Forecast biases result from a combination of accumulative model bias and data bias in the initial condition. When a biased model and/or biased data are used in a data assimilation system, it is conjectured that these biases will compulsorily be ingested into the system. Incidentally, the adjoint solution at its minimum from a variational data assimilation procedure, in particular, should contain information about model and data biases. It turns out that a variational data assimilation procedure can provide an approach to estimating model and/or data biases in forecasts, and the difference between a variational assimilated initial field and an observed initial field gives an estimation of forecast errors.

Because a data assimilation procedure allows for continuous data ingest into model integration, the retrieved forecast errors using this method may contain crucial time- and flow-variation information, thus may possess better error representativeness. One of the applications of the proposed method is the specification of the forecast (background) error-covariance matrix in a data assimilation system. This would suggest a two-step assimilation process: first, to conduct a simple (with no background term) and strong model-constraint assimilation to generate ``analysis-consistent" background forecast errors; second, to complete the full data assimilation (either 3D or 4D) by implementing in the developed forecast error covariances.