NIST A11103 110171

PUBLICATIONS

NISTIR 89-3918

X-BAND ATMOSPHERIC ATTENUATION

FOR AN EARTH TERMINAL

MEASUREMENT SYSTEM

Michael H. Francis

National Institute of Standards and Technology

U.S. Department of Commerce

Boulder, Colorado 80303-3328

July 1989

i

QC

100

U 5 6

89-3918

1989

C.2

NISTIR 89-3918

X-BAND ATMOSPHERIC ATTENUATION

FOR AN EARTH TERMINAL

MEASUREMENT SYSTEM

Michael H. Francis

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

July 1989

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director

CONTENTS

1. Introduction 1

1.1 Attenuation Mechanisms 2

1.2 Theoretical Determination 3

1 . 3 Measurement 4

2. Radiative Transfer in an Atmosphere 8

3. Sky Brightness Tipping-Curve Method 10

3.1 Equations 10

3.2 Error Analysis for Sky Brightness Tipping- Curve

Method 12

4. Attenuation From Radio Source Extinction Curve 25

4.1 Equations 25

5. Dual Frequency Radiometer Technique 29

5.1 Theory 29

5.2 Error Analysis for the Dual Channel Radiometer

Technique 31

6. Discussion 33

7. Conclusions and Recommendations 36

8. Acknowledgments 38

9. References 39

i i i
.

'
X-Band Atmospheric Attenuation for an Earth Terminal Measurement System

Michael H. Francis

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, Colorado 80303

The National Institute of Standards and Technology has developed an

Earth Terminal Measurement System to be used by the Camp Parks

Communications Annex in determining satellite effective isotropic

radiated power and antenna gain. In determining these quantities the

effects of atmospheric attenuation must be taken into account. This

paper provides an overview of the methods used for determining

atmospheric attenuation with emphasis on a tipping-curve method. An

error analysis is also provided.

Key words: antenna gain; atmosphere; atmospheric attenuation; error

analysis; satellite communications; satellite effective isotropic

radiated power (EIRP)

.

1. Introduction

The Electromagnetic Fields Division of the National Institute of Standards and

Technology (NIST) has developed an Earth Terminal Measurement System (ETMS) for

the Camp Parks Communications Annex of the Department of Defense. The ETMS is

designed to determine G/T for the earth terminal, satellite effective isotropic

radiated power (EIRP), and the gain of the ETMS antenna at its output feed [1].

The ETMS is designed to operate in the X-band from 7 to 10 GHz. In determining

these quantities the ETMS uses a calibrated radio star as a signal source. The

determination of G/T, EIRP, and antenna gain requires that the measurement data

be corrected for the effects of the atmosphere on the radio star flux and the

satellite signal. The methods of correcting for the atmospheric attenuation

effects and the errors associated with these methods are the subject of this

report

.

1
1.1 Attenuation Mechanisms

Two principal effects on a radio signal at frequencies of 7 to 10 GHz, traveling

through the atmosphere, are gaseous attenuation and hydrometeor attenuation [2].

Gaseous attenuation is the process in which gas molecules absorb part of the

radio signal and thereby reduce its amplitude. The main sources of gaseous

absorption in the frequency band from 7 to 10 GHz are oxygen molecules (O

2

) and

water vapor (^0) . Determining the level of absorption due to water vapor can be

a challenge since the water vapor content of the atmosphere varies considerably

with the atmospheric conditions. The level of absorption due to water vapor is

especially sensitive to variations in temperature and relative humidity.

However, it is relatively straight forward to determine the level of absorption

due to oxygen, since the atmospheric content of oxygen changes very little.

Hydrometeor attenuation is a reduction in the radio signal amplitude due to

scattering by hydrometeors. Hydrometeors are particles formed by the

condensation of water vapor in the atmosphere and include rain, clouds, fog,

snow, and ice [2]. Snow and ice are usually not important at frequencies below

30 GHz.

In addition to the effects of gaseous attenuation and hydrometeor attenuation

there are scintillation effects. Scintillation is a fluctuation in the amplitude

(and phase) caused by small atmospheric irregularities along the transmission

path. Dry scintillations are associated with the passage of cumulus clouds [3]

and cause mean signal variations of a few tenths of a decibel. Scintillation

lasts longer and occurs more frequently in the presence of rain than in its

absence. Scintillation in the presence of rain is called wet scintillation.

2
Scintillation can be difficult to correct for. For example, scintillation causes

a significant change in the mean temperature along the transmission path

especially for small sky brightness temperatures [3]

.

1.2 Theoretical Determination

Much effort has been expended in the study of atmospheric propagation [4]

.

Daywitt [5] derived theoretical equations to be used by the ETMS in estimating

the effects of the atmosphere. Considerable work has been done since then to

improve upon the values of the molecular absorption coefficients [6-10].

Shaw of the Institute of Telecommunications Sciences (ITS) developed a FORTRAN

program in 1981 based on the work of Liebe [6] to calculate the effects of the

atmosphere on the radio signal. The author has obtained this program from Liebe

and updated it to include Liebe 's more recent results [7-10]. This program will

be used in estimating some of the errors.

Despite these improvements, the uncertainties in the atmospheric loss remain

close to 50%, as found by Daywitt [5], primarily because there has been little

reduction in the uncertainties of various atmospheric quantities such as the

temperature, pressure, and water vapor profiles. The effects of water vapor,

cloud droplet concentrations, and rain are the major problems.

