Reduced‐rank Kalman filters applied to an idealized model of the wind‐driven ocean circulation

Abstract

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 mesoscale eddy activity. The model consists of about 104 prognostic variables with observations of the model state taken at 30 locations concentrated in 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. The filter was implemented using both temporally evolving and stationary error covariances. Additionally for the quasi‐periodic model configuration, the model state space was partitioned according to three distinct flow regimes exhibited by the model and the asymptotically stationary error covariances calculated for each regime. The importance of specifying appropriate model and observation error covariances and the difficulties related to using stationary basis functions are also discussed. 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 simple prescribed error covariances for the quasi‐periodic case. 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 forecast errors from the assimilation experiments are examined with respect to their consistency with the error statistics calculated by the filter and their projections onto the resolved and unresolved subspaces.