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

Weak Constraint 4DVAR in the R egional O cean M odeling S ystem ( ROMS ): Development and application for a baroclinic coastal upwelling system. Di Lorenzo, E. Georgia Institute of Technology Arango, H. Rutgers University Moore, A. and Powell B. UC Santa Cruz

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

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

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

  3. 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. 2003Di Lorenzo et al. 2006 Ensemble Ocean Prediction

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

  5. 4DVAR inversion Model x Model Hessian Matrix representer-based inversion Obs x Obs Representer Coefficients Stabilized Representer Matrix

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

  7. An example of Representer Functions for the Upwelling System Computed using the TL-ROMS and AD-ROMS

  8. Comparison of the IOM assimilation solutions with TRUE and BACKGROUNDCoastal Baroclinic Upwelling System Model Setup

  9. Comparison of SKILL score of IOM assimilation solutions with independent observations HIRES: High resolution sampling array COARSE: Spatially and temporally aliased sampling array

  10. Instability of the Representer Tangent Linear Model (RP-ROMS) SKILL SCORE RP-ROMS WEAK constraint solution RP-ROMS with TRUE as BASIC STATE RP-ROMS with CLIMATOLOGY as BASIC STATE

  11. Replacing the RP-ROMS with NL-ROMS in the outer loop

  12. PROGRESS • Developed and tested weak constraint 4DVAR in ROMS • The system is able t`o initialize the forecast extracting dynamical information from the observations. PENDING ISSUES • Tangent Linear Dynamics are unstable in realistic settings. • Background and Model Error COVARIANCE functions are Gaussian and implemented through the use of the diffusion operator. • Preconditioning • Posterior Statistics

  13. 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 Modelling, 7, 227-258. Di Lorenzo, E., A. M. Moore, H. G. Arango, B. D. Cornuelle, A. J. Miller, R. D. Powell, B. S. Chua, and A. F. Bennett, 2006: Weak and Strong Constraint Data Assimilation in the inverse Regional Ocean Modeling System (ROMS): development and application to a baroclinic coastal upwelling system. Ocean Modelling, in press.

  14. Application of IOM in realistic settings: • California Current System: produce a long term reanalysis of the CalCOFI Hydrography from 1950-2006 • Intra American Seas: implement a real time forecasting system

  15. ASSIMILATION SetupCalifornia Current 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. TRUE Mesoscale Structure SSH [m] SST [C]

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

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

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

  19. Normalized Observation-Model Misfit  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%

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