307
of the following three conditions is met: (i) the initial error is perfectly
described by the reduced basis; (ii) the truncation error is dynamically
uncoupled with the error components of the low-dimension space; (iii)
the sub-space must contain all the components of the growing error
during the forecast time period. As these three conditions are never
perfectly verified in realistic assimilation systems, an adaptive procedure was developed in order to introduce some feedback between the
data and the error sub-space used by the filter. The algorithm proposed
by Brasseur et al. [1999] updates the error sub-space of the SEEK filter along the geostrophic attractor by extracting information left in the
residual vector after each analysis step. This update of the reduced basis
is performed in such a way as to attenuate the truncation error and to
improve the projection of the next innovation onto the error sub-space:
this leads to the concept of adaptive sub-space. An advantage of this
variant of the SEEK filter is that it allows the evolution of the error subspace without incurring the cost of propagating the whole set of error
directions dynamically.
8.
Intermittent vs. time-continuous filtering
In the basic assimilation problem introduced in Section 1, two major
simplifications were considered: (i) the observations were available at
discrete time intervals, and (ii) the analysis was performed at the exact
time of the measurements. In oceanographic and atmospheric applications, the situation is quite dierent since the flow of observations can
be considered as almost continuous in time (for instance, the acquisition
of altimeter data). Therefore, ocean data assimilation with intermittent
sequential filters necessarily involves approximations.
In principle, sequential filters could perform an analysis step as often as a new piece of information arrives. Time-continuous formulations
of the KF exist [Gelb 1974] and have been applied to analogic signal
processing. However, their application to oceanographic or atmospheric
models is inappropriate: for practical reasons, it would be impossible
to incorporate the data at their exact time of acquisition. Experience
shows that it is necessary to accumulate a certain number of observations between two successive analysis steps to correct the ocean state
with su!cient impact. Besides, operational assimilation systems must
be scheduled on a regular temporal basis so as to avoid unnecessary
algorithmic complications, to account for human intervention, delay in
data delivery, etc.
OCEAN DATA ASSIMILATION
of the following three conditions is met: (i) the initial error is perfectly
described by the reduced basis; (ii) the truncation error is dynamically
uncoupled with the error components of the low-dimension space; (iii)
the sub-space must contain all the components of the growing error
during the forecast time period. As these three conditions are never
perfectly verified in realistic assimilation systems, an adaptive procedure was developed in order to introduce some feedback between the
data and the error sub-space used by the filter. The algorithm proposed
by Brasseur et al. [1999] updates the error sub-space of the SEEK filter along the geostrophic attractor by extracting information left in the
residual vector after each analysis step. This update of the reduced basis
is performed in such a way as to attenuate the truncation error and to
improve the projection of the next innovation onto the error sub-space:
this leads to the concept of adaptive sub-space. An advantage of this
variant of the SEEK filter is that it allows the evolution of the error subspace without incurring the cost of propagating the whole set of error
directions dynamically.
8.
Intermittent vs. time-continuous filtering
In the basic assimilation problem introduced in Section 1, two major
simplifications were considered: (i) the observations were available at
discrete time intervals, and (ii) the analysis was performed at the exact
time of the measurements. In oceanographic and atmospheric applications, the situation is quite dierent since the flow of observations can
be considered as almost continuous in time (for instance, the acquisition
of altimeter data). Therefore, ocean data assimilation with intermittent
sequential filters necessarily involves approximations.
In principle, sequential filters could perform an analysis step as often as a new piece of information arrives. Time-continuous formulations
of the KF exist [Gelb 1974] and have been applied to analogic signal
processing. However, their application to oceanographic or atmospheric
models is inappropriate: for practical reasons, it would be impossible
to incorporate the data at their exact time of acquisition. Experience
shows that it is necessary to accumulate a certain number of observations between two successive analysis steps to correct the ocean state
with su!cient impact. Besides, operational assimilation systems must
be scheduled on a regular temporal basis so as to avoid unnecessary
algorithmic complications, to account for human intervention, delay in
data delivery, etc.
OCEAN DATA ASSIMILATION