Semmering, 2002-10-17 H. SünkelSAG-BGÖ 2002 H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung Österreichische

Semmering, 2002-10-17 H. SünkelSAG-BGÖ 2002

H. Sünkel

Institut für GeodäsieTechnische Universität Graz

undInstitut für Weltraumforschung

Österreichische Akademie der Wissenschaften

Die Satellitenmission GOCE der ESADie Satellitenmission GOCE der ESAEine Herausforderung an

Mathematik, Numerik und Informatik


Galilei - Newton - Einstein

Mass

Gravitation Space-time

Gravity = Gravitation + Rotation

„Mass tells space-time how to curve

and space-time tells masshow to move“.


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 time2...81.9 ms 2...81.9 ms


A primitive Earth model

Core

Lower mantle

Upper mantle

Crust Radial-symmetric,not rotating, staticmass distribution

Radial-symmetric,static gravity field


Mantle convection

Mantle convection

CouplingMantle - Core

CouplingMantle - Core

RheologyRheology

Tectonic processes(Lithosphere)

Tectonic processes(Lithosphere)

Gravity anomalies due to mass anomalies


Post-glacialrebound

Post-glacialrebound

Ocean circulation& heat transport

Ocean circulation& heat transport

Ice SheetMelting

Ice SheetMelting

Sea level changeSea level change

VolcanicactivitiesVolcanicactivities

108 - 106 yr Time Scales 102 - 100 yr108 - 106 yr Time Scales 102 - 100 yr

The dual role of the gravity field


Turning inside out

massmass

shapeshape

Geoid Geoid

Earth

dvlGV 1Earth

dvlGV 1

Gravitational potential


mSmCPr

R

R

GMV lmlm

llm

ll

m

sincos)(cos2

1

0

The gravitational potential

Properties of the gravitational potential:

0 VT1. is harmonic outside the Earth:V

Consequence: is represented by a linear combination of harmonic functions (= solutions of )

3. belongs to an infinite dimensional spaceV

2. decreases to zero towards infinityV

V0 VT


The gravity potential

0.)( WconstPW Unique „global horizontal“ surface of constant gravity potential ( )at „mean“ sea level: geoidGlobal reference surface for „orthometricheight“

0W

)(PV Gravitational potential ( ) Rotational potential ( )Gravity potential ( )

V

)(P)(PW 2/)( 22

PhP W

)(PW Unique „local vertical“Reference direction for „local-horizontalreference system“


gravdensBGI.gifgravdensBGI.gif

Surface gravity: incomplete data coverage


POD for gravity field recovery

Mass distributionMass distribution Gravitational field

Gravitational field

Satellite orbit

Satellite orbit

The idea:

0 Vr



Equation of motion, defined in a space-fixedgeocentric reference systemfree fall (around the Earth)Vr Satellite motion due to surface forces F

=F

),;;,( 00 lmlm SCtrrrr Satellite orbit as a function of gravitational field parameters lmlm SC ,

),( 0000lmlm SCVV Reference gravitational field controlled by

parameters 00 , lmlm SC

),;;,( 0000

00

00lmlm SCtrrrr Reference satellite orbit as a function of

gravitational field parameters 00 , lmlm SC

0



),( 0000lmlm SCrr

Principle:

Real orbit from satellite tracking

Reference orbit based on a priori gravitational field

),(0lmlm SCrrrr

),( lmlm SCrr

0

0

lmlmlm

lmlmlm

SSS

CCC

Residual harmonic coefficientsunknowns

Functional relation


lmlm SC ˆ,ˆ

Harmonic coefficient(parameter) residuals

Observation residualsLSALSA

lmlmiiiT

i SCfzyxr ,,, Pseudo-observations


lmlm

iii

SC

zyxA

,

,,Design matrix from partials

iii zyx ,,


• JGM3 lmax = 70

• OSU91a lmax = 360

• EGM96 lmax = 360

2 0

1

1l

l

mlmlmlm

l

)msin(S)mcos(C)(cosPr

R

R

MG),,r(V

lmax

l m

0 0 0. 0.1 0 0. 0.1 1 0. 0.2 0 -0.48417e-03 0.2 1 0.85718e-12 0.28961e-112 2 0.24382e-05 -0.13999e-053 0 0.95714e-06 0.3 1 0.20297e-05 0.24943e-063 2 0.90465e-06 -0.62044e-063 3 0.72030e-06 0.14147e-05... ... ... ...

