Scattering of radio waves from atmospheric refractive-index irregularities induced by turbulence was invoked almost four decades ago to explain the characteristics of signals received on VHF/UHF ionospheric and tropospheric forward-scatter links. Due to the bistatic geometry of these links a slender, horizontally extended, common volume or cell is formed in space. The principal contribution to scattering arises from refractive-index fluctuations in this volume at the Bragg wave number K approx. sub B = K approx. sub i -k approx. sub s vectors. It has been surmised that the use of more than one frequency in probing the middle-atmosphere regions should help resolve several issues pertaining to the scattering mechanism. These issues are briefly re-examined in this note. The implications of the radar equation are discussed. The problems arising due to layered structure of turbulence and the choice of frequencies most suitable for multifrequency measurements are considered

Mathews, J. D.

Rastogi, P. K.

English

NASA Technical Reports Server

2.6B USEFUWESS OF MILTIFREQUENCY S T  RADAR MEASUREKENTS 
" P. K. Rastogi and 3. D. Mathews 
Department of Electr ical  Engineering and Applied Physics 
Case Western Reserve University 
Cleveland, CB 44106 
Scat ter ing of radio waves from atmospheric refractive-index i r r egu l a r i t i e s  
induced by turbulence was invoked almost four decades ago t o  explain the 
character is t ics  of signals received on V E F / W F  ionospheric and tropospheric 
forward-scatter l inks (WIESNEB, 1960). Due t o  the b i s t a t i c  geauetry of these 
l inks a slender, horizontally extended, common volume or c e l l  is  formed i n  
space. The principal contribution t o  scattering a r i ses  from refractive-index 
f luctuat ions i n  t h i s  volume a t  the Bragg wave number $ = 8 .  - &c 
corresponding t o  the difference of the incident and scattered wave propagation 
vectors. The length scale corresponding t o  the Bragg wave number is  2r/% = 
X/(Z sin€i/2), where 6 i s  the angle between 5. and g . For backscatter, 
6 = 180' and the Bragg wave number corresponhs t o  t f e  length scale 1/2A for  a 
radio wavelength X (BOOKER and GORDON, 1950; BOOKER, 1956). 
Since the early days of scat terpropagat ion research, it has been real ized 
tha t  multifrequency measutements of fe r  the .possibi l i ty  of monitoring the 
spectrum of ref r ac t i ve index  fluctuations a t  several d i s t inc t  Bragg wave numbers 
(WIESNER, 1960; BLAIR e t  al., 1961; BOLGIANO, 1963). A quanti ta t ive i n t e r  
pretat ion of such measurements has led t o  a c r i t i c a l  reexamination of the ro le  
of turbulence i n  producing these fluctuations (BOLGIANO, 1958; BULCIANO, 1960; 
WEEELON, 1959,1960; HILL and BOWAILL, 1976). I 
In  recent years, multiplefrequency MST radar capabi l i t ies  have become 
available a t  eeveral s i t e s  around the world a t  frequencies ranging from EF, 
through VHF to  UHF. It has been surmised that  the use of more than one 
frequency i n  probing the middle-atmosphere regions should help resolve several 
issues pertaining t o  the scat ter ing mechanism (LIB, 1983). These issues a re  
briefly re-examined i n  t h i s  note. The implications of the radar equation a r e  
diecussed i n  the next section. The two following sections consider the problems 
a r i s ing  due t o  layered s t ructure of turbulence and the choice of frequencies 
most sui table  for  multifrequency measurements, respectively. 
IMPLICATIONS OF THE RADAR EQUATION FOR MULTIFREQUENCY HEASUREHENTS 
The radar equation for  a uniform random medium with refractive-index 
f luctuat ions n re la tes  the received signal power (PSI t o  the transmitted 
power ( P ~ ) ,  the antenna parameters (e.g., i t s  physical aperture A), range 
(R), range resolution (AR), and a radar re f lec t iv i ty  (n) for the medim. For 
