Di Lorenzo, E. Georgia Institute of Technology Arango, H. Rutgers University

1. Weak and Strong Constraint 4DVAR in the Regional Ocean Modeling System (ROMS):Development and Applications Di Lorenzo, E. Georgia Institute of Technology Arango, H. Rutgers University Moore, A. and B. Powell UC Santa Cruz Cornuelle, B and A.J. Miller Scripps Institution of Oceanography

2. Short review of development and theory (an alternative derivation of the representer method) • Current applications (some pending issues)

3. Inverse Ocean Modeling System (IOMs) Chua and Bennett (2001) To implement a representer-based generalized inverse method to solve weak constraint data assimilation problems NL-ROMS, TL-ROMS, REP-ROMS, AD-ROMS Moore et al. (2004) Inverse Regional Ocean Modeling System (ROMS) Di Lorenzo et al. (2007) a representer-based 4D-variational data assimilationsystem for high-resolution basin-wide and coastal oceanic flows

4. ROMS Block Diagram NEW Developments Stability Analysis Modules Non Linear Model Tangent Linear Model Representer Model Adjoint Model Sensitivity Analysis Data Assimilation 1) Incremental 4DVARStrong Constrain 2) Indirect Representer Weak and Strong Constrain 3) PSAS Arango et al. 2003Moore et al. 2004Di Lorenzo et al. 2007 Ensemble Ocean Prediction

5. Inverse Ocean Modeling Portal Download: ROMS components http://myroms.org Arango H. IOM componentshttp://iom.asu.edu Muccino, J. et al.

6. ASSIMILATION Goal Initial Guess Best Model Estimate (consistent with observations) (A) (B) WEAK Constraint STRONG Constraint …we want to find the correctionse

7. Quadratic Linear Cost Function for residuals

8. Quadratic Linear Cost Function for residuals 1) corrections should reduce misfit within observational error 2) corrections should not exceed our assumptions about the errors in model initial condition.

9. ASSIMILATION Cost Function

10. is a mapping matrix of dimensions observations X model space def: ASSIMILATION Cost Function

11. is a mapping matrix of dimensions observations X model space def: ASSIMILATION Cost Function

12. ASSIMILATION Cost Function

13. def: 4DVAR inversion Hessian Matrix

14. def: 4DVAR inversion Hessian Matrix IOM representer-based inversion

15. def: 4DVAR inversion Hessian Matrix IOM representer-based inversion Representer Coefficients Stabilized Representer Matrix Representer Matrix

16. def: 4DVAR inversion Hessian Matrix IOM representer-based inversion Representer Coefficients Stabilized Representer Matrix Representer Matrix

17. An example of Representer Functionsfor the Upwelling System Computed using the TL-ROMS and AD-ROMS

18. An example of Representer Functionsfor the Upwelling System Computed using the TL-ROMS and AD-ROMS

19. Applications of inverse ROMS: • Baroclinic coastal upwelling: synthetic model experiment to test the development • CalCOFI Reanalysis: produce ocean estimates for the CalCOFI cruises from 1984-2006. Di Lorenzo, Miller, Cornuelle and Moisan • Intra-Americas Seas Real-Time DAPowell, Moore, Arango, Di Lorenzo, Milliff et al.

20. Coastal Baroclinic Upwelling System Model Setup and Sampling Array section

21. Applications of inverse ROMS: • Baroclinic coastal upwelling: synthetic model experiment to test the development 1) The representer system is able to initialize the forecast extracting dynamical information from the observations. 2) Forecast skill beats persistence 10 day assimilation window 10 day forecast

22. SKILL of assimilation solution in Coastal UpwellingComparison with independent observations Weak SKILL Strong Climatology Persistence Assimilation Forecast  DAYS Di Lorenzo et al. 2007; Ocean Modeling

