TlL13:i.
n,
C.
Harland
Archives
A-0!32
ESD-TR-66-447
ERRATA
SHEET
for
TECHNICAL
REPORT
NO.
426
The author
has detected
the following
errors
in Technical
l!Micr~wa~~
Scattering
Parameters
No. 426 (R. K. Crane,
this
page
I,
3
October
1966),
Kindly
insert
England
Rain,
co~y of that report.
~Page
9
In Table
Reference
IV.
column
heading
(’N)” should
readRadio
Report
for New
into
Your
“Radio
Refractivity
(N)
v
Pages
13 and
14
In Table
V,
“A (db/km)”
X’lo
/Pages
23 through
30
1967
to
X’to
heading
o
Ordinate
scale
identification
for
Figs.
7(a-b)
and 8(a-h)
should
read
ATTENUATION
15 March
under
column
change
COEFFICIENT
(db/km)
Publications
M. I.T.
Lincoln
Laboratory
PO.
Box 73
Lexington,
Massachusetts
02t73
ABSTRAC1
Scattergramsof attenuationcoefficient,
effective
reflectivity factor, single-
scattering al bedo, and radio refractivity vs Iiquid-.vater content, rain rate,
a“d reflectivity
factor are presented for a raindrop temperature of O.O°C and
frequencies
1.29, 2.80,
of
8.0,
9.35,
15.5,
35.0,
70.0,
and 94.0 GHz.
The scattergrams were ccmputed using Mie theory to compute the scattering
parameters for single raindrops, and sin~le-scattering
theory to compute the
i“tegr.a fed scattering effects of . . ensemble of raindrops.
size distributions were used to generate the scatterg rams.
Accepted for the Air Force
Fmnklin C. Hudson
Chief, Lincoln Laboratory Office
u,
Measured drcp-
CONTENTS
111
Abstract
\
I.
11. Computation
111. Raindrop
IV.
V.
i
Introduction
Measured
of Scattering
Parameters
5
Parameters
and Modeled
f
Scattering
Parameters
8
tz
Conclusions
i5
References
iv
MICROWAVE SCATTERING PARAMETERS
FOR NEW ENGLAND RAIN
I.
INTRODUCTION
As part of a study of the effects
scattering
ete rs,
volume
were
weather
below
effects
of measured
backs tattering,
and satellite
albedo
content,
normally
vs liquid-water
systems.
coefficient,
content,
investigated.
of these
reflectivity
sections
per-unit
per-unit
volume
and the single-scattering
section
to extinction
effects
of interest
in receiver
above,
cross
sections.
to satellite
noise,
the effective
11.
COMPUTATION
ical
drops
These
effective
scattering
computations
factor,
index of refraction
of radio
SCATTERING
reflectivity
albedo
param -
to both
are depicted
and singleThe liquid-water
data.
of the order
to Mie must be used.
a scatterer
of diffraction
in estimating
along a path and changes
In addition
to the scattering
medium
of a plane wave by dielectric
of the microwave
spheres.
radiation,
of a plane wave as observed
E = Ei + kjs . Ei +S(n, a,O)~l
.
.
= wave number
from
and tbe
parameters.
composed
of spher-
parameters
can be
Raindrops
and the theory
center
in free
-ikR
‘~
space
of scatterer
where
x is the wavelength
to observer
have diattributed
at a point at a distance
where
R . distance
parameters
was computed
vs the meteorological
is given by4
k = 2./k
the
PARAMETERS
of the wavelength
The scattering
of the total scat-
are useful
The many reports on rain scattering
for model raindrop distributions
i-3
show that, to first order,
the calculations
of the scattering
on the theory
to the backscatter
attentiaticm
of the scattering
refractivity
factor
to the ratio
parameters
the total
meteorological
in scattergrams
OF
volume,
communications,
using available
are depicted
ameters
J,:
the
per-unit
of interest
rain rate and reflectivity y factor.
section
cross
based
systems,
The scattering
cross
for frequencies
Results
effecti”e
communication
s tattering
distributions
cro6s
tering
results
communication
were
and total
drop-size
of attenuation
on space
rain rate and reflectivity
factor are drop-size
dependent meteorological
parameters
m ed to des u-ibe rainfall,
Tbe s tattering parameter
attenuation coefficient
is related
to the extinction
listed
distributions
absorption,
for measured
as scattergrams
s tattering
raindrop
extinction,
computed
radar
of the troposphere
from
__
dj’
electric
field vector with components
1 in plane
of scattering
and r perpendicular
to plane of
scattering
with superscripts
i (incident field)
and s (scattered
field)
Sz
~(n, a,e)
=
o
()
scattering
matrix
o
51
.
si(n,a,
e) =
~
&j
{al(n,a)
T1(cos e) + bl(n,a)
*
{bl(n,a)
mf(cos e) + al(n, aPCl(.Os e)}
L1(cos e))
I=i
.
s2(n, a,e)
.
~
f.i
aj(n,a) and bl(n, a) m-e Mie series
s tattering
coefficients;
amplitudes
n . complex index of refraction
a . radius
ffl(cOse)
.
(5ke)
energy
balance
or the specific
-i
PJCOS
Is .
e)
angle.
for scattering
intensity
of liquid water
of sphere
e . scattering
The
S, and S2 are called
is given
in terms
of the amplitude
of the Poynting
vector
1 as
I’v(n,a)
T
where
u is a s tattering
lost to the incident
t:red
by the sphere
the sphere
cross
plane wave
section.
In terms
is given by the s tattering
is given by the absorption
Oext(n, a) = *
Re
kz
[where
of the scattering
is given by tbe extinction
cross
cross
cross
section;
cross
section;
sections,
the total
and the total
energy
the energy
energy
scat-
absorbed
by
section.
{S(n, a)) . extinction
cross
section
S(n, a) . Si(n, a,O) . S2(”, a,0)]
m
a~cat(n,a)
= q
k
~
(21 + f ) { Ial(n,a)lz
+ /bl(i,
s) I 2} . scattering
cross
section
1.1
2
.——
= wextin, a) – o~c=t (n, a) . absorption
uab~(n,a)
The energy
cross
s tattered
section
backwards
and is derived
Uback(n,a)
along the direction
from
= ~
k
the scattering
[S; (n,a,r)
= backscatter
The coherent
energy
of the imaginary
If the spheres
(see
loss
and phase
and real parts
can be assumed
of incidence
matrix
Si(n, a,r)l
cross
of an effective
section
is given by the backs cantering
elements
as
[Sz(n,a, r) sj(n,a,~)l
= ~
k
section
shift due to an ensemble
to scatter
cross
of scatterers
index of refraction
energy
once,
is described
for the volume
the index of refraction
in terms
of scatterers.
is given by
Ref. 4, Ch. 4)
n.=
n:-in:
= i-i~~amax
S(n,a)N(a)da
am in
where
N(a) is tbe number
If the spheres
and phase
density
scatter
of spheres
more
of the received
for drop radius
than once,
field
a first-order
can be expressed
a or the drop-size
solution
in terms
distribution
for the expected
of a multiple-scattering
amplitude
index of
refraction
(n~–
where
in})
2
‘ma.
. (n~ – in~)2 + =
[f k’
Si(n, a,r) N(a) da
am in
1
Si(n, a,w) = –SZ(n, a,r).
