Geoscience Reference
In-Depth Information
Fig. 9.1
Contours of the
4
a
=
b;t
as a function of
the two variables
ratio
.The
contour interval is of 0.2. For
values of
.;
t
/
3.5
,
misspecification of the
observation and/or
background error variances
may result in a detrimental
observation impact (
shaded
region
)
t
>1
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
μ
The line
t
D
2
C
1
divides the positive quadrant of the
.;
t
/
plane in a region
a
=
b;t
<1
t
<2
C
1
of
benefic observation impact
,
,andaregion
t
>2
C
1
of
a
=
b;t
>1
detrimental observation impact
,
.Since
depends on the specification
o
b
of both
, this is a simple illustration that the observing system performance
(observation “value”) is closely determined by the representation in the DAS of both
observation and background error statistics.
and
9.3
Adjoint-DAS Sensitivity Analysis
The adjoint-DAS sensitivity analysis aims to provide an assessment of the response
of a functional
x
a
/
e.
to variations in the DAS input parameters. The first order
x
a
/
x
a
is defined as
variation
ıe.
induced by the analysis variation
ı
@e
@
x
a
@e
@
x
a
/
T
ıe
D
x
a
;ı
R
n
D
.ı
(9.17)
x
a
x
a
2
R
n
,is
For the functional (
9.8
), the forecast sensitivity to analysis,
@e=@
evaluated using a backward adjoint model integration from
t
f
to
t
0
along the
analysis trajectory
@e
@
M
t
0
;t
f
T
E
x
f
x
v
x
a
D
2Œ
.
f
/
(9.18)
where
M
t
0
;t
f
t
0
to
t
f
.
denotes the tangent linear model from
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