Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany

1. Quality Assessment of GOCE GradientsPhillip Brieden, Jürgen Müllerliving planet symposium28 June – 2 July 2010 | Bergen | Norway Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany

2. Introduction Power Spectral Density (PSD)of GOCE GG CorrectData? living planet symposium 28 June – 2 July 2010 | Bergen | Norway

3. Contents • Filtering of GGT L1b data • Why ? • The Method • Results • Two Validation Methods • Reference Gradient approach • Cross-Over (XO) approach • Basic ideas • Results based in real GOCE data • Conclusions • Hanover is part of the official Cal/Val team of ESA. • data access • preliminary results! living planet symposium 28 June – 2 July 2010 | Bergen | Norway

4. Comparison in Gradiometer Reference Frame: Measured GG – GPM (e.g. EGM 08) > 0.5 E GOCE Gravity Gradients validation within MBW filtering is necessary! long-wavelength errors(caused by accelerometer-drift) 1 E=10-9 1/s² MBW: between 0.005 and 0.1 Hz 0 E  Quality Assessment at the level of some mE living planet symposium 28 June – 2 July 2010 | Bergen | Norway

5. Filtering GGT Components - The Idea GOCE high-pass + GPM low-pass living planet symposium 28 June – 2 July 2010 | Bergen | Norway

6. Filtering - Used Filter • Finite Impulse Response filter (FIR) • Butterworth-filter • high-pass (GOCE) • low-pass (GPM) • cut-off frequency: 5 mHz  filtering and combination in time domain! • Additional filtering of the combined information • Butterworth-filter again • cut-off frequency: 50 mHz spherical harmonic degree l ≈ 270 • GOCE-only gravity field solutions up to degree ~250 living planet symposium 28 June – 2 July 2010 | Bergen | Norway

7. Filtering – Result (1) GOCE measurements high-pass filtered GOCE low-passfiltered EGM08 MBW living planet symposium 28 June – 2 July 2010 | Bergen | Norway

8. Filtering – Result (2) GOCE measurements filtering result time series used for analyses difference: GOCE – filter result • Selection of best cut-off frequency? living planet symposium 28 June – 2 July 2010 | Bergen | Norway

9. Reference Gradients from Gravity Anomalies (Reference Gradient Approach) terrestrial data (incl. airborne gravimetry and satellite altimetry) of well-surveyed regional areas combined with global geopotential model (GPM) Δg´ = ΔgG – ΔgM – ΔgRTM living planet symposium 28 June – 2 July 2010 | Bergen | Norway

10. Reference Gradient ApproachThe Evaluation Area • regional area: reference values (3D grid) available • residual values related to a GPM + terrestrial data • altitude interval: 5 km • resolution: 6 min latitudeφ: 40.05° - 54.95° longitudeλ: 00.05° - 19.95° altitude: 230.0 km - 280.0 km living planet symposium 28 June – 2 July 2010 | Bergen | Norway

11. Reference Gradient ApproachCalculation of the Differences • regional area: reference values (3D grid) available • residual values related to a GPM + terrestrial data • altitude interval: 5 km • resolution: 6 min • select GOCE data across the regional area • 3D-spline interpolation of reference gradients (Tij) in gradiometer position • restore-part of the reference gradients into the interpolation point & restore-step Tij Vij • analysis of the differences: • analysis for each track ΔVijRG= VijGOCE – VijRefGrad living planet symposium 28 June – 2 July 2010 | Bergen | Norway

12. Reference Gradient ApproachDifferences ΔVijRG • differences ΔVijRG [E] • color-coded (different scales!) • mean value reduced (each track) living planet symposium 28 June – 2 July 2010 | Bergen | Norway

13. spherical harmonic degree l ≈ 270 Reference Gradient ApproachPSD of GG-differences for all track pieces average of PSDs GOCE requirements living planet symposium 28 June – 2 July 2010 | Bergen | Norway

14. The Cross-Over (XO) Approach Basic idea Identical measurement position • identical gravity gradient: Vij,1 = Vij,2 Attention! No repeated measurement positions! • differences in attitude and altitude that have to be reduced • GPM used for reduction gravity gradient differences in XO  to be analyzed ij = {xx, xy, xz, yy, yz, zz} ΔVijXO = Vij1 – Vij2 – redijGPM living planet symposium 28 June – 2 July 2010 | Bergen | Norway y x z x y z

15. Cross-Over (XO) ApproachResults (1) • Statistical results • Set up a threshold of maximum difference in all XOs • Percentage of differences that exceed the threshold • Distinction for each GGT component main diagonal components living planet symposium 28 June – 2 July 2010 | Bergen | Norway

16. Cross-Over (XO) ApproachResults (2) GGT component: XXthreshold: 11 mE ‘outliers’: 0.66 % [mE] • Almost all ‘outliers’ have differences near the threshold • XO-approach is very suitable for GOCE data validation • Good data quality of GOCE gravity gradients living planet symposium 28 June – 2 July 2010 | Bergen | Norway

17. Conclusions • Longer-wavelength errors require a filtering of GG measurements • replacement of long wavelength by GPM information • selection ‘the best’ cut-off frequency • Reference Gradient Approach • results perfectly meet the requirements • Cross-Over (XO) Approach • only scattered unevenly distributed outliers  Both approaches… • confirm the somewhat higher noise level of Vzz compared to the other main diagonal components Vxx and Vyy • suitable for the validation of GOCE GG • confirm the very good quality of GOCE GG good data quality living planet symposium 28 June – 2 July 2010 | Bergen | Norway

18. Additional Slides living planet symposium 28 June – 2 July 2010 | Bergen | Norway

19. Differences Along One Track Crossing the Evaluation Area living planet symposium 28 June – 2 July 2010 | Bergen | Norway

20. Cut-off frequencies: 5 mHz - lower line50 mHz - upper line Different GPMs XO-Results different max-degree  no significant differences living planet symposium 28 June – 2 July 2010 | Bergen | Norway

21. Different Cut-Off Frequencies living planet symposium 28 June – 2 July 2010 | Bergen | Norway