A 50% uncertainty is not serious in the clear sky case because the zenith

attenuation remains below 0.05 dB at 8 GHz. The uncertainty in the zenith

attenuation is estimated to be less than 0.03 dB. However, when clouds are

present the zenith attenuation may exceed 0.5 dB; in the presence of rain the

3
zenith attenuation can exceed 1 dB. The uncertainties associated with these

conditions lead to unacceptably large errors in the determination of G/T, EIRP,

and antenna gain. It is desirable, therefore, to determine the atmospheric

attenuation by measurement.

1.3 Measurement

There are several methods for determining the atmospheric attenuation using

measurement techniques. Direct attenuation measurements can be made by observing

the extinction of an extraterrestial source (such as the sun) as a function of

zenith angle or elevation angle [11]. The attenuation can also be measured by

measuring the sky brightness temperature as a function of elevation [11]. Since

radiative equilibrium and local thermodynamic equilibrium hold for the

troposphere, where the attenuation of X-band signals occurs, the atmosphere must

reradiate whatever it absorbs and thus contribute to the sky brightness.

Finally, a dual channel radiometer can be used to determine the amount of total

water vapor along a ray path (Guiraud et al. [12]).

Direct attenuation measurement

In the direct attenuation measurement, which can take hours, the antenna is

pointed at an extraterrestrial source and the antenna temperature measured as a

function of the zenith angle. If the attenuation is measured in decibels then

the antenna temperature in K is given by [11]

T' 10" 0,la° a

CSC0

T

s W, ( 1 )

4
where T (9) is the temperature of the source at the antenna, T' is the

a a

temperature of the source in the absence of the atmosphere, T

g

is the apparent

sky temperature, a 0 is the zenith attenuation, and 9 is the elevation angle. If

T

g

is balanced out or is negligible then (1) can be written as

10 log T ( 9

)

- -a 0 esc# + 10 log T' . (2)

a a

Therefore if 10 log T is plotted against cs c9 the slope is equal to the zenith

Si

attenuation.

Skv brightness measurement

The zenith attenuation can also be determined by measuring the brightness

temperature of the sky and using values of the mean atmospheric temperature along

the transmission path as derived from atmospheric models. For this case the

zenith attenuation is given by Hogg et al. [13] as

a 0 = 10 log [ (T - T )/(T - T ) ] , (3) ° m c m z

5
where is the mean temperature along the transmission path, is the cosmic

background temperature, and is the brightness temperature in the zenith

direction. T and T are obtained by measurement while T is determined from

c z

J m

atmospheic models and is weakly model dependent with a value of about 270 K.

Dual channel radiometer

Guiraud et al. [12] showed that the total integrated water vapor and liquid water

along the transmission path can be determined by measuring the brightness at two

frequencies of millimeter waves, 20.6 and 31.6 GHz. The dual channel radiometer

is calibrated against another method of determining integrated water vapor and

liquid water (usually radiosonde) . This needs to be done for each geographical

location. For example, for Denver CO, Guiraud et al . found that the total

integrated water vapor, V (in cm), along the transmission path is given by

V = -0.19 + 0 . 118T, - - 0.0560T, ot bl bZ (4)

and the total integrated liquid water, L (in cm), is

L - -0.018 - 0 . 00114TU1 + 0.00284T, 0 . (5) bi bZ

6
In equations (4) and (5) is the brightness temperature of the sky at 20.6 GHz

in the direction of the transmission path and is the brightness temperature

at 31.6 GHz. The attenuation can be determined by combining the values for V and

L with theoretical absorption coefficients given in dB/cm. A limitation exists

for this technique. At 20.6 and 31.6 GHz radiometers saturate (that is,

approaches the ambient temperature) during conditions of medium to heavy

rainfall. As a result reliable observations can only be guaranteed in the

presence of clouds that do not produce rain [14, 15]. Hence, the dual frequency

radiometer technique cannot be used to determine the attenuation during rain

conditions

.

7
2. Radiative Transfer in an Atmosphere

The derivative of the specific intensity, I, of an electromagnetic signal

traveling through an atmosphere that emits, absorbs, and scatters is given by

(Chandrasekhar [16])

where a(s) is the absorption coefficient, J is the source function describing the

contribution due to emission and scattering, and s is the path length. When

local thermodynamic equilibrium (LTE) applies, as is the case for the troposphere

(Westwater [17]) then the source is equal to the Planck function, B(T). When the

Rayleigh- Jeans approximation also applies (that is, when hu « kT) as is the case

for microwave frequencies then

= -a(s)I(s) + q(s)J(s), ( 6 )

B(T) = (2kT)/A 2

, (7)

where k is Boltzmann's constant and A is the wavelength. The solution to

equation (6) is I=(2kT^)/A 2

, from which we get

8
exp

r

°° -| -f a(s ' )ds

+ f

T(s)a(s)exp \

00

- Ja(s '

)

ds '

L 0

J 0

L s-* ds , ( 8 )

where is the brightness temperature of the extraterrestrial source at the

antenna, is the brightness temperature of the extraterrestrial source (for

example, the sun, the moon, the cosmic background) with no intervening

- atmosphere, and T(s) is the atmospheric kinetic temperature.

For a plane parallel atmosphere, which is a good approximation for the earth's

atmosphere provided the elevation angle is greater than about 15° (the zenith

angle is less than about 75°), s can be replaced by s = h esc#

,

where h is the

height in the atmosphere. In addition, if we replace T(s) by a mean atmospheric

temperature, T , (see for example, Falcone et al . [11]), equation (8) becomes

T (0) = T' 10

(- a o csc */ 10 ) + T

b b m

where a 0 is the attenuation in the zenith direction in decibels.

