The goal of this study is to evaluate a specific type of reduced-rank Kalman filter for application to realistic ocean models. Data assimilation experiments were performed using an idealized nonlinear model of the wind-driven ocean circulation. Separate configurations of the model were employed that exhibit either a quasi-periodic behavior on the decadal timescale or a statistically stationary behavior accompanied by a high level of meso-scale eddy activity. The model consists of about 10e4 prognositic variables with observations of the model state taken at 30 locations concentrated in the the region of highest variability near the Western boundary.

The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances and corrections to the forecasts are only calculated in a reduced-dimension subspace spanned by a small number of empirical orthogonal functions (EOFs). The filter was implemented using both temporally evolving and asymptotically stationary error covariances. Additionally for the quasi-periodic model configuration, the model state space was partitioned according to the distinct flow regimes exhibited by the model and the asymptotically stationary error covariances calculated for each regime. The performance of these reduced-rank approaches is compared with the more traditional approach of using stationary error covariances with a simple prescribed functional form.

The results show that the reduced-rank Kalman filter is able to reduce the error in all assimilation experiments and consistently performs better than using prescribed error covariances. Also, the performance of the filter with stationary error covariances is surprisingly similar to the much more computationally expensive filter with flow-dependent covariances. The importance of specifying appropriate model and observation error covariances and the difficulties related to using stationary basis functions are also discussed.