Estimation of analysis error covariances from observation residuals

The problem of producing analysis error estimates from data assimilation systems has been lingering since optimal-interpolation-based assimilation systems have been upgraded to some type of global variational system. Slowly, however, approximate methods, mostly based on truncated modal representation of analysis error covariances, are becoming available to provide such estimates. Because current analysis systems rely still on relatively crude background error covariance models the estimates obtained for the analysis errors are expected to be only rough estimates.

A new approach based on observation-minus-forecast and observation-minus-analysis error statistics is proposed as a complementary method for estimating analysis errors. These estimates, available only over a dense observing network, serve to validate analysis error estimates obtained by modal truncation methods. The new approach can also serve as a guidance for parameterizing analysis error covariance matrices that would be necessary for implementing parameterized retrospective analysis data assimilation systems, much in the same way as background error covariances are parameterized in current assimilation systems. Examples of the usefulness of the method will be explored and discussed.