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GOCE Gravity Field Models –Overview, Performance and Impact on Height
SystemsThomas Gruber
Institute of Astronomical & Physical Geodesy (IAPG)Technische Universität München
Tutorial Height and Gravity, Leipzig, 02.06.2015
Tutorial Height and Gravity, Leipzig, 02.06.2015
1. GOCE-based Gravity Field Models Overview Signal Characteristics
2. Performance Analysis Estimated Errors External Validation Geoid Accuracy
4. Summary
Outline
3. GOCE & Height System Overview
Scientific Roadmap
Tutorial Height and Gravity, Leipzig, 02.06.2015
Overview of GOCE ModelsES
A
Rel.
5 G
OCE
Mod
els
Tutorial Height and Gravity, Leipzig, 02.06.2015
Overview of GOCE ModelsG
FZ/C
NES
Oth
erGO
CO
Tutorial Height and Gravity, Leipzig, 02.06.2015
Overview of GOCE ModelsESA Release 5 GOCE Models Characteristics
DIR5 TIM5
Maximum D/O 300 280
GOCE Data Volume 01.11.09-20.10.13; ~3.5 yrs (net) 01.11.09-20.10.13; ~3.5yrs (net)
Gravity Gradients Vxx, Vyy, Vzz, Vxz >400 Mio. Obs. Vxx, Vyy, Vzz, Vxz >439 Mio. Obs.
Gradient Filter Band-pass filter ARMA filter per segment (87)
GOCE SST (GPS) - Short arc approach (d/o 150)
GRACE SST (K-Band) 2003-2012 GRGS RL03 (d/o 130)
-
LAGEOS 1/2 (SLR) 1985-2010, ~25 yrs -
Regularization spherical cap based on GRACE/LAGEOS.Kaula zero constraint (d/o > 180)
Kaula zero constraint (nearzonals and for d/o > 200)
Tutorial Height and Gravity, Leipzig, 02.06.2015
Degree
SQ
RT
Sig
nalD
egre
eV
aria
n ce
inG
e oid
[m]
180 200 220 240 260 2800.02
0.03
0.04
0.05EGM2008Tscherning-RappDIR5TIM1TIM2TIM3TIM4TIM5
Signal Degree Variances (GOCE RL5 vs. earlier Models)
Full Signal Content up to d/o 210-220. Goal was d/o 200
Signal Characteristic
Tutorial Height and Gravity, Leipzig, 02.06.2015
Map Source: Pavlis, N. K., Holmes, S., Kenyon, S., Factor, J. 2012. “The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008).” Journal of Geophysical Research 117
EGM2008 Data Coverage
12.0% of Land
42.9% of Land
45.1% of Land
Signal Characteristic
Tutorial Height and Gravity, Leipzig, 02.06.2015
Signal CharacteristicGOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200)
RMS of Differences in Test Area [mgal]
Gravity Anomalies Signal
Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5
TIM 3.14
DIR 1.07
Tutorial Height and Gravity, Leipzig, 02.06.2015
Signal CharacteristicGOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200)
RMS of Differences in Test Area [mgal]
Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5
TIM 3.14 2.05
DIR 1.07 2.28
Gravity Anomalies Signal
Tutorial Height and Gravity, Leipzig, 02.06.2015
Signal CharacteristicGOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200)
RMS of Differences in Test Area [mgal]
Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5
TIM 3.14 2.05 1.55
DIR 1.07 2.28 1.85
Gravity Anomalies Signal
Tutorial Height and Gravity, Leipzig, 02.06.2015
Signal CharacteristicGOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200)
RMS of Differences in Test Area [mgal]
Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5
TIM 3.14 2.05 1.55 1.03
DIR 1.07 2.28 1.85 1.00
Gravity Anomalies Signal
Tutorial Height and Gravity, Leipzig, 02.06.2015
Signal CharacteristicGOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200)
RMS of Differences in Test Area [mgal]
Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5
TIM 3.14 2.05 1.55 1.03 0.71
DIR 1.07 2.28 1.85 1.00 0.70
Gravity Anomalies Signal
Tutorial Height and Gravity, Leipzig, 02.06.2015
Estimated ErrorsCoefficient Standard Deviations (log10)
GOCE-DIR4GOCE-TIM4
GOCE-TIM5 GOCE-DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Degree
SQ
RT
Sig
nalD
egre
eV
aria
nce
inG
eoid
[m]
0 60 120 180 2400
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08EGM2008DIR5TIM1TIM2TIM3TIM4TIM5
Estimated ErrorsCummulative Geoid Errors from Coefficient Errors
0.8 cm (d/o 200)
3.4 cm (d/o 200)
4.3 cm (d/o 220)
12.5 cm (d/o 280)
1.2 cm (d/o 220)
4.9 cm (d/o 300)
Tutorial Height and Gravity, Leipzig, 02.06.2015
Estimated ErrorsMaps of Geoid Error from VCM Propagation (Full Resolution)
Degree/Order & Area
TIM5[cm]
DIR5[cm]
