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JPL PUBLICATION 81-46 "_
Microwave Noise Temperatureand Attenuation of Clouds atFrequencies Below 50 GHz
Stephen D. Slobin
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_REQUENCI_S bELOW 50 GHz (Jet
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July 1, 1981
National Aeronautics andSpace Administration
Jet Propulldon LaboratoryCalifornia Institute of TechnologyPasa0ena, California
https://ntrs.nasa.gov/search.jsp?R=19810021789 2018-09-18T19:34:08+00:00Z
JPL PUBLICATION 81-46
Microwave Noise Temperatureand Attenuation of Clouds atFrequencies Below 50 GHz
Stephen D. Slobin
July 1, 1981
National Aeronautics and
Space Administration
Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California
The research described in this pub!ication was carried out by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the NationalAeronautics and Space Administration.
ABSTRACT
The microwave attenuation and noise temperature effects of clouds can re-
sult in serious degradation of telecommunications link performance, especially
for low-noise systems presently used in deep-space communications. Although
cloud effects are generally less than rain effects, the frequent presence of
clouds will cause some amount of link degradation a large portion of the time.
This report presents a general review of cloud types, water particle
densities, radiative transfer, attenuation and noise temperature calculations,
and examples of basic link signal-to-noise ratio calculations. The results of
calculations for twelve different cloud models are presented for frequencies of
from l to 50 GHz and elevation angles of 30-degrees and 90-degrees. These case
results may be used as a handbook to predict noise temperature and attenuation
values for known or forecast cloud conditions.
Ill
lJ
II.
Ill.
IV.
CONTENTS
ABSTRACT .............................iii
INTRODUCTION .......• . vii
o•oo•ooeeoooeeoee•
• . 1CLOUD DESCRIPTIONS .......................
gABSORPTION AND SCATTERING EFFECTS .................
EQUATION OF RADIATIVE TRANSFER .................. 13
SAMPLE CASE CALCULATIONS OF CLOUD ATTENUATION
AND NOISE TEMPERATURE ......................21
33REFERENCES .............................
APPENDIX: SAMPLE CASE CALCULATIONS OF CLOUD ATTENUATION AND....... 37
NOISE TEMPERATURE ..........
I.
2.
3.
2Model Cloud Drop Spectra ......................
Elements of Radiative Transfer Equation .............. 14
24Cloud and Clear Air Models .....................
Tables
I.
2
3.
4.
5.
6.
7.
8.
• . • 3Model Cloud Drop Size and Concentration ...........
Summary of Cloud Model Densities and Average Radii ......... 4
6Cloud Models Used in Reference 5 .................
• • • • • • • • • 8
Typical Fog and Cloud Models .........
One-Way Attenuation Coefficient, KI, in Clouds, dB/km/g/m 3 ..... II
Sample Cloud Models and S-, X-, KA-Band Zenith Effects ....... 25
27Profiles Used in Cloud Calculations ................
"Worst Cloud" Test Case of Integration Step Size .......... 32
_,H&C._5_?._I,I_PAGE. LL;..',"i !,,_"t, r_J-"E,.,
V
INTRODUCTION
Microwave propagation through the earth's atmosphere is affected
adversely by the presence of rain and clouds. As communications systems operate
at higher and higher frequencies (greater than 30 GHz), attenuation and noise
t_nperature effects become increasingly severe. Although rain effects are
generally greater than those of clouds, rain occurs less than about five-percent
of the time. Clouds, on the other hand, may be present fifty-percent of the
time as a yearly-average or continuously for periods of weeks on end. Thus,
the integrated cloud effects (dB-hours or Kelvin-hours) may be much larger than
those for rain.
Compared to rain studies, little has been done to characterize the
statistics of cloud effects. Clearly, the best method of determining noise
temperature statistics is to go out and measure noise temperature! Lacking the
resources and equipment to do this, an alternative method is to draw upon the
vast amount of historical weather data (surface observations, radiosonde
profiles, pilot reports, etc.) and turn this real weather data into estimates of
noise temperature and attenuation. To this end, a cloud model and computational
schBne have been developed to calculate attenuation and noise temperature using
real weather observations as program inputs. Forecasts of real weather
parameters can also be used to give forecasted cloud effects, using this model.
This report presents a general discussion of c|oud characteristics and
the computational model. Sample case calculations for twelve specific cloud
cases are given for a frequency range of i to 50 GHz. Future work will involve
calculation of cloud effect statistics based on real weather observations at
numerous locations throughout the United States.
I. CLOUD DESCRIPTIONS
A cloud may be described as a random distribution of liquid water
particles above the ground having diameters of from 0 to lO0 microns (um).
For comparison, raindrops have a size distribution of approximate]y
100 microns (0.1 mm) to 3 mm (Refs. I and 2). Rare cases will be found where
particle sizes will be outside the ranges stated. Clouds are not water vapor,,
which is a clear, colorless ag_as, like oxygen and nitrogen, although the
relative humidity is usually 100% within the cloud. Clouds can exist at high
temperatures (+20°C) as well as at temperatures below freezing (-IO°C) where
they remain liquid (supercooled) and pose a great icing threat to aircraft
penetrating them. High-level clouds, such as cirrus, are composed of ice
crystals and will not generally be found at temperatures above -12°C. (Ref. 2)
Figure 1 (Ref. 3) and Table 1 (Ref. 3) show typical model cloud drop
spectra for different cloud types. These spectra may be integrated over the
range of cloud drop radii (~0 to 30 microns) to determine the average cloud
density and average drop diameter for the various cloud types. Table 2 gives
the results of these calculations for the cloud types of Ref. 3.
in Figure | are for illustrative purposes only.
The spectra
120
I00
O0
60
4O
20
0
"f T
STRATUSI (TYPICAL)
RADIUS, MICRONS
3O
FIGURE I. MODEL CLOUD DROP SPECTRA
(after Carrler, et al, Ref. 3)
emil
TABLE I. MODEL CLOUD DROP SIZE AND
CONCENTRATION
(after Carrier, et al, Ref. 3)
CLQUD TYPE
Stratus I
A1tostratus
Stratocumu 1lJs
Nimbostratus
Fa ir-weather cumul us
Stratus II
Cumulus congestus
Cumul oni mbus
450
35O
330
300
260
207
72
3.5
4.5
3.5
3.5
3.5
4.5
3.5
5.0
L
= total concentration, no./cm3
rmi n rma x Ar
0
0
0
0.5
0
0
0
rmode = radius corresponding to the maximumnumber of droplets, microns
16.0
13.0
11.2
19.8
10.0
20.0
I 16.2
3.0
4.5
4.4
9.5
3.0
5.7
6.7
7.0
rmin = minimum radius, microns
rmax = maximum radius, microns
ar . bandwidth of the drop-size distributionat half-value points, microns
TABLE 2
SUMMARY OF CLOUD MODEL DENSITIES AND AVERAGE RADII
4
5
6
CLOUD TYPE
STRATUS I
STRATOCUMULUS
FAIR-WEATHER
CUMULUS
STRATUS II
CUMULONIMBUS
CUMULUS
CONGESTUS
NIMBOSTRATUS
ALTOSTRATUS
CONCENTRATIONI
(no/cm3)
464
350
300
260
72
207
330
450
DENSITY
(g/m3)
0.27
0.16
0.!5
0.49
0.98
0.67
0.99
0.46
AVERAGE RADIUS
(microns)
5.2
4.8
4.9
7.6
14.8
9.2
9.0
6.2
4
The stratus I cloud is based on observations taken off the coast of
California. Stratus II is found over land. The altostratus and
stratocumulus clouds observed had bases approximately 2000 meters above
ground and tops up to 4000 meters above ground, with a typical thickness of
1800 meters. For reference, the standard temperature at 4000 meters above sea
level is about -5°C. It is suggested in Ref. 2 that the drop size spectra
for nimbostratus and fair-weather cumulus be used for altocumulus clouds.
A standard pictorial listing of cloud types is given in the U.S. National
Weather Service Cloud Code Chart (Ref. 4). The clouds portrayed on the chart
conform to the standard types approved by the World Meteorological
Organization and serve as a common point of reference for use in cloud
observations and predictions.
Although Table 2 shows cloud densities of less than 1 g/m3, several
investigators (Ref. 2) have observed cloud densities of up to 10 g/m3.
