A Reduced-Order Kalman Filter for Data Assimilation in Physical Oceanography

A central task of physical oceanography is the prediction of ocean circulation at various time scales. Mathematical techniques are used in this domain not only for the modeling of ocean circulation but also for the enhancement of simulation through data assimilation. The ocean circulation model of concern here, namely, HYCOM, is briefly presented through its variables, equations, and specific vertical coordinate system. The main part of this paper focuses on the Kalman filter as a data assimilation method, and especially on how this mathematical technique, usually associated with a prohibitively high computing cost for operational sciences, is simplified in order to make it applicable to the simulation of realistic ocean circulation models. Some practical issues are presented, such as a brief explanation about ocean observation systems, together with examples of data assimilation results.