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TheThe satellitesatellite--onlyonly globalglobal
gravitygravity fieldfield modelmodel GOCO02SGOCO02S
Helmut Goiginger, Daniel Rieser, Torsten Mayer-Guerr
Institute of Theoretical Geodesy and Satellite Geodesy, TU Graz
Roland Pail, Thomas Fecher, Thomas Gruber, Alberta Albertella
Institute of Astronomical and Physical Geodesy, TU München
Andrea Maier, Eduard Höck, Sandro Krauss, Walter Hausleitner, Oliver Baur
Space Research Institute, Austrian Academy of Sciences
Adrian Jäggi, Ulrich Meyer
Astronomical Institute of University of Bern
Jan Martin Brockmann, Wolf-Dieter Schuh , Ina Krasbutter, Jürgen Kusche
Institute of Geodesy and Geoinformation, University of Bonn
2
EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
ObjectivesObjectives and and PrinciplesPrinciples
� Parametrization of model: spherical harmonic series expansion
� Basic equation: combination of consistent normal equation systems
� Optimum solution: variance component estimation
( ) ( ) ( ) ( )[ ]λλϑλϑ mSmCPr
R
R
GMrV
lmlm
l
m
lm
ll
l
sincoscos,,0
1
0
max
+
= ∑∑
=
+
=
( ) ( )......2121
++=++ nnxNN
( ) ( )......22112211
++=++ nwnwxNwNw
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
Data SetsData Sets
Data setGOCO01S
d/o 224
GOCO02S
d/o 250
GOCO02S
#obs. [Mio.]
ITG-Grace2010sd/o 180
7 years
d/o 180
7 years85
GOCE SGG
Satellite gravity gradients
d/o 224
2 months
d/o 250
8 months57
GOCE SST-hl
Sat.-to-sat. tracking in high-low
d/o 110
12 months72
CHAMPd/o 120
8 years63
SLRd/o 5
5 years, 5 sat.2
Kaula Regularization d/o 170-224 d/o 180-250
280
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
GOCE SGG GOCE SGG datadata setset
� gradient analysis:
– determination of observation segments
– outlier detection
– noise handling: estimation of individual filters for realistic stochastic
modelling
� Full normal equation system up to d/o 250 without the use of anyprior gravity information
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
GOCE SGG GOCE SGG datadata setsetE
rror
[mE
/sqrt
(Hz)]
zzV
IndividualIndividual contributionscontributions
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
Individual contributionIndividual contribution
Contribution to
(near-)sectorial coefficients
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
Individual contributionIndividual contribution
� GRACE: dominant up to 120
� GOCE: dominant from 140-220
� Regularization: dominant from 230-250
� very smooth transistions
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
Individual contributionIndividual contributionDegree variances of error estimatesDegree variances of error estimates
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
Cumulative Cumulative geoidgeoid height error height error
estimatesestimatesC
um
ula
tive
ge
oid
he
igh
t e
rro
rs [m
]
11
EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
GeoidGeoid height deviations [m] EGM2008 height deviations [m] EGM2008 –– GOCO01S up to GOCO01S up to d/od/o 180180
12
EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
GeoidGeoid height deviations [m] EGM2008 height deviations [m] EGM2008 –– GOCO02S up to GOCO02S up to d/od/o 180180
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
CovarianceCovariance propagationpropagation to to geoidgeoid heightheight errorserrors [m] up to d/o 180[m] up to d/o 180
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
SurfaceSurface velocitiesvelocities [m/s] [m/s] derivedderived fromfrom MDT (up to d/o 180)MDT (up to d/o 180)
ITG-Grace2010s
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
SurfaceSurface velocitiesvelocities [m/s] [m/s] derivedderived fromfrom MDT (up to d/o 180)MDT (up to d/o 180)
GOCO01S
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
SurfaceSurface velocitiesvelocities [m/s] [m/s] derivedderived fromfrom MDT (up to d/o 180)MDT (up to d/o 180)
GOCO02S
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
RMS of RMS of geoidgeoid heightheight differencesdifferences betweenbetween gravitygravity fieldfield modelsmodels and and
GPSGPS--levelingleveling observationsobservations
11,611,634,913,311,5837Japan
4,46,726,314,26,8675Germany
14,015,730,317,315,4430Canada
d/o 200
10,610,310,510,310,2837Japan
3,54,44,64,54,5675Germany
14,014,514,714,314,4430Canada
d/o 150
10,210,310,210,310,3837Japan
3,83,73,93,93,8675Germany
14,314,414,614,414,4430Canada
d/o 100
σN [cm]
EIGEN-51CTIM2*ITG-Grace2010sGOCO01SGOCO02S#points
*ESA GOCE-only model based on time-wise approach
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EGU General Assembly Vienna, 04.04.2011 GOCO Consortium
The satellite-only global gravity field model GOCO02S
SummarySummary and Outlookand Outlook
� major improvements in areas where only a few and less accurate terrestrial
measurements are available
� continuously increasing availability of GOCE and GRACE data
� further improvements due to extended GOCE mission can be assured
� inclusion of terrestrial data � work in progress
� Project webpage & Downloads (within upcoming weeks)
http://www.itsg.tugraz.at/goco
� International Centre for Global Earth Models webpage:
http://icgem.gfz-potsdam.de/ICGEM