The Doppler, spaced-antenna and interferometric methods of measuring wind velocities all use the same basic information, the Doppler shifts imposed on backscattered radio waves, but they process it in different ways. The Doppler technique is most commonly used at VHF since the narrow radar beams are readily available. However, the spaced antenna (SA) method has been successfully used with the SOUSY and Adelaide radars. At MF/HF the spaced antenna method is widely used since the large antenna arrays (diameter  1 km) required to generate narrow beams are expensive to construct. Where such arrays of this size are available then the Doppler method has been successfully used (e.g., Adelaide and Brisbane). In principle, the factors which influence the choice of beam pointing angle, the optimum antenna spacing will be the same whether operation is at MF or VHF. Many of the parameters which govern the efficient use of wind measuring systems have been discussed at previous MST workshops. Some of the points raised by these workshops are summarized

Vincent, R. A.

English

NASA Technical Reports Server

3. RELATIONSHIP OF SPACED ANTENNA AND DOPPLER TECHNIQUES 
FOR VELOCITY MEASUREMENTS 
(Keynote Paper) 
R. A. Vincent 
Department 0.f Physics 
University of Adelaide 
Adelaide, South Austra l ia  5001 
The Doppler, spaced-antenna and in terferometr ic  methods of measuring wind 
v e l o c i t i e s  a l l  use the same basic  information"-- the Doppler s h i f t s  imposed on 
backscat tered rad io  waves - but they process i t  i n  d i f f e r e n t  ways. The Doppler 
technique i s  most commonly used a t  VHF s ince  the narrow radar bems  a r e  r ead i ly  
avai lable .  However, the spaced antenna (SA) method has been successfully used 
wi th  the SOUSY and Adelaide radars.  A t  MF/HF the  spaced antenna method i s  
widely used since the l a rge  antenna arrays  (diameter > 1 km) required 20 gener- 
a t e  narrow beams a r e  expensive t o  construct .  Where such arrays  of t h i s  s i z e  
a r e  ava i l ab le  then the  Doppler method has been successfully used (e.g. Adelaide 
and Brisbane). I n  pr inciple ,  the  f a c t o r s  which influence the choice of bean 
pointing angle,  the optimum antenna spacing w i l l  be the same whether opera- 
t i o n  i s  a t  MP o r  VW. 
Many of the parameters which govern the  e f f i c i e n t  use of wind measuring 
systems have been discussed a t  previous MST workshops (e.g. ROTTGER, 1983; 
STBBUCII, 1983; HOCKING, 1983; FARLEY, 1983). I n  the following some of the 
points  r a i s e d  by these workers and o the r s  a r e  summarized. 
SPACED ANTmNA TECHNIQUES 
The SA method uses 3 or more antennas t o  sample the moving d i f f r a c t i o n  
pa t t e rn  produced by backscatter from a given range from the atmosphere. The 
pa t t e rn  can be decomposed i n t o  Fourier components which a re  formed by in te r -  
ference between s igna l s  sca t t e red  a t  complementary angles t o  the zeni th  (Figure 
1). The d i f f e r e n t i a l  Doppler s h i f t s  induced by the hor izonta l  ve loc i ty  u, 
cauee the  pa t t e rn  t o  move with veloci ty  2u (BRIGGS, 1980). 
Usually only 3 antennas a r e  used, arranged i n  the form of an e q u i l a t e r a l  
t r i a n g l e  s ince  the symmetry i s  l e s s  l ike ly  t o  introduce a b i a s  i n  determining 
the  veloci ty .  The auto- and cross-correlation functions of the s igna l s  a r e  
computed (Figure 2)  i n  order t o  determine the pa t t e rn  veloci ty .  The th ree  time 
delays o t  the  maxima of the cross  co r re la t ion  functions between the th ree  p a i r s  
of spaced antennas give  the apparent veloci ty .  This i s  an overestimate of the 
a c t u a l  ( t rue )  veloci ty  since random motions e tc .  w i l l  cause the pa t t e rn  t o  
change a s  i t  moves. The so-called f u l l  correct ion analys is  (FCA) i s  used t o  
correct  f o r  these changes a s  wel l  as  f o r  the anisometry of the pattern.  The 
FCA makes use of such information a s  the lag  a t  which the autocorre la t ion 
funct ion i s  the  same as  the instaneous cor re la t ion  between 2 spaced antennas. 
