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Solving Geographically Correlated Errors in Altimetry: Insights from TOPEX and Jason-1

This study addresses the challenge of estimating geographically correlated mean errors in altimetry, particularly during the Tandem phase of TOPEX and Jason-1 missions. Traditional single-satellite crossover differences often fail to reveal mean error components, which cancel each other out. By employing dual-satellite crossovers and a multi-mission crossover analysis, we explore more accurate estimates of these mean errors. The utilization of enhanced gravity field adjustments and the integration of GRACE orbits showcases significant improvements in sea surface height accuracy.

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Solving Geographically Correlated Errors in Altimetry: Insights from TOPEX and Jason-1

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  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

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