Forward scatter cross section measurement in melting layer of snow flake

Dennis, A. S.

Fernald, F. G.

English

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MEASUREMENT OF FORWARD-SCATTER CROSS SECTIONS I N  THE MELTING LAYER 
F. G .  Fernald and A. S .  Dennis 
S tanford  Research I n s t i t u t e  
1. IWTRODUCTION 
The enhanced back-sca t te r  from mel t ing  snowflakes compared t o  d r y  snow or r a i n  of equ iva len t  
i n t e n s i t y  g i v e s  rise t o  t h e  w e l l  known b r igh t  band i n  t h e  mel t ing  l a y e r .  Published computations 
by s e v e r a l  au tho r s ,  when considered toge the r ,  i n d i c a t e  t h a t  fo rward - sca t t e r  c r o s s  s e c t i o n s  i n  t h e  
mel t ing  l a y e r  occas iona l ly  exceed t h e  back-sca t te r  c r o s s  s e c t i o n  by 1 t o  2 o r d e r s  of magnitude 
a t  cen t iwa te r  wavelengths [ A t l a s  e t  a l . ,  1953; Gunn and E a s t ,  1954; Herman and Battan,  1961; 
Stephens,  19611. However, no complete t h e o r e t i c a l  t rea tment  of s c a t t e r i n g  by mel t ing  snowflakes 
has  been g iven  t o  d a t e  because of t h e i r  complex s t r u c t u r e s  and i r r e g u l a r  shapes.  Therefore,  an 
experiment was undertaken t o  ob ta in  simultaneous de te rmina t ions  of €orward-sca t te r  and back- 
s c a t t e r  c r o s s  s e c t i o n s  i n  t h e  mel t ing  l a y e r .  
2 .  EXPERIMENTAL SET-UP 
The experiment w a s  conducted i n  t h e  v i c i n i t y  of Sonora, C a l i f o r n i a ,  i n  t h e  western foo t -  
h i l l s  of t h e  S i e r r a  Nevada n e a r  l a t i t u d e  38 N .  The propagation pa th  w a s  chosen so t h a t  t h e  
common volume (F ig .  1) w a s  l oca t ed  near  t h e  mel t ing  l aye r  dur ing  t y p i c a l  w in te r  storms, and so 
t h a t  p o s s i b l e  s ide- lobe  and d i f f r a c t i o n  e f f e c t s  were minimized by t h e  t e r r a i n .  
' 
A complete C-band weather r ada r  w a s  opera ted  a t  t h e  t r a n s m i t t e r  s i te.  I t  t r ansmi t t ed  3-bsec 
pu l ses  of 250 kw peak power a t  5.90 Gc a t  a pu l se - r epe t i t i on  frequency of 333 p e r  second. The 
antenna had an e f f e c t i v e  a p e r t u r e  of 0.5 m2 and a p e n c i l  beam approximately 3.5' wide. 
antenna-feed s y s t e m  permi t ted  t h e  use  of e i t h e r  v e r t i c a l  or h o r i z o n t a l  p o l a r i z a t i o n .  During t h e  
experiment, ope ra t ions  i n  sec tor -scan  mode were a l t e r n a t e d  wi th  pe r iods  dur ing  which t h e  r ada r  
antenna remained f i x e d  i n  t h e  d i r e c t i o n  of t h e  remote r e c e i v e r .  Photographs were taken  of an 
a u x i l i a r y  PPI d i s p l a y  du r ing  t h e  sec tor -scan  opera t ions  t o  record p r e c i p i t a t i o n  a r e a s  along or 
nea r  t h e  propagat ion  pa th .  An A-scope, monitored v i s u a l l y ,  provided q u a n t i t a t i v e  d a t a  on re- 
ce ived  power. 
The 
The remote receiver w a s  b u i l t  up from a marine radar ,  w i th  t h e  antenna mounted on i t s  s i d e .  
