The estimation of forecast error covariance is the principal task of tuning an atmospheric data assimilation system. The main sources of forecast error can be divided into inherent model error and the error associated with the uncertainty of initial data. Both uncertainties evolve in a numerical weather prediction model during the assimilation cycle so that the associated forecast error covariance is not constant but varies with respect to time and space depending on the flow. Singular vectors, the most rapidly growing perturbations over a specified time period for a prescribed norm in a given model, can be used to construct a time and space-dependent forecast error covariance matrix.

SVs calculated for QG channel model show different structures with different metrics. SVs in the potential enstrophy norm show large scale and zonal structure while those in the L² norm show smaller and localized structure. These results are similar to results found in Eady model.

In this presentation the flow dependent forecast error covariance calculated using singular vectors will be compared with the forecast error covariance statistically averaged in time and space. Since singular vectors are norm(metric) dependent, the most appropriate norm to determine singular vectors in constructing forecast error covariance will also be investigated. A quasigeostrophic channel model and 3D VAR data assimilation system will be used to perform the experiment under the perfect model assumption.