lmC lmS

The Earth’s gravitational field: models


• 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

Open problems


Gravity field: current knowledge

The geoid: a surface of constant gravity potential at zero level

+ 100 m

- 100 m

0 m

Offset fromreferenceellipsoid:

m1

cm1

Accuracy

Now:

Required:


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

Gravity field exploration from space



CHAMP (2000)

GRACE (2002)

GOCE (2006)

Love affairs with body Earth(... “move your body close to mine”)


CHAllenging

Minisatellite

Payload

The CHAMP mission: spacecraft


GPS - satellites

Earthmassanomaly

3-D accelerometer

sst_hl.epssst_hl.eps

SST - hl

)msin(S)mcos(C

)(cosPr

R

R

MG),,r(V

nmnm

2n

n

0mnm

1n

)x(VV k

ii

i VVx

a

The CHAMP Mission: SST - hl


Earth‘s gravity field

and its temporal variations

Gravity Field Model „Eigen 1S“ Geostrophic currents

The CHAMP mission: objectives


Earth‘s magnetic field

and its temporal variations



Earth‘s atmosphere and ionosphere

and temporal variations



• Electrostatic STAR Accelerometer• GPS Receiver TRSR-2• Laser Retro Reflector• Fluxgate Magnetometer• Overhauser Magnetometer• Advanced Stellar Compass • Digital Ion Drift Meter

STAR accelerometer

FluxgateMagnetometer

OverhauserMagnetometer

Laser retro-reflector

The CHAMP mission: payload


front side view

rear side view

The CHAMP mission:spacecraft


• 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

The CHAMP mission: launch & orbit


The CHAMP mission: altitude


The GRACE Mission


SST - hl

GPS - satellites

Earthmassanomaly

sst_ll.epssst_ll.eps

SST - ll

)(i)(

i

)(i VV

xa 1

11

)(i)(

i

)(i VV

xa 2

22

j

i)(

j)(

j

)(i

)(i

x

V

xx

VV

12

12

The GRACE Mission: SST-hl and SST-ll combined


• 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

The GRACE Mission: constellation


The GRACE Mission: constellation


• 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)

The GRACE Mission: payload


The GRACE Mission: spacecraft structure


• Launch: March 17, 2002, Cosmodrome Plesetsk• almost circular orbit: e < 0.005• near polar orbit: i = 89°• initial altitude: 485 - 500 km• satellite system lifetime: 5 years

The GRACE Mission: launch & orbit


The CHAMP mission: altitude


Gravity Field and Steady-state

Ocean

Circulation

Explorer

The GOCE Mission


The GOCE mission: team structure

GOCE Project Team GOCE Industry Team

GOCE - MAGProject scientist (ESA) and

members

European GOCE GravityConsortium (EGG-C)

Team leaderand Task leaders

Science Data Use:Solid Earth

Science Data Use:Solid Earth

Science Data Use:Oceanography

Science Data Use:Oceanography

Science Data Use:Ice

Science Data Use:Ice

Science Data Use:Geodesy

Science Data Use:Geodesy

Science Data Use:Sea Level

Science Data Use:Sea Level


SGG

Earthmassanomaly

GPS - satellites

gradiometry.epsgradiometry.eps

SST - hl

ijji

)(j

)(j

)(i

)(i

xV

xx

V

xx

VVlim

j

2

12

12

0

The GOCE Mission: SST-hl and SGG combined


• 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

The GOCE mission: launch & orbit


Mission duration: 20 months– Commission phase: 3 months

– Phase 1: 6 months– Hibernation phase: 5 months – Phase 2: 6 months

Design orbit altitude:– Phase 1: 250 km– Phase 2: 240 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 mbwHz

GOCE: mission parameters


2 5 0 k m

2 4 0 k m

T 0 T 0 + 3 m o n th s T 0 + 9 m o n th s T 0 + 1 4 m o n th s T 0 + 2 0 m o n th s

2 6 0 k m

2 7 0 k m

O rb itA ltitud e

E clip seD ura tio n

5 m in .

1 0 m in .

1 5 m in .

4 3 d 3 5 d3 5 d 1 3 5 d

S pacecra ftC o m m issio n ing

G rad io m ete rC a lib ra tio n

1 .5 1 .5 6 m on th s 4 .5 m o n th s .5 6 m on th s

G rad io m ete rS e t-up andC alib ra tio n

M easu rem en tIn te rrup tio n

F irs t M easu rem en tP hase

S eco nd M easu rem en tP hase

3 0 m in .

