1. GOCE ITALY scientific tasks and first results Fernando Sansò and the GOCE Italy group

2. General Purpose A research project supported by ASI to study scientific applications of GOCE solutions to Earth sciences and engineering, in particular intermediary products of the space-wise solution.

3. A Scientific conjecture In the “corners” of the space-wise solution (grids of gradients at satellite altitude) there is more information, in particular locally, than what can be expressed in terms of a global truncated spherical harmonics expansion.

4. Local applications with GOCE data Geoid ondulation errors of Piemonte (Italy) using ground Δg (on the right) plus GOCE T rr (on the left)

5. Local applications with GOCE data Mean dynamic sea surface topography (MDSST) using ground Δg, N from altimetry plus GOCE T rr and T

6. Solid Earth signal in Gravity Data The static gravity together with the dynamic component allows us to better constrain the Earth model for PGR simulation.  Gal/yr An example of time variable gravity Post Glacial Rebound (PGR) fingerprint

7. Solid Earth signal in Gravity Data Some examples of static gravity PGR fingerprint By changing Earth parameters, in particular mantle viscosity, we get different patterns for the PGR fingerprint in the static gravity.

8. Targets and Structure of GOCE Italy 1 PoliMi 1 PoliMi 2 UniMi 2 UniMi 3 UniPd 3 UniPd 4 OGS 4 OGS 5 ALTEC 5 ALTEC 6 UniTs 6 UniTs The GOCE POD recomputed The GOCE POD recomputed Solid earth dynamics: analysis of direct signals Solid earth dynamics: analysis of direct signals Global gravity field Global gravity field Very local geoids for engineering and civil protection (test area Piemonte) Very local geoids for engineering and civil protection (test area Piemonte) Archive of geological signals in GOCE observable Archive of geological signals in GOCE observable Local gravity field Local gravity field GOCE and Post glacial rebound GOCE and Post glacial rebound Flows of salt and temperature through straits (test area Mediterranean) Flows of salt and temperature through straits (test area Mediterranean) A GOCE toolbox A GOCE toolbox Interpretation for case studies South America Interpretation for case studies South America Galileian Plus: Project management and engineering support GOCE marine geoid and geostrophic currents Best tidal model for correction of GOCE data

9. GOCE Italy website

10. First results already presented Here we concentrate only on one of the problems we want to tackle within the GOCE-Italy project: Combination of the GOCE model with an existing Global Gravity Model (e.g. EGM 08)

11. Philosophy of the space-wise approach At satellite level, apply the Wiener Orbital Filter to damp measurement noise and shorten the timewise correlation length. At satellite level (or little below) predict grids of T rr and T by collocation on a sphere. T rr Orbit

12. The final result is estimate of the coefficients estimate of the (full) covariance function Harmonic analysis of the grid at satellite level Monte Carlo tricks, empirical adjustments and iterations! Philosophy of the space-wise approach

13. The combination procedure The target is: Combine with assuming to be block diagonal (by orders). The problems are: is too large to be inverted exactly (also a problem of conditioning of Monte Carlo approximation); but fortunately it is almost block diagonal; we do not have a “normal matrix” for GOCE data, while has a known “normal matrix”

14. The combination procedure The solution is in principal trivial: apply least squares to where is the projector on the coefficients up to the maximum degree of GOCE, and with the solution in the updating form:

15. The problem is computability Remember: dimension of full but with prevailing blocks ≠0

16. The problem is computability Remember: dimension of block diagonal. 0 0 By orders

17. Reordering of the unknowns Always by order… but first 1, than 2, than 3 Reordered covariance matrix of the model T M 1 2 3 213

18. Reordering of the unknowns Note that: A G is a block diagonal matrix AGAG A GM A MG AMAM So the numerical problem becomes: find such that block diagonal and compute

19. Expected results Note that: in this way all coefficients with |m|≤ n ≤ N G and 0 ≤|m|≤ N s are corrected, in particular also those of area 2. -N G NGNG If we disregard the non-diagonal part of C G (i.e. R G ) then only 1 will be corrected!

20. Expected results In a low degree simulation with a “realistic” C G we can see the effects of changes in error variances for coefficients in area 2 due to the non diagonal part of C G

21. And then… …all the rest of the never ending story.