Estimating Model-Error Covariances for Application to Atmospheric Data Assimilation

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Abstract
Forecast-error statistics have traditionally been used to investigate model performance and to calculate analysis weights for atmospheric data assimilation. Forecast error has two components: the model error, caused by model imperfections, and the predictability error, which is due to the model generation of instabilities from an imperfectly defined initial state. Traditionally, these two error sources have been difficult to separate. The Kalman filter theory assumes that the model error is additive white (in time) noise, which permits the separation of the model and predictability error. Progress can be made by assuming that the model-error statistics are homogeneous and stationary, an assumption that is more justifiable for the model-error statistics than for the forcast-error statistics. A methodology for estimating the homogeneous, stationary component of the model- error covariance is discussed and tested in a simple data-assimilation system. Abstract Forecast-error statistics have traditionally been used to investigate model performance and to calculate analysis weights for atmospheric data assimilation. Forecast error has two components: the model error, caused by model imperfections, and the predictability error, which is due to the model generation of instabilities from an imperfectly defined initial state. Traditionally, these two error sources have been difficult to separate. The Kalman filter theory assumes that the model error is additive white (in time) noise, which permits the separation of the model and predictability error. Progress can be made by assuming that the model-error statistics are homogeneous and stationary, an assumption that is more justifiable for the model-error statistics than for the forcast-error statistics. A methodology for estimating the homogeneous, stationary component of the model- error covariance is discussed and tested in a simple data-assimilation system.

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