200 Global
200 Germany
220 Global
220 Germany
Full Global 12.5 4.9
Full Germany 10.0 4.5
Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation)
TIM5
DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Estimated ErrorsMaps of Geoid Error from VCM Propagation (Degree/Order 220)
Degree/Order & Area
TIM5[cm]
DIR5[cm]
200 Global
200 Germany
220 Global 4.3 1.2
220 Germany 2.4 0.8
Full Global 12.5 4.9
Full Germany 10.0 4.5
Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation)
TIM5
DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Estimated ErrorsMaps of Geoid Error from VCM Propagation (Degree/Order 200)
Degree/Order & Area
TIM5[cm]
DIR5[cm]
200 Global 3.4 0.8
200 Germany 1.4 0.5
220 Global 4.3 1.2
220 Germany 2.4 0.8
Full Global 12.5 4.9
Full Germany 10.0 4.5
Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation)
TIM5
DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationGPS Levelling Data for Gravity Field Validation
Map Source: Pavlis, N. K., Holmes, S., Kenyon, S., Factor, J. 2012. “The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008).” Journal of Geophysical Research 117
EGM2008 Data Coverage & Coverage of GPS/Levelling Data
12.0% of Land
42.9% of Land
45.1% of Land
GPS/LEVELLING POINTS
Tutorial Height and Gravity, Leipzig, 02.06.2015
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 2400.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Germany
2.7 cm2.9 cm
Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main
Tutorial Height and Gravity, Leipzig, 02.06.2015
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 2400.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
EGM2008DGM-1SITG-GOCE02SGOGRA02SGOGRA04STIM5DIR5
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Germany
2.7 cm2.9 cm
Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Acknowledgement: GPS levelling data for have been provided for validation purposes by Brazilian Institute of Geography and Statistics - IBGE, Directorate of Geosciences - DGC, Coordination of Geodesy - CGED
Australia
Acknowledgement: GPS levelling data for have been provided for validation purposes by AUSLIG.
Brazil
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.27
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Canada Europe (EUREF EUVN)
Acknowledgement: GPS levelling data for have been provided for validation purposes by National Resources of Canada (NRCan).
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Acknowledgement: GPS levelling data for Japan have been provided for validation purposes by the Japanese Geographical Survey Institute
Greece Japan
Acknowledgement: Access to GPS levelling data for GREECE has been provided by technical University Thesssaloniki.
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 300
0.15
0.2
0.25
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 300
0.1
0.15
0.2
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Acknowledgement: GPS levelling data for have been provided for validation purposes by King Abdulaziz City for Science and Technology KACST.
Saudi Arabia United Kingdom
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.49
0.5
0.51
0.52
0.53
0.54
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 300
0.04
0.06
0.08
0.1
0.12
0.14 EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
USA (2009 Data Set) Finland (EUREF EUVN)
Degree
RM
SG
eoid
Hei
ght D
iffer
ence
[m]
60 120 180 240 3000.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Degree
RM
SG
eoid
Hei
ghtD
iffer
ence
[m]
60 120 180 240 3000.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
EGM2008TIM1TIM2TIM3TIM4TIM5DIR5
Tutorial Height and Gravity, Leipzig, 02.06.2015
Model ValidationRMS of Geoid Differences at GPS-Levelling Points after planar Fit
(Omission Error estimated from EGM2008)
Areas with High Quality GPS/Levelling Data
Area RMS [cm] No. Points
Germany 2.8 675
UK 3.9 177
Netherlands (EUREF) 1.8 15
Sweden (EUREF) 2.6 84
USA2009 - DC 1.9 16
USA2009 – MD 2.4 511
USA2009 - NH 2.6 14
USA2009 - NJ 2.5 326
USA2009 - RI 2.2 29
USA2009 - MN 3.3 4089
Tutorial Height and Gravity, Leipzig, 02.06.2015
What is the GOCE Geoid Accuracy ?
