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Baptiste MOURRE ICM – Barcelona (Spain) Pierre DE MEY Matthieu LE HENAFF Yves MENARD

Performance of a Wide Swath Altimeter to control a model of North Sea dynamics. 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).

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Baptiste MOURRE ICM – Barcelona (Spain) Pierre DE MEY Matthieu LE HENAFF Yves MENARD

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  1. Performance of a Wide Swath Altimeter to control a model of North Sea dynamics 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) Joint OS & SWH meeting in support of Wide-Swath Altimetry Measurements Washington D.C. – October 30th, 2006

  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 Objective Perform Observing-Systems Simulation Experiments(OSSEs) toestimate the contribution of a Wide Swath Altimeter to monitor North Sea dynamics. 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. Model and study area • Modelling area: the European shelf focus on the North Sea MOG2D model • (2D Gravity Wave Model) • Barotropic • Finite-element • Nonlinear • 7 31 Dec 1998 Model and data assimilation approach • 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)

  4. time t1 time t2 Observations Observations N analysis N analysis N model N model ... integrations In our case, bathymetry perturbations integrations Pf(t1) Pf(t2) Assimilation of observations: the ensemble Kalman filter (Evensen 2003) Proper representation of model error covariances: tricky issue when approaching coastal areas ! 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. Model and data assimilation approach

  5. 12 2 days 2 days 0 10 10 20 20 15 15 25 25 30 30 Days (December 1998) 10 1 day 0 Days (December 1998) 3 0 Sea level ensemble variances Saptio-temporal scales of model error 100 km Mean variances over the study period (cm2).

  6. Contribution of a Wide Swath Altimeter • 200-km swath • 15-km resolution • Jason 10-day orbit 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. Jason+T/P 5 0 WS Alt. TideGauges 5 5 0 0 Instantaneous reduction of sea level ensemble variances Jason One example : track on 31 December 1998, 0am. 5 0 Wide Swath Altimeter performance Sea level ensemble variances after analysis (cm2) ANALYSIS 5 0 Sea level ensemble variances before analysis (cm2) 12/31/1998 0am

  8. Local reduction of sea level ensemble variances Sea level ensemble variances (cm2) Jason Reduction by the assimilation - 29.7 % Wide Swath Altimeter performance Wide Swath Atlimeter - 52.6 % Days (December 1998)

  9. Local reduction of sea level ensemble variances Sea level ensemble variances (cm2) Jason - 24.3 % Wide Swath Altimeter performance Wide Swath Atlimeter - 39.7 % Days (December 1998)

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

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

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

  14. Summary of Wide Swath performance (with uncorrelated obs. error) • 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. Wide Swath Altimeter performance

  15. Impact of the along-track correlated roll error • New study with simplified measurement model: Wide Swath Altimeter performance 1 nadir + 1 slope measurement 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) Observation error

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

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

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

  19. Results linked to the particular North Sea dynamics. Generalization 1) toother model error sources (e.g. wind & pressure): reasonable (same spatio-temporal scales) 2) toother 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... 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).

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

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