narrow-bean monostatic radars, the radar equation can be written i n  several 
different  forms. & simple form following ROTl'GER (1980) i s  
where the factor L accounts for  the system losses. The re f lec t iv i ty  n for a 
homogeneous, isotropic  f i e l d  of f luctuations i s  obtained as  
https://ntrs.nasa.gov/search.jsp?R=19850024174 2020-03-20T18:07:49+00:00Z
where q! ( s )  i s  the three-dimensional spectrum of refractive-index 
f luc tua f ions ,  evaluated over a spherical  s h e l l  of radius i n  phase space. 
For small-scale f luc tua t ions  i n  the i n e r t i a l  range or2beyond, On (k) i s  
r e l a t e d  t o  the r e f r a c t i v e  index s t ruc tu re  constant Cn 
rl = 0.033 Cn 2 k-11/3 exp [-k2/ k: 1 
with km = 5.91/\, and the  inner sca le  of turbulence. These r e s u l t s  
have.been discussed by I~HIMAI(U (19781, and TATARSKII (1971). 
Several conditions a r e  e s s e n t i a l  fo r  obtaining equations (1) and (2). It 
i s  assumed t h a t  the radar  c e l l  l i e s  i n  the f a r  f i e l d  of the antenna. Refractive 
index (and o the r )  f luc tua t ions  i n  the medium must be homogeneous and i so t rop ic ,  
and the medium is assumed t o  en t i r e ly  f i l l  the  beam and the radar  c e l l .  Single 
s c a t t e r i n g  and quasi -s ta t ic  approximations must a l s o  hold. The numerical 
coe f f i c i en t  i n  equation (1) depends on the  antenna rad ia t ion  pat tern ,  and AR i s  
a rectangular  approximation t o  the convolution of the pulso shape with receiver- 
system impulse response. 
A s t rong motivation f o r  multifrequency experiments i s  the  p o s s i b i l i t y  of 
measuring the  form of the spectrum @ (k) a t  several  Bragg wave numbers 
through s igna l  power measurements. f t  should be emphasized t h a t  such measure- 
ments r equ i re  absolute  radar ca l ib ra t ion  f o r  each frequency. The current 
approaches and problems i n  such ca l ib ra t ions  were b r i e f ly  discussed a t  the 
p r w i o u s  workshop (BOWILL, 1983). 
CONSEQUENCES OF LAYERED TURBULm CE STRUCTURES 
The assumptions of homogeneity and isotropy of ref ractive-index 
f luc tua t ions ,  and t h a t  they f i l l  the radar  beam and the radar c e l l ,  a r e  most . 
. r ead i ly  v io la ted  i n  the presence of turbulent  layers.  These layers  have indeed 
been observed throughout the middle atmosphere (WOODMAN and RASTOGI, 1984; 
- 
, ROTTGER e t  a l . ,  1979). 
The f i r s t  consequence of layered turbulence i s  t h a t  the re  i s  a range of 
-- _ _ _  - _ -  wave numbers i n  the v i c i n i t y  of t h a t  contr ibute  t o  scat ter ing.  This range 
A k g  depends inversely on the  layer  thickness LT (RASTOGI and BOWHILL, 1976) 
A k g  % $ ( 4 )  
This produces a smearing of the underlying spectrum i n  the v i c i n i t y  of k . 
The extent  of t h i s  smearing depends on the d i s t r i b u t i o n  of refractive-in8ex 
variance i n  the layer ,  and can be q u i t e  ser ious  fo r  a normal layer thickness of 
100 m (Figure 1 ) .  
The second consequence of layered turbulence i s  due t o  quasi-specular or 
d i f fused r e f l e c t i o n s  t h a t  a r e  produced from the edges of these layers.  HOCKING 
and ROTTGEE (1983) have considered modifications t o  the radar  equation due t o  
t h i s  ef fect .  
To minimize the e f fec t  of layered turbulence i n  multifrequency experiments 
i t  i s  important t o  keep the  common volume fixed. This requires  t h a t  the 
antennas be scaled with frequency t o  give the  same beam widths, and i n  addit ion,  
the  pulse shape, receiver  system impulse response and range delays be kept 
i d e n t i c a l  fo r  a l l  frequencies. 
I ~ower law s~ectrum 
'53 
Wavenunber k 
Figure 1. Two poss ible  d i s t r i b u t i o n s  ( a )  and 
