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This study demonstrates how the incremental 4D-Var data assimilation methodcan be applied efficiently preconditione d in an application to anoceanographic problem. The approach consists in performing a few iterations ofthe reduced-order 4D-Var prior to the incremental 4D-Var in the full space inorder to achieve faster convergence. An application performed in the tropicalPacific Ocean, with assimilation of TAO temperature data, shows the method tobe both feasible and efficient. It allows the global cost of the assimilationto be reduced by a factor of 2 without affecting the quality of the solution.

Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method