Inclusion of Wave Model Data in Sea State Bias Correction Refinement

1. Inclusion of Wave Model Data in Sea State Bias Correction Refinement D. Vandemark, N. Tran, H. Feng, B. Chapron, B. Beckley, T. Moore Ocean Surface Topography Science Team, Hobart March 2007 SGT, Inc.

2. APPROACH • Driving Assumption – information on wave steepness from global wave model can be integrated with altimeter Hs and U10 to improve routine sea state range corrections • TRACK 1 Nonparametric global SSB solutions using 2 input variables – SLA averaging method • Inputs are [ Hs, family of alternatives ] • Tran et al., 2006 JGR - methods and 1st results • TRACK 2 Three step clustering approach • Partition measurements using fuzzy clustering • Develop multi-class SSB solutions • Combine to give single global result

3. UPDATED DATA and 2nd PASS RESULTS Ocean surface wave model at UNH WaveWatch III (H. Tolman/NCEP; Feng et al., 2006) 2000-2006 complete, 6 hourly time step, 1 x 1 deg grid Composite altimeter + wave model data sets at UNH – many new correction field updates TOPEX 2000-2003 - latest NASA/GSFC pathfinder Jason-1 2002-2005 - GDRa, GDRb correction versions Key new corrections have SSB implications – MOG2D and ITRF2005 orbits – Do we see impacts? How robust/significant are these two SSB approaches?

4. Track 1 update: Global two parameter NP solutions • 1- Recomputation of alternate models with residual sea surface heights that take into account latest geophysical correction versions and on longer time period (1-year dataset at the time instead of 1/10 of the 2002 year dataset): • - altimeter retracking (GDRa: MLE3 + 1st order Brown model) • - JMR wet troposphere (GDRb: calibration parameters from cycles 1-115) • - dry troposphere (GDRb: from ECMWF atmospheric pressures and model for S1 and S2 atmospheric tides) • - Mog2D ocean model (GDRb: model forced by ECMWF atmospheric pressures after removing S1 and S2 atmospheric tides) • - Tide (GDRb: GOT00.2 +S1 ocean tide) • - Solid Earth tide • - pole tide • - dual-frequency ionospheric correction • CLS01 mss (GDRb) • 2- Consolidation of the OSTST’06 (Venice) results with models developed on 1-year period. • 3- Analysis of 2002, 2003 and 2004 results are presented as follows: • → datasets (2002) (2003) (2004) • Models ↓ • (2002) ↓ • (2003) ↓ • (2004) ↓

5. Jason-1 SSB Skill Map for H_swell vs Tm vs U_alt (benchmark is 3.8%Hs) H_swell dark = best performer 2002 SSB models, 2002 data results 2004 SSB models, 2004 data results

6. Jason-1 SSB Skill Map for PseudoWaveAge() vs InverseWaveAge vs U_alt (benchmark is 3.8%Hs)  = b(Hs/U2)0.62 note:  uses no wave model data  dark = best performer 2002 SSB models, 2002 data results 2004 SSB models, 2004 data results

7. Summary on Two Input NP work • Most results follow Tran et al., 2006 • Relatively stable and positive performance observed with swell height (H_swell) and Hs in the tropics • Results with mean wave period (Tm) parameter are fluctuating, its contribution to improved SSB is less compelling in these analyses • Pseudo wave age shows surprisingly improved performance (over Venice results) compared to the usual parameterization with U_alt. Possible reason: results are now from full year model • Development of global NP 3-parameter SSB models are on-going

8. Track 2: Objective classification of wave steepness using WW3 and altimeter data older seas – low sea state mixed seas – low sea state • Method assigns all ocean data samples to dynamic provinces • Useful for dealing with transient and noisy wind-wave process, imperfect wave model information • This illustration applies to sea state bias work, 6 classes young seas – low sea state mixed seas – mod sea state steep seas – mod. sea state high seas

9. Clustering Results – 6 classes Clustering input variables Variable Data source v1: Hs T/P , Jason1 v2: DH=Hsea/Hs WW3 model v3: DS=mssl/msst Alt. & WW3 where mssl = (2π )4/(g2 m4): (m4 accel. variance ) & msst = Reff / -Ku (where Reff=0.45) Rationale : combination of empiricism, theory, and pragmatism. Effectively using Pseudo Wave Age (v2) and rms slope (v3) Resulting classification yields: Low wave height classes (1-3): 1 = swell-dominated 2 = mixed sea 3 = young seas Moderate wave height classes (4-5): 4 = older seas/mix 5 = young seas (steep) Extreme wave height (6): 6 = high seas

