| In the high-dimensional context of geophysics, efficient implementation of the ensemble
Kalman filter (EnKF) requires the use of ad hoc techniques such as inflation and localisation.
They are meant to compensate for the misspecification of background errors (resulting from a
previous ensemble forecast) that often leads to underestimated analysed errors. The main
intrinsic source of error in EnKF is sampling error. External sources of error, such as model
error, or model-induced non-Gaussian deviations of the probability density function of errors,
are not considered in this study. In this new approach, the data assimilation system is
informed of the ensemble nature of the forecast, and not only of the empirical mean and of
the empirical error covariance matrix as is usually done. We obtain under general
assumptions a prior that takes into account potential sampling flaws. This generates a new
class of ensemble Kalman filters. One variant is the finite-size ensemble transform Kalman
filter (ETKF-N). It is tested on the Lorenz 95 model. Accounting for sampling issues,
ETKF-N is optimal without inflation. However localisation is still mandatory, and a
local version of the new class of filters is tested (LETKF-N). Whatever the size
of the ensemble, the filter is best without inflation or with a small deflation. Its
overall performance without tuning compares well with optimally tuned LETKFs. |