305
in the family of techniques used for this purpose is the concept of adaptivity. A comparison between dierent sophisticated adaptive KFs is
provided by Blanchet et al. [1997]. In this section, we examine more
closely dierent examples of adaptive methods that have been explored
in the literature to identify and correct model biases, to tune the parameterization of model errors and to build the error sub-space of low-rank
KFs.
Research eorts aimed at improving error covariance modelling in assimilation systems are of limited interest if biases are left in the models
or the observations, i.e. if criterion (51) is not verified. The correction
for biases in operational systems is expected to have a very strong impact
on assimilation performances. In the context of sequential assimilation,
Dee and Da Silva [1998] proposed a rigorous method for estimating the
forecast bias and correcting the forecast prior to the analysis, assuming unbiased observations. The algorithm is designed to perform on-line
and its implementation does not require substantial modifications to the
assimilation system. The basic idea consists in running a simplified KFtype algorithm to estimate d i in addition to the KF for the state itself.
Assuming temporal persistence of the bias, the extra cost of the method
is equivalent to one additional computation of the statistical analysis
step.
The question of model error parameterization can been addressed by
means of adaptive methods too. In many practical studies, the model
error covariance Q is probably the least well known statistical quantity
impacting the forecast error. Mitchell and Houtekamer [2000] developed
an adaptive EnKF using a maximum likelihood method to estimate the
parameterization of model errors from the innovation sequence. The approach recently developed by Brankart et al. [2003] can also be viewed
as an adaptive parameterization of the model error. By adjusting the
coe!cient of Eq. (38) according to the local innovation variance, the
method is able to account for regional properties of the ocean dynamics.
The estimation of the innovation variance is based on a weighted average of the latest innovations, using a weight that decreases exponentially
with the age of the innovation.
This mechanism was explored in the context of hindcast experiments
conducted for the 1993-1996 period. The SEEK filter was implemented
in two dierent models : the 1/3
North Atlantic OPA model of the
MERCATOR prototype system, and the Atlantic/Arctic MICOM model
of the European DIADEM system. Sea-surface temperature from the
NASA Pathfinder project and altimetric data from the Topex/Poseidon
and ERS missions were assimilated in both systems every 10 days. Testut [2000] studied the distribution of the 10-day forecast error in the
OCEAN DATA ASSIMILATION
in the family of techniques used for this purpose is the concept of adaptivity. A comparison between dierent sophisticated adaptive KFs is
provided by Blanchet et al. [1997]. In this section, we examine more
closely dierent examples of adaptive methods that have been explored
in the literature to identify and correct model biases, to tune the parameterization of model errors and to build the error sub-space of low-rank
KFs.
Research eorts aimed at improving error covariance modelling in assimilation systems are of limited interest if biases are left in the models
or the observations, i.e. if criterion (51) is not verified. The correction
for biases in operational systems is expected to have a very strong impact
on assimilation performances. In the context of sequential assimilation,
Dee and Da Silva [1998] proposed a rigorous method for estimating the
forecast bias and correcting the forecast prior to the analysis, assuming unbiased observations. The algorithm is designed to perform on-line
and its implementation does not require substantial modifications to the
assimilation system. The basic idea consists in running a simplified KFtype algorithm to estimate d i in addition to the KF for the state itself.
Assuming temporal persistence of the bias, the extra cost of the method
is equivalent to one additional computation of the statistical analysis
step.
The question of model error parameterization can been addressed by
means of adaptive methods too. In many practical studies, the model
error covariance Q is probably the least well known statistical quantity
impacting the forecast error. Mitchell and Houtekamer [2000] developed
an adaptive EnKF using a maximum likelihood method to estimate the
parameterization of model errors from the innovation sequence. The approach recently developed by Brankart et al. [2003] can also be viewed
as an adaptive parameterization of the model error. By adjusting the
coe!cient of Eq. (38) according to the local innovation variance, the
method is able to account for regional properties of the ocean dynamics.
The estimation of the innovation variance is based on a weighted average of the latest innovations, using a weight that decreases exponentially
with the age of the innovation.
This mechanism was explored in the context of hindcast experiments
conducted for the 1993-1996 period. The SEEK filter was implemented
in two dierent models : the 1/3
North Atlantic OPA model of the
MERCATOR prototype system, and the Atlantic/Arctic MICOM model
of the European DIADEM system. Sea-surface temperature from the
NASA Pathfinder project and altimetric data from the Topex/Poseidon
and ERS missions were assimilated in both systems every 10 days. Testut [2000] studied the distribution of the 10-day forecast error in the
OCEAN DATA ASSIMILATION