Strategies to achieve order reduction in four dimensional variational data assimilation (4D-Var) search for an optimal low dimensional state subspace for the analysis update. A general framework of the proper orthogonal decomposition (POD) method is considered and adjoint modeling is used to enhance the efficiency of the reduced order basis. The adjoint model approach to sensitivity analysis is used to implement a dual-weighted proper orthogonal decomposition (DWPOD) method. Preliminary numerical results with a global shallow-water model indicate that with an appropriate selection of the basis vectors the optimization in the low-order space is able to significantly reduce the computational cost while preserving the quality of the solution. Qualitative and quantitative aspects of the reduced-order control strategy are analyzed by comparison with results in the full model space. The reduced DWPOD basis provides an increased efficiency in representing an a priori specified forecast aspect and as a tool to perform reduced order optimal control. A condition number analysis to the optimization problem is obtained with a second order adjoint model and further used to assess the efficiency of the POD-based optimization.