Mayer-Gürr et al. ESA Living Planet, Bergen
1
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
Mayer-Gürr et al. ESA Living Planet, Bergen
2
27.06.2008
Overview
ITG-Goce:
Global GOCE SGG only solution
ITG-Goce:
Global GOCE SGG only solution
Regional gravity field refinement
GRACE + GOCE + Altimetry
Regional gravity field refinement
GRACE + GOCE + Altimetry
Regional gravity field refinement
GRACE + GOCE
Regional gravity field refinement
GRACE + GOCE
Mayer-Gürr et al. ESA Living Planet, Bergen
3
27.06.2008
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
Mayer-Gürr et al. ESA Living Planet, Bergen
4
27.06.2008
Median degree variances
formal errorsformal errors
signalsignal
Mayer-Gürr et al. ESA Living Planet, Bergen
5
27.06.2008
Median degree variances
formal errorsformal errors
signalsignal
Difference
ITG-Goce –
EIGEN-05c
Difference
ITG-Goce –
EIGEN-05c
Mayer-Gürr et al. ESA Living Planet, Bergen
6
27.06.2008
Median degree variances
formal errorsformal errors
signalsignal
Difference
ITG-Goce –
EIGEN-05c
Difference
ITG-Goce –
EIGEN-05cDifference
ITG-Goce –
ITG-Grace2010s
Difference
ITG-Goce –
ITG-Grace2010s
Mayer-Gürr et al. ESA Living Planet, Bergen
7
27.06.2008
Regional gravity field recovery
Global reference solution Regional refinement
Spherical harmonics Spherical splines
GOCEGOCEGRACEGRACE
Mayer-Gürr et al. ESA Living Planet, Bergen
8
27.06.2008
ITG-Grace2010s gravity anomalies
Mayer-Gürr et al. ESA Living Planet, Bergen
9
27.06.2008
ITG-Grace2010s gravity anomalies
Mayer-Gürr et al. ESA Living Planet, Bergen
10
27.06.2008
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)
Mayer-Gürr et al. ESA Living Planet, Bergen
11
27.06.2008
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)
Mayer-Gürr et al. ESA Living Planet, Bergen
12
27.06.2008
ITG-Grace2010sITG-Grace2010s
Results – gravity anomalies
+
Mayer-Gürr et al. ESA Living Planet, Bergen
13
27.06.2008
Regional gravity field recovery
Global reference solution Regional refinement
Spherical harmonics Spherical splines
GOCEGOCEGRACEGRACE
Mayer-Gürr et al. ESA Living Planet, Bergen
14
27.06.2008
Regional gravity field recovery
Global reference solution Regional refinement
Spherical harmonics Spherical splines
GOCEGOCEGRACEGRACE
AltimetryT/P, ERS 1/2, ...
AltimetryT/P, ERS 1/2, ...
Mayer-Gürr et al. ESA Living Planet, Bergen
15
27.06.2008
Altimetry data(T/P, ERS 1/2, …)
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
Mayer-Gürr et al. ESA Living Planet, Bergen
16
27.06.2008
Altimetry data(T/P, ERS 1/2, …)
Altimetry data(T/P, ERS 1/2, …)
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
Mayer-Gürr et al. ESA Living Planet, Bergen
17
27.06.2008
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
Mayer-Gürr et al. ESA Living Planet, Bergen
18
27.06.2008
Results – gravity anomalies
+ + +
Mayer-Gürr et al. ESA Living Planet, Bergen
19
27.06.2008
Results – mean dynamic topography
Mayer-Gürr et al. ESA Living Planet, Bergen
20
27.06.2008
Results – gravity anomalies
+ + +
Mayer-Gürr et al. ESA Living Planet, Bergen
21
27.06.2008
Results – gravity anomalies
+ +
Mayer-Gürr et al. ESA Living Planet, Bergen
22
27.06.2008
EGM2008EGM2008
Results – gravity anomalies
+ +
Mayer-Gürr et al. ESA Living Planet, Bergen
23
27.06.2008
EGM2008EGM2008
Results – gravity anomalies
+ +
Differences (RMS 8 mGal)Differences (RMS 8 mGal)
Mayer-Gürr et al. ESA Living Planet, Bergen
24
27.06.2008
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)