1. Die Satellitenmission GOCE der ESA
Eine Herausforderung an
Mathematik, Numerik und Informatik
H. Sünkel
Institut für Geodäsie
Technische Universität Graz
und
Institut für Weltraumforschung
Österreichische Akademie der Wissenschaften

2. Galilei - Newton - Einstein
Gravitation
Space-time
„Mass tells space-time
how to curve
and space-time tells mass
how to move“.
Mass
Gravity = Gravitation + Rotation

3. Gravity in control of our daily life
Shape of the Earth‘s surface
Distribution of land and water on Earth
Speed of processes inside, on and outside the Earth
Density and constitution of the Earth‘s atmosphere
Biological processes
Growth of plants
Anatomy and physiology of men and animals
Motion of living organism
Architecture of buildings
Mechanical design and structure of machines and vehicles
Gravity scales life in space and time

4. A primitive Earth model
Crust
Radial-symmetric,
not rotating, static
mass distribution
Upper mantle
Lower mantle
Core
Radial-symmetric,
static gravity field

5. Gravity anomalies due to mass anomalies
Tectonic processes (Lithosphere)
Coupling Mantle - Core
Rheology
Mantle convection

6. The dual role of the gravity field
yr Time Scales yr
Volcanic activities
Ice Sheet Melting
Ocean circulation & heat transport
Post-glacial rebound
Sea level change

7. Gravitational potential
Turning inside out
mass
Gravitational potential
shape ?
Geoid

8. The gravitational potential
Properties of the gravitational potential:
is harmonic outside the Earth:
decreases to zero towards infinity
belongs to an infinite dimensional space
Consequence: is represented by a linear combination of
harmonic functions (= solutions of )

9. The gravity potential Gravitational potential ( )
Rotational potential ( )
Gravity potential ( )
Unique „global horizontal“ surface
of constant gravity potential ( )
at „mean“ sea level: geoid
Global reference surface for „orthometric
height“
Unique „local vertical“
Reference direction for „local-horizontal
reference system“

10. Surface gravity: incomplete data coverage
gravdensBGI.gif
Surface gravity: incomplete data coverage

11. POD for gravity field recovery
Satellite orbit
The idea: ?
Mass distribution
Gravitational field

12. POD for gravity field recovery
Equation of motion, defined in a space-fixed
geocentric reference system
free fall (around the Earth) =
Satellite motion due to surface forces
Satellite orbit as a function of gravitational
field parameters
Reference gravitational field controlled by
parameters
Reference satellite orbit as a function of
gravitational field parameters

13. POD for gravity field recovery
Principle:
Real orbit from satellite tracking
Reference orbit based on a priori
gravitational field
Residual harmonic coefficients
unknowns
Functional relation

14. POD for gravity field recovery
Pseudo-observations
Design matrix from partials
LSA
Observation residuals
Harmonic coefficient
(parameter) residuals

15. The Earth’s gravitational field: models
lmax
JGM3 lmax = 70
OSU91a lmax = 360
EGM96 lmax = 360
l m
e e e e e e e e e e e e

16. Open problems
Solid Earth Physics anomalous density structure of lithosphere and upper mantle
Oceanography quasi-stationary dynamic ocean topography
Sea Level Change
Glaciology ice sheet balance
Geodesy unification of height systems, levelling by GPS, inertial navigation,
orbit prediction

17. Accuracy Now: Required:
Gravity field: current knowledge
The geoid: a surface of constant gravity potential at zero level
Offset from
reference
ellipsoid:
Accuracy
Now:
+ 100 m
Required:
0 m
- 100 m

18. Gravity field exploration from space
3 Mission scenarios:
1. Satellite-to-Satellite Tracking in high-low mode
SST - hl
2. Satellite-to-Satellite Tracking in low-low mode
SST - ll
3. Satellite Gravity Gradiometry
SGG

19. Gravity Field Satellite Missions

20. Love affairs with body Earth (... “move your body close to mine”)
CHAMP (2000)
GRACE (2002)
GOCE (2006)

21. CHAllenging Minisatellite Payload
The CHAMP mission: spacecraft
CHAllenging
Minisatellite
Payload

22. The CHAMP Mission: SST - hl
sst_hl.eps
The CHAMP Mission: SST - hl
GPS - satellites
SST - hl
CHAMP
2000
3-D accelerometer
Earth
mass
anomaly

