Accounting for ensemble variance inaccuracy with Hybrid Ensemble 4D-VAR
Abstract
Inevitably, neither ensemble covariances nor static covariance models are equal to the true error covariance matrix given past observations. To better understand the distribution of true error covariances given a single imperfect ensemble covariance, we begin by considering an idealized univariate model in which Bayes' theorem can be used to derive the distribution of true error variances given an imperfect ensemble variance. The equation for the mean of this distribution shows that a Hybrid error variance formulation is more accurate than either formulations based solely on ensemble variances or formulations based solely on static climatological variances. We show how this Hybrid best estimate of error variance may be derived from a large number of realizations of (innovation, ensemble-variance) pairs. The approach assumes that the climatological distribution of true error variances is an inverse-gamma distribution and that the distribution of ensemble variances given a single true error variance is a gamma distribution. To help explain and justify this approach we use a "replicate Earth" paradigm and an Ensemble Kalman filter applied to Lorenz's (2005) simple model 1. We then apply these theoretically derived weights to the newly built Navy-Hybrid-4DVAR scheme. The forecast performance using the theoretical weights was found to be as good as that from weights obtained from a much more computationally expensive brute force tuning method. Thus, the new theory provided a justification for the Hybrid plus tools to facilitate its implementation.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2011
- Bibcode:
- 2011AGUFMNG22A..01B
- Keywords:
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- 3315 ATMOSPHERIC PROCESSES / Data assimilation;
- 3325 ATMOSPHERIC PROCESSES / Monte Carlo technique