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Optimization of ROMS with 4D-Var for California Current System: Methodologies and Impacts

This research explores the implementation of the Regional Ocean Modeling System (ROMS) using a 4D-Var assimilation framework for the California Current System. It details the methodologies for correcting initial conditions and boundary forces to reduce model errors, analyzing both primal and dual formulations. The study employs various observational data sources like CalCOFI and GLOBEC to assess the impacts of assimilation cycles on transport and temperature dynamics. It also discusses the Lanczos formulation's advantages for optimization and sensitivity analysis in ocean modeling.

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Optimization of ROMS with 4D-Var for California Current System: Methodologies and Impacts

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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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