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ROMS/TOMS TL and ADJ Models: Tools for Generalized Stability Analysis and Data Assimilation

ROMS/TOMS TL and ADJ Models: Tools for Generalized Stability Analysis and Data Assimilation. Andrew Moore, CU Hernan Arango, Rutgers U Arthur Miller, Bruce Cornuelle, Emanuele Di Lorenzo, Doug Neilson UCSD. Major Objective.

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ROMS/TOMS TL and ADJ Models: Tools for Generalized Stability Analysis and Data Assimilation

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  1. ROMS/TOMS TL and ADJ Models:Tools for Generalized Stability Analysis and Data Assimilation Andrew Moore, CU Hernan Arango, Rutgers U Arthur Miller, Bruce Cornuelle, Emanuele Di Lorenzo, Doug Neilson UCSD

  2. Major Objective • To provide the ocean modeling community with analysis and prediction tools that are available in meteorology and NWP, using a community OGCM (ROMS).

  3. Overview • NL ROMS: • Perturbation:

  4. Overview • NL ROMS: • TL ROMS: (TL1) • AD ROMS: (AD)

  5. Overview • Second TLM: (TL2) • TL1= Representer Model • TL2= Tangent Linear Model

  6. Current Status of TL and AD • All advection schemes • Most mixing and diffusion schemes • All boundary conditions • Orthogonal curvilinear grids • All equations of state • Coriolis, pressure gradient, etc.

  7. Generalized Stability Analysis • Explore growth of perturbations in the ocean circulation.

  8. Available Drivers (TL1, AD) • Singular vectors: • Eigenmodes of and • Forcing Singular vectors: • Stochastic optimals: • Pseudospectra:

  9. Two Interpretations • Dynamics/sensitivity/stability of flow to naturally occurring perturbations • Dynamics/sensitivity/stability due to error or uncertainties in forecast system • Practical applications: ensemble prediction, adaptive observations, array design...

  10. Southern California Bight (SCB) • Model grid 1200kmX1000km • 10km resolution, 20 levels • Di Lorenzo et al. (2003)

  11. SCB Examples

  12. Eigenspectrum

  13. Eigenmodes (coastally trapped waves)

  14. Pseudospectrum • Consider • Response is proportional to • For a normal system • For nonnormal system

  15. Pseudospectrum

  16. Singular Vectors • Consider the initial value problem. • We measure perturbation amplitude as: • Consider perturbation growth factor:

  17. Singular Vectors • Energy norm, 5 day growth time

  18. Confluence and diffluence

  19. SV 1

  20. SV 5

  21. Boundary sensitivity

  22. Seasonal Dependence

  23. Forcing Singular Vectors • Consider system subject to constant forcing: • Forcing singular vectors are eigenvectors of:

  24. Stochastic Optimals • Consider system subject to forcing that is stochastic in time: • Assume that: • Stochastic optimals are eigenvectors of:

  25. Stochastic Optimals (energy norm)

  26. Interpretation • Optimal forcing for coastally-trapped waves? • Optimal forcing for recirculating flow in the lee of Channel Islands?

  27. Stochastic Optimals (transport norm)

  28. Transport Singular Vector

  29. North East North Atlantic • 10 km resolution • 30 levels in vertical • Embedded in a model of N. Atlantic • Wilkin, Arango and Haidvogel

  30. SV t=0 SST SV t=5

  31. Summary • Eigenmodes: natural modes of variability • Adjoint eigenmodes: optimal excitations for eigenmodes • Pseudospectra: response of system to forcing at different freqs, and reliability of eigenmode calculations • Singular vectors: stability analysis, ensemble prediction (i.c. errors)

  32. Summary (cont’d) • Forcing Singular Vectors: ensemble prediction (model errors) • Stochastic optimals: stochastic excitation, ensemble prediction (forcing errors)

  33. Weak Constraint 4DVar • NL model: • Initial conditions: • Observations: • For simplicity, assume error-free b.c.s • Cost func: • Minimize J using indirect representer method • (Egbert et al., 1994; Bennett et al, 1997)

  34. OSU Inverse Ocean Model System (IOM) • Chua and Bennett (2001) • Provides interface for TL1, TL2 and AD for minimizing J using indirect representer method

  35. Outer loop, n TL2 • Initial cond: • Inner loop, m AD TL1 TL2

  36. Strong Constraint 4DVar • Assume f(t)=0 • Outer loop, n • Inner loop, m TL1 AD

  37. Drivers under development • Ensemble prediction (SVs, FSVs, SOs, following NWP) • 4D Variational Assimilation (4DVar) • Greens function assimilation • IOM interface (IROMS) (NL, TL1, TL2, AD)

  38. Publications • Moore, A.M., H.G Arango, E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. Neilson, 2003:A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modelling, Final revisions. • H.G Arango, Moore, A.M., E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. Neilson, 2003:The ROMS tangent linear and adjoint models: A comprehensive ocean prediction and analysis system. Rutgers Tech. Report, In preparation.

  39. What next? • Complete 4DVar driver • Interface barotropic ROMS to IOM • Complete 3D Picard iteration test (TL2) • Interface 3D ROMS to IOM

  40. SCB Examples

  41. Confluence and diffluence

  42. Boundary sensitivity

  43. Stochastic Optimals

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