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Three-dimensional variational data assimilation system in the Mediterranean Sea

Summer School on Ocean Observation with remote sensing satellites 18-23 June 2010. Three-dimensional variational data assimilation system in the Mediterranean Sea. Lecture by: Srdjan Dobricic, CMCC, Bologna, Italy.

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Three-dimensional variational data assimilation system in the Mediterranean Sea

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  1. Summer School on Ocean Observation with remote sensing satellites 18-23 June 2010 Three-dimensional variational dataassimilation system in the Mediterranean Sea Lecture by: Srdjan Dobricic, CMCC, Bologna, Italy

  2. 3DVAR finds the minimum of a cost function linearized around the background state: Formulation Increments: Small and can be neglected Misfits: Linearisation:

  3. Preconditioning using a control vector v defined by: Control space and

  4. is modelled as a sequence of linear operators: Model of B - Vertical EOFs to physical space. - Horizontal covariances. - Barotropic model. • Diagnose u and v. - Divergence damping filter.

  5. The code contains inner and outer loops: • inner loops iterate the minimizer • outer loop applies the multi-grid method (the minimum is found first on a low resolution grid and the solution is used as the first guess for the higher resolution grid) • The minimum is found using a minimizer based on the quasi-Newton method with the limited memory (free code L-BFGS) Numerical implementation

  6. Transformation operators: vertical EOFs Notice that, in order to eliminate jumps between regions, spatial covariances Vs are modeled by first applying vertical and then horizontal operators (computationally more expensive)

  7. Transformation operators: vertical EOFs

  8. G – 1-d recursive filter, W – diagonal matrix with normalization factors Parameters of the filter and normalization factors depend on the horizontal resolution and may be estimated for each model point from a look-up table Transformation operators: horizontal Covariance bubble without accounting for variable lat-lon resolution Covariance bubble which accounts for variable lat-lon resolution (Lambert projection at 40N)

  9. Coastal boundary conditions may be implemented by adding imaginary points at coastlines: Transformation operators: horizontal

  10. Transformation operators: horizontal Example of filtered field corresponding to 3 unit perturbations close to the coast of Sardinia

  11. It finds stationary solution of free-surface equations forced by constant perturbations of salinity and temperature: , Transformation operators: barotropic model

  12. Transformation operators: barotropic model Sea level correction corresponding to an ARGO float observation without barotropic model Sea level correction corresponding to an ARGO float observation with barotropic model

  13. Velocity close to coasts is adjusted by using the divergence damping filter: Transformation operators: divergence damping

  14. Transformation operators: divergence damping Filtered Unfiltered

  15. Time Loop (DAYS) NEMO Time Loop (model steps) Coupling with NEMO Misfits (FGAT) Model restart Misfits 3DVAR Corrections

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