esa living planet symposium, bergen, 29.6.2010 t. gruber, c. ackermann, t. fecher, m. heinze...

ESA Living Planet Symposium, Bergen, 29.6.2010

T. Gruber, C. Ackermann, T. Fecher, M. HeinzeInstitut für Astronomische und Physikalische Geodäsie (IAPG)

Technische Universität München

P. VisserDepartment of Earth Observation and Space Systems (DEOS)

Delft University of Technology

Validation of GOCE Gravity Field Models

and Precise Science Orbits


What is Validation ?

Check Plausibility of Products, Data, Algorithms etc. Why plausibility and not a real quality check?

We want to determine the quality of something, which is better than everything we ever had before!

For this we need tools to test plausibility. What are such tools?

(1) Look on error estimates,

(2) Compare solutions,

(3) Compare to independent (hopefully better) information.

(4) Others


Example for Plausability – Role of Reference Data


Outline of Talk

1. GOCE Orbit Validationa) Compare Orbit Positions and Velocities from different Solutions

b) Residuals to independent Observations (e.g. SLR)

2. GOCE Gravity Field Validationa) Results of Least-Squares Adjustment: Signals and Errors

b) Error Propagation (Variances & Co-variances)

c) Orbit Residuals

d) Geoid Comparisons

e) Sea Surface Topography (Level 3) (not shown here)


GOCE Orbit Validation – Product Overview

Identifier Description

SST_PSO_2 Precise Science Orbits (reduced dynamic and kinematic): GOCE precise science orbits final product Quality report for precise orbits

Kinematic Orbit GPS time in [sec]X,Y,Z position in [m] in Earth fixed frameClock correctionStandard deviation of position and clockVariance-covariance matrix for positions (over 9 Epochs)

Reduced Dynamic Orbit

GPS time in [sec]X,Y,Z position in [m] in Earth fixed frameX,Y,Z velocity in [m/sec] in Earth fixed frameStandard deviation of position and clock

Rotation Matrix from EFRF to IRF

GPS time in [sec]Quaternions (4) describing rotation angles

Detailed Content


GOCE Orbit Validation – SLR Residuals

Range residuals between computed range from SLR station to satellite position from reduced-dynamic orbit and observed range with laser system [mm]

Statistic: reduced–dynamic orbit: mean = 8.75 mm, RMS = 20.52 mm


GOCE Orbit Validation – SLR Residuals

Range residuals between computed range from SLR station to satellite position from kinematic orbit and observed range with laser system [mm]

Statistic: reduced–dynamic orbit: mean = 8.75 mm, RMS = 20.52 mm kinematic orbit: mean = 8.83 mm, RMS = 22.25 mm


GOCE Gravity Field Validation – Product Overview

Identifier Description

EGM_GOC_2 Gravity Field Model: Final GOCE Earth gravity field model as spherical harmonic series

including error estimates. Grids of geoid heights, gravity anomalies and deflections of the

vertical computed from final GOCE Earth gravity field model. Grid of propagated geoid height error estimates (variances) Quality report for GOCE gravity field model

EGM_GVC_2 Gravity Field Error Structure: Complete variance-covariance matrix of final GOCE Earth gravity field

model


GOCE Gravity Field Validation – Definition of Models

Direct Approach – DIR

Start with a state-of-the-art combined gravity field model (GRACE + terrestrial data + altimetry) and use GOCE reduced-dynamic orbits and gradiometry as observation data set.

Three independent preliminary GOCE Gravity Field Solutions have been computed from 2 months of data focusing on different approaches & goals !

Time-Wise Approach – TIM

Start with zero knowledge and only use GOCE kinematic orbits and gradiometry as observation data set.

Space-Wise Approach – SPW

Start with a-priori knowledge for long wavelengths and use GOCE kinematic orbits and gradiometry as observation data set.


GOCE Gravity Field Validation – Signal

Signal Degree Variances (Square Root) in Terms of Geoid Height

Signal power at high degrees shows Impact of a-priori information depending on what type of information has been used.


GOCE Gravity Field Validation – Signal & Errors

DIR

SPW

TIM

Number of significant Digits:

Log10(Signal / Error)

• Significance up to d/o 170• A-propri information defines mapping

of polar gap to spectral bevaviour.• A-priori information defines

significance for high degrees.


GOCE Gravity Field Validation – Signal & Errors

Significant GOCE contribution between d/o 90 and170.

Error Degree Median vs. Mean Signal per Degree:


GOCE Gravity Field Validation – Errors

Cumulative Geoid & Gravity Anomaly Error

With 2 months GOCE we can reach between 4 – 7 cm geoid accuracy at d/o 170 (120km spatial resolution) compared to 9 – 10 cm from a combined GRACE model.


