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Three dimensional variational analysis with spatially
inhomogeneous covariances

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Wan-Shu Wu, R. James Purser, and David F. Parrish

NOAA/NWS/NCEP/EMC

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Abstract:
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A global three-dimensional variational analysis system is formulated in
model grid space.
This formulation allows greater flexibility for background error
statistics. A simpler
formulation was chosen for these initial tests. The background error
statistics are defined as
functions of the latitudinal grid and are estimated with the NMC
method. The horizontal
scales of the variables are obtained through the variances of the
variables and of their
Laplacian. The vertical scales are estimated through the statistics of
the vertical correlation of
each variable and are applied locally using recursive filters. For the
multivariate correlation
between wind and mass fields, a statistical linear relationship between
the stream function and
the balanced part of temperature and surface pressure is assumed. A
localized correlation
between the velocity potential and the stream function is also used to
account for the positive
correlation between the vorticity and divergence in the planetary
boundary layer.
Horizontally, the global domain is divided into three pieces so
that efficient spatial
recursive filters can be used to spread out the information from the
observation locations.
This analysis system is tested against the operational Spectral
Statistical-Interpolation analysis
system at the National Centers for Environmental Prediction. The results
indicate that 3D Var
in physical space is as effective as 3D Var in spectral space in the
extratropics and yields
superior results in the tropics as a result of the latitude dependence
of the background error
statistics.