Illustration ©ESA. Outline 1.Mission Goal 2.Gravity Sensor System 3.Ground Processing 4.Conclusions

Illustration ©ESA

Outline

1. Mission Goal

2. Gravity Sensor System

3. Ground Processing

4. Conclusions

Dynamic Ocean Topography

The Geoid

Equipotential Surface

Reference of Physical Height Systems

Geoid

Topography

Ellipsoid

Mean Ocean Surface

Geometric Height

Physical Height

Sea Surface Height

Geoid Height

Mission Goal

Mission Goal

[mGal]=[10-5 m/s2]

1-2 cm in Geoid corresponding to 1-2 mGal in Gravity

with 100 km spatial Resolution [mGal]=[10-5 m/s2]

Mission Goals1-2 mGal in Gravity [mGal]=[10-5 m/s2]

Illustration ©ESA

-160 0 160 [mGal]

Arctic Gravity Project

Mission GoalsThe Earth Gravity Field (Equipotential Surface)

seen on Ground

The Earth Gravity Field (Equipotential Surface)

seen at Satellite Height

Mission Goals

Observing the Earth Gravity Field from Space

Gravitational Forces: EarthMoon SunPlanets& Indirect Effects

Center of Mass in Free-Fall

The Gravity Sensor System

Non-Gravitational (Surface) Forces:

Atmospheric Drag

Solar Radiation Pressure

Earth Albedo

Test Mass in Center of Mass in Free-Fall

Thrust

Drag-Free in Flight Direction

The Gravity Sensor SystemObserving the Earth Gravity Field with GOCE

Zero-drag satellites or equivalently "drag-free satellites" are satellites where the payload follows a geodesic path through space only affected by gravity and not by non-gravitational forces such as drag of the residual atmosphere, light pressure and solar wind.

Non-Gravitational (Surface) Forces:

Atmospheric Drag

Solar Radiation Pressure

Earth Albedo

Test Mass in Center of Mass in Free-Fall

The Gravity Sensor SystemObserving the Earth Gravity Field with GRACE

The Gravity Sensor SystemKey Features

1. The first Gravity Gradiometer in Space with High Precision Thermal Control

50 cm

Pictures ©ESA



2. Newly developed European Space GPS-Receiver with Geodetic Precision

Pictures ©ESA




3. Very Low Orbit in 260 km Height with Drag Compensation

Illustration ©ESA Picture ©ESA




3. Very Low Orbit 260 km with Drag Compensation

4. Smooth Spacecraft Attitude Control SystemRadial

Along Track

Cross Track

Picture ©ESA

INCOSE 2008 System Engineering for our Planet, Utrecht, The Netherlands, Academic Forum, 17.6.2008




3. Very Low Orbit 260 km with Drag Compensation

4. Smooth Spacecraft Attitude Control System

5. Largest Carbon Construction of a Satellite for Stiffness and Thermal Stability

Pictures ©ESA

The Gravity Sensor SystemGravity Gradiometer – Primary Sensor

Observation

6 Accelerometers measure Accelerations in 3 Directions.

Measurement Accuracy:

10-12 ms-2

Differential Mode Accelerations

By Subtraction of Accelerations along 1 Gradiometer Arm.

Gravity Gradients

Divide differential Accelerations by Arm Length and correct for rotational Accelerations

Common-Mode Accelerations

By Computation of Mean Value of Accelerations along 1 Gradiometer Arm.

Measurement Bandwidth of the Gradiometer: 5mHz bis 0,1 Hz, corresponds to wavelenghths of about 1500 km to 80 km.

The Gravity Sensor SystemGravity Gradiometer – Primary Sensor

The Gravity Sensor SystemSatellite-to-Satellite Tracking – Secondary Sensor

Illustration ©ESA

Step 1:Compare true Orbit with computed Orbit using a- prioiri Gravity Field

Step 2:Analysis of Orbit Perturbations to improve Gravity Field

Computed Orbit

True Orbit

Orbit Perturbation

GPSConstellatio

n

Observation of the low Fequencies

The Gravity Sensor SystemSystem Approach

translational forces

angular forces

star sensors

drag control

*

*

angular control

GPS/GLONASSSST -hl

A B

GRAVITY GRADIOMETER

measures:

gravity gradients

angular

acceleration

common mode acc.Illustration ©ESA

The Gravity Sensor SystemSystem Approach

Ground ProcessingGradiometry

( r)a V r r the linear acceleration of accelerometer proof mass induced by satellite angular accelerations

the centrifugal acceleration of accelerometer proof mass induced by satellite angular rotation

the linear acceleration of accelerometer proof mass induced by the gravity potential

Not taking into account accelerometer bias and scale factors, misalignments, centre of mass displacements, etc.