Th i s  arrangement produced a beam 15' wide i n  azimuth and 2' i n  t h e  v e r t i c a l .  A t  t h e  range of 
t h e  common volume (- 8 km), t h e  v e r t i c a l  ex ten t  of t h e  r e c e i v e r  beam approximated t h a t  of t h e  
b r i g h t  band (F ig .  1) .  The r ece ive r  antenna was s e n s i t i v e  t o  v e r t i c a l l y  po la r i zed  r a d i a t i o n  on ly .  
The ou tpu t  of t h e  r e c e i v e r  w a s  f e d  t o  2 osc i l l o scopes ,  one se rv ing  as a monitor scope and t h e  
o t h e r  be ing  photographed. 
3 .  h%l"OD OF ANALYSIS 
Both t h e  r a d a r  r e c e i v e r  and t h e  remote rece ive r  were c a l i b r a t e d  wi th  a test set dur ing  t h e  
course of t h e  experiment.  The c a l i b r a t i o n  curves thus  ob ta ined  provide  a ready means f o r  i n t e r -  
p r e t i n g  ou tpu t  vo l t ages  as shown on t h e  osc i l l o scopes  i n  terms of s i g n a l  p o w e r  a t  t h e  an tennas .  
However, f u r t h e r  a n a l y s i s  i s  r equ i r ed  be fo re  a d i r e c t  comparison of forward-sca t te r  and back- 
scat ter  cross s e c t i o n s  i s  p o s s i b l e .  
F igu re  2 i s  a sample of t h e  d a t a  recorded a t  t h e  remote r e c e i v e r .  The o s c i l l o s c o p e  w a s  
running on i n t e r n a l  t r i g g e r  wi th  t h e  ho r i zon ta l  w r i t i n g  speed a t  1 cm/sec. The 
pu l ses  are not  reso lved;  t h e  i r r e g u l a r  trace i s  t h e  envelope of t h e  tops  of t h e  
f l u c t u a t i o n s  r e s u l t  from v a r i a t i o n s  i n  t h e  r e l a t i v e  p o s i t i o n s  and (poss ib ly )  i n  
of t h e  p a r t i c l e s  i n  t h e  common volume. 
Mean s i g n a l  i n t e n s i t i e s  have been der ived  from records  o f  t h e  form of F ig .  
th reshold-cross ing  method descr ibed  by Marshall and Hi t sch fe ld  [1953]. Let t h e  
t e n s i t y  be denoted by H, and t h e  mean i n t e n s i t y  a t  t h e  remote r e c e i v e r  by 5,. 
t aneous  va lues  of i n t e n s i t y  o u t  of a sample of k exceed H, t h e  b e s t  estimate of - 
Hard copy (HC) UL- 
Microfiche (MF J L ,  
(NASA CR OR TMX OR AD NUMBER1 
i n d i v i d u a l  
pu l se s .  The 
t h e  o r i e n t a t i o n s  
2 us ing  t h e  
th re sho ld  in-  
I f  i n s t an -  
Prr i s  g iven  by 
(1) 
https://ntrs.nasa.gov/search.jsp?R=19650010268 2020-03-17T00:37:48+00:00Z
c 
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TRANSMITTER REMOTE RECEIVER VOLUME 7 
1800 c 
FIG. I PLAN AND PROFILE VIEWS OF PROPAGATION PATH 
In  ou r  ana lys i s ,  100 ins tan taneous  va lues  of t h e  signal envelope taken  a t  50 msec i n t e r v a l s  have 
been used i n  each de termina t ion  of Frr. 
proper ly  chosen, t h e  e r r o r s  i n  t h e  e s t ima te  of Brr would be of t h e  o r d e r  of 1 db. 
I f  t h e s e  w e r e  s t a t i s t i c a l l y  independent and H w e r e  
The a u t o c o r r e l a t i o n  of t h e  s i g n a l s  a t  50 msec i n t e r v a l s  have been de r ived  by n o t i n g  t h e  fre- 
quency o f  t h re sho ld  c r o s s i n g s  i n  t h e  samples used t o  compute frrr  [ H i t s c h f e l d  and Dennis,  19561. 
