Development and validation of a diagonal ensemble transform Kalman filter
A variant of the ensemble transform Kalman filter (ETKF) has been developed with the following property: analysis perturbations run independently from each other. The independence of each perturbation helps to maintain physical structures of perturbations associated with large-scale systems like tropical cyclones or fronts in a consistent and coherent manner through multi assimilation cycles. This property dictates a special form for the ensemble transform matrix (ETM) in ETKF: that is a scalar multiple of the identity I. Therefore, this variant of ETKF is called the diagonal ETKF.
In this study, we show that the diagonal ETKF can be derived from the two very different approaches: (1) the diagonally predominant property of the unique positive symmetric ETM Ts, i.e. the diagonal elements are at least an order of magnitude larger than the off-diagonal elements; and (2) constant inflation functions, i.e. the spectrum of Ts is replaced by a constant function. Experiments using real observations show that the diagonal ETM produces forecasts better than the ones obtained from the conventional ETM Ts.
Dr. Le Duc Japan Agency for Marine-Earth Science and Technology