Weak reflections from sharp discontinuities in radio refractivity are usually invoked to explain the results of radio propagation experiments. The characteristics of refractivity structures required to produce Fresnel returns are examined and experimental evidence for Fresnel returns in middle-atmosphere radar experiments is reviewed. The consequences of these returns on estimating the turbulence and wind parameters are outlined

Rastogi, P. K.

English

NASA Technical Reports Server

280 
4.5A PARAMETRIZATION OF FRESNEL RETURHS I N  MIDDLE-ATMOSPHERE 
RADAR EWERIMENTS 
P. K. Rastogi 
Haystack Observatory 
Massachusetts I n s t i t u t e  of Technology 
Westford, MA 01866 
ABSTRACT 
Weak r e f l e c t i o n s  from sharp d i scon t inu i t i e s  i n  radio r e f r a c t i v i t y  have been 
invoked over many years t o  explain the r e s u l t s  of radio propagation experiments. 
I n  t h i s  contribution, the cha rac t e r i s t i c s  of r e f r a c t i v i t y  s t ructures  required t o  
produce Fresnel r e tu rns  a r e  f i r s t  examined. 
Fresnel re turns  i n  middle-atmosphere radar experiments i s  then reviewed. The 
consequences of these r e tu rns  on estimating the turbulence and wind parameters 
are b r i e f l y  outlined. 
The experimental evidence fo r  
INTRODUCTION 
The r o l e  of turbulence-induced i r r e g u l a r i t i e s  i n  producing sca t t e r ing  and 
r e f l e c t i o n  of radio waves w a s  f i r s t  considered over two decades ago i n  connec- 
t i o n  with tropospheric and ionospheric forward-scatter experiments. The shape 
of the i r r e g u l a r i t i e s  t h a t  could cause the supposed r e f l ec t ions  was described i n  
terms such as  b l i n i s  (pancakes) or f e u i l l e t s  (sheets or leaves) t o  emphasize 
t h e i r  planar nature. 
a r e  required to  produce the r e f l ec t ions ,  were indeed observed with microwave 
refractometers  ca r r i ed  a l o f t  by balloons t o  heights of several  kilometers. Much 
of the r e l a t ed  work i s  described i n  t ex t s  such as B E W N  and SPIZZICHINO 
(1963) and DU CASTEL (1966). 
weak ”partial-ref lect ions” of 2-3 MHz radio waves from the D-region (GARDNER and 
PAWSEY, 1953). 
Regions of sharp t r ans i t i ons  i n  radio r e f r a c t i v i t y ,  t h a t  
A s imi l a r  mechanism w a s  invoked t o  explain the 
The relevance of such r e f l ec t ions  t o  the middle atmosphere radar experi- 
ments (ROTTGER, 1980; BALSLEY 19811, i n  addi t ion t o  backscatter from the 
turbulence-induced r e f r a c t i v i t y  f luc tua t ions  a t  half  the radar  wavelength 
(BOOKER, 19561, has been emphasized by several  groups i n  recent years (GAGE and 
GREET?, 1978; ROTTGER, 1978; FUKAO et  al.,  1979). The terms t h a t  have been used 
f o r  these r e f l ec t ions  -- p a r t i a l ,  specular,  d i f fuse ,  aspect-sensit ive and 
Fresnel -- tend t o  ascr ibe an underlying physical mechanism t o  explain the re- 
turns.  Thin regions of r e f r a c t i v i t y  gradients t h a t  extend horizontally over a 
a Fresnel zone a r e  c ruc ia l  t o  a l l  these mechanisms. The term “Fresnel r e f l ec -  
t ion” i s  therefore  more appropriate. 
Here, w e  f i r s t  examine those cha rac t e r i s t i c s  of r e f r a c t i v i t y  s t ruc tu res  
t h a t  are e f f ec t ive  i n  producing r e f l ec t ions  as opposed t o  scat ter ing.  Evidence 
f o r  the occurrence of r e f l ec t ions  i n  middle-atmosphere radar experiments i s  re- 
viewed next, and f i na l ly ,  the consequences of such r e f l ec t ions  on in fe r r ing  the 
parameters of turbulence and the wind f i e l d  from radar observations a r e  d i s -  
cussed br ief ly .  