Estimated error from GOCE-DIR5 at D/O 200 in Germany (formal): 0.5 cm
Estimated error from GOCE-TIM5 at D/O 200 in Germany (calibrated basedon gradient residuals): 1.4 cm
Differences at GPS/Levelling Stations in Germany for both models at D/O 200 (after planar fit) using EGM2008 for omission error: 2.8 cm
GPS/Levelling geoid error is composed by: GPS height error: ≈ 1.5 cm Normal height accuracy after planar fit: ≈ 1.5 cm Error of EGM2008 used for omission error: ≈ 1.0 cm Total after error propagation: 2.4 cm
Attempt to derive a realistic error: GOCE geoid error (reverse error propagation) → 1.4 to 1.5 cm
Tutorial Height and Gravity, Leipzig, 02.06.2015
Summary GOCE Models Full signal of GOCE-based satellite-only model up to degree and
order 210-220.
Fit to “quiet” ocean area at a level of 0.7 mgal in terms of gravity anomaly or 2.6 cm in terms of geoid – geoid more sensitive to dynamic ocean topography.
Estimated cumulative geoid error at d/o 200 for Germany, 0.5 and 1.4 cm respectively.
GPS-leveling fits significantly improved wrt. release 4 models (now 2.8 cm RMS in Germany , about 1 cm better than rel. 4).
Estimated absolute geoid error of rel. 5 models at d/o 200 roughly 1.8 cm or better.
Tutorial Height and Gravity, Leipzig, 02.06.2015
GOCE Equipotential Surface (long wavelengths)
Local Vertical Datum (Equipotential Surface)Local Physical Height
True Equipotential Surface (short wavelengths)
Local Geoid Height
GOCE Physical Height
Omission Error
Height Systems - Problem Overview
Vertical Datum A
Vertical Datum C
AC B
Vertical Datum B
GPS Benchmarks
Tide Gauge BenchmarkLevelling Network
GOCE Geoid Height
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Essential Tasks
The geopotential and geoid improvements resulting from GOCE are the basis of a reassessment of global height systems
Diagnosis of existing height systems by comparison with GOCE geoid
Tutorial Height and Gravity, Leipzig, 02.06.2015
110 120 130 140 150 160-40
-35
-30
-25
-20
-15
-10
-1.4 -1.3 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4
Scientific Roadmap – Diagnosis of Height SystemsDiagnosis of existing Height Systems by Comparison of GPS/Levelling with GOCE Geoid
Reference: Long-wavelength errors of the US vertical datum (Wang et al., 2012)
Australian GPS/Levelling vs. GOCE-TIM5 GeoidUS GPS/Levelling vs. GOCE-TIM5 Geoid
Canadian GPS/Levelling vs. GOCE-TIM5 Geoid
220 230 240 250 260 270 280 290 300 31040
50
60
70
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Tutorial Height and Gravity, Leipzig, 02.06.2015
-5 0 542
43
44
45
46
47
48
49
50
51
52
-0.5 -0.4 -0.3 -0.2 -0.1
Scientific Roadmap – Diagnosis of Height SystemsDiagnosis of existing Height Systems by Comparison of GPS/Levelling with GOCE-TIM5
Geoid for some European Countries
France
-6 -4 -2 0 250
51
52
53
54
55
56
57
58
59
-0.1 0 0.1 0.2
5 10 1547
48
49
50
51
52
53
54
55
56
-0.45 -0.35 -0.25
UK Germany
10 15 2036
38
40
42
44
46
48
-0.6 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2
Italy
3 4 5 6 750
50.5
51
51.5
52
52.5
53
53.5
54
-0.3 -0.29 -0.28 -0.27 -0.26 -0.25
Netherlands
40 cm30 cm
25 cm
40 cm
5 cm
Tutorial Height and Gravity, Leipzig, 02.06.2015
GOCE Equipotential Surface (long wavelengths)
Vertical Datum A
Vertical Datum C
AC B
Vertical Datum B
GPS Benchmarks
Tide Gauge BenchmarkLevelling Network Regional Height Reference Surface (Geoid?)
