  A new ensemble filter that allows for the uncertainty in the prior
distribution is proposed and tested. The filter relies on the conditional
Gaussian distribution of the state given the model-error and
predictability-error covariance matrices. The latter are treated as random
matrices and updated in a hierarchical Bayes scheme along with the state. The
(hyper)prior distribution of the covariance matrices is assumed to be inverse
Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble
members as generalized observations and allows ordinary observations to
influence the covariances. The actual probability distribution of the ensemble
members is allowed to be different from the true one. An approximation that
leads to a practicable analysis algorithm is proposed. The new filter is
studied in numerical experiments with a doubly stochastic one-variable model of
"truth". The model permits the assessment of the variance of the truth and the
true filtering error variance at each time instance. The HBEF is shown to
outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of
filtering regimes in terms of performance of its primary and secondary filter.

Data Analysis, Statistics and Probability;Atmospheric and Oceanic Physics