T. Gruber, C. Ackermann, T. Fecher, M. Heinze

1. Validation of GOCE Gravity Field Models and Precise Science Orbits 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

2. What is Validation ? • Check Plausibilityof 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? Look on error estimates, Compare solutions, Compare to independent (hopefully better) information. Others

3. Example for Plausability – Role of Reference Data

4. Outline of Talk • GOCE Orbit Validation • Compare Orbit Positions and Velocities from different Solutions • Residuals to independent Observations (e.g. SLR) • GOCE Gravity Field Validation • Results of Least-Squares Adjustment: Signals and Errors • Error Propagation (Variances & Co-variances) • Orbit Residuals • Geoid Comparisons • Sea Surface Topography (Level 3) (not shown here)

5. GOCE Orbit Validation – Product Overview Detailed Content

6. 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

7. 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 kinematicorbit: mean = 8.83 mm, RMS = 22.25 mm

8. GOCE Gravity Field Validation – Product Overview

9. GOCE Gravity Field Validation – Definition of Models Three independent preliminary GOCE Gravity Field Solutions have been computed from 2 months of data focusing on different approaches & goals ! 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. 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.

10. 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.

11. GOCE Gravity Field Validation – Signal & Errors TIM DIR 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. SPW

12. GOCE Gravity Field Validation – Signal & Errors Error Degree Median vs. Mean Signal per Degree: Significant GOCE contribution between d/o 90 and170.

13. 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.

14. GOCE Gravity Field Validation – Error Propagation Geoid Variances (SQRT) from propagated Variance-Covariance Matrix TIM DIR SPW • 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.

15. 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.

16. GOCE Gravity Field Validation – Geoid Comparisons Principle of Geoid & Sea Surface Topography Comparisons (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. Topography Mean Ocean Surface Sea Surface Height Geometric Height Ellipsoid

17. GOCE Gravity Field Validation – Geoid Comparisons Principle of Geoid & Sea Surface Topography Comparisons (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. Topography Physical Height Geoid Mean Ocean Surface Sea Surface Height Geoid from Global Model Geometric Height Ellipsoid Geoid Height

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

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

20. GOCE Gravity Field Validation – Geoid Comparisons Geoid Differences Germany 675 Points – Cut off d/o = 60 (top) ; d/o = 120 (bottom) EIGEN-5S DIR TIM SPW EIGEN-5C

21. GOCE Gravity Field Validation – Geoid Comparisons Geoid Differences Germany 675 Points – Cut off d/o = 160 TIM SPW DIR EIGEN-5C ITG-GRACE2010S EGM2008 Full Resolution (incl. German Gravity Data)

22. GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Differences Germany for 675 Points, different cut-off d/o 15 cm 6 cm

23. GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Height Differences Germany for 675 Points, different cut-off d/o

24. GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o d/o 30 d/o 40 d/o 50 d/o 60 d/o 70 d/o 80 d/o 90 d/o 100

25. GOCE Gravity Field Validation – Geoid Comparisons RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o d/o 130 d/o 140 d/o 110 d/o 120 d/o 150 d/o 160 d/o 170 d/o 180

26. 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.

27. 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.

28. 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.