23. Day=0 Day=2 Day=6 Day=10

24. Assimilation solutions Day=0 Day=2 Day=6 Day=10

25. Day=14 Day=18 Day=22 Day=26

26. Day=14 Day=18 Day=22 Day=26

27. Forecast Day=14 Day=14 Day=18 Day=18 Day=22 Day=22 Day=26 Day=26

28. Intra-Americas Seas Real-Time DAPowell, Moore, Arango, Di Lorenzo, Milliff et al. www.myroms.org/ias April 3, 2007

29. CalCOFI Reanlysis: produce ocean estimates for the CalCOFI cruises from 1984-2006. Di Lorenzo, Miller, Cornuelle and Moisan

30. Things we struggle with … • Tangent Linear Dynamics can be very unstable in realistic settings. • Background and Model Error COVARIANCE functions are Gaussian and implemented through the use of the diffusion operator. • Fitting data vs. improving the dynamical trajectory of the model.

31. Assimilation of surface Salinity True Initial Condition True

32. Assimilation of surface Salinity True Initial Condition Which model has correct dynamics? Model 1 Model 2 True

33. Wrong Model Good Model True Initial Condition Model 1 Model 2 True

34. Time Evolution of solutions after assimilation Wrong Model DAY 0 Good Model

35. Time Evolution of solutions after assimilation Wrong Model DAY 1 Good Model

36. Time Evolution of solutions after assimilation Wrong Model DAY 2 Good Model

37. Time Evolution of solutions after assimilation Wrong Model DAY 3 Good Model

38. Time Evolution of solutions after assimilation Wrong Model DAY 4 Good Model

39. RMS difference from TRUE Less constraint RMS More constraint Days Observations

40. Applications of inverse ROMS (cont.) • Improve model seasonal statisticsusing surface and open boundary conditions as the only controls. • Predictability of mesoscale flows in the CCS: explore dynamics that control the timescales of predictability. Mosca et al. – (Georgia Tech)

41. inverse machinery of ROMS can be applied to regional ocean climate studies …

42. inverse machinery of ROMS can be applied to regional ocean climate studies … EXAMPLE:Decadal changes in the CCS upwelling cells Chhak and Di Lorenzo, 2007; GRL

43. Observed PDO index Model PDO index SSTa Composites Cold Phase Warm Phase 1 2 3 4 Chhak and Di Lorenzo, 2007; GRL

44. -50 -50 -100 -100 -150 -150 -200 -200 -250 -250 -300 -300 -350 -350 -400 -400 -450 -450 50N 50N -500 -500 40N 40N -140W -140W -130W 30N -130W 30N -120W -120W Tracking Changes of CCS Upwelling Source Waters during the PDOusing adjoint passive tracers enembles WARM PHASEensemble average COLD PHASEensemble average April Upwelling Site Pt. Conception Pt. Conception depth [m] Chhak and Di Lorenzo, 2007; GRL

45. Changes in depth of Upwelling Cell (Central California) and PDO Index Timeseries Concentration Anomaly Adjoint Tracer year Model PDO PDO lowpassed Surface 0-50 meters (-) 50-100 meters (-) 150-250 meters Chhak and Di Lorenzo, 2007; GRL

46. References Arango, H., A. M. Moore, E. Di Lorenzo, B. D. Cornuelle, A. J. Miller, and D. J. Neilson, 2003: The ROMS tangent linear and adjoint models: A comprehensive ocean prediction and analysis system. IMCS, Rutgers Tech. Reports. Moore, A. M., H. G. Arango, E. Di Lorenzo, B. D. Cornuelle, A. J. Miller, and D. J. Neilson, 2004: A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modeling, 7, 227-258. Di Lorenzo, E., Moore, A., H. Arango, Chua, B. D. Cornuelle, A. J. Miller, B. Powell and Bennett A., 2007: Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): development and application for a baroclinic coastal upwelling system. Ocean Modeling, doi:10.1016/j.ocemod.2006.08.002.

47. Adjoint passive tracers ensembles physical circulation independent of

48. Regional Ocean Modeling System (ROMS) Pacific Model Grid SSHa (Feb. 1998) Canada Asia USA Australia

49. What if we apply more smoothing? Wrong Model Good Model True Initial Condition True Model 1 Model 2

50. Assimilation of data at time True Initial Condition True Model 1 Model 2