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The sequential variational (SVAR) method minimizes the weakly constrained four-dimensional cost function by splitting it into a set of smaller cost functions. This study shows how it is possible to apply SVAR in practice by reducing the computational effort required by the algorithm. A major finding of the study is that, instead of using tangent linear and adjoint models, it is possible to estimate the largest eigenvalues and the corresponding eigenvectors of the evolution of the background error covariances only by applying successive nonlinear model integrations. Another major finding is that the impact of future observations on previous state estimates may be obtained in an accurate and numerically stable way by using suitably defined cost functions and control space transformations without any additional model integrations. The new method is applied in a realistic data assimilation experiment with a primitive equations ocean model.

An Application of Sequential Variational Method without Tangent Linear and Adjoint Model Integrations