*

ecknical rlote

Moulder laboratories

PB 161597

92o. 96

ON THE CLIMATOLOGY

OF GROUND-BASED RADIO DUCTS

AND

ASSOCIATED FADING REGIONS

BY

E.J. DUTTON

S. DEPARTMENT OF COMMERCE

IATIONAL BUREAU OF STANDARDS
"HE NATIONAL BUREA1 tRDS

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of Documents, Government Printing Office, Washington 25. D.C.
NATIONAL BUREAU OF STANDARDS

technical CY\ote,

96

June 16, 1961

ON THE CLIMATOLOGY OF GROUND-BASED RADIO DUCTS

AND ASSOCIATED FADING REGIONS

by

E. J. Dutton

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

DISTRIBUTED BY

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Price $1.75
The material contained in this report is drawn in part

from Telecommunications Performance Standards,

Tropospheric Systems, prepared under the sponsorship

of the Ground Electronics Engineering and Installation

Agency (Directorate of Engineering, ROZM), United

States Air Force. It has been prepared in Technical

Note form for use as lecture notes for the course of

Radio Propagation given by the Boulder Laboratories

of the National Bureau of Standards, July 31 - August

18, 1961.
ON THE CLIMATOLOGY OF GROUND-BASED RADIO DUCTS

AND ASSOCIATED FADING REGIONS

by

E. J. Dutton

ABSTRACT

An atmospheric duct is definedas occurring when geometrical optics

indicates that a radio ray passing upwards through the atmosphere is

sufficiently refracted that it travels parallel to the earth's surface.

Maximum observed incidence of ducts was determined to be 13%, 10%,

and 5% by analysis of three to five years of radiosonde data for a tropical,

temperate, and arctic location, respectively. Annual maxima are observed in the winter for the arctic and summer for the tropics. Arctic

ducts arise from ground based temperature inversions with the ground

temperature less than -25 C; temperate zone ducts arise from radiation

inversions and accompanying humidity lapse; while tropical ducts occur

with slight temperature and humidity lapses when the surface temperature

is 30 C and greater. The mean initial elevation angle of a radio ray

trapped by these ducts is found to be about 3 mr, with the maximum value

about 5.8 mr. The steepest gradient of N observed is -420 N units/km.

Observed ducts trap radio-waves of frequency 2: 1 kMc at all locations

for at least 50% of the time.

Fading regions arising from abnormal defocussing of radio-rays

passing from an elevated antenna down through the duct to a ground-based

receiver are analyzed. The horizontal extent of these regions is determined for the same arctic, tropic, and temperate conditions given above.

ON THE CLIMATOLOGY OF GROUND-BASED RADIO DUCTS

AND ASSOCIATED FADING REGIONS

by

E. J. Dutton

Part I: Ground Based Radio Ducts

1. INTRODUCTION

The occurrence of atmospheric ducts places limitations upon ray

tracing of VHF-UHF radio waves. Ducting is defined as occurring when a

radio ray originating at the earth's surface is sufficiently refracted so

that it either is bent back towards the earth's surface or travels in a

path parallel to the earth's surface. Although the rigorous treatment of

ducting involves consideration of the full wave equation solution [Booker

and Walkinshaw, 1946] rather than a simple ray treatment, the present

study will be based upon a geometrical optics definition of the limiting

case in which ray tracing techniques may be used. This simple criterion

is then applied to several years of radiosonde observations from stations

typical of arctic, temperate, and tropical climates to derive estimates of

the variation of the occurrence of radio ducts with climatic conditions.

2. METEOROLOGICAL CONDITIONS ASSOCIATED WITH RADIO

REFRACTIVE INDEX PROFILES

The path followed by a radio ray in the atmosphere is dependent

upon the gradient of the refractive index along that path. Of the vertical

and horizontal gradient components that compose the path gradient, the

horizontal gradient is normally negligibly small. Thus, the atmosphere

is considered horizontally homogeneous and only the vertical gradient of

the refractive index is utilized. The numerical value of the vertical gradient of the index of refraction depends on the vertical distribution of atmospheric temperature, humidity, and pressure.
-2-

Normally, temperature and humidity decrease with height in the

atmosphere, since turbulence prevents any great changes in structure.

However, there are periods of time in which the air becomes fairly calm,

whereupon temperature inversions and humidity lapses can be built up and

maintained. Temperature inversions have a two-fold importance in that

(a) they can be widespread in area and persist over a relatively long period

of time, and (b) they exercise a stabilizing influence on air motion such

that turbulence is suppressed and strong humidity gradients may develop.

Layers in which there is intense super refraction, to the point of duct formation may be formed as a result of these gradients and trapping of radio

waves may follow. The inversions may start at ground level or at some

greater height. The thickness of the layer can show great variability.

Three processes that form temperature inversions are:

Advection: Advection is the horizontal transport of air having certain

properties. Such a process is of importance in microwave propagation

since it may lead to a different rate of exchange of heat and moisture between the air and the underlying ground or ocean surface, thus affecting

the physical structure of the lowest layers of the atmosphere. This process results in air with different refractive index characteristics being

brought into the area. The most common and important case of advection

is that of dry air above a warm land surface flowing out over a cold sea. This type of advection frequently appears in the English Channel during

the summer when the weather has been fine for several days.

Advective duct formation depends on two quantities: (a) the excess

of the unmodified air temperature above that of water, and (b) the humidity

deficit (the difference between the water vapor pressures of the modified

and unmodified air). If these quantities are large, especially the humidity

deficit, an intensive duct may form.
-3-

Important advective processes can also occur over land, but the

conditions required for duct formation occur less frequently. However,

a duct may be formed when dry, warm air flows over cold, wet ground

with resultant temperature and humidity structure previously discussed.

