The I nverse R egional O cean M odeling S ystem

1. The Inverse Regional Ocean Modeling System Development and Application to Variational Data Assimilation of Coastal Mesoscale Eddies. Di Lorenzo, E. Georgia Institute of Technology Moore, A. UC Santa Cruz Arango, H. Rutgers University Cornuelle, B and A.J. Miller Scripps Institution of Oceanography Chua B. and A. Bennett Oregon State University

2. Regional Ocean Modeling System (ROMS) Pacific Model Grid SSHa (Feb. 1998) Canada Asia USA Australia (source: modeling team Rutgers, UCLA, GaTech, Scripps)

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. (2003) Inverse Regional Ocean Modeling System (IROMS) Di Lorenzo et al. (2006) 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 Arango et al. 2003Moore et al. 2003Di Lorenzo et al. 2006 Ensemble Ocean Prediction

5. ASSIMILATION Goal Initial Guess Best Model Estimate (consistent with observations)

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

7. Cost Function

8. 4DVAR inversion Model x Model Hessian Matrix

9. 4DVAR inversion Model x Model Hessian Matrix IROMS representer-based inversion Obs x Obs Representer Coefficients Representer Matrix Stabilized Representer Matrix

10. WEAK CONSTRAINT

11. TRUE Mesoscale Structure ASSIMILATION Setup Sampling: (from CalCOFI program) 5 day cruise 80 km stations spacing Observations: T,S CTD cast 0-500m Currents 0-150m SSH Model Configuration: Open boundary cond.nested in CCS grid 20 km horiz. Resolution20 vertical layersForcing NCEP fluxesClimatology initial cond. SSH [m] SST [C]

12. SSH [m] TRUE day=5 1st GUESS day=5

13. SSH [m] ASSIMILATION Results STRONG day=5 TRUE day=5 WEAK day=5 1st GUESS day=5

14. ASSIMILATION Results SSH [m] STRONG day=5 ERROR or RESIDUALS WEAK day=5 1st GUESS day=5

15. ERROR or RESIDUALS ASSIMILATION Results Sea Surface Temperature [C] WEAK day=5 1st GUESS day=5

16. Reconstructed Initial Conditions STRONG day=0 TRUE day=0 1st GUESS day=0 WEAK day=0

17. Normalized Observation-Model Misfit  before assimilation T S U V observation number Assimilated data: TS 0-500m Free surface Currents 0-150m

18. Normalized Observation-Model Misfit  after assimilation T S U V observation number Assimilated data: TS 0-500m Free surface Currents 0-150m Error Variance Reduction STRONG Case = 92%WEAK Case = 98%

19. SKILL = 1 – (SST RMS error) Persistence WEAK STRONG Climatology Initial Guess days assimilation window forecast

20. Subsurface Temperature Salinity Persistence Free Surface Height Velocity Initial Guess

21. THOUGHTS on the SCB test • Choosing climatology as the 1st guess leads to dynamically unbalanced fields, a strong initial shock, which degrades the quality of assimilated solution. • Assimilating the data greatly improves the model trajectory for 10 days after the assimilation window when compared to the 1st guess. • We should be able to exploit the long persistence timescale associated with the slow moving California Current eddies. • A 5 day assimilation window may be too short to extract the time dependent dynamical information required to improve the model trajectory. • Different definition of skill may be more appropriate to isolate the ability of the model to correct and predict the spatial structure of the eddies. • Explore and characterize the dynamical sensitivities of the flow field, and the predictability timescales of the California Current.

22. PROGRESS • Developed and tested assimilation capability of ROMS for a realistic nested model setup (the California Current eddies • ROMS can be used with IOM framework  IROMS

23. ASSIMILATION Results Velocity (V) STRONG day=5 ERROR or RESIDUALS WEAK day=5 1st GUESS day=5

24. TANGENT LINEAR INSTABILITY SST [C] AHV=4550 AHT=4550 AHV=0 AHT=0 AHV=4550 AHT=0 AHV=4550 AHT=1000

25. TANGENT LINEAR INSTABILITY Non Linear Model Initial Guess TLMAHV=4550 AHT=4550 TLMAHV=0 AHT=0 TLMAHV=4550 AHT=1000

26. PROGRESS • Developed and tested assimilation capability of ROMS for a realistic nested model setup (the California Current eddies • ROMS can be used with IOM framework  IROMS PENDING TECHNICAL ASPECTS • Tangent Linear Dynamics are very unstable in realistic settings. Need to find the “optimal” combination of increased viscosity/diffusivity and reduced physics to recover stability. • Background and Model Error COVARIANCE functions are Gaussian and implemented through the use of the diffusion operator. We are implementing spatially dependent decorrelation length scales and additional dynamical constraint (e.g. geostrophy)

27. …end

29. temp salt V zeta

30. WEAK day=0 WEAK day=5

31. TRUE day=5 CLIMA day=5 STRONG day=5 WEAK day=5

33. Velocity FULL

34. Weak Constraint Results

35. WEAK - dimensional zeta = 81.303 temp = 88.112 salt = 97.177 u = 96.591 v = 95.9 TOTAL non-dimnensional=98% Strong - dimensional zeta = 84.374 var_red = 92.131 var_red = 94.522 var_red = 86.654 var_red = 88.683 TOTAL = 92%