DATA ASSIMILATION
335
s are used to integrate the corresponding
Ric
5.2.
plementation
Although the derivation of P assumed a 3-day assimilation interval,
actu
ion employs an alternate form
of t
satellite altimeter data within the 10-day repeat period is available but with
3-times the assumed data error.
The resulting system matrice
cati Equation to its asymptotic limit utilizing the doubling algorithm.
5 Im
al assimilation is performed every 6-hours (model time-step is 1 hour),
assimilating all available observations within 3-hours of the assimilation
instant. No observation is utilized more than once as dictated by standard
estimation theory. The 6-hour assimilation interval is a compromise
between computational requirements associated with applying the Kalman
filter more frequently and the resolution of high frequency variability of the
ocean (e.g., wind-driven barotropic motion).
For computational efficiency, the assimilat
he Kalman gain matrix from the common formulation of Eq (5),
1
1
f
T
f
T
a
T
t
t
t
t
t
P H HP H R
P H R
(37)
he alternate form on the right hand side of Eq (3
ate formulation, the filter (data) increment
(the
t i
(38)
where,
T
7) employs the analysis
error covariance instead of the forecast error covariance, and has fewer
computational steps than the left hand side, when the respective state error
covariance matrices are given.
In the partitioned reduced-st
difference between analyzed state and forecast state, i.e., the third term
of Eq 7), ˆ
a
t
'x , can be written as a sum of the increments in different
partitions,
,
ˆ
ˆ
a
a
t
i
i
c
'
'
¦
x
B x
1
,
,
ˆ
ˆ
T
a
a
f
t i
i
t i
t
t
t
H
c
c c
'
x
P H R y
x
(39)
the filter increment of an individual partitioned r
is
educed-state (subscript i).
In Eq (39), the reduced state observation matrix c
H (Eq 36) can be used.
Alternatively, Eq (39) could be implemented as,
1
,
ˆ
ˆ
T
a
a T
f
t i
i
i
t
t
t
H
c
c
t
'
x
P B H R
y
x
(40)
sing the adjoint of the model observation o
e marine geoid estimate, the analysis
assimilates altimetric sea level anomaly relative to its temporal mean instead
u
perator H as the left
multiplication H
T
. Eq (40) involves less approximation and is of particular
convenience when the observation operator is an implicit function of the
state and its adjoint is available.
Due to inaccuracies in th
335
s are used to integrate the corresponding
Ric
5.2.
plementation
Although the derivation of P assumed a 3-day assimilation interval,
actu
ion employs an alternate form
of t
satellite altimeter data within the 10-day repeat period is available but with
3-times the assumed data error.
The resulting system matrice
cati Equation to its asymptotic limit utilizing the doubling algorithm.
5 Im
al assimilation is performed every 6-hours (model time-step is 1 hour),
assimilating all available observations within 3-hours of the assimilation
instant. No observation is utilized more than once as dictated by standard
estimation theory. The 6-hour assimilation interval is a compromise
between computational requirements associated with applying the Kalman
filter more frequently and the resolution of high frequency variability of the
ocean (e.g., wind-driven barotropic motion).
For computational efficiency, the assimilat
he Kalman gain matrix from the common formulation of Eq (5),
1
1
f
T
f
T
a
T
t
t
t
t
t
P H HP H R
P H R
(37)
he alternate form on the right hand side of Eq (3
ate formulation, the filter (data) increment
(the
t i
(38)
where,
T
7) employs the analysis
error covariance instead of the forecast error covariance, and has fewer
computational steps than the left hand side, when the respective state error
covariance matrices are given.
In the partitioned reduced-st
difference between analyzed state and forecast state, i.e., the third term
of Eq 7), ˆ
a
t
'x , can be written as a sum of the increments in different
partitions,
,
ˆ
ˆ
a
a
t
i
i
c
'
'
¦
x
B x
1
,
,
ˆ
ˆ
T
a
a
f
t i
i
t i
t
t
t
H
c
c c
'
x
P H R y
x
(39)
the filter increment of an individual partitioned r
is
educed-state (subscript i).
In Eq (39), the reduced state observation matrix c
H (Eq 36) can be used.
Alternatively, Eq (39) could be implemented as,
1
,
ˆ
ˆ
T
a
a T
f
t i
i
i
t
t
t
H
c
c
t
'
x
P B H R
y
x
(40)
sing the adjoint of the model observation o
e marine geoid estimate, the analysis
assimilates altimetric sea level anomaly relative to its temporal mean instead
u
perator H as the left
multiplication H
T
. Eq (40) involves less approximation and is of particular
convenience when the observation operator is an implicit function of the
state and its adjoint is available.
Due to inaccuracies in th