Radiation: Differences in daytime and night-time radiation are the causes

of diurnal variation in refractive conditions. A subrefractive layer may

be present during the day, especially at the time of maximum surface

heating. Clear skies and light surface winds at night result in considerable cooling of the earth, thus causing the formation of temperature inversions. The surface heat loss produced by nocturnal radiation is a

prime factor in the formation of temperature inversions. Atmospheric

stratification formed by such a combination of meteorological parameters

may cause trapping. A temperature inversion is seldom strong enough

to produce a duct in the middle and low latitudes, but it is of major importance in the formation of ducts in the northern latitudes. Low stratus

clouds or extreme amounts of moisture (as in the tropics) tend to prevent

loss by radiation which lessens the possibility of duct formation.

If the ground temperature in a nocturnal inversion falls below the

dewpoint temperature, the water vapor in the lowest layers of the air

condenses and the heat of condensation is released directly to the air.

Under conditions of radiative fog formation, the humidity lapse tends to

counteract any temperature inversion present and may cause substandard

refraction if the humidity "inversion" is sufficiently strong. However,

the temperature inversion may be strong enough to keep the layer standard

or superrefractive.

Subsidence: Subsidence is the slow settling of air from a high pressure

system. The air is heated by adiabatic compression as it descends and

spreads out in a layer well above the earth's surface. This process
-4-

produces stable layers and inversions of temperature with an accompanying decrease in relative humidity. Since the air has come from a high level in the atmosphere, it is dry and may overlie a cooler, moist

air mass. This type of inversion may cause the formation of an elevated

superrefractive layer where the air temperature usually decreases immediately above the ground, rises through the inversion layer and decreases above the layer. This is a common occurrence which may be

observed at any time. Subsidence has a tendency to destroy subrefractive

layers and to intensify superrefractive layers. Although the effects of

subsidence are generally observed at high levels, they are occasionally

observed at lower levels, especially in the subtropics. Since subsidence

frequently occurs in the lee of mountains and in the southeastern regions

of northern hemisphere highs, elevated ducts may also be observed.

Conditions Inimical to Ducting: Conditions inimical to ducting are those

which induce mixing of the lower atmosphere. Small scale atmospheric

motions (turbulence) and consequent mixing and mass exchange result

from differential surface heating and surface roughness effects. Both of

these processes work to destroy stratification. They ultimately result in

uniform vertical distribution of moisture through considerable depths of

the lower atmosphere and the establishment of neutral temperature lapse

rates. Accordingly, where the process of mechanical and convectively

induced mixing are at work, the probability of the occurrence of ducting

is vanishingly small. Thus, few, if any, ducts are observed over snowfree, low albedo land areas from mid-morning to late afternoon when the

skies are clear, or in areas of moderate to great surface roughness when

the surface winds are more than a few meters per second, irrespective

of cloud conditions or the time of the day.
-5-

Refractive Conditions Due to Local Meteorological Phenomena

Land and Sea Breeze: Land and sea breeze may produce ducts along the

coastal regions since the winds are of thermal origin, resulting from

temperature differences between land and sea surfaces. During the day,

when the land gets warmer than the sea, the air above the land rises and

is replaced by air from the sea, thus creating a circulation from the sea

to the land, called a sea breeze. During the night, the land becomes

colder than the sea and a circulation, called a land breeze, is set up in

the opposite direction. This type of circulation is generally shallow and

does not extend higher than a few hundred meters above the land or sea

surface.

A land or sea breeze may modify the refractive conditions in

different ways depending upon the distribution of moisture in the lower

layers. Since these breezes are of a local nature and generally extend

only a few miles, only coastal locations are usually affected. The very

nature of sea and land breezes results in a marked refractive index

pattern. With a sea breeze a duct may be formed over the water due to

subsidence. The land breeze is accompanied by subsiding air over the

land with resultant duct formation.

Fog: The formation of fog results in a decrease of superrefractive or

ducting possibilities. When fog forms by nocturnal radiation, the water

content of the air remains practically the same; however, part of the

water changes from the gaseous to the liquid phase thus reducing the

vapor pressure. The resulting humidity lapse rate tends to counteract

the temperature inversion and cause sub-standard refraction. However,

the temperature inversion may be strong enough to keep the layer standard

or superrefractive. This process may also occur with advection fogs

.
-6-

Nocturnal Ducts: The night-time temperature profile is a result of the

interaction, between nocturnal radiation, turbulence, and heat conduction.

The associated refractive index profiles are such that a radar duct begins

to form about the time of sunset, developing quickly during the early evening, more slowly after midnight, and dissipating rapidly after sunrise.

This is mainly an inland effect resulting from large diurnal temperature

variations observed in the interiors of large continents. However, a shallow body of water may have an appreciable diurnal temperature variation, as compared to the open ocean so that superrefraction may occur

over such a location from time to time.

Limitations of Radiosonde Observations: It is generally recognized that

radiosonde observations (RAOB's) do not have a sufficiently high degree

of accuracy to be completely acceptable for use in observing changes in

the degree of stratification of the very lowest layers of the atmosphere;

however, until more accurate methods such as meteorological towers and

refractometer measurements are more commonly used, the RAOB will

continue to be used as a basis for forecasting the occurrence of superrefractive conditions.

3. BACKGROUND

The property of the atmosphere basic to radio ray tracing is the

radio refractive index of the atmosphere, n, which, for VHF-UHF frequencies at standard conditions near the surface, isanumber of the

order of 1.0003. Although the refractive index is used in ray tracing

theory, it is more convenient when evaluating refraction effects from

common meteorological observations to use the refractivity [Smith and

Weintraub, 1953], N, which, for the frequency range - 30,000 Mc> is

given by:
-7-

. 4810 e RH

(n - 1) 10

6

= N = ^

P+—=-± (1)

where P is the station atmospheric pressure in millibars, and RH is the

percent of the saturation vapor pressure, e , in millibars at the absolute temperature, T, in degrees Kelvin.

When evaluating the meteorological conditions that give rise to

refractive phenomena, it is frequently instructive to examine separately

the behavior of the dry component, D, and wet component, W, of N.

