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of modes). Operational spectral models employ a primitive equation version of the
spectral transform method described in Section 13.5. In this method the values of all
meteorological fields are available in both spectral and grid point domains at each
time step. Vorticity and divergence are employed as predictive variables rather than
u and v. Physical computations involving such processes as radiative heating and
cooling, condensation and precipitation, and convective overturning are calculated
in physical space on the grid mesh, whereas differential dynamical quantities such
as pressure gradients and velocity gradients are evaluated exactly in spectral space.
This combination preserves the simplicity of the grid point representation for
physical processes that are “local” in nature, while retaining the superior accuracy
of the spectral method for dynamical calculations.
As of early 2003 the ECMWF deterministic global model employed a series of
spherical harmonics truncated at M
511, where (N, M) are the maximum
retained values of (n, m). This truncation is referred to as a
triangular truncation
(T511) because on a plot of m versus n the retained modes occupy a triangu-
lar area. Another popular spectral truncation is
rhomboidal truncation
, which has
N
=
N
=
=|
|+
M. Both of these truncations are shown schematically in Fig. 13.7. In tri-
angular truncation, the horizontal resolution in the zonal and meridional directions
is nearly equal. In rhomboidal truncation, however, the latitudinal resolution is the
same for every zonal wave number. Rhomboidal truncation has some advantages
for low-resolution models, but at high resolution the triangular truncation appears
m
Fig. 13.7
Regions of wave number space (n, m) in which spectral components are retained for
the rhomboidal truncation (left) and triangular truncation (right). (After Simmons and
Bengtsson, 1984.)