10. CLUSTERING APPROACH ISSUES 1. Partition measurements using fuzzy clustering Can we develop a single classifying algorithm for full mission partitioning? For multiple missions? 2. Develop multi-class SSB solutions Do multi-year analyses show stability in results? Do Topex and Jason altimeters yield similar results? – physics (EM bias) vs. sensor engineering. Do NP solutions help to clean up class-based results? Is there a MOG2D impact? 3. Combine to give single global result What is the improvement level? How systematic is the improvement level in spatial domain?

11. Multi-year stability in solution- TOPEX 2000 2001 2002 Top panel shows the global direct SSB mapping on H10 and Hs for 2000, 2001, and 2002 Low panel shows the 200 samples of data samples for each of the 6 classes in the 2D domain. from TOPEX-WW3ecmwf ((NASA-GSFC Pathfinder datasets: 1/10 of the total points)

12. 2000 2001 2002 Figure 7. Hard partition (max membership) class-specific direct SSB maps on U10 and Hs domain for 2000, 2001, and 2002. from TOPEX+ WW3-ecmwf (NASA-GSFC Pathfinder datasets: 1/10 of the total points) (200 samples in a cell)

13. 2000 2001 2002 Figure 8. Anomaly between the global and class-specific SSB models for each of the six classes for the hard partition (max membership) class-specific direct SSB maps on U10 and Hs domain for 2000, 2001, and 2002. from TOPEX+ WW3-ecmwf (NASA-GSFC Pathfinder datasets: 1/10 of the total points) (200 samples in a cell)

14. Multi-year stability in solution, Jason-1 2002 2003 2004 Anomaly between the global and class-specific SSB models for each of the six classes for the hard partition (max membership) class-specific direct SSB maps on U10 and Hs domain for 2002, 2003, and 2004. from Jason-gdra+WW3-ecmwf by CLS collocation ( 5,000,000 samples were randomly selected from ~17,000,000 total samples).

15. Radar-to-radar stability in SSB anomaly – an EM bias test 2002 TOPEX 2002 Jason-1

16. CORRECTION EFFECTS- MOG2D Result: MOG2D impact apparent in global SSB algorithm but not in SSB residual between global model and class-based Conclusion: Not a strong correlation between ocean gravity wave-induced and HF Barotropic corrections 2000 TOPEX w/o MOG2D 2000 TOPEX with MOG2D

17. Now creating NP solutions for the class-based data at CLS Jason-1 2004: Anomaly between the global and class-specific SSB models Class 1 Class 2 Class 3 Class 4 Class 5 Class 6

18. Jason-1 2004 results using clustering-based NP SSB solution (6 classes) • Systematic improvements at all latitudes and most regions in the spatial benchmark at right • Not optimized yet so results will improve

19. SUMMARY • Both approaches showing measurable improvement in global SSB estimation – increased at equatorial and southern ocean locations • Stability of the methods appears solid across wave model runs, altimeter systems, and altimeter correction changes • Optimization and combination of these two approaches is ongoing and they blend well • Expected improvement level to be documented in coming months: crossovers + present metrics (20-30%) • Operational solution appears feasible and obtainable

20. We acknowledge the groundbreaking efforts and the always fruitful collaborations with our colleagues: Roman Glazman and Tony Elfouhaily They are fondly remembered and sorely missed.

22. Blended Retrieval Retrieval of constituent C is weighted sum: of retrievals from class-specific algorithms, Ci where weights are based on memberships, fi

23. Membership Function • Mahalanobis distance • Zi2 = (Rrs - mi)t i-1 (Rrs - mi) • Rrs – satellite pixel reflectance vector • mi – ith class mean vector • i– ith class covariance matrix • Compute chi-square probability • fi = 1 – Fn(Zi2) • for n degrees of freedom.

24. SSB modeling for each class vs. global avg. - An illustration of the potential for improved sea surface estimates through combination of the 6 class-based SSB models (RED = positive skill in cm2)