1. Multi-Mission Cross Calibration – results with upgraded altimeter data Wolfgang Bosch Deutsches Geodätisches Forschungsinstitut (DGFI), München Email: bosch@dgfi.badw.de

2. OST ST Meeting, Hobart, March 12-15, 2007 TOPEX as Reference? TOPEX orbits taken as „reference“ for other altimeters (Le Traon & Ogor 1998) See, however, the SSH differences TOPEX - Jason1 during the tandem phase

3. OST ST Meeting, Hobart, March 12-15, 2007 Objectives Use single- and dual satellite crossover in all combinations of TOPEX, ERS-2, GFO, Jason1, ENVISAT, … Strongest possible network with high redundancy Don´t let TOPEX orbits fixed – let it also get radial corrections

4. OST ST Meeting, Hobart, March 12-15, 2007 Altimeter data base is rather inhomogeneous Ocean tide corrections for all missions were based on FES2004 ERS1, Phase C and G processed with OPR, Version 6, DEOS orbits, pole tides, 1.5ms time bias ERS1, Phase E and F with OPR, version 5, DEOS orbits and corrections, pole tide, 1.5ms time bias ERS2 all Cycles with DEOS orbits, 1.3ms time bias ENVISAT as provided by GDR/ESA GFO with GDR NOAA TOPEX MGDR-C (CNES) still with JGM3 orbits, Chambers SSB correction, Jason1 Cycle 22-118 GDR-A (JGM3 orbits), SBB+2cm Jason1 Cycle 1-21, 119 – 136 GDR-B (GRACE orbits) Tandem phase TOPEX/Jason1 analysed separately with both data sets re-tracked and with GRACE based orbits

5. OST ST Meeting, Hobart, March 12-15, 2007 „Discrete“ Crossover Analysis (DCA) No functional error model (polynomials, splines, …) Minimizing both, crossover and adjacent differences Rank defect =1 => constraint: sum of TOPEX errors to vanish; Huge but sparse Normals - solved by iteration (Conjugate Gradient)

6. OST ST Meeting, Hobart, March 12-15, 2007 Segmentation of DCA Sequence of DCA’s for ten day periods (the TOPEX cycles) extended by 3 days overlap Crossover skipped if |  x| > 1m or   x > 0.1 m Crossovers taken only if time difference  t < 3 days Crossover weighted byσ(Δx), cosφ With 20.000 – 120.000 XO’s per analysis period

7. OST ST Meeting, Hobart, March 12-15, 2007 Error estimates (m) for TOPEX(black), Jason1(blue), ERS2(red), and GFO(green) 4,3 cm 3,7 2,0 1,7

8. OST ST Meeting, Hobart, March 12-15, 2007 Error Consistency in Overlapping Periods At most 1-2 mm differences

9. OST ST Meeting, Hobart, March 12-15, 2007 Empirical Autocovariance Functions

10. OST ST Meeting, Hobart, March 12-15, 2007 Relative range biases and center-of-origin shifts Systematic error pattern? For every 10 days the final error components of all altimeters were adjusted by the model

11. OST ST Meeting, Hobart, March 12-15, 2007 Relative range biases  r cyc of altimeter missions The range biases are relative to TOPEX (later TOPEX-EM) because the sum of TOPEX (TOPEX-EM) errors was forced to zero. weak annual oscillations with similar phasing and amplitude for ENVISAT, Jason1, and GFO since late 2002 – an indication for systematic variations in the TOPEX-EM data.

12. OST ST Meeting, Hobart, March 12-15, 2007 Centre-of-origin shifts (mm)

13. OST ST Meeting, Hobart, March 12-15, 2007 Mean values of single satellite crossovers TOPEX/Poseidon (top) and ERS-2 (bottom panel with pronounced annual variation of SXO - unexplained)

14. OST ST Meeting, Hobart, March 12-15, 2007 Mean and Variable Orbit Errors „Book-keeping“ allows to separate asc/desc errors Kaula first order theory (Rosborough 1986): „Mean“ and „variable“ error component Mean error not visible by single satellite crossovers

15. OST ST Meeting, Hobart, March 12-15, 2007 Topex mean errors of ascending/descending passes

16. OST ST Meeting, Hobart, March 12-15, 2007 Topex – geographically correlated/anticorrelated errors

17. OST ST Meeting, Hobart, March 12-15, 2007 Geographic correlated errors (TOPEX versus Jason1)

18. OST ST Meeting, Hobart, March 12-15, 2007

19. Conclusions discrete crossover analysis for up to five contemporary atimeter systems gives complete time series for radial errors of all satellites and allows estimating the error-covariance functions is able to sense relative range biases and centre-of-origin differences between the satellites involved Capable to assess the geographical correlated errors GCE of Topex & Jason1 below 2cm – with clear but slightly different geographical pattern Most pronounced GCE-patterns are found for GFO

20. OST ST Meeting, Hobart, March 12-15, 2007 Thank you!