Convective type clouds (cumulus, cumulonimbus) in the sumner have unaximum
water contents of 3 (cumulus humilis) to 10 (cumulonimbus) g/m 3, although
for clouds with large vertical development (cumulonimbus exceeding 10 km in
height), there is some question as to the relative proportions of actual cloud
particles and suspended precipitation particles.
Four cloud models used by other investigators (Ref. 5) are summarized
in Table 3. These models are consistent with descriptions above, except in
the case of altostratus clouds.
TABLE3
CLOUD MODELS USED IN REFERENCE 5
TYPE
BASES*
TOPS*
WATERDENSITY
MODEL I
COASTALSTRATUS
O. 500 km
i. 030 km
O. 33 g/m 3
MODEL 2
STRATO-CUMULUS
!.GO0 km
2.000 km
0.33 g/m 3
MODEL 3
STRAIO-CUMULUS
1.000 km
2.500 km
0.20 g/m 3
MODEL 4
ALTO-STRATUS
2.500 km
4.500 km
0,15 g/m 3
*above ground level
6
Table 4 (Ref. 6) gives typical fog and cloud models which are
representative of midlatitude conditions. This table is of particular
interest because of its listing of cloud bottom and top heights.
The term "precipitable water" is used to describe the total amount of
water thro,,gh which one looks along a path through the entire atmosphere.
!_recipiLable water has the units %/cm2, or simply cm (i.e., I cm3 of water
we!ghs I g.). For a cloud with a density of i g/m 3, i km thick, the
precipitable wateF (vertically) is 0.I g/cm 2 or 0.i cm. By comparison, a
t vplcal val,_e of preci_itable water vapor is 1.5 g/cm 2 along a vertical path
through the entire atmosphere.
TABLE 4. TYPICAL FOG AND CLOUD MODELS
(Ref. 6)
Cloud Type
Heavy Fog 1
Heavy Fog 2
Moderate Fog 1
Moderate Fog 2
Cumulus
Al tostratus
Stratocumulus
Nimbostratus
Stratus
Stratus
Stratus-
Stratocumulus
Stratocumulus
Nimbostratus
Cumulus-
Cumulus Congestus
_psi_Y HeightBSottomab°ve gr°unTo_(m)
0.37 0 150
0.19 0 150
0.06 0 75
0.02 0 75
1.00 660 2700
0.41 2400 2900
0.55 660 1320
0.61 160 1000
0.42 160 660
0.29 330 1000
0.15 660 2000
0.30 160 660
0.65 660 2700
0.57 660 3400
I[. ABSORPTION AND SCATTERING EFFECTS
The total attenuation (or extinction) of a radio wave by a cloud is tile
sum of the absorption and scattering by particles in the cloud. Absorption of
microwave enerLjy by a cloud particle heats it up slightly, and it then
re-radiates isotropically (eq_lally in all directi,)ns)with an er_lissivity
less than 1.0 at its particular physical temperature. Scattering results in
a re-direction of the incident energy so that it does not arrive at its
"straight line" destination. Scattering in certain directions is enhanced
depending on the wavelength of incident energy, particle size distribution,
and dielectric constant of the scattering particles. Scattering _y be
advantageous for some applications, such as in troposcatter communication
systems.
The absorbed energy is lost and does not contribute to the noise
temperature (power) received by a radiometer. The absorbing medium itself
does radiate power into tile receiver and contributes to tile total system noise
temperature. This is discussed further in Sections Ill and IV.
A good general description of scattering by water and ice particles
is found in Battan (Ref. 7), who draws on the original work of Mie (Ref. 8).
A detailed discussion of scattering theory is beyond tile scope of this
survey article, but for the case of microwave radiation (i to 50 GHz for
coi(mlunications bands) and cloud particles (diameters i to I00 microns)
certain computational simplifications become possible.
A common parameter used in scattering calculations is
: 2.a/_
where a = drop radius
),= wavelength of incident radiation
For the case _<<I, the scattered component of the incident radiation
is small compared to the absorptive component; and the total attenuation
(extinction) is due to absorption. For the shortest wavelength (0.6 cm for
50 GHz) and the largest cloud drop diameter (100 microns), _ = 0.052, which
satifies the relationship _<<I. Using the cloud drop spectrum suggested by
Diermendjian (Ref. 9), Dutton and Doughertv (Ref. 10) make the argument that
even for frequencies as high as 350 GHz(_ : 0.086 cm) "Rayleigh" approximations
are valid (see Battan, Ref. 7) and extinction of ii1icrowaveener_Lv is almost
entirely due to absorption.
The attenuation of cloud drops is given by (Ref. 7, Eqn. 6.14):
: r0.4343 6,/_ Im{-(m2-1)/(m2+2)}IMkc
= KIM
where m = complex index of refraction of water,
function of temperature and wavelength
M = density of cloud water particles, g/m3
(range ~ 0 to 10 g/m J)
lO
Values of KI, taken from Gunnand East (Ref. II) are given in Table 5.
Bean and Dutton (Ref. 12) also use these values in their discussion of cloud
attenuation.
TABLE5
_ Attenuation Coefficient_in Clouds_LdB/k_
TEMPERATURE(oc.)
Water 20 ....
Cloud 10....Oi.oo
-- 8....
Ice 0 ....
Cloud -10 ....-20 ....
WAVELENGTH (Cm.)
0.9(33.31GHz)
0.647
0.681
0.99
1.25
I).74XI0-3
2.93XI0-3
2.0 X10-3
1.24(24.18Gllz )
0.311
0.406
0.5320.684
6.35XI0-3
2.11XI0-3
1.45XI0-3
1.8(16.66GIIz)
0.128
0.179
0.267
O.34(ex-
trapolated)
4.36X10-3
1.46XI0-3
1.0 XI0-3
3.2(9.37Gllz)
0.0483
0.0630
0.0858
O.112(ex-
trapolated)
2.46XI0-3
8.19X10-4
5.63X10 -4
Note that ice clouds have attenuation coefficients about two orders of
magnitude less than water clouds. Their attenuation (absorption) effects may
be neglected as long as the ice particles continue to satisfy the relationship
a<<1. In the absence of liquid water clouds, scattering by ice clouds will be
the only contribution to signal attenuation.
11
Rather than using the tabulated cloud attenuation values (Table 5), a
convenient expression to use for cloud absorption (in the region I to 50 GHz)
is (following Staelin, Ref. 13):
where
4.343 x M x I00"0122(291-T)'IA = x 1.16
cloud _2 dB/Km
M = cloud water particle density, g/m 3
T = cloud particle temperature, Kelvins
= wavelength, cm.
4.343 = changes nepers* to dB
1.16 = factor to match the Staelin expression
to the Gunn and East values, within 10%
For use in radiative transfer calculations, an absorption coefficient
a (nepers/km) must be used where
(nepers/km) = A (dB/km)/4.343
*The neper is used here in the "power" sense (I neper = 4.343 dB) rather thanthe traditional "voltage" sense (I neper : 8.686 dB).
P2 " P1e'ax
P21PI (dB) = 10 1Og1oe'aX
= -I0 a 1og10e
= -4.343 a
(x = I km)
12
Ill. EQUATION OF RADIATIVE TRANSFER
The description and use of the equation of radiative transfer is given
by numerous authors (Refs. 14-20, et al). The noise temperature at a given
frequency received by an idea] antenna with infinitely narrow beamwidth
looking upward at a source outside the atmosphere and ignoring scattering is
given by (See Figure 2):
S
-jrTa : T'e-_a + T(s) _(s)e o ds
o
where Ta = effective antenna temperature, Kelvins.
I
anoise temperature of source outside the atmosphere(e.g., black body disc temperature of the moon), Kelvins
T(s) = physical temperature of a point s in the atmosphere,Kelvins.
= total atmosphere attenuation (optical depth), nepers
: total absorption coefficient at a point s in the
atmosphere, nepers/km (neglecting scattering)*
s = distance from anLenna to a point in the atmosphere, km
* In the case of scattering (attenuation = scattering + absorption), simple
first-order considerations will show that _(s) wil] be the absorption co-efficient and _(s') will be the total attenuation coefficient. This con-
dition is not considered for this cloud survey, but scattering must be
considered for propagation through rain, particularly at frequencies greaterthan I0 GHz.