(b) of r e f r a c t i v e i n d e x  variance across a 
t h i n  layer.  The arrow shows the idea l  Bragg 
f i l t e r  a t  wave number b;B fo r  an i n f i n i t e  
s c a t t e r i n g  volume. The shapes label led  ( a )  
and (b) show the Bragg f i l t e r s  corresponding 
t o  the d i s t r i b u t i o n s  above. The power law 
spectrum i s  only a p laus ib le  form fo r  Q n(k). 
The range of frequencies current ly  ava i l ab le  f o r  MST radars  i s  -3 MHz t o ,  
we l l  above 1 GHz. Only the HF and lower VHF radars  a r e  sens i t ive  t o  turbulent 
f luc tua t ions  i n  the  mesosphere. Sensi t ive  UfIF r ada r s  can be used t o  probe the 
D-region ionizat ion (MATHEWS, 1984). The widest  choice of frequencies is 
ava i l ab le  a t  EISCAT and Arecibo. 
Figure 2 shows schematically the  Bragg length scales  associa ted with 
several  radars. Also shown i n  t h i s  f i g u r e  a r e  the energy spectra  associated 
with strong and weak turbuleilce i n  the  troposphere and mesosphere. The form of 
these spect ra  a r e  q u a l i t a t i v e  and no d i s t i n c t i o n  i s  made between energy spectra  
and the  spect ra  of refractive-index f luctuations.  
In  the  mesosphere, the  Bragg length sca le  fo r  VHF radars  i s  comparable t o  
the  inner s c a l e  of turbulence. For t h i s  reason two VHF r ada r s  with a frequency 
spacing of a few MHz can provide useful information about the  spectra associa ted 
with small-scale turbulence. The use of a UHF radar  i n  addi t ion can provide 
information about D region electron-densit ies and t h e i r  gradients  t h a t  i s  v i t a l  
f o r  in te rp re t ing  the  behavior of VHF returns.  . 
1 HF ' PARIAL REF. 3 )Hz 
2 MfF tST 50 Mz 
3 YHF EISUT 224 Hlz 
4 UIF ARECIBO 430 Htz 
5 UIF EISUT . 933 !Hz 
6 5-BAN0 ARECIBO 2380 Mz 
0.01 0.1 1 .o 10.0 100.0 
. Tl~L%El!CE AHD BRAG SCALES (meter) 
Figure  2. Bragg length sca les  (X/2) f o r  s i x  backscat ter  radars a re  shown by t h e  
arrows. Tropospheric and mesospheric spect ra  f o r  strong and weak (by 10,000 
t imes) turbulence have been superimposed. The form of these spect ra  a r e  . 
q u a l i t a t i v e  and no d i s t i n c t i o n  i s  made between energy spectra  and spectra  of 
r e f r a c t i v i t y  f luctuat ions .  Dots show a length sca le  t h a t  i s  5 x the  wave- 
length associated with the turbulence inner  scale. A t  smaller length scales ,  
the  iner t ia l - range form i s  invalid.  A t  Bragg scales  &50 m. anisotropy + 
e f f e c t s  become s ignif icant .  
- - - 
RF r ada r s  usually lack a f i n e  a l t i t u d e  reso lu t ion  ( typ ica l ly  3 km or  
worse). The X- and 0-mode re tu rns  suffer ,  however, d i f f e ren t  a t tenuat ions  and 
. t h e i r  corresponding propagation vectors  kx and ko become s ign i f i can t ly  
.- ....- .- -. A,. d i f f e r e n t  i n  the upper D region. For t h i s  reason, a range-time cross- 
c o r r e l a t i o n  ana lys i s  of several  closely spaced HF frequencies w i l l  complement 
the  conventional partial-ref l e c t i o n  experiments (RASTOGI and HOLT, 1981 ) . 
In the  v i c i n i t y  of the tropopause , t he  turbulence inner sca le  is  jus t  a few 
centimeters. Two widely separated frequencies (e.g., 224 MHz and 933.5 MHz fo r  
the  EISCAT radars)  o f f e r  the p o s s i b i l i t y  of detect ing l a rge  va r i a t ions  i n  the 
i n t e n s i t y  of turbulence through t h e i r  e f fec t  on the inner scale.  
In  some cases, especia l ly  with VHF radars ,  it may be possible,  even 
advantageous, t o  use two r a t h e r  closely spaced frequencies. This would allow 
the  use of the  same radar a t  two frequencies with only a s l i g h t  degradation i n  
performance . 
A care fu l  reexamination of the frequency dependence of the turbulence and 
