A Preliminary Study on Dimension-Reduction Algorithm for Variational Methods in Three Dimensions

Abstract

Numerical weather prediction is an initial-value problem, for determination of the initial conditions, there are many methods and one of the most classical methods is variational methods in three dimensions, or 3D-Var. In this approach, with a defined cost function proportional to the square of the distance between the analysis and both the background and the observations, one can obtain the analysis. In the cost function, the background and the observations are reshaped to vectors; within this step, the order of the background error covariance matrix and the observational error covariance matrix becomes huge, which is not convenient to one to obtain the analysis. In this paper, according to the matrix analysis approach, we put forward some possible improvements to the dimension-reduction algorithm of 3D-Var, so that provide some references for data assimilation.