  A data-driven method for improving the correlation estimation in serial
ensemble Kalman filters is introduced. The method finds a linear map that
transforms, at each assimilation cycle, the poorly estimated sample correlation
into an improved correlation. This map is obtained from an offline training
procedure without any tuning as the solution of a linear regression problem
that uses appropriate sample correlation statistics obtained from historical
data assimilation products. In an idealized OSSE with the Lorenz-96 model and
for a range of cases of linear and nonlinear observation models, the proposed
scheme improves the filter estimates, especially when the ensemble size is
small relative to the dimension of the state space.