⎛Vxx

Vxy

Vxz ⎞

Vyy

zx Vzy

V

⎜ Vyx

Vyz ⎟zzV V

⎜ ⎟

⎜ ⎟⎝ ⎠

with

Ground Processing

V Vxx xy xz ⎟

V 0 y za rz yx

⎟⎟ ⎪

⎜ x ⎟

⎜ a

⎟

⎨

⎜ V

V V⎟ ⎜ yx yy yz ⎟

Vzy

0

⎟ ⎬ ⎜ r y z

y

⎟

z x

⎟

x

y⎟ ⎪

⎜ y ⎟0⎝ a z

⎠⎝ V

x

Vzz 2 2 ⎟

⎝

r

y xz z x

z

x y

⎠⎭

⎪

⎟

⎜⎜

⎛ ⎞ ⎞⎜ ⎟

⎪

⎪ ⎜⎪

⎜ ⎜ ⎟ ⎜⎟

⎪

⎜

⎜ ⎜ ⎜⎪

⎜ ⎜

⎟⎟

⎜⎟

⎟⎠ ⎟ ⎪

⎜

⎟

⎜⎜⎝ ⎠⎠⎪

⎩

⎝

Gradiometry

a V r r ( r)⎛ 2 2

x y

2 2

x z

y z

x

z

⎧

⎛

⎞⎫

⎛

⎞⎛⎞

angular ratesangular accelerations

observed accelerations

gravity gradients

offset from CoM

A

A

A3

A4

A6

A2

X5

X 3

X1

X6

X2

X 4

Z1

Z6 Z 5

Z 3

Z 4

Z2

Y1

Y6 Y5

Y3

Y4

Y2

O5

O1

O6

O2

O4

O3

1

5

OGRF

ZGRFYGR

F

Gradiometry

Common-Mode AccelerationsX GRF

1,x 4,x

c,1,4,x

V 2 2 V 2 2 Lx xxx y z xx y z

V 2 2 Vy

z

xx

2 2 0 Lx xx y z

1

2

a a a

L1

2 1

2 2 2 ⎠

4

⎛ ⎞ ⎜ ⎟⎝

Ground Processing

c,1,4, y

c,1,4, x

c,1,4, z

;a

;a

ain analogy

ac,2,5,x ac,2,5, y ac,2,5,x; ;

ac,3,6, yac,3,6,

x

ac,3,6,

z

; ;

A

A

A3

A4

A6

A2

X5

X 3

X1

X6

X2

X 4

Z1

Z6 Z 5

Z 3

Z 4

Z2

Y1

Y6 Y5

Y3

Y4

Y2

O5

O1

O6

O2

O4

O3

1

5

OGRF

X GRF

ZGRFYGR

F

a 1 a a

x

d,1,4,x 1,x 4,x

V 2 2

y

z

V 2 2 Lx 1 x

xx xx y z

2V 22 22 V 2 2

Lx

Lxxx y z xx y z

2L

12 2 2 2 ⎠

4 2

⎛ ⎞ ⎜ ⎟⎝

GradiometryDifferential-Mode Accelerations

a 1 a a V y x z

d,1,4,z

1,z 4,z zxL

2 2

Ground Processing

d ,1,4, y

d ,1,4, x

c,1,4, z

; a ; aa

ad ,2,5,x ad ,2,5,

y

ad ,2,5,

z

; ;

ad ,3,6,

y

ad ,3,6,

x

ad ,3,6,

z

; ;


Correction for Gradiometer Imperfections due to:

scale factors

misalignments

non-orthogonality

Example:

