290 Pierre De Mey and Mounir Benkiran
SOFA data assimilation code has is also used for projects outside the Mediterranean (chiefly North Atlantic and Global).
The Mediterranean General Circulation Model (GCM) is an eddy-permitting 1/
8°, 31-level version of MOM-l implemented by both the Toulouse and Bologna
teams (see e.g. Pinardi and Masetti, 2000). It is forced with ECMWF 6-hour operational analyses: 10-meter winds, air temperature to calculate interactive heat
fluxes. Baroclinic exchanges are allowed at Gibraltar and Sicily Straits. Constant
vertical diffusion is used for efficiency. In alI experiments reviewed below, a 5-year
spin-up from climatology was carried out, folIowed by one year forced with
ECMWF analyses before the assimilation experiments start. Reanalyzed ERA forcing fields were avaible up to 1993, the operational analyses starting in 1994. The
salinity relaxation at the surf ace typicalIy uses the MED5 MODB database
(www.modb.oce.ulg.ac.be).
The sequence of operations is the folIowing: (1) the MOM model mns for a week
while collecting misfits between model and observations (the "innovation"); (2)
the forecast model fields (the "background solution") are corrected by SOFA from
the innovation vector along the lines ofthe algorithm described in the previous section, i.e. OI on a base of pre-calculated vertical EOFs. Estimates are calculated at
each model grid point using the local inverse approach. The time differences
between the observations and the analysis time are taken into account in the estimates. Then the sequence restarts as MOM is re-initialized from the corrected
fields and a Euler foward time step. Only past data are used for each correction
step. Therefore the statistics of the misfits for any cycle are truly a measure of the
capacity of the assimilating model to predict the data which have not yet been
assimilated. We will use second-order misfit statistics, spatially averaged over
regions or temporalIy averaged, to illustrate the benefit of the assimilation in the
examples below.
In SOFA, the model grid must be nonsingular (no poles) and can be periodic in
one dimension; it is not restricted to being rectangular, although it is in the cases
studied here. In the calculation ofthe innovation vector in step (1), the full observation operator H( ) is used. This can be a global, non-linear operator. On the contrary, in the analysis step (2), local, tangent linear observation operators as
discussed in section 15.2.4 are used to form the ROOI gain. When needed to calculate misfits, the model variables are interpolated at the data points by means of
hyperbolic paraboloid functions (which come back to bilinear interpolation in the
case of a rectangular grid). Data search on the grid is performed by a Kd-Tree algorithm (e.g. Skiena, 1997).
We schematically present the interface between SOFA and the Mediterranean
GCM. The state vector in MOM, i.e. the list of independent and dependent variables, is defined as
x = {"" ue' w, T, S, p}
(21)
i.e. the transport streamfunction, baroclinic horizontal velocities, vertical velocity,
temperature, salinity, and density. The estimation problem is entirely written in
SOFA data assimilation code has is also used for projects outside the Mediterranean (chiefly North Atlantic and Global).
The Mediterranean General Circulation Model (GCM) is an eddy-permitting 1/
8°, 31-level version of MOM-l implemented by both the Toulouse and Bologna
teams (see e.g. Pinardi and Masetti, 2000). It is forced with ECMWF 6-hour operational analyses: 10-meter winds, air temperature to calculate interactive heat
fluxes. Baroclinic exchanges are allowed at Gibraltar and Sicily Straits. Constant
vertical diffusion is used for efficiency. In alI experiments reviewed below, a 5-year
spin-up from climatology was carried out, folIowed by one year forced with
ECMWF analyses before the assimilation experiments start. Reanalyzed ERA forcing fields were avaible up to 1993, the operational analyses starting in 1994. The
salinity relaxation at the surf ace typicalIy uses the MED5 MODB database
(www.modb.oce.ulg.ac.be).
The sequence of operations is the folIowing: (1) the MOM model mns for a week
while collecting misfits between model and observations (the "innovation"); (2)
the forecast model fields (the "background solution") are corrected by SOFA from
the innovation vector along the lines ofthe algorithm described in the previous section, i.e. OI on a base of pre-calculated vertical EOFs. Estimates are calculated at
each model grid point using the local inverse approach. The time differences
between the observations and the analysis time are taken into account in the estimates. Then the sequence restarts as MOM is re-initialized from the corrected
fields and a Euler foward time step. Only past data are used for each correction
step. Therefore the statistics of the misfits for any cycle are truly a measure of the
capacity of the assimilating model to predict the data which have not yet been
assimilated. We will use second-order misfit statistics, spatially averaged over
regions or temporalIy averaged, to illustrate the benefit of the assimilation in the
examples below.
In SOFA, the model grid must be nonsingular (no poles) and can be periodic in
one dimension; it is not restricted to being rectangular, although it is in the cases
studied here. In the calculation ofthe innovation vector in step (1), the full observation operator H( ) is used. This can be a global, non-linear operator. On the contrary, in the analysis step (2), local, tangent linear observation operators as
discussed in section 15.2.4 are used to form the ROOI gain. When needed to calculate misfits, the model variables are interpolated at the data points by means of
hyperbolic paraboloid functions (which come back to bilinear interpolation in the
case of a rectangular grid). Data search on the grid is performed by a Kd-Tree algorithm (e.g. Skiena, 1997).
We schematically present the interface between SOFA and the Mediterranean
GCM. The state vector in MOM, i.e. the list of independent and dependent variables, is defined as
x = {"" ue' w, T, S, p}
(21)
i.e. the transport streamfunction, baroclinic horizontal velocities, vertical velocity,
temperature, salinity, and density. The estimation problem is entirely written in