期刊名称：Tellus A: Dynamic Meteorology and Oceanography
电子版ISSN：1600-0870
出版年度：2019
卷号：71
期号：1
页码：1-22
DOI：10.1080/16000870.2019.1613142
摘要：We examine the perturbation update step of the ensemble Kalman filters which rely on covariance
localisation, and hence have the ability to assimilate non-local observations in geophysical models. We show
that the updated perturbations of these ensemble filters are not to be identified with the main empirical
orthogonal functions of the analysis covariance matrix, in contrast with the updated perturbations of the
local ensemble transform Kalman filter (LETKF). Building on that evidence, we propose a new scheme to
update the perturbations of a local ensemble square root Kalman filter (LEnSRF) with the goal to minimise
the discrepancy between the analysis covariances and the sample covariances regularised by covariance
localisation. The scheme has the potential to be more consistent and to generate updated members closer to
the model’s attractor (showing fewer imbalances). We show how to solve the corresponding optimisation
problem and discuss its numerical complexity. The qualitative properties of the perturbations generated from
this new scheme are illustrated using a simple one-dimensional covariance model. Moreover, we demonstrate
on the discrete Lorenz–96 and continuous Kuramoto–Sivashinsky one-dimensional low-order models that the
new scheme requires significantly less, and possibly none, multiplicative inflation needed to counteract
imbalance, compared to the LETKF and the LEnSRF without the new scheme. Finally, we notice a gain in
accuracy of the new LEnSRF as measured by the analysis and forecast root mean square errors, despite
using well-tuned configurations where such gain is very difficult to obtain.