Obviously, i f  the antennas a r e  too c losely  spaced then the e r r o r s  become 
l a rge  and experimentally it i s  found t h a t  the corrected ('true') veloci ty  i s  
too smell. On the other  hand i f  the spacing i s  too l a rge  then random changes 
i n  the  pa t t e rn  can dominate over the t r ans la t iona l  e f f e c t s  (e.g. ROYRVIK, 1983) 
and the co r re la t ion  values a r e  so small t h a t  the analys is  breaks down. On 
pragmatic and experimental grounds it i s  found t h a t  the optimum spacing i s  where 
the  average zero lag  cor re la t ion  i s  about 0.5. 
https://ntrs.nasa.gov/search.jsp?R=19850024175 2020-03-20T18:08:02+00:00Z
0RIG;NAL FL:G, ' 
OF PO02  QUALITY 
Figure 1. Two-dimensional radar  s i t u a t i o n  
with a uniform wind u i n  the  x d i rec t ion  
h t e r  BRIGGS, 1980). 
0 T 
Figure 2. The cross- and autocorre la t ion 
-- functxons of the s igna l s  from two antennas 
? ( o , o , r )  separated along the x d i rec t ion  by a 
d is tance C .  a<, 0,o) 
- - -L. 
I 1  
0 Tx T 
- - 
- 
. . -  
The mean pa t t e rn  s i ze  and hence the dis tance a t  which the mean cor re la t ion  
i s  about 3 . 5 - i s  determined by the  angular d i s t r i b u t i o n  of the backscattered 
-- - - -. 
--. i energy. I n  turn,  t h i s  angular d i s t r i b u t i o n  i s  determined by the  polar pa t t e rn  
of the t ransmit t ing and the receiving antennas a s  well  a s  the angular d is t r ibu-  
t i o n  imposed by the nature of the sca t t e r ing  i r r e g u l a r i t i e s .  It i s  poss ible  t o  
show (BRIGGS and VINCENT, 1973) t h a t  the complex s p a t i a l  co r re la t ion  funct ion 
a s  a funct ion of spacing a ( i n  wavelengths) i s  
where R(s) and T(.s) a r e  the receiver and t r ansmi t t e r  power polar  diagrams, re- 
spect ively ,  and S(s )  i s  the angular d i s t r i b u t i o n  of backscattered power; a l l  
&re evaluated as  a funct-ion of s s ine  where 8 i s  zeni th  angle and c i r c u l a r  
symmetry i s  assumed. J i s  the  zero order Bessel function. 0 
A t  MF/RF, the  antenna polar  diagrams a r e  usually broader than the irregu- 
l a r i t y  angular d i s t r i b u t i o n s  so tha t  i t  i s  usually the l a t t e r  (half  power-half 
widths -eO - 2-20'] which determine .(a). I t  may be expected t h a t  since 0 
va r i e s  a s  a funct ion of height and time tha t  .(a) w i l l  a l so  be va r i ab le  bu? on 
average i t  i s  found t h a t  spacings of the order of 150-200 m ( a  - 1-1.51) a r e  
optimum f o r  r ad io  frequencies near 2 MHz. 
A t  VHF the  antenna polar  diagrams a r e  of the order of a few degrees i n  
width i.e. comparable i n  width t o  the angular spectra of the i r r e g u l a r i t i e s  
(eO - 1-5*). The minimum spacing may be computed f o r  a given R(s) and T(s)  
by assuming i so t rop ic  s c a t t e r  (S(s) - 1). A t  Adelaide, with a t ransmit ter  beam 
having a half  width of BT - 1.6' it i s  found t h a t  t h i s  minimum spacing i s  5h 
(about 30 m a t  a frequency of 50 MHz) but i n  pract ice  i t  i s  found t h a t  a mean 
spacing of about 50 m (a - 9 ~ )  i s  optimum fo r  the troposphere. Incidenta l ly ,  
t h i s  implies a mean e - 2'. 0 
Despite the narrowness of the  angular spect ra  of backscatter from the lower 
mesosphere a t  ME' and from the lower atmosphere a t  VHF, it  i s  found experi- 
mentally t h a t  the SA method gives r e l i a b l e  measurements of the wind veloci ty .  
I n  each case i t  is  found t h a t  the importance of random changes i n  producing 
temporal changes i n  the s igna l s  a r e  small compared with those changes caused by 
movement of the  pattern.  This may not always be t rue  i n  the mesosphere when 
working a t  VHF and with narrow bem antennas. I n  t h i s  case the random motions 
may become dominant leading t o  a breakdown i n  the SA ana lys i s  (ROYRVIK, 1983). 