^ _ ^q(

a o csc0/lO)

(9)

9
3. Sky Brightness Tipping-Curve Method

3.1 Equations

If we wish to look at the sky and determine the sky brightness, we want to look

in directions that have only the cosmic background as an extraterrestrial radio

source. For this case equation (9) becomes

V') lo (-a o csc0/lO)

+ T ^ lo (-a o csc0/lO)J

( 10 )

where T

g

is the apparent sky brightness temperature. If we put all the terms

involving a 0 on one side of the equation and then take 10 times the logarithm of

both sides of the equation we get

a ou csc0 = 10 logol[ (T - T )/(T - T (0))]. m c ' m s

J (ID

Equation (11) can be written as the equation of a line if we make the

substitutions

y

- 10 log [ (T - T )/(T - T (0))] , m c m s

10
x = cscd .

Equation (11) then becomes

where b is nominally equal to 0 (that is, in the absence of measurement errors

b = 0).

Thus if we plot the value of (T - T )/(T - T ( 9 )) in dB against the value of

m c m s

cscd we should get a straight line. We can therefore make measurements at many

values of the elevation angle and fit a least- squares line to the results; the

resulting slope is the zenith attenuation. Once the zenith attenuation is known

the attenuation in the direction of interest can be determined by a(9) = a 0 cs c9

provided that the weather conditions are similar to those in the directions of

the sky brightness data. This is known as the tipping- curve method. The

advantage of the tipping-curve method is that for a least- squares fit, errors

that are constant with 9 do not cause errors in a 0 since they affect the

intercept and not the slope. Note from equation (11) that as T

g

(0) -+ T^, that is

as the sky brightness temperature approaches the mean atmospheric temperature, we

get saturation and it becomes impractical to determine a 0 using this method. For

11
microwave frequencies ~ 270 K [12] so that saturation occurs for an elevation

angle of 6 = 15° when a 0 » 3 dB. This occurs for X-band only if it is raining at

a rate of greater than about 50 mm/h (about 2 in/h)

.

3.2 Error Analysis for Sky Brightness Tipping-Curve Method

To estimate the error associated with the tipping-curve method as applied to sky

brightness measurements we can take the differential of equation (11) and then

evaluate the individual terms. We then find after some rearrangement of terms

that the uncertainty 6a in the attenuation is

8a(0) = 4.343

T (T (0)-T ) m

v s' ' c'

(Tme-T )(Tms-T (0))

ST

m

m

+

(T -T (0)) m s

6T

v*> 6T

(T -T (0)) m s + a o cot0 86 ( 12 )

Due to the least-squares fit, errors which are independent of 6 do not affect a 0

Therefore, since T and its error are independent of 6 , 6T =0, and the second

c c

term in the brackets of equation (12) can be neglected. We will assume that the

uncertainty 86 in the pointing is approximately 20% of the half -power beamwidth.

12
A value of T ~ 270 K is used by Guiraud et al. [12] for moderate humidity

m

y

conditions at a frequency of 21 GHz. This is based on the US Standard

Atmosphere. Changes in the ground temperature, the relative humidity, and nonuniform stratification effects would cause the value of T to change. Falcone et

m

°

al. [11] used a value of T

m

= 1.12T^ - 50, where is the ground temperature.

For the US Standard Atmosphere conditions Slobin [18] finds that using a two

component model for T^ gives better results and the best temperatures are 265 K

for the oxygen component and 280 K for the water vapor component. From this we

would expect that for a US Standard Atmosphere and 0% humidity T^~265K. Because

the ratio of the water vapor absorption to the oxygen absorption coefficient at

X-band is less than at K-band we expect r that T will be closer to

m

the average temperature of oxygen at X-band than at 21 GHz. To estimate the

value of T^, Shaw's program was modified to calculate the value of T^ along the

transmission path. Our results are that T 265 K would be a better value for

the mean atmospheric temperature for X-band. There are several variables that

contribute to the uncertainty in T^. They are uncertainties in (l)the dependence

of T^ on ground temperature, (2) the dependence of T^ on the relative humidity at

ground level, (3) the atmospheric temperature and density profiles, and (^nonuniform stratification. Only uncertainty (4) varies with the antenna pointing

direction.

To estimate the uncertainties in T due to nonuniform stratification we can

m

calculate T^ using our computer model for different conditions. The worst case

occurs when most of the sky is clear with a thick cloud in one direction. Our

computer model predicts a maximum error of about ±10 K in T for this case.

m

13
A word of caution: in the presence of scintillation the value of T can be

m

considerably reduced even for rms variations of only 0.2 dB especially if the sky

brightness is below 100 K [3]. In extreme cases the mean atmospheric temperature

can be reduced below 200 K. In this error analysis we will assume measurements

will be avoided at such times.