These components are given by:

D=^P. (2)

and

3.73 x 10

5 e RH

W= -

7

* (3)

T*

The gradient of the refractivity, AN, with respect to height may

then be expressed:

AN = AD + AW (4)

Average values of AN, AD and AW are given for two increments between

the earth's surface and one kilometer above sea level for Fairbanks,

Alaska; Washington, D. C; and Swan Island, W. I.; in Table I.
-8-

Table I Gradient of N, D and W in (N units per kilometer)

Station Height

Increment

F<

-AN

ebrua

-AD

ry

-AW -AN

August

-AD -AW

Fairbanks,

Alaska

surface -0.5 Km

0.5 Km - 1.0 Km

37

35

41

35

-4 31

36

27

24

4

12

Washington,

D. C.

surface -0.5 Km

0.5 Km - 1.0 Km

41

30

34

26

7

4

60

46

28

24

32

22

Swan Island,

W. I.

surface - 0.5 Km

0.5 Km - 1.0 Km

39

58

24

24

15

34

47

66

26

24

21

42

Several general observations may be made of the data of Table I: The gradient of the dry term is relatively less variable than that of

the wet term when considered as a function of season or height; the increase of AN from winter to summer at a particular location or from

arctic to tropical climate at a given time is most strongly reflected in

AW rather than in AD. The marked increase of gradient with height

for Swan Island reflects the drop of refractivity across the interface of

the trade wind inversion where dry subsiding air overlies the moist

oceanic surface layer.

A fundamental equation used in radio ray tracing is Snell's law

which, for polar coordinates, is given by:

nrcos 9 = n r cos 9 , (5) o o o

where n is the radio refractive index of the atmosphere, r is the radial

distance from the center of the earth to the point under consideration,
-9-

9 is the elevation angle made by the ray at the point under consideration

with the tangent to the circle of radius r passing through that point. The

radius to any point, r, is usually given as (a + h) where a is the radius

of the earth and h is the height of the point above sea level. The zero

subscript refers to the value of n, r, or 9 at the earth's surface.

For the present study, geometrical optics techniques, similar to

those considered by Bremmer [ 1949], are used to indicate when refrac -

tion is sufficiently great to direct a ray either back to earth or in a circular path at a constant height above the earth, i.e.:

n r cos 9 ° ° -^ > 1. (6)

n r

This condition then allows one to obtain the value of 9 which divides

o the rays into two groups; those that penetrate the duct and those that

are trapped within the duct. This particular value of 9 , called the

angle of penetration and designated 9 , is obtained by noting those

instances where

n r ^ 1 (7)

n r

and solving for the value of 9 such that (6) is equal to unity.

It is instructive to consider the order of magnitude of refractive

index gradient needed for trapping for several commonly observed refractive index profiles. If we rewrite Snell's law,

n r cos 9 = n A r . cos 9 , (8)

t t t A A d
-10-

where the subscripts t and A refer to the values of the variables at the

transmitter height and the top of the trapping layer, then trapping

occurs when

n r _t t_ nA

rA

^ 1. (9)

and the angle of penetration at the transmitter, , is given bysetting

n r _t t_ nA

r A

cos 0=1

P

(10)

The maximum permissible n gradient for a given value of is then

given by:

An

Ar

n n . t - A

A t (ID

where n must satisfy (10), i. e.

n r n.= cos

r A

(12)

By designating r = r + h (11) becomes

An

Ar

n

1 - r n

1 \ cos e„

r

t + hA

P

(13)

By rewriting (13),

An

Ar

n

cos

1 + P J1. (14)
-11-

hA N->

and expanding f 1 + ] and cos , one obtains the expression:

\

r

t / P

e

2

An _

| _L _p_

Ar t I r 2h A

"- t A -'

p 1 by neglecting terms of the order / and ( — ) . r

t

(15)

For the case of 8 = (15) reduces to: P

—— = — ~ — f 157 N units /kilometer , (16) Ar a a

It is seen from (15) that the n gradient necessary to trap a

radio ray at a given value of 9 is practically independent of transmitting antenna height above the earth. For example, a =0 ray will

be trapped by an n gradient of -157.0 N units/kilometer at sea level,

where n. = 1.0003, while the necessary n gradient at 3 kilometers above

sea level will be -156. 9 N units/kilometers for an n^ = 1.0002. This

indicates for all practical applications, that the necessary n gradient

for trapping is independent of altitude. Further, by considering the

temperature and humidity gradients encountered in the troposphere, one

is led to the conclusion that ducting gradients would not be expected to

occur at altitudes greater than 3 kilometers. In fact, Cowan's [1953]

investigation indicates that trapping gradients are nearly always confined

to the first kilometer above the surface.

A consideration of (15) indicates that the magnitude of the negative gradient necessary for ducting is 1/a for 0=0 but increases in

proportion to /2h as increases. The gradients necessary for

Jr p
-12-

atmospheric ducts as a function of 9 are given for several different

profiles in figure 1. An analysis of radiosonde data indicates that

gradients in excess of 0. 5 N units per meter are seldom exceeded

within atmospheric layers. It is interesting to note how rapidly the

necessary gradients increase to the approximate upper limit of radiosonde-observed gradients: a ground-based layer 100 meters thick attains

this gradient at 8. 3 milliradians while the maximum observed gradient

is intercepted by the 30-meter layer curve at =4.5 milliradians.

A third example was calculated for an elevated layer 0.5 km above the

ground and 100 meters thick by assuming normal refraction between

the ground and the base of the layer and solving for the necessary

ducting gradient within the layer. The large values of n gradient

necessary for this case explains why elevated ducts were not observed.

Although the preceding examples were calculated for a ground transmitter,

the combinations of 9 , An/Ar, and Ar are very nearly the same as would

P

be obtained for any other transmitter height within the first 3 kilometers

above the surface.

