1. ESA living planet symposium 2010 - Bergen Combination of GRACE and GOCE in situ data for high resolution regional gravity field modeling M. Schmeer 1, C. Gruber 1, M. Schmidt 2, F. Flechtner 1 1 German Research Centre for Geosciences, Helmoltz Centre Potsdam (GFZ), Germany 2 German Geodetic Research Institut (DGFI), Germnay schmeer@gfz-potsdam.de

2. ESA living planet symposium 2010 - Bergen Outline GRACE in situ observations New method using calibrated K-Band observations Multi-resolution representation Combination of GRACE and GOCE observations for regional application (simulation).

3. ESA living planet symposium 2010 - Bergen Motivation In situ observationsRepresentations Regional Gravity field Modeling

4. ESA living planet symposium 2010 - Bergen GRACE in situ observations Transformation of residual K-Band range rate observations relative to adjusted K-Band range rates from GFZ GRACE L2 processing into residual potential differences by simplified relation (Jekeli 1999): Residual K-Band observations from GFZ processing-chain (EPOS-OC) for monthly GRACE solutions by applying reductions for: static gravity field (EIGEN-4C/EIGEN-5C) ocean and atmospheric mass variations (AOD) third body attractions ocean and solid earth tides

5. ESA living planet symposium 2010 - Bergen GRACE in situ observations GRACE L2 solution Using calibrated K- Band observations Disturbing potential differences [m 2 /s 2 ] across Africa and Europe relative to EIGEN-4C Correlation between GRACE L2 and method using calibrated K-Band observations > 0.80

6. ESA living planet symposium 2010 - Bergen Theory of Multi-resolution Representation (MRR)

7. ESA living planet symposium 2010 - Bergen Multi-resolution Representation Multi-resolution representation (MRR) splits an input signal into detail signals related to specific resolution levels, i.e., frequency bands: the higher the level the finer the spatial-temporal structures. Modeling the spatial behavior of the gravity field by means of spherical scaling and wavelet functions, i.e., maintaining relation to spherical harmonics. Example based on Blackman scaling function. (Schmidt et al., 2007)

8. ESA living planet symposium 2010 - Bergen Results from MRR Mass distributions [EWH] from regional gravity modeling using calibrated K-Band observations due to EIGEN-4C for Jan. 2008 MRR up to detail level i = 4 → spatial resolution comparable to spherical harmonics d/o = 60

9. ESA living planet symposium 2010 - Bergen January 2008 March 2008 Results from MRR Differences between GRACE L2 solution and method using calibrated K-Band observations. characteristic patterns (stripes) residual signal level decreasing (RL04 → RL05) spherical scaling function = optimal filter Mass differences [EWH] between GRACE L2 solution (left: GRACE RL04 standards; right: GRACE RL05 standards) and method using calibrated K-Band observations.

10. ESA living planet symposium 2010 - Bergen Inversion of observations into discrete values of geopotential Integral inversion based on scalar-valued integral kernels (locally extended) allows for evaluation of discrete values of gravitational functionals at a geocentric sphere. Integral inversion of GRACE data (Novák 2007) GRACE: scalar-valued Abel-Poisson kernel function GOCE: second order Abel-Poisson kernel function (non-scalar)

11. ESA living planet symposium 2010 - Bergen Integral Inversion Mutltivariate Gauss-Markov model Numerical simulation computation of residual observations from L2 models (EIGEN5C – EGM96) introduction of spherical cap definition of different zones (far and near zones) calculation of normal equations, regularization superposition of GRACE and GOCE equation system, inversion With observation vector I for combined observations from GRACE and GOCE For real data: variance components estimation, high-pass filtering

12. ESA living planet symposium 2010 - Bergen Results: GRACE and GOCE-only Simulated gravity field recovery (geoid height residuals) for GRACE (left) and GOCE (right) surrounded by low-resolution FAR-zone in [m] Regional gravity field recovery from GRACE and GOCE separately due to their spectral behaviour.

13. ESA living planet symposium 2010 - Bergen Results: Combination GRACE and GOCE Reproduction of residual signal by combination of GRACE and GOCE

14. ESA living planet symposium 2010 - Bergen Conclusion GRACE: Regional gravity field modeling using calibrated K- Band observations (residuals). Differences between GRACE L2 und regional gravity field modeling reflecting in characteristic patterns (stripes). Optimal filtering due to application of spherical scaling functions (MRR). Validation with external data outstanding. Combination of GRACE and GOCE: Integral inversion. GRACE and GOCE spectral complementary. Complementary coverage (e.g. Antarctica)