Parallel filter algorithms for data assimilation in oceanography

A consistent systematic comparison of filter algorithms based on the Kalman filter and intended for data assimilation with high-dimensional nonlinear numerical models is presented. Considered are the Ensemble Kalman Filter (EnKF), the Singular Evolutive Extended Kalman (SEEK) filter, and the Singular Evolutive Interpolated (SEIK) filter. Within the two parts of this thesis, the filter algorithms are compared with a focus on their mathematical properties as Error Subspace Kalman Filters (ESKF). Further, the filters are studied as parallel algorithms. This study includes the development of an efficient framework for parallel filtering. In the first part, the filter algorithms are motivated in the context of statistical estimation. The unified interpretation of the algorithms as Error Subspace Kalman Filters provides the basis for the consistent comparison of the filter algorithms. The efficient implementation of the algorithms is discussed and their computational complexity is compared. Numerical data assimilation experiments with a test model based on the shallow water equations show how choices of the assimilation scheme and particular state ensembles for the initialization of the filters lead to significant variations of the data assimilation performance. The relation of the data assimilation performance to different qualities of the predicted error subspaces is demonstrated by a statistical examination of the predicted state covariance matrices. The comparison of the filters shows that problems of the analysis equations are apparent in the EnKF algorithm due to the Monte Carlo sampling of ensembles. In addition, the SEIK filter appears to be a numerically very efficient algorithm with high potential for use with nonlinear models. The application of the EnKF, SEEK, and SEIK algorithms on parallel computers is studied in the second part. The parallelization possibilities of the different phases of the filter algorithms are examined. In addition, a framework for parallel filtering is developed which allows to combine filter algorithms with existing numerical models requiring only minimal changes to the source code of the model. The framework has been used to combine the parallel filter algorithms with the 3-dimensional finite element ocean model FEOM. Numerical data assimilation experiments are utilized to assess the parallel efficiency of the filtering framework and the parallel filters. The experiments yield an excellent parallel efficiency for the filtering framework. Furthermore, the framework and the filter algorithms are well suited for application to realistic largescale data assimilation problems.