Geoscience Reference
In-Depth Information
J(x
a
)/m
s
B
s
R
3
2.5
2
1.5
1
0.5
0
11/23
11/24
11/25
11/26
11/27
11/28
11/29
Date [mm/dd]
Fig. 12.4
NAVDAS-AR posterior error diagnostics. The reduced value of the objective function
divided by the number of observations is consistently smaller than unity (
J
.
x
a
/=m < 1
;
solid line
),
its expected value if both background and observation errors are correctly scaled (
12.19
). Analysis
of the separate background and observation errors,
s
B
(
12.31
)and
s
R
(
12.32
), respectively, shows
that the background error variance is under-estimated (
s
B
>1
;
solid line
,
square markers
)andthe
observation error variance is over-estimated (
s
R
<1
;
dashed-line
,
circle markers
). The sawtooth
(
up
-
down
) pattern in these curves is due to the twice-daily timing of radiosonde observations,
resulting in twice-daily changes in the number of observations assimilated.
Table 12.1
Tuning coefficients
Obs-type TEMP UWIND VWIND WINDSPD H2O TPW RADIANCE
s
k
1.15 0.72 0.72 0.23 1.46 0.29 0.28
TEMP
tuning coefficients for temperature,
UWIND
zonal wind,
VWIND
meridional wind,
WINDSPD
wind speed,
H2O
moisture,
TPW
total precipitable water, and
RADIANCE
satellite
radiances
error for wind-speed, total precipitable water, and radiances should be adjusted
downward. In contrast, the standard error for moisture data should be increased.
12.4
Summary
Variational data assimilation systems based on representer-based solution methods
are being used to perform analyses and prediction in the ocean and atmosphere. One
such weather prediction system, NAVDAS-AR, is currently in operational use (
Xu
et al. 2005
;
Rosmond and Xu 2006
).
The inner iterative linear solvers at the core of these systems may display non-
monotonic convergence in the norm defined by the primal objective function, and
this behavior makes problematic the development of practical stopping criteria.
One approach to this problem has been described, namely, using an inner solver
that permits more diagnostics of the solution progress and objective function to
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