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Research Supported by: NSF, ONR, NOPP

The Regional Ocean Modeling System (ROMS) 4D-Var Assimilation Systems applied to the California Current System. Andy Moore, Gregoire Broquet, Hernan Arango, Chris Edwards, Brian Powell, Milena Veneziani and Javier Zavala-Garay. Research Supported by: NSF, ONR, NOPP. initial condition

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Research Supported by: NSF, ONR, NOPP

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  1. The Regional Ocean Modeling System (ROMS) 4D-Var Assimilation Systems applied to the California Current System Andy Moore, Gregoire Broquet, Hernan Arango, Chris Edwards, Brian Powell, Milena Veneziani and Javier Zavala-Garay Research Supported by: NSF, ONR, NOPP

  2. initial condition increment corrections for model error boundary condition increment forcing increment The Incremental Control Vector fb(t), Bf ROMS bb(t), Bb xb(0), B State vector: x=(T,S,u,v,z)T Controls: initial conditions, x(0) surface forcing, f(t) boundary conditions, b(t)

  3. initial condition increment corrections for model error boundary condition increment forcing increment Cost/Penalty: Tangent Linear Model Obs Error Cov. Innovation Prior error covariance The Incremental Control Vector fb(t), Bf ROMS bb(t), Bb xb(0), B

  4. Primal vs Dual Formulation ROMS has primal and dual 4D-Var options & strong vs weak constraint Analysis: Gain (primal): Gain (dual):

  5. Primal vs Dual Formulation Analysis: Gain (primal): Gain (dual):

  6. Primal vs Dual Formulation The Lanczos formulation of the CG algorithm lends considerable utility to 4D-Var: Analysis: Gain (primal): Gain (dual): Vp = matrix of Lanczos vectors of the Hessian Vd = matrix of dual Lanczos vectors

  7. Primal vs Dual Formulation The Lanczos formulation of the CG algorithm lends considerable utility to 4D-Var: • Posterior (analysis) error variance (dual) • Posterior (analysis) error EOFs (dual) • Observation impact (primal & dual) • Observation sensitivity (dual) Analysis: Gain (primal): Gain (dual):

  8. fb(t), Bf bb(t), Bb xb(0), B Previous assimilation cycle ROMS: California Current System (CCS) COAMPS forcing ECCO open boundary conditions 30km, 10 km & 3 km grids, 30- 42 levels Veneziani et al (2009) Broquet et al (2009)

  9. Observations (y) CalCOFI & GLOBEC/LTOP SST & SSH Ingleby and Huddleston (2007) TOPP Elephant Seals ARGO

  10. Total DI DI SSH DI SST DI XBT DI T CTD DI T Argo DI S CTD DI S Argo DI TOPP Total N N SSH N SST N XBT N T CTD N T Argo N S CTD N S Argo N TOPP Observation Impact (37N transport, 0-500m) 7 day assim cycle (strong) Transport Increment Nobs

  11. Total DI DI SSH DI SST DI XBT DI T CTD DI T Argo DI S CTD DI S Argo DI TOPP Total N N SSH N SST N XBT N T CTD N T Argo N S CTD N S Argo N TOPP Observation Impact (37N transport, 0-500m) 7 day assim Cycle (strong) Transport Increment Nobs

  12. Total DI Total DI DI SSH DI SSH DI SST DI SST DI XBT DI XBT DI T CTD DI T CTD DI T Argo DI T Argo DI S CTD DI S CTD DI S Argo DI S Argo DI TOPP DI TOPP Obs Impact vs Obs Sensitivity Impact Transport Increment 7 day assim cycle (strong) Sensitivity: based on adjoint of 4D-Var Transport Increment

  13. Total DI Total DI DI SSH DI SSH DI SST DI SST DI XBT DI XBT DI T CTD DI T CTD DI T Argo DI T Argo DI S CTD DI S CTD DI S Argo DI S Argo DI TOPP DI TOPP Obs Impact vs Obs Sensitivity Impact Transport Increment 7 day assim cycle (strong) Sensitivity: based on adjoint of 4D-Var Transport Increment

  14. Expected Posterior Error SST 75m

  15. Expected Posterior Error SST 75m Posterior variance – Prior variance

  16. Gulf of Alaska NJ Bight Philippine Archipelago California Current Intra-Americas Sea East Australia Current Current Applications

  17. Primal vs Dual Space (I4D-Var vs 4D-PSAS vs R4D-Var) 1 - 4 July, 2000 (1 outer, 75 inner, Lh=50 km, Lv=30m, Obs errors: SSH 2 cm SST 0.4 C hydrographic 0.1 C 0.01psu) Jmin (Slow convergence of dual form also noted by El Akkraoui and Gauthier, 2009) July 2000: 4 day assimilation window STRONG vs WEAK CONSTRAINT

  18. Jmin i.c. = initial condition wind = wind stress Q = heat flux (E-P) = freshwater flux b.c. = open boundary conditions (R4DVAR: 1 outer-loop; 75 inner-loops)

  19. SSH error SST error ROMS 4D-Var in the CCS no assim 4D-Var forecast

  20. ROMS 4D-Var Diagnostics The Lanczos formulation of the CG algorithm lends considerable utility to 4D-Var: Analysis: Gain (primal): Gain (dual): Vp = matrix of Lanczos vectors of the Hessian Vd = matrix of dual Lanczos vectors

  21. ROMS 4D-Var Diagnostics The Lanczos formulation of the CG algorithm lends considerable utility to 4D-Var: • Posterior/Analysis error variance (dual) • Posterior/Analysis error EOFs (dual) • Observation impact (primal & dual) • Observation sensitivity (dual) Analysis: Gain (primal): Gain (dual):

  22. Assimilation impacts on CC No assim Time mean alongshore flow across 37N, 2000-2004 (30km) IS4D-Var (Broquet et al, 2009)

  23. Analysis Increment: upper 500 m Transport at 37N 5 – 11 April, 2003 Number of Obs 980 obs (6%) Nobs NSST NSSH NT NS NT NS NT NS NT XBT CalCOFI GLOBEC ARGO 11 April, 2003 Sv 0.49Sv (63%) T S T S T S T Total SST SSH XBT CalCOFI GLOBEC ARGO

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