4. DESCRIPTION OF OBSERVED GROUND-BASED ATMOSPHERIC DUCTS

Approximately three years of radiosonde data typical of an arctic

climate (Fairbanks, Alaska), a temperate climate (Washington, D. C.) , and a tropical maritime climate (Swan Island, W. I. ) were examined by

means of a digital computer for the occurrence of ducts during the months

of February, May, August, and November. The percentage occurrence

of ducts is shown on figure 2. The maximum occurrences of 13. 8% for

August at Swan Island and 9. 2% for Fairbanks in February are significantly greater than the values observed at other times of the year.
REFRACTIVITY GRADIENTS

NEEDED FOR RADIO DUCTS

1300

1200

MOO

1000

Q> 900

Q_

V) 'E

x

<

800

700

600

500

400

300

200

100

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03km thi N = 320

Layer —

Ground Bt

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r N = 320

milnimum Gruoienr — i /a

9 in Milli radians

Figure
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14

12

II

10

9

8

5

4

FREQUENCY OF OCCURRENCE

OF GROUND BASED DUCTS

o

Nun

num

<bers o ber of n curvt

profile

?s are > s anal)

fotal

'sed.

,218

226

SWL7/7 Isla nd^ 166

473, s496

151

14'ashinc,lion, L\CS

472

247

'175 Fairbanks, 4/#.ska —J

447 247* 247 FMAMJJASOND

Months of the Year

Figure 2
-13-

The Washington data display a summertime maximum of 4.6%. These

data indicate that the temperate zone maximum incidence is about onehalf the wintertime maximum incidence in the arctic, and about one-third

of the summertime tropical maximum.

The range of observed values of 9 is shown in figure 3. The mean

value calculated for each month as well as the maximum and minimum

values of observed for the limiting cases are given for each month and

location. The mean value of the angle of penetration under these conditions

is between 2 and 3 milliradians and appears to be independent of climate.

The maximum value of observed during ducting is 5. 8 milliradians.

The refractivity gradients observed during ducting are given on

figure 4. The maximum gradient of 420 N units per kilometer was observed during February at Fairbanks, Alaska. The mean values of N

gradient appear to follow a slight climatic trend from a high value of

230 N units per kilometer at Fairbanks to a value of 190 N units per

kilometer at Swan Island.

Another property of radio ducts is their thickness which is given

in figure 5. Again there is observed a slight climatic trend as the median thickness increases from 66 meters at Fairbanks to 106 meters at

Swan Island. These values of thickness correspond to the gradients

given in figure 4. One can then obtain, by linear extrapolation the thickness at which the gradient is equal to -l/a; i. e. , the height corresponding

to the gradient just sufficient to trap the ray at =0. These values,

shown on figure 6, display an increase in the median thickness of about

25% for Swan Island, 100% for Washington, and 200% for Fairbanks,

which results in a reversal of the climatic trend of the observed thickness

between Fairbanks and Swan Island. This increase in height emphasized

the preceding conclusion. Fairbanks is characterized by shallow layers

with relative intense gradients.
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These maximum duct widths may be used to estimate the maximum radio wavelengths trapped. Kerr [ 1951] gives the maximum

wavelength, X, trapped by given thickness, d:

X =CV l/2

d

3/ 2

, (17) max

by assuming a linear decrease of n within the duct. The coefficient

c is a constant and y is a function of the n gradient excess over the

minimum value of AN/AH = l/a. Expressing X in centimeters, and

d in meters, then

N - NJ

* d

- .157 VlO'6

, (18) d /

and c = 2.514 x 10

2

.

The maximum wavelengths trapped during ducting conditions were

estimated by (17) for the maximum duct thicknesses of figure 6. These

values, given in Table II, were determined for the month with the

maximum occurrence of ducts, thus allowing an estimate of the radio

frequencies likely to be effected by ducting conditions. Note, for ex- ample, that the data of Table II indicate that 1000 Mc rays (X. = 30 cm)

will be trapped by 50% of the ducts regardless of location.

The reader is cautioned that an atmospheric duct does not have

the sharp boundaries of a metallic waveguide. Thus the maximum

wavelengths obtained by (17) do not represent cut-off frequencies but, as

Kerr is so careful to emphasize, merely suggest lower limits under the

assumptions of this rudimentary theory.
-15-

Table II

Estimated Maximum Wavelength Trapped at 9 Q

=

Percentage of ducts that trap wavelengths in centimeters

Station equal to or shorter than tabulated value

95% 90% 75% 50% 2 5% 10ft 5%

Fairbanks, Alaska 20.5 22.6 25.5 34.0 43.5 61.5 69.0

(February)

Washington, D. C. 7 10 27 50 112 164 200

(August)

Swan Island 12 23 41.5 60 82.3 92 132

(August)

5. TEMPERATURE AND HUMIDITY DISTRIBUTIONS

ASSOCIATED WITH DUCTS

An example of the temperature and humidity distribution typical

of each station is given on figure 7. The Fairbanks duct is accompanied

by a surface temperature of -25 C with a strong temperature inversion

and a slight humidity lapse, indicating temperature inversions associated

with wintertime cooling of the air next to the ground. The Washington

example appears to be typical of the temperate zone temperature inversion. The Swan Island profile shows a moderate lapse of both temperature and humidity. This apparent contradiction is explained by the

strong lapse in vapor pressure associated with the moderate lapse in

temperature when the initial temperature is near 30 C. The strong vapor

pressure lapse presumably arises from evaporation from the sea surface.

This effect was further examined by studying the percentage of the total

N gradient of each duct that was contributed by the gradient of the dry

and wet terms. The median contribution of the dry term gradient, summarized in Table III, displays strong seasonal and geographic differences.
-16-

Table III Median Contribution of AD/AH to AN/AH for Ducting Conditions

Washington, D. C.

