S LR m 
  
b) 
L I EU TL 
  
Id LL AI 
  
  
  
  
  
  
  
2 14 16 
are 
pear 
m s 0). 
o*^ fo 
It is 
latitude 
ra to 
is 
hat of 
ed from 
  
(b) | 
09 10 
try in 
Ling. 
wards 
elimi- 
explicit 
y (1982a) 
optic 
space- 
relates 
Bo. 
  
E au 
à a NO E RN 
a discrete data string to its Fourier transform (Bath, 1974). When this 
procedure is implemented, and most likely, only if this is done, the Nyquist 
wavenumber can be extended to k N xi tc ? , and the full information 
content of the combined data recovered. 
5, Discussion and Conclusions 
The rectangle defining the information content, [-k_,,k i SIE 
with k,,, given by (10) and k,,, 3/1 * c. ^ , is analogous to thal of twice. 
daily, Synoptic sampling on Euispaced longitudes equal, in number, to approxi- 
mately the number of orbits/day. This is easily seen if one notes that 
k N € y /2 , and k, Z 2m. Rotation of the rectangle by the angle o so that 
it'coin£ides with tlle wavenumber (k.) frequency (k,) axes, indicates a maximum 
wavenumber of approximately v _/2 and maximum frequéncies of + 2m rads/day or 
+ 1.0 cpd. Since the angle a is shallow, these values correspond, roughly, 
to the actual sampling limitations. 
We now return to the questions of zonal resolution, broached 
previously. From these results it is clear that higher wavenumbers (small- 
scale features), that are slowly evolving, are not legitimately resolvable in 
asynoptic data. Lack of simultaneity and the discrete character of the 
observations make such components indistinguishable from lower wavenumbers 
which are evolving. As an example, consider the stationary wavenumber 10 
component: (m,o) = (10,0.). This component aliases to, among others, (m,o) = 
(4,2.75) (see Fig. 5). Behavior of each of these components is shown in 
Fig. 8 as observed from the reference frame of the satellite, i.e. along s. 
Although the continuous evolutions are distinct, dicretely sampled values, 
separated As, are "indistinguishable." As for the latitudes where ascending 
and descending nodes coincide, zonal resolution there is no different than 
elsewhere. Because the observations are not made concurrently, they correspond 
to distinct pieces of information. 
  
16 
14 = 
12 r 
10 
08 
06 
04 
0.2 
00 
-02 
-04 
-06 
-08 
-10 
mi? 
-l4 
-16 
—— (m, o) * (IO, O) 
—-—7(mso,*(4,275) | 
* Discrete Observations 
Cos(msA* ot) 
     
|: T4 340 34 013.4 01-1 
IT -T-T | T I 
  
  
  
Fig. 8 Continuous evolution of the alias pair shown in Fig. 5b, as observed 
from the reference frame of the satellite. Discrete versions, 
sampled every Ne, are indistinguishable. 
er M