E. Schrama TU Delft, DEOS e-mail: schrama@geo.tudelft.nl

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

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. 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. Characteristics of errors

9. EGM96 geoid error map Lemoine et al

10. Mean Circulation • Hydrographic inversion • 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) (2 - 2.5 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. 119 121 120 122 T/P sampling

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 1997-1998

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 1 - 1.5 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