Torsten Mayer-Gürr, Annette Eicker, Judith Schall

Mayer-Gürr et al. ESA Living Planet, Bergen

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27.06.2008

Torsten Mayer-Gürr, Annette Eicker, Judith Schall

Institute of Geodesy and GeoinformationUniversity of Bonn

Regional high resolution geoid and mean sea surface topography

determination by a combination of GOCE, GRACE and altimetry data


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Overview

ITG-Goce:

Global GOCE SGG only solution

ITG-Goce:

Global GOCE SGG only solution

Regional gravity field refinement

GRACE + GOCE + Altimetry


GRACE + GOCE + Altimetry


GRACE + GOCE


GRACE + GOCE


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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


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Median degree variances

formal errorsformal errors

signalsignal


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signalsignal

Difference

ITG-Goce –

EIGEN-05c

Difference

ITG-Goce –

EIGEN-05c


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signalsignal

Difference

ITG-Goce –

EIGEN-05c

Difference

ITG-Goce –

EIGEN-05cDifference

ITG-Goce –

ITG-Grace2010s

Difference

ITG-Goce –

ITG-Grace2010s


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Regional gravity field recovery

Global reference solution Regional refinement

Spherical harmonics Spherical splines

GOCEGOCEGRACEGRACE


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ITG-Grace2010s gravity anomalies


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ITG-Grace2010s gravity anomalies


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Representation of geoid heights

The residual gravity field represented by a linear combination of localizing basis functions

The residual gravity field represented by a linear combination of localizing basis functions

1

( ) ( , )N

i ii

V c

x x xHarmonic SplinesHarmonic Splines

1

2

( , ) ( ) ( )n n

i n nm nm in m n

Rk Y Y

r

x x x x

shape coefficients (expected spectral content)


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Observation equations

Observation equationsObservation 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

0GOCE GOCE

A lx e

I

normal equationsnormal equations

G G

T TG G A A I x A l

GOCE

GRACE field

For the descripition of the theory see Eicker (2006)For the descripition of the theory see Eicker (2006)


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ITG-Grace2010sITG-Grace2010s

Results – gravity anomalies

+


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GOCEGOCEGRACEGRACE


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GOCEGOCEGRACEGRACE

AltimetryT/P, ERS 1/2, ...

AltimetryT/P, ERS 1/2, ...


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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 heightSSH

Sea surface

Geoid

Ellipsoid


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Altimetry

Observation equationObservation equation

MDT

Geoid heightSSH

Sea surface

Geoid

Ellipsoid

),(),(),( iiMDTiiiiSSH hNh

meansea surface

height

geoidheight

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 residual gravity field

2

( ) ( ) ( )n

i n nm nm ii n m n

N c k Y Y

x x xLocalizing basis functions adapted to the

spectral contenent of the MDT

Localizing basis functions adapted to the spectral contenent of the MDT

2

( ) ( ) ( )n

MDT i n nm nm ii n m n

h a s Y Y

x x x


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Observation equations

Complete observation equationsComplete observation equations

Relative weighting of each set of observations by thevariance component estimation method (VCE)

(Koch & Kusche 2001)

Relative weighting of each set of observations by thevariance component estimation method (VCE)

(Koch & Kusche 2001)

0

0

0

0

0 GOCE

SSH

GOCE

MDTAlti

l

h

ey

x

I

I

A

BA Altimetry

GRACE field

apriori (stochastical)information from MDT

GOCE

gravity MDT


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+ + +


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Results – mean dynamic topography


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+ + +


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+ +


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EGM2008EGM2008


+ +


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EGM2008EGM2008


+ +

Differences (RMS 8 mGal)Differences (RMS 8 mGal)


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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)

Geoid Topography

- GOCE improves the gravity fieldcompared to GRACE in the high degrees

- Our first GOCE solution (ITG-Goce) fits better toITG-Grace2010s than to EIGEN-05Cin the medium degrees (n=90…150)

- GOCE improves the gravity fieldcompared to GRACE in the high degrees

- Our first GOCE solution (ITG-Goce) fits better toITG-Grace2010s than to EIGEN-05Cin the medium degrees (n=90…150)

Torsten Mayer-Gürr, Annette Eicker, Judith Schall

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