Ensemble-based Data Assimilation: a Review

The literature on ensemble-based data assimilation techniques has been growing rapidly in past decade. These techniques are being explored as possible alternatives to current operational analysis techniques. Ensemble-based assimilation techniques are typically comprised of an ensemble of parallel data assimilation and forecast cycles. The background-error covariances used in the data assimilation are estimated from the ensemble. Though computationally expensive, these techniques are easy to code, since no adjoint nor tangent-linear models are required, and tests in simple models suggest that dramatic improvements over existing operational methods may be possible. A review of the ensemble-based assimilation is provided here, starting from the basic concepts of Bayesian assimilation. Without some approximation, Bayesian assimilation is computationally impossible for large-dimensional systems. Under assumptions such as Gaussianity and linearity of error growth, the discrete Kalman filter equations are derived. Kalman filter techniques are still computationally impractical without further simplification. A derivation of the more computationally tractable ensemble Kalman filter (EnKF) is then provided. As ensemble size increases, the mean and covariance estimates from the EnKF converge to those produced by the Kalman filter. Techniques for making the EnKF more accurate and more computationally efficient on parallel computers are discussed, and an example of ensemble data assimilation in a dry general circulation model is provided.