GOCE Gravity Field Validation – Error Propagation

Geoid Variances (SQRT) from propagated Variance-Covariance Matrix

DIR

SPW

TIM

• Polar gaps well recovered.• Similar geoid variance structure for all

models.• Ground track pattern more significant

for DIR and TIM.• Note different colour bar for DIR.


GOCE Gravity Field Validation – Orbit Residuals

• Orbits are recomputed by exchanging gravity field model. • Observation residuals to new orbits are computed. Smaller RMS means better suited

for a satellite.• For altimeter missions in addition radial altimeter crossover differences are

computed.

Polar Satellites:CHAMPGRACE-AGRACE-B

For non-polar Satellites similar results but on a significant lower level.


GOCE Gravity Field Validation – Geoid Comparisons

Principle of Geoid & Sea Surface Topography Comparisons

Topography

Ellipsoid

GeometricHeight

(1) Evaluate global gravity field model with external & independent data. Here we consider heights on land and on ocean.

(2) From GPS positioning and satellite altimetry we get geometric heights on land and sea surface heights on ocean.

Mean OceanSurface

Sea SurfaceHeight



Geoid

GeometricHeight

PhysicalHeight

Sea SurfaceHeight

Geoid Height

Mean OceanSurface

Geoid fromGlobal Model

Topography

Ellipsoid

(3) From levelling we get physical (orthometric) heights on land.

(4) From difference between ellipsoidal and physical heights we get geoid heights on land, which can be compared with geoid heights computed from the global model.

Principle of Geoid & Sea Surface Topography Comparisons



Geoid Comparisons – The Problem of Omission

spectral domain

spat

ial d

omai

n

(from zero frequency to infinity – d/o 0 to infinity)

(fro

m p

oin

t va

lue

s to

blo

ck m

ea

n v

alu

es)

Point observation (e.g. GPS levelling)

N=360 ≈ 30'x30'

N=60 ≈ 3ºx3º

Global Model Solution to D/O 180 - point value

Omission Error

Global Model Solution to D/O 180 – Point Value

N=180 ≈ 2ºx2º

N=180 ≈ 10'x10'

N=180 ≈ 1°x1° N=180 ≈ 1ºx1º

The omission error has to be estimated before comparison of observation and model can be done !



GPS-Levelling Data

Longitude

Longitude

Longitude

Australia

197 points

Germany

675 points

Longitude

Canada 430 points

Longitude

(Veronneau, 2007)(Ihde, 2007)(Johnston, 1998)

Europe (EUVN-DA)

1233 points(Ihde, 2007)

Japan

837 points(Nakagawa, 1999)

USA

5168 points(NGS, 1999)

Longitude



Geoid Differences Germany 675 Points – Cut off d/o = 60 (top) ; d/o = 120 (bottom)

DIR SPWTIM

EIGEN-5S

EIGEN-5C



Geoid Differences Germany 675 Points – Cut off d/o = 160

SPWTIMDIR

EGM2008 Full Resolution(incl. German Gravity Data)

EIGEN-5C ITG-GRACE2010S



RMS Geoid Differences Germany for 675 Points, different cut-off d/o

6 cm

15 cm



RMS Geoid Height Differences Germany for 675 Points, different cut-off d/o



RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o

d/o 30 d/o 40 d/o 50 d/o 60

d/o 70 d/o 80 d/o 90 d/o 100



RMS Geoid Slope Differences Germany for 675 Points, different cut-off d/o

d/o 110 d/o 120

d/o 130 d/o 140

d/o 150 d/o 160 d/o 170 d/o 180


Conclusions (1)

Precise science orbits show high quality 2-3 cm.

Three preliminary gravity field models based on 2 months of GOCE data are validated by different techniques.

Orbit tests for gravity fields are according to expectations (low frequencies better determined from GRACE type missions).

Tests based on estimated errors show significance of GOCE models up to approx. d/o 170. GOCE improves gravity field between d/o 100 and 170.

Estimated geoid error at a level of 7 cm @ d/o 170 and 12 cm @ d/o 200.

External geoid comparisons confirm internal error estimates: 6 cm @ d/o 170 and 15 cm @ d/o 200.

GOCE fields show remarkable good performance for areas, where high quality comparison data are available.

We can expect significantly improved gravity field knowledge in areas, where sparse or poor terrestrial data is available.


Conclusions (2)

How to decide, which model performs best ?

There is no unique answer. In many cases this depends on the application !

Be aware about the characteristics of the preliminary GOCE models in order to choose the right one for your application.

In any case we already can see that GOCE data will provide us new insights to Earth system science.


GOCE Award

Therefore, this year the gravity field cup will awarded to all groups involved in GOCE satellite operations and ground data processing.

They do a great job and we expect even more spectacular results based on more GOCE data.

esa living planet symposium, bergen, 29.6.2010 t. gruber, c. ackermann, t. fecher, m. heinze...

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