Accelerometer Pair 1-

4

⎛ a

c ,1 4

⎛ a

c ,1 4

⎛ a

c ,1 4

⎛ a

c ,1 4d ,1 4

d ,1 4⎝ a d

,1 4

⎝ a d

,1 4

i j ⎟ M I i j ⎝

a

⎝

a

⎟ M

⎞⎜

⎟⎠

⎞⎞ ⎞⎜ ⎜ ⎜ ⎟

⎠⎠ ⎠

measured accelerations true accelerations measured accelerations

A

A

A3

A4

A6

A2

X5

X 3

X1

X6

X2

X 4

Z1

Z6 Z 5

Z 3

Z 4

Z2

Y1

Y6 Y5

Y3

Y4

Y2

O5

O1

O6

O2

O4

O3

1

5

OGRF

Gradiometry

Angular AccelerationsX GRF

ZGRFYGR

F

Ground Processing

2a - d ,3,6, y -V

2ad ,2,5, z V2

- x yz y z zy y zz yL L

a -d ,3,6, y

ad ,2,5,

zz y

xL L

ad ,1,4,z ad ,3,6,

x

y

Lx Lz

a a d ,1,4, y d ,2,5,

x

Lx

Ly

z

2ad ,1,4,

xV

2 2

y

zxx

Lx

2ad ,2,5, y

V 2 2

x

zyy

Ly

2ad ,3,6, z

V 2 2

x

yzz

Lz

a a d ,1,4, y d ,2,5, x

x yLx Ly

xyV

a a d ,1,4, z d ,3,6, x

xzLx Lz

x zV

a a d ,2,5, z d ,3,6, y

y zLy Lz

zyV

Angular Rate Reconstruction


A

A5

A3

A 4

A6

A2

X5

X

X1

X6

X

X 4

Z1

O6

Y6

Z6

O5

Y5 Z 5

Z 3

Z

Z2

Y1

Y3

Y

Y2

O1

O2

O4

O3

1

2

4 4

3OGRF

X GRF

ZGRFYGRF

Gravitational Gradients

Angular Accelerations from Gradiometer

Noise specification for single accelerometer within MBW (5– 100 mHz) 2e-12 m/s2 /Hz0.5

Low frequency drift (1/f3)

Attitude Quaternions from Star Sensor

Accuracy of attitude measurements< 3 arcsec for the boresight direction< 24 arcsec for rotations about boresight

White noise

0,2 mHz

Kalman Filter with 3 individual

hybridisation frequencies

a a d ,1, 4 , z d ,3,6 ,

x

Lx

L z

y

MBW


Ground Processing

2ad ,1,4,

xV

2 2

y

zxx

Lx

2ad ,2,5, y

V 2 2

x

zyy

Ly

2ad ,3,6, z

V 2 2

x

yzz

Lz

a a d ,1,4, y d ,2,5, x

x yLx Ly

xyV

a a d ,1,4, z d ,3,6, x

xzLx Lz

x zV

a a d ,2,5, z d ,3,6, y

y zLy Lz

zyV

Gradiometry

A

A5

A3

A 4

A6

A2

X5

X 3

X1

X6

X2

X 4

Z1

O6

Y6

Z6

O5

Y5 Z 5

Z 3

Y4 Z 4

Z2

Y1

Y3Y2

O1

O2

O4

O3

1

OGRF

X GRF

ZGRFYGR

F

Gravitational Gradients

FOSFlight Operations

@ ESOC

Commands Telemetry

PDSPayload Data System L0 to L1 Processing

@ ESRIN

HPFHigh-Level Processing

FacilityL1 to L2 Processing

@ EGG-C

Science Data Housekeeping Data

L1 DataL2 Products Monitoring Products

Ancillary Data ILRS

IGS ECMWFOther

Main Contractor

SatelliteAlenia

Housekeeping Data & others

Anillary Data

AncillaryData

RPFReference Planning Facility

@ESRIN

CMFCalibration Monitoring

Facility@ESRIN

Archive& User Service@ESRIN

Reports

Rules

Monitoring Products

L1 & L2Products

Calibr. Rules

Ground ProcessingGround Segment

Ground ProcessingHigh Level Processing Facility

Astronomical Institute, University Berne, Switzerland (AIUB)

Centre Nationale d‘Etudes Spatiales, Toulouse, France (CNES)

Politechnico di Milano, Italy (POLIMI)

PI & Project Management: Institute of Astronomical and Physical Geodesy, Techn. Univ. Munich, Germany (IAPG)

Institute for Navigation and Satellite Geodesy, Graz University of Techn., Austria (TUG)

Institute of Theoretical Geodesy, University Bonn, Germany (ITG)

Institute of Astrodynamics and Satellite Systems, Techn. University Delft, The Netherlands (FAE/A&S)

Project Management: Netherlands Institute for Space Research (SRON)

Institute of Geophysics, University Copenhagen, Denmark (UCPH)

GeoForschungsZentrum Potsdam, Dept. 1 Geodesy and Remote Sensing, Germany (GFZ)

Key Features

• Developped & operated by European GOCE Gravity Consortium (EGG-C)

• EGG-C is a group of European universities & institutes with comple- mentary expertise in gravity field research

• Distributed system: 10 institues in 7 countries

• Independent validation by overlap of expertise

Central Processing FacilityDe- Encoding, Archive, Data Distribution

Scientific Pre-Processing and External Calibration

Orbit Determination (2 Methods)

External Interfaces

GOCE Ground Segment I/F

Gravity Modeling: Direct Approach

Gravity Modeling: Time-wise Approach

Gravity Modeling: Space-wise Approach

Product Validation and Selection of Final Products

Ground ProcessingHigh Level Processing Facility

Central Processing FacilityRolling Archive, De- and Encoding, XML, Aux. Data Archive, Data Distribution