REFLECTIONS FROM REFRACTIVITY STRUCTURES 
The sca t t e r ing  of radio waves from a random f i e l d  of r e f r a c t i v i t y  fluctua- 
t ions,  assumed hopogeneous and i so t rop ic  fo r  s implici ty ,  has been discussed i n  
d e t a i l  by TATARSKII (1971) and ISHIMARU (1978). The sca l e  of r e f r a c t i v i t y  
https://ntrs.nasa.gov/search.jsp?R=19840019055 2020-03-22T09:43:14+00:00Z
281 
t h a t  i s  half  the radar wavelength for  monostatic radars. 
f luctuat ions a r e  produced local ly  by turbulent mixing of r e f r a c t i v i t y  gradients.  
There now i s  ample widence tha t ,  i n  a convectively s t ab le  atmosphere, turbu- 
lence occurs i n  t h i n  layers.  The assumption of homogeneity of turbulence 
throughout the radar c e l l  of ten i s  inva l id  due t o  the presence of such layers. 
Depending on the Bragg scale and the  length scales associated with turbulence, 
the assumption of isotropy of Bragg-scale turbulence may a l s o  be v io l a t ed  within 
t h i n  layers.  Radio waves would be sca t t e red  by r e f r a c t i v i t y  f luc tua t ions  within 
the layers ,  but are l i a b l e  t o  be r e f l ec t ed  by sharp r e f r a c t i v i t y  gradients a t  
the layer interfaces.  
The r e f r a c t i v i t y  
I n  order t h a t  r e f l ec t ions  may be a v i ab le  mechanism for  producing the radar 
re turns ,  the r e f r a c t i v i t y  s t ruc tu res  must s a t i s f y  several  conditions. F i r s t ,  
the surfaces of constant r e f r a c t i v i t y  must be oriented approximately normal t o  
the  Bragg vector ,  and the average d i r ec t ion  of the r e f r a c t i v i t y  gradients a t  
these surfaces must be p a r a l l e l  t o  the Bragg vector.  Second, these surfaces 
must be su f f i c i en t ly  smooth. Final ly ,  they must be horizontally extended t o  
cover a subs t an t i a l  part  of a Fresnel zone. 
Due t o  the horizontal  s t r a t i f i c a t i o n  of the atmosphere, the iso-refracti-  
v i t y  s t ructures  a l s o  are predominantly horizontal  and w i l l  produce r e f l ec t ions  
f o r  v e r t i c a l  Bragg-vector or ientat ions.  For monostatic radars,  the radar must 
be pointed close t o  the v e r t i c a l .  
receiver antenna must be oriented symmetrically about the v e r t i c a l .  
t e r ion  for  smoothness of iso-refract ivi ty  surfaces i s  s t a t ed  by the Rayleigh 
condition, t ha t  a roughness-scale f o r  these surfaces (parametrized e.g., by the  
standard deviation of the surface height above a reference l w e l )  be smaller 
than one-fourth of the Bragg scale  (BECKMANN and SPIZZICHINO, 1963; ISHIMARU, 
1978). For middle-atmosphere applications,  t h i s  roughness-scale should be 
smaller than 0.75m for  VHF and 0.1 m for  UHF radars. For horizontally extended 
i so - re f r ac t iv i ty  surfaces,  the contributions from those p a r t s  of the surface 
t h a t  a r e  i n  a Fresnel zone a r r i v e  i n  phase a t  the receiver  and therefore add 
coherently. 
the diameter of the f i r s t  Fresnel zone exceeds the antenna dimension, and i s  
smaller than the s i z e  of the region i l luminated by the radar beam. 
For b i s t a t i c  radars ,  the transmitter and 
The c r i -  
This i s  i l l u s t r a t e d  schematically i n  Figure 1. I n  the f a r  f i e l d ,  
When the individual layers  of turbulence a r e  not adequately resolved by the 
radar ,  a radar cell  may contain several  r e f l ec t ing  s t ruc tu res  d i s t r ibu ted  along 
the range. 
produce l a rge  amplitude and phase f luctuat ions.  
s a t i s f i e d ,  then the  requirement on the horizontal  s i z e  of the s t ructures  i s  not 
too stringent.  Within a Fresnel zone, the s ignal  power a t t r i b u t a b l e  t o  the 
r e f l ec t ed  component increases approximately as the square of the surface area 
contr ibut ing t o  the ref lect ions.  
uniform. For s t ructures  of larger  s ize ,  contributions over d i f f e ren t  Fresnel 
zones would mutually in t e r f e re .  
The contributions of these s t ructures  can mutually i n t e r f e r e  t o  
I f  the other conditions are 
It i s  not necessary tha t  the s t ructures  be 
It i s  also in s t ruc t ive  t o  consider the r e f l e c t i n g  s t ructures  as antenna. 