Determining the uncertainty in T is a little more complicated. A simple

s

radiometer system measures the output temperature for two conditions. In the

first condition we consider the situation where the sum of the signals from the

antenna and the reference source is measured. Then the output temperature, T^^

T

(l)

out

T A6)r, ant W1 r?) + T + T

n

(13a)

For the second condition we consider the situation where only the reference noise

( 2 ) source is measured. Then the output temperature, T^ is

t

(2) = T

out e + T

n

(13b)

where T

ant

is the antenna temperature at the antenna

transmission efficiency from the antenna output feed

output feed, q is the

to the receiver input,

‘Amb

14
is the ambient temperature, T

e is the effective receiver noise temperature, and

is the reference noise temperature. The output y of a radiometer is then

given by [3]

y H

( 1 )_ ( 2 )

' out out'

T

(l)

out

(14)

where H is the receiver gain factor which can be determined using a calibrated

precision r IF attenuator. We solve for T ^ in terms of y, n, H, T , T , and

ant J n e

T

Amb> We Set

T

ant (*) =

yJ (T + T ) n e HV

(15)

This indicates that T

ant

is determined not only by the brightness temperature in

the antenna pointing direction but also by contributions from other directions

that occur in the side- and backlobes . Thus the sky temperature in the direction

9 is given by

T

s W " T

ant ( *>/kW ’ (16)

15
where

jT

b

(0) D(Q-fl

0 («)) dfl

T

s («) JD(Q-Q0

(tf)) an-

(17)

D is the antenna directivity pattern, and is the brightness temperature.

Equation (17) is approximately given by

k(0)

T (0)GA + 0.5(G • s' 0

v a V<V V

T (0) 0

s a

(18)

where Gq is the solid angle subtended by that part of the sky at T

g

as described

following equation (20), G is the total solid angle subtended by the antenna, T

8. S

is the average sky brightness temperature, and is the temperature of the

ground. Ideally we would like the side- and backlobes to be low enough so that

the contribution of the second terra in the numerator of equation (18) will be

small. Note that as GA

-> G , k -+ 1 and T -*• T . However, unless the capability

0 a’ ant s

r J

to shape the beam exists, Gq does not normally approach G^ so, unless T

g

(^) is

much greater than T + T , the second term in the numerator of equation (18)

s 8

cannot be neglected. This condition on T (9) will not be met at any frequency.

s

16
Further, even at millimeter-wave frequencies Qq is unlikely to approach 0^ in

value for the 18 m (60 ft) dish.

The peak antenna directivity is given by

_

47r (peak power emitted per solid angle)

u

0

~~ total radiated power

(19)

If the peak power is then the total radiated power is P^Q^. Thus the peak

directivity is given by

4ttP

D

0 P„Q

0 a

0 47r

Q

( 20 )

By assuming that the pattern for the antenna has the form

(sin(ffl)) 2 (f0) 2

we can estimate the value of and Q if we know the value of f. In this

0 a

equation 6 is the angle relative to the z-axis of the antenna. The value of f

can be determined by knowing the value of the location of the first null. Then f

17
is given by f—?r/0 .j^. At ® GHz bhe location of the first null for the Camp

Parks 18 m (60 ft) dish is 0.16°. To obtain we will integrate from 0 to 1.5°

We choose this range of 9 since T changes by about 10% over this range of 9 s

values. We find ~ 1.15 x 10 ^ steradians, and fl « 2.18 x 10 These

0 a

numbers imply a peak directivity of 57.6 dB which is a little less than the value

of the gain found for the Camp Parks 18 m (60 ft) dish. To get an improved value

of k(0) detailed knowledge of the pattern is necessary. In addition, an initial

guess for T

g

is necessary. Using the above values for and we find that

k(0) is approximately

k(0) - 0.54 +

(0.23) (T + T ) ? £_

( 21 )

We will assume that the uncertainty in k is approximately one -third of the value

of the second term in equation (21)

.

k can be strongly dependent on 0 when the

second term in equation (21) is large compared to the first. This is the case

when measuring the sky brightness since T is greater than T

g

.

Combining equations (15) and (16) we get

T

s (*) -

1

k( 0

)

V(T + T )

- n e H r,

(l-i?)TAmb

V

( 22 )

18
If we take the differential of equation (22) to find 6

T

g

and simplify terms we

get

6T

s 1

T k(0)

s

1.5 6 T _

(r?kT + (l-r?)T A , )(6T + 6 T ) out * s ' Amb n e

>?T rjT (T + T ) s n e«»T

6k 1 (TAmb ' "kT

s> in +

(l-r,)TA

- -,kTs 6H

k k(0) cs H

to V "T

s H’

where we have used

6T

6 y

~ 1.5H out

(T

n

+ TVe

and is the measurement uncertainty in determining and Most of

the terms in equation (23) are independent of 9. Uncertainties in T^, T , T , rj

,

and H are independent of 9 and therefore do not cause uncertainties in a 0

. If we

drop the terms that are 0 in equation (12) then we get

19
8 a ~ 4.343

(T (0) - T ) (6T ) s c m ns

(T - T )(T -T (0)

)

m c m s +

T

s (0) 5k

(T - T (0)) k

in s

1.5 T

s (0)

^(T - T (0)) m s

ST

out

kT

+ a0 cot# 89, ( 24 )

where (ST ) is the uncertainty in T due to nonuniforra stratification. The

m ns J m

error due to nonuniform stratification is determined by assuming a clear sky in

all directions but one in which there is a thick cloud.

We will use the following values for various variables, some based on March and

April 1988 Camp Parks measurements: n ~ 0.8, T ~ 800 K, T ~ 300 K, and T ~ r r ' n e out

1100 K, and ST ^ ~ 5 K. The variable 6T ^ represents random noise in the

out out r

receiver

.

We will evaluate the errors for four different weather conditions: (1) clear sky

(zenith T ~ 6 K, a 0 = 0.05 dB) , (2)medium clouds (zenith T ~ 14 K, a0 = 0.2

s s

dB) , (3)heavy clouds (zenith T

g ~ 31 K, a 0 = 0.5 dB) , and (4)moderate rain

(zenith T^ ~ 56 K , a 0 = 1 dB) . We will also assume that the errors at an

elevation angle of 30° are approximately equal to the average errors at other

angles

.

