1. TOPEX & Jason Retracking OSTST ‘07 Retracking and SSB Splinter TOPEX and Jason Retracking Ernesto Rodriguez, Phil Callahan, Ted Lungu March 13, 2007 Jet Propulsion Laboratory California Institute of Technology

2. TOPEX & Jason Retracking 2007/03/14 psc-f2 2 OSTST Retracking & SSB Splinter – Overview Discussion –Goal: Allow studies of global and regional variations using the whole TOPEX + Jason time series to determine sea level changes to a few tenths of a mm per year –Recommend approaches for final processing for Jason (reprocessing?), TOPEX RGDR, in particular, the SSB for final cross-calibration  see proposal for options Would like OSTST recommendation –Estimate error structure of Jason and TOPEX data

3. TOPEX & Jason Retracking 2007/03/14 psc-f2 3 Retracking TOPEX & Jason – Outline Identical software used for both –Avg Jason WF to TOPEX structure (10/frame, 64 bins) –Software has skewness fixed to 0 or solves (cannot set specific value) No significant changes to TOPEX retracking since Mar ’06 (LSE & MAP) Jason Changes since Mar ’06: Using WF weighting, slightly revised PTR Tests on Jason simulated Waveforms Results to Date –Greatly improved agreement between CNES/JPL on Jason data –MAP not providing expected benefits – has lower noise but has bias, SWH dependence

4. TOPEX & Jason Retracking 2007/03/14 psc-f2 4 Retracking Progress Retracked 2 yr TOPEX Alt-B and produced RGDRs with improved orbits –LSE skewness absorbs WF leakages so much reduced N/S Asc/Des (“Quadrant”) difference, but still some MAP skewness much smaller so large variations with SWH –Need to assess waveform residuals to correction for leakages, OR rely on empirical correction Worked issues with CNES on differences of MLE4, LSE, MAP –Processed large set of simulated data, numerous PTRs –Found no anomalies in Jason waveform residuals –However, MLE4 only agrees with LSE when solve for skewness, not fixed skewness. MAP has SWH dependence –Similar results found from simulated WF

5. TOPEX & Jason Retracking 2007/03/14 psc-f2 5 June ’06 CNES Simulated Waveform Results New simulations with 10,000 pts: –SWH = 2, 4, 6, 8; Attitude = 0, 0.1; Skewness = 0, 0.1 Some findings –LSE had small SWH bias at higher SWH –MAP height std dev a factor of 2-3 smaller –MAP std dev on other parameters was negligible –Solving for skewness prevented height changes of a few mm at higher SWH –Skewness was recovered, but LSE std dev ~ 0.1 –Additional terms in Gaussian expansion of PTR generaly had expected effect, although somewhat larger than expected – showed the need to extend PTR to farther sidelobes

6. TOPEX & Jason Retracking 2007/03/14 psc-f2 6 Jason Features (Cycles 19-21) Jason LSE SWH, solving for skewnessJason LSE-GDR Range Correction Des Asc

7. TOPEX & Jason Retracking 2007/03/14 psc-f2 7 TOPEX Waveform Contamination Evidence TOPEX SkewnessJason Skewness Cyc 19-21 (avg = 0.06) Des Asc

8. TOPEX & Jason Retracking 2007/03/14 psc-f2 8 Height Differences -20 Range difference (mm) 30 As with Jason, LSE and MAP retrackers exhibit a SWH dependence difference. In order to make TOPEX and Jason compatible at the 1cm level, the waveform leakage contamination be mitigated. TOPEX LSE-GDR (toward) Vs Att / SWH TOPEX LSE-MAP(toward) vs Att / SWH 0 Range difference (mm) 40 Jason LSE-MAP vs Att / SWH

9. TOPEX & Jason Retracking 2007/03/14 psc-f2 9 Jason: Are LSE and MAP Biases Consistent? Skewness vs no Skewness Estimation When skewness is not estimated, the mean difference between LSE and MAP increases. The SWH dependence is similar, but not identical

10. TOPEX & Jason Retracking 2007/03/14 psc-f2 10 Track Point Difference Statistical Results Examined mean SSH differences using different retracking methods and behavior of the residuals after subtracting the mean differences for Jason cycles 7-21 SSH surfaces examined: –Topex GDR –JPL Topex LSE and MAP retracking –Jason GDR –JPL Jason LSE and MAP retracking Topex SSH constructed with improved acceleration correction and new orbits and media corrections Jason and Topex data interpolated to a common grid and differenced for coincident passes Retracking compared against the SGDR retrack estimate CNES dh = -[ku_range + ku_range_20Hz - (ku_tracker20Hz + total_instr_correction)]