The c o e f f i c i e n t s  range from 0 .1  t o  0 .7 ,  so t h a t  t h e  r a t i o ,  ('r".1/A.), where 70 .1  i s  t h e  t i m e  re- 
qu i r ed  for t h e  a u t o c o r r e l a t i o n  c o e f f i c i e n t  t o  dec rease  to 0 . 1  and ,A i s  t h e  wavelength,  ranges  
upward irom 10 msec cm-1. Thus, t h i s  ra t io  excceds i n  cvery case t h e  range of expe r imen ta l  
va lues  found f o r  i t  by H i t s c h f e l d  and Dennis L1956: 111 ana lyz ing  back- sca t t e r  s i g n a l s  from snow. 
The r e l a t i v e l y  l e i s u r e l y  f l u c t u a t i o n s  i n  t h e  fo rward - sca t t e r  s i g n a l  a r e  e x p l a i n a b l e  on t h e  b a s i s  
o f  pa th  geometry. In  b i s t n t i c  experinients i nvo lv ing  small s c a t t e r i n g  a n g l e s ,  p a r t i c l e  motions a r e  
very i n e f f i c i e n t  i n  producing changes i n  t h e  t o t a l  l e n g t h  of t h e  p a t h  from t r a n s m i t t e r  t o  scat- 
terer  t o  r e c e i v e r .  
Due t o  t h e  p a r t i a l  c o r r e l a t i o n  of t h e  ins tan taneous  va lues  of s i g n a l  t i t t e n s i t y  used i n  t h e  
p re sen t  case,  each sample i s  equ iva len t  t o  something less than  
s t anda rd  e r r o r  of o u r  e s t ima te  of Prr i s  s l i g h t l y  g r e a t e r  than  
t h a t  measurement and c a l i b r a t i o n  e r r o r s  amount t o  upwards of 5 
garded as adequate f o r  t h e  p re sen t  purpose. 
100 independ-::  da t a ,  and so t h e  
1 db. However, it 
db, so t h e  samples 
i s  es t ima ted  
can be  re- 
t h e  common volume, T f ,  i s  g iven  by The mean forward-sca t te r  c r o s s  s e c t i o n  p e r  u n i t  volume i n  
where r is  one-half t h e  length  of t h e  propagat ion path,  i .e.,  8.8 km, 
Pt is t h e  t r a n s m i t t e r  power, 
Gt and Gr a r e  t h e  ga ins  of t h e  t r a n s m i t t i n g  and r ece iv ing  antennas,  
V i s  t h e  common volume, 
and t h e  o t h e r  symbols a r e  a s  p rev ious ly  def ined .  
volume can be considered a s  t h e  d i f f e r e n c e  of 2 c o n i c a l  f rus t rums ;  geomet r i ca l  c o n s t r u c t i o n  shows 
it t o  be equal  t o  0.5 km3. 
I n  t h e  p re sen t  case (see Fig .  11, t h e  common 
The back-sca t te r  c ros s  s e c t i o n  p e r  u n i t  volume a t  t h e  middle  of t h e  common volume, qb, i s  
2 
given by t h e  weather radar  equat ion  as 
8 n r  Pr 
(3) 'b = Pt Ae h 
179 
< -70 
- -75 
2 
(3 
v) 
I I I I I I 
0 2 4 6 8 IO 
FIG.2 FORWARD SCATTER SIGNAL RECORDED 
TIME - SECONDS 
1327 PST, I APRIL 1964 
where Pr is  t h e  mean power c o l l e c t e d  a t  t h e  r ada r  antenna from a c o n t r i b u t i n g  reg ion  a t  range r, 
A, i s  t h e  e f f e c t i v e  a p e r t u r e  of t h e  radar  antenna, 
h i s  t h e  length  of t h e  r ada r  pu l se  i n  space,  
and t h e  o t h e r  symbols are as previous ly  def ined .  