73.0%

33.5%

26 . 5%

55.0%

Fairbanks

February 103%

May- 40. 5%

August 37. 0%

November 62. 0%

Swan Island

9 .5%

2 • 0%

4. 5%

6. 0%

The dry term contribution decreases from summer to winter and from

arctic to tropical climates. The Swan Island ducting gradients are at

least 90% due to humidity lapse, while the Fairbanks winter time maximum is due to the strong temperature inversion associated with very

low surface temperatures. In fact, under these conditions, vapor pres

sure increases with height with the result that the dry term contributes

more than 100% of the ducting gradient.
TEMPERATURE AND HUMIDITY PROFILES

FOR TYPICAL GROUND-BASED DUCTS


 o>

"CD

(JOM—

V_

CD

CD>o

<

'cd 1

300

200

100

300

200

100

300

200

100

SWAN SLAND

8-2C)-53. 1500 GMT

i

1 -Duct

t ness1

i

1

1

i

WASHINGTON, D.C. 8-19 -53, 0900 GMT

\

u 7

Duct Thickness

i I /

FAIRBANKS .ALASKA 1 3-2-53, 1 500 G.MT

i /

Duct Thickness

1 /

/

25 50 75 100 -40 -30 -20 -10 10 20 30 40

Relative Humidity Temperature in Degrees Centigrade

Figure 7
SHADOW ZONE OCCURRENCE ON A CURVED EARTH

WITH THE TRANSMITTER ABOVE THE DUCT

Figure 8
-17-

6. CONCLUSIONS: Part I

The results given above were derived from a consideration of

radiosonde data. Although the radiosonde is not an extremely sensitive

instrument, it is readily available and is the only source of climatic

information involving the temperature and humidity structure of the

atmosphere. It is believed that the radiosonde data will at least yield

the climatic trend of radio ducts as well as their probable temperature

and humidity distributions. Further, it is evident that the choice of

stations will definitely affect the percentage of ducts observed. For

example, it is almost certain that a greater percentage of ducts would

be observed over water in the sub-tropics than over Swan Island.

With these reservations ?in mind, the present study has shown:

(a) .Ducts ocGur no more than 15% of the time.

(b) The annual cycle of the incidence of ducts is

reversed for the arctic and tropical stations studied. The

arctic station has a wintertime maximum and the tropic

station a summertime maximum. The temperate station

has a summertime maximum incidence of less than 5%.

(c) The maximum initial elevation angle is limited to 5. 8 mr

with a mean value of about 3 mr.

(d) The steepest gradient of N observed is -420 N units per

kilometer.

(e) The maximum thickness of observed ducts is

such as to trap radio-waves of 1000 Mc and above at all

locations for at least 50% of the observed ducts.
-18-

(f) Ducts in the arctic appear to be associated with

temperature inversions at ground temperatures of

-25 C or less; temperate zone, with the common radiation

inversion and accompanying humidity lapse; tropics, with

a moderate temperature and humidity lapse for temperatures

of about 30 C.

Part II. A Study of Fading Regions Within the Horizon Caused by A Surface

Duct Below a Transmitter.

7. INTRODUCTION

Among the factors influencing the choice of an antenna site for a microwave receiver operating on a line-of-sight path is the desirability

of locating in a region relatively free from space-wave fadeouts. Although

line-of-sight propagation is normally characterized by steady, high, dependable signals, deep, prolonged space-wave fadeouts are observed from

time to time. Since serious disruptions occur during such fadeouts, a systematic discussion of fading phenomena is of considerable interest to

the radio circuit engineer.

This section describes the conditions under which fading occurs,

fading variations, and locations that favor the occurrence of fading within

the radio horizon.

Fading, or fadeout, of a radio wave may be defined as a drop in

power or field strength below a specified level of intensity. For a given

site, criteria may be set up by the communications engineer to establish

the magnitude of drop that defines the onset of fading conditions. This

magnitude usually ranges from about 5 to 30 db below the specified level

of intensity. The specified level is derived from some ideal propagation

condition.
-19-

Fading is also a time-dependent occurrence. It may be classified

as (a) prolonged fading, which is fading of sufficient interval to cause

continued communication disruptions, and (b) short-term or "roller"

fading, which is only instanteously observed by a receiver. The differentiation between prolonged and short-term fading is left to the discretion

of the communications engineer.

One of the main causes of deep fading of field strength within the

horizon as compared with the free space field strength value is the structure of the atmosphere. When one refers to the "structure" of the atmosphere, one generally means the refractive index structure. An easier

way of representing the structure of the atmosphere is by means of the

radio refractivity, N. Theoretically, the atmosphere might be considered

horizontally homogeneous and in spherical stratifications concentric with

the earth, and N can be considered to decrease exponentially with increasing height above the earth's surface. However, in reality, this picture of

the atmosphere is rarely, if ever, realized, because of the synoptic meteorological conditions that are perpetually present. Stratifications caused

by the synoptic meteorological pattern give rise to field strength fading

within the horizon by defocusing the lobe pattern of the transmitter along

a given path. Whenever the rate of change of refractivity from the surface value with height (called the gradient of N with height) is less than -157

N units per kilometer, a "ducting" condition is said to exist at the surface,

and, as shown in figure 1, certain rays will tend to be "trapped" or guided

within the surface duct. It is this atmospheric condition of surface ducting

which will be further explored herein with respect to fading within the radio

horizon.
-20-

8. REGIONS AND EXTENT OF FADING WITHIN THE HORIZON IN

THE PRESENCE OF SUPERREFRACTION

Serious disruptions in reception from a transmitter above a

duct to a receiver within a duct can occur at particular points within the

horizon. It is these disruptions, and these locations, which are of interest to the communications engineer establishing a given transmittingreceiving path. Whenever these disruptions occur between a transmitter

and receiver within the horizon, a corresponding increase in the field

strength characterized by steady high, dependable signals, is usually

expected beyond the horizon. The high signal strength is in keeping

with the properties of a surface duct. Nevertheless, deep, prolonged

fadeouts can occur in regions beyond the horizon as well as within the

horizon.

Price [ 1948] has theoretically determined regions of deep radio

fading associated with surface ducts, which he has termed "shadow zones".

In the case of a transmitter above a surface duct, a representation of what

occurs is shown in figure 9. It shows the location of a shadow zone above

the radio horizon line in the normal interference region. In the interference region, a fadeout of signal strength due to the presence of superrefraction must be compared with the value of the field when only the

interference pattern is present. Papers such as those by Norton [ 1941],

and Kirby, Herbstreit, and Norton [ 1951] give methods for calculation

of the normal interference field. Ikegami [ 1959] gives a more general

method for the calculation of received power in the presence of groundbased ducts.