DOPPLER TECHNIQUES 
It is, i n  pr inciple ,  q u i t e  straightforward t o  measure the v e r t i c a l  wind 
component w by using a v e r t i c a l l y  pointing .beam. The hor izonta l  wind components 
must, however, be estimated by project ing the r a d i a l  veloci ty  vr measured 
along a beau o f f e e t  a t  an aqgle 6 from the  v e r t i c a l ,  onto the hor izonta l  plane. 
STBdUCH (1983) has summarized the f a c t o r s  which determine the optimum value of 
8. 
' Among those f a c t o r s  which favor the  use of a small angle e are: ( a )  t h e  
d e s i r e  t o  make use of the aspect s e n s i t i v i t y  of the s c a t t e r e r s  which gives en- 
hanced power from near the zeni th ;  (bl2the e f f e c t s  of hor izonta l  va r i a t ions  i n  
the  wind f i e l d  a r e  reduced; ( c )  the r e f f e c t  i s  minimized. 
I 
On the  other  hand i f  6 i s  l a rge  then: (d)  e r r o r s  i n  v t r a n s l a t e  i n t o  
smaller e r r o r s  i n  the horizontal  veloci ty ;  ( e )  the e f f e c t s  6f the v e r t i c a l  
ve loc i ty  i s  l e i s  pronounced and (f) t he  influence of the aspect s e n s i t i v i t y  on 
e f f e c t i v e  beam d i rec t ion  i s  l e s s  important i f  0 i s  large.  
- - 
. .. 
Probably , ( f )  . is  the  key factor. .  A s  RQTTGER (1983) emphasizes, the  effec- 
tive bean pointing d i rec t ion  is determined by the product of the beam pa t t e rn  
-- - - .  i and the  angular d i s t r i b u t i o n  of the sca t t e r .  The e f fec t ive  bean zenith angle 
i s  smaller than the physical  angle and the  hor izonta l  ve loc i ty  component i s  
underestimated. This can be a serious problem when using antennas with r e l s -  
t i v e l y  broad beans (OH > 3"). For example, a t  Adelaide with a beam angle of 
6 > 4.5' it i s  found t h a t  the hor izonta l  ve loc i ty  can be up t o  a f ac to r  of H 2 too small when the physical pointing angle i s  12'. I n  pr inciple ,  t h i s  f ac to r  
can be allowed f o r  i f  e0 i s  known (e.g. WHITHIEAD e t  a l .  1983) but t h i s  
probably e n t a i l s  measurements of the sca t t e red  power a t  more than one angle and 
of course e0 w i l l  change with height and time so t h a t  only a s t a t i s t i c a l  
ana lys i s  can be used. Overall ,  Strauch recommends an angle ~f 6 = 15" f o r  W 
s tud ies  of the lower atmosphere. A t  t h i s  angle the s c a t t e r  from i so t rop ic  ir- 
r e g u l a r i t i e s  i s  presumed t o  overcome the anisot ropic  sca t t e r .  
RADAR INTERFEROMETRY 
The radar  interferometer exp lo i t s  the Doppler information inherent i n  
coherent spaced antenna measurements. Cross spec t ra l  ana lys i s  of the s igna l s  
received a t  separated antennas can be used t o  loca te  and t rack i r r e g u l a r i t i e s  
whi le  Doppler so r t ing  can be used t o  d iscr iminate  against  mul t ip le  t a rge t s  -- 
provided they have d i f fe ren t  r ad ia l  v e l o c i t i e s  (FARLEY e t  a l . ,  1981). PFISTER 
(1971) seems t o  have been the  f i r s t  t o  use t h i s  method i n  a study of g rav i ty  
motions i n  the E-region. This method seems t o  have merit  fo r  studying s p a t i a l  
va r i a t ions  i n  the wind f i e l d .  
I n  another va r i a t ion  of t h i s  method, ROTTGER and VINCENT (1978) d i g i t a l l y  
' s teered '  the lobes of an interferometer formed from widely spaced antennas i n  
order t o  study the f i n e  s t ruc tu re  and hor izonta l  t i l t s  of r e f r a c t i v e  index ir- 
regu la r i t i e s .  This method has s ign i f i can t  po ten t i a l  for  correct ing f o r  the 
"ve r t i ca l "  v e l o c i t i e s  induced by these t i l t e d  i r r e g u l a r i t i e s .  