13
///
/s = oo(TOP Of ATMOSP_tERE)
/
"MOON '_
//
/
/
/; ._" .4,-----a(s), a(s' ), T(s) _)
/// _ EMISSION als)T(s)ds/ /
s//j / _ LOSSL.•FACTOR"°
/ " r_s a(s' )d='
FIGURE_ .2_ EL EM.ENTS OF R_A_OXA.TI_VET_RANSF.ER__EQU_AF_X_ON
14
The total absorption coefficient (_(s) neperslkm) is the sunlof the
individual absorption coefficients of all atmospheric constituents (water
vapor, oxygen, clouds, rain). If any component is absent, its individual
absorption coefficient equals zero. The loss ("loss factor") through the
entire atmosphere is:
T f'_(s')ds'L(ratio) = e = e o • 1.0
where /" represents the total path through the atmosphere, approximately 30 kmO
at zenith, and T is the optical depth (nepers).
The "transmissivity" of the atmosphere is defined as:
"T
T = I/L = e , 0 _ T _ I
The "absorptivity" or "opacity" is defined as:
"T
A = I-T = i - e = I-I/L , 0 < A < I
The first term of the radiative transfer equation gives the net
brightness temperature of a so_rce located outside the atmosphere after"
transmissivity reduction I/L. The second terT_l re;_resents the su,;lof
infinitesimal [)rightness tefllperatLlrecontribt_tions rT($) 1(S) ds _ , each
attenuated hy the atmosphere between it ,_r_dthe recei,i'ig antenna (;)ath
length s). For atmospheric studies using passive radiorletry only, and no
source in or outside of the atmosphere, the ter,_ (T' e-T) is equal to zero.a
15
Sun- and moon-tracker studies (sources outside the atmosphere) enable one to
determine space diversity improvBnent and various atmospheric parameters
(Refs. 21-25).
The total atmospheric absorption, A(dB), through the atmosphere, can be
derived from the |oss factor L by:
A(dB) : I0 log_o(L )
= 10 T logloe = 4.343 T
where T = /®_(s)dso
along a path through the
entire atmosphere (nepers)
An effective mean physical temperature, Tp, of the atmosphere l_laybe
derived from the relationship*
Ta = Tp x (Absorptivity)
= Tp (i - e-T)
= Tp (i - I/L)
where Ta = antennj temperature due to emlssion from the absorptive("lossy") atmosphere, Kelvins
Tp = _;lean physical temperature, Kelvins
L = loss factor, • 1.0
* This eqt_ation is strictly true only fur jr. isother_al ata;_os_,nere,h,_t is a
g(_ed practic,ll approximatiovl f,Jr the earth's atmosphere, where the hLIli_of
attenuation occurs in regions _¢hose temperatures are within 10% of 273 K.
16
A more rigorous derivation of this expression begins with the equation
of radiative transfer:
Ta
® -_ _(s' )ds'
= f T(s)_(s) e o
o
ds
For an isothermal, homogeneous atmosphere
_(s) = _, the mean absorption coefficient
T(s) = Tp, the mean physical temperature
Then,
Ta = _Tpj_e__Sds,r where c = top of atmosphere
o
= Tp (l-e-_)
=Tp(I-IIL)
This relationship is discussed in more detail by Waters (Ref. 14).
17
As a specific example (based on an actual calculation using the
equation of radiative transfer) consider an atmosphere (heavy clouds, at
32 GHz) whoseantenna temperature and attenuation at zenith are:
Ta = 99.04636 Kelvins
A = 1.93854 dB iL = 1.56262)
Tp is found to be
Tp : Ta [L/(L-I)I = 275.091Kelvins
This physical temperature corresponds to a region in the atmosphere
where the "bulk" of the attenuating material lies (in this case, clouds at an
altitude of approximately 3 kin). The surface temperature for this case was
293.16 Kelvins and the lapse rate was 6.3 K/kin downto a minimumtemperature
of 220 K.
It should be noted that Tp is an artifact and not a "constant" of the
atmosphere. It is found after performing the radiative transfer calculation.
For the cas_ of temperature and/or attenuation gradients in the atmosphere,
the Tp found will depend on whether the atmosphere is "viewed" (integrated)
from below or above.
A further discussion of abnospheric modelling and noise temperattJre
errors is given by Stelzried and Slobin (Ref. 2{i).
18
Using these simplified formulae, it is instructive to attempt to
predict the antenna temperature for this cloud model at an elevation angle of
30° . To a good approximation, the attenuation at 30°-elevation is twice the
zenith attenuation. Thus,
A(dB) = 3.87708 dB (L = 2.44179)
Using TP = 275.091 K, the antenna temperature is calculated to be:
Ta = 162.431K
Actual radiative transfer integration at 30°-elevation yields:
Ta = 161.660 K
a difference of 0.771K.
Using
Ta = 161.660 Kand
A = 3.87708 dB (L = 2.44179)
the 30°-elevation mean physical temperature is calculated as
Tp = 273.785 K
which is different by 1.306 K from the zenith mean physical temperature.
These one-Kelvin differences reflect an equivalent resolution well
within present ability to _Tleasureor forecast cloud parameters. Thus,
elevation angle modelling of attenuation and noise temperature is adequate for
stratified atmospheres. For the case of scattered clouds, non-simple
geometries, or low elevation angles, complete radiative transfer calculations
should be carried out.
19
IV. SAMPLE CASE CALCULATIONS OF CLOUD ATTENUATION AND NOISE TEMPERATURE
A computer program has been written ted calculate the atmospheric noise
temperature and absorption of water vapor, oxygen, clouds, and rain, (using
the equation of radiative transfer) along various paths in the atmosphere.
For computational purposes, the atmosl)her_ is divided into 300 layers, each
i00 meters thick, up to a height of 30 ki,1 above the ground. For specific
cloud/rain models and/or frequencies at which tile attenuation coefficient s
very large (,_ _ I neper/km (4.34 dB/km)), the I00 meter step size must be
reduced (~ lore) and the number of steps increased (~ 3000) in order to avoid
large computational errors. The effect of ti_ese errors is to calculate a
value of noise temperature that is too low (lot the case of very dense clouds,
at least). The present version of the i)rogra_H is not "smart" (or self-
adjusting); but the calculations appear to be adequate for all cloud ca,,es,
excluding rain, excerpt very near the peak of the oxygen absorption band
(60 GHz), or for very heavy clouds at high frequencies (> 60 GHz). The
presentation here is restricted to frequencies less than 50 GHz.
Since clouds do not exist independent of water vapor and oxygen, the
effects of these two spe'ies must be included in any calculation of cloud
noise temperature and attenuation.
PRECEDING PAGE BLANK NOT FILMED
21
The narticular constituent models are described as follows:
WATER VAPOR
Io
2.
3.
4.
5.
6.
7.
CCIR Profile (Ref. 27)
7.5 g/m3 at surface
2 km scale height
20°C at surface
6.3 K/km temperature ]apse rate
220 K minimurn te_;iperature
Bean and Dutton absorption coefficient (Ref. 12), modified slightly to
yield agreement with values calculated by the JPL Radiative TransferPrograrn (Ref. 28)
OXYGEN
.
2.
3.
.
5.
6.
7.
CCIR Profile (Ref. 27)
1013.6 mb at s:_face
-0.116h
Pressure profile curve-fit P=Poe. ,h in km(pressure scale height = 8.62 km)
20°C at surface
6.3 K/km temperature lapse rate
220 K minimum temperature
Bean and Dutton absorption coefficient (Ref. 12)modified slightly toyield agreement with values calculated by the JPL Radiative TransferProgram (Ref. 28)
CLOUD
I.
2.
3.
Absorption model frown Staelin (Ref. 13)
Modified to fit Gunn and East values (Ref. Ii)
Water particle densities derived from drop size distribution
in Carrier, Cato, and von Essen (Ref. 3)
#
22
Figure 3 showsa schematic view of the cloud and clear air models used
in the calculations. In these models, h is the height (km) above the ground;
h is the height of the ground above sea level.o
The cloud model has up to two layers, base and top heights specified,
and water particle density determined by specification of cloud type _s
defined by the World Meteorological Organization Cloud CodeChart (Ref. 4).
