In the standard 4D-Var the regularising background error covariance matrix remains essentially static. In contrast, the hybrid approach we present here has been designed to address the question of possible benefit that the 4D-Var could draw from dynamical adaptation of this matrix. To be more precise, the notion of hybrid in this study refers to a method merging an incremental 4D-Var with an equivalent Kalman smoother, the latter delivering a recipe on how to update the error covariance matrix at each transition between successive assimilation windows. Feasibility requirements may result in a reduction of the size of the control vector and confine data assimilation correction to a low-dimensional subspace of the original state space. Hence, the necessity of an appropriate definition of such a control subspace. An ensemble of vectors spanning the subspace should be of a relatively small size. At the same time it must be capable of preserving the regularising properties of the background error covariance matrix it defines. Consequently, in our hybrid approach which ensures the evolution of the error covariance matrix, the problem of adapting the definition of the control subspace to reflect additional information gained in the data assimilation procedure arises. Indeed, while the analysis update modifies the reduced size error covariance matrix according to the quality of the measurements assimilated into the system, in the forecast step the ensemble spanning the control subspace evolves along the optimised trajectory of the system. A series of OSSEs implementing the hybrid method into a shallow water model mimicking wind driven double-gyre circulation has been performed. It has been opted for a definition of the low-dimensional control subspace which reflects the directions of the largest variability of the system. These directions have been obtained via principal component analysis of several different samples of model trajectory representing either the background or the true state, or both. A number of configurations has been tested and the circumstances where the hybrid outperforms the standard 4D-Var have been identified. The general conclusion inferred from this study indicates that the propagation of the ensemble of vectors spanning the control subspace is capable of compensating for some imperfections in their initialisation. Moreover, as the information contained in the observations is gradually assimilated into the background trajectory, the control subspace evolving accordingly approaches an idealised one defined with the help of the true trajectory of the system.