The role of the background error covariance matrix in spreading observational information is particularly crucial in oceanography since some of the state variables are often not observed. Feasibility requirements in actual applications often result in an additional constraint requiring that the effective analysis increment is confined to a lowdimensional subspace of control. This study tackles the problem of adaptation of the definition of the subspace of control and the associated reduced rank error covariance matrix in order to account for additional information which is being gradually gained in data assimilation procedure. The problem has been studied in a framework of a hybrid approach to data assimilation. The skeleton of the hybrid is formed by the 4D-Var enriched with an admixture of an equivalent Kalman smoother. The latter provides a recipe for the evolution of the error covariance matrix which is modified at each transition between successive 4D-Var assimilation windows. In the analysis step it is updated according to the quality of the measurements assimilated into the system. Following system's trajectory, the basis spanning the control subspace is, in turn, adjusted in the forecast step. A series of numerical experiments implementing the hybrid method in a shallow water model has been performed. It has been opted for an initialization of the subspace of control with the empirical orthogonal functions arising from different samples of model trajectory. A number of tests have been performed in various configurations of twin experiments and the circumstances where the hybrid outperforms the standard 4D-Var have been identified. The information content in the initial and final subspaces of control has also been assessed. The general conclusion inferred from this study indicates that propagating the background error covariance matrix may result in compensation of its imperfect initialization.