The relative humidity is not adjusted to be 100% within the cloud layer; the
absolute humidity is defined by an exponential decrease with a 2 km scale
height.
A number of specific weather cases were considered for calculation
using the equation of radiative transfer to determine noise temperature and
attenuation. Table 6 lists the 12 cases (i clear, Ii cloudy); they represent
increasingly dense and thick cloud layers.
This table will be discussed further with respect to S, X, and KA-Band
noise temperature and attenuation effects of clouds.
23
h . 30 km TOP OF ATMOSPHERE
/
/
/
TEMPERATURE PROF ILE
-6.3 K/kin220 K MINIMUM
/
/
/
/
ABSOLUTE HUMIDITY
PROFILE • "h/'2" 0
UPPER
CLOUD
/
LOWER
CLOUD
//
PO
AllO
PRESSURE PROF ILE
-.116(h_ )• O
F.I!;.URE_3+..._CL_0UD..AND_Ct._AR_AIR M.0[IE_LS
24
U-
U-
UJ
Z
W
N
!
v.
._J
L..)
._J
r_
5-
r_AI,,,,1"I"
n Z
enO0N¢'d
I
• • • • • • • • J •
un_r o0 _ N O ,..4 u_ O _ u_ (_
O C) _ C) C3 ,..4 _ .-_ N 05
C_ .1.- nr
_t_Z• la3
uSN_I
wn_
0 0 0 0 0 0 0 0 0 0 0 0
C•_ 0 _
I,,,. e,- _ O
,_ "0 _ _'P "_._ _ -"r- _
i_ '
Cl£
,,..-4 ,,.-4 ,-,4 _ C_I
c'_ _ _ _ _ _. O0 _ 0 _
¢I
X _ ON _..-
U ',._ "_ _"_._ 0
_ _._ _,_ ._ _x_ _. _ 0
_0 _ _; O _-
25
Table 7 shows a printout of the temperature, pressure, and absolute
humidity profiles used in the calculations up to a height of 10 km above the
ground. The va|ues are given at the center of the 0.I km-thick layers. The
receiving antenna is considered to be located at sea level and the clouds are
horizontally stratified. The specific case shown in Table 7 is for clouds
plus rain (10 mm/hr at the ground). The columns labeled ALPHTI and ALPHT2 are
the extinction (total attenuation) and absorption coefficients (nepers/km) at
32 GHz, respectively, for the case where scattering from rain is considered.
The clouds are not considered to scatter at frequencies below 100 GHz for the
purpose of these calculations. DENC is the cloud water particle density,
1.00 g/m3 for the lower cloud and 1.00 g/m3 for the upper cloud. The rainrate
(mm/hr) is given in the last column, based on a specific model. The rain is
considered to start at 3.5 km above the ground and the rate increases in a
downward direction.
Returning to Fable 6, the last columns show the S-, X-, and KA-Band
zenith noise temperature and attenuation effects for the cloud models shown.
The notes at the bottom of the table describe the models used and will
clarify the tabulated values.
Table 6 shows the increasingly severe effects of clouds as the
frequency changes from S-thru KA-Band" S-Band is affected only slightly by
even the heaviest clouds, whereas KA.Band shows very large effects, which
are quite severe for the case of low-noise receiving systems.
26
TABLE 7
PROFILES USED IN
CLOUD CALCULATIONS
HEIGHT
• I'5, L:u
._o00_
• 2bD( :.
.35 c :.0
045'_LG
oSSGO0
.650_fJ
• 75 L: ('©
• 85 ? _,tl
.9_000
1005f._0
TEMP PRESS. ABS HUM. ALPHT1 ALPHT2 DENC RNRT
_ 52.045_ Jl _.1 1062124. 7.31482 .t6u16 • 34.,_3 9 .09009 9. 995 :.;.a
292.21500 9_6.'b0037 b. 958"8 04.6355 • 53.51 1 • "J(, "- _.") 909551C
291.SPSG _3 984.51351 e..£ 1073 .4_880 • ._`547 b 000000 9087578
;, Q009'_5 0 _ '915015914. 6. _9593 04.5255 .33t_?b .fgOOC'_ 9075798
29J*325JO %1093571 5.98887 o44465 .32465 on 00'lw't 9.&{,3,_ 9
2 P90159500 %0084174 50L9679 o4.$521 o317)9 o00000 9.91294
2t_90 OF50b 959087559 5*41896 042430 • 31J34. .0 Ol_O_, 9018972
268.435 _ " 929.03613 5.15467 041206 03C178 ._0030 8093597
257 oil L5 _; ,' 916052|57 4.090327 .398bl 029240 0000'?,0 8,.65455
28.'017500 9_ 1013059 4. 056914. 038488 0_8227 000000 8034.853
:"06* 54.500 8Y 702& 17_ 4. 04_667 051843 o4212R 1000000 8o02%18
1015;J:_ 21_5.915GC 886.91365 4..22©29 050490 .4.126* 1.000_9 7067590
1.25_r, 0 •e!5o285r, G 87606848:J 4.:_14.46 049080 04036% 1.0300.n 7031616
1.35060 2R4o65500 866051410 3.81867 .41631 039428 1000060 609454.4
1045_&C 284002500 8:16057992 3.63243 °46150 038477 1.00000 6056718
1.55:_(_ _830395_(, 8460701¢0 3.4.5528 04.4676 .37517 100000_l 6_018479
1065JC_, 26207550_ 83_093602 30_8676 04.3280 036559 loO_OC'_J 508_,,1_2
1.15000 28;013500 821028._b_ $012b4.1 041143 *_5&12 1000000 50419_q
1085009 281.5053'/1 817.74.261 2.97399 .4.J318 034.684. 10003C_ 5.04.342
1.95:00 21_)o_750( 800031159 2.1'2894 038937 .337_!* 1o0000,,I 40674._."2005'; CO 21'.)024500
4..31455
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7'_ 8.98936 2.69097 • 19731 ., 15C4 . .0000_)
2.15000 ,_79051500 78907"/4k$ 2._5913 018148 o138:)8
2.250t_U 278.9_500 780.666,18 2.4.3489 .1_629 01279_
2-35U'_0 27e*3550(' T?_0k5277 2.3161_ -,15182 011741
2.4.5000 .,t7.175(_0 752.15320 2.20,518 .1,5809 010735
2055_GL 277009500 7_3095626 2.09573 .12516 009783
20&50i)0 27_,._.5Q_ 74.5.27078 1.99552 011304 008885
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3.05000 27_.94.5&(' 711.98022 1.53216 .28515 .,_71953.150C& 2730 _15('0
,5.250[_0 •l,_.G(:Su(j
5.55000 2 72. rbsot"
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30950..r_ 2t I70_ 751.'
• 00000 3.96753
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• 00C?0 2. 7239_,
0')09C0 2.454.9&oOOO_O 2*2:3_
• 00000 1.9701G• 05000 1. 754.33
1.0009_ 1.%55957;J 3.27975
t_3.15389
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1o4.04.81 .27570 026667 1030CUO 10,)_9_ 1
) .3363.. .27373 ..21;604. 1.0C _'0 .925041027113
023891 o238')1 10_. L'_C _ . ._t_C.Ob _,
102091,5 024.290 024290 1.00000 .OOGO0 (,..)1.1501(, 0246_7 • 29i,9 7 I.O_3L'O .C¢_.L.
10('Q407 025113 02_113 1.00J"O * _0_.. :l.;.qO?l 025537 025537 1 ._0_;._ _ . ?'..( C :
09899:_ .004.97 0004.97 *O00CO *OOOO0
• 94.167 ._,0483 . Oo,_._ .COCC_ ._C:.O
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27
4.;,,_' .-- ' _ ." "i, ."'
