Mayer-Gürr et al.ESA Living Planet, Bergen 1 27.06.2008 Torsten Mayer-Gürr, Annette Eicker, Judith Schall Institute of Geodesy and Geoinformation University.

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Mayer-Gürr et al.ESA Living Planet, Bergen Torsten Mayer-Gürr, Annette Eicker, Judith Schall Institute of Geodesy and Geoinformation University of Bonn Regional high resolution geoid and mean sea surface topography determination by a combination of GOCE, GRACE and altimetry data

Mayer-Gürr et al.ESA Living Planet, Bergen Overview ITG-Goce: Global GOCE SGG only solution ITG-Goce: Global GOCE SGG only solution Regional gravity field refinement GRACE + GOCE + Altimetry Regional gravity field refinement GRACE + GOCE + Altimetry Regional gravity field refinement GRACE + GOCE Regional gravity field refinement GRACE + GOCE

Mayer-Gürr et al.ESA Living Planet, Bergen GOCE data ITG-Goce (preliminary results) 1 month of data: - gradiometer data - star camera data - orbit data Computed with the short arc method: For each short arc (15 min) - full variance covariance - bias parameter for each SGG component - SST contribution is missing yet ITG-Goce (preliminary results) 1 month of data: - gradiometer data - star camera data - orbit data Computed with the short arc method: For each short arc (15 min) - full variance covariance - bias parameter for each SGG component - SST contribution is missing yet

Mayer-Gürr et al.ESA Living Planet, Bergen Median degree variances formal errors signal

Mayer-Gürr et al.ESA Living Planet, Bergen Median degree variances formal errors signal Difference ITG-Goce – EIGEN-05c Difference ITG-Goce – EIGEN-05c

Mayer-Gürr et al.ESA Living Planet, Bergen Median degree variances formal errors signal Difference ITG-Goce – EIGEN-05c Difference ITG-Goce – EIGEN-05c Difference ITG-Goce – ITG-Grace2010s Difference ITG-Goce – ITG-Grace2010s

Mayer-Gürr et al.ESA Living Planet, Bergen Regional gravity field recovery Global reference solution Regional refinement Spherical harmonics Spherical splines GOCE GRACE

Mayer-Gürr et al.ESA Living Planet, Bergen ITG-Grace2010s gravity anomalies

Mayer-Gürr et al.ESA Living Planet, Bergen ITG-Grace2010s gravity anomalies

Mayer-Gürr et al.ESA Living Planet, Bergen Representation of geoid heights The residual gravity field represented by a linear combination of localizing basis functions Harmonic Splines shape coefficients (expected spectral content)

Mayer-Gürr et al.ESA Living Planet, Bergen Observation equations This approach has similarities to: - regularization - combination with spectral weighting - least squares collocation This approach has similarities to: - regularization - combination with spectral weighting - least squares collocation normal equations GOCE GRACE field For the descripition of the theory see Eicker (2006)

Mayer-Gürr et al.ESA Living Planet, Bergen ITG-Grace2010s Results – gravity anomalies +

Mayer-Gürr et al.ESA Living Planet, Bergen Regional gravity field recovery Global reference solution Regional refinement Spherical harmonics Spherical splines GOCE GRACE

Mayer-Gürr et al.ESA Living Planet, Bergen Regional gravity field recovery Global reference solution Regional refinement Spherical harmonics Spherical splines GOCE GRACE Altimetry T/P, ERS 1/2,... Altimetry T/P, ERS 1/2,...

Mayer-Gürr et al.ESA Living Planet, Bergen Altimetry data (T/P, ERS 1/2, …) Altimetry Altimetry can improve the resolution of the GRACE/GOCE geoid. But: Altimeter satellites measures the sea surface height (SSH) and not the geoid height => Combined estimation of geoid and MDT Altimetry can improve the resolution of the GRACE/GOCE geoid. But: Altimeter satellites measures the sea surface height (SSH) and not the geoid height => Combined estimation of geoid and MDT MDT Geoid height SSH Sea surface Geoid Ellipsoid

Mayer-Gürr et al.ESA Living Planet, Bergen Altimetry data (T/P, ERS 1/2, …) Altimetry Observation equation MDT Geoid height SSH Sea surface Geoid Ellipsoid mean sea surface height geoid height mean dynamic topography =+ Localizing basis functions adapted to the spectral contenent of the residual gravity field Localizing basis functions adapted to the spectral contenent of the MDT

Mayer-Gürr et al.ESA Living Planet, Bergen Observation equations Complete observation equations Relative weighting of each set of observations by the variance component estimation method (VCE) (Koch & Kusche 2001) Altimetry GRACE field apriori (stochastical) information from MDT GOCE gravityMDT

Mayer-Gürr et al.ESA Living Planet, Bergen Results – gravity anomalies + + +

Mayer-Gürr et al.ESA Living Planet, Bergen Results – mean dynamic topography

Mayer-Gürr et al.ESA Living Planet, Bergen Results – gravity anomalies + + +

Mayer-Gürr et al.ESA Living Planet, Bergen Results – gravity anomalies + +

Mayer-Gürr et al.ESA Living Planet, Bergen EGM2008 Results – gravity anomalies + +

Mayer-Gürr et al.ESA Living Planet, Bergen EGM2008 Results – gravity anomalies + + Differences (RMS 8 mGal)

Mayer-Gürr et al.ESA Living Planet, Bergen Summary Refinenemt of GRACE + GOCE gravity field with Altimetry (T/P, ERS 1/2,...) leads to: - Regional high resolution Geoid - Estimation of the mean dynamic topography (MDT) Refinenemt of GRACE + GOCE gravity field with Altimetry (T/P, ERS 1/2,...) leads to: - Regional high resolution Geoid - Estimation of the mean dynamic topography (MDT) GeoidTopography -GOCE improves the gravity field compared to GRACE in the high degrees - Our first GOCE solution (ITG-Goce) fits better to ITG-Grace2010s than to EIGEN-05C in the medium degrees (n=90…150) -GOCE improves the gravity field compared to GRACE in the high degrees - Our first GOCE solution (ITG-Goce) fits better to ITG-Grace2010s than to EIGEN-05C in the medium degrees (n=90…150)