2 5 m in .

2 0 m in .

The GOCE mission: timeline


Scientific payload:• 3-axis gravity gradiometer• GPS receiver• SLR retroreflector• Star tracker

Auxiliary equipment:• Ion thrusters• FEEPS• Solar panels (8 m²) • On board computer• Telemetry

S 44

The GOCE mission: spacecraft design

center of mass


Gravity gradiometer:

• 3-axis• mbw: 5 - 100 mHz• Precision: < 1 mE

XY

Z

The GOCE mission: gravity gradiometer

1 mE: curvature radius of equipotential surface of 10 Mill. km !


3 mE / Hz

specified

(Predicted per-

formance curve

derived from a

combination of

analysis and test)

5 mHz 100 mHzmbw

Specified noise psd

Predicted noise psd

The GOCE mission: gradiometer noise


dragfx)]2(V[Ladragfx)]2(V[Ra

Accelerometer equations:

Common mode:

dragLR f

2

aa

x)](V[

2

aa 2LR

Differential mode:

V ... gravitational tensorV ... gravitational tensor

The GOCE mission: gravity gradiometry


Attitude:

d)()t()t(

)(2

1

t

ot

o

T

Gravitational tensor:

x2

aa LR

Measurement tensor:

2T )(2

1V

The GOCE mission: gravity gradiometry


Ion thruster(for drag compensation)

Micro thruster(for attitude control)

Gas: Xenonthrust level: 1 - 20 mN thrust level: 0.0001 - 0.1 mN

The GOCE mission: attitude & drag control

Field emission electric propulsion system (FEEPS)

Gas: Indium (Austrian system)Caesium (Italian system)


The GOCE mission: observation sensitivities

22

22

222

2

2

1

12

1

1

1

123

1

n

lk

n

n

lik

Rr

R

z

y

x l

21

1

11 22

2

2

3

ll

lk

lk

Rr

R

V

V

V l

zz

yy

xx

Orbit perturbations Gradiometer dataSST (hi-lo): SGG:

Sat. alt. smoother Sat. alt. smoother

SST amplifier SGG amplifier


jiij xx

PVPV

)(

)(2

]sincos[

)(cos)(2

1

0

PlmPlm

L

lPlm

l

P

l

m

mSmC

Pr

R

R

GMPV

Gravitational potential as a function of position P:)(PV

The GOCE mission: data processing

Gravity gradiometer observations:

LSALSA100 000 000 observations

100 000parameters


vik.bw.epsvik.bw.eps

yyV

xyVxxV xzV

yzV

zzV

100 000 000 observations

100 000 parameters

The GOCE mission: gravity field recovery


SpacewiseSpacewiseTimewiseTimewise

OtherwiseOtherwise

SpacewiseSpacewiseTimewiseTimewise

OtherwiseOtherwise

The GOCE mission: processing methods


The Real Life: Distributed Non-approximative Adjustment (DNA)

Strict solution of the normal equation system

Flexible, but enormous computation requirements

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


SGG observations regarded as a function of space position P

)P(Vij

]msinSmcosC[

)(cosPr

R

R

GM)P(V

PlmPlm

L

2lPlm

1l

P

l

0m

]msinSmcosC[

)(cosPr

R

R

GM)P(V

PlmPlm

L

2lPlm

1l

P

l

0m

Potential regarded as a function of space position P)P(V

The GOCE mission: spacewise processing


lmlm S,C

Harmonic coeff.SGG observ.LSALSA

)P(Vij

Iterative Direct

serial parallel serial parallel



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)



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



SGG observations regarded as a function of time)t(Vij

even:ml

odd:mllm

lmL

]2min[ll

klm

1l

km

L

Lkkmkmkmkm

L

0m

S

C)I(F

r

RA

)]t(sinB)t(cosA[R

GM)t(V

Potential regarded as a function of time t)t(V

The GOCE mission: timewise processing


lmlm S,Ckmkm B,A

Harmonic coeff. Lumped coeff.Sensitivity coeff.Sensitivity 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

