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
R n D
(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
.
f /
(9.18)
where M t 0 ;t f
t 0 to
t f .
denotes the tangent linear model from
 
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