GOCE Gravity Field Models – Overview, Performance and...

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

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

Overview of GOCE ModelsES

Overview of GOCE ModelsG

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)

Degree

180 200 220 240 260 2800.02

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

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

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

TIM 3.14 2.05

DIR 1.07 2.28

TIM 3.14 2.05 1.55

DIR 1.07 2.28 1.85

TIM 3.14 2.05 1.55 1.03

DIR 1.07 2.28 1.85 1.00

TIM 3.14 2.05 1.55 1.03 0.71

DIR 1.07 2.28 1.85 1.00 0.70

Estimated ErrorsCoefficient Standard Deviations (log10)

GOCE-DIR4GOCE-TIM4

GOCE-TIM5 GOCE-DIR5

Degree

0 60 120 180 2400

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)

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)

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

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

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

Degree

60 120 180 2400.01

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

Degree

60 120 180 2400.01

EGM2008DGM-1SITG-GOCE02SGOGRA02SGOGRA04STIM5DIR5

Germany

2.7 cm2.9 cm

Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main

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

60 120 180 240 3000.17

Degree

60 120 180 240 3000.27

Canada Europe (EUREF EUVN)

Acknowledgement: GPS levelling data for have been provided for validation purposes by National Resources of Canada (NRCan).

Degree

60 120 180 240 3000.08

Degree

60 120 180 240 3000.13

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

60 120 180 240 300

Degree

60 120 180 240 300

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

60 120 180 240 3000.49

Degree

60 120 180 240 300

0.14 EGM2008TIM1TIM2TIM3TIM4TIM5DIR5

USA (2009 Data Set) Finland (EUREF EUVN)

Degree

60 120 180 240 3000.05

Degree

60 120 180 240 3000.06

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

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

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.

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

Vertical Datum B

GPS Benchmarks

Tide Gauge BenchmarkLevelling Network

GOCE Geoid Height

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

110 120 130 140 150 160-40

-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

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

-5 0 542

-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

-0.1 0 0.1 0.2

5 10 1547

-0.45 -0.35 -0.25

UK Germany

10 15 2036

-0.6 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2

3 4 5 6 750

-0.3 -0.29 -0.28 -0.27 -0.26 -0.25

Netherlands

40 cm30 cm

GOCE Equipotential Surface (long wavelengths)

Vertical Datum A

Vertical Datum C

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

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

-0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-6 -4 -2 050

-0.1 -0.05 0 0.05 0.1 0.15 0.2

-6 -4 -2 0 250

-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?

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.

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)

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= −

GOCEiNresiN

Observation Equation

from spirit levelling referring to height datum A (e.g. tide gauge)

from GNSS positioning referring to a specific ellipsoid

GOCE resi i iN N N= +

Computed Geoid Height referring to “mean” Geoid

Geoid0NA

Height System Offset wrt. Geoid

0 ( )AN Mean N= ∆

per degree from degree (to infinity)

Omission error can be estimated from EGM2008 and/or residual terrain modelling

Omission Error

0 ( )AN Mean N= ∆GOCE –TIM5 Model truncated at D/O 200

GOCEGeoid

Australia(Mainland)

England

Germany

USA(1999)

USA(2009)

Greece-72

Canada-59

Brazil+67-81

GOCE-TIM5 (0-200) &EGM2008 (201-2190)

GOCEGeoid

Australia(Mainland)

England

Germany

USA(1999)

USA(2009)

Greece-67

Canada

Brazil+63-77

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.

Open Oceans and Coastal Zones

Global Height System Unification

Realization of a globally consistent model ofmean dynamic ocean topography at tide gauges and at sea (Ocean Levelling).

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)

Global Height System Unification Well Surveyed Areas (Land)

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”.

Scientific Roadmap – Well Surveyed Areas

GOCE EquipotentialSurface (long wavelengths)

True Equipotential Surface(short wavelengths)

True Geoid Height

GNSS Receiver GOCE Geoid Height

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 - N

H = h - NGOCE

Omission Error = N - NGOCE

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

+0.493-0.605

Marianas

Samoa Guam & Marianas

Scientific Roadmap – Well Surveyed Areas

Global Height System Unification Well Surveyed Areas (Land)

Sparsely Surveyed Areas (Land)

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

Scientific Roadmap – Sparsely Surveyed Areas

Model EquipotentialSurfaceModel Geoid Height

GNSS Receiver

NModel

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)

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.

Final Remarks on Height Systems

Project results are available at the following web-site:

http://www.goceplushsu.eu

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