In the procedure that follows, a model for the determination of the

location and extent of shadow zones, rather than the determinations of the

actual received field strengths and powers at any particular point, will be
RADIO RAYN

Figure 80
>- z < o

(Z

M

q:ox

UJ

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LU LU LU

Z. _l (Z

X

O U_ , 1— M LU LU 1

-^11 (£ <^>

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c/)

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oo

h-o

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-21-

given for conditions typical of the arctic, temperate, and tropical climates

to aid the radio circuit engineer in avoiding these troublesome interference

areas.

Washington, D.C. , is taken to represent an average temperate

zone climate, Swan Island an average tropical zone climate, and Fairbanks,

Alaska, an average arctic zone climate. Considerable work has been done

in determination of various ducting conditions at these three stations as

well as with the average exponential refractivity above these stations.

Therefore, these three stations will be used as models for all following

calculations.

The gradient of N with height determines whether or not a surface

duct will exist. Therefore, surface ducting atmospheres corresponding to

conditions at Washington, D. C, Swan Island, and Fairbanks, consisting of

a ducting gradient up to any desired height and the N =313.0, 377. 2, and

313.0 exponential atmospheres of Bean and Thayer [ 1959] above this height,

have been chosen for this study. The ducting gradients chosen are maximum, mean, and minimum values for February, May, August, and November (representing the middle of winter, spring, summer, and fall,

respectively) taken from figure 4 and given in Table IV. Also in these

particular models the duct is assumed to be of uniform height throughout

the region considered in the calculations.

9. THEORY AND RESULTS

In figure 8, although it is known that ray theory does not explain

what happens to the radio ray at the point A when the ray is tangent to the

top of the duct, because of the apparent ray intersection, it is sufficient

to define the first shadow zone as that zone between the two possible paths

of the ray tangent to the duct at a point A (this is the ray emitted from the

transmitter with an initial angle of 9 with the horizontal).
-22-

TABLE IV

Duct

Gradients

at Washington D.C

Ranges of Surface Ducting Gradients

N units/ km N units/ km N units/ km

February May August

N units/ km

November

Max -200 -372 -395 -195

Mean -185 -230 -240 -170

Min -175 -162 -158 -159

Duct

Gradients

at Swan Is land

N units/ km N units/ km N units/ km N units/ km

February May August November

Max -195 -268 -282 -282

Mean -173 -193 -193 -203

Min -160 -158 -158 -170

Ducts N units/ km

Gradients February

at Fairbanks, Alaska

N units/ km N units/ km N units/ km

May August November

Max -420 -159 -286 -222

Mean -242 -159 -286 -177

Min -169 -159 -286 -159

This is possible because it can be readily seen that no radiation will be able

to enter the shadow zone, and thus, a receiver located in the shadow zone

will theoretically receive no signal from the transmitter. The portion of

the "split" ray that enters the duct at A will be reflected at point B to point

C, where it "splits" again. The distance, d, from point A to C projected

along the earth's surface will be designated the "length" of the first shadow

zone. If the surface duct is homogeneous throughout, the ray will be

symmetrical about point B and, therefore,
-23-

d

l =d2

= d/^ d

h.<' (19)

where d , and d, are the "half-lengths", d ., of the shadow zone.

1 c. h£

Schulkin [ 1952] shows that the bending, t , of a radio wave

1 , L, between any two points in the atmosphere is given by

T i,2= -r

1 +(9 i- 8 2>- « 20>

where d is the distance between the two points 1 and 2 (See figure 8a)

1 , £

projected along the earth's surface, a is the radius of the earth, and

and 6 are the angles in radians the ray makes with the horizontal at points

1 and 2 respectively. Schulkin [ 1952] also gives Tj

2

* n radians as

= An

x " An

2 for o<9 < 10°, (21)

1,2 —

m

where An, = n, -1, An_ = n -1, 6 = (8 + 0J/2. In terms of refrac- 11 2 L m 1 &

tivity, equation (21) becomes

(N - NJxlO"6

A1VT in -6

1 2 AN x 10 .,_, r =

g

= — . (22)

m m

Considering now the case of the half-length, d , equation

(22) becomes

dM

T, , = — + 8 , (23)

1,2 a p

since Q^ = at the top of the duct, and 0=9 (See figure 8). Now substituting equation (22) in equation (23):

2AN x 10' 6

= ^h£_ + e i (24)

9 a p P
24-

since here 6 =9/2. Rearranging equation (24) m p

I 2AN x 10 . fl , ,. 1 l? c\ d = a T-—-. —— + 6 (rad) . («)

hi 6 (rad) p*

Since

n . r -1 A A ~ N/,f AM -6 (r -a)

9 = cos = 2! AN x 10 - A , (26)

p n a i —__

(rad)

where n is the index of refraction at the top of the duct, r is the

A. A

distance from the center of the earth to the top of the duct, and n is the

index of refraction at the earth's surface, it is seen that d is uniquely

determined from the surface gradient of N with height inside the duct,

provided the height of the duct is known.

If one desires to know the distance, d , for a particular height, h,

h

from the reflection point of the ray in the duct (point B in figure 8), where

d, is such that

h

,Sdh

J V (27)

then equation (20) becomes

^6

d

h

= a s^rS- <%-•«> (28)

p 2

since 9 is no longer just equal to zero, but is such that

< o < 9 (29)

2 p

'

and AN will no longer be the same as the AN for the duct width.
-25-

may be determined from the formula:

Cm

e o s ^e2 + ih _ 2AN> {30)

Z pa

In figures 10 - 18 the shadow zone half-lengths are given as a function of duct height for the various seasons of the year. In figures 19 -

22 the Washington, D. C. , values of shadow zone half-length are again

given as a function of duct height, but this time the ducting gradient is

used as a parameter . This was done specifically to point out the seasonal

trend of the half-lengths. Washington is the only station plotted since it

is the only station of the three considered that has an appreciable seasonal

variation in weather along with sufficient data with which to plot the trend.

