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.