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GOCE ITALY. scientific tasks and first results. Fernando Sansò and the GOCE Italy group. General Purpose. A research project supported by ASI to study scientific applications of GOCE solutions - PowerPoint PPT Presentation
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GOCE ITALYGOCE ITALYscientific tasks and first resultsscientific tasks and first results
Fernando Sansò and the GOCE Italy group
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.
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.
Local applications with GOCE data
Geoid ondulation errors of Piemonte (Italy) using ground Δg (on the right) plus GOCE Trr (on the left)
Local applications with GOCE data
Mean dynamic sea surface topography (MDSST) using ground Δg, N from altimetry plus GOCE Trr and T
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
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.
Targets and Structure of GOCE Italy
1PoliMi
1PoliMi
2UniMi
2UniMi
3UniPd
3UniPd
4OGS
4OGS
5ALTEC
5ALTEC
6UniTs
6UniTs
The GOCE PODrecomputed
The GOCE PODrecomputed
Solid earth dynamics:analysis of
direct signals
Solid earth dynamics:analysis of
direct signals
Global gravityfield
Global gravityfield
Very localgeoids for
engineering andcivil protection
(test areaPiemonte)
Very localgeoids for
engineering andcivil protection
(test areaPiemonte)
Archiveof geological
signals inGOCE
observable
Archiveof geological
signals inGOCE
observable
Local gravity
field
Local gravity
field
GOCEand
Post glacialrebound
GOCEand
Post glacialrebound
Flows of salt and
temperaturethrough straits
(test area Mediterranean)
Flows of salt and
temperaturethrough straits
(test area Mediterranean)
A GOCEtoolboxA GOCEtoolbox
Interpretationfor
case studiesSouth America
Interpretationfor
case studiesSouth America
Galileian Plus: Project management and engineering supportGalileian Plus: Project management and engineering support
GOCE marine geoid and
geostrophiccurrents
Best tidalmodel for
correction ofGOCE data
GOCE Italy website
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)
T G T M
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 Trr and T by collocation on a sphere.
Trr
Orbit
The final result is
estimate of the coefficients
estimate of the (full) covariance function
Harmonic analysis of the grid at satellite level
Tlm T
Monte Carlo
tricks, empirical adjustments and iterations!
CTT
T̂GCG
Philosophy of the space-wise approach
The combination procedure
T̂G ,CG T̂M ,CM CM
CG
TMDM CM
1
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”
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:
TG T̂ eG CG
TM T̂ eM CM
IG 0
T T TM
T CMT CG CMT 1TG TM
The problem is computability
Remember:
dimension of full but with prevailing blocks
CG BG RG
BG ? RG≠0
≠0
The problem is computability
Remember:
dimension of block diagonal.
0
0
By orders CM
Reordering of the unknowns
Always by order… butfirst 1, than 2, than 3
Reordered covariance matrix of the model TM
1
2
3
21 3
CM
Reordering of the unknowns
Note that:
AG is a block diagonal matrix
CM AG AGM
AMG AM
CMT CMIG0
AGAMG
CMT AG
So the numerical problem becomes:
find such that BG AG RG TG TM block diagonal
and compute T̂ AGAMG
Expected results
Note that:in this way all coefficients with |m|≤ n ≤ NG and 0 ≤|m|
≤ Ns
are corrected, in particular also those of area 2.
-NG NG
If we disregard the
non-diagonal part of CG (i.e.
RG) then only 1 will be
corrected!
Expected results
In a low degree simulation with a “realistic” CG
we can see the effects of changes in error variancesfor coefficients in area 2 due to the non diagonal part of
CG
And then…And then…
……all the rest of all the rest of
the never ending story.the never ending story.
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