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In-Depth Information
to be superior. The deterministic ECMWF T511 spectral model has an equivalent
horizontal grid spacing of about 40 km. The ECMWF ensemble prediction system
in 2003 was based on a T255 spectral model (horizontal grid spacing of about
80 km). As of 2003 the deterministic ECMWF model had 60 vertical levels extend-
ing from the surface to about 64 km, while the ensemble prediction system had
40 levels extending from the surface to about 30 km.
Due to the high resolutions of the ECMWF T511 and T255 models, a time
integration scheme based on the centered difference leapfrog method or other
explicit scheme would require very small time steps in order to satisfy the CFL
conditions (13.18) for the fastest propagating gravity wave modes and for the
advection terms in areas of high wind speed. To avoid the computational overhead
of such a model, the time integration is carried out using a semi-implicit technique
in which terms associated with gravity wave propagation are treated implicitly;
and a semi-Lagrangian technique is employed for computation of the nonlinear
advection terms. A time step of 15 min or more can then be used.
13.6.3
Physical Parameterizations
The physical processes included in modern operational forecast models are gen-
erally the same as those included in general circulation models and were shown
schematically in Fig. 10.22. Inclusion of such processes as boundary layer fluxes,
vertical mixing by dry and moist convection, formation of clouds and precipita-
tion, and the interaction of cloud and radiation fields requires that the relevant
subgrid scale processes be represented in terms of model predicted fields. The
approximation of unresolved processes in terms of resolved variables is referred
to as
parameterization
; it is probably the most difficult and controversial area of
weather and climate modeling.
Perhaps the most important physical process that must be parameterized is con-
vection. Vertical heat transfer by convection is essential in maintaining the observed
tropospheric lapse rate and moisture distribution. The simplest way to mimic this
effect of unresolved convective motions is through
convective adjustment
. In a sim-
ple version of this method, the relative humidity and lapse rate in each grid column
are examined at the end of each time step. If the lapse rate is super adiabatic, the
temperature profile is adjusted to dry static neutrality in a manner that conserves
energy; if the column is conditionally unstable, and the humidity exceeds a spec-
ified value, the column is adjusted to moist static neutrality. More sophisticated
schemes utilize the fact that moist convection is dependent on low-level moisture
convergence and include a moisture budget as part of the parameterization (see
Section 11.3).
Various methods are used to relate clouds to the resolved humidity, tempera-
ture, and wind fields. None is completely satisfactory. In some models the model-
predicted cloud fields are used only in the portion of the model concerned with