DISCUSSION 
The i n t r i n s i c  e r r o r s  i n  each ve loc i ty  determination by e i t h e r  the Doppler 
or SA methods a r e  determined by such f a c t o r s  a s  the signal-to-noise r a t i o s  and 
the  record lengths.  Expressions have been derived fo r  the rms e r ro r  of a l ine- 
of-sight Doppler ve loc i ty  by, f o r  example, DOVIAK e t  a l .  (1979). The precis ion 
of SA v e l o c i t i e s  has not been a s  r igorously determined but, provided the random 
- changes a r e  small the e r ro r  i s  determined by the  accuracy t o  which Tx' 
(Figure 2 )  can be measured. The f r a c t i o n a l  e r r o r  i s  independent of wind speed 
because the  width i s  narrower f o r  l a r g e r  v e l o c i t i e s  (small lag)  and becomes 
broader a s  the  ve loc i ty  becomes smaller ( l a rge  lag).  For e i t h e r  technique the 
ve loc i ty  measuranents can be improved by averaging the  power spect ra  ( ~ o p p l e r )  
o r  the  unnormalized cross  co r re la t ion  funct ions  (SA). However, t h i s  process 
can only be ca r r i ed  out f o r  durations which a r e  short  compared with the time 
f o r  s ign i f i can t  changes i n  the mean wind. 
Another f ac to r  l imi t ing  the precis ion of horizontal  wind determinations i s  
t h e  "noise1' imposed by unresolved v e r t i c a l  ve loc i t i e s .  Since the Doppler and 
SA methods u t i l i z e  the same information, it may be expected t h a t  they w i l l  be 
a f fec ted  i n  the same way by such fac to r s  a s  s p a t i a l l y  and temporally varying 
v e r t i c a l  ve loc i t i e s .  S ign i f i can t  short-period v e r t i c a l  v e l p c i t i e s  such a s  those 
encountered i n  the mesosphere where nus amplitudes -1-2'ms a r e  poss ible  can 
lead t o  i t i f f i c u l t i e s  i n  es t imat ing the mean zonal wind. BOWHILL (1983) e s t i -  
. . .  . . F t e s . t i i a t .  averaging times of an hour a r e  required f o r  Doppler measurements of " 
u but t h a t  the e f f e c t s  can be minimized by using tilt angles of 10'. ROYRVIK 
(1983) has shown t h a t  the d i f f e r e n t i a l  v e l o c i t i e s  caused by v e r t i c a l  v e l o c i t i e s  
which vary i n  the horizontal  w i l l  be in te rp re ted  as  horizontal  motions by the  
SA method. The importance of t h i s  e f fec t  i s  not ye t  c l ea r  s ince  the SA method 
- - 
i s  not  a s  easy t o  model a s  the Doppler technique. 
.... . 
. .' . . 
I n  smmaary, the  choice of operating p a r m e t e r s  f o r  a given radar w i l l  be 
--- - 
- -  - -  - determined by compromise between a number of opposing factors .  What i s  optimum 
f o r  one height range (e,g. the lower atmosphere) may not be the  most s u i t a b l e  
f o r  another height (e.g. the mesosphere). 
REFEW CES 
BowhiI1, S. A. (1983), Proceedings of Workshop on Technical Aspects of MST 
Radar, Handbook f o r  MAP, Vol. 9, SCOSTEP Secre ta r i a t ,  Dep. Elec. Eng., 
Univ. IL, Urbana, 235. 
Briggs, B. H. (19801, J., 823. 
Briggs, B. H. and R. A. Vincent (19731, Aust. J. Phvs. 
Doviak, R. J., D. S. Zrnic and D. S. Sirmans (19791, m, a, 1522. 
Farley,  D. T., H. M. I e r k i c  and B. G. Fe je r  (1981), J, Geoohvs. Res., 86. 
1467. 
Hocking, W. K. (19831, Proceedings of Workshop on Technical Aspects of MST 
radar ,  Handbook f o r  MAP,Vol 9, SCOSTEP Secre ta r i a t ,  Dep. Elec. Eng., 
Univ. IL, Urbana, 171. 
- P f i s t e r ,  W. (1971), J. Atmos. Terr. Phvs., 32. 999. 
