Autoregressive models of background errors for chemical data assimilation

The task of providing an optimal analysis of the three state of the atmosphere requires to efficiently integrate the observational data and the models, a process called data assimilation. The background, or initial state of an atmospheric model, is not known exactly, and can be correctly represented only in a probabilistic framework that accounts for the uncertainty. It is widely accepted that a key ingredient of successful data assimilation is a realistic estimation of the background error distribution. This paper introduces a new method for modeling the background errors as autoregressive processes. The method is motivated by a theoretical analysis of error propagation through the linearized transport and chemical equations. The proposed approach is computationally inexpensive, captures the error correlations along the flow lines, and results in nonsingular background covariance matrices. We illustrate the benefits of the autoregressive background covariance matrix in a four‐dimensional Var experiment that uses real data.