1. Status and perspectives of the T O P A Z system Laurent.Bertino@nersc.no An EC FP V project, Dec 2000-Nov 2003 http://topaz.nersc.no http://topaz.nersc.no NERSC/LEGI/CLS/AWI Continued development of DIADEM system… Continuing with the MerSea Str.1 and MerSea IP EC-projects

2. The monitoring and prediction system

3. From DIADEM to TOPAZ Model upgrades –MICOM upgraded to HYCOM –2 Sea-Ice models –3 ecosystem models (1 simple, 2 complex) –Nesting: Gulf of Mexico, North Sea (MONCOZE)

4. From DIADEM to TOPAZ Assimilation already in Real-time –SST ¼ degree from CLS, with clouds. –SLA ¼ degree from CLS. Assimilation tested –SeaWIFs Ocean Colour data (ready) –Ice parameters from SSMI, Cryosat (ready) –In situ observations: ARGO floats and XBT (ready) –Temperature brightness from SMOS (ready)

5. Assimilation methods Kalman filters: full Atlantic domain –Ensemble Kalman Filter (EnKF) –Singular Evolutive Extended Kalman Filter (SEEK) Optimal Interpolation: Nested models –Ensemble Optimal Interpolation (EnOI)

6. Grid size: from 20 to 40 km

7. SSH from assimilation and data

8. EnKF: local assimilation of SST

9. Perspectives EnKF: one generic assimilation scheme (global/local) Possibilities for specific schemes –using methodology from geostatistics –Estimation under constraints (conservation) –Estimation of transformed Gaussian variables (Anamorphosis)

10. Thus TOPAZ is Extension and utilization of DIADEM system Product and user oriented with strong link to off shore industry Contribution to GODAE and EuroGOOS task teams To be continued with Mersea IP EC-project. CUSTOMERS TOPAZ GODAE

11. Summary HYCOM model system completed and validated Assimilation capability for in situ and ice observations ready Development of forecasting capability for regional nested model (cf Winther & al.) Operational demonstration phase started http://topaz.nersc.noResults on the web http://topaz.nersc.no

12. Assimilating ice concentrations Assimilation of ice concentration controls the location of the ice edge Correlation changes sign dependent on season A fully multivariate approach is needed Largest impact along the ice edge

13. Ice concentration update

14. Temperature update

15. Assimilating TB data Brightness temperature TB will be available from SMOS (2006) Assimilation of TB data controls SSS and impacts SST TB (SST, SSS, Wind speed, Incidence, Azimuth, Polarization) Results are promising using the EnKF

16. TB data SST SSS TB

17. TB Assimilation SST impact SSS impact

18. Bibliography The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation, Geir Evensen, in print, Ocean Dynamics, 2003. About the anamorphosis: Sequential data assimilation techniques in oceanography, L. Bertino, G. Evensen, H. Wackernagel, (2003) International Statistical Review, (71), 1, pp. 223-242.

19. An Ensemble Kalman Filter for non-Gaussian variables L. Bertino 1, A. Hollard 2, G. Evensen 1, H. Wackernagel 2 1- NERSC, Norway 2- ENSMP - Centre de Géostatistique, France Work performed within the TOPAZ EC- project

20. Overview “Optimality” in Data Assimilation –Simple stochastic models, complex physical models → Difficulty: feeding models with estimates The anamorphosis: –Suggestion for an easier model-data interface Illustration –A simple ecological model

21. Data assimilation at the interface between statistics and physics State Observations stochastic model –f, h: linear operators –X, Y: Gaussian –Linear estimation optimal “optimality” for non-physical criteria => post-processing physical model –f, h: nonlinear –X, Y: not Gaussian –… sub-optimal

22. The multi-Gaussian model underlying in linear estimation methods state variables and assimilated data between all variables and all locations Gaussian histogram s Linear relations The world does not need to look like this...

23. Why Monte Carlo sampling? Non-linear estimation: no direct method –The mean does not commute with nonlinear functions: E(f(X))  f(E(X)) With random sampling A={X 1, … X 100 } E(f(X))  1/100  i f(X i ) EnKF: Monte-Carlo in propagation step Present work: Monte-Carlo in analysis step

24. The EnKF Monte-Carlo in model propagation Advantage 1: a general tool –No model linearization –Valid for a large class of nonlinear physical models –Models evaluated via the choice of model errors. Advantage 2: practical to implement –Short portable code, separate from the model code –Perturb the states in a physically understandable way –Little engineering: results easy to interpret Inconvenient: CPU-hungry

25. Ensemble Kalman filter basic algorithm (details in Evensen 2003) State Observations nonlinear propagation, linear analysis A a n = f(A a n-1 ) + K n (Y n - HA f n ) A a n = A f n. X 5 Notations: Ensemble A = {X 1, X 2,… X 100 }, A’ = A - Ā Kalman gain: K n = A n f A’ f n T H T. ( H A’ f n A’ f n T H T + R ) - 1

26. Anamorphosis A classical tool from geostatistics More adequate for linear estimation and simulations Physical variable Cumulative density function Statistical variable Example: phytoplankton in-situ concentrations

27. Anamorphosis in sequential DA separate the physics from statistics Physical operations: Anamorphosis function Statistical operation: A and Y transformed Forecast A f n = f (A a n-1 ) Forecast A f n+1 = f (A a n ) Analysis A a n = A f n + K n (Y n -HA f n ) Adjusted every time or once for all Polynomial fit, distribution tails by hand

28. The anamorphosis Monte-Carlo in statistical analysis Advantage 1: a general tool –Valid for a larger class of variables and data –Applicable in any sequential DA (OI, EKF …) –Further use: probability of a risk variable Advantage 2: practical implementation –No truncation of unrealistic/negative values (no gravity waves?) –No additional CPU cost –Simple to implement Inconvenient: handle with care!

29. Characteristics Sensitive to initial conditions Non-linear dynamics Nutrients PhytoplanktonHerbivores Illustration Idealised case: 1-D ecological model Spring bloom model, yearly cycles in the ocean Evans & Parslow (1985), Eknes & Evensen (2002) time-depths plots

30. Anamorphosis (logarithmic transform) Original histograms asymmetric Histograms of logarithms less asymmetric NPH Arbitrary choice, possible refinements (polynomial fit)

31. EnKF assimilation results Gaussian assumption –Truncated H < 0 –Low H values overestimated –“False starts” Lognormal assumption –Only positive values –Errors dependent on values RMS errors GaussianLognormal N P H

32. Conclusions An “Optimal estimate” is not an absolute concept –“Optimality” refers to a given stochastic model –Monte-Carlo methods for complex stochastic models The anamorphosis and linear estimation –Handles a more general class of variables –Applications in marine ecology (positive variables) Can be used with OI, EKF and EnKF. Next: combination of EnKF with SIR …