The GOCE mission: timewise processing


mSmCPr

R

R

GMV lmlm

L

llm

ll

m

sincos)(cos2

1

0

The gravitational potentialand derived quantities

mSmCPRN lmlm

L

llm

l

m

sincos)(cos2 0

mSmCPlg lmlm

L

llm

l

m

sincos)(cos12 0

Geoid:Resolution: 100 kmAccuracy: 1 cm

Gravity anomaly:Resolution: 100 kmAccuracy: 1 mGal

100 km resolution requires L = 20000 km / 100 km = 200


simulated GOCE performance

spatial resolution D(half wavelength)

maximum degree L(corresponds to D)

geoid height[mm]

gravity anomaly[mGal]

1000 km 20 0.4 0.0006

400 km 50 0.5 0.001

200 km 100 0.6 0.03

100 km 200 2.5 0.08

65 km 300 ~ 45 ~ 2

< 10 mm < 1 mGal

Goal:

The GOCE mission: performance( cumulative error )


Slm order Clm

EGM spherical harmonic error spectrum

The GOCE mission: error spectrum

Closed loop simulation Gravity fieldGravity field

Gradiometersignal

Gradiometersignal

Harmonicanalysis

Harmonicanalysis

Harmonic coeff.Harmonic coeff.

Colourednoise

Colourednoise

FilteringFilteringObservationsObservations


“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

The GOCE mission: closed loop simulation


0

500

1000

1500

2000

2500

min

utes

0 2 4 6 8 10 12 14 16

Iterations

DEC-Alpha CRAY (25 PEs)CRAY (50 PEs) CRAY (75 PEs)

Near linear speed-up

with additional processing

elements (PE)

Near linear speed-up

with additional processing

elements (PE)

The GOCE mission: solution time


method # PEs iteration timepcgma 25 10 12h20min

SA 25 5 20min

DNA 49 - 14.5d

338h / 10h

The GOCE mission: test performance

Solution time:


• 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 2.4.19) , MPICH, ...• TU Graz cluster outperforms Columbus / Ohio cluster by a

factor of 2• Same performance as the CRAY T3E in Columbus / Ohio

The TU Graz clusterComponents and performance


• 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

• 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

HP SC-45 cluster

Realization: October 2002

The TU Graz cluster: future plans (1/2)


• 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

• 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

The TU Graz cluster: future plans (2/2)


Gravity satellite missions: comparison

2 years5 years5 yearsduration

250 km~450 km454 kmaltitude

96.5°89.0°87.3°inclination

SST-hl/SGGSST-hl / llSST-hlmode

200620022000start

GOCEGRACECHAMP


70 km250 km650 kmresolution(half wavelength)

< 1 cm~ 1 cm~ 1 cmaccuracy

GOCEGRACECHAMP

3008030Harmonic degree

Gravity satellite missions: comparisonAccuracy and resolution


SST - hlSST - hl

SST - llSST - ll

KaulaKaula

SGGSGG

Gravity satellite missionsAccuracy and resolution

EGM 96EGM 96


The GOCE missionOcean topography


x

Hgvf

y

Hguf

s

s

Steady - state flow:

H ... Sea surface height (SSH) relative to geoidx, y ... Local cartesian coordinates (W-E, S-N)u, v ... Surface velocity (W-E, S-N)g ... Gravityf ... Coriolis term

0vu

The GOCE missionDynamic ocean topography

Navier-Stokes equation


Signal l = 20

Range: -75 to +75 cm

l = 80 l = 200

Gravity satellite missionsOcean topography signal


The GOCE missionMean dynamic ocean topography


The GOCE missionGeostrophic current


Problem: conversion velocity density

Propagation of seismic waves

The GOCE mission: geotomography


RiftingRifting

OrogenyOrogeny

Volcanoes,Hot Spots

Volcanoes,Hot Spots

SpreadingSpreading

SubductionSubduction

The GOCE mission: solid Earth


The GOCE mission: surveying


CHAMPmagnetic field determinationtemporal variations of the gravity field

GRACEimproved knowledge of the geoidestimates of time variable components

GOCEhighly precise static geoid determination

Gravity satellite missions: summary


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

Gravity satellite missions: benefits


GOCE will cover Theme 1 of ESA‘s Living Planet Programme (with the exception of the magnetic field part)

Geodesy

Solid Earth Physics

Absolute OceanCirculation

Sea Level Change Studies

Ice Sheet Mass Balance

Gravity satellite missionsBenefits for geosciences


The End

Documents

Semmering, 2002-10-17 H. SünkelSAG-BGÖ 2002 H. Sünkel Institut für Geodäsie Technische Universität Graz und Institut für Weltraumforschung Österreichische