  This paper presents a reduced-order approach for four-dimensional variational
data assimilation, based on a prior EO F analysis of a model trajectory. This
method implies two main advantages: a natural model-based definition of a mul
tivariate background error covariance matrix $\textbf{B}_r$, and an important
decrease of the computational burden o f the method, due to the drastic
reduction of the dimension of the control space. % An illustration of the
feasibility and the effectiveness of this method is given in the academic
framework of twin experiments for a model of the equatorial Pacific ocean. It
is shown that the multivariate aspect of $\textbf{B}_r$ brings additional
information which substantially improves the identification procedure. Moreover
the computational cost can be decreased by one order of magnitude with regard
to the full-space 4D-Var method.