For clear sky conditions the largest contributions to the uncertainty in the

attenuation is caused by the uncertainty in k. The uncertainty in k that we have
used in our calculations requires that (Q^- Oq) be known to about 30%. This

requires a detailed knowledge of the antenna pattern and a good initial estimate

of T . Improving on the uncertainty in k is difficult since the antenna

backlobes are likely to be affected by the direction in which the antenna is

pointing

.

As we can see from table 1 the uncertainty in the attenuation for clear sky

conditions is about 120% of the attenuation and exceeds the theoretical

uncertainty for clear sky conditions. We conclude that for clear sky conditions

it is better to determine atmospheric attenuation using theory. This agrees

with the conclusions of Brussard [3],

The uncertainty for medium cloud conditions is found in table 2. The total

uncertainty for medium cloud conditions is about equal to the attenuation. Ther<

is considerable uncertainty in the attenuation using the sky brightness tippingcurve method for medium cloud conditions but it can be used as a check and is

perhaps as good as theory since estimates of cloud droplet densities are

necessary for the theory.

The uncertainty for heavy cloud conditions is found in table 3. The total

uncertainty for heavy cloud conditions is about 60% of the attenuation and equal

to about 0.3 dB. This may be adequate for many measurements but may be larger

than is acceptable for calibrations of gain, G/T, or EIRP.

For moderate rain conditions of 10 mm/h (0.4 in/h) the total uncertainty in the

attenuation is about 0.5 dB as indicated in table 4. This is about 50% of the

attenuation. In rain conditions, however, scintillation often has a significant

effect on the attenuation. If significant scintillation occurs it will be

21
virtually impossible to determine the attenuation at a given time since

statistical methods must be used to determine a distribution of attenuations due

to scintillation. Because of the probability of scintillation it is recommended

that EIRP, G/T, and gain measurements not be done during rain conditions.

In examining the uncertainties of tables 1-4 we find that the greatest source of

uncertainty under all conditions is the uncertainty in the value of k. To get

even a moderately good value of k the uncertainty in the antenna pattern must be

no greater than 30% in the back- and sidelobes. The requirement on knowledge of

the antenna pattern is difficult to meet for the backlobes since the backlobes

usually depend on the orientation of the antenna relative to its mount. In

addition, a good initial guess for T

g

is necessary.

22
Table 1. Sky brightness tipping curve atmospheric attenuation uncertainties

for clear sky conditions (a 0 -0.05 dB)

Contribution to

the uncertainty

Error source Value Uncertainty in attenuation

e 30° ±0.03° < 0.001 dB

T (nonuniform

m

265 K ±10 K 0.01 dB

strat .

)

T

s

k 8.4 ±2.6 0.05 dB

T

out_ 1100 K ±5 K 0.02 dB

RSS attenuation error for a 0 - 0.05 dB 0.06 dB

Linear sum attenuation error for a^ = 0.05 dB 0.08 dB

Table 2. Sky brightness tipping curve zenith

for medium cloud conditions (a

attenuation uncertaintie

o * 0.2 dB)

Error source Value Uncertainty

Contribution to

the uncertainty

in attenuation

e 30° ±0.03° < 0.001 dB

T^ (nonuniform 265 K ±10 K 0.02 dB

strat .

)

T

s k 3.4 ±1.0 0.14 dB

T

out_ 1100 K ±5 K 0.05 dB

RSS attenuation error for a 0 - 0.2 dB 0.15 dB

Linear sum attenuation error for a 0 - 0.2 dB 0.21 dB

23
Table 3. Sky brightness tipping curve zenith attenuation uncertainties

for heavy cloud conditions (a 0 « 0.5 dB)

Contribution to

the uncertainty

Error source Value Uncertainty in attenuation

e U> o

© ±0.03° < 0.001 dB

T (nonuni form

m

265 K ±10 K 0.04 dB

strat .

)

T

s

k 2.0 ±0.5 0.3 dB

T . out

1100 K ±5 K 0.09 dB

RSS attenuation error for a 0 - 0.5 dB 0.32 dB

Linear sum attenuation error for a 0 = 0.5 dB 0.43 dB

Table 4. Sky brightness tipping curve zenith

for moderate rain conditions

attenuation uncertainties

(a 0 ~ 1.0 dB)

Error source Value Uncertainty

Contribution to

the uncertainty

in attenuation

9 30° ±0.03° < 0.001 dB

T^ (nonuniform 265 K ±10 K 0.1 dB

strat .

)

T

s k 1.5 ±0.3 0.5 dB

T

out 1100 K ±5 K 0.16 dB

RSS attenuation error for a o = 1.0 dB 0.53 dB

Linear sum attenuation error for a 0 = 1.0 dB 0.76 dB

24
4. Attenuation From Radio Source Extinction Curve

4.1 Equations

If we measure the signal from a radio star then equation (9) becomes

( -a o csc0/lO) + T U 1Q

(- a 0 csc e/io)]

(25)

m

where 1^(0) is the brightness temperature of the radio star at the antenna, T^, is

the brightness temperature of the star in the absence of the atmosphere. If we

subtract the sky contribution (equation (10)) from equation (25) then

Just as in the case of measuring the sky brightness, if the log of the argument

in equation (26) is plotted versus csc0 we should get a line. We can as before

make a least- squares fit to the data and eliminate errors that are independent of

9 since they contribute only to the uncertainty in the intercept and not the

slope, a 0

. To obtain a good extinction curve in a few hours the brightness

temperature of the radio source should be measured about every 10 min. Once the

zenith attenuation is determined the attenuation in other directions can be

a o csc0 = 10 log

(T*(0) - T

s (*))

(26)

25
determined by noting that a (0) = a o csc0 provided that the weather in that

direction is similar to the weather in the direction of the extinction curve

data

.

