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

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

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

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

  2. Major Objective • To provide the ocean modeling community with state-of-the-art analysis, prediction and data assimilation tools (currently used in meteorology and NWP) using a community OGCM (ROMS). • Generalized stability analysis. • 4D Variational data assimilation.

  3. Tangent and Adjoint Models: An Overview • NL ROMS: • TL ROMS: (TL1) • AD ROMS: (AD)

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

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

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

  7. Overview • NL ROMS: • Perturbation:

  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

  10. Applications • Test problems (double gyre, etc) • Southern California Bight • NE North Atlantic (w/Wilkin) • Gulf of Mexico (w/Sheinbaum) • Intra-Americas Sea (w/Sheinbaum) • East Australia Current (w/Wilkin) • 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,7, 227-258.

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

  12. Southern California Bight

  13. Eigenspectrum

  14. Eigenmodes (coastally trapped waves)

  15. Nonnormal Systems • Most if not all circulations of interest are nonnormal in that they possess nonorthogonal eigenmodes. • Linear eigenmode interference can produce can produce rapid perturbation growth, even in absence of unstable modes.

  16. Nonmodal Growth and Eigenmode Interference: A Simple Example

  17. Pseudospectra – Nonmodal Growth • Consider • Response is proportional to • For a normal system • For nonnormal system

  18. A Pseudospectrum

  19. Singular Vectors • The fastest growing of all nonmodal perturbations. • We measure perturbation amplitude as: • Consider perturbation growth factor:

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

  21. Confluence and diffluence

  22. Boundary sensitivity

  23. Seasonal Dependence

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

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

  26. Stochastic Optimals (energy norm) Optimal excitation for coastally trapped waves

  27. Sensitivity Analysis – Forcing and transport

  28. Sensitivity Analysis – initial value problem

  29. 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)

  30. Summary (cont’d) • Forcing Singular Vectors: ensemble prediction (systematic model errors) • Stochastic optimals: stochastic excitation, ensemble prediction (forcing errors) • 4-dimensional variational data assimilation (weak and strong constraints)

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

  32. SV t=0 SST SV t=5

  33. Intra-Americas Sea and Gulf of Mexico (Julio Sheinbaum) Initial Final

  34. SV 1

  35. 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)

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

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

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

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

  40. 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.

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

  42. SV 5

  43. SCB Examples

  44. Confluence and diffluence

  45. Boundary sensitivity

  46. Stochastic Optimals

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