Status and perspectives of the T O P A Z system

1. Status and perspectives of the TOPAZ system Laurent.Bertino@nersc.no An EC FP V project, Dec 2000-Nov 2003http://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 • Results 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 SSTSSS TB

17. TB AssimilationSST 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. Bertino1,A. Hollard2, G. Evensen1, H. Wackernagel2 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 physical model • f, h: nonlinear • X, Y: not Gaussian • … sub-optimal “optimality” for non-physical criteria => post-processing

22. The multi-Gaussian modelunderlying in linear estimation methods Gaussian histograms Linear relations • state variables • and assimilated data • between all variables • and all locations 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={X1, … X100} E(f(X)) 1/100if(Xi) • EnKF: Monte-Carlo in propagation step • Present work: Monte-Carlo in analysis step

24. 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 The EnKFMonte-Carlo in model propagation

25. Ensemble Kalman filterbasic algorithm (details in Evensen 2003) State Observations nonlinear propagation, linear analysis Aan = f(Aan-1) + Kn (Yn - HAfn ) Aan= Afn . X5 Kalman gain: Kn = Anf A’fnT HT . ( H A’fn A’fnT HT + R ) -1 Notations: Ensemble A = {X1, X2,… X100}, A’ = A - Ā

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

27. Anamorphosis in sequential DAseparate the physics from statistics Physical operations: Statistical operation: A and Y transformed Anamorphosis function Forecast Afn = f (Aan-1) Analysis Aan = Afn+ Kn(Yn-HAfn) Forecast Afn+1 = f (Aan) • Adjusted every time or once for all • Polynomial fit, distribution tails by hand

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

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

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

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 …