Geographically Correlated Errors – Problem Solved?

1. Geographically Correlated Errors – Problem Solved? Wolfgang Bosch Deutsches Geodätisches Forschungsinstitut (DGFI) München Email: bosch@dgfi.badw.de

2. Geographically correlated (mean) error estimate • for TOPEX (344-364) and Jason1 (001-021) Tandem phase (both retracked, GRACE orbits, FES2004 tides, but GDR corr.) • TOPEX >> • Jason1>>

3. Motivation … Mean or geographically correlated error is of particular concern, because • It is not visible in single satellite crossover differences (it cancels each other). • it maps, however, directly into sea surface heights!

4. Basics from Kaula (1966) and Rosborough (1986): • Radial orbit errors of ascending and descending tracks are composed of • With a “mean”, geographically fixed component • And a “variable” component

5. Single satellite crossover differences (SX) • If radial errors of ascending and descending tracks • are taken to model the observed crossover differences • The “mean” component Dg cancels and thus • The mean error is not estimable from single satellite crossovers

6. Dual satellite crossovers • There are four different types, AD, DA, AA and DD • are (partly) sensitive to the mean error • E.g. if one orbit is much more precise than the other

7. Long-term mean of dual satellite crossover differences (TOPEX/ERS-1, type AA, DD, DA, AD) All crossover data provided by NOAA

8. Correction to spherical harmonics

9. Radial orbit errors from gravity field corrections

10. Latitude-lumped coefficients • Estimating linear combinations of Stokes-coefficients allows assessment of accuracy of gravity fields used to compute the altimeter orbits • Intensively applied by Wagner, Klokocnik and others with many publications See poster of Klokocnik, “Review in using crossover altimetry”

11. Tuning of the gravity field by DEOS: DGM-04 • Harmonizing TOPEX and ERS data • Orbits of TOPEX and ERS processed with JGM3 • Single- and dual-satellite crossover differences • Set up normal equations according to theory of Kaula & Rosborough • Adding this to the JGM3-normal equations • Solve the system for new Stokes coefficients  DGM-04 (Scharroo & Visser 1998)

12. Gain by DGM04 Gravity field tuning • Geographically correlated (mean) errors with OPR-orbit >> DGM04-orbit >>

13. There is something else than just gravity field induced errors • Differences of sea surface heights between TOPEX and Jason1 during the Tandem phase • Both, TOPEX and Jason1 with JGM3 orbits

14. How to estimate the mean error with two or more satellites having similar orbit accuracy ? • Assuming that errors of ascending and descending tracks are composed of a mean and a variable part • Mean and variable part would be known if errors of ascending and descending tracks are known

15. Multi-mission crossover analysis (1) • Common adjustment for all contemporary altimeter systems (ERS-1, TOPEX, ERS-2, GFO, Jason1, ENVISAT) • Sequence of 10-day analysis periods with 2x3 days overlap (corresponding to TOPEX cycles 001-480) • Dt < 3 days minimizing the impact of sea level variability • Set up single- and dual- satellite crossover in all combination

16. Multi-mission crossover analysis (2) • Up to 150000 dual-and single- crossovers give a dense sampling of the orbits of all satellites • Rigid network with high redundancy allows to estimate the radial error components • Discrete Crossover Analysis (DCA) see OST-ST poster on Thursday

17. Radial error estimates • TOPEX, Jason1, ERS-2, GFO

18. Empirical Autocovariance function • Skipping the overlaps and concatenating the central periods gives complete time series of radial errors for all satellites

19. Mean errors ERS-1 phase C and G • ERS-1 Phase G • ERS-2

20. Mean errors of ENVISAT and GFO • ENVISAT • GFO

21. Mean errors of TOPEX-EM and Jason1 (still JGM3) • TOPEX-EM • Jason1

22. GRACE based orbits • available or being processed for nearly all missions • Provide another essential progress in orbit accuracy • Orbit errors are no longer dominated by gravity field errors • Uncertainty in SSB correction, about 1% of SWH causes 6-10 cm mean errors in the southern ocean

23. Geographically correlated (mean) error estimate • for TOPEX (344-364) and Jason1 (001-021) Tandem phase (both retracked, GRACE orbits, FES2004 tides, but GDR corr.) • TOPEX • Jason1

24. Conclusions: • Theory of Kaula/Rosborough was successfully applied to improve the Earth gravity field • However, today, the mean error is no longer dominated by gravity field errors. • If there are two or more satellites operating simultaneously the mean radial error can be estimated by global multi-mission crossover analysis • This was demonstrated with ERS-1, TOPEX, ERS-2, GFO, Jason1, ENVISAT