If T! is much greater than both T and T . as is the case in general only for the "* cm

sun, then is much greater than T . In this case equation (26) becomes

a o csc0 = 10 log

T'

•k T*<«>

} (27)

and the uncertainty in a 0 becomes

6a ~ 4.343 6k

k

1.5 6T

+

out

r?kl\(0)

+ a o cot0 66 . (28)

4

For the sun T* ~ 10 K for X-band [19]

.

Because the sun is so bright the

contribution of the sky and the ground to the antenna temperature is small and k

= 0.330 ± 0.005 for all conditions. Also, k is very nearly independent of 9 so
that T. can be replaced by T /k in equation (27) with k a constant. Thus we

* anu

can plot log(T ) against csc0 and get a good value for a 0

. We will assume that

ani

(5T /T ) ~ 0.01 so that 6T ^ ~ 40 K for the sun, v out' out out

We will estimate the error due to nonuniform stratification by considering the

case where the sun is mostly in a clear sky region but a light cloud passes in

front of the sun at some time during the measurements. Other types of clouds

must be considered to be a change in weather conditions.

When the sun is the source the attenuation uncertainty is the same for most

conditions. This uncertainty is found in table 5. The results of table 5 show

that the atmospheric attenuation can be determined to within an RSS uncertainty

of about ±0.14 dB for most weather conditions.

Since this technique uses the sun as the source it is necessary that the weather

conditions remain stable over several hours so the sun can cover a large enough

range of elevation angles without the stratification changing significantly.

This will permit a meaningful least squares fit to be made. When the weather

conditions change a new fit of the antenna temperature versus esc# must be made.

In addition, at the time measurements are made the sun must not be producing

radio bursts such as those that are associated with solar flares. Finally, this

technique is no better at measuring attenuation due to scintillation than any

other technique.

27
Table 5. Extinction curve zenith attenuation uncertainties

using the sun as the source

Error source Value Uncertainty

Contribution to

the uncertainty

in attenuation

$ 30°

non-uniform stratification

±0.03° < 0.001 dB

0.1 dB

k

T . out

0.330

4000 K

±0.005

±40 K

0.07 dB

0.07 dB

RSS attenuation error for a 0 = 1.0 dB 0.14 dB

Linear sum attenuation error for a 0 = 1.0 dB 0.24 dB

28
5. Dual Frequency Radiometer Technique

5 . 1 Theory

A dual frequency radiometer uses two frequencies such that one is more sensitive

to water vapor and the other is more sensitive to liquid water [12]. It is usual

for one frequency to be near, but less than, the frequency of the water vapor

absorption line at 22.2 GHz and the other to be near 30 or 32 GHz. The first

line is more sensitive to water vapor and the second to liquid water.

If the total atmospheric transmission at frequency u is exp( -a^/4 . 343) then a^

can be determined by [15]

a =10 log

v °

(T - T ) m c (T - T ) m s v (29)

where a^ is the attenuation in dB, T^ is the mean atmospheric temperature along

the transmission path, T

c is the cosmic background, and T

g ^

is the sky brightness

in the direction of the transmission path. This is equivalent to equation (11)

with the subscript u added to explicitly show that the attenuation is a function

of frequency. The attenuation can also be written as (Westwater [15])

a

v “v,

v + aT L + a , , Im dis (30)

29
where aTT and aT Vi/ 1m

are path-averaged mass absorption coefficients for water vapor

and liquid water respectively, a, is the dry air attenuation, and V and L are

the integrated amounts of water vapor and liquid water.

In the usual circumstances , and a^ are not known since they depend on

the unknown temperature, pressure, and humidity profiles (Hogg et al. [20]). It

is necessary, therefore, to determine V and L using statistical methods. This is

accomplished by taking many radiosondings and correlating the temperature,

pressure, and humidity profiles with different ground conditions (Westwater [15],

Guiraud et al. [12]). Such a process must be repeated for each location. In

addition, since radiosondes do not measure liquid water, theoretical cloud models

are necessary.

Equations (29) and (30) can be evaluated for hotL the upper (y=2) and lower (i/=l)

frequencies and we can then solve for V and L. We obtain

(31)

and

L “ ^' aV2 f

l

+

°Vl f2^aVla

L2

’ aV2

a

Ll'

) ’ (32)

where
f

l = al

a

dl

f

2 “ a

2

ad2

a^ and a£ are determined using equation (29) and a^and a^ are determined from

theory plus average radiosonde data.

Also, V and L are usually measured in centimeters of precipitable water vapor.

The a's can be determined from their value in dB/km and further noting that 1

g/m3 over a path length of 1 km is equal to 1 mm of precipitable water vapor.

5.2 Error Analysis for the Dual Channel Radiometer Technique

According to Westwater [15], V and L can be measured to an accuracy of about 15%

The molecular absorption constants can be determined theoretically to an accuracy

of about 15% and can be path averaged to an accuracy of about 15%. As a result

we get the uncertainties found in table 6.

Table 6. Attenuation uncertainties for the dual frequency radiometer

conditions Zenith attenuation RSS uncertainty Linear sum uncertainty

clear 0.05 dB 0.01 dB 0 . 02 dB

mod. cloud 0 . 2 dB 0.05 dB 0.09 dB

hvy . cloud 0 . 5 dB 0.12 dB 0.22 dB

31
The dual frequency radiometer gives results accurate to about 0.2 dB even for

heavy cloud conditions. During rain conditions the dual frequency radiometer

does not give accurate results because the radiometer becomes saturated.

