An Adaptive Ensemble Kalman Filter

Abstract To the extent that model error is nonnegligible in numerical models of the atmosphere, it must be accounted for in 4D atmospheric data assimilation systems. In this study, a method of estimating and accounting for model error in the context of an ensemble Kalman filter technique is developed. The method involves parameterizing the model error and using innovations to estimate the model-error parameters. The estimation algorithm is based on a maximum likelihood approach and the study is performed in an idealized environment using a three-level, quasigeostrophic, T21 model and simulated observations and model error. The use of a limited number of ensemble members gives rise to a rank problem in the estimate of the covariance matrix of the innovations. The effect of this problem on the two terms of the log-likelihood function is that the variance term is underestimated, while the χ2 term is overestimated. To permit the use of relatively small ensembles, a number of strategies are developed to deal w...

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