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Let us consider first the simplest case of equatorial nadir data, 
where Ad'_, = T, Ar, = Ar, = R/2, and the observations are equispaced along 
rm. TIU foi tous then that the Nyquist wavenumber in the k_ direction is Kun = 
I =y1 + c_2. Then the region of allowed spectra (waŸenumbers and 
fPéfuencies),°or the information content, is the rectangle in the transform 
plane with sides parallel to the k_,k axes: [-k_,.k nJXC-k k ul. Wavenumber- 
frequency points outside this región Ire contamifidted by afa of spectra 
within the permitted rectangle. 
Consider the simple harmonic behavior y(A,t) = cos(k_ x) with 
k = (m T = (3,1.05). The true space-time spectrum consist? öf 2 delta 
fünctiofis, each of amplitude 1/2, located at k = +k_. "V, derived from 30 
days of equatorial nadir data, corresponding to NiñBus-7 sampling (v_ = 13.8 
orbits/day), is shown in Fig. 5. Calculated spectra within the perm? tted 
rectangle (heavy border) are "exact to machine precision." An array of 
aliases separated 2k_, units along k, and 2k,, units along k_, can also be 
seen. Because of tni! spacing betweàn alias68, it is clear that no component 
within the rectangle will contaminate another. 
Re (¥ (contour increment =0.20) Im!V (contour increment =0.20) 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
bi n ef TT 
5 = E] Il] = a) 9 14 H il I | 
H4. kl a 
12H / "rr | 12 / I Hi i 
el Lb HTH or NT H 
er MITA + = &r LT HH AA. / - 
of ||] [HE HR s HA | 
4 P a ud 
Ar TH aft TH 
2 HEED u - . 2. -HA-. FMH 44.279) | |j 
oc OFF 4 41 - L- k e. 0 HELL HL p miofef. [- 
-2.- k] sl > FTT m -2 | TT + ] T1 
ei | HE LTT PST 
TTA / A" M in in -4. E SAL | k d 
-6. | Bam SAL d -6 pb PTT LÀ | i 
-8. : 4- | THA “| -&.L "TL HE 
-40. LET |. |. I | d -0 ) ~~] ri 
-12.- HI pon] Hu TT t= : Pr HH / "1 
2 
Hl A RHENO] IE TERR | 
Ts 1 B i 7 -4.- | | TH 
| I 
  
  
  
  
  
  
  
16. i 
i 16. A 
-16 -14 42 -10 -8 -6 -4 -2 
0246810102416 716 44 42 -10 8 -6 4-2 0 2 4 6 8 1012 14 I6 
m 
m 
Fig. 5 Space-time spectrum Y computed on integer wavenumbers m for simple harmonic input y » cos(m À + 0 t), 
sampled asynoptically at v_ = 13.8 orbits/day over the interval T = 30 days. Hermitian image and? 
ite aliases also appear. Also shown on (b): the spectral component (m, 0) = (4, 2.75) and its first 
alias (m, 0) = (10, 0.) (c.f., Fig. 8). 
Let us now return to the more general case, where the asynoptic 
data are not equispaced along r. It can be shown in this case (Salby, 1982a) 
that the aliases are no longer separated by 2v1 * c ? units, as before, but 
rather they appear everw/l * c 7 The space-time spectrum calculated for 
the same input as Fig. 5 but für sampling with a 30?-limb scanner at -50? 
latitude, where the traversal separation AA',, = 140°, is shown in Fig. 6. 
By comparison with Fig. 5, the additional alf9ses, introduced by the irregular 
sampling along r, can be seen. In particular, an alias now resides within 
the rectangle defined by |k.| </1 + c 7 . The size of this alias is roughly 
:50% of the true value: it i5 not neglfgible. 
The relative magnitude of the additional contamination increases 
with decreasing traversal separation. Figure 7 shows the traversal separation 
and relative alias for both nadir and 30?-limb sampling for Nimbus-7, as 
functions of latitude. Both are characterized by rapidly increasing con- 
tamination at middle and high latitudes, approaching 1002 relative alias 
where ascending and descending nodes converge (AA > 0). 
161 
€ KE ME A ES Er Srna 022