289
[Cane et al., 1996]. This kind of representativeness error typically corresponds to spatially correlated signals, and in this case o-diagonal
elements must be included in R.
In the open ocean, dynamical considerations can justify the omission
of some of the PE variables in the state vector, such as the horizontal velocity components which are expected to adjust very quickly to
the density properties. Dierent choices of estimation space, motivated
also by the faith in the error statistics to be prescribed for the selected
variables, are discussed by Brankart et al. [2003] for primitive equation
circulation models.
The question of assimilating satellite altimetric data into ocean circulation models has been approached many times by reducing the statistical estimation problem to the surface variables. The downward penetration of assimilated information is then achieved empirically, using a
variety of statistical (e.g. Hurlburt [1986]; Mellor and Ezer [1991]; De
Mey and Benkiran [2002]) or physical (e.g. Cooper and Haines [1996];
Oschlies and Willebrand [1996]) extrapolation schemes on the vertical
direction. These dierent vertical projection methods, as well as the
dynamical adjustment process described by Brankart et al. [2003] in the
context of HYCOM, can be considered as approximations of the pseudoinverse of T needed to convert the reduced state back to the full model
space after statistical estimation.
5.2
Reducing the dimensionality of the error
space
A number of other methods are based on approximations of the error
with fewer degrees of freedom than the model itself. Error sub-spaces
are built with the aim of selectively correcting the model state along
the most representative directions of the forecast error. The concept fits
well with statistical assimilation schemes because the analysis increment
computed by (20) can only take place within the sub-space spanned by
the forecast error covariance. The unknown are the coe!cients of the
correction projected along the multivariate error directions. The concept
of Error Subspace Statistical Estimation (ESSE) introduced by Lermusiaux [1999] has been developed on the basis of this principle. Note that
recent oceanographic studies have also started to explore the potential
benefit of order reduction using variational assimilation methods [Robert
et al., 2005].
The sub-space can be prescribed as a time-invariant set of error directions. The success of assimilation depends essentially on the capacity of
the sub-space to capture the observed variability of the system. A numOCEAN DATA ASSIMILATION
[Cane et al., 1996]. This kind of representativeness error typically corresponds to spatially correlated signals, and in this case o-diagonal
elements must be included in R.
In the open ocean, dynamical considerations can justify the omission
of some of the PE variables in the state vector, such as the horizontal velocity components which are expected to adjust very quickly to
the density properties. Dierent choices of estimation space, motivated
also by the faith in the error statistics to be prescribed for the selected
variables, are discussed by Brankart et al. [2003] for primitive equation
circulation models.
The question of assimilating satellite altimetric data into ocean circulation models has been approached many times by reducing the statistical estimation problem to the surface variables. The downward penetration of assimilated information is then achieved empirically, using a
variety of statistical (e.g. Hurlburt [1986]; Mellor and Ezer [1991]; De
Mey and Benkiran [2002]) or physical (e.g. Cooper and Haines [1996];
Oschlies and Willebrand [1996]) extrapolation schemes on the vertical
direction. These dierent vertical projection methods, as well as the
dynamical adjustment process described by Brankart et al. [2003] in the
context of HYCOM, can be considered as approximations of the pseudoinverse of T needed to convert the reduced state back to the full model
space after statistical estimation.
5.2
Reducing the dimensionality of the error
space
A number of other methods are based on approximations of the error
with fewer degrees of freedom than the model itself. Error sub-spaces
are built with the aim of selectively correcting the model state along
the most representative directions of the forecast error. The concept fits
well with statistical assimilation schemes because the analysis increment
computed by (20) can only take place within the sub-space spanned by
the forecast error covariance. The unknown are the coe!cients of the
correction projected along the multivariate error directions. The concept
of Error Subspace Statistical Estimation (ESSE) introduced by Lermusiaux [1999] has been developed on the basis of this principle. Note that
recent oceanographic studies have also started to explore the potential
benefit of order reduction using variational assimilation methods [Robert
et al., 2005].
The sub-space can be prescribed as a time-invariant set of error directions. The success of assimilation depends essentially on the capacity of
the sub-space to capture the observed variability of the system. A numOCEAN DATA ASSIMILATION