Since
the scattering
“~
amplitude
Si(n, a,r)
2*
2
(-) {[f
. n:++
a max
k’
—
is small,
amax
[f
this can be expressed
2
N(a) Re
{St(n,a,
?r) da)
amin
1
2
N(a) Im {Si(n, a,r))
da
H
amin
‘:=”:-
as
(:)2
[L:::N(’)R’
{sin’”)}
“]
a
x
‘u
[f
N(a) Im {Si (n, a,m)} da
1
amin
With either
in terms
index of refraction,
of the radio
the real and imagin.m y terms
refractivity
coefficient
A = n~8(2klogio
more
easily
N given by
N=(nr–i)xi06
and the attenuation
can be expressed
given
e)x
I
“N units”
,
by
i06
,
db/km
for a, L in centimeters
TABLE I
COMPARISON
OF
FOR THE LAWS AND
SINGLE-
AND
PARSONS
DROP-SIZE
MULTIPLE-SCATTERING
INDEX
DISTRIBUTION
FOR
OF
REFRACTION
101.6-mm/h
RAIN
RATE
A
A
(dbflm)
(db;m)
Frequency
(G Hz)
Drop Temperature
4.0
0.0
5.671114
5.671101
0.1885542
O. 1885544
4.0
18.0
5.703791
5.703778
0.1027994
0.1027995
8.0
0.0
5.731942
5.731528
1.761978
1.761983
8.0
18.0
6.011033
6.011021
2.113060
2.113068
15.5
0.0
5.079693
5.079674
6.734227
6.734224
15.5
18.0
4.749057
4.74904>
7.239070
7.239074
34.86
0.0
2.319696
2.319603
21.85193
21.85190
34.86
18.0
2.247630
2.247626
20.72679
20.72676
(“c)
Index Of refraction
“1=1.
N
N
s
m
n = n’ + in”
-6
O+ NXIO
-5
_— AxIO
‘“2k lcgloe
A comparison
averaged
liquid-water
quencies.
lected.
cross
distribution
show that,
is given
for coherent
the multiple-scattering
is extremely
The per-unit
sphere
and multiple-scattering
content
The results
to describe
result
of the single-
process
index of refraction
in Table
scattering,
because
for the Laws and Pars
I for selected
the single
the correction
temperatures
scattering
to the single-scattering
small.
scattering
vchme
sections
Integrated
since.
scattering
p(n) .
J:::
cross
section
for incoherent
cross
energy
sections
can be derived
transmission,
or scattering
directly
from
the phase
coefficients
the single-
effects
are given
N(a) u(n, a) da
from which
Pe xt = 2kn” = A(logio
‘scat
‘~j~~
‘(a)
e) ‘ixio
-5
‘s.at(n>a)da
8 abs = P
ext – D,cat
%-=
and fre-
is sufficient
~:::
N(a) aback(v)
da
4
,
cm
-i
for
A in centimeters
by
are neg-
1s
—
For
in describing
ease
integrated
single-scattering
The parameters,
energy
the relationship
attenuation
balance
relationship
The final per-unit
scatter
cross
describe
albedo,
the radar
the expression
coefficient,
return
scattering
from
given
- f
-
and 13abs, the parameter,
albedo
prefer
of rain.
in terms
IK12
the
w is introduced:
albedo
therefore
describe
tbe
of scatterers.
parameter
a “olume
Bback, R.ayleigh
~~cat,
and single-scattering
volume
Radiometeorologists
for backscattering
Pext,
or single-scattering
per-unit
“olume
section.
between
to be considered
the “se
The reflectivity
of the Rayleigh
farnax
is the integrated
of an effective
reflectivity
factor
Z is derived
scattering
N(a) (ka)6 da=<
backfactor
to
from
theory,
]Klz
Z
A
‘mm
where
1
amax
z.
N(a)
(2a)6da
amin
K_n2—4
~2+2
Rayleigh
scattering
is of the order
tivity
factor
pback
eff
u~cat
IU.
are better
“sing
Mie theory
described
of the scattering
of z
frequencies
where
can be retained
the wavelength
if an effective
reflec-
quadrature
.s above.
.abo”e were
coefficients
than one part in 106.
Gaussian
RAINDROP
Tbe per-unit
numerical
computed
cm a“ IBM 7094 computer.
S1 and S2 and the scattering
volume
integration
parameters
crOss
are generated
of the parameters
over
each
sectiOn
by a
drop-size
distribution.
PARAMETERS
The per-unit
distribution.
Tbe concept
~4
@back
parameters
of the drop-size
parameters
not hold for the microwave
X5 IK12
accuracies
three-point
interval
.—
i~ calculated
The scattering
Estimated
does
Zeff is used as
z
where
theory
of the drop diameter.
volume
Drop-size
parameters
distributions
used by meteorologists
L.
I
amx
N(a)
are generated
using
are not generally
are
Z,
tbe per-unit
volume
used to characterize
the liquid-water
content,
raindrop
rainfall.
size
The
and the rain rate.
(+ a3)Pda
amin
I
where
L = liquid-water
p = density
content
of water
(taken asl.0
gm/cm3).
I amax(~
a3)pv(a)
N(a)
R=
da
am in
where
R = rain rate
v(a) = terminal
The raindrop
size
samples
velocity
of the raindrops
of Gun
and Rinzerb
V(a)
Two types
Radar
Research
using
of drops
converted
above.
pieces
of filter
separate
drop-size
an extreme
variation
is possible
very small
sample
drop-size
distribution
z-R
for adjacent
The data were
is the parent
by their
Z-R
II.
frequency
is low enough for Zeff
relationship.
The Laws
Washington,
rain-rate
D. C.
types
average
liquid-water
the drop-size
rain rates.
area.
intervals.
the rainfall
expected
and Parsons
to equal
model
All their
These
are similar
value
distribution
The resultant
Z,
data,
for each interval
given
from
three
averaged
after
as
on
it is evident
to the problem
that
of using
a
that the measured
is not quite valid,
but no
distributions
are
distributions,
i. 29 GHz.
years
the
In this case
of rain data obtained
division
The model
to a number
the
model
used by converting
This
assumption
was scaled
and
may indicate
density.
in Table
in%he
data because
data were
The distribution
are listed
into drop radius
with the New England
and the Laws and Parsons
in Fig. i.
rain parameters
taken with two
as measured
Raindrop
Zeff vs R for
used as a comparison
in each area
curves
distribution.
relation-
as shown in Fig. i t(a).
data were
for the New England
content
This points
the
data were
processed
parameters
For this set of drop-size
was generated
data were
were
were
This assumption
relationship is given by Fig, ! O(b) which gives
and sizing
These
ed with tbe assumption
of the parent
at Cambridge,
the data in the table,
samples.
process
Laws
Weather
drop velocity
samples
raindrop
From
distribution.
to give an estimate
often characterized
resultant
in Table
measured
measurements
adjacent
using
the M. I .T.
of counting
using the terminal
two simultaneous
and typical
i964 are listed
distribution
from
in a given length of time.
meter
The data for these
distributions,
were
which consisted
area
per cubic
instances,
paper.
a model
obtained
distributions
technique
on a 440-cm2
size.
processed:
distributions
The drop-size
i July and 26 August
data are available
were
drop-size
of drops
In some
adjacent
‘“21}
distributions
collected
and pressure
eXp[–(&)
the filter-paper
to the number
ship given
temperature
and measured
Laboratory.t
Massachusetts
number
{i.0–
950.0
data,
were all taken at the ground.
The terminal
\,
by an empirically
determined
equation fitting the data
was described
for standard
.
in a quiet atmosphere.
used in this report
of drop-size
and Parsons7
velocity
the
the
I
generated
to give the listed
V.
f Courtesy of Dr. Pauline Austin.
6
. ,-..—-_
...
..
