A 3D-variational data assimilation scheme for a quasi-geostrophic channel model (Morss, 1999) is used to study the structure of the analysis error and its relationship to the corresponding bred vectors. Results are used to develop an inexpensive approach to include the “errors of the day” in the background covariance matrix.

We simulate a data assimilation system by defining a model integration as the “true” evolution of the model atmosphere. This allows for the explicit computation of the analysis error and for direct comparisons of the analysis error to bred vectors, as well as their statistical relationships (spatial correlation, local dimensional analysis).

Rawinsonde observations used in the analysis cycle are simulated by randomly perturbing the true state at a fixed number of observation points. Bred vectors are obtained by the method of breeding (Toth and Kalnay, 1993) from the analysis. Their evolution and statistical properties of their spatial distribution are compared to the evolution of the analysis error.

The results show good performance of the bred vectors in describing the local patterns of the analysis error, with reliable estimates of the majority of the large local errors in the analysis fields.

Different applications to the data assimilation scheme either based on local or global approaches are discussed. It is shown that the inclusion of the information obtained from the bred vectors produces sensible reductions in the errors of the analysis and of the forecasts at a negligible computational cost.

Results related to the modification of the breeding cycle based on the local definition of the bred vectors are also shown.