Retracking & SSB Splinter OSTST ‘07 Retracking and SSB Splinter Report Juliette Lambin and Phil Callahan March 14, 2007 Hobart, Tasmania

Retracking & SSB Splinter 2007/03/13 psc-d1 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

Retracking & SSB Splinter 2007/03/13 psc-d1 3 Retracking & SSB – OSTST Recommendaton Options (1 of 2) JPL and CNES groups would like direction on approach for next generation (TOPEX final) products Considerations –CNES MLE4 shows good agreement with JPL LSE with skewness –MAP does not behavior as expected. Also, finds very small skewness (not suitable for use with TOPEX leakages) –JPL should complete Reprocessing during the term of this OSTST (or proposal extension will be needed) Retracking can be somewhat decoupled from RGDR production. RGDR production is about 10X as fast as retracking –RGDR requires in addition to retracking Latest orbits (ITRF2005 ?) Final TMR correction SSB to provide consistency between TOPEX quadrants and TOPEX-Jason durring overlap period

Retracking & SSB Splinter 2007/03/13 psc-d1 4 Retracking & SSB – OSTST Recommendaton Options (2 of 2) SSB Options –(1) Consider that Jason MLE4 is validated. With same generation orbits as RGDR will use and best JMR cal, other corrections, solve for SSB. Declare that to be the TRUTH Find TOPEX quadrant SSB adjustments (a0(q) +a1(q)*SWH) to make best match during overlap For Alt-A find new quadrant SSBs that give good match for 1-3 year avg of Alt-A with Alt-B –(2) Instead of taking Jason SSB as Truth, solve for global TOPEX SSB from retracked data. Find additional TOPEX quadrant SSB adjustments to make best match during overlap Follow same procedure for Alt-A, again with average comparison –(3) Solve for TOPEX quadrant SSBs with no global solution

Retracking & SSB Splinter 2007/03/13 psc-d1 5 JPL Retracking TOPEX & Jason 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

Retracking & SSB Splinter 2007/03/13 psc-d1 6 TOPEX Waveform Contamination Evidence TOPEX SkewnessJason Skewness Cyc (avg = 0.06) Des Asc

Retracking & SSB Splinter 2007/03/13 psc-d1 7 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

Retracking & SSB Splinter 2007/03/13 psc-d1 8 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)]

Retracking & SSB Splinter 2007/03/13 psc-d1 9 GDR Differences There appears to be a discontinuity at the equator which is different for ascending and descending passes

Retracking & SSB Splinter 2007/03/13 psc-d1 10 JPL Topex LSE vs Jason GDR Equatorial discontinuity present and more marked

Retracking & SSB Splinter 2007/03/13 psc-d1 11 JPL Topex LSE vs JPL Jason LSE Equatorial discontinuity present, notice change in bias value = 8mm

Retracking & SSB Splinter 2007/03/13 psc-d1 12 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 …

Retracking & SSB Splinter Backup / Previous Material OSTST ‘07 TOPEX and Jason Retracking

Retracking & SSB Splinter 2007/03/13 psc-d1 14 Retracking Algorithm Comparison

Retracking & SSB Splinter 2007/03/13 psc-d1 15 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

Retracking & SSB Splinter 2007/03/13 psc-d1 16 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

Retracking & SSB Splinter 2007/03/13 psc-d1 17 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.

Retracking & SSB Splinter 2007/03/13 psc-d1 18 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

Retracking & SSB Splinter 2007/03/13 psc-d1 19 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.