TABLE II
DESCRIPTION
OF SCATTERING
DROP-SIZE
DISTRIBUTION
1 JI
Rain
Rate
The
(mm/lw)
Liquid-Water
Median
Diameter
Content
(gm/m3)
(mm)
No./m3
No.
in
Sample
No.
of
Intervals
1424L
3.25
O.11
16.6
6.0
1.45
3-5
14
1424R
3.65
0.13
28.0
7.3
1.45
52
17
1451L
2.21
0.10
73.7
2.6
0.95
91
11
1451R
3.11
0.13
70.4
5.7
1.05
91
14
1500L
16.33
0.62
155.9
2B.8
1.25
73
16
I
1500R
31,98
1.11
138.3
B2. 1
1.55
77
19
I
1504L
25.59
0.86
120. I
117.9
1.90
51
19
1504R
22.41
0.78
134.3
63.7
1.90
58
18
1507L
11.70
0.40
110.4
50.4
1.s5
61
18
1507R
8.92
0.34
163.7
20.0
1.45
86
15
1509L
3.51
0.14
105.2
5.2
1.25
82
13
1509R
4.51
O.l B
130.2
6.6
1.35
10.5
15
1530L
5.26
0.26
236.8
2.7
0.85
Ill
10
1530R
7.46
0.37
325.6
4.0
0.85
155
10
1552L
7.80
0.37
370.0
6.I
0.95
158
12
379.6
11.0
0.95
I 88
13
10.9
1.25
82
16
7.9
1.15
92
14
60
14
1552R
12.81
0.58
1555L
7.33
0.29
85. I
1555R
7.34
0.29
95.0
:1964
71.2
10.2
1.15
0.33
6B.2
16.8
1.15
1315L
8.11
0.31
1315R
8.84
1322L
107.86
4.25
1959.9
212.B
1.25
1322R
111.45
4.46
2713.3
206.5
1.25
1331L
56.18
2.8B
2706.7
26.9
0.85
1331R
88.84
3.91
215B.4
74.0
1.05
1339L
4.42
0.21
216.8
5.9
0.85
1339R
3.12
O.l B
252.7
1.2
0.65
I
59
14
Ill
18
139
18
146
10
128
12
133
13
159
9
—.—.
IV.
MEASURED
Measured
AND MODELED
drop-size
SCATTERING
distributions
made in New England
variability
of the scattering
parameters
parameters
are calculated
by integrating
observed.
The dielectric
using the Debye
constants
formula8
water
is,
to he expected
required
using the above
recent
Their
measurements
equation
O, O”C,
~
measurements
are needed
tbe differences
indicate
between
to investigate
occurring
over
for the scattering
computations
(Table
rain data.
rainfall.
the range
82).9
the
The
of drop sizes
were
calculated
A drop temperat”m
The index of refraction
of
‘incentimeter’
of the index of refraction
to express
densities
as given in Kerr
using natural
processed
assumptions,
“m
More
were
in naturally
the parameter
with the constants
Of 0.0 “C was used for all computations
liquid
PARAMETERS
that slight
changes
of wa~er ha”e been made by Grant,
in both the form
the index of refraction
the two formulations
frequencies
and dist rib”tions
considered.
frequencies
used and the Laws and Parsons
over
zr-e small,
A comparison
model
and constants
a wide
of the above
range of frequencies,
by less
than 3 percent
of the s tattering
is given in Table
q ~,
parameters
111, Because
At
for the
for the
the differences
TABLE Ii I
cOMPARISON
OF SCATTERING
PARAMETERS FOR REFRACTIVE
INDEX
OF WATER USED AND THAT ATTRIBUTED TO GRANT,
St ~.
(DroD Temoemture:
Cmnputed
O. O°C;
Rain Rate:
12.7
Using Debye Model with Kerr Coefficients
z
eff
Freq uen.y
(G Hz)
mm/hr)
..
“,,
n’
(db$km)
(mm6/m3)
0
N
8.00
7. 47&
-2.7721
0.139
1.55 XIO+4
0.051
0.855
9.35
7.0969
-2.9C60
0.210
1.71
0.065
0.855
15.50
5.7619
-3.0278
0.666
2. O5X1O
0.166
0.831
35.00
3.9533
-2.4301
3.29
8. 19x
10+3
0.424
0. 5s5
70.00
3.0179
-1.6856
5.71
5.63
X 10+2
0.494
0.169
?.
1
Computed Using Data Attrib”t{
800
x 10+4
o Grant,
+4
G%
1764741
-27’~lo
1401’~x
lo+41005’lo856
7.2788
-2.8692
0.213
I.72X
10+4
o. C64
0.857
15.50
5.9459
-3.
0.675
2.0SX
10+4
0.165
0.829
35.00
4.055
-2.5465
3.28
8.30x
10+3
0.430
0.587
70.00
3.0410
-1.8093
5.72
5.68
X 10+2
0.501
0.169
35
@594
8
io
are
small
the Debye
and
reported
model
equation
computations,
The fluctuations
which
depict
giving
approximately
ferent
times
fewer
small
is the result
small
drop sizes.
Scattering
marked
1 -drop
collected
parameters.
drops,
Since
drops
For
parameters
the parent
sampling
distribution
11 and IV).
process
The data also
may be caused
drop
drops.
a fixed
intervals
Roughly,
up to a factor
better
measurements
show that up to a factor
by different
of spatial
giving
curve
is used
sampling
characteristics
strongly
volume
for the Large
for the parent
error
distribution.
may be made by
? July and 26 August
precise
and temporal
in the attenuation
the same
This
may be present
A more
of 5.4 difference
drop distributions
made o“
of 2 difference
The curves
to find the per-unit
vary
rain rate.
for the
if one drop were
for short
of this sampling
coefficient.
of 8.0 GHz.
about the “alue
measurements
of drops
The scattering
parameters
has
for the extremely
occur
paper.
be populated.
di~trib~tiOns
taken at 1552 hours
number
because,
in the integration
an estimate
filter-paper
and the attenuation
requires
of the filter
wide fluctuations
is unknown,
that would
measurement
will
total
content
5
taken at dif-
at 1507 hours
for a frequency
density
the exposure
were
the sample
The large
2 through
raindrop
that the sample
liquid-water
are computed
are emphasized
ca” gi”e
different
model;
at which the scattering
process
reflectivity,
during
sampled
the simultaneous
Tables
rain rate,
large
was used.
in Figs.
distributions
shows
Parsons
of the filter-paper
frequencies
the sampling
considering
(see
and more
only a few of the Larger
of tbe particular
and
of assuming
interval
the coarseness
of refraction
are illustrated
for two basically
give the value of parameter
in a drop-size
to illustrate
times,
locus
size
The number density
drops
distribution
of the index
by Ket-I? have been used for most
Both the measured
well to the Laws
model
reported
with drop
rain rate.
storm.
reasonably
formulation
density
in the parameters
the same
in the same
considerably
this
of parameter
the variations
corresponds
with the constants
%964
in estimating
consideration
raindrop
coefficient
of the
distributions.
at 8.o GEfz
The increase
in this
TABLE IV
EFFECT OF
DISTRIBUTION
DIFFERENCE
ON
SCATTERING
PARAMETERS
Uef.ect:”:
Radio~
(N)
hoi. Rate
%equency
remperat.n
(mm/hr)
(G Hz)
(“c)
L and P
12.7
4.0
0.0
0.017
0.82
0.024
1507L
11.7
4.0
0.0
0.030
0.64
0.047
1552R
12.8
4.0
0.0
0.016
0.86
0.019
12.7
8.o
0.0
0.139
0.86
0.051
1507L
11.7
8.0
0.0
0.278
0.60
0.103
1552R
12.8
8.0
0.0
0.120
0.89
0.041
L and P
12.7
15.5
0.0
0.666
0.83
0.166
1507L
11.7
15.5
0.0
0.910
0.49
0.393
1552R
12.8
15.5
0.0
0.638
0.88
0,129
L and P
12.7
34.84
0.0
3.27
0.59
0.423
1507L
11.7
34.86
0.0
2.05
0.17
0.532
1552R
12.8
34.86
0.0
3.42
0.65
0.413
Distribution
L md
P
~ttenuoti.n
C.effi
(db/’km)
cient
Albeda
(~)
-J
9
number
over the factor
drop distributions.
differences
Again,
An illustration
Figure
the existence
is apparently
of large
of possible
changes
where
2 compares
model.
differences
the rain rates
two individual
Figures
in scattering
measurements
3 through
differences
of a rainstorm
in the rain-
having
locus
afi idea of the limitation
curve
the contribution
gives
to the right of the i -drop
these
basic
the slight
number
4.o-,
8.0-,
curve
coincides
of small
drops
and 34. 86-GHZ
is evident
drops
coefficient
for 4552L
The scattergram
data given
error.
in Figs,
rain,
while the data for the higher
data are presented
of the integrated
from
rain rates
depending
process
from
can lie
drops
and
coefficient
section
at 34.86 GHz.
of 2 higher
for tbe
vs radius
The
than the attenuation
at 34.86 GHz.