('. _,,,;_. l, .,,.,
TABLE 7 Icont.),
S.OS.luO
S.15800
b.25800
5.35000
.dis C O(J
5.55 (,_u
S.&SOSO
5.75000
5.85e10
5015080
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6.15080
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28
J
The change in signal-to-noise ratio (ASNR, dB) is given by:
ASNR = AdB + 10 lOglo(Top/Tbase)
where adB
Top
= change in attenuation, relative to clear air baseline
= system noise temperature with clouds, Kelvins
Tbase = baseline system noise temperature, including ground,
waveguide horn, clear air, and cosmic backgroundcontributions, Kelvins
As an example, consider a low-noise receiving system at KA-Band with
a baseline zenith system noise temperature of 35 Kelvins. Using Case 10
(Table 6), it is seen that the zenith attenuation increases from 0.228 dB
to 1.939 dB. The atmospheric noise temperature increases from 14.29 Kelvins
to 99.05 Kelvins. The 2.7 Kelvin cosmic background effect decreases from
2.56 Kelvin (2.7 attenuated by .228 dB) to 1.73 Kelvin (2.7 K attenuated by
The new Top is 35 + (99.05-14.29) + (1.73-2.5_) = 118.93 Kelvins.i.939 dB).
Thus,
ASNR = (1.939-0.228) + 10 lOglo
= 7.021 dB, at zenith
(118.93/35.) = 1.711 + 5.312
Most of the signal-to-noise degradation in low noise receiving systems
comes from the noise temperature increase. For high noise receiving systems
(> 500 Kelvins), the atmospheric attenuation will cause the greatest SNR
degradation.
The Appendix of this report contains numerous curves of total
atmospheric attenuation coefficients, atmospheric noise temperature, and
atmospheric attenuation for the cloud models in Table 6.
sets of five, one set for each of the twelve cases listed.
of each set are:
The curves are in
The five curves
29
I) Total atmospheric attenuation coefficient at 32 GHz, vs. height,
all constituents, no scattering because clouds only (labelled -1)
2) Atmospheric noise temperature at zenith vs. frequency (labelled -2)
3) Atmospheric attenuation at zenith vs. frequency (labelled -3)
4) Atmospheric noise temperature at 30°-elevation vs. frequency
(labelled -4)
5) Atmospheric attenuation at 30°-elevation vs. frequency (labelled -5)
The eight parameters of each plot are printed at the bottom.
They are:
I)
2)
3)
4)
5)
6)
7)
8)
ELEV = elevation angle from horizontal, degrees
LAST LOOP = counting loop, internal use only
DENCLOW = density of lower cloud, g/m3
LOWCLDTHK = thickness of lower cloud, km
DENCLMID = density of upper cloud, g/m3
MIDCLDTHK = thickness of upper cloud, km
RAINRATE = rainrate at the ground, mm/hr
RAINTHICK = thickness of the rain, km
30
Table 8 shows results of tests of integration step size on the
determination of atmospheric noise temperature and attenuation for the
"worst-case" cloud, Case 12, at five different frequencies. NL is the number
of layers in the atmosphere up to 30 km above the ground. For NL=300,
layer thickness = 100 meters; NL=IO00, 30 meters; NL=3000, 10 meters.
Assuming the NL=3000 case to give the "correct" answer, noise temperatures
at the same frequency but different step sizes are compared to that value.
At all frequencies shown, the errors at zenith are less than two percent.
However, at higher frequencies or for cases including rain (where the
attenuation coefficient exceeds approximate|y I neper/km), care must be
exercised in choosing an optimum number of tropospheric layers. Carrying out
all calculations at NL=3000 makes computation of even a few cloud cases
prohibitively expensive. Future work will involve the development of
computational methods which strike an acceptable balance between accuracy and
cost.
31
TABLE 8
"WORST CLOUD"* TEST CASE OF
INTEGRATION STEP SIZE
** FREQ 90°-ELEV 30°-ELEVNL GHz
300
(1oom)
RC=I
1000
(3om)
RC=3.4
3000
(10 m)
RC=38.3
,J..
t**
10
20
30
40
50
10
2O
30
4O
5O
10
20
30
40
50
CASE NO. 12,
T(K)
26.84
94.35
159.18
214.08
251.92
26.96
94.88
160.64
216.89
255.98
26.87
94.66
160.52
217.21
256.85
| ii
TABLE 6
0.457
1.864
3.891
6.912
11.682
0.460
1.875
3.910
6.943
11.737
0.458
1.869
3.895
6.917
11.697
ii
% ERROR
-0.11
-0.33
-0.83
-1.44
-I .92
+0.33
+0.23
+0.07
-0.15
-0.34
0.00
0.00
0.00
0.00
0.00
T(K)
51.01
155.97
224.41
258.09
269.91
51.26
157.11
227.50
263.50
276.86
51.11
156.94
227.93
264.80
278.75
0.915
3.729
7.782
13.823
23.364
0.919
3.749
7.819
13.887
23.473
0.916
3.738
7.790
13.835
23.395
% ERROR
-0.20
-0.62
-1.54
-2.53
-3.17
+0.29
+0.11
-0.19
-0.49
-0.68
0.00
0.00
0.00
0.00
0.00
NUMBER OF LAYERS IN 30-KM-THICK ATMOSPHERE, THICKNESS OF LAYERAND RELATIVE COST
NOTE THE ANOMALOUS BEHAVIOR OF ATTENUATION AT NL=IO00 AND 3000,
FREQUENCY=50 GHz, WHERE NOISE TEMPERATURE INCREASES AND ATTENUATION
DECREASES; ALSO OSCILLATORY BEHAVIOR OF ERROR
TEMPERATURE ERROR COMPARED TO VALUE AT SAME FREQUENCY WITH NL=3000;VALUE AT NL=3000 ASSUMED TO BE CORRECT
32
REFERENCES
i.
.
.
.
e
o
.
9.
lil.
II.
12.
R. R. Rogers, "Statistical Rainstorm Models", IEEE Trans. Ant.
and Prop., July 1976, pp. 547-566.
S. L. Valley, editor, Handbook of Geophysics and Space Environments,1965 edition, McGraw-Hill Book Co., New York, 1965.
L. W. Carrier, G. A. Cat,, K. J. von Essen, "The Backscattering and
Extinction of Visible and Infrared Radiation by Selected Major Cloud
Models", Applied Optics, Vol. 6, page 1209, July 1967.
Cloud Code Chart, National Weather Service, U. S. Dept. of Conm_rce,
Supt. of-Documents, U. S. Govt. Printing Office, Washington, D.C.
N. E. Gaut, E. C. Reifenstein, "Degradation by the Atmosphere of
Passive Microwave Observations from Space in the Frequency Range
0.5 to 20 GHz", Environmental Research and Technology, Inc.,
Stamford, Connecticut.
V. J. Falcone, L. W. Abreu, "Atmospheric Attenuation of Millimeterand Submillimeter Waves", EASCON '79 Record, IEEE Publication 79CH
1476-I AES.
L. J. Battan, Radar MeteorolosLv, Univ. of Chicago Press, Chicago,lIIinois, 1959.
G. Mie, "Beitrage zur Optik ...", Ann. Phys., XXV (1908), p. 377.
t). I)eirmendjian, "Complete Microwave Scattering and ExtinctionProperties of Polydispersed Cloud and Rain [lements", ReportR-42/-PR, Tile Rand Corporation, Santa Monica, Calif., 1963.
_. J. :)utton, !!. T. Dougherty, '[sti_:_aLesof tileAt_iospheric
Transfer Function at SHF and [HF", NTIA Report 1_-8, U. S. i]eHt.of Co,_merce, Washington, D.C., August 1978.
k. L. S. Gunn and T. W. R. Last, "The i,licrowave Properties ofPrecipitation Particles", _uart. Jour. Ro_. Meteorol. S.c.,LXXX (1954), pp. 5Z2-545.
B. R. Bean, E. J. Duttcn, Radio Meteor.lowLY, Dover Publications,Ne_ York, 1968.
33
13.
L4.
15.
16.
i/.
18.
19.
20.
21.
22.
23.
24.
D. H. Staelin, "Measurements and Interpretation of the Microwave
Spectrum of the Terrestria| Atmosphere near 1-Centimeter Wavelength",Journal of Geophysical Research, Vol. 71, No. 12, June 15, 1966,pp. 2875-2881.
J. W. Waters, "Absorption and Emission by Atmospheric Gases", inMethods of Experimental Physics, Vol. 12 Academic PressNew York, 1976. ' '
E. D. Damosso, S. de Padova, "Some Considerations about Sky Noise
Temperature at Frequencies above 10 GHz.". Alta Frequenza, Vol. XLV,No. 2, Feb. 1976, pp. 98-10E to i06-18E.