These s t ructures  should then produce a d i f f r a c t i o n  pat tern a t  the ground level.  
The s i z e  of t h i s  d i f f r a c t i o n  pat tern depends inversely on the horizontal  s i z e  of 
the r e f l ec t ing  s t ructures .  
provides information on horizontal  motion of the s t ructures  using the  spaced 
antenna d r i f t s  method (ROTTGEB, 1981). 
RADAR EVIDENCE FOR FRESNEL RETURNS 
Three d i f f e ren t  methods have been used t o  discriminate r e f l ec t ions  from 
Movement of "d r i f t "  of t h i s  d i f f r ac t ion  pat tern 
sca t t e r ing  i n  radar  observations of the middle atmosphere - (1) from observa- 
t i ons  of s ignal  power along the v e r t i c a l  and off-ver t ical  direct ions,  (2)  from 
temporal coherence of the r e f l ec t ed  components, and (3) from Observations of the 
282 
(ii) ( iii ) 
Figure 1. A schematic illustration of scattering and reflection from 
refractivity structures in a radar cell (shaded region). w(r) is a 
weighting function along the range. In case (i), signals scattered 
from randomly distributed irregularities (a,b,c..) add incoherently at 
the receiver as shown by the vector diagram at the bottom. In case 
(ii), signals scattered from the different parts (d,e,f..) of a 
horizontally extended surface arrive in phase at the receiver to pro- 
duce a reflected component. In case (iii), irregularities at several 
horizontally extended surfaces (a,b,c..) produce reflections that 
mutually interfere at the receiver (from RASTOGI and HOLT, 1981). 
d i f f r a c t i o n  pat tern a t  the ground with spaced antennas. These methods are sche- 
matically shown i n  Figure 2. 
been made with VHF radars.  
r e f l e c t i o n s  from the troposphere and stratosphere.  This i s  probably because t h e  
roughness scale (0.1 m) required f o r  UHF re f l ec t ions  becomes comparable t o  t h e  
Ko lmogor ov micro scale. 
Almost a l l  the observations of r e f l ec t ions  have 
There i s  y e t  scant empirical evidence f o r  UHF radar  
Radar measurements along the v e r t i c a l  and an off-ver t ical  d i r ec t ion  show an 
enhancement i n  s igna l  power along the v e r t i c a l  direct ion.  Such observations 
have been reported by GAGE and GREEN (1978) a t  Sunset f o r  the stratosphere,  and 
by FUKAO et al. (1979) at  Jicamarca f o r  the s t ra tosphere and the mesosphere. 
GAGE and GREm in t e rp re t ed  t h e i r  r e s u l t s  as due t o  r e f l e c t i o n  from an extended 
layer  of l - m  thickness. GAGE and BALSLEY (1980) considered anisotropic  scat-  
t e r ing  from model i r r e g u l a r i t i e s  t o  show t h a t  the obsenred enhancements along 
the v e r t i c a l  d i r ec t ion  can be reconciled with weakly anisotropic  d i sc  and rod- 
shaped i r r e g u l a r i t i e s .  GAGE e t  al .  (1981) suggest t h a t  the observations a t  
Sunset can a l s o  be reconciled with sca t t e r ing  from Bragg-scale f luc tua t ions  
within a thin,  extended l aye r  - a process f o r  which they suggest the term 
"Fresnel Scattering". 
been observed only below 75-km a l t i t u d e  (FUKAO e t  al., 1979; ROTTGER et al.,  
1979; FUKAO e t  al., 1980). 
Enhanced mesospheric r e f l ec t ions  along the v e r t i c a l  have 
This i s  probably due t o  the increase i n  the 
283 
EFLECTED 
60 
ANGULAR SPECTRUM 
* INCIDENT 
--• SCATTERED 
- REFLECTED 
ASPECT SENSITIVITY 
( C t  
SCATTERED 
TEMPORAL COHERENCE 
Figure 2. A schematic i l l u s t r a t i o n  of three methods of discriminating 
r e f l ec t ions  from sca t t e r ing .  In the spaced-receiver method ( a ) ,  the 
d i f f r ac t ion  pa t t e rn  produced by the i r r e g u l a r i t i e s  is measured at  
ground level.  
i r r e g u l a r i t y  produce a d i f f r a c t i o n  pat tern with a narrow angular spectrum. 
In the angular va r i a t ion  o r  aspect s e n s i t i v i t y  method (b), s igna l s  
received from the v e r t i c a l  and an off-ver t ical  d i r ec t ion  are compared. 