i 7(a-h)
show the effect
tend to come
from
the severe
from
of differing
general,
thundershowers.
as low as 0.2 mm/hr.
upon s tattering
1.29 to 94.0 GHz.
scattering
come
can have rain rates
in sections
vary
through
The data for low rain rates
thundershowers
the frequencies
6(a-h)
drops
is a factor
of 2 lower
cross
This
points
of large
density
in Fig. 2.
method.
of attenuation
for 4.0 GFfz and the smaller
for tbe 1507R sample
and sampling
number
The peak of the +xtinetion
at 4,o G13z, and a factor
sizes
from
in the comparison
shown
No measured
great
IV.
with the Laws and
of refraction
sampling
interval.
dis-
5 and Table
density
and tbe model
of the filter-paper
of tbe relatively
frequencies.
with the large
attenuation
coefficient
Tbe effect
by drop-size
2 through
and real index
for the two samples
of one drop in each radius
loci.
caused
number
tbe imaginary
The i -drop
gives
density
parameters
is given in Figs.
of drop-size
5 compare
coefficient
samples
volumes
are the same
and the total scattering
resultant
due to basic
is not certain.
t ribution
Pat-sons
of 2 due to sampling
However,
Tbe scattergram
and rain parameters.
This variation
drop
widespread
in frequency
For
shows
that describable
by Rayleigb
theory
small
compared
with the wavelength
amplitude
is gi”en
each section,
the transition
to that by Mie
theory.
For
Rayleigh
scattering
Rayleigh
scattering,
for drops
occurs
the forward
s tattering
(see
Ref. 4, C h. 6).
by
S(n, a) = ik3a
= iK(ka. )3 . i ~
Kk3V
where
k, K are as defined
a = polarizability
V . volume
This
formula
For larger
1
series
of sphere
of sphere.
holds for the raditm
a<<
spheres,
~
Zmlnl
previomly
smaller
than the wavelength
n = index of refraction
‘
the expression
for the forward
in ka as
S(n,a)
= iK(ka)3
+ ~K2(ka)6
+ ...
to
as
of water
s tattering
amplitude
can be expanded
in a
These
small
particle
ficient
depend only upon the drop volume
is describable
water
content
[Figs.
content
attenuation
coefficient
line for frequencies
departure
has an imaginary
or liquid-water
This
is evident
The departure
is evident
only for frequencies
on liquid-water
content
[Figs.
rams
from
6(a-h)]
shows
Rayleigh
causes
coefficient
the second
the imaginary
from
of 5 percent
term
or less
of the expansion
The scattergrams
theory
for Zeff
of the hacks catter
coincides
a straight
The lower
of the scattering
part of S(a,n).
by Rayleigh
from
is due to K, which
the real part of S(a, n) at a lower
the departure
with the frequency
less
amplitude
frequency
section
in
than
f~(a-h)l
vs Z [Figs.
cross
on
of the
part for frequencies
for calculating
marking
dependence
content.
s tattering
of its real
vs liquid-
The dependence
a departure
of the attenuation
process
of refractivity
a linear
i 0.0 GHz.
coef-
per-unit
of departure
volume
for refrac-
or about iO GHz.
teorological
of the uncertainty
parameter
he used to define
model.
to the Laws and Parsons
the maximum
The distance
the maximum
spread
between
to minimum
and drop temperature
Fig. i 8 for the three
in an estimate
these
possible
used.
as a function
ratio,
of frequent
y, a relative
at 35 GHz,
peak in the uncertain
of 7 times
at 94.0 GHz.
These
maximum
in the spread
between
coefficient
at 5. O-cm
increase
8 (a-h)]
shows
for rain rates
5.4 times,
and in A vs
a Z value
measurement
for rain rates
superior
below
to those
with increasing
greater
based
at i. O-cm
values
show,
at 8.0 GHz,
based
For
at
the uncertain
in A with
y
Z value,
FOr tbe 8.@GHz
in A vs rain rate is
an estimate
on rain rate.
uncertainties
encountered,
the peak uncertainty
and
Z scattergrams
with maximum
The uncertainty
In this region,
of attenuation
(30. O-GHZ) wavelength,
The width of the A vs
of attenuation
in
of attenuation
the other
on rain-rate
based
frequencies,
on
and
measurements
are
on Z measurements.
albedo
to that lost to a wave propagating
to 1, the energy
is mainly
and is available
for multiple
i2(a-h)
and minimum
rain rate.
to that based
estimates
7 (a-h)]
of 5.4 times
Z or rain rate at 8.0 and 9.35 GHz.
is superior
5 mm/hr,
frequency
is plotted
at the higher frequencies
ii
who predicts
with Medhupst
of the frequencies
than 5 mm/hr,
of
attenuation.
y at a factor
at about 10.0 GHz,
most
Z it is 2.0 times.
The single - scattering
[Figs.
For
with increasing
frequency,
a minimum
factor,
A vs rain rate [Figs.
are in accOrd
than i. Ocm.
the ratio
in uncertainty
the maximum
uncertainty
limits.
in A with rain rate increases
decreases
less
a minimum
the low - and high-frequency
however,
res~ts
(6. O-GHZ) wavelength,
for wavelengths
coefficient
can
to the Laws and Parsons
rain rate gives
uncertainty
used to estimate
and a rapid increase
a relative
drawn on the
all the data points
for the drop distributions,
an attenuation
parameters
for a given me-
Curves
with reference
at a constant
coefficient
called
of attenuation
to a value
a rapid
coefficient
curve and including
measured
attenuation
This
meteorological
of i.8 times
model
of the data points
curves
The width of the scattergrams
a minimum
of the attenuation
can be found using the width of the scattergram.
s catterg ram parallel
grams
of the refractivity
above
and attenuation
when the scattering
of liquid-water
This
A measure
[Figs.
content
in the scatterg
as low as i. 3 GHz and high values
that describable
tivity,
show that the refractivity
i 5(a-h)].
show that the frequency
from
theory.
of ka to be important
for calculating
formulas
part of the order
than 15.5 GHz.
powers
scattering
hy Rayleigh
liquid-water
frequency
size
parameter
through
absorbed
through
the ratio
the volume
of drops.
by the drops.
scattering.
i4(a-h)]
w gives
For
w near
The wide spread
shows
over
an order
of the energy
scattered
When u is small
i,
the energy
by drops
compared
is largely
of data points
depicted
of magnitude
uncertainty
scattered
in the scatterat the lowest
frequency
to less than a factor
The data show that most
At the higher
frequencies,
about one-half
V.
is absorbed
the amount
for the higher
of energy
rain rates
frequency
for all rain parameters
by the drops
absorbed
for frequencies
continuously
less
decreased
used.
than 8.0 GHz
to a value
of
at 94.0 GHz.
CONCLUSIONS
The scattergrams
in part,
the scatter
of microwaves
data to estimate
meteorological
be due,
of limited
is due to the natural
model,
refractivity
and effective
of attenuation
agrees
results
coefficient
well with the center
factor
Rayleigh
theory
for frequencies
theory
are,
A vs
of the natural
useful
using the
Z and A vs rain
rain data.
used to calculate
up to about iO GHz,
however,
may
that much of
Computations
maybe
in using
in data points
it is expected
distributions.
scattering
encountered
The scatter
However,
V and shown on the curves
reasonably
reflectivity
results.
sizes.
of the raindrop
in Table
show that Rayleigh
using
show the difficulty
propagation
sample
variation
as given
show that the model
The computed
rain parameters
microwave
to the effects
Laws and Parsons
rate,
of two at the highest
of the energy
the
Computations
only for frequencies
below
about 2.0 GHz,
Comparisons
frequencies
of the attenuation
in the 8.0-
to 9. O-GHZ range
best made using weather
rain rate is best.
urements
weather
best
over
radar
estimation
are extremely
rates
data.
and the higher
For
other
this conclusion
“olmmes
of space.
with meteorological
of attenuation
from
depends
high for the higher
basis
frequency.
for converting
measured
frequencies
i
measurements
data.
and reduce
12
estimates
upon the availability
The scattet’grams
radar
parameters
and rain rates,
these
rainfall
The data further
weather
rain ratm,
frequencies
Currently,
data are the only data available.
and an 8.o-GHz
a reasonable
radar
Howe”er,
large
coefficient
of attenuation
are
of rainfall
of
rate meas-
are not a“ailable
of A vs
Z represent
and
the
in attenuation
of 2 for high rain
show that the Laws and Parsons
data to attenuation
for
a measurement
The uncertainties
to about a factor
show that,
estimates.
model
makes
I
TABLEV
RAIN AND SCATTERINGPARAMETI
[D,..