Scientific Roadmap – Diagnosis of Height Systems
GOCE Physical Height
Regional Height
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Diagnosis of Height SystemsDiagnosis of existing Height Systems by Comparison of GPS/Levelling with GOCE-TIM5
- before and after subtracting a regional Correction SurfaceGPS-Lev. Geoid Differences
-6 -4 -2 050
51
52
53
54
55
56
57
58
59
-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
-6 -4 -2 050
51
52
53
54
55
56
57
58
59
-0.1 -0.05 0 0.05 0.1 0.15 0.2
-6 -4 -2 0 250
51
52
53
54
55
56
57
58
59
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
Correction Surface Residual Differences
What causes these systematic differences: GOCE geoid, Levelling or GPS Heights?• GOCE geoid error is below 2 cm globally – cannot be the reason.• Levelling is sensitive to systematic distortions – most likely the main reason. • Observation GPS height error 1-2 cm randomly distributed – cannot be the reason. • But what about the coordinate frames?
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Diagnosis of Height Systems
Impact of Coordinate Frame Transformations on GPS Heights(Study performed by G. Liebsch, BKG)
• GPS and geoid heights need to be in a consistent frame.
• GOCE geoid heights refer to CoM.• GPS heights refer to an ITRFxxxx with a
center of origin which is not consistentto CoM.
• ITRF2008 is known to be close to CoM.• ITRF1989 (ETRF1989) to ITRF2008
offset is (x,y,z): 2.8 - 3.9 - 10.1 cm• 7 parameter Helmert transformation
(plus linear trends) result in heightchange of up to 7 cm in Europe (seefigure).
• When GPS and GOCE geoid heightsare jointly used in GPS-Levelling thisneeds to be taken into account.
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Essential Tasks
The geopotential and geoid improvements resulting from GOCE are the basis of a reassessment of global height systems
Realization of a globally unified height systembut confined to a global set of primary stations (national datum points, fundamentalstations, primary tide gauges, primary clocks).
Global Height System Unification
Diagnosis of existing height systems bycomparison with GOCE geoid (100 km)
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Global Height System Unification
( )A GOCE resi i iN N N N∆ = − +
Observed Geoid Height referring to vertical Datum A
Geoid Height Offset of vertical Datum A wrt. “mean” Geoid.
Geoid height from GOCE modelResidual geoid height (omission)
Ai i iAN h H= −
0AN
GOCEiNresiN
Observation Equation
from spirit levelling referring to height datum A (e.g. tide gauge)
from GNSS positioning referring to a specific ellipsoid
iAH
ih
GOCE resi i iN N N= +
Computed Geoid Height referring to “mean” Geoid
AiN
Geoid0NA
Height System Offset wrt. Geoid
0 ( )AN Mean N= ∆
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Global Height System Unification
per degree from degree (to infinity)
Omission error can be estimated from EGM2008 and/or residual terrain modelling
Omission Error
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Global Height System Unification
0 ( )AN Mean N= ∆GOCE –TIM5 Model truncated at D/O 200
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Global Height System Unification
GOCEGeoid
Australia(Mainland)
-101
England
-34
Germany
-3
-115
USA(1999)
USA(2009)
-11
Greece-72
Japan
-2
Canada-59
Brazil+67-81
+14
GOCE-TIM5 (0-200) &EGM2008 (201-2190)
+4
GOCEGeoid
Australia(Mainland)
-97
England
-34
Germany
+3
-111
USA(1999)
USA(2009)
-15
Greece-67
Japan
+11
Canada
-52
Brazil+63-77
+14
+4
GOCE-TIM5 (0-200)
Results from Rapp (1994) (Bulletin Geodesique 69, p.26-31) based on JGM-2 / OSU91A and Geoid Heights on Doppler Stations.
-76
+4
+72
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Essential Tasks
The geopotential and geoid improvements resulting from GOCE are the basis of a reassessment of global height systems
Realization of a globally unified height systembut confined to a global set of primary stations (national datum points, fundamentalstations, primary tide gauges, primary clocks).
Open Oceans and Coastal Zones
Global Height System Unification
Diagnosis of existing height systems bycomparison with GOCE geoid (100 km)
Realization of a globally consistent model ofmean dynamic ocean topography at tide gauges and at sea (Ocean Levelling).
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Ocean Levelling
Sea level slope at tide gauges along the east coast of North America from • classical geodetic leveling
(top: USA in red, Canada in blue),
• from an ocean circulation model (black) and
• from GNSS-Levelling based on GOCE DIR5 & EGM2008 (bottom: red & blue)
(Study performed by Phil Woodworth, NOC)
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Essential Tasks
The geopotential and geoid improvements resulting from GOCE are the basis of a reassessment of global height systems
Realization of a globally unified height systembut confined to a global set of primary stations (national datum points, fundamentalstations, primary tide gauges, primary clocks).
