282
PIERRE BRASSEUR
periods of time and provide considerable information about the ocean’s
horizontal and temporal variability. Figure 4 illustrates a typical SST
picture obtained from composite AVHRR (Advanced Very High Resolution Radiometer) images, and a network of altimetric ground tracks covered by two satellites flying simultaneously over a 7-day period. Along
the altimeter tracks, the measurements are available every 7 km and the
separation between two tracks of Topex-Poseidon is about 300 km at the
Equator. These data can be assimilated “along track” as shown in figure 4, providing in principle the best possible utilization of the observed
information if the assimilation scheme is optimally tuned. Otherwise,
the raw measurements can be transformed into gridded products using
sub-optimal interpolation methods before assimilation.
The surface nature of satellite data poses specific challenges with
regard to data assimilation because the surface information has to be
projected downward to reconstruct the 3D-content of the ocean signal.
As illustrated in the next section, the extrapolation process is achieved
through the use of 3D, multivariate error covariances in the assimilation
scheme. These surface data remain insu!cient, however, for describing
aspects of sub-surface variability, and other data available in the form of
vertical temperature and salinity profiles from hydrographic casts, moorings or expandable bathythermographs (XBT) and profiling floats from
the ARGO international program provide valuable information about
the vertical stratification. It is therefore essential to assimilate both data
types in a consistent manner.
Two additional operators related to the data must be introduced:
the observation error covariance matrix R and the observation operator
H (or a non-linear H). The observation operator converts the forecast state into “first guesses” of the observations. This conversion is
needed because the observed variables may not be located on the model
grid points so that horizontal or vertical interpolations are necessary.
In addition, relationships of varying complexity may exist between the
observed quantity and the model variables. One example is the ocean
colour, which is related to the phytoplankton concentration through a
fairly complex, and sometimes approximate, relationship. Another example is the relationship between sea-level (measured by altimetry) and
the prognostic variables of a rigid-lid ocean model [Pinardi et al., 1995].
In order to avoid too complex observation operators in the algorithms,
it is sometimes advisable to augment the state vector with diagnostic
variables (such as the surface pressure of a rigid-lid model which can be
diagnosed as a function of the prognostic variables) that can be linked
to the observed variables more easily.
PIERRE BRASSEUR
periods of time and provide considerable information about the ocean’s
horizontal and temporal variability. Figure 4 illustrates a typical SST
picture obtained from composite AVHRR (Advanced Very High Resolution Radiometer) images, and a network of altimetric ground tracks covered by two satellites flying simultaneously over a 7-day period. Along
the altimeter tracks, the measurements are available every 7 km and the
separation between two tracks of Topex-Poseidon is about 300 km at the
Equator. These data can be assimilated “along track” as shown in figure 4, providing in principle the best possible utilization of the observed
information if the assimilation scheme is optimally tuned. Otherwise,
the raw measurements can be transformed into gridded products using
sub-optimal interpolation methods before assimilation.
The surface nature of satellite data poses specific challenges with
regard to data assimilation because the surface information has to be
projected downward to reconstruct the 3D-content of the ocean signal.
As illustrated in the next section, the extrapolation process is achieved
through the use of 3D, multivariate error covariances in the assimilation
scheme. These surface data remain insu!cient, however, for describing
aspects of sub-surface variability, and other data available in the form of
vertical temperature and salinity profiles from hydrographic casts, moorings or expandable bathythermographs (XBT) and profiling floats from
the ARGO international program provide valuable information about
the vertical stratification. It is therefore essential to assimilate both data
types in a consistent manner.
Two additional operators related to the data must be introduced:
the observation error covariance matrix R and the observation operator
H (or a non-linear H). The observation operator converts the forecast state into “first guesses” of the observations. This conversion is
needed because the observed variables may not be located on the model
grid points so that horizontal or vertical interpolations are necessary.
In addition, relationships of varying complexity may exist between the
observed quantity and the model variables. One example is the ocean
colour, which is related to the phytoplankton concentration through a
fairly complex, and sometimes approximate, relationship. Another example is the relationship between sea-level (measured by altimetry) and
the prognostic variables of a rigid-lid ocean model [Pinardi et al., 1995].
In order to avoid too complex observation operators in the algorithms,
it is sometimes advisable to augment the state vector with diagnostic
variables (such as the surface pressure of a rigid-lid model which can be
diagnosed as a function of the prognostic variables) that can be linked
to the observed variables more easily.