As an example of an unresolvable feature, consider diurnal vari-
ations, for instance in a photochemically active species. The evolution of
such a constituent will contain a number of tidal harmonics, each moving with
zonal wavenumber is c, - 2mm rads/day, or m cpd. Wavenumber 1 contribution
lies precisely on the Nyquist fold. A11 higher wavenumbers lie outside the
region permitted by aliasing.
In addition to guarding against contamination by unresolvable
components, the converse must also be avoided. Resolvable spectra within the
allowed region must not be allowed to project upon their aliases outside it.
From the standpoint of computing space-time spectra, this simply means that
only values within the permitted region of wavenumber-frequency space are
calculated. The situation in determining synoptic fields, however, is more
delicate. Consider a spectral approach where the asynoptic data are expanded
synoptically in a set of wavenumbers and assimilated by integrating forward
in time to derive synoptic charts. The wavenumbers allowed in computation digi
must be restricted in accordance with the aliasing limitations. Similarly, been
albeit implicit, the time integration must be filtered. Otherwise aliases scan
will manifest themselves in the synoptic products. This holds equally for pixe
the additional contamination inherent to combined data. Failure to eliminate orth
this contamination can result in a complete aberration of the true behavior panc
(Salby, 1982b; 1982c). Clearly the aliases should be excluded from model of t
initialization. Since they obey none of the physical laws prescribed in the à ne
model, it is unlikely that their presence would be benign. dise
Acknowledgment | digi
This research was performed while the author was employed at the
National Center for Atmospheric Research, sponsored by the National Science of t
Foundation. and
of a
References fore
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Hayashi, Y., 1980: A method for estimating space-time spectra from polar
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; 4 digi
>» 1982b: Sampling theory for asynoptic satellite observations. Part II: tion
Fast Fourier Synoptic Mapping. Submitted to Uc Aui. Sci. 10 x
. 1982c: Synoptic field reirieval from asynoptic satellite observations.
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Toulouse, France, 1982. S in 1
the
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