (bottom) DIRSPWTIM EIGEN-5S EIGEN-5C

23. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons Geoid Differences Germany 675 Points – Cut off d/o = 160 SPWTIM DIR EGM2008 Full Resolution (incl. German Gravity Data) EIGEN-5CITG-GRACE2010S

24. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Differences Germany for 675 Points, different cut-off d/o 6 cm 15 cm

25. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Height Differences Germany for 675 Points, different cut-off d/o

26. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o d/o 30d/o 40d/o 50 d/o 60 d/o 70d/o 80d/o 90d/o 100

27. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o d/o 110d/o 120 d/o 130 d/o 140 d/o 150d/o 160d/o 170d/o 180

28. ESA Living Planet Symposium, Bergen, 29.6.2010 Conclusions (1)  Precise science orbits show high quality 2-3 cm.  Three preliminary gravity field models based on 2 months of GOCE data are validated by different techniques.  Orbit tests for gravity fields are according to expectations (low frequencies better determined from GRACE type missions).  Tests based on estimated errors show significance of GOCE models up to approx. d/o 170. GOCE improves gravity field between d/o 100 and 170.  Estimated geoid error at a level of 7 cm @ d/o 170 and 12 cm @ d/o 200.  External geoid comparisons confirm internal error estimates: 6 cm @ d/o 170 and 15 cm @ d/o 200.  GOCE fields show remarkable good performance for areas, where high quality comparison data are available.  We can expect significantly improved gravity field knowledge in areas, where sparse or poor terrestrial data is available.

29. ESA Living Planet Symposium, Bergen, 29.6.2010 Conclusions (2)  How to decide, which model performs best ?  There is no unique answer. In many cases this depends on the application !  Be aware about the characteristics of the preliminary GOCE models in order to choose the right one for your application.  In any case we already can see that GOCE data will provide us new insights to Earth system science.

30. ESA Living Planet Symposium, Bergen, 29.6.2010 GOCE Award Therefore, this year the gravity field cup will awarded to all groups involved in GOCE satellite operations and ground data processing. They do a great job and we expect even more spectacular results based on more GOCE data.