A hybrid approach to generating search subspaces in dynamically constrained 4-dimensional data assimilation

•A hybrid adjoint-free (ha4dVar) method of data assimilation is proposed.•The method is based on the ensemble technique.•In the linear case ha4dVar converges to the 4dVar solution.•Performance is tested against the standard data space 4dVar in a realistic setting.•Ha4dVar is found to be 4dVar-compatible in terms of the computational cost and the forecast skill.