23. The CHAMP mission: objectives
Earth‘s gravity field
and its temporal variations
Gravity Field Model „Eigen 1S“
Geostrophic currents

24. The CHAMP mission: objectives
Earth‘s magnetic field
and its temporal variations

25. The CHAMP mission: objectives
Earth‘s atmosphere and ionosphere
and temporal variations

26. The CHAMP mission: payload
STAR accelerometer
Laser retro-reflector
Electrostatic STAR Accelerometer
GPS Receiver TRSR-2
Laser Retro Reflector
Fluxgate Magnetometer
Overhauser Magnetometer
Advanced Stellar Compass
Digital Ion Drift Meter
Fluxgate Magnetometer
Overhauser Magnetometer

27. The CHAMP mission:spacecraft
front side view
rear side view

28. The CHAMP mission: launch & orbit
Launch: July 15, 2000, Cosmodrome Plesetsk
almost circular orbit: e = 0.004
near polar orbit: i = 87°
initial altitude: 454 km
satellite lifetime: 5 years
COSMOS launch vehicle

29. The CHAMP mission: altitude

30. The GRACE Mission

31. The GRACE Mission: SST-hl and SST-ll combined
sst_ll.eps
The GRACE Mission: SST-hl and SST-ll combined
GPS - satellites
SST - ll
SST - hl
GRACE
2002
Earth
mass
anomaly

32. The GRACE Mission: constellation
Two satellites following each other on the same orbital track
Position and velocity of the satellites are measured using onboard GPS antennae
Interconnected by a K-band microwave link
S-band radio frequencies used for communication with ground stations

33. The GRACE Mission: constellation

34. The GRACE Mission: payload
K-Band Ranging System (KBR)
Accelerometer (ACC)
GPS Space Receiver (GPS)
Laser Retro-Reflector (LRR)
Star Camera Assembly (SCA)
Coarse Earth and Sun Sensor (CES)
Ultra Stable Oscillator (USO)
Center of Mass Trim Assembly (CMT)

35. The GRACE Mission: spacecraft structure

36. The GRACE Mission: launch & orbit
Launch: March 17, 2002, Cosmodrome Plesetsk
almost circular orbit: e < 0.005
near polar orbit: i = 89°
initial altitude: km
satellite system lifetime: 5 years

37. The CHAMP mission: altitude

38. Gravity Field and Steady-state
The GOCE Mission
Gravity Field and Steady-state
Ocean
Circulation
Explorer

39. Project scientist (ESA) and
The GOCE mission: team structure
GOCE Project Team
GOCE Industry Team
GOCE - MAG
Project scientist (ESA) and
members
European GOCE Gravity
Consortium (EGG-C)
Team leader
and Task leaders
Science Data Use:
Solid Earth
Science Data Use:
Oceanography
Science Data Use:
Ice
Science Data Use:
Geodesy
Science Data Use:
Sea Level

40. The GOCE Mission: SST-hl and SGG combined
gradiometry.eps
The GOCE Mission: SST-hl and SGG combined
GPS - satellites
SST - hl
GOCE
2006
SGG
Earth
mass
anomaly

41. The GOCE mission: launch & orbit
Launch: Feb. 2006, Cosmodrome Plesetsk (62.7° N, 40.3° E)
Total satellite mass: 800 kg
Orbit inclination: i = 97°
Injection altitude: 270 km
Passive descent from 270 km to 250 km
Altitude controlled by ion thrusters
Satellite lifetime: 2 years

42. GOCE: mission parameters
Mission duration: months
Commission phase: 3 months
Phase 1: 6 months
Hibernation phase: 5 months
Phase 2: 6 months
Design orbit altitude:
Phase 1: km
Phase 2: km
Orbit characteristics:
Dawn-dusk sun-synchronous, Inclination: 96.5°
Injection eccentricity: 0.000
phase 1: two months repeat, phase 2: eventually drifting ground track
Maximum air drag during gradiometer operation: 0.3 mGal / in mbw

43. The GOCE mission: timeline

44. The GOCE mission: spacecraft design
Scientific payload:
3-axis gravity gradiometer
GPS receiver
SLR retroreflector
Star tracker
center of mass
Auxiliary equipment:
Ion thrusters
FEEPS
Solar panels (8 m²)
On board computer
Telemetry
S 44

45. The GOCE mission: gravity gradiometerZ
Gravity gradiometer:
3-axis
mbw: mHz
Precision: < 1 mE Y X
1 mE: curvature radius of equipotential surface of 10 Mill. km !

