Geoscience Reference
In-Depth Information
Tabl e 9. 1
Forecast sensitivity to various input parameters of a data assimilation system with a
single outer loop iteration
Parameter
Significance
Dimension
Sensitivity equation
K
T
@e
@
x
a
R
p
y
Observation vector
@e
R
p
p
@
y
z
T
R
Observation error
covariance model
o
ı
@e
@
T
C
o
R
p
p
Observation error
correlation model
.
o
ı
z
/
y
@e
@
y
ı
.
Rz
/
C
R
@e
@
y
ı
z
o
ı
R
p
o
Observation error
standard deviation
@e
@
y
i
Œ
y
h
.
x
b
/
H
.
x
a
x
b
/
T
i
s
i
R
1
Observation error
covariance weight
@
x
a
H
T
@e
@e
x
b
R
n
Background state
vector
a
@
y
H
T
z
T
@e
@
x
b
R
n
n
B
Background error
covariance model
b
ı
H
T
z
T
b
ı
@e
@
C
b
R
n
n
Background error
correlation model
x
b
@e
@
x
b
ı
.
x
a
x
b
/
C
B
@e
@
x
b
ı
H
T
z
b
ı
R
n
b
Background error
standard deviation
@e
@
y
Œ
y
h
.
x
b
/
H
.
x
a
x
b
/
T
s
b
Background error
covariance weight
R
1
a
See Sect.
9.3.1
on the interpretation of the
x
b
-sensitivity equation
and may be expressed using the elementwise vector product (
9.60
)as
b
ı
H
T
z
T
@e
@
b
ı
@e
@
2
R
n
n
C
b
D
(9.56)
x
b
b
2
R
n
denotes the vector of values assigned in the DAS to the background
error standard deviation,
where
˙
b
D
diag.
b
/
.
A similar reasoning strategy may be used to derive the equations of the forecast
sensitivity with respect to the specification of the observation and background error
standard deviation vectors
b
respectively, in the covariance representation
(
9.25
). A summary of equations to evaluate the forecast sensitivity with respect
to various input parameters of a data assimilation system with a single outer loop
iteration is provided in Table
9.1
.
o
and
9.3.4
The Adjoint Sensitivity Guidance: A Proof-of-Concept
The derivative information obtained through adjoint-DAS techniques provides
guidance on the local behavior of the forecast aspect as a function of various
parameters in the DAS. For a generic parameter
u
, the steepest descent direction
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