In the temporal-coherence method ( e ) ,  r e f l ec t ions  are detected on the 
bas i s  of t h e i r  longer co r re l a t ion  t i m e .  
function of t he  received s igna l  (from FiASTOGI and ROTTGER, 1982). 
Reflected components produced by a horizontal ly  extended 
p s ( ~ )  is  the autocovariance 
Kolmogorov microscale associated with turbulence, t h a t  makes the Rayleigh 
condition rather  d i f f i c u l t  t o  s a t i s fy  i n  the upper mesosphere. 
ROTTGER and LIU (1978) have used the longer coherence time of the r e f l ec t ed  
s igna l s  (up t o  several  tens  of seconds) t o  discriminate tropospheric r e f l ec t ions  
from scat ter ing.  ROTTGER (1980) and USTOGI and ROTTGER (1982) have used the 
temporal coherence of the r e f l ec t ed  r e tu rns  t o  detect  s t ab le  s t ructures  i n  the 
lower stratosphere.  
The d i f f r a c t i o n  cha rac t e r i s t i c s  of the r e f l ec t ed  and scat tered components 
i n  the  troposphere have been studied with spaced antennas by VINCENT and ROTTGER 
(1980) and the app l i cab i l i t y  of t h i s  method t o  measure winds up t o  mesospheric 
heights  has  been establ ished by ROTTGER (1981). 
has a l so  been used t o  detect  i n  some cases a s l i g h t  tilt i n  the r e f r a c t i v i t y  
s t ructures  (VINCENT and ROTTGER, 1980). 
The spaced-antenna technique 
The s t a t i s t i c a l  d i s t r i b u t i o n  of the received s igna l s  i s  affected signi-  
For sca t t e r ing  alone, the f i can t ly  by the presence of r e f l ec t ed  components. 
real and imaginary pa r t s  of the received s ignal  envelope are expected t o  have a 
Gaussian d i s t r i b u t i o n  and i t s  rrmplitude, a Rayleigh d i s t r i b u t i o n  (ISHIMMU, 
1978). I n  presence of a constant r e f l ec t ed  component, the amplitude has a Rice 
d i s t r ibu t ion .  For several  dominant ref lectors ,  the d i s t r i b u t i o n  r eve r t s  t o  
Rayleigh. 
detect  strong r e f l ec t ions  i n  the presence of scat ter ing.  The statist ical  dis- 
t r i bu t ion  of MST radar  s ignals  does not seem t o  have received much at tent ion.  
BASTOGI and HOLT (1981) discuss  the use of these d i s t r ibu t ions  t o  
DISCUSSION 
The cha rac t e r i s t i c s  of radar r e f l ec t ions  from the  middle atmosphere have 
been studied i n  several  W F  experiments. 
horizontally extended r e f r a c t i v i t y  s t ructures  play a s ign i f i can t  r o l e  i n  
It i s  generally recognized t h a t  thin,  
284 
producing these ref lect ions.  
the observed cha rac t e r i s t i c s  of ref lect ions,  on the bas i s  of assumed or i n fe r r ed  
propert ies  of small-scale r e f r a c t i v i t y  f luctuat ions.  
Several mechanisms have been proposed t o  explain 
A t  d i r ec t ions  close t o  the v e r t i c a l ,  r e f l ec t ions  can produce undesirable 
Measurements of 
e f f ec t s .  
lence parameters (e.g., Cn2) from the received s ignal  power. 
v e r t i c a l  wind are a l so  l i k e l y  t o  be biased by the winds a t  r e f l e c t i o n  heights,  
especial ly  when the a l t i t u d e  resolut ion i s  coarse. 
In the presence of r e f l ec t ions ,  care is  needed t o  estimate the turbu- 
Most of the reported radar  s tudies  of r e f l ec t ions  t a c i t l y  assume tha t  the 
i so - r e f r ac t iv i ty  surf aces are planar. 
expected, however, i n  t h e  presence of atmospheric waves and shears. These undu- 
l a t i o n s  can produce a focussing and defocussing e f f e c t  on the s ignals  received 
a t  ground level .  Such e f f e c t s  become important with small antennas, and a l s o  
influence the v a l i d i t y  of estimating instantaneous horizontal  veloci ty  from 
simultaneous Doppler observations along beams pointed i n  d i f f e ren t  directions.  
ACKNOWLEDGEMENT 
Weak undulations of these surfaces a r e  
This mater ia l  i s  based on work supported by the National Science Foundation 
under grant number ATM-8000060. 
