SYNOPTIC FIELD RETRIEVAL FROM 
ASYNOPTIC SATELLITE OBSERVATIONS 
MURRY L. SALBY 
Geophysical Fluid Dynamics Program 
Princeton University 
P.0. Box 308 
Princeton, New Jersey 08540 USA 
ABSTRACT 
A "one-to-one" correspondence between alias-free asynoptic data 
and twice-daily synoptic maps is established in the Synoptic Retrieval 
Theorem. 
Fast Fourier Synoptic Mapping (FFSM), a Fast Fourier transform 
scheme, is prescribed for retrieving the "unique" sequence of synoptic maps 
from alias-free, combined asynoptic observations. Twice-daily synoptic 
sequences retrieved in this fashion contain exactly the correct spectral 
contribution resolvable in both types of data. The information content of 
the combined data is fully utilized. Synoptic evolutions are retrieved 
equally well for both statistically stationary at nonstationary processes. 
Availability of global spectra during the retrieval process facilitates the 
expansion of fields in arbitrary sets of spherical functions. In particular, 
the projection of remotely derived geopotential fields onto Hough harmonics 
promotes the construction of "global" wind fields, avoiding geostrophic 
singularity at the equator. 
  
]. Introduction 
As discussed in a preceding paper (Salby, 1982c), a fundamental 
aspect of analyzing meteorological satellite data is the reconstruction of 
observed fields in an Eulerian or synoptic representation. While several 
methods for estimating synoptic behavior from asynoptic observations have 
been proposed, none is free of distortion, ambiguity, or is uniquely related 
to the asynoptic measurements and their information content (see for example 
Hartmann, 1976; Chapman and McGregor, 1978; Rodgers, 1976, 1977). These 
techniques range in sophistication from binning daily observations, by 
presuming simultaneity over a day's cycle, to statistical estimation of the 
synoptic behavior. 
  
It has been shown (Salby, 1982c) that the region, in wavenumber- 
frequency space, permitted by combined asynoptic observations, i.e. the 
information content, is analogous to that of twice-daily, synoptic sampling 
with the number of nodes approximately equal to the number of orbits/day. 
The principal difference between regions of spectra allowed by synoptic and 
asynoptic sampling is a rotation relative to the wavenumber-frequency axes, 
the latter introduced by the nonconcurrent nature of asynoptic observations. 
This rather close correspondence between the information content of synoptic 
and asynoptic data will be used here to 1.) establish a unique relationship 
between alias-free, asynoptic measurements and the true synoptic evolution, 
and 2.) retrieve the unique sequence of synoptic charts from alias-free 
asynoptic observations. The prescription for retrieving the synoptic 
structure and evolution is termed Fast Fourier Synoptic Mapping (FFSM). 
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