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a
b
12 hr
0 hr
50N
50N
40N
40N
30N
30N
20N
20N
140W
130W
120W
110W
100W
90W
80W
70W
60W
140W
130W
120W
110W
100W
90W
80W
70W
60W
c
−
0.5
−
0.4
−
0.3
−
0.2
−
0.02
0.02
0.2
0.3
0.4
0.5
d
−
0.5
−
0.4
−
0.3
−
0.2
−
0.02
0.02
0.2
0.3
0.4
0.5
Radiosondes
Aircraft
50N
50N
40N
40N
30N
30N
20N
20N
140W
130W
120W
110W
100W
90W
80W
70W
60W
140W
130W
120W
110W
100W
90W
80W
70W
60W
−
3
−
2.2
−
1.7
−
1.2
−
1
−
0.7
−
0.5
−
0.3
−
0.1
−
0.05
0.05 0.1
0.3
0.5
0.7
1.2
−
3
−
2.2
−
1.7
−
1.2
−
1
−
0.7
−
0.5
−
0.3
−
0.1
−
0.05
0.05 0.1
0.3
0.5
0.7
1.2
g
f
g
f
Fig. 6.1
The vertically integrated components of (
a
)
e
(
b
) and the model space estimate
ıe
g
f
at the analysis time. Also, the subset of observation space estimate
mapped to (
c
) radiosonde,
and (
d
) aircraft observation locations. All calculations are for a 12 h COAMPS forecast valid 1200
UTC 05 May 2010. Values are in units of J kg
1
ıe
Fig.
6.2
indicate the box edges for the error calculation in Cases 1-3. For Case 1, the
error was calculated at every model grid point, while in Case 2, the outermost seven
grid points along each edge were removed. In Case 3, the box was placed over
the eastern United States to allow information to flow upstream in the COAMPS
adjoint model and still stay on the model's grid. Impacts were computed for a 12 h
COAMPS forecast valid 0000 UTC Sep 25 2011 with 90 km horizontal grid spacing.
The ratio of
g
f
g
f
ıe
e
is shown at each of the 12 h of the
COAMPS adjoint integration by the black bars in Fig.
6.3
for each of the three cases.
At 12 h, the value
in model space to
g
f
g
f
ıe
e
1:0
.However,the
adjoint model is linear and does not account for all of the contributions in
and
are exactly equal so their ratio is
g
f
e
.
Therefore, the ratio drops as the COAMPS adjoint model is integrated backward
in time. The ratio is just above
0:5
by the end of adjoint model run in Case 1.
Removing some points near the boundary improves the situation in Case 2, and the
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