Ulrich MeyerA. Jäggi, G. Beutler, H. Bock

September 20, 2010

Ulrich.meyer@aiub.unibe.ch2nd Internat.

Gravity Field

Symposium

Fairbanks

Alaska

Sep. 20-22

2010

GRACE and GOCE gravity field determination

with the Celestial Mechanics Approach at AIUB

Astronomical Institute University of Bern

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

2

GOCE&GRACE

The Celestial Mechanics Approach ...

Definition (Beutler, 2010):

... generates ensembles of orbits and gravity

fields fully exploiting the degrees of freedom

offered by Celestial Mechanics and using the

power of applied mathematics to generate

precise solutions in an efficient way.

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

3

GOCE&GRACE

Key features of the CMA

• Kinematic orbits (from GPS) as pseudo-observations (efficiency)

• Reduced dynamic orbits (GPS & K-Band) with stochastic pulses (flexibility)

• Intelligent way to compute variationalequations (efficiency)

• NEQ-manipulation: relative weighting in combination, parameter pre-elimination, accumulation (flexibility and efficiency)

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

4

GOCE&GRACE

... in more detail

• A priori orbits from GPS observations (iterative) => GPS-NEQs

• Set up of K-Band-NEQs (same orbit parameterization as above)

• Combination of NEQs => a priori orbits of constellation (absolute cm, relative µm)

• Set up of gravity-NEQs, combination of NEQs, pre-elimination of arc- and satellite specific parameters

• Solution: final orbits and gravity field

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

5

GOCE&GRACE

Static multi-year solutions from GRACE

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

6

GOCE&GRACE

Static multi-year solutions from GRACE

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

7

GOCE&GRACE

Static multi-year solutions from GRACE

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

8

GOCE&GRACE

Static multi-year solutions from GRACE

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

9

GOCE&GRACE

Comparison to other GRACE-fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

10

GOCE&GRACE

Comparison to other GRACE-fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

11

GOCE&GRACE

Comparison to other GRACE-fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

12

GOCE&GRACE

Comparison to other GRACE-fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

13

GOCE&GRACE

Validation with leveling (IAPG)

10.1

21.8

14.9

4.0

3.9

24.2

ITG2010S

22.022.522.622.623.3EUREF (GPS)

14.314.815.514.415.1Canada (GPS)

10.210.611.810.711.0Japan (GPS)

6.2

5.4

24.2

GGM03S

4.5

4.5

24.3

AIUB6YR

4.6

4.0

24.1

GGM03C

6.3

5.9

24.5

EIGEN5S

EIGEN5C

4.9

4.1

24.4

Germany (GPS)

Germany (EUVN)

Australia (GPS)

RMS (cm) of geoid height differences up to degree 120

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

14

GOCE&GRACE

2.21)2.23.4AIUB-6YR

2.82.94.0EGM2008

1.71.83.3ITG-GRACE2010S

1.8

-

2.3

-

2.2

-

180x180

2.73.2EIGEN-51S

2.03.2EIGEN-51C

2.43.6GGM03C

2.43.4GGM03S

2.33.4EIGEN-5C

3.03.6EIGEN-5S

150x150120x120Gravity field model / max. d/o

1) Maximum d/o = 160

GOCE orbit adjustment fit for different gravity field modelsObservations: GO_CONS_SST_PKI_2I (kin. orbit positions, consolidated product)60 arcs (01.11. – 31.12.2009), arc length = 1.25 daysRMS [cm] of the orbit fit residuals (mean values from the 60 arcs)

Validation by GOCE orbits (GFZ)

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

15

GOCE&GRACE

Monthly solutions and time variations

• a priori gravity field: AIUB-6YR to lmax=160

• monthly solutions to lmax=30• time variations: bias, trend, annual, biannual

� direct estimation� a posteriori estimation

• F-test for significance of parameters• non-significant variations are constrained to

zero (Davis et al., 2008)

• no further filtering/smoothing

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

16

GOCE&GRACE

Time variable gravity from GRACE

significant terms

(1-yearly, ½-yearly)

non-significant terms

(1-yearly, ½-yearly)

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

17

GOCE&GRACE

Significance of periodic time variations

not significant

significant

not significant

significant

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

18

GOCE&GRACE

Linear time variation (trend)

not significant

significant

Ice mass loss

over Greenland,

South-Alaska and

West-AntarcticaPost glacial rebound

over northern Canada

and Fennoscandia Sumatra Earthquake

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

19

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

20

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

21

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

22

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

23

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

24

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

25

GOCE&GRACE

Consistency of monthly fields

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

26

GOCE&GRACE

Calibration of errors and residual signal

⇒ residual time

variable signal in low

degrees/orders

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

27

GOCE&GRACE

Spectral analysis of monthly fields

biannual/annual

sampling

~160d

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

28

GOCE&GRACE

Spectral analysis of monthly fields

S2-tide

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

29

GOCE&GRACE

Processing of GOCE data

• Two months of data (11+12/2009)• GPS-NEQs up to lmax=120• Processing of time differences (10s) of

gradiometer observations (no further filtering)

• Gradiometer-NEQs (XX, YY, ZZ) up to lmax=160 (200)

• Combination of NEQs and solution• Due to polar gap the near zonal coefficients

are deteriorated

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

30

GOCE&GRACE

Two month GOCE gravity field

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

31

GOCE&GRACE

Conclusions

• AIUB-6YR is based on nearly 6 years of data and is comparable in quality to other recent state-of-the-art static GRACE gravity fields.

• Static solution independent of a priori gravity field, good a priori information needed for handling of resonant months.

• Annual, biannual and trend signals may be estimated simultaneously or a posteriori from monthly solutions.

• Analysis of monthly solutions shows residual time variable signal (to be investigated).

• Processing of GOCE time differences yields promising results

Sep. 20, 2010

2nd Internat.

Gravity Field

Symposium

Ulrich Meyer

32

GOCE&GRACE

Outlook

• Release of 6 year GRACE solution and time series of monthly gravity fields

• Further refinement of GOCE-only analysis

• Combination of GOCE and GRACE solutions in preparation