Gravity Modeling Time-wise ApproachQuick-Look and Precise Solutions:•SST: Energy Conservation•SGG: Semi-Anal. & Normals•Combination by Normals

Gravity Modeling Space-wise Approach•SST: Energy Conservation•SGG: Wiener Filtering•Combination by Collocation

Gravity Modeling Direct Approach•SST: Orbit Perturbation•SSG: Normal Equations•Combination by Normals

Scientific Pre-Processingand External Calibration

•Gradiometer External Calibration•Corrections for Temporal Gravity•Data Screening and Data Gaps

Orbit Determination(kinematic and reduced dynamic)•Rapid Science Orbits•Precise Science Orbits

Product Validation and Selection of Final Products•QL-Validation of Gravity Models•Precise Validation of Gravity Field and Orbits

Rapid & Quick Look Processing Off-line Processing Facility

Long Term Archive

Calibration and Monitoring Facility

Payload Data System

External Data:•IGS•IERS•ILRS•ECMWF•others

OIRF,OEFRF

OLNOF

ZLNOFXLNOF

YLNOF

Ground ProcessingGravity Gradient Product Reference Frames

OLORF

OGRF

Ground ProcessingGravity Gradient Products

EGG_NOM_2 Data Content:• GPS Time

• Corrected Gravity Gradients: Vxx, Vyy, Vzz, Vxy, Vxz, Vyz

• Standard Deviation for each Gravity Gradients (estimated)• Flags for each Gravity Gradient• Tidal Correction for each Gravity Gradient (Direct, Solid

Earth, Ocean, Pole Tide)• Non-tidal Correction for each Gravity Gradient• Correction for external Calibration• Inertial Attitude Quaternions

EGG_TRF_2 Data Content:• GPS Time• Location in Latitude, Longitude, Height

• Corrected Gravity Gradients: Vxx, Vyy, Vzz, Vxy, Vxz, Vyz

• Standard Deviation for each GravityGradients (estimated)

• Flags for each Gravity Gradient

Identifier Description

EGG_NOM_2 Gravity Gradients in Instrument System: Externally calibrated and corrected gravity gradients Corrections to gravity gradients for temporal gravity variations Flags for outliers, fill-in gravity gradients for data gaps with flags

EGG_TRF_2 Gravity Gradients in Earth-fixed System: Externally calibrated gravity gradients in Earth fixed reference frame

including error estimates for transformed gradients Transformation parameters to Earth fixed reference frame

Example: Raw Gravity Gradients with Bandpass Filter applied

Ground Processing

Ground ProcessingOrbit Products

RMS of Kinematic vs. Reduced Dynamic Orbit for period 14.5.2009 to 21.6.2009 in Local Orbit System [m]

Radial [m] Along-track [m] Cross-track [m]


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

SST_AUX_2 Non-tidal Time-variable Gravity Field: Spherical harmonic coefficients of non-tidal potential from atmosphere,

ocean and GRACE time series every 6 hours

Ground ProcessingGravity Field Products

From Simulations:

Left: Geoid Height Error

Right: Var- Cov. Matrix (Subset)


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

including error estimates. Target: 1-2 cm / 1 mGal up to degree and order 200 corresponding to 100km spatial resolution.

Grids of geoid heights, gravity anomalies and geoid slopes computed from final GOCE Earth gravity field model including propagated error estimates

Quality report for final GOCE gravity field model

EGM_GVC_2 Gravity Field Error Structure: Variance-covariance matrix of final GOCE Earth gravity field model

Gravity Field Products Spherical harmonic series represents the main result of GOCE. For computation of derived quantities approximations are applied.

Computation point on reference ellipsoid Spherical approximation of fundamental equation of physical

geodesy (approximating real plumb line by geocentric vector) For computing derived quantities on Earth surface use GOCE User

Toolbox together with topography information.

Ground Processing

r

P

a

b

' O

h

rN

Q

S

0 h 0 h T 1

TPΔ g g

2a REF

Δ g T

r

T

1 N 1

NaREF cos

; a REF

Important Documents - See: http://earth.esa.int/GOCE/

Ground Processing

http://earth.esa.int/GOCE/

Conclusions GOCE is designed to improve our knowledge of the Earth

gravity field by an order of magnitude.

From the preliminary analyses we are confident to reach this goal after completion of at least two measurement phases.

It is expected that GOCE will open new views in various Earth science disciplines.

The EGG-C consortium is starting to operationally analyze GOCE data during measurement phases.

It is recommended to potential users to take a look to the available products documentation in order to become familiar.