A hybrid ensemble transform Kalman filter (ETKF)-3DVAR analysis scheme
is compared to an ensemble square-root filter (EnSRF) analysis scheme
in a two-layer primitive equation modelunder perfect-modelassumptions.
The ETKF-3DVAR updates the ensemble mean with a hybridized ensemble
covariance and the 3DVAR covariance, and it can be incorporated to the
operational3DVAR data assimilation framework conveniently. The ensemble
perturbations are generated by the computationally efficient ETKF
scheme. The EnSRF runs comparatively expensive parallel data
assimilation cycles for each member and serially assimilates the
observations. The EnSRF background-error covariance is estimated fully
from the ensemble, and covariances are localized. The intent of this
study is to determine whether the hybrid ETKF-3DVAR method provides
much of the potential improved accuracy of the EnSRF.
It was found that depending on the norm, the analyses of the hybrid
ETKF3DVAR corresponding to the optimal linear combination coefficient
were slightly less accurate or similar to the EnSRF using its optimal
covariance localization scale. The ETKF-3DVAR system was less prone to
spurious gravity wave activity than the EnSRF that requires covariance
localization. Maximal growth in the ETKF ensemble perturbation space
exceeded that in the EnSRF ensemble perturbation space. The skill of
the ETKF ensemble variance to estimate the ensemble mean error variance
is similar to that of the EnSRF ensemble. It was also found that
applying covariance localization to the ensemble part of the hybrid
error covariance when updating the mean did not improve its analysis.
The hybrid ETKF-3DVAR approach is thus judged to be a promising, less
expensive approach to utilize ensemble forecasts effectively in data
assimilations.
Xuguang Wang, Thomas M.
Hamill, Jeffrey S. Whitaker, and Craig H. Bishop