A Reduced Rank Estimate of Forecast Error Variance based on the Analysis Error Covariance of Retrospective Optimal Interpolation

A new method for adaptive observations using singular vectors is proposed. When the certain set of observations is added to the observing network, it is obvious that the forecast error variance is changed. The predicted forecast error variance can be estimated in a low dimension subspace spanned by the leading singular vectors. In the previous research, the hessian of the cost function of a variational assimilation scheme was used to solve the singular value problem. In this paper, however, the inverse of the analysis error covariance of a retrospective optimal interpolation (ROI) is employed instead of the hessian of the cost function. ROI is a new data assimilation scheme which was derived from the quasi-static variational assimilation (QSVA) algorithm and introduced by Song et al. (2009). The merit of this adaptive observations strategy is to examine the effects of four dimensional distributions of additional observing network by reflecting changes of the background error covariance caused by the routine observing network. Experiments are performed with the Lorenz 40-variable model.

Key words: adaptive observation, hessian singular vector, generalized eigenproblem, retrospective optimal interpolation