**The Decade of the Geopotential – **

**techniques to observe the gravity **

**field from space **

Matthias Weigelt Tonie van Dam Olivier Francis

**Geophysical implications of the gravity field **

2

© ESA

**Gravity field modelling **

3

with gravitational constant times mass of the Earth radius of the Earth

spherical coordinates of the calculation point Legendre function

degree, order

(unknown) spherical harmonic coefficients

**Gravity field modelling **

4

with gravitational constant times mass of the Earth radius of the Earth

spherical coordinates of the calculation point Legendre function

degree, order

(unknown) spherical harmonic coefficients

5

**S****nm**** - order m - C**

**nm**

**d****e****g****re****e**** n**

**Spherical harmonic spectrum of ITG-GRACE2010s**

**-80** **-60** **-40** **-20** **0** **20** **40** **60** **80**

**0**

**20**

**40**

**60**

**80**

**-12**
**-11**
**-10**
**-9**
**-8**
**-7**

Spherical **-6**

harmonic

representation

degree-RMS

**Spectral representation **

6

**S****nm**** - order m - C**

**nm**

**d****e****g****re****e**** n**

**Spherical harmonic spectrum of ITG-GRACE2010s**

**-80** **-60** **-40** **-20** **0** **20** **40** **60** **80**

**0**

**20**

**40**

**60**

**80**

**-12**
**-11**
**-10**
**-9**
**-8**
**-7**

Spherical **-6**

harmonic

representation

degree-RMS

**Spectral representation **

**Pre CHAMP era **

**Space geodetic observation techniques **

courtesy Oliver Baur

SLR:

Optical:

courtesy NOAA BC-4

### 1966:

**Development of the gravity field precision and resolution **

### 1972:

**Development of the gravity field precision and resolution **

### 1976:

**Development of the gravity field precision and resolution **

### 1982

^{: }

**Development of the gravity field precision and resolution **

### 1987:

**Development of the gravity field precision and resolution **

### 1990:

**Development of the gravity field precision and resolution **

### 1996:

**Development of the gravity field precision and resolution **

**The Decade of the Geopotentials - **

**the concepts **

**Satellite missions **

17

High-low SST

Low-low SST

Gradiometry

CHAMP

GRACE GOCE

© GFZ-Potsdam

© CSR Texas

© ESA

**CHAMP **

**Satellite system CHAMP **

**CHAMP = CHAllenging **
**Minisatellite Payload **

• Initial orbit height: ~ 485 km

• Inclination: ~ 87.5°

• Key technologies:

– GPS

– Accelerometer – (Magnetometers)

• Observation quantity:

– Position by GPS

– Non-gravitational forces by accelerometers

**Newton‘s equation of motion **

**Newton‘s equation of motion **

→

**Newton‘s equation of motion **

→ →

**Newton‘s equation of motion **

→ →

Observation: (position)

**Newton‘s equation of motion **

→ →

Observation: (position)

Differentiation: (acceleration)

**Newton‘s equation of motion **

→ →

Observation: (position)

Differentiation: (acceleration)

**Newton‘s equation of motion **

→ →

Observation: (position)

Differentiation: (acceleration)

**Newton‘s equation of motion **

→ →

Observation: (position)

Differentiation: (acceleration)

### 2010:

**GAIN due to CHAMP **

**GRACE **

**Satellite system GRACE **

**GRACE = Gravity Recovery **
**and Climate Experiment **

• Initial orbit height: ~ 485 km

• Inclination: ~ 89°

• Key technologies:

– GPS

– accelerometer

– K-Band ranging system

• Observation quantity:

– distance (range)

– change of distance (range rate)

30

**© CSR, UTexas **

**Geometry of the GRACE system **

31

**Differentiation **
**Integration **

Rummel et al. 1978

### 2013:

**GAIN due to GRACE **

### 2013:

**GAIN due to GRACE and GOCE **

### 2013:

**GAIN due to GRACE: time variable gravity (TVG) **

**Achievements **

**in terms of the TVG **

**Spatio-temporal resolution ? **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

**Spatio-temporal resolution ? **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

GRACE

**Spatio-temporal resolution ? **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

GRACE

**Spatio-temporal resolution ? **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

GRACE CHAMP

**Change in water storage **

40

GRACE GFZ Rel. 4 High-low SST

**Water is stressed … **

41

• Water balance in India (Rodell et al., Nature, vol. 460, 2009)

**The Future **

**GRACE und GRACE Follow-On (GFO) **

43

Low-low

© CSR Texas

• K-Band + Laser

• GPS

• Accelerometer

**year **

**GRACE und GRACE Follow-On (GFO) **

44

Low-low

© CSR Texas

• K-Band + Laser

• GPS

• Accelerometer

**year **

up to 4 year data gap

**Bridging the gap … **

45

High-low

GOCE

**year **

**Bridging the gap … **

46

High-low

GOCE GOCE

© ESA

**year **

**Bridging the gap … **

47

High-low

GOCE GOCE

© ESA © EADS Astrium

SWARM

**year **

**Beyond GRACE Follow-On **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

GRACE CHAMP

**Beyond GRACE Follow-On **

10^{-3} 10^{-2} 10^{-1} 10^{0} 10^{1} 10^{2} 10^{3} 10^{4} 10^{5}

10^{0}
10^{1}
10^{2}
10^{3}
10^{4}
10^{5}

10000km

1000km

100km

10km

1km

sea ice

vulcanos

PGR

ocean currents ice mass balance solid

Earth and ocean

tides

lithosphere mantle tectonics

postseismicdeformation

coseismic deformation

groundwater snow soil moisture

runoff water balance storage balance

sea - level

quasi-staticocean circulation

atmosphere

GRACE CHAMP

**Summary **

*• The decade of the potential yield an improvement *

*in the gravity field by three orders of magnitude. *

*• Time variable gravity can be observed for the first *

*time with a monthly sampling. *

*• Ongoing strive for higher spatial and temporal *

*resolution (with a likely setback in the coming *

*years). *

**Thank you **

Matthias Weigelt Tonie van Dam Olivier Francis