A direct way of specifying flow-dependent background error correlations for meteorological analysis systems

Identifying a viable strategy for specifying the background error covariance remains an important problem in meteorological data assimilation. From a formal point of view the number of independent parameters needed for this is n²/2 where n is the dimension of the model state space. In most analysis systems used in operational mode at the present time, the error covariance is modeled using assumptions about homogeneity and isotropy, and the resulting background error covariance matrix thus does not depend on the state of the atmosphere. In this paper, we propose a simple and inexpensive method for specifying univariate background error correlations in terms of the background field itself. We illustrate the positive impact of the implementation of this model by a simple example in which we reconstruct a total ozone field from a sparse set of observations. We finally discuss the generalization of the basic idea involved to univariate correlations for general meteorological models.