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on ! SAMPLING THEORY FOR ASYNOPTIC 
| SATELLITE OBSERVATIONS 
MURRY L. SALBY 
emic Geophysical Fluid Dynamics Program 
Princeton University 
P.0. Box 308 
for Princeton, New Jersey 08540 USA 
ABSTRACT 
art I: 
J The information content of asynoptic satellite data is determined. 
Orbital sampling patterns are shown to uniquely define the space-time spectrum. 
The allowed region of spectra, defining the information content, is a rectangle 
rt II: . in Fourier space, rotated relative to the wavenumber frequency axes. Aliasing 
limitations for "single-node" data correspond, roughly, to a maximum wavenumber 
of half the orbital frequency (orbits/day) and frequency extrema of + 0.5 Cpd. 
Sampling restrictions for "combined-node" data, are degraded by additional 
yf aliases, which arise from the irregular spacing between ascending and descending 
xcd nodes. This additional contamination, which is serious at middle and high 
latitudes, can be eliminated, thereby allowing resolution of frequencies up 
to + 1.0 cpd. Otherwise, frequencies only up to +0.5 cpd can be faithfully 
recovered, as for the case of single-node data. 
1. Introduction 
Fundamental to the analysis of meteorological satellite data is the 
reconstruction of observed fields in an Eulerian representation. The Fourier 
analogue of this process is the construction of space-time spectra in the 
wavenumber-frequency domain. In either case, knowledge of which space and 
time scales can legitimately be resolved in the data is crucial. The latter 
is equivalent to the information content and is determined by the discrete : 
sampling pattern in space and time. 
  
  
Ideally, synoptic (simultaneous) measurements at uniform increments 
in time are desirable, as they are directly amenable to analysis. Unfortu- 
nately, the reality of a single instrument makes synoptic observation 
impossible. In its place is asynoptic observation: measurements taken at a 
single location at any given time. The asynoptic nature of satellite data 
has historically posed difficulty in its interpretation. Moreover, because 
of the nonconcurrent and irregular character of satellite observations, their 
information content has hitherto eluded definition. 
Asynoptic observations are made sequentially on a latitude circle, 
covering 2m rads every 24 hr. During this sampling cycle, the fields may 
evolve freely. A number of methods have been proposed to estimate the 
synoptic behavior, or equivalently the space-time spectrum. However, because 
of the lack of simultaneity in the observations, all of the techniques put 
forth to date suffer from some degree of distortion and ambiguity (see 
Hartmann, 1976; Hayashi, 1978; Chapman et al., 1974). 
In addition to their nonconcurrent character, ascending and de- 
scending nodes are not equispaced, nor even coincide from day to day. When 
the number of orbits/day is noninteger, as is invariably the case, the sample 
set does not return to the same set of longitudes as on the previous day. 
Rather, the sample points drift from day to day around the latitude circle, 
never coinciding with a previous set. After a sufficiently long period, a 
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