Four-dimensional Variational Dimension Reduction Methods For Data Assimilation And Ocean Data Assimilation

Data assimilation is an analysis technique which provides a powerful tool with which link observations and numerical models to obtain more useful information. At present this method becoming a more promising approach with the rapid advances in ocean observing systems, ocean numerical simulations and operational applications. First of all, the concept, progress and basic principle of data assimilation is reviewed in this paper and more attention is paid on variational methods (Three Dimensional Variational and Four Dimensional Variational) which are widely used in oceanography nowadays.Four dimensional variational data assimilation (4D-VAR) is a powerful tool. However, a major hurdle in use of 4D-VAR is the huge dimension of the control space. Therefore a new scheme based on POD (Proper Orthogonal Decomposition) is proposed to 4D-VAR to explore the feasibility of significant reduction the dimension of control variable and the size of dynamical system. In this paper, some numerical experiments are designed to test the performance of POD technique in simulating large-scale tropical Pacific model. Then identical twin data assimilation experiments to examine the performances of POD 4DVAR and adaptive POD 4DVAR are presented by comparing them with standard 4D-VAR. Results show that the computational cost of POD 4DVAR and adaptive POD 4DVAR is much cheaper than that of the full 4D-VAR however the precision is similar. This accounts for the good performance of the reduced order method.As an initial effort to dramatically reduce computational cost of 4D-VAR, a series of assimilation experiments in this study are shown successfully.