r e f r a c t i v e i n d e x  spectra,  and of sca t t e r ing  from t h i n  turbulent  l aye r s  i s  
e s s e n t i a l  fo r  in te rp re ta t ion  of multifrequency measuranents. 
REFERa CES 
Blair .  J. C., R. M. Davis and R. C. Kirby '(1961), Frequency dependence of D- 
region sca t t e r ing  a t  WF, J. Res. NBS, m, 417-425. 
Bolgiano, R. (19581, The r o l e  of turbulent mixing i n  s c a t t e r  propagation. 
IRE Trans., e, 161-168. 
Bolgiano, R. (1960), A theory of wavelength dependence i n  u l t rahigh frequency 
transhorizon propagation based on meteorological considerations,  J. Res. 
m, m, 231-237. 
Bolgiano, R. (19631, The r o l e  of radio  wave sca t t e r ing  i n  the  study of 
atmospheric microstructure.  Electromagnetic Scattering,, ed. M. Kerker . 
MacMillan Co., 261-267. 
' Booker. H. G. (19561, A theory of sca t t e r ing  by nonisotropic i r r e g u l a r i t i e s  
with appl ica t ion t o  radar  r e f l e c t i o n s  from the aurora. J. Atmos. Terr. 
PhvsL, .& 204-221. 
Booker. H. G. and W. E. Gordon (1950). A theory of radio sca t t e r ing  i n  the  
tropospherre. Broc. IRE, 38, 410-412. 
- 
Bowhill. S. A. (19831, Design considerations f o r  MST radar  antenuas. Bandbook 
f o r  MAP, Vol. 2, S. A. Bowhill and B. Edwards (eds.), 447-455. 
H i l l ,  R. J. and S. A. Bowhill (19761, Small-scale f luc tua t ions  i n  D-region 
ion iza t ion  due t o  hydrodynamic turbulence. Aeron. Reo. No. 72, Aeron. 
Lab., Dept. Elec. Eng., Univ. Ill., Orbana-Champaign. 
Hocking, W. K. and J. Rottger (19831, Pulse length dependence of radar  s ignal  
s t rengths  f o r  Fresnel backscatter.  Radio Sci,, a, 1312-1324.. 
Ishimsru, A. (1978). Wave Propagation and Sca t t e r inn  i n  Random Media, Academic 
Press, New York, 572. 
Liu, C. 8. (19831, In te rp re ta t ion  of IST radar  r e tu rns  from c l e a r  a i r .  
andbook f o r  MAP, vol. 9, S. A. Bowhill and B. Edwards (eds.), 49-56. 
Matftews, J. D. (19841, The incoherent s c a t t e r  radar as  a t o o l  f o r  studying the  
ionospheric D-region. submitted t o  J. Atmos. Terr. Phys. ' 
Rastogi, P. K. and S, A. Bowhill (19761, Scat ter ing of radio  waves from the 
mesosphere - 2. Evidence f o r  intermit  t e n t  mesospheric turbulence. J. Atmos. 
Terr. Phvs,, 28, 449-462. 
Rastoni. P. K. and 0. Holt (1981). On detect ing r e f l e c t i o n s  i n  presence of 
- - - - 
sca t t e r ing  from amplitude s t a t i s t i c s  with a ~ p l i c a t i o n a  t o  ~ - r e ~ i o n  p a r t i a l  
ref  l ec t ions ,  Radio Sci,, &, 1431-1443. I 
Rottger,  J. (19801, Ref lect ion and sca t t e r ing  of VHP radar  s igna l s  from 
atmospheric r e f r a c t i v i t y  s t ructures ,  Radio Sci., u, 259-276. 
Rottger. J, ,  P. K. Rastogi and R. F. Wooden (19791, High reso lu t ion  VFlF rada r  
observations of turbulence s t ructures  i n  the mesosphere. Geovhvs. Res. 
Lett.,  a 617-620. 
Tatarski i .  V. I. (19711, The e f f e c t s  of turbulent  atmosphere on wave 
propagation, Nat. Tech. In f .  Serv., 472 ( t r eas la t ed  from the  Russian). 
Wheelon, A. D. (1959), Radio wave sca t t e r ing  by tropospheric i r r e g u l a r i t i e s ,  
J. Res. NBS, m, 205-233. 
Wheelon, A. D. (19601, Relation of turbulence theory t o  ionospheric forward 
s c a t t e r  propagation experiments, 3. Res. NBS, &D, 301 -309. 
Wiesner. J. B. (19601, Radio transmission by ionospheric & tropospheric 
s c a t t e r  - A repor t  of the  It. Tech. Adv. Corn., Proc. IRE, 48, 4-29. 
Woodman. R. F. and P. K. Rastogi (1984), Evaluation of e f f e c t i v e  eddy d i f fus ive  
coe f f i c i en t s  using radar  observations of turbulence i n  the  stratosphere.  
Geovhvs. Res. Lett.,  u, 243-246. 


Usefulness of multifrequency MST radar measurements, part 2.6B

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server