Rottger,  J. (19831, Proceedings of 'Workshop on Technical Aspects of IST Radar, 
Handbook f o r  MAP, Vol. 9, SCOSTEP Secre ta r i a t ,  Dep. Elec. Eng., Univ. 
IL, Urbana, 150. 
Rottger,  J. and R. A. Vincent (19781, ~ e o ~ h ~ s .  Re . Let t . ,  5, 917. 
Royrvik, 0. (1983), Radio Sci., 18, 461. 
Strauch, R. G., Proceedings of Workshop on Technical Aspects of MST Radar, 
Handbook f o r  MAP, Vol. 9, SCOSTEP S e c r e t a r i a t ,  Dep. Elec. Eng., Univ. 
IL,  Urbana, 232. 
Whitehead, J. D., W. R. From, K. L. Jones and P. E. Monro (19831, J. Atmos. 
Terr. Phvs., 45, 345. 
SUMMARY AND RECOWNDATIONS 
OPTIMUM POINTING ANGLE: There a r e  a number of f a c t o r s  which deternine  the  
choice of the  off-zenith point ing angle f o r  Doppler ve loc i ty  measurements. At 
frequencies near 50 MHz the main f ac to r  i s  the  strong aspect  s e n s i t i v i t y  of the 
s c a t t e r i n g  which can cause the e f f e c t i v e  point ing d i r e c t i o n  t o  be smaller  than 
the  physical  bean di rec t ion.  There i s  consensus t h a t  zeni th  pointing angles 
of 10 to 15" a r e  s u i t a b l e  f o r  tropospheric,  s t r a tospher i c  and mesospheric 
s tudies .  At these angles however, s igna l s  received through sidelobes pointing 
near the zen i th  may become s ign i f i can t .  Such s i g n a l s  can be d is t inguished by 
t h e i r  s ignature  i n  the  Doppler spec t ra  and so  t h e i r  contr ibut ion should be re- 
jec ted  by the  use of appropr ia te  algorithms a t  the  ana lys i s  stage.  
OPTIMUM SPACINGS FOR SA MEASUREMENTS: The receiving antennas should be 
separated by dis tances  comparable t o  the mean pa t t e rn  sca le  (i.e., the  separa- 
t i o n  where the  zero-lag co r re l a t ion  i s  0.5 on average. A MF/HF separa t ion of 
about 1.0 to  1.5A have proved sa t i s f ac to ry .  At VHF, the sca le  w i l l  be deter-  
mined i n  genera l  by. the  use of the t ransmit t ing  antenna and the  angular d i s t r i -  
but ion of the  backscattered s ignals .  While it is poss ib le  t o  ca lcu la t e  the  
spacing, the  optimum spacing has t o  be determined experimentally. For a radar  
wi th  a t ransmit t ing  antenna with a 3' bean, a spacing of about 50 m has been 
found t o  be sa t i s f ac to ry .  
. . 
. . 
RECOMMENDATION: Noting t h a t  t h e r e  a r e  some unce r t a in t i e s  associa ted  with the 
v e r t i c a l  v e l o c i t i e s  measured by MST radars  working i n  the lower VHF range where 
specular  r e f l e c t i o n s  a re  important and noting t h a t  f o r  radars  working a t  UHF 
such echoes a r e  not observed, it i s  recommended t h a t  comparative s tudies  of 
v e r t i c a l  v e l o c i t i e s  be made as soon as poss ib le  with co-located VHF and UHF 
- - - r ada r s  and other  s u i t a b l e  techniques such as  l i d a r .  Where p rac t i cab le ,  i n t e r -  
ferometr ic  techniques should be used t o  remove the e f f e c t s  of any t i l t s  i n  
- A -- t h e  specularly r e f l e c t i n g  surfaces.  
RECOMMENDATION: I t  i s  noted t h a t  the aspect  s e n s i t i v i t y  a t  zeni th  angles 
smaller  than 10 - 15' causes the  e f fec t ive  antenna pointing d i r e c t i o n  t o  be 
c lose r  t o  the zeni th  than the physical  point ing-di rec t ion.  This e f f e c t  w i l l  be 
most important fo r  wide beans and w i l l  g ive  e r r o r s  i n  es t imat ing the hor izonta l  
wind ve loc i ty .  Inves t iga t ions  t o  ob ta in  es t imates  of the l i k e l y  e r r o r s  and how 
they can be minimized a r e  necessary. 


Relationship of spaced antenna and Doppler techniques for velocity measurements (keynote paper), part 3

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