THE ECMWF PERSPECTIVE
365
4d-var is cutting-edge technology and only a few operational weather
forecasts centres have been able to adopt it. First was ECMWF, then Meteo
France. The UK Met Office has recently introduced it. It is expensive, as
one has to integrate the model forwards and its adjoint backwards through
the data window (12 hours) of order 100 times. Simplifications are needed
to make it feasible. First, an incremental approach is used (Courtier et al
1994). In this approach one assumes that only relatively small departures
from the first guess will be made. The forward model is simplified,
sometimes adjusting the physics to be more linear, so helping the derivation
of the tangent linear (TL) and its adjoint. Although the TL can be a
simplification of the forward model, the adjoint must normally be the exact
adjoint of the tangent linear. The cost function, based on the tangent linear
and its adjoint, is quadratic and convergence is faster than for a more general
function. Further acceleration is achieved by using a lower resolution for the
TL and its adjoint. At ECMWF, the resolution drops from T511 to T95 for
the first 70 iterations of the inner loop. It is necessary to keep track of the
full nonlinear model: so the trajectory is recalculated using the full nonlinear
model at full resolution. This is followed by another 30 iterations of the
inner loop at the slightly higher resolution of T159.
Because the ECMWF model is formulated in spectral space, rather than in
gridpoint space, it is harder to impose covariances which vary
geographically, e.g. to have different scales for the tropics to those for the
extratropics and to have different degrees of isotropy. It can be done
partially by using a variable such as vorticity, combined with linear balance
constraints (Derber and Boutier 1998). Later, the implementation in an
ocean context will be discussed and contrasted with the atmospheric case.
Although the same assimilation approach is used throughout the
reanalysis, one can still get spurious low-frequency variability. This is
because the observing system is not stationary. Although the number of
observations generally increases as one approaches the present time, this
increase is not monotonic. Some observing systems decline while other new
systems come on stream.
An important component of any assimilation system is quality control:
deciding which observations to keep and which to reject. In Rabier (op.cit),
there is discussion of how to handle correlated observation error and how to
thin potentially too-high-density observations such as those which can come
from high-resolution satellites. Without getting into detail, as this is a
difficult area (See Andersson and Jarvinen 1999), one counterintuitive
example will be shown.
The late summer of 2004 has seen several intense hurricanes, several of
which have caused substantial damage. When a hurricane is seen to be
developing or tracking towards the Caribbean, additional meteorological
observations are taken by flying aircraft into the storm and releasing
dropsondes. These measure temperature, humidity and wind on their
descent. In principle they should provide useful information on the location
365
4d-var is cutting-edge technology and only a few operational weather
forecasts centres have been able to adopt it. First was ECMWF, then Meteo
France. The UK Met Office has recently introduced it. It is expensive, as
one has to integrate the model forwards and its adjoint backwards through
the data window (12 hours) of order 100 times. Simplifications are needed
to make it feasible. First, an incremental approach is used (Courtier et al
1994). In this approach one assumes that only relatively small departures
from the first guess will be made. The forward model is simplified,
sometimes adjusting the physics to be more linear, so helping the derivation
of the tangent linear (TL) and its adjoint. Although the TL can be a
simplification of the forward model, the adjoint must normally be the exact
adjoint of the tangent linear. The cost function, based on the tangent linear
and its adjoint, is quadratic and convergence is faster than for a more general
function. Further acceleration is achieved by using a lower resolution for the
TL and its adjoint. At ECMWF, the resolution drops from T511 to T95 for
the first 70 iterations of the inner loop. It is necessary to keep track of the
full nonlinear model: so the trajectory is recalculated using the full nonlinear
model at full resolution. This is followed by another 30 iterations of the
inner loop at the slightly higher resolution of T159.
Because the ECMWF model is formulated in spectral space, rather than in
gridpoint space, it is harder to impose covariances which vary
geographically, e.g. to have different scales for the tropics to those for the
extratropics and to have different degrees of isotropy. It can be done
partially by using a variable such as vorticity, combined with linear balance
constraints (Derber and Boutier 1998). Later, the implementation in an
ocean context will be discussed and contrasted with the atmospheric case.
Although the same assimilation approach is used throughout the
reanalysis, one can still get spurious low-frequency variability. This is
because the observing system is not stationary. Although the number of
observations generally increases as one approaches the present time, this
increase is not monotonic. Some observing systems decline while other new
systems come on stream.
An important component of any assimilation system is quality control:
deciding which observations to keep and which to reject. In Rabier (op.cit),
there is discussion of how to handle correlated observation error and how to
thin potentially too-high-density observations such as those which can come
from high-resolution satellites. Without getting into detail, as this is a
difficult area (See Andersson and Jarvinen 1999), one counterintuitive
example will be shown.
The late summer of 2004 has seen several intense hurricanes, several of
which have caused substantial damage. When a hurricane is seen to be
developing or tracking towards the Caribbean, additional meteorological
observations are taken by flying aircraft into the storm and releasing
dropsondes. These measure temperature, humidity and wind on their
descent. In principle they should provide useful information on the location