An ensemble of perturbed analyses to approximate the analysis error covariance in 4dvar

The analysis error covariance is not readily available from four-dimensional variational (4dvar) data assimilation methods, not because of the complexity of mathematical derivation, but rather its computational expense. A number of techniques have been explored for more readily obtaining the analysis error covariance such as using Monte-Carlo methods, an ensemble of analyses, or the adjoint of the assimilation method; but each of these methods retain the issue of computational inefficiency. This study proposes a novel and less computationally costly, approach to estimating the 4dvar analysis error covariance. It consists of generating an ensemble of pseudo analyses by perturbing the optimal adjoint solution. An application with a nonlinear model is shown.