Open Oceans and Coastal Zones
Global Height System Unification Well Surveyed Areas (Land)
Diagnosis of existing height systems bycomparison with GOCE geoid (100 km)
Realization of a globally consistent model ofmean dynamic ocean topography at tide gauges and at sea.
Regional geoid based on GOCE model. Establishment of national or regional height systems at primary points (first and second order) based on the technique of “GNSS-leveling”.
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Well Surveyed Areas
GOCE EquipotentialSurface (long wavelengths)
True Equipotential Surface(short wavelengths)
True Geoid Height
GNSS Receiver GOCE Geoid Height
h
NGOCE N
Assumptions:
(1) Network of permanent, high quality GNSS stations. Observation of h
(2) GOCE geopotential/geoid model. Determination of NGOCE
(3) Regional gravity and topographic data.
(4) Refined GOCE geoid model leading to a regional geoid. Determination of N
(5) Consistent reference frames for h and NGOCE / N
H
H = h - N
H = h - NGOCE
Omission Error = N - NGOCE
Tutorial Height and Gravity, Leipzig, 02.06.2015
Mean Differences of GOCE TIM5 and GPS-Levelling Geoid Heights & Omission Error from EGM2008 from D/O 181 to 2190
with omission error (signal)w/o omission error (signal)
-1.221-3.729
+0.422-0.840
Guam
+0.493-0.605
Marianas
Samoa Guam & Marianas
Scientific Roadmap – Well Surveyed Areas
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Essential Tasks
The geopotential and geoid improvements resulting from GOCE are the basis of a reassessment of global height systems
Realization of a globally unified height systembut confined to a global set of primary stations (national datum points, fundamentalstations, primary tide gauges, primary clocks).
Open Oceans and Coastal Zones
Global Height System Unification Well Surveyed Areas (Land)
Sparsely Surveyed Areas (Land)
Diagnosis of existing height systems bycomparison with GOCE geoid (100 km)
Realization of a globally consistent model ofmean dynamic ocean topography at tide gauges and at sea.
Establishment of national or regional height systems at primary points (first and second order) based on the technique of “GNSS-leveling”.
Establishment of a master plan:• realization of datum point• first-order GNSS reference points• diagnosis of regional gravity and/or
leveling and/or topographic data base
Tutorial Height and Gravity, Leipzig, 02.06.2015
Scientific Roadmap – Sparsely Surveyed Areas
Model EquipotentialSurfaceModel Geoid Height
GNSS Receiver
h
NModel
H
Height of Mount Everest:h = 8821.47 m (average from GPS and classicaltechniques for snow surface)(Chen, J. et al, 2006, Science in China; doi: 10.1007/s11430-006-0531-1
NGOCE = -26.58 mNEGM = -22.90 m
(GOCE-TIM5 d/o 280)
(EGM2008 d/o 2190)
this leads to heights above sea level:HGOCE = 8848.05 mHEGM = 8844.37 m
Ellipsoidal Height
Height above Sea Level
Large uncertainty in omission errorestimate due to lack of gravimetric data.
NGOCE/EGM = -22.19 m (GOCE-TIM5 d/o 200 & EGM2008 d/o 201-2190)
Model geoid height for H=0
Model geoid height from height anomaly and correction terms (c.f. Rapp, 1997, JoG).
NEGM/Rapp = -28.50 m (EGM2008 d/o 2190)
HEGM/Rapp = 8849.97 mHChen = 8847.93 m (based on local geoid)
Tutorial Height and Gravity, Leipzig, 02.06.2015
Summary Height Systems
The GOCE geoid represents a reference for global and regional heightsystems with unprecedented spatial resolution.
GOCE enables the diagnosis of systematic distortions in existing heightsystems.
GOCE enables global height system unification if the omission error atheight reference stations can be quantified.
The GOCE geoid supports results obtained from ocean models at tidegauges.
GOCE supports GNSS/Levelling.
In well surveyed areas a GOCE based regional geoid and consistentreference frames shall be used.
In sparsely surveyed areas the GOCE geoid in many casesrepresents the best possible reference surface. Data for regional geoid modelling have to be acquired.
Tutorial Height and Gravity, Leipzig, 02.06.2015
Final Remarks on Height Systems
Project results are available at the following web-site:
http://www.goceplushsu.eu