microwave noise temperature and attenuation of clouds at

JPL PUBLICATION 81-46 "_

Microwave Noise Temperatureand Attenuation of Clouds atFrequencies Below 50 GHz

Stephen D. Slobin

(N AS A_CR. 16_,70Z) RICROWAV P-TEMPERATU[RE AND AT'£ENUAT£ON O_

_REQUENCI_S bELOW 50 GHz (Jet

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CLOUDS A

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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

o.U

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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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

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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 _,

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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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• 810_1 .Q0'*45 .0.0445 .00009 .OOO00

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4.005000 .e 1.64.50U

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51 ]r.4. b 71`5

570.747q1

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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252.52500

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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

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i.

.

.

.

e

o

.

9.

lil.

II.

12.

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34

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26.

27.

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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,


HEIGHT

Z _s-

KH

£LEV

9 J'3C0000.01

_AINr_ICK

O. 0000C00


57

1001

ATMOS NOISE TEMP VS FREQ

CASE 4-2

+ +

58

CASE 4-3


^

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


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


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


- 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


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


69

CASE 6-2


I0o

AT i

M

os

N0I 80sE

TEM

P

K

E 60L

VI

N

s

70

CASE 6-3


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


^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


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


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


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.


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


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


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


HEI

GH

T

Z is.

K1'I

P_C_DI_!c PAG5 _LANt( NOT fILMED

99

CASE 11-2


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


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