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covariance in spectral space, the structure function is limited to being geographically
homogeneous and isotropic about its center (
Parrish and Derber 1992
;
Courtier
et al. 1998
). One has little control over the spatial variation of the error statistics
when a simplified diagonal background error covariance in spectral space is used.
With some computational cost associated with the extra transforms in and out of the
physical space in each iteration of the optimization solver, spatially inhomogeneous,
for example, latitude-dependent, variances can be applied, but it is not as easy to
construct inhomogeneous and/or anisotropic shapes for the covariance profiles in
spectral space. The GSI helped overcome this shortcoming.
The current GSI regional analysis system employs NCEP's Nonhydrostatic
Mesocale Model (NMM) WRF and NCAR's ARW WRF mass core (
Liu and
Weng 2006
;
Xu et al. 2009
;
Xu and Powell 2011
;
Wan and Xu 2011
), and the input
data can be either binary or netcdf format datasets. DAS/forecast model interface has
been adapted separately for the WRF NMM core and the WRF mass core. For the
ARW WRF mass core, the inputs/outputs are made on a C-grid, no interpolation is
needed for the mass variables (T,Q), but the wind variables (u & v) are interpolated
in x and y to mass points respectively
All interpolations are linear in each direction; the projection information is not
required. The code automatically determines the local scale information needed
for transforming from global coordinates to local coordinates, properly rotating
winds to the model frame, and dx, dy are needed for local derivatives. All of these
procedures can be determined from the two dimension fields available in both NMM
and ARW mass core files given the earth latitude and longitude and dx, dy for every
grid point.
Eventually, GSI can be connected to other models in a systematic way. Part of this
has already been accomplished by eliminating the need to specify map projections
for the horizontal domain definition.
The Assimilation system produces an analysis through the minimization of an
objective function given by
J D
x
T
B
1
x
C
.
T
R
1
.
H
x
y
/
H
x
y
/
x
T
B
1
x
T
R
1
.
J D
1=2.
/
C
.
H
x
y
/
H
x
y
/
where
x
is a vector of analysis increment, B is the background error covariance
matrix,
y
is innovation vector,
y
D
y
obs
H
x
guess
, R is the observational and
representativeness error covariance matrix, and H is the transformation operator
from the analysis variable to the form of the observations.
For the SSI which is tied to isotropic and homogeneous background error covari-
ance matrix (B), the spectral model can conveniently and easily handle the pole.
In contrast, the GSI allows for non-homogeneous and anisotropic B formulation
(
Wu et al. 2002
), distinguishes between land and sea, the tropics, and midlatitudes,
and is easy to use in both global and regional applications. Currently background
error cannot change in outer iteration (due to preconditioning in the inner iteration).
In regard to this problem, Derber suggests that the two outer iterations appear to
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