Geoscience Reference
In-Depth Information
to short-range forecast error measures (
Baker and Langland 2009
;
Cardinali 2009
).
An intercomparison study on OBSI assessment at various NWP centers is provided
by
Gelaro et al.
(
2010
).
9.2.2
Suboptimal Observation Performance: A Scalar Example
A simple scalar example of statistical estimation is used to illustrate the suboptimal
observation performance for misspecified information error statistics. Consider a
prior estimate
x
b
D
x
t
C
b
and a measurement
y
D
x
t
C
o
to the true value
x
t
and let assume that the errors
b
and
o
are unbiased
E.
b
/
D
0;E.
o
/
D
0
,and
E.
b
/
D
b;t
E.
o
/
D
o;t
uncorrelated
E.
b
o
/
D
0
. The error variances
and
are
b
o
assumed to be unknown and are specified in the analysis equation as
and
,
respectively. A suboptimal analysis estimate to
x
t
is obtained as
o
b
C
o
x
b
C
b
1
C
x
b
C
1
1
C
y
x
a
D
b
C
o
y
D
(9.12)
D
o
=
b
where
denotes the ratio
. The observation performance on improving
the prior estimate
x
b
is investigated in terms of the specification
versus the optimal
t
D
o;t
=
b;t
ratio
. The analysis variance is
2
2
1
C
1
1
C
a
D
b;t
C
o;t
(9.13)
and the ratio
2
2
a
b;t
1
C
1
1
C
D
C
t
(9.14)
provides a measure of the statistical quality of the analysis as compared with the
prior estimate
x
b
. The minimum value of the ratio (
9.14
) as a function of
is
achieved at
D
t
and corresponds to the
optimal analysis
x
a;t
,
a;t
b;t
t
1
C
t
<1
D
(9.15)
In the practical situation when the specification of the information error statistics
is such that
ยค
t
, the observation performance is suboptimal and, in certain
situations, the assimilation of data
y
may provide an estimate
x
a
of lower quality as
a
=
b;t
D
compared to
x
b
. Contours
const
of the ratio (
9.14
) as a function of the
two variables
.;
t
/
are shown in Fig.
9.1
. A threshold value to the
specification
a
=
b;t
D
1
is obtained when
,
a
b;t
D
1
,
t
D
2
C
1
(9.16)
Search WWH ::
Custom Search