REFERENCES 
Balsley, B. B. (19811, The MST Technique - A brief review, J. Atmos. Terr. 
Phvs., 43, 495-509. 
Beckmann, P. and A. Spizzichino (19631, The Scat ter ing of Electromagnetic Waves 
From Rough Surfaces, Pergamon, N e w  York, 503 pp. 
Booker, H. G. (1956), A theory of s ca t t e r ing  by nonisotropic i r r e g u l a r i t i e s  with 
appl icat ions t o  radar r e f l ec t ions  from the aurora, J. Atmos. Terr. Phvs., 
- 8, 204-221. 
du Castel, F. (1966), Tropospheric Radio Wave Propagation Bevond the  Horizon, 
Pergamon, N e w  York. 
Fukao, S., T. Sato, R. F. Woodman and W. E. Gordon (19791, Mesospheric winds and 
waves over Jicamarca on May 23-24, 1974, J. Geouhvs. Res.. 84, 4379-4386. 
Fukao, S., T. Sato, R. M. Harper and S. Kat0 (19801, Radio wave sca t t e r ing  from 
the t rop ica l  mesosphere observed with the Jicamarca radar,  Radio Sci., 
15, 447-457. 
Gage, K. S. and J. L. Green (19781, Evidence fo r  specular r e f l e c t i o n  from mono- 
static VHF radar  observations of the stratosphere,  Radio Sci.. 13, 991- 
1001. 
Gage, K. S. and B. B. Balsley (19801, On the  sca t t e r ing  and r e f l e c t i o n  mecha- 
nisms contr ibut ing t o  c l ea r  a i r  radar echoes from the troposphere, s t ra to-  
sphere and mesosphere, Radio Sci.. 15, 243-257. 
Gage, K. S., B. B. Balsley and J. L. Green (19811, Fresnel s ca t t e r ing  model fo r  
t he  specular echoes observed by VBF radar,  Radio Sci.. 16, 1447-1453. 
Gardner, F. F. and J. L. Pawsey (19531, Study of ionospheric D-region using 
p a r t i a l  r e f l ec t ions ,  J, Atmos. Terr. Phvs.. 3, 321-344. 
Ishimaru A. (19781, Wave Propagation and Sca t t e r ing  i n  Random Media, Academic, 
New York, 572 pp. ( i n  two volumes). 
285 
Rastogi, P. K. and 0. Holt (19811, On detecting r e f l ec t ions  i n  presence of scat- 
t e r ing  frora amplitude s t a t i s t i c s  with appl icat ion t o  D-region p a r t i a l  
r e f l ec t ions ,  Radio Sci., 16, 1431-1443. 
Rastogi, P. IC. and J. Rottger (19821, VLIF radar observations of coherent ref lec-  
t i ons  i n  the v i c i n i t y  of the tropopause, J. Atmos. Terr. Phvs., 44, 461- 
469. 
Rottger, J. (19781, Evidence f o r  p a r t i a l  r e f l e c t i o n  of VEF radar  s igna l s  from 
the troposphere, J. GeoDhvs. Res., 44, 393-394. 
Rottger, J. (1980), Structure  and dynamics of the stratosphere and mesosphere 
revealed by VEF radar  investigations,  Pure A p ~ l .  Geophvs., 118, 494-527. 
Rottger, J. (1981), Invest igat ion of lower and middle atmosphere dynamics with 
spaced antenna d r i f t s  radar,  J. Atmos. Terr. Phvs.. 43, 277-292. 
Rottger, J. and C. H. Liu (19781, Par t ia l  r e f l ec t ion  and sca t t e r ing  of VHF radar  
s ignals  from the c l ea r  atmosphere, Geophvs. Res. L e t t , ,  5, 357-360. 
Rottger, J., P. K. Rastogi and R. F. Woodman (19791, High-resolution VHF radar  
observations of turbulence s t ructures  i n  the mesosphere, Geophvs. Res. 
Le t t . .  6, 617-620. 
Ta ta r sk i i  V. I. (19711, The e f f ec t s  of the turbulent atmosphere on wave pro- 
pagation, Nat. Tech. Inf.  Serv., Springfield,  Va. , 472 pp. ( t ranslated 
from the Ruesian). 
Vincent, R. A. and J. Rottger (19801, Spaced antenna VHF radar observations of 
tropospheric v e l o c i t i e s  and i r r e g u l a r i t i e s ,  Radio Sci., 15, 319-335. 


Parametrization of Fresnel returns in middle-atmosphere radar experiments

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server