Te
.,
Rain
Frq
(c
I
I
2.
a.
Po,...
+.,>
z
L
(m.$1
(9./.3)
OR LAWS AND PARSONSMODEL DATA
,1”,., 0. OK)
(mm6/m3)
(dbjm)
Zeff
(mm6/m3)
0.027
102
0.001
0.107
103
0. C@
0.194
0.004
0.809
104
0. C@6
1,51
I.00X
105
0. CQ3
2.36
2.60x
105
0,010
5.45
0.019
5.45x
10’
3.19x
10-5
5.43x101
1.27
0,073
5.63x1
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I.28x
104
5.64x
2,54
0.134
T.55XI03
2.35x
104
(.54x
12.7
0.555
1,47x104
I. O1X1O-3
I.45
25.4
1,04
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1.94X
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50.8
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1. O2X1O5
3.76
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101.6
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6.73
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1.28x
12.7
0,555
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25.4
1.04
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50,8
1.96
1.02
101,6
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5,66
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105
0.012
7,99
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104
5.40x
101
0, C02
0.027
5.55x102
0.035
0.107
10-3
I.51
0.W18
0, 196
6,18x
10-3
1,40x
0.015
0.817
1.26x
10-2
3.68X104
0.020
1.53
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10-2
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0. G-25
2.91
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0,030
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101
0.013
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0.026
0.110
2,08x
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0.034
0.202
1.39x
10-1
1.55x104
0.051
0.855
104
3.24x
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0. C60
1.61
105
7,60x
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1.25x105
0. C69
3.05
0.079
5.81
0.034
8.44
105
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104
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X 10-4
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104
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9,:
10!,6
3.74
2.65
152,4
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2,54
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3.48x
105
2,93x
10°
6.34x105
5.45x101
2.54x
10-3
5.25x
10]
0.017
0,028
0.073
5.63x102
1.42x
10-2
5.50x
d
0.033
0,111
0, 134
1.55x
103
3.15
12.7
0.555
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104
2.09x
25.4
1,04
3.89x
104
4.82
50.8
1.96
I. O2X1O5
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lo”
I.37
101.6
3.74
2.65x
2.53x
10°
3.81
152.4
5.47
4.63x105
4.07x
10*
6.90x
105
105
i3
.
N
0. COOS
0.254
104
.
x IO-2
1.57
x103
0.042
0.203
10-1
1.71
x104
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0.855
0.078
1.60
x105
Owl
3.02
X 105
0.107
5.70
105
0.117
8.26
X 10-1
4.90x
104
TABLEV (C..,; ..ed)
R.:”
Frqumcy
(GHd
15.5
35.0
70.0
94.0
P’=ranwters
Sc.flering
z
L
(m%)
(9m/m3)
zef f
(.m6/m3)
0,254
0.019
5.45X
1.27
0.073
5.63xl#
2.54
0.124
1,55X
12.7
0.555
I,47x
25.4
1.@4
3.89x
50.8
1.96
1.02
101.6
3.74
2.65x
152.4
5.47
4,63x105
0.254
0,019
5.45x
1,27
0.073
2.54
P.m.
(dbjm)
N
(mm6/m3)
8.33x 10-3
5,52
x1O’
0,041
0.028
4.83x 10-2
6.61
X 102
0.080
0.111
103
1.07X !0”1
I.94X
103
0. /04
0.203
104
6.d6 X 10-1
2.@4x
104
o. Idd
0.832
10’
1.45x10°
5.51
X104
0.201
1.53
3.17x10°
1.44
XI05
0,240
2.81
6.83x 10°~
3.70x
105
0.283
5.15
1.MX 101
6,33x
105
0.311
7.34
10’
5.44x IO-2
6.45x
10’
0.182
0,028
5,63x
102
3. 10X 10-’
5,81x1
02
0.291
0.102
0.134
1,55X
103
6.42x 10-’
1.36X103
0.335
0. I 77
12,7
0.555
1.47x104
3.29x !0”
8.18x103
0.423
0.537
25.4
1.04
3,89x
6.40 X10D
1.62x104
0.456
0,950
50.8
1.96
I. O2X1O5
1.21 XI0’
3.03
0,484
1,50
101.6
3.74
2,65x
105
2.23x 101
5.24x
0. 5m
2.33
152.4
5.47
4.63x
105
3.15x 101
6.95
X 104
0.519
3.02
0.254
0.019
5.45x
10’
2.23x 10-’
2.95
x10]
0.?47
0.6-20
1.27
0.073
5,63xld
9.18x 10”1
1.19x1#
0.422
0.053
2.54
0.134
I.55x
I.62x1O”
2. CQX 102
0.45s
0,077
12.7
0,555
l,47xlo4
5.71 X 10°
5.63x1$
0.494
0.169
25.4
1.04
3.89x
9,68x10°
8,43x1
$
0.5%
0.235
50,8
1.96
1.02
1.64x 101
1.29x
103
0.515
0.336
101.6
3.74
2.65x105
2.81x10’
2.11X103
0.322
0.510
152.4
5.47
4.63x105
3,87x 10’
2,34X103
0,526
0.664
0.254
0,019
5,45x
101
1.22x10’
0,419
0,0!9
1.27
0.073
5,63X
v+
3.11 XI O-1
e
1.1OX1O
3.63x10’
0.459
0.020
2,54
0.134
1.55x103
1,83x10*
5,23
0,472
0.041
12.7
0.555
1.47X104
5.95x 10”
1.32x1
0.497
0.078
25.4
1.04
3.89x
9.88 x106
2,04xd
0,505
0.102
50.8
!.96
1.02
1.66X 10’
3.27x
102
0.513
0.139
101.6
3.74
2,65X
2.83x 101
5.49x
1$
0.520
0.205
152,5
5.47
4.63x105
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7.45X12
0,523
0.267
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105
104
103
104
XI05
104
XI05
105
.—
x104
104
x 10’
02
REFERENCES
1.
J.w.
Rydeand
Hail,
Fcg,
Laboratory,
Y
D. Ryde, “Atten.atimIo
and Clouds}
Ldon(
Report No.
fCentimetrea
&570,
ndMillimetre
Electric
T. Oguchi,
“Attenuationof
J. Radio Res. Lab(J.aWn)~,
D. Deirmen~ia”,
“Cmmpfete Microwave
3“
of Polydispersed
Cioud and Rain Elements;
Corp.araticm,
Sa”t.
Moni.o,
S..attering
and Extinction
(December
5.
V. Twersky, “On Scattering of Waves by Random Distributions.
No.4,
700(1962).
Scatterer Fomnolism} J. Math. Phys.3,
6.
K. L.S.
G. D. Kinzer,
Mete.r.l.
J.O.
Am.
8.
P. Debye,
“Pol.arMOle..les,’’C
D.E.
~OP2@iC,”Of
K.s,,,
(McGrMv-Hill,
(Wiley,
AD-426-139.
New York,
heroical
Rain Drop-Size
C&~log
Short Radio Waves,
New York,
19$7),
Ch.9.
1. Free-Space
Draplets
243 (1949).
Lw,vscznd D.A. Parsons, “The Rel.tionof
Ge.phys.
U“ion Trcms. 24, 452(1943).
M. I.T.
Properties
“The Tennincd Velo. ity of Fall fOr Water
Q, No.4,
7.
9.
Sm.lJ Particles
1963),
4.
Nr~J.
Raindrops?
19(1964).