As might be expected, a wider range of distance variations is to be found

in the spring and summer months than in the fall and winter months because of the greater percentage of ducts at Washington, D. C. , during the

spring and summer seasons. As shown in figure 5, the 50% level, or

median of observed ground-based duct thickness at Washington, D. C. , is

about 100 meters, at Swan Island about 108 meters, and at Fairbanks, Alaska,

about 65 meters. The 50% levels of observed maximum ground-based duct

thicknesses are about 200, 135, and 185 meters, respectively, for Washington, D. C. , Swan Island, and Fairbanks, Alaska. In Table V, the values

of d during the four seasons are shown for the 65, 100, 108, 135, 185, and

200 meter surface duct heights.

As previously mentioned, the atmospheres above the assumed duct

were taken to coincide with the N =313.0, 377.2, and 313. exponential

atmospheres of Bean and Thayer [ 1959] because these values most nearly

correspond to the annual average N value at Washington, D. C, Swan

Island, and Fairbanks, respectively. Figures 23 - 26 show the distance

measured along the earth's surface that a ray with an initial elevation angle
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TABLE V

Half-lengths for Various Duct Heights and Surface

Gradient Conditions

Feb.

May

Aug.

Nov.

Washington,

D.C.

Fairbanks,

Alaska

Swan I sland

C\Duct

nVht. 100m 200m 65m 185m 100m 135m

Max 68.21 96.46 22.08 37,25 74.00 98.96

Mean 84.50 119.50 38.63 65. 18 112.80 147.63

Min 105.35 148.98 100.54 169.61 248.75 325.56

Max 30.53 43. 17 231.60 390.71 43.65 57. 13

Mean 52.37 74.05 231.60 390. 71 75,99 99.46

Min 199.42 281.95 231.60 390.71 401.86 525.95

Max 29.02 41.04 31.43 53.03 41. 16 53.87

Mean 49. 12 69.46 31.43 53.03 75.99 99.46

Min 440.73 622. 53 31.43 53.03 401.86 525.95

Max 72.56 102.60 44. 10 74.40 41. 16 53.87

Mean 123.93 175.24 78.53 132.49 67.38 88. 19

Min 313.61 443.23 231.60 390.71 124.70 163.20

of zero will travel in the N =313.0 and 377. 2 exponential atmospheres.

The value of zero for an initial elevation angle is used because the ray

can be thought of as leaving the position A, tangent to the duct in figure 8

and "arriving" at the transmitter, even though the reverse process is

actually what is occurring. Thus, from figures 23 - 26, knowing the height

of the transmitter, h., and the height of the ground-based duct, h^, the

distance, d , that the radio ray travels from the transmitter to the top of

the duct is given by
27

i.e., the distance obtained by using the difference of h. and h« as the

value of height on the abscissa in figures 23 - 26 gives the distance d .

The distance, d, , to the standard radio horizon from the trans

ho

mitter is

d, = N/2h" (32) ho t

if h , the transmitter height, is in feet and cL is in miles. Using this

fact and figures 23 - 26, Table VI, which shows the ratio of d to d, , is 6 o ho

derived for various transmitter heights and various duct heights. This

table is useful in determining the portion of the distance (measured from

the transmitter) within the horizon where fading due to the presence of super

refraction has no effect on transmission. Table VII shows the number

(sometimes a fraction) of half-lengths of shadow zones contained within

the standard radio horizon for the maximum, mean, and minimum ducting

gradients during the four seasons. Table VII is for the 50 per cent level,

mean, and maximum surface duct thicknesses - to represent ordinary and

maximum conditions of ground-based ducts described previously.

10 SAMPLE COMPUTATIONS

It can be seen from figure 51 that

h ^ loss region < h + h , (33)

1 J\ &

where h can be determined from figures 27 - 50, which depend upon the

station location and the season of the year; h is the height of the duct; and

h is determined from figures 23 - 26. The following example will illustrate the determination of the shadow zone.

As an illustrative problem, assume a 500-meter transmitting antenna in the spring of the year at 40°N latitude, and that one desires to

place the receiving antenna at (a) 40 km and (b) 90 km from the transmitter.
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How high should the receiving antenna be to be free from fading loss caused

by a ground-based superrefractive layer?

Since both of the distances required are within the standard horizon

distance, d, , which, for a 500 meter transmitter is

ho

d, = 92. 181 km,

ho

this is a case of within-the-horizon propagation.

Since the 40 N latitude position is within the temperate zone, use

will be made of the Washington, D. C. , model ducting atmosphere. As

previously mentioned, 100 meters is the median mean duct thickness at

Washington, D. C. , and 200 meters is the median maximum duct thickness

observed at Washington. These are the two duct thicknesses to use in this

calculation. Also, since it is the spring of the year, figures 30 - 32 must

be used to determine h .

For the 40 kilometer distance (case (a)), the subscript of equation

(31) becomes

h - h A = 500 - 100 = 400 meters,

t A

which is then entered on the abscissa of figure 23, where,

d = d. nn = 83 km.

o 400

For a 200 meter thick duct,

Therefore, in this case,

h - h . = 300 meters

t A

d = d 0rtrt = 72 km.

o 300

In either case, as can be seen from figure 8, d is greater than 40 kilometers. Therefore, any height of the receiving antenna will be
-34-

satisfactory at this point, since the first shadow zone has not yet been

reached.

For the 90-kilometer distance (case (b)), it can be seen that this

distance is beyond the onset point of the first shadow zone, and figures

30 - 32 must be used here.

All of figures 27 - 50 are used differently depending upon which

side of the reflection point B of figure 51 one desires to locate an antenna.

