Data assimilation is a key element to improve the performance of biogeochemical ocean/marine forecasting systems. Handling the very big dimension of the state vector of the system (often of the order of 106) remains an issue, also considering the computational efficiency of operational systems. Indeed, simple product operations involving the covariance matrices are too heavy to be computed for operational forecasting purposes. Various attempts have been made in literature to reduce the complexity of this task, often adding strong hypotheses to simplify the problem and decrease the computational cost. The MedBFM model system, which is responsible for monitoring and forecasting the biogeochemical state of the Mediterranean Sea within the European Copernicus Marine Services (see http://marine.copernicus.eu/) assimilates surface chlorophyll data through a 3D Variational algorithm, that decomposes the background error covariance matrix into sequential operators to reduce complexity. In this work, we developed a novel Kalman Filter for the MedBFM system. The novel Kalman Filter scheme starts from a SEIK approach but benefits from advanced Principal Component Analysis to reduce the dimension of covariance matrices and improve the computational efficiency. We compared the standard SEIK filter and the new Kalman filter implementations in a one dimensional transport model with 2 biological variables in terms of root mean square distance. In the vast majority of the experiments, the new Kalman filter had better performances.
