Ulrich MeyerA. Jäggi, G. Beutler, H. Bock
September 20, 2010
[email protected] 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