If on the left-hand side of point B, one must subtract the desired distance

from the distance from B to the top of the duct traversed by the ray and

use this new distance to determine height, h, in figures 27 - 50. This

procedure must be followed every time the ray heads downward. If on

the right-hand side of point B of figure 51 (or any other reflection point),

one simply uses the distance from the reflection point directly. One must

keep in mind that any previous half-lengths must be subtracted from the

desired distance from the transmitter, as well as subtracting d , in order

to obtain the distance used in figures 27 - 50.

Applied to the problem where figures 30 - 32 are used, for the

maximum midspring ducting conditions ( figure 30) and the 100-meterthick duct, recalling d =83 kilometers, the antenna is to be located

90 - 83 = 7 km

beyond the onset point of the shadow zones. For the 200-meter duct the

antenna is located

90 - 72 - 18 km

beyond point A of figure 51. From figure 10, the half-length traveled by

a ray in a 100-meter duct under maximum midspring ducting conditions is

30.5 kilometers. Thus, as described above, the distance used in figure

30 is

30.5 - 7.0 = 23.5 km
-35-

to find h , because at 25 kilometers the ray is still sloping downward and

hence is on the left-hand side of point B of figure 51. From figure 10,

d, = 43 kilo:

hi

figure 30 is

d, = 43 kilometers for a ZOO meter duct; therefore, the distance used in

ru

43 - 18 = 25 km.

Similarly, utilizing figures 11 and 12 for mean ducting and minimum

ducting conditions for a 100-meter and 200-meter duct:

Figure 31 distance to be used for the 100-meter duct = 45 km.

Figure 31 distance to be used for the 200-meter duct = 56 km.

Figure 32 distance to be used for the 100-meter duct =191 km.

Figure 32 distance to be used for the 200-meter duct = 262 km and

hence

h for a 100-meter duct under max. spring ducting conditions = 92. 3 m.

h for a 200-meter duct under max. spring ducting conditions = 166.0 m.

h for a 100-meter duct under mean spring ducting conditions = 96.0 m.

h for a 200-meter duct under mean spring ducting conditions = 187.0 m.

h for a 100-meter duct under min. spring ducting conditions = 99.0 m.

h. for a 200-meter duct under min. spring ducting conditions = 199.0 m.

Figures 23 and 24 will be used to determine h from the total distance, d. The distance to be used is obtained by subtracting the distance,

d , from the desired distance. For the 100-meter duct, d = 83 kilometers u o and

d = 90 - 83 = 7 km.

Likewise for the 200-meter duct, d = 72 km and

o d = 90 - 72 = 18 km.

Thus it is found that for the model assumed:

h^ for the 100-meter duct height case will always be 3 meters,

h^ for the 200-meter duct height case will always be 18 meters.
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-36.

Since from equation (33)

h. ^ loss region < h + h .

Therefore, in answer to part (b) of the problem, for maximum ducting

conditions with a 100-meter thick duct:

92. 3 m. ^ loss region S3 + 100 m.

92.3m. ^ loss region^ 103m.

with a 200-meter thick duct:

166m. ^ loss region < 18 + 200m.

166m. ^ loss region ^ 218m.

For mean ducting conditions with a 100-meter thick duct:

96 m. ^ lo ss region^ 103 m.

with a 200-meter thick duct:

187m. ^ loss region^ 218m.

For minimum ducting conditions with a 100-meter thick duct:

99 m. < loss region^ 103m.

with a 200-meter thick duct:

199.3m. ^ loss region^ 218m.
-37-

It should be pointed out that this method does not guarantee prevention of all fadeouts due to superrefraction, but merely affords an

estimate. It is therefore recommended that if RAOB equipment is available, actual computations using equations (25) - (30) be made over a period of time to completely determine the ducting fadeout regions at a particular point.

1 1 . VARIATIONS IN FADING

It should be remembered that the three-station model is representative of the arctic, temperate, and tropical zones only, and that great

variations could be found within specific subdivisions of these areas.

Furthermore, temporal variations are to be considered with respect to

formation and decay of ducts. One must also consider the waveguide

effect of ducts, in that they have a particular "cut-in" frequency, and will

not respond to all frequencies as discussed in section 4. Thus, a fadeout

may appear at one frequency and not at another. The fact that the atmosphere is never ideally homogeneous should also be considered., To obtain

precise results, one should try to have RAOB or similar readings as close

to the transmission path as possible when actually trying to run shadow

zone calculations of his own. One should also avail himself of as many

daily profiles for the purpose of determining N as possible, so as to get

a closer picture of the hours during which superrefractive conditions can

be anticipated, and also to obtain a picture of how the duct height varies

between the times of its buildup and decay.
-38-

REFERENCES

Bean, B. R., and G. D. Thayer, C.R.P.L. exponential reference

atmosphere, NBS Monograph 4 (October 29, 1959).

Booker, H. G. , and W. Walkinshaw, The mode theory of tropospheric

refraction and its relation to wave-guides and diffraction,

pp. 80-126 of Meteorological Factors in Radio Wave Propagation.

Report of a conference held on 8 April 1946 at The Royal

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the Conference on Radio Meteorology, November 9-12, 1953.

The University of Texas, Austin, Texas.

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finitely conducting spherical earth, Proc . IRE 29, 623-639

(December, 1941).

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USCOMM-NBS-BL
r. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Atrin, Dirtetor THE NATIONAL BUREAU OF STANDARDS

The scope of arlivilies of ihe National Bureau of Standards at its major laboratories in Washington, D.C.. and Roidder,

Colorado, is suggested in the following listing of the divisions and sections engaged in .technical work. In general,

ea< li section carries out specialized research, development, and engineering; in the field indicated hy its title. A brief description of the activities, and of the resultant publications, appears on the inside of the front cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetry. Refiactometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry. Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Analytical

Chemistry. Inorganic Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

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Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth.

Physical Properties . Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials,

Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog Systems*

Applications Engineering.

Atomic Physics. Spectroscopy. Radiomelry. Solid Slate Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Molecular Kinetics. Mass Spectrometry. Molecular Structure and Radiation Chemistry.

• Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas Liquefaction.

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere

Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tioposphcric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter- Wave

Research. Miciowave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Reseaich. Antenna Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.
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