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