A. W. Straiton, "The Absorption and ReradiaLion of Radio Waves by
I)xygen and I _ter Vapor in the Atmosphere", IEEE Trans. Ant. and Prop.,July 1975,, pp. 595-597.
L. Tsang, J. A. Kong, E. Njoku, D. H. Staelin, j. W. Waters,
"rheory of Microwave Thermal Emission from a Layer of Cloud or
Rain", IEEE Trans. Ant. and Prop., Sept. 1977, pp. 650-657.
D. C. Hogg, "Ground-Based Remote Sensing and Profiling of the Lower
Atmosphere Using Radio Wavelengths", IEEE Trans. Ant. and Prop.,March 1980, pp. 281-283.
V. J. Falcone, K. N. Wulfsberg, S. Gitelson, "Atmospheric Emission
and Absorption at Millimeter Wavelengths", Radio Science, Vol. 6,No. 3, pp. 347-355, March 1971.
A. T. C. Chang, T. T. Wilheit, "Remote Sensing of Atmospheric
Water Vapor, Liquid Water ...", Radio Science, Vol. 14, No. 5,pp. 793-802, Sept-Oct 1979.
M. T. Decker, Millimeter anu Submillimeter Waves_ Scatter,
Absorption_ and Radiation, ERL/ESSA (Boulder) Radio PropagationCourse, Lecture VII-5.
R. J. Coates, "Measurements of Solar Radiation and Atmospheric
Attenuation at 4.3-millimeters Wavelength", Proc. IRE, Vol. 46,No. i, pp. 122-126, January 1958.
R. W. Wilson, "A Three-Radiometer Path-Diversity Experiment",
Bell Sxstem Technical Journal, July-August 1970, pp. 1239-1242.
R. W. Wilson, "Sun Tracker Measurements of Attenuation by Rain
at 16 and 30 GHz", Bell System Technical Journal May-June 1969pp. 1383-1404. ' '
34
25.
26.
27.
28.
W. V. T. Rusch, S. D. S1obin, C. T. Stelzried, T. Sato,"Observations of the Total Lunar Eclipse of October 18, 1967at a Wavelength of 3.33 Mill" ,,
Imeters , _sical Journalrot. 155, March 1969, pp. 1017-1021.
C. T. Stelzried, S. D. Slobin, "Calculations of Atmospheric Lossfrom Microwave Radiometric Noise Temperature Measurements , TDA
_Report 42-62. Jet Propulsion Laboratory, Pasadenacalif.
CCIR, R__s an_d.Re o.rts of the CCIR, 1978 Volume V,__ Media. IntTelecommu__ . ernational
E. K. Smith and j. W. Waters, "A Comparison of CCIR Values of Slant
Path Attenuation and Sky Noise Temperature With Those From the JPL
Radiative Transfer Program", presented at URSI National Radio ScienceMeeting, Boulder, Colorado, January 12-16, 198].
m
35
APPENDIX
SAMPLE CASE CALCULATIONS
OF CLOUD ATTENUATION AND
NOISE TEMPERATURE
PRECEDING PAGE EL.AI'.!K r40T FILI',._ED
37
CASE 1-1
HEIGHT
z
F,1'I
ATMOS ATTN COEF NEPERS/KM
30. __j _ ....
II
2O
ABSORPTION ONLY AT 32 GHz
-----_-Z..... _ww
I
I
.... J_
o
..... jm
i=
I
i!!
.... _m
i
I
I
--1
dI
-q-----4
I
d
_q----.-__
.---tI
-4......
-1-"--1
I
.-----4
-i
ppF.,CEDtNG PAGE ELANK NOT R_
39
ATMOS NOISE
CASE 1.2
AI
H0S LhL1
N0I
SE
.I,O
TEMP
K[ 4oLVI
NS
)o
IrklvIp OOnO000. Ot
m. 40.
glAIIIA_O+0OOO000
40
CASE 1-3
1 '3TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
A
TH
0
S _ o
ATT
ENUATI
0N
DB
5
0O.
[L[V
5 10.
) OJCO0_O.Ol 0 _OCJO0
1_. 20.
LOI,_LDTI'_0 00O0000
4_=_• . _10.
R E L1UE NC Y _Hz
Oi£_K_LmlO "IOCLDY'_
0 0000000 0 0000000
.l_, 40.
IAIe_IIAT[
0 OOOOCO0iJl_TNIC.,K
0 00000O0
41
CASE1-4
^T
Mos
N0ISE
TEM
P
KELVI
N$
ATMOS NOISE TEMP VS FREO.
II
II
I
4,2
CASE 1-5
30
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
25
AT
H0S ,_o
^T
T
ENU^TI I 5
0N
0B
I 0
5
00
) 00000o0.0l
43
CASE 2-1
ATMOS ATTN COEF NEPERS/KMABSORPTION oNLY AT 32 GHz
25
to.
015 .020
ALPHTI
LO_aO.011_ OE_IO
2 0000000-01 O. 0000000
PNECEDING PAGE BLANK NOT FILMED
45
CASE2.2
T
OS
NoIsE
TEI'IP
KELVI
NS
ATMOS NOISE TEMP VS FREO
O.I
lIIN
I,-,
M.
46
CASE 2-3
I 6
TOTAL ATM ATTENUATION VS FREQABSORPTION ONLY
4
TH0S
AT I o
TENUATI II
0N
D0
00
• 0000000"01
47
CASE 2-4
140+ATMOS NOISE TEHP VS FRE_
t_
AT
S
N lea
0I
SE
TEM eoP
K
EL.#I
N 60
S
40.
20.
O+O+
L"L(V). 0000000 *01
9. 10. I5. 20. _,. 30.
FREQUENCY GHz
L_ST 1.00A _'xO,. L 01+ L0M2,. 0 rt,4K 0l_l.mlD RI00,.DT_4aC)+.,TO00000. Ol 1.0000000 01 I. 0000000-0l 0. 0000000 O. 0000000
36. 40. 46.
IA |itlIA I'E IAINmI4_0. 0000000 0 0000000
48
CASE 2-5
)0
2 5
?,0
I 0
.1._ R
__ --p
O.
TOTAL ATM ATTENUATION VS FREQ
I
!
I
i
ii
6. 10.
_-.wN m_ D
= Z
I
15, 20.
(L(V LAST L(X_ O(_'t c O_ c OMOL OTHIK
$.0000000o01 1 ,?O0_,O00 • 0,2 2. 0000000-0| 20000000-0!
M_
I
I
49
CASE3-1
30.
ATMOS ATTN COEF NEPERS/KM ABSORPTION ONLY AT 32 GHz
HEI
GHT
Z 1_,.
K1'1
10.
0.
• 300
9.0000000-01
.00'3 .010 .015 .020 .0_3 .030
• ALPHTI NE PE RS/KPI
LASI' L0a P 0CNCL LOh4 L OIdCt.DTHK 0(NCL _ |O M i 0Q.DTI,(K
1. 4300000-02 _. 0000000 0. 0000000 2. 0000000-01 !. 9_J98_J - 01e
.0315 .040 .045
tMXNmA_E ItAXNI_41CK
0. 000000O 0. 0000000
.050
pP_.EnIN_ PA_E E_I./l,_!K NOT FtLI_[D
51
AT-H ;'g,j3
N
0IS 6o
E
T
E
H
K
ELV
I 4oN
S
ATROS NO SE TEMP VS FREQ,
CASE 3-2
10
EL[V LAST LOOP Ot'NCL L OM
9 . 0000000.01 I 1 _00_0 * _ 0 . 00_ _
52
CASE 3-3
0s
=,T
rENU
TIoN
DB
TOTAL ATM Ar TENL,tATION VS FREQ
)
I
10
ABSORPTION ONLY
I I I I
f
53
AT
M
0S
N
0IS
E
T
EM
P
K
EL
VIN
S
1 O0
Z. 0000000- 01 1. _- O| 0 .0000000
CASE 3-4
ilAINT_41¢J(O. 00OOOO0
54
CASE 3-5
$.S
mw_ _u3.0
2.5
20
1.5 .....
I
I ....
i
1.0 .....
!
-4 ....
.0 .....
0. 5.
TOTAL ATM ATTENUATION VS FREQ
I
10.
