  The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent
covariance information, and are affected by sampling errors in operational
settings where the number of model realizations is much smaller than the model
state dimension. To alleviate the effects of these errors EnKF relies on
model-specific heuristics such as covariance localization, which takes
advantage of the spatial locality of correlations among the model variables.
This work proposes an approach to alleviate sampling errors that utilizes a
locally averaged-in-time dynamics of the model, described in terms of a
climatological covariance of the dynamical system. We use this covariance as
the target matrix in covariance shrinkage methods, and develop a stochastic
covariance shrinkage approach where synthetic ensemble members are drawn to
enrich both the ensemble subspace and the ensemble transformation. We
additionally provide for a way in which this methodology can be localized
similar to the state-of-the-art LETKF method, and that for a certain model
setup, our methodology significantly outperforms it.

Methodology;Numerical Analysis;Numerical Analysis