Just some more clarification to James' explanation:
So-called spectral models, both as numerical weather forecast models
and as the atmospheric part of climate models with full dynamics, are
spectral _in space_. They use something like Fourier expansion
(actually spherical harmonic transformation, of which the
transformation in the east-west direction is just Fourier expansion) in
space. Variables are given in the wavenumber domain rather than in the
spatial domain. They are not spectral _in time_. Variables are given
in the time domain rather than in the frequency domain.
On the other hand, there are other types of climate models which are
spectral in time. In those models, it is assumed that everything is
periodic in time. If the base period of a model is one year, only such
phenomena that have a period of 1 year, 1/2 year, 1/3 year ... can
happen in the world of the model. It is impractical to implement full
atmospheric (or oceanic) dynamics this way. Models with simpler
dynamics (less real-like-ness) can be built this way, and sometimes
used either in theoretical studies or obtaining empirical parameters
(such as effective thermal inertia) by fitting to observational data.
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