Four-dimensional data assimilation method based on SVD: Theoretical aspect

A new method of four-dimensional data assimilation based on Singular Value Decomposition (SVD) is proposed. In it, a set of atmospheric states is obtained by integrating a numerical weather prediction model and simulated observations are taken and calculated from the model variables. Then the SVD technique is used to create the base vectors from this coupled data set. Finally, the analysis is obtained by projecting actual observation data into a space spanned by the base vectors. Using this approach, the four-dimensional data assimilation becomes a simple linear inverse problem the linearization of the nonlinear forward model is avoided, and the developments of the adjoint and background error covariance matrix are no longer needed. Since the SVD technique is used here, the method is simply called 4DSVD.