32
6. Discussion

None of the methods that we have evaluated are ideal. Overall, however, the most

accurate results can be obtained by using a dual frequency radiometer to measure

the integrated water vapor and liquid along the transmission path.

The dual frequency radiometer cannot be used during rain since it becomes

saturated. This is not a serious problem since it is also undesirable to make

measurements during rainstorms because scintillation usually occurs. The dual

frequency radiometer would require the acquisition of an additional system.

Also, much effort would be needed to develop a large statistical data base so

that atmospheric profiles can be correlated with ground conditions and thus

accurate path averaged absorption coefficients determined. Also, the dual

frequency radiometer can account for nonuniform stratification better than the

other techniques especially at millimeter waves. Only the Camp Parks

Communications Annex can decide if its needs warrant the time and expenditure

required for this technique.

The extinction curve method with the sun as the radio source is the next most

accurate technique to use. The most serious constraint for this technique is

that it can be used only when the sun is above the horizon. Second, it cannot be

used during violent solar events such as solar flares since the sun's brightness

temperature changes rapidly with time; however, as long as there are no such

transient events the sun's actual brightness temperature need not be known.

Third, the weather must be stable for at least two hours so that the sun can

cover a large enough portion of the sky for a least- squares line to be

meaningful. Finally, the weather conditions in the direction of the sun must be

33
similar to those in the direction of the radio calibration source so that the

zenith attenuation derived from the extinction curve can be used in determining

the attenuation in the direction of the radio calibration source. The advantage

of this technique is that it gives results accurate to about 0.15 dB under many

weather conditions. It is necessary to find a separate extinction curve if the

weather conditions change (for example, when the type of clouds are different).

Also, this technique can be used at millimeter wave frequencies since the sun is

a strong source at these frequencies.

The sky brightness tipping curve technique will be difficult to implement since

it requires a detailed knowledge of the antenna pattern including the side and

backlobes. Because the backlobes of an antenna are partly determined by the

interaction of the antenna with its mount the backlobes will change with antenna

orientation. This makes acquiring the necessary information on the antenna

pattern extremely difficult if not impossible. A good first guess of the sky

temperature, accurate to at least 30%, is also necessary to determine k. Since

we are trying to measure T

g

in order to determine the attenuation this is not

desirable. The sky brightness tipping curve technique could be used with a horn

or small dish which is designed to direct a large portion of the energy into the

mainbeam (about 90% or more at X-band) . A smaller antenna also has the advantage

that its entire pattern can be characterized on a near- field range.

The accuracy of the extinction curve method can be improved by combining it with

a modified tipping-curve method. This modified technique would consist of

measuring the sky temperature difference profile; that is, we measure AT -

T (AZ(sun) , 8 )- T (AZ(radio star), 8 ). Then the attenuation in the direction of

s s

the radio star is given by

34
a(AZ(radio star), 9 ) = a 0 (AZ(sun), 9 ) + Aa(0) (33)

where a 0 is determined from equation (27) using the extinction curve method and

Aa is given by

Aa esc 9 - 10 log( (T - T )/(T - T - AT)). & m s' m s (34)

In equation (34) the value of T is determined from equation (10) using the value

s

of a 0 as determined from the extinction curve method.

For millimeter waves nonuniform stratification of the atmosphere will be a more

serious problem for both the tipping- curve method and the extinction curve

method. This is because clouds cause a larger change in the attenuation at

millimeter waves than at X-band.

A theoretical determination of the attenuation can be very useful for clear sky

conditions. For these conditions it is nearly as accurate as the dual frequency

radiometer technique. The atmospheric attenuation computer program developed at

ITS can also be used as a check on other techniques of attenuation determination

since it can estimate attenuation due to clouds if they can be classified (for

example, cirrus, cumulus). The value of the theoretical method for determining

attenuation could be increased if radiosonde data is used to create a database

that correlates atmospheric profiles with ground conditions. Profiles specific

to weather conditions can be used in this program.

35
7. Conclusions and Recommendations

We recommend that the modified version of the computer program written by Shaw at

ITS be implemented for the Camp Parks ETMS . This program gives accurate results

for clear sky conditions and can also be used to estimate attenuation in the

presence of clouds.

In addition, we recommend that the extinction curve method with the sun as the

radio source be combined with the modified tipping-curve method to determine the

atmospheric attenuation. Other than the dual frequency radiometer technique this

method is the most accurate technique for determining the atmospheric

attenuation.

Third, the Camp Parks Communications Annex should determine whether they need to

be able to determine accurately the atmospheric attenuation during the night as

well as the day and if increased accuracy for nonuniform stratification

conditions is required. In this event they should consider implementing the dual

frequency radiometer.

Fourth, the Camp Parks Communications Annex should consider the acquisition of a

smaller antenna for millimeter-wave measurements. A smaller antenna with a

diameter of less than about 3 m (10 ft) could have its entire pattern determined

on a spherical near-field range. Since gains generally increase with increasing

frequency, smaller antennas are possible at millimeter-wave frequencies. For

example, a 50% efficient 3 m dish at 22 GHz would have a gain of about 54 dB.

A final caution: calibration measurements should not be made during rain

conditions since scintillation is likely to be present. Scintillation may also

36
occur in the presence of cumulus clouds. Under no circumstances should

calibrations of gain. G/T. or EIRP be made during scintillations since

atmospheric attenuation cannot be accurately determined under these conditions .