ELEV LA.ST LO_ =' _ _*0. L Om, d
3.0000000*'1X 1 8000000.02 0.0U0O_ 00
L Ot4CLDTHK
0. 0000000
ABSORPTION
- _ -
)NLY
--
FREQUENCY GHz
0CNCEMi0 M| [X_DTHK
2.0000000-01 1. _" 01 0. 000000O
IA | NIBATI[ mAIN?_|CK
0. 0000_0
60.
55
CASE4-1
3O
25,
ABSORPTION ONLY AT 32 GHz
HEIGHT
Z _s-
KH
£LEV
9 J'3C0000.01
_AINr_ICK
O. 0000C00
PRECEDING PAGE BLANK NOT FILMED
57
1001
ATMOS NOISE TEMP VS FREQ
CASE 4-2
+ +
58
CASE 4-3
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
^
T
M
0 : 4
$
A
T
T t2EN
U
^
T
I I 0
ON
1313
an
00
EL[v• o0OO0O0.0|
CASE 4-4
ATMOS NOISE TEMP VS FREO,
ATM0$ l_o
N0I
SE
100.
TEMP
KE eoLVINS
O.
O. li. 10. IS. I0. ZS. 30.
FREQUENCYGHz
[kEY LAST LOQP O(NQ.L OM kOMCLDTI_[ CINCL ;ql 0 MIOQ. Otl,_). 0000000.01 ? 4000000-01 $. 0000000- 01 S 10000000- Ol O. O000000 0 0000000
3J. 40. 41_.
l,tl_l,t[ I" I m/+,+l Ol
O. 0000000 O. 0000000
_0o
6O
CASE 4-5
TOTAL ATM ATTENUATION VS FREQABSORPTION ONLY
AT
M
0S
TT
ENUA
TI
oN
oG
30
CASE 5-1
HEIGHT
Z
KH
30.
20.
10.
j
j
s. -1i,--- --
ATMOS ATTN COEF NEPERS/KM
o..00 .04
ABSORPTION ONLY AT 32 GHz
I
.02 .oe
I[LKV LJ_KT LOGIB O_ICL LGMt. 0000000"01 2.4)00000- 02 O. 0000000
.OI
ALPHT| NE PE RS/KPI
LaMCLOTIqKO. Ot,v_.vO0
OtMCI.MIO MI OCLOTI,I(5. 0000000-01 5.0000000-01 O. 0000000
I
PRECEDING PAGE BLANK NOT FILMED
- 63
CASE 5-2
lO0,
ATM05
N0I eO5E
TEMP
KE 6oLVI
NS
O.O.
ATHOS NOISE TEHP VS FREQ
IlllllllllllllllIlilililllIlllllll[llfllillllllllllII1111II1i1111111II!1111!1!li11111!III11lllllllii1I1111111!111111111111111ilIIIIIIIII1111!1111111IIII111.I
llllllllllllIIlllliill!lIllllllillllllfffJlllJll!l
I[llll/lllllllllllllilIIJ!Illlllilllllllililt1111111ill
IPLI_ LAST LOOP OLrlIQ. L q_,l• ,O_OOO0 * 01 • 7000000.01 O. 0000000
11JlillJflllilllllllllljil JllliiflllllillllllJllli
Jilllllllllllll!llJllll IIIIII 111111
I1; IIII!!111111111111, 1111111iiI!IIII!1111II. _. _. _. _. 40.
FREQUENCY GHz *
L Ot,_Cl,,C_ _tO ml_O_ BAI_A_O, 0000_ S+_O000-Ol S. 0000_-01 0.0000000
llllilflllllflllll,IlJllI'flll[/lll l1 111
"llilJl!!111IIII!IIIIii!IIIII!II
41. N.
II'Ai IlYl_I_O. OOCO00O
64
CASE 5-3
T
M
0q
TT
NUAT
i
0N
oB
O.0000000
ABSORPTION ONL_
1
65
CASE 54
ATHos
N0ISE
TEHP
KELVI
NS
180.
ATMOS NOISE TEMP VS FREG
i
FREQUENCY GHz
I
U.
66
TOTAL ATM ATTENUATION VS FREQABSORPTION ONLY
CASE 5-5
).5
AT
H
0S 3o
AT
T
ENU a5AT
I
0N
200[3
15
I 0
5
(LEV
) GO00000. Ol
_', 10,
3 JO00000-_ 0 0000000
FREQUENCY GHz
5 0000000- O! 5000000001
67
CASE 6-1
EI
GHT
Z
K
,'I
30
25
:5.
0.
.00
E'LEVg.0000C00.01
A.TMOS ATTN COEF NEPERS/KM
.0! .0,2
LAST LOOP O_'_LkOt,_) _00000-_ _10000000-01
!lllll
II111
.o0
o.ooooooo o ooooooo
.ol
_IMT1.41C=(0.0000000
,10
PRECEDING PAGE BLANK NOT FILMED
69
CASE 6-2
ATMOS NOISE TEMP VS FREQ
I0o
AT i
M
os
N0I 80sE
TEM
P
K
E 60L
VI
N
s
70
CASE 6-3
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
ATH0S
ATT lENUATI
0N
DG t o
.oO.
FREQUENCY GHz
C_NO..M ! O MIOCLDTHK0. 0000000 0. 0000GO0
71
CASE 64
ATM0s
N8IsE
TEMP
KEt.VI
Ns
Lq.rv
$. OOO0000*Ol
ATMOS NOISE
i i i
II |
I I I
IllI ! I
IIIIII
I ! |
I I I| i i
! ! I
-.LM-
Ill
III
i i •
• , o
i i l
I f I ,
6.
L_TLO_P
$._000_*_
TEMP VS FREO.
10. 15. ,ZO.
OC_CLL_ k GI, iCL DI'WI(
5. 0000000- Ol l. 0000000-00
FREQUENCY _Hz
_._ID RIOCLDTIwK
O. GO00000 O. 00001)00
3_, 40. 4,5.
I&lNllatl ItAINTWIGK
O.OOOO000 O.0000000
72
CASE 6.5
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
^TM0S
A1"TENUATI
0N
O13
• 4 •
. ¢1
73
ATMOS ATTN COE F NEPERS/KM ABSORPTION ONLY AT 32 GHz
CASE 7-1
20.
Z 15.
KH
lO.
\
0..00 .02
[I.[V kJ_;V LOGP O(IK_LL nu
9. 0000000-01 3.11300000- 0_' O. O000OO0
!I
.04
LOk_.Dn<X0.0OO0000
.01 .01 .10
^L.PHT] NEPER$/KM
(_MCLRIO R|OQ.DTHK mAI_AT[
5. O00_o0-gl 1.0000_*00 O. OOOO000
Jf
• 12
mAINV'NICKO.0000000
.14
pRECEDiNG PAGE BLANK NOT FILMED
75
TM0S
N0I5E
TEMP
KELVI
NS
ATHOS NOISE TEHP VS FREO_
CASE 7-2
J
76
CASE 7-3
IlINI"_I ¢1(O. 0000000
77
ATHOS NOISE TEMP VS t:REQ
CASE 7-4
180
78
CASE7-5
T
M0
S
A
TT
EN
UAT
I
0N
08
0. 0000000
ABSORPTION ONLY
79
CASE 8-1
30.ATMOS ATTN COEF NEPERS/KM ABSORPTION ONLY AT 32 GHz
20.
HEIGHT
Z I_
K
M
i
1o
O. i
.00 .02
ELEV LAST LOIOPq) 0(]00000-01 4.4)00000,02
,,,J
.04 .04 .0e .10
ALPHTI NE PE RS/KM
O['NQ. L I_l L OMCt. D TINK O_NCL Iq I 0 M |04_ DTI.IK BA |NmAT_
S. 0000000- 0! 1.0000000 • O0 S. 0000000- Ol ]. 0000000 • O0 O,0000000
Jf
IIIAIMT_IO(O. 0000000
.14
PRECEDING PAGE BLANK NOT RLMED
81
CASE 8-2
160,ATMOS NOISE TEMP VS FREQ,
82
CASE 8-3
ATH0s
ATTENUATI
ON
DB
4,0
31,5
).o
25
2.0
t.5
1.0
0O.
