Variational data assimilation techniques for optimal state estimation in very large environmental systems currently use approximate Gauss-Newton (GN) methods. The GN method solves a sequence of linear least squares problems subject to linearized system constraints. For very large systems, low resolution linear approximations to the model dynamics are used to improve the efficiency of the algorithm. We propose a new approach for deriving low order system approximations based on model reduction techniques from control theory which can be applied to unstable stochastic systems. We show how this technique can be combined with the GN method to retain the response of the dynamical system more accurately and improve the performance of the approximate GN method.
