solution 
e 
ing and 
latitudes 
that 
f the 
s are 
eS 
à 
Ib for 
os, the 
  
  
1.1) 
1:2) 
2.1) 
nd 
orbital 
2.2) 
Similarly, coordinates of the descending nodes are given by 
^aj = Aaj + A d (3.1) 
dj = taj * At d" 
t (3.2) 
where AA d and At., are the longitudinal and temporal separation between 
ascending and des&Énding nodes, both functions of latitude and tending to 
zero near the orbital extremeties where ascending and descending nodes 
converge. 
Coordinates of the ascending and descending nodes, (1) and (3), 
describe lines in the longitude-time plane, inclined an angle -o relative to 
the A axis, where 
a = tan”! qu (4) 
(Fig.2). Note, although contiguous observations along either ascending or 
descending locus are equispaced, separations between ascending ^ descending 
locus vs descending + ascending locus differ (Fig. 2) 
SAMPLE POINTS 
9 Ascending 
O Descending 
te 
DO Twice-Doily 
0000098 Synoptic 
  
    
  
[7e > 
I3 Donopnnoouolil 
3609 
Covered Aag 
T rr ee at te EE 
AX od 
Fig. 2 Sampling pattern of observations on a latitude circle in the Longitude- 
time plane. The latitude circle is completely sampled by combined 
(ascending + descending) data in 1/2 day. Note ascending and descending 
trajectories are not equidistant. Twice-daily, synoptic sampling 
pattern also shown. 
  
  
  
  
  
3. Space-time Spectra 
Consider the evolving field y(A,t) over the sample period [-T/2, 
T/2]. From the Fourier theorem, it follows that y may be expressed as the 
double Fourier series 
157