Report No. RAN D-R-422-PR,
California
de Hulst t-—
Light Scatte,ing_by
G“n”a”d
Research
Electromagnetic
Wove Duet.
Rain with Distorted
467(1960);
P.mtll,
J. Radio Res. Lab(J.pan)l_l,
H. C. Va.
i“ Stagna”t
Waves by Rain,
Compmy
1945).
2.
RAND
General
1951),
Company<
Radiation
VOI.
tO Intensity;
New York
Labwatwy
(1929),
Ch.6.
5eries,
13.
Behavicw Of Water
and H. F. Cook, “Dielectric
Chem. Phys. &,
No. 1, 156 (1957).
10.
E. H. Grant, T. J. Buchanan,
at Micr.owcwe Freque.cies,”J.
Il.
R. G. Medhurst,
‘Rainfall Atten..ation of Centimeter Wave=
Comparison of Thewy
550 (1965).
and Measurement,’
lEEE Trans. Antennas Prop.~.
.-—. AP-13, No.4,
i
15
—.——.——
. . . -----
..%,.-.—-
*-
“M!s!!l
\
Fig.
1.
DrOp-size
(curves labeled
I
distribution
for Lawsa.d
with rain rate in mmhr).
Parsons model
t
,..3
5Fig. 2. Ccm?parison of measured and mcdeled drop
distributions,
number density (No. /cm3, cm).
~
:
!0-,
1
‘“-’i
!0-’
DROP
RADIUS
IcI”)
!0
+
:
LAWS ANO PARSONS, 12.7
%:
,~
../h,
M% }1‘“” “64
/
.Gcw,.oy.
m
A“A /’.,
~cu,,552,,
A
A
Fig. 3. Ccmprison
of measured and mcdeled drop
distributions,
imaginary index of refraction
denFrequency
sily (n’’/cm).
perature = O. O°C.
,3”
A“
. ./Ir/
/
...
,NTEGRATED
ATTEN”&T#ON
, = 0., ?.8 (Law.
!,
c9,FF,C(ENT
.nd
. 0.278
( ! 507R1
.0.120
11552L1
1
m
t
0.2
1
0.!
DROP RADIUS
[..
(Wk.)
P.r’o”sl
!
17
,,
= 8.0
GHz;
drop tem-
:*
,0-
1
+
LAWS AND PARSONS, 1?.5 mm/hr
:
M
::%}’
‘“L’
mz!m
‘“4
A
Fig. 4. COmpariscm of measured and modeled drop
real index of refraction
density
Frequency = 8,0 GHz; drOptem-
distributions,
[(”’ –l)/cm].
pemture
= O. O“C.
.
,,..
I
INTEGRATED
N .0..47
RADIo
(L...
R, FRACTIV IT”
md
= 0.593
[ 1507R)
= 0,S91
(1552L)
Pwmnsl
,.-~
DROP RADIUS
(.”!1
F
,.-’ .
/
A
/’
f-m., m,”,,, ,,,
,,
; to-’.
:
Fig.5.
Comparison ofmeas.red
dropdistributicms,
siy (p~cOt/cm).
temperature = O. O°C.
.“:
andmdeled
scattering coefficientdenFrequency =8. OGHz; drop
{
~~
.
/
,..,
.
P
11
f
/.
.“
/
L
INTEGRATED
SCATTERING
COEFFICIENT
D-d=,.64 . 10-” (Law...d P.,.. ”.)
/
= 6.62
xl.-’
=1.14
x!&(!S52Ll
!o-~
m.,
....
Rb.o,”$
1<”7)
(1507R1
.
1
1
I Iii
1
I
1
1
I
,.
1
l!~l
.,,
0..!
LIOU! O-WATER
(a)
Fig, 6(a-h).
Attenuation
coet%cient
Frequency:
CC2.TCNT
,,./.3)
1.29
GHz.
A vs I iquid water
content
L.
Drop temperature
= O. O“C,
?,TTEN”AT,ON
3,
s,
cOEFFICIENT
[dbtk-.l
s
:.
ATTENUATION
COEFFICIENT
6,
Mb/km)
L(o” IO-WATER
(e)
Frequency:
CONTENT
15.5
1,./.’)
GHz.
!0-,
UW!D-WATER
(f)
CONTENT
Frequency:
Fig. 6.
35.0
Continued.
Z*
1,./.’ i
GHz.
-
,..,
(g)
.-
L8Q” ID- W.?TE.
CoM,EN,
Frequency:
70.0
,,.,.31
G&.
1
,,::
I
,d
4
1
1
i
r
1
111(1
I
1
1
..:
. .
, .< .,
.
. .:.
”
. ?.”
,. ~;
. .. .:
,... ..\,:
7
.,:&?$ . .
.
.
. .%:
.
.. .
..
. .
u
f
II
I
1:
1:
1(1!
L, O”(O- WATER CONTENT
(h)
Frequency:
Fig. 6.
94.0
Continued.
I
22
1.
(,./.31
G&.
..
(a)
!.-,
I II
[ ,
I
I
Frequency:
1.29
+1 x
.,.
I
1111
x?
I .
1
1 ,,!
/f
!.
!0-.
GHz.
‘
i
!],
i
,
I
1
i
I
7,,
7
,
,
,.?
(b)
Fig. 7(a-h).
Attenuation
Frequenc~
coefficient
2.80
GHz.
A vs rain rate
23
R.
Drop ternpemture
= O. O“C.
,.-3
“
. . .. ..
. .
.
I
III
............
.... ~ ,:,-1 A444N
,0
!.”
..4.
(c)
RATE [r”r”/hrl
Frequency:
8.0
GHz.
.
RAIN
(d)
RbTE
Frequency:
Fig. 7.
(mm/hrl
9.35
Continued.
24
GHz.
!0”
,.,.
(e)
(../,,1
RATE
Frequency:
I
11111
‘-,~lill
15.5
GHz.
!
Ilillll
I
Illllil
!
1.,
1
I
I I 111111
,.
.?,(.
(f)
RATE
Frequency:
Fig. 7.
(..AY)
35.0
G1-k.
Continued.
25
—
—.
——-..—.
.—
,.,
1
1
1
,
[ 1 1111
1
I
I
,0,
,0RAIN ,...
(g)
Frequency:
{.,”/,,
70.0
)
GHz,
,.,
,..,
1d
R.,.
(h)
RATE (m./hrl
Frequency:
fig.
7.
94.0
Cmtinued.
26
GHz.
!.$
,0-
,.-
,.,
,o?
!.,
z
(a)
Frequency:
z
(b)
Fig. 8(a-h).
Attenuation
coefficient
,0.
MEASURED
1.29
Gt!z.
MEASURED
Frequency:
2.8o
A vs reflectivity
27
Gt!z.
factor
Z.
Drop temperature
= O.o”c.
I
r—
““1
.
!.’
4.3
%
(c)
,.-,
‘ENURED
Frequency:
d
,d
“
8.0
(d)
GHz.
,0.
MEMURED
Frequency:
Fig. 8.
9.35
Continued.
28
“z
$.8
2.” ‘Hz
!d
z
u
GHz.
,d
(e)
,.,
Frequency:
GHz.
‘0,
!d
z
(f)
15.5
Frequency
Fig. 8.
,..
.,.$”.6,
35.0
Continued.
29
GHz.
!o~
-
--------
1
+“”--++-/
,,,
,,, I
I
13EEL +———
--1
I /.
MWSANOPARSONS
MODEL+&
!J
—
—
—
I
I
.,
I
I
I
I
1
I
_..
,~,
Tw++-
,0
(g)
z
MEM”RED
Freq.enc~
70.0
GHz.
,.,
(h)
z
ME.S”WO
Frequencfi
94.0
fig.
8.
Continued.
30
GHz.
.!.,,
,
I
I
!
‘ :V’y
. .. .
.“
.,
.
.. . .
..
.
0.,
0.0!
CONTENT
(,./.’1
L, W, BW,TER
Fw
. . ..y.
(o)
1.29 G*.
,..
10.
J
1d
,d
(d
..’
0.0,
UW,..WA,
(b)
Fig. 9(a-h).
