1. Joint OS & SWH meeting in support of Wide-Swath Altimetry Measurements Washington D.C. – October 30th, 2006 Baptiste MOURRE ICM – Barcelona (Spain) Pierre DE MEY Matthieu LE HENAFF Yves MENARD Christian LE PROVOST Florent LYARD LEGOS – Toulouse (France) Pierre-Yves LE TRAON IFREMER – Brest (France) Performance of a Wide Swath Altimeter to control a model of North Sea dynamics

2. Outline Model and data assimilation approach Spatio-temporal scales of model error Wide Swath Altimeter performance First case: with uncorrelated observation error Impact of the along track correlated roll error 1 2 3 Perform Observing-Systems Simulation Experiments (OSSEs) to estimate the contribution of a Wide Swath Altimeter to monitor North Sea dynamics. Objective Particular case of Coastal ocean/continental shelf region. Integrated approach: optimal combination of the observations with a numerical ocean model thanks to data assimilation techniques.

3. Simulated processes: ocean response to meteorological forcing (wind and pressure). No tides included. high-frequency gravity waves (Kelvin-type, characteristic scales: 1d / 100 km / 50 cm) (2D Gravity Wave Model) Barotropic Finite-element Nonlinear 7 31 Dec 1998 Modelling area: the European shelf focus on the North Sea Model and study area MOG2D model Model and data assimilation approach

4. Assimilation of observations: the ensemble Kalman filter (Evensen 2003) N analysis Observations time t 2 P f (t 2 ) N analysis Observations time t 1 P f (t 1 ) N model integrations... N model integrations Proper representation of model error covariances: tricky issue when approaching coastal areas ! Model and data assimilation approach In our case, bathymetry perturbations Use of ensemble methods: model error statistics are empirically computed from an ensemble of “possible states” of the ocean. Ensemble variances approximate model error variances.

5. 3 0 Saptio-temporal scales of model error Mean variances over the study period (cm2). Sea level ensemble variances 100 km 10 15 20 2530 Days (December 1998) 12 0 10 15 20 2530 Days (December 1998) 0 10 2 days 1 day

6. 200-km swath 15-km resolution Jason 10-day orbit Contribution of a Wide Swath Altimeter Wide Swath Altimeter performance Observation error: White noise, from 3,9 to 5,3 cm rms, depending on the distance to nadir. (Uncorrelated observation error first)

7. Sea level ensemble variances before analysis (cm2) 12/31/1998 0am 0 5 One example : track on 31 December 1998, 0am. Jason 0 5 Jason+T/P 0 5 Instantaneous reduction of sea level ensemble variances WS Alt. 0 5 Sea level ensemble variances after analysis (cm2) Wide Swath Altimeter performance ANALYSIS 5 0 TideGauges

8. - 29.7 % Sea level ensemble variances (cm 2 ) Days (December 1998) Jason Wide Swath Atlimeter - 52.6 % Reduction by the assimilation Local reduction of sea level ensemble variances Wide Swath Altimeter performance

9. Local reduction of sea level ensemble variances - 39.7 % Sea level ensemble variances (cm 2 ) Jason Wide Swath Atlimeter - 24.3 % Wide Swath Altimeter performance Days (December 1998)

10. Global space-time reduction of ensemble variances Wide Swath Altimeter performance Jason + T/P Jason Wide Swath (10-day orbit) Sea level ensemble variance reduction (%)

11. Global space-time reduction of ensemble variances Sea level ensemble variance reduction (%) Zonal velocity ensemble variance reduction (%) Wide Swath Altimeter performance Jason + T/P Jason Wide Swath (10-day orbit)

12. Global space-time reduction of ensemble variances Wide Swath Altimeter performance Jason + T/P Jason Wide Swath (10-day orbit) Nadir (3-day o.) Wide Swath (3d) Nadir (17-day o.) Wide Swath (17d) Sea level ensemble variance reduction (%) Zonal velocity ensemble variance reduction (%)

13. Global space-time reduction of ensemble variances Wide Swath Altimeter performance Jason + T/P Jason Wide Swath (10-day orbit) 2 Jason 3 Jason Temporally interleaved Sea level ensemble variance reduction (%) Zonal velocity ensemble variance reduction (%)

14. Significant contribution compared to conventional altimeters. Performance score: + 70 % for sea level correction + 130 % for velocity correction 1 Wide Swath Altimeter ~ 2 nadir alt. for sea level control ~ 3 nadir alt. for velocity control Here (particular context of high-frequency oceanic processes), temporal resolution is still lacking to control the main part of model error. Interesting complementarity with tide gauges. Summary of Wide Swath performance (with uncorrelated obs. error) Wide Swath Altimeter performance

15. Impact of the along-track correlated roll error Wide Swath Altimeter performance New study with simplified measurement model: White noise 3,9 cm rms White noise 4 cm rms + along-track correlated roll error f ≃ 0.02 Hz  L ≃ 350 km amplitude = 11.6 cm (Enjolras, 2006) 1 nadir + 1 slope measurement Observation error

16. Wide Swath Altimeter performance Global space-time reduction of ensemble variances Sea level ensemble variances reduction (%) Zonal velocity ensemble variances reduction (%) Nadir alone (no roll error) Nadir + slope (no roll error)

17. Wide Swath Altimeter performance Global space-time reduction of ensemble variances Sea level ensemble variances reduction (%) Zonal velocity ensemble variances reduction (%) Nadir alone (no roll error) Nadir + slope (no roll error) Nadir + slope (roll error - in obs. & analysis)

18. Wide Swath Altimeter performance Global space-time reduction of ensemble variances Sea level ensemble variances reduction (%) Zonal velocity ensemble variances reduction (%) Nadir alone (no roll error) Nadir + slope (no roll error) Nadir + slope (roll error - in obs. & analysis) Nadir + slope (roll error - correlations ignored in the analysis)

19. Conclusions Without roll error: 1 Wide Swath Altimeter ~ 2 nadir alt. for sea level control ~ 3 nadir alt. for velocity control With roll error: - Slight degradation of the performance, but contribution still valuable (if correlations represented in the analysis !). - True even if the roll frequency is not precisely known (not shown here). Results linked to the particular North Sea dynamics. Generalization 1) to other model error sources (e.g. wind & pressure): reasonable (same spatio-temporal scales) 2) to other shelf/coastal areas: with maximum caution ! (spatio-temporal scales have to be considered, generalization a priori only possible in areas with energetic wind-driven barotropic dynamics…) ! The contribution of the Wide Swath should improve when considering longer time scales and shorter spatial scales...

20. Results in: Mourre et al., Ocean Dynamics, 2006 Le Hénaff et al., in preparation, 2006