Geoscience Reference
In-Depth Information
2. Diagnostic studies of synoptic-scale and mesoscale processes in mid-latitude
weather systems [
Brill et al.
(
1991
),
Stauffer et al.
(
1985
),
Stauffer and
Seaman
(
1990
),
Yamada and Bunker
(
1989
), and
Wa r n e r
(
1990
)].
3. Observation System Simulation Experiments (OSSE's) using observations from
wind profilers as found in the work of
Kuo and Guo
(
1989
).
4. Application of the nudging assimilation method to operational prediction has
been made in both meteorology and oceanography. In meteorology, the following
publications have explored nudging:
Bell and Dickinson
(
1987
)and
Lorenc
et al.
(
1991
). In oceanography,
Derber and Rosati
(
1989
)and
Derber et al.
(
1990
)
have used nudging.
Beyond this divisional breakdown of nudging processes in research and operations,
the following studies are noteworthy: A non-operational application of nudging
to analyses from FGGE (First GARP Global Experiment) as found in
Stern
et al.
(
1985
), a sensitivity of assimilation and prediction to the nudging coefficient
by
Bao and Errico
(
1997
), and a series of explorations into the “back-and-
forth” nudging method by Auroux and collaborators [
Auroux
(
2009
),
Auroux and
Nodet
(
2010
), and
Auroux and Blum
(
2005
)and(
2008
)].
We begin our review by providing a historical examination of the empirical
methods used in nudging. This is followed by a study of the work that searched
for optimal nudging coefficients including an account for serial correlation errors
in the nudging process. We then examine the observer-based methods and explore
the ideas behind the back-and-forth nudging process. We summarize and discuss the
work on nudging in the final section of the paper.
2.2
Early Empirical Method
For completeness and to give a flavor of the ideas used in the early era, in this section
we describe a method for determining the scalar nudging coefficient
. Following
Brill et al.
(
1991
) consider the analysis nudging scheme in continuous time. Let
G
x.t/
D
F.x.t//
C
Gf .t/ Œx
a
.t/
x.t/
(2.9)
F
W
R
n
!
R
n
,
where
G
2
R
is an unknown positive scalar to be estimated,
f
W
Œ0;T
!
R
is a non-negative real valued function such that
0
f.t/
1f.0/
D
0
D
f.T/
(2.10)
and
obtained
from the available observations at these times.
Brill et al.
(
1991
) postulate that
x
a
.0/
and
x
a
.T/
are the known analyses at times
t
D
0
and
t
D
T
x
a
.t/
in (
2.9
) varies linearly and is given by
x
a
.t/
D
x
a
.0/
C
t
T
Œx
a
.T/
x
a
.0/
(2.11)
The dynamics is then integrated from the initial condition
x.0/
D
x
a
.0/
.
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