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V. B. Zalesny, A. S. Rusakov
Numerical algorithm of data assimilation based on splitting and adjoint equation methods
We present a numerical procedure of variational assimilation of observation data in the ocean. The procedure is intended for the σ-coordinate model of oceanic general circulation (OGC) developed at the Institute of Numerical Mathematics (INM) of the RAS. Model equations are written in a special symmetrized form. The numerical algorithm for solving a direct problem is based on the splitting method with respect to physical processes and space coordinates. Due to the splitting method the model is effectively realized by implicit schemes and uses a rather large time step in simulation.
We obtained a differential system of adjoint equations for the OGC INM model. We write adjoint equations for each subsystem of the split model, which are then combined to form a full adjoint model. The procedure reduces to the construction of a number of relatively simple split subsystems for the adjoint model, which are also solved by implicit time schemes. The special symmetrized form of writing the primitive equations allows us to use the basic procedures from the direct model. The variational assimilation procedure is applied to solving the problem of the initialization of the Indian Ocean.
Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter
Print ISSN: 0927-6467
Volume: 22, 05/2007
Pages: 199 - 219