DATA ASSIMILATION
325
(e.
s o
e rewritten as,
where E describes the sampling operation and H denotes measurement errors
g., instrument error).
In term f the model, Eq (16) can b
^
`
t
t
t
t
H
y Hx
Ew HȆ
w
(17)
The last two terms of Eq (17),
^
`
t
t
H
Ew HȆw
(18)
can
ation t
t
y Hx
be identified as the error of the observation equ
that
efines the data assimilation problem (Eq 1), i.e.,
e difference between error free observations
) and error-free equivalent of the m
tire spec
model
r.” Other common examples of
repr
cally employ larger
“data”
o
ervations so as to
maximi
with
observa n
ting
the data o
rrors in the model
evo
93). Such measurements (Lagrangian
traj
d
the covariance of Eq (18)
is R. The first part of (18) is th
(
odel (
t
HȆw ). The two are
t
Ew
generally different because the model does not simulate the en
trum
of the ocean but only parts of it (Eq 15).
For instance, a coarse resolution model of 1º horizontal resolution does
not simulate meso-scale variability, and a 1.5-layer reduced-gravity model
does not simulate barotropic motion. What a
cannot simulate
constitutes part of the errors of the observation equation as described by Eq
(18) and is termed “representation erro
esentation error include,
x Baroclinic variability for a barotropic model
x External gravity waves for a rigid-lid model
x Skin temperature for most models with thick surface layers
x Micro-structure for most large-scale models
In numerical weather forecasting, meteorologists typi
err r than the measurement accuracy of the obs
ze the skill of their forecasts. Forcing models to agree
tio s that the models cannot simulate, result in models propaga
c rrection incorrectly in time, causing larger e
lution than otherwise.
Some observations are dominated by representation error, making them
difficult to utilize. For instance, individual drifter and float trajectories can
depend on small-scale variabilities of the ocean, such that two floats
deployed a short distance away from each other have dramatically different
trajectories (e.g., Paduan and Niiler, 19
ectory as opposed to Eulerian velocities along the trajectory) that are
dominated by representation errors do not provide strong data constraints,
and cannot be used effectively.
4.2 “Model” Error
The nature of model process noise Q can be deduced in a similar fashion
as data error above. The model can be written in shorthand as,
325
(e.
s o
e rewritten as,
where E describes the sampling operation and H denotes measurement errors
g., instrument error).
In term f the model, Eq (16) can b
^
`
t
t
t
t
H
y Hx
Ew HȆ
w
(17)
The last two terms of Eq (17),
^
`
t
t
H
Ew HȆw
(18)
can
ation t
t
y Hx
be identified as the error of the observation equ
that
efines the data assimilation problem (Eq 1), i.e.,
e difference between error free observations
) and error-free equivalent of the m
tire spec
model
r.” Other common examples of
repr
cally employ larger
“data”
o
ervations so as to
maximi
with
observa n
ting
the data o
rrors in the model
evo
93). Such measurements (Lagrangian
traj
d
the covariance of Eq (18)
is R. The first part of (18) is th
(
odel (
t
HȆw ). The two are
t
Ew
generally different because the model does not simulate the en
trum
of the ocean but only parts of it (Eq 15).
For instance, a coarse resolution model of 1º horizontal resolution does
not simulate meso-scale variability, and a 1.5-layer reduced-gravity model
does not simulate barotropic motion. What a
cannot simulate
constitutes part of the errors of the observation equation as described by Eq
(18) and is termed “representation erro
esentation error include,
x Baroclinic variability for a barotropic model
x External gravity waves for a rigid-lid model
x Skin temperature for most models with thick surface layers
x Micro-structure for most large-scale models
In numerical weather forecasting, meteorologists typi
err r than the measurement accuracy of the obs
ze the skill of their forecasts. Forcing models to agree
tio s that the models cannot simulate, result in models propaga
c rrection incorrectly in time, causing larger e
lution than otherwise.
Some observations are dominated by representation error, making them
difficult to utilize. For instance, individual drifter and float trajectories can
depend on small-scale variabilities of the ocean, such that two floats
deployed a short distance away from each other have dramatically different
trajectories (e.g., Paduan and Niiler, 19
ectory as opposed to Eulerian velocities along the trajectory) that are
dominated by representation errors do not provide strong data constraints,
and cannot be used effectively.
4.2 “Model” Error
The nature of model process noise Q can be deduced in a similar fashion
as data error above. The model can be written in shorthand as,