Effective
reflectivity
E.
Frequency:
Factor Zeff
CONTENT
1,./.’1
2.80
GHz.
vs I iq.id-wt-
. ..te.t
L.
D,cjp tempemtwe
= O. O“C.
!
—
I
I
1!!!!
,d
!..
1 .
UO”KJ -WATER
(c)
Frequency:
CONTENT
. 1111
10./.’1
8. OGHZ.
,d
..!
0,0!
L, O,, D. WA,E,
(a)
rreq”ency:
Fig. 9.
CONTENT
9.35
GHZ.
Continued.
32
(,./.’1
1
d
,d
j
d
,.$
d
. ..
...>
LIO” IO-WATER
(e)
1,./.31
CONTENT
Frequency:
15,5
GHz.
! 0.
!.,
.,
“.:0
,
..!
L, O., D-WNER
(f)
CONTENT
Frequency:
Fig. 9.
35. oGHz.
Continued.
33
(g./.’)
.~<
~
I
!,,
Ill
Ill
I
1
I 111111I I
I
I
,.,
M
I ..
I
.
.
111111.
,
,d
0.’
..0 t
LIQIJO-W
ATE.
(g)
Frequency:
II
I
I
I I 11.1
II
I
I
1.4 Hil? . . ... .
l!!.
I
I I I [1111
I
I
Iii
CONTENT
,,.,.S,
70. OGI-!2.
.
1 I I 11111
I Ill
..0,
. ..
L,.”,0-W,ER
(h)
cONTENT
Frequency:
Fig.9.
(,.,.3)
94. OGF!z.
Ccmti.ued.
34
..
,...
I
I
HtH
I .[
. ..v
.. .
,
,.
t
d
I .“ 1111111
1
I
!
I II
,.,
,.-,
,d
RAIN
(.)
,.,
.QATE (“).,,,1
Frequencn
1.29
GHz.
-imEl
!
J
1
!
1
1
!
1 1 1111
I
1
r 1
1
1
[X
1
IIIT
t.
t
1
$
1 Il+li
I
,.2
,0
Effective
1
1
4.’
40
(b)
10(a-h).
1
Ii.
,.-,
m,.
Fig.
1
reflectivity
,,,6
(mm/”r)
Frequency: 2.80 GHz.
facfor
Zeffvsminmte
35
R.
Drop temperature = O.O°C.
.3.
%
.
,0,
d
N
d
d
d
.
,.
..!
.
m,.
(e)
Frequency
15.5
“~
‘-
RATE [..,,<)
,*
GHz.
4..
]ili
11-
..
,.,
=M##b
,,.,.. ”1 11111111
I 11111111
I 11111111
!.,.,
R?.,.
(f)
RATE
Frequency:
Fig. 10.
[mm!,.)
35.0
G*
Continued.
37
RAIN
(g)
1
I
1 1 !(
Frequency
!
I
GHz.
,
II
,,, ,
I
70.0
I 111111
,
I I
1 1
I
I
1
(11
11111
r
I II
! of
(h)
1 [1
, .!
RATE [..,,,1
Frequency:
Fig. 10.
1
Hilt
,0-’
RAIN
.
‘-
RATE (..,bd
94.0
GHz.
Continued.
38
“---m
___—.,..
—w.
,,...
=..
,04
I
‘[i
,j
,d
,,=
!J
(a)
Frequency:
1.29 GHz.
(b)
Frequency:
2.80
,d
d
d
1
4
Fig. 11 (a-h).
Effective
reflectivity
factor
Zeff
GHz.
VS reflectivity
39
f..fo,
Z.
Drop fempe,ot.re
=, O.o”c.
m’
{.?’
:
~40’
{0’
(c)
d
Frequency:
,0,
z
(d)
II.
GHz.
1d
14E.*”R,L!
Frequency
fig.
8.0
9.25
,..
GF!z.
Continued.
40
40,
(e)
Frequency:
15.5
GHz.
,,,
,d
,.?
,.,
z
(f)
Freqwency:
Fig.
11.
,.,
MEAS”REO
35.0
GHz.
Continued.
41
,.,
1
,.,
! 0,
,0.
.
70.0
Frequency:
!d
4.+
Frequency:
Fig. 11.
GHz.
,d
!.,
z mf,surlm
(h)
,0,
,0.
MC. s”, m
94.0
,.’
GHz.
C.nfinwed.
42
——J
-—.
● ✎ ✎✎✎☞
-
!
,.
“-
,..
.
.$
.
.
....t .....j+...
.—
“ :., ‘., .
_._...+
,..
‘,.+-
+i..+.+
}:
+ , ,.,_\.~
;-
‘w
m
;-144+
Ammo
m
-.,:....
S,NOLE-SCATTERING
.~l--l-
! “!!k!!.” “..
....
. ..
UQU,D -WATER
(c)
.,0 !
CONTENT
Frequency
8.0
(Q.,.>,
GHz.
0.,
u.2”,0-wATER
(d)
02”,,.,
Frequency:
Fig. 12.
9.35
(9,”,,”s)
GHz.
Continued.
44
-%--
--
-.....-.—.
.,
..04
LIou,
(e)
o-w.,m
CONTENT
15.5
Frequency:
(9.,.3
G Hz.
0.!
L8.”(D-w.4TER
CON,ENT
(f)
FrequencV
Fig. 12.
35.0
C-mfinued.
45
(g.,.>,
G%.
,
1
0
..:
... .
UQ”, C- W,TE.
(,.,.’)
CONTENT
(d Frequency: 70.0 G1-k.
..1.1”......i.1. ..
.. . . .
‘...-.,’
,..
*
-. .1.,
.
: :
,.$,
Ill ‘“
. ..
LIO”,.
(h)
-WAT..
CONTENT
Frequency,
Fig. 12.
94. OGti.
Continued.
46
(,.,,”3)
I
,.-.
,,,
,,
!
,,,
,,,
!
,,,
.
f
$
1
) .:, I
:
I I
IJ
i
III
.
,)
.
i.}:
. ..
k:
[11~
--nTti
.,
I 1.,,-,.:.
:,..!,
I
1~1.
.. .
.
,,.;
—
~M-tt;:l
1- ------+
(0)
.
I
.
I
,~.z
I
2.
.
Frequency:
GHz,
I,,,
Ill
I Illilll
I
1.29
1 ..
,
I.
I-,
—--+
’.JI.
1 i (u
-.
I
I
5
<
1.11
{11.1
!
%iwk
.
:
+-,.,
,!.,
!lli~l{ .
‘“-33!#L..-....l
M=
.,4
.,
. . .
.!..
,.
–
,..
!
I ;., ii+ll-...l~.... .....i
,
R*CN
RATE
d
!
d
(../),,)
.
(b)
Fig. 13(a-h).
Single-scatteri.g
Frequency:
albedo
2.80
u vsroin
47
GHz.
rate
R.
Drop tempemture
= O. O°C.
i
I
1 1 1111
(
1
i
1.
I
III*
I
I... , bjllll
. .. .
... ..
.
.
“.
““.‘I;”’.I’-:HL1L1Il.
,!
“+4
,.-,
.?.,, mm
+–-4W
(m./tic1
(c) Frequency: 8. OGHZ.
,..
!
,
RN.
(d)
..,,
Frequency:
Fig. 13.
[../,,
9.35
GHZ.
Continued.
48
d
)
!d
T2mL
,
“f
:0
..
,#,$
(e)
!0,
,.,,
,.,,
Frequency,
,d
,../,,,
15.5
GHz.
-T
,d
,.,.
(f)
,.,,
Frequency:
Fig. 13.
(“,./
35.0
G
Continued.
49
”,,
HZ.
,d
.
—
—
.
—
,,-,
(g)
T!E
Frequency:
70.0
GHz.
—
0., --+
. ..
,,
,.
.:”,
. .
.“..
.. .
—
..3 —
F!.(N
(h)
RATE (../,.
Frequency:
Fig. 13.
94.0
)
GHz.
Continued.
50
I
d
,d
(b)
Fig. 14(a-h).