11. TOPEX & Jason Retracking 2007/03/14 psc-f2 11 GDR Differences There appears to be a discontinuity at the equator which is different for ascending and descending passes

12. TOPEX & Jason Retracking 2007/03/14 psc-f2 12 JPL Topex LSE vs Jason GDR Equatorial discontinuity present and more marked

13. TOPEX & Jason Retracking 2007/03/14 psc-f2 13 JPL Topex LSE vs JPL Jason LSE Equatorial discontinuity present, notice change in bias value = 8mm

14. TOPEX & Jason Retracking 2007/03/14 psc-f2 14 Retracking Conclusions TOPEX retracking must use LSE solving for skewness –Residual Quadrant bias has SWH dependence, so needs correction like dSSH(q) = a0(q) + a1(q) * SWH Jason LSE does not have major SWH dependence, but must solve for skewness –Avg skewness ~0.06 Check of software have not found any problems in MAP implementation, so behavior is not fully understood –Since MAP is weighted and uses a priori information, it is more likely to be biased. However, MLE4 is unweighted … Jason data seem very sensitive to small changes in retracking setup

15. TOPEX & Jason Retracking Backup / Previous Material OSTST ‘07 TOPEX and Jason Retracking

16. TOPEX & Jason Retracking 2007/03/14 psc-f2 16 Retracking Algorithm Comparison

17. TOPEX & Jason Retracking 2007/03/14 psc-f2 17 Topex: Are LSE and MAP Biases Consistent? There appears to be a SWH dependent bias between MAP and LSE, but no apparent discontinuity at the equator

18. TOPEX & Jason Retracking 2007/03/14 psc-f2 18 Jason: Are LSE and MAP Biases Consistent? There appears to be a SWH dependent bias between MAP and LSE, as in Topex. However, differences seem to be larger

19. TOPEX & Jason Retracking 2007/03/14 psc-f2 19 JPL Topex MAP vs Jason GDR

20. TOPEX & Jason Retracking 2007/03/14 psc-f2 20 JPL Topex MAP vs JPL Jason MAP

21. TOPEX & Jason Retracking 2007/03/14 psc-f2 21 TOPEX Waveform Artifacts Averaging Time: 40 seconds Due to onboard signal leakages, TOPEX waveforms are contaminated by spurious signals which appear in the leading edge and are hard to model. Rodriguez and Martin (JGR, 1994) estimated height biases of ~+/-1 cm which were geographically dependent by comparing with LSE retracking.

22. TOPEX & Jason Retracking 2007/03/14 psc-f2 22 Maximum a Posteriori Retracking: a 3rd Generation Retracking Scheme 1st Generation retracking (Rodriguez and Martin, JGR 94): –Decomposition of the PTR into sum of Gaussians –Arbitrary attitude angle (expansion to higher order terms) –Linearized least squares estimation, including Skewness 2nd Generation retracking (Callahan and Rodriguez, MG 04) –Added iterative estimation of parameters until retracker fully converged 3rd Generation retracking: Maximum a Posteriori (MAP) –1st and 2nd generation retrackers operated on 1 second frames without constraints –Retracker unbiased, but noisy and retrieved parameters could be highly correlated –MAP estimation constrains the parameter space for the inversion using a priori knowledge (data are still estimated from 1 sec frames) Attitude varies slowly, SWH correlation distance ~100 km and known to better than 60cm, Track Point known to better than 20 cm, |skewness|<1

23. TOPEX & Jason Retracking 2007/03/14 psc-f2 23 Retracking Algorithms Maximum Likelihood Estimator (MLE) Minimizes: Maximum a Posteriori (MAP) Minimizes: Where x is the data, a are the parameters to be estimated, A are the parameter a priori values,  i are the measurement errors and  n measures the prior confidence level. Setting the priors and their confidence levels is the trick! Prior Values: smooth LSE SWH and attitude data over an extent < 80 km relative to center Prior Uncertainties: Root Squares Sum residual values in smoothing window with conservative estimate of minimum uncertainty of SWH and attitude variance. Use 1.5 as uncertainty on the skewness, and infinite variances (no priors) on the other parameters, including height.

24. TOPEX & Jason Retracking 2007/03/14 psc-f2 24 MAP Retracking Simulation Results By putting very moderate constraints on the retrieved parameters, the estimated parameters are almost completely uncorrelated. Even better, the estimation noise drops by a factor of 3 for height and an order of magnitude for SWH and skewness! If one uses the SGDR to set a priori constraints, the increased burden on computation is small or negative (faster convergence). However, biases must be quantified. To remove biases, one can retrack using least squares, derive priors, and retrack again with MAP. Computation doubles (still feasible, though).