46. The GOCE mission: gradiometer noise
5 mHz
mbw
100 mHz
Specified noise psd
3 mE / Hz
specified
(Predicted per-
formance curve
derived from a
combination of
analysis and test)
Predicted noise psd

47. The GOCE mission: gravity gradiometry
Accelerometer equations:
Common mode:
Differential mode:
V ... gravitational tensor

48. The GOCE mission: gravity gradiometry
Measurement tensor:
Attitude:
Gravitational tensor:

49. The GOCE mission: attitude & drag control
Ion thruster
(for drag compensation)
Micro thruster
(for attitude control)
Field emission electric
propulsion system (FEEPS)
Gas: Indium (Austrian system)
Caesium (Italian system)
Gas: Xenon
thrust level: mN
thrust level: mN

50. The GOCE mission: observation sensitivities
SST (hi-lo):
SGG:
Orbit perturbations
Gradiometer data
Sat. alt. smoother
Sat. alt. smoother
SST amplifier
SGG amplifier

51. The GOCE mission: data processing
Gravitational potential as a function of position P:
parameters
Gravity gradiometer observations:
observations
LSA

52. The GOCE mission: gravity field recovery
vik.bw.eps
The GOCE mission: gravity field recovery
observations
parameters

53. The GOCE mission: processing methods
Spacewise
Timewise
Otherwise

54. The GOCE mission: processing methods
The Runner: Semi-Analytic approach (SA)
Approximative, iterative algorithm: works partially in the frequency domain (FFT) and uses the dominant block-diagonal structure of the normal equations
The Progressive Worker: Parallel pcgma package
Approximative algorithm, using a block-diagonal preconditioner as a first guess (initialization step) and applying iteratively a conjugate gradient method
The Real Life: Distributed Non-approximative Adjustment (DNA)
Strict solution of the normal equation system
Flexible, but enormous computation requirements

55. The GOCE mission: spacewise processing
Potential regarded as a function of space position P
SGG observations regarded as a function of
space position P

56. The GOCE mission: spacewise processing
LSA
SGG observ.
Harmonic coeff.
Iterative
Direct
serial
parallel
serial
parallel

57. The GOCE mission: spacewise processing
Preconditioned Conjugated Gradient Method (PCGM)
Iterative solution
Preconditioning by appropriate representative matrix
Inclusion of prior information possible
Extended by frequency selective filters to account for
coloured noise SGG data
Serial and parallel versions operational
Successfully tested up to degree 300 on different platforms
(DEC-Alpha, SGI Origin, CRAY T3E, Graz Beowulf Cluster)

58. The GOCE mission: spacewise processing
Distributed Non-approximative Adjustment (DNA)
Direct solution
Inclusion of prior information possible
Inclusion of non-gravitational parameters (non-conservative
force model, calibration parameters, ...)
Extended by frequency selective filters to account for
coloured noise SGG data
Parallel versions successfully tested up to degree 180 on the
Graz Beowulf Cluster

59. The GOCE mission: timewise processing
Potential regarded as a function of time t
SGG observations regarded as a function of time

60. The GOCE mission: timewise processing
Sensitivity coeff.
Harmonic coeff.
Lumped coeff.
In case of a periodic SGG time series:
Lumped coefficients = Fourier coefficients of SGG time series
Lumped coefficients considered as pseudo observations in
LSA for the estimation of the harmonic coefficients
Ideally the normal matrix has block diagonal structure
In reality it is (strongly) block diagonally dominant
Iteration required due to sun-synchronous orbit and varying
orbit parameters

61. The gravitational potential and derived quantities
100 km resolution requires L = km / 100 km = 200
Geoid:
Resolution: 100 km
Accuracy: cm
Gravity anomaly:
Resolution: 100 km
Accuracy: 1 mGal