4.  SAMPLE RESULTS AND CONCLUSIONS 
Observa t ions  w e r e  conducted over a period of 7 weeks (19 February-9 A p r i l  1964).  The storms 
Computed values of yf and Tb i n  t h e  d ry  snow were about t h e  same when p a r a l l e l  
dur ing  t h e  f i r s t  p a r t  of t h i s  per iod  were r a t h e r  cold,  w i th  d r y  snow occupying t h e  common volume 
most of t h e  t i m e .  
p o l a r i z a t i o n  w a s  used, but Tf w a s  g e n e r a l l y  too  small t o  be measured a c c u r a t e l y  when c r o s s  
p o l a r i z a t i o n  w a s  used. 
The s torm of 31 March-1 A p r i l  1964 proved i d e a l  f o r  bright-band measurements. A t  t h e  start,  
t h e  0"-C i so therm w a s  nea r  1.8 km, a t  t h e  top of t h e  common volume. 
throughout  t h e  storm, wi th  t h e  0"-C isotherm dropping t o  1.4 km by t h e  end. 
b r i g h t  band w a s  occupying t h e  lower p a r t  of t h e  common volume and ex tending  perhaps 200 m below 
i t s  lowest p o i n t .  
Temperatures f e l l  g radua l ly  
A t  t h a t  t i m e ,  t h e  
Computed va lues  of Tf and Tb a r e  shown i n  F ig .  3 .  The PPI scope i n d i c a t e d  q u i t e  uniform 
p r e c i p i t a t i o n  i n  t h e  common volume dur ing  the  la te  evening of 3 1  March, which is borne ou t  by 
t h e  r e l a t i v e l y  s teady  va lues  of 
w i th  vf as h igh  a s  -68 db m - l  and exceeding Tb by 6 t o  15 db. and Tb. A preponderance of forward s c a t t e r  i s  ind ica t ed ,  
During t h e  morning of 1 Apr i l ,  numerous s m a l l  showers wi th  d iameters  of 1 t o  3 km were 
p resen t  a long  and nea r  t h e  propagat ion pa th .  
because t h e  common volume was l a r g e  enough t o  ho ld  s e v e r a l  p r e c i p i t a t i o n  cells  a t  once (Fig.  3). 
S c a t t e r i n g  w a s  predominantly forward. 
1110 PST when one of t h e  showers passed through t h e  middle of t h e  common volume. 
The func t ion  qb  f l u c t u a t e d  widely, but 7, d id  not  
I f  it had been i s o t r o p i c ,  +$, would have exceeded If a t  
Cross-polar ized  measurements were made from 1205 t o  1300 PST. They co inc ided  wi th  t h e  
passage  of a l a r g e  shower o f  moderate i n t e n s i t y ,  which probably conta ined  some sma l l  h a i l .  The 
va lues  of vf ranged from 0-10 db below Tb, i n d i c a t i n g  t h a t  t hey  were 10-25 db below t h e  cor re-  
sponding va lues  of qf f o r  p a r a l l e l  p o l a r i z a t i o n .  
on back-sca t te red  s i g n a l s  from t h e  mel t ing  l aye r .  
This  i s  compatible  wi th  Wexler 's  [1955] r e s u l t s  
P a r a l l e l - p o l a r i z e d  measurements around 1330 PST, as t h e  last showers w e r e  moving o f f  t h e  
The va lue  of vf a t  1402 PST, -100 db m - l ,  was pa th ,  showed qf only  s l i g h t l y  i n  excess of qb. 
c o n t r i b u t e d  e i t h e r  by p r e c i p i t a t i o n  at  t h e  edge of t h e  common volume of t h e  main beams or i n  
s i d e l o b e s .  
