Ensemble data assimilation : theory and practice
Peter OkeCSIRO, Hobart, Tasmania
Wednesday, June 24th, CERFACS Conference Room - 14h30
The development of the ensemble Kalman filter (EnKF) has taken two distinct paths - statistical and deterministic. In both cases, an ensemble of model anomalies, or perturbations, is used to implicitly represent and evolve the system's background error covariance. The statistical, or probabilistic, EnKF, treats observations as random variables, and involves the use of perturbed observations. For most practical applications, the EnKF suffers terribly from sampling error, owing to the insufficient ensemble size. The deterministic options include many flavours of Ensemble square root filters (ESRFs). In practice, ESRFs involve an ensemble update, or transformation, that "matches" the ensemble- and theoretical-analysis error covariance. However, almost without exception in practice, ESRFs subsequently employ an arbitrary covariance inflation - so the much-heralded covariance matching is violated. ESRFs also involve somewhat questionable practices to employ localisation - a necessary evil for any large-dimension application. In this study, we propose an alternative filter - the Deterministic EnKF (DEnKF) - representing "the best of both EnKF-worlds" and include a series of experiments using small models to demonstrate its viability.
For many large-dimension applications, any flavour of EnKF may be impractical. For these applications, ensemble optimal interpolation (EnOI) can be considered, using a stationary ensemble to approximate the time-mean background error covariance. While sub-optimal, EnOI may be hard to beat in practice. Examples from an EnOI-system applied to a global eddy-resolving ocean model will be presented, along with a series of inter-comparisons with a suite of systems using other methods.
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