Geoscience Reference
In-Depth Information
12.3.3
Practical Implementation and Application
to NAVDAS-AR
Computation of the tuning parameters requires the evaluation of the trace of the large
matrices,
Tr
T
T
Œ
…
l
H
T
D
/
1
…
l
Œ
…
k
/
1
…
k
HB
.
s
/
.
s
and
Tr
R
.
s
/
D
.
s
. Because the
matrices
HBH
T
and
D
/
1
are not explicitly formed (
Chua and Bennett 2001
), the
trace is computed using the randomized trace estimator (
Girard 1989
;
Hutchinson
1989
)whichwasusedby
Wahba et al.
(
1995
) for an adaptive tuning of parameters
in a numerical weather prediction application.
It is the randomized trace technique which makes feasible the posterior analysis
of
Desroziers and Ivanov
(
2001
) for large-scale data assimilation, and this approach
has been applied to the NAVDAS-AR. The forecast model associated with the
NAVDAS-AR system is the United States Navy Operational Global Atmospheric
Prediction System (NOGAPS). NOGAPS is a global spectral numerical weather
prediction model (
Hogan and Rosmond 1991
) with 42 vertical levels and T239
spectral horizontal resolution.
The research version of NAVDAS-AR routinely assimilates conventional in
situ observations (including radiosondes and pibals, and surface observations from
land and sea) and satellite observations (including geostationary rapid-scan and
feature-tracked winds; winds from QuikScat, WindSat, ASCAT, ERS-2, AVHRR,
MODIS, SSM/I and SSMIS; and total precipitable water from WindSat, SSM/I and
SSMIS). NAVDAS-AR also assimilates remotely-sensed microwave and infrared
sounder radiances from AMSU-A, SSMIS, AIRS and IASI. The representation of
the background error covariance matrix
B
(in (
12.7
)) is based on the NAVDAS 3D-
Var analysis system (
Daley and Barker 2001
), and the observation error covariance
matrix
R
is diagonal. Because the space-time error covariance
F
(in (
12.7
)) is set to
zero, the current system is 4D-Var, rather than the W4D-Var targeted for the future.
Figure
12.4
shows the behavior of the NAVDAS-AR system based on the
diagnostics:
.
s
,
s
B
and
s
R
. The values are computed over a 7 day period
from 23 to 29 November 2008, with all available observations assimilated. If
the background and observation errors are correctly modeled, one would expect
J
.
x
a
/=m
J
.
x
a
/=m
D
s
B
D
s
R
1
x
a
/=m
. The figure shows that
J
.
varies from
0:4
to
0:6
and is smaller than the expected value of
. Also, the background errors are
underestimated and the observation errors are overestimated, as shown by values
of
s
B
varying from
1
, and values of
s
R
varying from
1:8
to
2:4
0:4
to
0:6
, nearly
x
a
/=m
overlapping the values of
. The diagnostics also indicate that the analysis
system is sensitive to the number of observations (more radiosonde observations at
0
J
.
UTC), with stable values over the observation period.
The observation error tuning coefficient
s
R
may be further broken down to diag-
nose the observation error variances for different types of observations. Table
12.1
shows the components for temperature, wind velocity, wind speed, moisture, total
precipitable water, and satellite radiances. The values indicate that the temperature
standard errors should be kept unchanged, but the standard error of the zonal and
meridional components of wind should be slightly reduced. Likewise, the standard
and
12
UTC than at
6
and
18
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