Re ¥) (contour increment = 0.20) Im V! (contour increment =0.20) a di: 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
    
   
  
  
  
  
  
  
  
  
  
  
  
  
ls. [TF Ir proce 
I4. " TI PT s J | | 
Bb al of TH J | wave 
10. E | TH |] cont: 
& i P | fi 
6. _ sL TLL Fr 5. 
4 L.] | al min 7| 
2F 4 1 
e Q k =] 2+ FT | Lacie k 1 .. 
„EHE | °c Q an + with 
Hf h ! 2| H HH dail, 
- IF- k, |^] * 
4. kon A -4l- ks : 
"SF ; - TTT MM ct Kon I m mate 
-&H: ref U J | K N : 
! ; -&L > 1 HL 3 : 
: ] e | i i$ 
-12.} À cz FTAA NN wavel 
=l4 -I4 Ll 14 = |] Bn || | x 1 ul 
ETE we ot 8 012 14 ze to tl 
14 16 -16-41210-8-6-4 -2 O 2 4 6 8 10 12 14 16 
m 
m 
Fig. 6 As for Fig. 5 but for 300-limb sampling at -50° latitude. In addition to the standard aliases, are prev’ 
other spurious entries resulting from the irregular spacing of the combined data. The latter appear scal 
midway between the standard aliases along ks and are nearly 60% of the principle magnitude at (m, 95)- asyni 
obse! 
The problem of additional contamination is a serious one. It is whicl 
intrinsic to combined asynoptic data, whether assimilated latitude by latitude comp 
or globally (Salby, 1982a). It "may" be handled by restricting spectra to {4,2 
k 1/3/1 * c . Although remedying the difficulty, this approach is Fig. 
uhdersirable, ad it in fact reduces the utility of combined data to that of Alth 
single node data. The information content, thus, is effectively halved from sepa 
that possible. and 
else 
80 Ir TE 7 TT T T T : to d 
\ A 
60 \ 7 L + 
\ eot V (o kot I2) | 
40r 1 1 40 | V (ko, kp) 
wm [ ! 7 “ r \ ; 
$ 20} ! AxaiNodi) 1 Bol Nodir 
= | 4 rua cdm E uU a em Tas Limb 
= 2 7 0 7 
e - / 
E20} ; lE A 
E ; i 720 1 
< L / ] < | 
-40 + 7 7 -40 M 7 
-60$ :#f 7 -60 Les, + 
(a) | (b) 4 
-B80 deed ded diea À. À À À. À -80 À À À 1 À À À À 
60 100 140 180 220 260 300 O OI O2 O3 O4 O5 O6 O7 O8 O9 IO 
TRAVERSAL SEPARATION (degrees) RELATIVE MAGNITUDE OF ALIASES 
7 a) Instantaneous separation between ascending and descending traversals. There is inherent symmetry in 
nadir sampling with AX'., = 180° at the equator. No such symmetry exists, in general for limb sampling. 
Both cases contain a sfdrp departure from 180° as the poles are approached. b) Relative magnitude of 
additional aliasing resulting from the irregular sampling. Both cases exhibit a steep increase towards 
the poles. 
Fig. 
It turns out that the additional aliasing can be completely elimi- 
nated by replacing that part of the space-time transform along k_, by explicit 
evaluation of the Fourier components. The reader is referred to Salby (1982a) 
for the details. Formulae given in Salby (1982a) constitute the Asynoptic 
Sampling Theorem, uniquely relating combined, asynoptic data to their space- 
time spectrum, in the same manner that the Sampling Theorem uniquely relates 
162 
D 
EN 
| 
% 
à 
nn NN LR -— 
= - au