180 
. -  
k 
' n  
U 
I 
I I I I I I I I 1 
PO LA R I Z ATION 
PAR AL LE L PARALLEL CROSS PARALLEL 
c------l c - - - - - - - - - - - l I  I 
W 
-70 
3 
0 > -80 
z 
I- u w 
v) 
v) 
0 
0 -IOC 
v, -IIC 
5 -12c 
I -._.- BACK SCATTER(flb1 u 
x xx 
x x x  x 1  
x FORWARD SCATTER (nf) 
31 MARCH TI ME - PST I APRIL 
FIG. 3 CALCULATED CROSS SECTIONS PER UNIT VOLUME 
The r e s u l t s  obtained, a l though l imi t ed  for t h e  most p a r t  t o  one storm, do confirm t h e  ex- 
p e c t a t i o n  t h a t  Tf should exceed Tb  i n  t h e  b r i g h t  band a t  cen t ime te r  wavelengths.  
mentation i s  needed t o  e s t a b l i s h  t h e  range of t h e  r a t i o  T f f l b .  I t  would be advantageous i f  such 
experiments provided f o r  simultaneous measurements of t h e  p a r a l l e l - p o l a r i z e d  and c ross -po la r i zed  
forward-sca t te r  s i g n a l s .  
Fu r the r  exper i -  
5 .  ACKNOWLEDGMENTS 
Th i s  work w a s  sponsored by t h e  Nat iona l  Aeronautics and Space Adminis t ra t ion  under Cont rac t  
NASr-49(02) wi th  Stanford Research I n s t i t u t e .  
Mi-. R .  T.H. C o l l i s ,  Head o f  t h e  I n s t i t u t e ' s  Radar Aerophysics Group played a major role i n  
t h e  planning of t h e  f i e l d  ope ra t ions .  Qu i t e  ex tens ive  equipment mod i f i ca t ions  were necessary  i n  
conver t ing  s u r p l u s  r ada r  sets f o r  t h i s  experiment.  Th i s  work w a s  handled by M r .  G .  E .  Davis, 
Senior  E l e c t r o n i c s  Technician.  
6 .  REFERENCES 
At l a s ,  D . ,  M .  Kerker and W .  H i t sch fe ld  (1953), S c a t t e r i n g  and At t enua t ion  by Non-Spherical 
Gunn, K .  L .  S . ,  and T .  W .  R .  East (October 1954), Microwave P r o p e r t i e s  o f  P r e c i p i t a t i o n  
Herman, B. M . ,  and L .  J .  Bat tan  (1961), Ca lcu la t ions  of t h e  T o t a l  A t t enua t ion  and Angular 
Atmospheric P a r t i c l e s ,  J .  Atmos. and T e r r e s t .  Phys., Vol. 3, pp. 108-119. 
P a r t i c l e s ,  Q u a r t .  J .  Royal Meteorol. SOC., Vol. 80, pp. 525-545. 
S c a t t e r  of Ice Spheres,  Proc .  Ninth Weather Radar Conference, Kansas C i t y ,  Missouri ,  
pp. 259-265, Amer. Meteorol.  SOC., Boston, Massachuse t t s .  
Radar Echoes from Snow, S c i .  R e p o r t  MW-23, Cont rac t  AF-19(122)-217, M c G i l l  Un ive r s i ty ,  
Montreal, Quebec. 
Pos i t ioned  S c a t t e r e r s :  P a r t  I ,  Canadian J .  Phys., V o l .  31, pp. 962-995. 
18, pp. 348-359. 
H i t sch fe ld ,  W . ,  and A .  S .  Dennis (July 1956), Measurement and Ca lcu la t ion  of F l u c t u a t i o n s  i n  
Marshall ,  J .  S . ,  and W .  H i t sch fe ld  (1953), I n t e r p r e t a t i o n  of t h e  F l u c t u a t i n g  Echo from Randomly 
Stephens,  J .  J .  (June 1961), Radar Cross Sec t ions  f o r  Water and Ice Spheres,  J.  Meteorol., V o l .  
Wexler, R .  (1955), An Evalua t ion  of  t h e  Phys ica l  E f f e c t s  i n  t h e  Mel t ing  Layer, Proc .  F i f t h  
Weather Radar Conf., pp. 329-334, S igna l  Corps Engineering Laboratories. 
18 1 


Measurement of forward-scatter cross sections in the melting layer

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