62. The GOCE mission: performance ( cumulative error )
Goal:
< 10 mm
< 1 mGal

63. The GOCE mission: error spectrum
Slm  order  Clm
EGM spherical harmonic error spectrum

64. Closed loop simulation
Gravity field
Harmonic coeff.
Gradiometer signal
Harmonic analysis
Coloured noise
Observations
Filtering

65. The GOCE mission: closed loop simulation
“Delft data-set”:
29 days repeat orbit
~ 1.5 million observations (SGG diagonal components)
lmax = 180
Size of full normal equation matrix 4.1 GByte
Very different time behaviour of the three methods

66. The GOCE mission: solution time
Near linear speed-up
with additional processing
elements (PE)

67. The GOCE mission: test performance
Solution time:

68. The TU Graz cluster Components and performance
March 2001: TU Graz started to build up a Beowulf cluster
24 Dual-Pentium (866 MHz) PC’s (computing nodes)
1GB RAM / 18 GB local HD
1 Master server PC
1.5 GB RAM
5*73 GB RAID 5
Linux (Redhat, Kernel ) , MPICH, ...
TU Graz cluster outperforms Columbus / Ohio cluster by a factor of 2
Same performance as the CRAY T3E in Columbus / Ohio

69. The TU Graz cluster: future plans (1/2)
HP SC-45 cluster
10 ES45 Alphaserver
4 CPUs each / 1.25 GHz
2 ES45 with 32 GB RAM
8 ES45 with 16 GB RAM
120 GB local hard disks
connected via 16 ports Quadrics switch
Realization: October 2002

70. The TU Graz cluster: future plans (2/2)
System based on Linux
connection between the nodes via Myrinet (Cluster 1)
connection between the nodes via GigaBit Ethernet (Cluster 2)
24 nodes (Cluster 1) 36 nodes (Cluster 2)
Intel / 2.6 GHz CPUs
0.5 GB RAM per CPU
5*73 GB SCSI RAID5
Realization: January 2003

71. Gravity satellite missions: comparison
2 years
5 years
duration
250 km
~450 km
454 km
altitude
96.5°
89.0°
87.3°
inclination
SST-hl/SGG
SST-hl / ll
SST-hl
mode
2006
2002
2000
start
GOCE
GRACE
CHAMP

72. Gravity satellite missions: comparison Accuracy and resolution
70 km
250 km
650 km
resolution
(half wavelength)
< 1 cm
~ 1 cm
accuracy
GOCE
GRACE
CHAMP
Harmonic degree 30 80
300

73. Gravity satellite missions Accuracy and resolution
Kaula
EGM 96
SST - hl
SGG
SST - ll

74. The GOCE mission Ocean topography

75. The GOCE mission Dynamic ocean topography
Navier-Stokes equation
Steady - state flow:
H Sea surface height (SSH)
relative to geoid
x, y ... Local cartesian coordinates
(W-E, S-N)
u, v ... Surface velocity (W-E, S-N)
g Gravity
f Coriolis term

76. Gravity satellite missions Ocean topography signal
Range: -75 to +75 cm
Signal
l = 20
l = 200
l = 80

77. The GOCE mission Mean dynamic ocean topography

78. The GOCE mission Geostrophic current

79. The GOCE mission: geotomography
Propagation of seismic waves
Problem: conversion velocity  density

80. The GOCE mission: solid Earth
Volcanoes, Hot Spots
Spreading
Rifting
Subduction
Orogeny

81. The GOCE mission: surveying

82. Gravity satellite missions: summary
CHAMP
magnetic field determination
temporal variations of the gravity field
GRACE
improved knowledge of the geoid
estimates of time variable components
GOCE
highly precise static geoid determination

83. Gravity satellite missions: benefits
Oceanography:
Absolute ocean circulation
Sea level changes
Ice mass balance
Solid Earth Physics:
Geotomography
Processes in the deep Earth‘s interior
Earthquake prediction
Geodesy:
Unified height datum
GPS levelling
Orbit prediction
Inertial navigation

84. Gravity satellite missions Benefits for geosciences
Ice Sheet Mass Balance
Geodesy
Absolute Ocean
Circulation
Sea Level
Change Studies
Solid Earth Physics
GOCE will cover Theme 1 of ESA‘s Living Planet Programme
(with the exception of the magnetic field part)

85. The End