Four-dimensional Error Covariance Models in Data Assimilation for NWP: A Comparison of Incremental 4D-Var and the Ensemble Kalman Filter

Monday, April 29, 2002 - 9:45am - 10:30am
Keller 3-180
Andrew Lorenc (United Kingdom Metereology Office)
Practical data assimilation for a large Numerical Weather Prediction (NWP) system is considered. It is impossible to fully represent the multivariate probability distribution functions (PDFs) needed for a full Bayesian treatment, let alone to calculate their evolution. This work follows the Extended Kalman Filter in assuming PDFs are (mostly) Gaussian, and NWP models are discrete, allowing the representation of PDFs by covariance matrices. Further simplifications and modelling assumptions are needed for a practical NWP scheme; I review and discuss different approaches.

In algorithms such as multivariate optimal interpolation and 3D-Var, covariances are modelled using physical relationships such as geostrophy and the hydrostatic equation. I show how incremental 4D-Var can be thought of as an extension to this approach, using a perturbation forecast model as part of a four-dimensional covariance model. Aspects of the 4D-Var design such as allowing for model error, and coping with thresholds, follow naturally from this outlook.

In the Ensemble Kalman Filter (EnKF) the covariances are represented by an ensemble of NWP predictions. As long as stochastic processes such as model and observational error are properly represented when generating the ensemble, and the NWP model is realistic in its approach to balance, other covariance modelling assumptions are avoided. The major weakness is that the covariance estimates are inaccurate because of the limited sample size. This forces the use of assumptions about the physical distance over which significant covariances should exist, modifying the EnKF covariances to have compact support.