| Abstract: The background error covariance
(correlation) between model state variables is of central importance for
implementing data assimilation and understanding model dynamics.
Traditional approaches for estimating the background error covariance
involve many heuristic approximations, and often the estimated
covariance is flow-independent, i.e., only reflecting statistics of the
climatological background. This study examines temporally and
spatially varying estimates of error covariance in a spectral barotropic
model using a Monte Carlo approach, an implementation of an ensemble
square root filter called the ensemble adjustment Kalman filter (EAKF).
The EAKF is designed to maintain as much information about the
distribution of the prior state variables as possible, and results show
that this method can produce reasonable estimates of error correlation
structure with an affordable sample (ensemble) size. The impact of
using temporally and spatially varying estimates of error covariance in
the EAKF is examined by using the time and spatial mean error
covariances derived from the EAKF in an ensemble optimal interpolation (OI)
assimilation scheme. Three key results are: (1) for the same
ensemble size, an ensemble filter such as the EAKF produces better
assimilations since its flow-dependent error covariance estimates are
able to reflect more about the synoptic-scale wave structure in the
simulated flows; (2) an ensemble OI scheme can also produce reasonably
good assimilation results if the time-invariate covariance matrix is
chosen appropriately; (3) when using the EAKF to estimate the error
covariance matrix for improving traditional assimilation algorithms such
as variational analysis and OI, a relatively small ensemble size may be
used to estimate correlation structure although larger ensembles produce
progressively better results. |