1. E. Schrama TU Delft, DEOS e-mail: schrama@geo.tudelft.nl
Error characteristics estimated from CHAMP, GRACE and GOCE derived geoids and from altimetry derived mean dynamic topography
E. Schrama
TU Delft, DEOS

2. Contents Static Gravity Mean circulation inversion problem
Satellite altimetry
Temporal Gravity
Conclusions

3. Static gravity Existing gravity field solutions New gravity missions
Gravity mission performance
Cumulative geoid errors
Characteristics of errors

4. Existing gravity solutions
Satellite geodesy
Range/Doppler observations
Model/observe non-conservative accerations
large linear equations solvers
Sensitivity in lower degrees, resonances
Physical geodesy
Terrestrial gravity data, altimetric g
Relative local geoid improvement wrt global models
Surface integral relations
Sensitivity at short wavelengths
Quality determined by: data noise, coverage, combination

5. New gravity missions
Measuring (rather than modeling) non-conservative forces (CHAMP concept)
Low-low satellite to satellite tracking (GRACE concept)
Observation of differential accelerations in orbit: (GOCE concept)
New gravity surveys (airborne gravity projects)

6. Gravity mission performance
Bouman & Visser

7. Cumulative geoid errors
SID 2000 report
T = 1 year

8. Characteristics of errors
All calculations so far considered geoid errors to by isotropic and homogeneous.
We only considered commission errors, and did not average spatially (beta operator)
In reality there is only one static gravity field
Data subset solution Tailored cases.
Optimal data combination is a non-trivial problem.
The temporal gravity field is an error source for GOCE.

9. EGM96 geoid error map
Lemoine et al

10. Mean Circulation Hydrographic inversion Dynamic topography examples
density gradients and tracer properties
geostrophic balance
Dynamic topography examples
Hydrography
Satellite Altimetry

11. Hydrographic inversion
thermal wind equations
conservation tracers
geostrophic balance

12. Dynamic Topography from hydrographic inversion
Le Grand,1998

13. Dynamic topography from altimetry
JPL web site

14. Satellite Altimetry System accuracy Averaging the mean sea level
Mesoscale variability
Gulf stream wall detection
Sampling characteristics
Correlated Noise
Correlated Signals

15. System accuracy definition of the reference frame (?)
orbits (Laser+Doris, GPS, Altimeter) ( cm)
accuracy/stability of the instrument (5 mm)
accuracy of environmental corrections (troposphere, ionosphere, EM-bias) ( 1.5 cm )
accuracy of geophysical corrections ( 3 cm )
tides (ocean, earth, load, pole), inverse barometer
Net system accuracy: 4-5 cm for T/P

16. Averaging the mean sea level
GOCE: 12 months, GRACE: 60 months.
White noise fades out as a sqrt(N) process
If you had 300 T/P cycles then
5 cm r.m.s. goes down to 0.3 cm
30 cm r.m.s. goes down to 1.7 cm
Spatial averaging helps to reduce this error.
Yet we can’t average further than the required resolution of the geoid.

17. Mesoscale variability map
JPL web site

18. Gulf stream wall detection
Lillibridge et al

19. Gulfstream T/P in COFS model
Lillibridge et al

20. Gulfstream T/P + ERS2 in COFS
Lillibridge et al

21. Infrared Gulfstream
Lillibridge et al

22. Gulf stream velocity (ERS-2)
DEOS (Vossepoel?)

23. Sampling the sea level Gravity mapping orbits Repeat track orbits
Sun synchronous
Frozen orbits
Repeat length vs intertrack spacing

24. T/P sampling
119
121
120
122

25. Topex/Poseidon groundtrack

26. Examples systematic errors
Errors that are definitely not white are:
reference frame
stability
definition issues
instrument biases
geographical correlated orbit errors
tides aliasing
inverse barometer

27. Examples of time correlated SLA
Equatorial Rossby and Kelvin waves
ENSO
Annual behavior
Tides
Internal tides

28. Equatorial Kelvin and Rossby waves
Equator: 2.8 m/s
20 N: 8.5 cm/s

29. El Niño

30. Four seasons (Annual cycle)
JPL web site

31. M2 tide

32. Internal tides Hawaiian Island chain is formed on a sub-surface ridge
wave hits ridge (perpendicular)
energy radiates away from ridge

33. Temporal gravity Current situation Overview processes Challenges
Separation Signals/Noise

34. Current situation Currently observed in the lower degree and orders
Signal approximately at the 1e-10 level
Traditional observations by SLR: Lageos I + II, Stella, Starlette, GFZ, Champ
Various geodynamic processes are responsible for changes in the gravity field.
Increased spatial resolution by the new proposed missions

35. Source: NRC 1997

36. Temporal gravity and geodynamic processes (Chao,1994)

37. Challenges
Extreme sensitivity of low-low satellite to satellite tracking in the lower degree and orders (till L=70)
The entire gravity field can be solved for after 30 days of data, temporal variations can be observed
It opens the possibility to study e.g.:
the continental water balance
ocean bottom pressure observations.
Open questions:
How do you separate between signals.
How do you suppress nuisance signals

38. Surface mass layer to geoid
Model
Purpose: convert equivalent water heights (h) to geoid undulations (dN)

39. Properties Kernel function

40. Geophysical contamination
Approximately mbar error (now-cast) is typical ECMWF and NCEP (Velicogna et al, 2001)
averaging over space and time helps to drive down this error, better than 0.3 mbar is unlikely.
Some regions are poorly mapped (South Pole) and the errors will be larger
The low degree and orders are more affected and probably the gravity performance curves are too optimistic (see kernel function)

41. Other Temporal gravity issues
Unclear how to separate different signals ( criteria: location, spatial patterns? EOF? Other?)
Accuracy tidal models (3 cm rms currently)?
Aliasing of S1/S2 radiational tides in sun-synchronous orbits used for gravity missions
Edge effects near coastal boundaries
Data gaps

42. Round up
Gravity missions: new missions discussed and their error characteristics, isotropy, homogeneity.
Mean circulation: thermal wind, tracers, assimilation of observations, results from exiting approaches
Satellite altimetry: typical results averaging and sampling in oceanic areas with high mesoscale signal, a sample of the scientific progress since 1992.
Temporal gravity: current research and processes that are visible, contamination with geophysical signals, separation of individual signals and noise