1. OVERVIEW OF THE IMPROVEMENTS MADE ON THE EMPIRICAL DETERMINATION OF THE SEA STATE BIAS CORRECTION S. Labroue, P. Gaspar, J. Dorandeu, F. Mertz, N. Tran, O.Z. Zanife P. Vincent, N. Picot, P. Femenias

2. Empirical Estimation of the SSB correction Why empirical estimation? Theoretical EM bias models not accurate enough. An accurate empirical estimation is based on 3 issues. Regression method => empirical models based on correlatives measured by the altimeter (SWH and Wind speed) => 2 kinds of regression methods –Parametric based on an a priori formulation –Nonparametric estimation free of any assumption on the data Data accuracy => orbit improvements => geophysical corrections (Ocean tide models, MOG2D correction…) Good knowledge of residual SSH errors

3. Regression Method - Parametric models Parametric models are generally fitted on SSH differences at crossovers. TOPEX BM3 (NASA correction 1992) a*SWH + b*SWH*U + c*SWH*U 2 TOPEX BM4 (Gaspar et al. 1994) a*SWH + b*SWH*U + c*SWH*U2 = d*SWH 2

4. Regression Method - Parametric limitations Simulation of a BM4 model with TOPEX data. Regression at crossover differences with a BM3 model => Error between the estimated SSB and the simulated one, due to the a priori formulation (Gaspar et al. 1998) => Development of nonparametric methods

5. Regression Method - Several methods without a priori model Direct method (Vandemark et al. 2002) Direct SLAs Average of SLA= SSH – MSS per bin of (U,SWH). Long time series needed. Hybrid method (Scharoo et al. 2004) Direct SLAs Average of SLA= SSH – MSS per bin of (U,SWH). Merge with a parametric model and smoothing to extend the SSB model where no data are available. Nonparametric method (NP) (Gaspar et al. 2002) SSH differences or SLAs Locally linear estimator. Kernel smoothing (weights) adapted to the data density. => 2 approaches with the NP technique : SSH differences / Direct SLAs

6. Direct SLAs The direct approach assimilates all the residual SSH errors. The MSS is equivalent to a mean profile for a given track/mission (Topex, ERS2, GFO). What is the influence of the residual errors for each mission used in the MSS calculation? Direct estimate derived on Topex A is the only one in agreement with other methods. The SSB derived with the direct method appears to be correlated with oceanic variability. Regression Method - NP method - Direct vs Difference approaches SSH Differences (Crossover or Collinear) Forming differences at the same location cancels all geographically correlated errors. Self consistent : use of the measurements. The SSH differences are more likely to cancel oceanic variability (crossovers or repeat cycles differences).

7. Regression Method - NP method - Direct vs Difference approaches -3 cm 2 +3 cm 2 Variance gain on SLA, Jason, Cycles 1-90 Variance(SSB_Direct) - Variance(SSB_Collinear) The direct approach assimilates all the residual SSH errors. The SSB derived with the direct method appears to be correlated with oceanic variability. Orbit error (gravity field models) - 5 mm + 5 mm

8. Data accuracy - MOG2D correction Jason SSB difference, MOG2D correction - IB correction 3 cm

9. Data accuracy - Orbit Orbit improvements (gravity field model…) EnviSat crossovers Impact on SSB estimation EnviSat crossovers -5 cm+5 cm

10. Good knowledge of residual SSH errors Effect of a time tag bias of 150 microsec on the estimation SSB. => SWH gradient of 1.5 cm This error only affects the crossover SSH. Such an error on the data orientates the choice of the method towards the collinear approach.

11. Topex ATopex BGFO JasonERS2EnviSat Higher SSB On board tracker Ground retracking 18 cm15 cm 34 cm 30 cm 42 cm

12. SSB Results with the NP method - Topex comparison Topex A – Topex B SSB NP estimates Topex A – Topex B SSB BM4 Chambers et al 2003

13. SSB Results with the NP method GFO - Topex B SSB = -2% SWH Jason - Topex B SSB = -1.5% SWH

14. SSB Results with the NP method ERS2 – EnviSat SSB = -1.5% SWH EnviSat – Jason SSB No difference

15. Quality assessment of the SSB correction IB data, Topex AMOG2D data, Topex A 0 2 0 2

16. SSB Results with the NP method - C-band and S-band SSB Ku-band SSB – C-band SSB, JasonKu-band SSB – S-band SSB, EnviSat Empirical SSB estimates in Ku-band, C-band and S-band confirms that the SSB increases as the frequency decreases. 10 cm13 cm

17. Conclusions NP technique with kernel smoothing has demonstrated to be an efficient tool for the empirical SSB estimation. Important improvement have been made on the IB correction which has an impact on the retrieved SSB accuracy. Ku-band SSB have been compared between 5 altimeters. They still exhibit differences in the SSB magnitude and (U,SWH) variations which are not fully understood. Results have been obtained in C-band and S-band and should help in modelling the frequency dependence of the SSB.