37
8 . Acknowledgments

The author wishes to thank Bill Daywitt for his suggestions and discussions

regarding this topic. The author also thanks Hans Liebe of the Institute of

Telecommunications Sciences for providing the author with several relevant

references as well as for providing the atmospheric attenuation computer program

developed at ITS. Finally, the author acknowledges the support of this work by

the Camp Parks Communications Annex.

38
9. References

[1] Wait, D.F., "Satellite earth terminal G/T measurements," Microwave Journal,

vol. 20, No. 4, pp 49-58, April 1977.

[2] Ippolito, L.J., Radiowave propagation in satellite communications . Van

Nostrand Reinhold Company, New York, 1986.

[3] Brussard, G., "Radiometry a useful prediction tool?" European Space Agency

Tech. Rep., ESA SP-1071, Paris, April 1985.

[4] Hill, D.A.

,

"A survey of earth- to-satellite propagation factors between 2.5

and 275 GHz," Office of Telecommunications Report, OT Report 74-43, July

1974.

[5]

Daywitt, W.C., "Atmospheric propagation equations used in the NBS earth

terminal measurement system," Natl. Bur. Stands. Int. Rep., NBSIR 78-883,

April 1978.

[6]

Liebe, H.J., "Modeling attenuation and phase of radio waves in air at

frequencies below 1000 GHz," Radio Sci., vol. 16, pp 1183-1199, 1981.

[7] Liebe, H.J., "An updated model for millimeter wave propagation in moist

air," Radio Sci., vol. 20, pp 1069-1089, 1985.

[ 8 ] Liebe, H.J., "A contribution to modeling atmospheric mm-wave properties,"

Frequenz ( J . Telecom.), vol. 41, pp 31-36, 1987.

39
[9]

Liebe , H.J.; Manabe , T. ; Stricklen, J.P., "Millimeter-wave attenuation and

delay for a fog event," IEEE Digest 12th Int. Conf. Infrared and Millimeter

Waves, Orlando, Florida, December 1987.

[10] Liebe, H.J., "The atmospheric water vapor continuum below 300 GHz," Int. J.

Infrared and Millimeter Waves, vol. 5, pp 207-227, 1984.

[11] Falcone, V.J. Jr.; Wulfsburg, K.N.

;

Gitelson, S., "atmospheric emission and

absorption at millimeter wavelengths," Radio Sci., Vol. 6, pp 347-355,

1971.

[12] Guiraud, F.O.; Howard, J.; Hogg, D.C., "A dual-channel microwave radiometer

for measurement of precipitable water vapor and liquid," IEEE Trans.

Geosci. Electron. GE-17, pp 129-136, 1979.

[13] Hogg, D.C.; Guiraud, F.O.

;

Westwater, E.R.

,

"Emission measurements of 31.6

GHz absorption by atmospheric water vapor," Radio Sci., vol. 18, pp 1295-

1300, 1983.

[14] Decker, M.T.

;

Westwater, E.R.

;

Guiraud, F.O.

,

"Experimental evaluation of

ground-based microwave radiometric sensing of atmospheric temperature and

water vapor profiles," J. Appl. Meteorol., vol. 17, no. 12, Dec. 1978.

[15] Westwater, E.R., "The accuracy of water vapor and cloud liquid determination

by dual -frequency ground-based radiometry," Radio Sci., vol. 13, pp 677-

685, 1978.

[16] Chandrasekhar, S., Radiative transfer . Dover, New York, 1960.

40
[17] Westwater, E.R. , "Ground based passive probing using the microwave spectrum

of oxygen," J. Res. NBS , vol. 69D, pp 1201-1211, 1965.

[18] Slobin, S.D., "Microwave noise temperature and attenuation of

clouds : Statistics of these effects at various sites in the United States,

Alaska, and Hawaii," Radio Sci., vol. 17, pp 1443-1454, 1982.

[19] Allen, C.W., Astrophvsical Quantities , third ed.

,

Athlone Press, London,

1976.

[20] Hogg, D.C.; Guiraud, F.O.

;

Snider, J.B.; Decker, M.T.; Westwater, E.R.,

"Microwave radiometry for measurement of water vapor," Reviews of infrared

and millimeter waves , vol. 1, pp 113-154, ed. K.J. Button, Plenum Press, New

York, 1983.

* U. S. GOVERNMENT PRINTING OFFICE: 1989 -676-135/ 5105 41

JRS.114A (REV. 2-80

U.s. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publ ication Date

NISTIR 89-3918 July 1989

4. TITLE AND SUBTITLE

X-BAND ATMOSPHERIC ATTENUATION FOR AN EARTH TERMINAL MEASUREMENT SYSTEM

5. AUTHOR(S)

Michael H. Francis

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

10. SUPPLEMENTARY NOTES

~j Document describes a computer program; SF-185, FIPS Software Summary, is attached.

LI. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

The National Institute of Standards and Technology has developed an Earth Terminal

Measurement System to be used by the Camp Parks Communications Annex in determining

satellite effective isotropic radiated power and antenna gain. In determining these

quantities the effect of atmospheric attenuation must be taken into account. This

paper provides an overview of the methods used for determining atmospheric attenuation with emphasis on a tipping-curve method. An error analysis is also provided.

2. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

antenna gain; atmosphere; atmospheric attenuation; error analysis; satellite

communications; satellite effective isotropic radiated power (EIRP)

3. AVAILABILITY

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