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Annette Eicker, Torsten Mayer-Gürr, Atef Makloof, Karl-Heinz Ilk

Regional solutions from GOCE data considering topographic-isostatic models. Annette Eicker, Torsten Mayer-Gürr, Atef Makloof, Karl-Heinz Ilk Institute of Theoretical Geodesy, University of Bonn November 6, 2006 GOCE User Workshop, Frascati. Introduction.

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Annette Eicker, Torsten Mayer-Gürr, Atef Makloof, Karl-Heinz Ilk

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  1. Regional solutions from GOCE data considering topographic-isostatic models Annette Eicker, Torsten Mayer-Gürr, Atef Makloof, Karl-Heinz Ilk Institute of Theoretical Geodesy, University of Bonn November 6, 2006 GOCE User Workshop, Frascati

  2. Introduction GOCE: high resolution static gravity field Regionally adapted refinements of the global field to optimally exploit the signal content Gravity field shows varying roughness in different geographic areas Regionally adapted regularization Consideration of topographic – isostatic models

  3. Analysis concept GROOPS - Gravity Recovery Object Oriented Programming System Parameterization in space Observations Solver CHAMP sphericalharmonics localizingsplines normal- equations GRACE Parameterization in time conjugate gradients GOCE variance-component-estimation linearsplines mean values

  4. Analysis concept GROOPS - Gravity Recovery Object Oriented Programming System Parameterization in space Observations Solver CHAMP sphericalharmonics localizingsplines normal- equations GRACE Parameterization in time conjugate gradients GOCE variance-component-estimation linearsplines mean values

  5. Regional solutions • satellite data cut out over the regional • area • global solution subtracted as • reference field (e.g. GRACE field) • spline representation: • resolution: 67 km nodal point distance • => 5000 – 9000 parameters per region [cm]

  6. Regional solutions • satellite data cut out over the regional • area • global solution subtracted as • reference field (e.g. GRACE field) • spline representation: • resolution: 67 km nodal point distance • => 5000 – 9000 parameters per region

  7. Regional solutions • satellite data cut out over the regional • area • global solution subtracted as • reference field (e.g. GRACE field) • spline representation: • resolution: 67 km nodal point distance • => 5000 – 9000 parameters per region [cm]

  8. Regional solutions • satellite data cut out over the regional • area • global solution subtracted as • reference field (e.g. GRACE field) • spline representation: • resolution: 67 km nodal point distance • => 5000 – 9000 parameters per region Degree variances [cm]

  9. Solution of the system of equations

  10. varying signal content in different regional areas => adaption of the regularization Regularization regularization parameter determined by variance component estimation

  11. Regionally adapted regularization

  12. Regionally adapted regularization

  13. Regionally adapted regularization regularization continent

  14. Regionally adapted regularization regularization continent regularization ocean

  15. Combination of GRACE and GOCE „real“ Field: EGM96 up to degree 300reference field: GRACE solution up to n = 120, OSU91 from n = 121 GOCE refinements up to degree 300 30 days, sampling 5 sec. GRACE: SST: white noise,σ = 10 μm Orbits: white noise, σ = 3 cm GOCE: SGG: Txx, Tyy, Tzz, colored noise, σ = 1,2 mEOrbits: white noise, σ = 3 cm

  16. Regional solutions (diff. to EGM96)

  17. Regional solutions (diff. to EGM96)

  18. Regional solutions (diff. to EGM96)

  19. Global „patching“-solution (quadrature) RMS: 6,71 cm nmax = 240

  20. Uniform regularization per region RMS: 6,71 cm nmax = 240

  21. Adapted regularization parameters RMS: 6,51 cm nmax = 240

  22. Adapted regularization parameters RMS: 6,51 cm nmax = 240

  23. Uniform regularization parameter [cm] RMS (uniform): 9,24 cm nmax = 240

  24. Adapted regularization parameters [cm] RMS (uniform): 9,24 cm nmax = 240 RMS (adapted): 8,08 cm

  25. Adapted regularization parameters RMS: 6,51 cm nmax = 240

  26. Uniform regularization parameter [cm] RMS (uniform): 8,98 cm nmax = 240

  27. Adapted regularization parameters [cm] RMS (uniform): 8,98 cm nmax = 240 RMS (adapted): 8,65 cm

  28. signal error reference error combination Adapted regularization parameters RMS: 6,51 cm nmax = 240

  29. Kruste Mantel Topographic-isostatic models Flexible tool for the combination with different kinds of prior information (global and regional) Previous test: combination with satellite data (GRACE) and global terrestrial data Next test: combination with gravity field signal derived from topographic – isostatic models

  30. Topographic-isostatic models EGM96 uncompensated topography Pratt-Hayford

  31. Without consideration of topography [cm] RMS (no topo): 10,42 cm nmax = 240

  32. Pratt-Hayford, adapted regularization [cm] RMS (no topo): 10,42 cm nmax = 240 RMS (P.-H.): 9,12 cm

  33. Summary and outlook Flexible tool for the combination with different kinds of prior information (global and regional) Improvement of the solution by regionally adapted regularization is possible => further refinement of the regularization areas Multiscale analysis => hierarchical splines, wavelets => timevariable, regional gravityfield (GRACE) GOCE real data analysis

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