Single-scattering
,0.
,0,
z
Frequency:
a!bedo
,.,
14EA$”RELI
2.80
u w reflectivity
5i
GHz.
factor
Z.
Drop temperature
= o.o”c.
,.,
!.,
!.,
z
(.)
,..
!46,
Frequency:
!#
s”.,0
8.0
GHz.
!1
TIE
—
z .,.,
(d)
Frequency:
Fig. 14.
”.,0
9.35
GHz.
Continued.
52
r
,.,
(e)
Frequency:
15.5
GHz,
-L
,0,
(f)
Frequency:
Fig. 14.
35. OGHZ.
Continued.
,., -
z kASUREO
Frequency,
70. OGHZ.
1
z
(h)
ME
A*”.,,
Freque.cfi
fig.
14.
94. o G~.
C.ntin.ed.
54
‘“l
4.-’
!.-,
L!o”, o-w.,ER
(a)
CONTENT
FrequencV
1.29
(,./.31
Gti.
.
!.-
U.”,l
-WATER
CONTENT
@) Frequency:
Fig. 15(.-h).
Radio refractivity
N vs I iq.id-water
55
u
[,.,.”’)
2.80 Gt!z.
content
L.
Drop temperature
= O. O“C.
-
,..
.
! o-
co. rmr
L, Qu,o-wATE.
(c)
Frequency:
8.0
I,r”/m’]
GHz.
,..,
UO”, O -WATER
(d)
Frequency:
Fig. 15.
(,./.’1
CONTENT
9.35
GHz.
Continued.
56
. .. ... ..
,.-=
!O-f
w2”,D-w
ATER
(e)
CONTENT
(red]
15.5
GHz.
Frequency:
,..,
,(ou,D-wATER
CONTENT
(,.,.31
,0-,
(f)
Frequency
Fig. 15.
35. OGHZ.
Continued.
57
il.
,.-,
‘o-~
uQLuO
-WATER
CONTENT
l,m,m’)
(g)
,..,
1
d.,
Frequency:
70.0
..
Gtlz.
.
r u..
JILuuMl
,..,
,~.,
L, O”, D-WATER
(h) Frequency:
Fig. 15.
94.0
Gttz.
Continued.
58
““”l
(m/m’1
CONTENT
,
1
,.8.
(a)
RATS
FrequencV
(.. /h.)
1.29
GHz.
—
-TEE
——.—.L—
I
‘ “=4=
,.,
.,,)4
(b)
Fig. 16(a-h).
Radio refractivity
RATE
Frequency:
(.m/hrl
2.80
N vs rain rate
59
GHz.
R.
Drop temperature
= O. O°C.
T
,.,,
‘9
3
.
?
.
fd
1.-,
,,,,
(c)
,,,,
,d
,mm/*r)
Frequency:
8.0
GHz.
,.-,
. .
I
I
I +11111
I
I
! I 1 [111
I
1 1 1 111!!
1
1 1 1
11111
!.,
RAIN
(d)
m,,
Frequency:
Fig. 16.
(.,”/,,,
9.35
GHz.
Continued.
60
.
I
I I Ill
1
I
1
1 Ill
1.11111111
I 11111111
I 111[11
,.-,
...
I
,.,
.
,0-
(e)
.
,
,
I
I
Frequency:
I I
I
15.5
I
GHz.
I“li%’n
....
. I II
I
111111
mm
(f)
RATE
Frequency:
Fig. 16.
I
I 1111
I
( ../,.1
35.0
GHz,
Continued.
..-~
i
I 1111111
1
1 1 I 1! 111
,.-,
RAIN
(g)
RATE ,“,./,,,
Frequency:
,.-,
70.0
GHz.
4
.
,..
!
I
I
I
1
111111
(h)
I
Frequency:
Fig. 16.
C.ntin.4.
62
‘-l
94.0
GHz.
I
!
..
‘“-’4
=?=
[
d
1.+
,d
,0+
,.3,
Z MEASURED
(a)
Freq.e.cy:
1.29
GHz.
.
,o-
!
,.,
1.+
(b)
Fig. 17(a-h).
Radio refractivity
40.
,.,
,
,.,
Irasu.r”
Frequency:
N w reflectivity
63
2.80
GHz.
factor
Z,
Drop tempemture
= O. O°C.
.
..
:TI
3
I
‘4
!
d
!
d
,J
z
(c)
.E.
! .3.
s”lwo
8.0
Frequency:
GHz,
.
,0
d
,0,
,.’
z
(d)
,..
.,0
!4,.$”
Frequency:
Fig. 17.
9.35
Gi-k.
Continued.
64
,.,
.
,..
z
(e)
!d
MEASURED
Frequency:
GHz.
,d
,.,
z
(f)
15.5
‘
WAS”REO
35.0
Frequency:
GHz.
Fig. 17. Continued,
65
0.
z
(g)
Frequencfi
70.0
Gliz,
,.
/.
z
MEASURED
(h) Frequency:
Fig. i 7.
94.0
GHz.
Cont;nued.
66
q—...—
lEmzcL
NEW
OROP
DIsTRIBUTIONS
TEMPERATURE
= O.O-C
ENWANO
DROP
hTTEN”A;
,ONCOEFFICIENT
G,VEN
UQ”,D-WATER
CONTENT
d
!
1
,0
1
,.s0
FREQUENCY
Fig. 18.
Attenuation
uncertainty
factor
calculated
67
(G!+?)
using Laws and Parsons mOdel os reference.
. . . . .... . .. . . .. .. . . . ..
DOCUMENT
<S...,,,,
,.
cl...,
0.1.,..,,
!4.
AC,
fe,,,m.m
!,,,,
.,
,1,1.,
(C.rp.,.t.
bed,
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abstract
and
CONTROL
indexing
DATA
mn.t.t,on
m.,,
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R&D
M
en,.r.d
author)
when
2..
REPORT
2b.
GROUP
the
ov.rmll
raw,,
5ECURITY
,.
.Iassift.d)
CL AS.S, F, CATION
Unclassified
Lincoln Laboratory,
M. 1. T.
Ncme
,. ,.,0.,
TITLE
Microwave Scattering Parameters
,. 0~,.,lP,,vE
.0,~3 (Tw.e 01rwort and
Technical Report
,, ,.,.0.1s]
?“.l”
.;”.
date.)
(L...: name,[!,.1 “m% l“lfl al>
Crane,
,. ..,0..
for New England Rain
Robert K.
..,.
30ctober
7..
,..
NO.
OF
PAGES
7b.
NO.
OR, GIN ATOR,
Q,. . . . . .
. .
..si@.d
S REPORT
REF$
NUMBER(S)
Report
REPORT
this
OF
11
Technical
649L
426
Nom
(A.r.lher.mb.r.
lh.t.w’
r.J=orf)
ESD-TR-66-447
d.
LA81,, T,(L, ~,,,
Distribution
t. s“,,
NO.
72
).. CONTRACTOR OR ANT
AF 19(628)-5167
,, ..0, ,.,
NO.
1. ,V.l
TOTAL
1966
T10.
~OT,CSS
of this document
is unlimited.
,2.
LEMENr ARr NOTES
s,..,.,,..
Air Force
N.”,
M,. !,,.,
AC, [”ITY
Systems
Command,
USAF
,. ABSTRACT
Scatcergrams
of attenuation
coefficient,
effective reflectivity
faccor, single-scatteri”g
albedo,
and radio refractivityvs
liquid-water
content, rain rate, and reflectivity
factor arepresenced
fora
raindrop temperature
of O. O°C and frequencies
of 1.29, 2.80, 8.0, 9.35, 15.5, 35.0, 70.0, and
94. OGHZ. The scattergrams
were computed using Mie theory to compute the scattering
parameters
for single raindrops,
and single-scattering
theory to compute the integrated
scattering
effects of an
ensemble of mimirops.
Measured drop-size
distributions
were used to generate the scattergr.ams.
,. K,,
WORDS
atten.a. ticm
rain
reflectivity
scattering
refractivity
Mie theory
68
UNCLASSIFIED
Security Classification
b.