TOTAL ATM ATTENUATION VS FREO
ELEV LAST L00 j 0ENE¢ L 0M L 0MC_. O'f _'.k
9.0000000.01 4. 5000000.0_ 5. 0000000- 01 I. 0000000.00 5,0000000-01 !. 0000000o00 0.0000000
I& INIIATIE
0.0O00000
83
CASE 8-4
250
A
M
os
N
0I
SE
T 15o.EMP
KELVIN
S _oo
50
0O.
ELEV
$.0000000o0!
LAST LOOP
4 e030000o02
D_NCLLOW
S.O000000-OI
/F
/!
II[I
L
I!
i
/
tAINI"WICK
0 00011000
84
CASE 8-5
T
0%
_kTT
6N
UJ_T
L2
D
) O000OO0oO! ¢ RO00OO0o_ 5 0000000-01 ! OgO0000*O0 5.0000000-0% l.O000000+O0 0 3000O00
85
CASE 9-1
HE!GH].
z
KH
ATMOS ATTN COEF NEPERS/KM30. _ .....
i m
m m
¢_. m m
m m
m m
m i
m
20. .mi
15.
10, _
m
m
m
|
|
tm
0.• 00
_'LEv9 0000000o01
ABSORPTION ONLY AT 32 GHz
m m,m m _
.02 .04
L_T L00P 0E hIKe. L 01,d
5. 03100000- 0_ 7.0G00000 Ol
m m
m
m
-- m
m
m m
m
m m
m
m
m
n
m
m m
m
m m
R
w m
I
m
.06
L OkCl. DT_
1 0000000-00
_m
m_
.OI .10 .12
ALPHTI NE PE RS/KH
0[_CLP_XD MIDQ.DI_._7. ooooooo-ol 1. ooooooo.oo
k m
m m
.14
ItMINRA/1E
0. 0000000
m_
--4--
.16 .It
I_AIN'I'_-_Iel<0. 0000000
PRECEDING PAGE BLANK NOT FI_
87
CASE 9-2
AT
M
0S
N
0I
SE
T
EMP
KE
LVI
N
S
ATMOS NOISE TEMP VS FREQ
Z_t'II
40.
_LEV LAST LO_ OEM, CLLOW LOI,,ICLOTHI( C{I, KI.MID MIDCLDI'_ RA|M, IQAT[
9.0000000.01 51000000.(12 ?0O0O000-0% 1.0000000-00 Y.0000000-01 1.0000000.00 0.0000000
45.
IAINTHICWO.O000000
l_iO.
88
CASE 9-3
4.5
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
4.0
31'3
AT
M
0S 3.o
ATTENU 2.'3ATIoN
2.0
0[3
1.'3
l.O
'3
0O.
(.L(V9. 000o0o0-01
S. 10. IS. 20.
L_T LOOP 0Em_,.l,. 0M LC_dCLDY_"3.1000000-02 ?. O000000-Ol t . 0000000*00
FREQUENCYGHz
O(NO.MlO N10CI.DT_4C7. 0000000- 0! I. O_'.O000O* O0
J. 40. 4S.
BAINII'ATt IIA |Nll,4| O(O. OOO0000 O. O00000O
89
CASE 9-4
ATHOS NOISE TEMP VS FREO.
ATM0S
N0ISE
T
I.tP
KELVI
NS
9O
...... ,r.....
CASE 9-5
TOTAL ATM ATTENUATION VS FREQ A_ORPTION ONLY
7
ATMoS 6
ATTEN
ATIoN
4
o13
ELEV) 0000000.01
CASE 10-1
30.
ATMOS ATTN COEF NEPERS/KM ABSORPTION ONLY AT 32 GHz
I
HEI
GHT
Z
KH
20
15.
!
10.
O.\
._, .10
IJ
.lm ._0
ALPHTI NIEPE RSl KPI
LrL(v **liST LOOP O[MQ.L OM LGI,ICLOYl41( O[llO,.m |O mlOCLDlrt_ lea Iml'At'K
I
i.IS
IrA 1et'1'141_
O. 0000000
.m
• _, .... IT,. PRECEDING PAGE BLANK NOT FILMED
93
CASE10-2
200.ATMOS NOISE TEMP VS FREO,
1¢0
100.
94
CASE 10-3
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
G.[vI. 0000000.01
FREQUENCY GHz
O(NO..RI0 mlOCLDTMK! 0000000-00 1. U000000*00
95
CASE 10-4
ATHOS NOISE TEMP VS FREQ,
ATM0S
N0I 200
SE
TEMP
KE lso.LVINS
5O
96
• T
TOTAL ATM ATTENUATION VS FREQABSORPTION ONLY
CASE 10-5
0.
0.
I_L['V$. 0000000.01
_" .10.
FREQUENCY GHz
0ENQ.nlO MIDQ.0T_rI 000oo00.00 I 00(.0000.00
97
CASE 11-1
ATMOS ATTN COEF NEPERS/KM ABSORPTION ONLY AT 32 GHz
HEI
GH
T
Z is.
K1'I
P_C_DI_!c PAG5 _LANt( NOT fILMED
99
CASE 11-2
ATMOS NOISE TEMP VS FREQ
A1 2OO.
M
oS
N
oI
sE
f 15oEMP
K
EL
VIN
SIO0.
I I I I
II
I
I
IIII
I_0.
1 O0
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY
CASE 11-3
8.
7
ATM
0S 6
ATTENU s.A1"IoN
4.
0B
3.
2.
Q.
O.
S.O000000*OI
6. 10. IS. gO.
LAs'r L0CP O[NCt.LC_d t 0MCI.D'rNl(I. 3oooooo. o2 l. 0000000-00 1.5oooooo.oo
FREQUENCY GHz
OENQ.MIC NIDCCDTt4K1. 0000000.00 1.5000000-00
_. *0. 4S.
IIAI NnN'AT1E gl'al_TI,qt 0_O. 0000000 O.0000000
.IW.
lOl
CASE 11-4
ATM
0S
N
0I
sE
T
EMP
K
EL
VI
NS
300.
L_O.
ATMOS NOISE TEMP VS FREq
_00
XO0.
III I
o.o. 5, 10. 15. 210. _m3. 30. 3_. 40. 45.
FREQUENCY. GHz
(LEV LO4S T LCOB O(NCt. L Ok4 LOWCL DTI,4K OENC1. M I O M|OC_. OTHK IIA I NRAT[ IA| NTt41 (](
$. 0000000"01 6. 6000000"02 1. 0000000"00 1. _000000"00 1. 0000000"00 1.5000000" O0 0.0000030 09000000
IO2
CASE 11-5
]8.TOTAL ATM ATTENUATION V$ FREQ ABSORPTION ONLY
_6.
14
A
T
M
o
A
T
T
EN
U io
A
T
I
0N
8
08
4_
2,
O.O.
3.0_0000-01
103
CASE 12ol
ATMOS ATTN COEF NEPERS/KMABSORPTION ONLY AT 32 GHz
25.
2(3
H
EI
GH
T
Z is.
KM
1o.
o.• oo
ELEVg.0000000,01
,2O .Z5 .3O ._
ALPHTI NE PERS/KM
OI:NCI.MIO MIDCLDII'I( RAINRATE IAINTMI_
1.0000000"00 2 ,0000000°00 0.0000000 0.0000000
I05
CASE 12-2
:300.ATMOS NOISE TEMP VS FRE_
2'50.
ATH
0S
N
oI 2'00.5E
TEMP
K
E lr,oL
VI
NS
100
lo6 _ - "--_-
CASE 12-3
TOTAL ATM ATTENUATION VS FREQ ABSORPTION ONLY"T-'
A
I"
M
os
A
T
T
EN
U
A
T
i
0N
D8
IO
• OQO_O00.O|
I_,*,IleYt,*l ¢K0. 0000000
I
.....t,..,.
I
!.-4,,-
I,,....4-.
I
I...L
1 07
ATHOS NOISE TEHP VS FREQ
CASE 12-4
ATML)S
N0I aooSE
TEMP
KE 1_oLVI
NS
CASE12-5
TOTAL ATM ATTENUATION VS FREOABSORPTION ONLY
ATM
os
AT
T
EN
UAT
I
oN
0 Io
O.O+
I_[V11ooooooo.ot
,Ins. 40. 41b+
IlIA | llll_[ IAIOIYt41Clt
0 0000000 0 0000000
1 09