Assimilation of satellite observations in the Mediterranean Forecasting System

1. Summer School on Ocean Observation with Remote Sensing Satellites 18-23 June 2010 Assimilation of satellite observations in the Mediterranean Forecasting System Lecture by: Srdjan Dobricic In collaboration with Nadia Pinardi , Jenny A.U. Nilsson, Vincent Taillandier, Daniele Pettenuzzo and Mario Adani

2. The MFS general circulation model BATHYMETRY (m)‏ • MFS 1671 Sys3a2: OPA 8.1 Code • Implicit free surface, 1/16º * 1/16º hor. resol., 49 islands • 71 vertical levels (1.5-5000m)‏ • Atlantic box closed

3. XBT VOS high resolution system (12 nm along track and full profile transmission) Argo floats Daily satellite SST interpolated in RT on model grid JASON-1, GFO, ENVISAT, T/P Sea Level Anomalies RT products Open ocean monitoring by gliders Basin scale observing system

4. 1. Assimilation of SLA observations

5. SLA observational bias: Mean Dynamic Topography error

6. SLA observational bias: Mean Dynamic Topography error

7. 2. Assimilation of SST observations

8. Assimilation of satellite SST observations Full misfit Large scale Observation – model SST (0C) Small scale

9. 3. Assimilation of float positions

10. 3DVAR cost function 3DVAR finds the minimum of a cost function linearized around the background state: Increments: Small and can be neglected Misfits: Linearisation:

11. Modelling the observational operator for trajectories The observational operator connects the float position data to velocity by the following equations: The non-linear equation is linearised around the background velocity field and the non-linear trajectory:

12. The MedARGO system: 350 meters trajectories Descending position and time - r(tb), tb 350m Ascending position and time – r(t), t 700m (each 10 cycles to 2000m)‏

13. Numerical experiments Two numerical experiments for the 3 yr period 2005-2007 • NOTRAJ exp: SLA, SST, XBT, T&S profiles from Argo floats , • TRAJASS exp: SLA, SST, XBT, Argo float T&S profiles and trajectories. Assimilation parameters Trajectory data from floats drifting in shallow areas (depth <400 m) were excluded in order to avoid spurios trajectory data (approx. 4% of the data was removed). Observational error was chosen 2 km accounting for surface drift Initial float position of each assimilation cycle is re-set to observational float position

14. Argo data sampling 2006 2007 2005

15. 2 Second (next) observation Analysed position (after traj. ass)‏ ”Forecasted” position (background)‏ 1 First observation Simulated position Diagnostics of assimilation of observed float positions Difference btwn Observations and background Difference btwn Observations and analysis

16. Argo float position RMS error 2006 2007 2005 Observations- simulation Observations- background Observations- analysis Assimilation has improved the forecast of trajectories

17. Difference between Traj-noTraj assimilation mean fields at 350m and after 1 months assimilation Observed Argo floats 1-25 january 2005 The effects of trajectory assimilation on the Mediterranean sub-surface currents (~1-7 cm/s) are consonant with the results published by Taillandier et al 2009 for the Provencal basin.

18. Local effects of trajectory assimilation in the vertical plane

19. Assimilation of trajectories from surface drifters Positions of surface drifters in the period 10 april – 26 april 2006

20. Impact of the assimilation of trajectories from surface drifters Assimilation of trajectories observed by surface drifters Salinity at depth 100m on 26 April 2006 Control analysis

21. 4. Assimilation of glider drifts

22. Assimilation of glider observations Path of the glider (October - December 2004)

23. Assimilated observations from other instruments Colored squares – number of SLA observations Black circles – Argo floats Black crosses – XBT temperature observations

24. Temperature along glider path Observations Analyses without glider data Analyses with glider data

25. Salinity along glider path Observations Analyses without glider data Analyses with glider data

26. RMS of misfits in different experiments Yellow - improvement compared to the control analyses Red - degradation compared to the control analyses * - minimum RMS of misfits

27. Sea level, temperature and salinity in top 200m Sea level (cm) Temperature (0C) Salinity (PSU)

28. Differences in sea level between glider and control analyses (cm) No glider Glider Weekly RMS of SLA misfits (cm) in the whole basin Sea level (cm) on 28 Feb 2005

29. Evolution of Sea Level (cm) from October 2004 to March 2005 Position of the Atlantic Ionian Stream in October Eddy pinching off the Atlantic Ionian Stream Position of the Atlantic Ionian Stream in March

30. 5. Data assimilation in a regional model

31. Implementation in the Adriatic Sea regional system Bathimetry of the Adriatic Sea (m)

32. Time Loop (DAYS) Sigma coordinate interface SIGMA COORDINATE MODEL Time Loop (model steps) Coupling with the sigma coordinate ocean model Misfits (FGAT) Model restart Misfits 3DVAR (Z COORDINATE) Corrections

33. Implementation in the Adriatic Sea regional system Sea level (cm)

34. Implementation in the Adriatic Sea regional system Magnitude of velocity (cm/s)

35. 6. Accounting for uncertainties in the analyses: BHM approach

36. The outlook: forecast uncertainity estimation • Forecast uncertainty can be estimated with ensemble techniques (Montecarlo methods) • Ocean ensemble members can be produced with perturbed atmospheric forcing (uncertainty no.1) and initial conditions perturbations (uncertainty no.2) Perturbed I.C. Ensemble forecast day j-14 day j day j+10 Ensemble ANALYSES FORECAST

37. The perturbed winds: a Bayesian Hierarchical Model (BHM) for surface winds 0:00 UTC 6:00 UTC 12:00 UTC 18:00 UTC

38. The perturbed winds: a Bayesian Hierarchical Model (BHM) for surface winds Space scale Analyses winds 2000 2001 2002 2003 2004 2005 2006 2007 2008 QSCAT Kinetic Energy ECMWF

39. The process model stage: from continuos to stochastic 1. Discretization of the process model 2. Add uncertainty term and stochastic parameters where εu,v are error models to be prescribed (nested Wavelets)‏

40. The perturbed winds: a Bayesian Hierarchical Model (BHM) for surface winds

41. Geostrophic Validation Modes for posterior distributions of parameters for geostrophic terms are +/- inverse Coriolis; ageostrophic parameters are 0. With and Without QuikSCAT Posterior Distributions Process Model Parameters: QuikSCAT data increase spread (non-Gaussian), and shift distributions farther from Geostrophy. Is the prior sophisticated enough to be interpretable in physical terms

42. Background Error versus Ensemble Spread TEMPERATURE RMS RMS BHM-SPREAD BHM-SPREAD FEB DEC FEB DEC RMS- 90’s Re-An RMS- 90’s Re-An

43. The sea level forecast uncertainity due to errors induced by wind forcing BHM ensemble ocean spread Mean of SSH Forecast uncertainty Init. Cond. Pert. ocean spread ECMWF ensemble ocean spread

44. The forecast spread at t0+10days EEPS forced ensemble BHM-SVW ensemble