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jSoulder laboratories

RADIO REFRACTOMETRY

BY JACK W. HERBSTREIT

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREA1 ,RDS

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

technical ^Ttote

66

July I960

RADIO REFRACTOMETRY

by

J. W. Herbstreit

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

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CONTENTS

I. Introduction 1

II. Surface Measurements 3

III. Radiosonde Measurements 3

IV. Radio Frequency Refractometers 5

V. Applications of Radio Refractometry to

Radio Propagation Problems 9

Bibliography 15

Radio Refractometry

By

J. W. Herbstreit

I. Introduction

The fact that the sun can be seen to rise some three minutes

before it is actually above the geometrical horizon of an observer has

long been known to astronomers. The fact that the twinkling light from

stars is more pronounced near the horizon than at the zenith is also

well known. The shimmering of light waves as they pass through

the atmosphere above a heated highway or desert is commonly observed.

Less common, but frequently reported, are the appearances of mirages.

All of these phenomena are governed by the same basic physical

principle, the passage of electromagnetic energy through a medium

of variable refractive index. Radio waves, although not being visible

to our eye, are known to be affected in a similar manner as they are

propagated through an atmosphere of variable refractive index above

the large refractive index discontinuity where the atmosphere meets

the earth. Thus, radio waves originating at an aircraft or earth

satellite are known to be bent downward as they pass through the thin

outer layer of the atmosphere of refractive index near that of a vacuum

(unity), into the heavier region of the atmosphere near the earth's
2

surface just as the rays of the sun are bent downward when the sun

appears to rise before geometrical sunrise. The intensity of radio

waves twinkles and the apparent direction of arrival shimmers, just

as in the optical case.

The optical refractive index is known to be determined principally by the temperature and pressure of the atmosphere, whereas

the radio refractive index is, in addition, affected by the water content

of the atmosphere, the relationship between these quantities being

expressed in the following way:

N = (n-1) 10

6

= (H^r-) (P+[4810e/T]) (1)

where total air pressure P, and water vapor e, are in millibars, and

the temperature T is in degrees Kelvin [Smith, 1953], The quantities

P, e, and T have long been routinely measured at the surface of the

earth by standard weather bureau stations. For some time they have

been measured from the surface up to great heights using balloon-borne

radiosonde equipment at a large number of places over the earth's

surface. More recently, equipment has been developed to measure

rapidly and directly the radio refractive index of the atmosphere using

radio techniques. The measurement of the radio refractive index

properties of the atmosphere and the application to radio propagation

problems is the subject of this paper.
II. Surface Measurements

The temperature, pressure and humidity at the surface of the

earth has long been observed in almost every country of the world.

These observations have been the basis of the study of the world's

weather. These data form the basis for calculations of the radio

refractive index throughout the world using equation (1). Long term

means of the meteorological data have been published monthly by the

United Nations in their publication, "Climatic Data for the World."

The computation of a large number of radio refractive indices by

manual methods is generally tedious and time consuming and special

computer aids have been developed to assist in these calculations

[Johnson, 1952], More recently, large scale digital computers have

been put to use in this regard. A radio refractive index data center has

been established at the National Bureau of Standards where data from

approximately 300 locations throughout the world have been collected

to date.

III. Radiosonde Measurements

In addition to easily obtained data concerning the surface values

of radio refractive index, the refractive index as a function of height

above the surface is of importance. There exists a large number of
4

weather observatories which regularly send aloft balloons carrying

with them temperature and humidity elements that transmit information to the ground by radio as the balloon ascends to heights of the

order of 20 or 30 kilometers. These observations are normally made

twice daily, at 0300 and 1500 GMT. The temperature elements carried

by these balloons are either of the bimetallic or thermistor type. The

humidity elements are in general either hair hygrometers or a specially

prepared strip of lithium chloride whose resistivity changes with water

vapor content. Small thermistor temperature elements have a relatively rapid response to changes in temperature. However, bimetallic

temperature elements and commonly used humidity elements are

notably sluggish in response, and with a rapidly ascending balloon will

not record the variations in the radio refractive index of the atmosphere

with sufficient speed to detect the existence of rapid changes of radio

refractive index with height. Radiosonde measurement techniques

used by the weather services also involve a sampling process whereby

the temperature is recorded for a short period and then the humidity for

a short period, so that simultaneous observations of both of these

quantities are not obtained. During recent years a number of radio

meteorologists have developed special radiosonde devices to attempt

to overcome some of these difficulties. One of these developed in

France [Misme, 1956] rapidly switches between temperature, pressure
5

and humidity at the balloon borne element. A device developed in the

United States combines the information from the temperature and

humidity elements in such a way that the radio refractive index itself

is telemetered to the ground [dinger, I960], A similar device

developed in Japan utilizes a small thermistor wetted from cotton

threads to serve as a wet bulb thermometer in combination with a

thermistor for the dry bulb thermometer to provide radio refractive

index data directly [Hirao, 1957]. The use of barium fluoride films

rather than lithium chloride films for humidity sensing elements, which

offer promise of providing a very rapid response, is at present being

investigated in the United States [ Jones, 1958],

IV. Radio Frequency Refractometers

One of the most important developments in the past decade is a

radio frequency device for measuring directly the radio refractive index

of the atmosphere. Since the velocity of propagation of radio waves is

a direct function of the radio refractive index, the resonant frequency

of cavity resonators and tuned resonant frequency devices in general

are also a direct function of the radio refractive index of the material

within the resonant cavity or the dielectric material in the capacitor

determining the frequency of resonance. There appeared in the

literature, almost simultaneously, descriptions of devices which
6

measure the radio refractive index of the atmosphere in terms of the

resonant frequency of microwave cavity resonators which contain as

a dielectric a sample of the atmosphere under study. One of these

devices developed by Crain [ 1950] employs two microwave resonant

cavities, one sealed to exclude changes in composition of the air inside

it to serve as a reference cavity, and the other having small holes at

strategic locations in the ends of the cavity to allow the passage of a

sample of the atmosphere through it. These two cavities serve as the

resonant circuits for two highly stabilized microwave oscillators, the

frequency difference of which is a measure of the variations of the

radio refractive index of the atmosphere in the sampling cavity. The

other device developed by Birnbaum [1950] uses two similar cavities

as passive resonant circuits which are excited by a klystron oscillator

that is swept linearly with time across the slightly different resonant

frequencies of the two cavities. Variations between the time of passage

of the oscillator between the two resonant frequencies of the cavities,

is a measure of the variations of the radio refractive index of the air in

the sampling cavity. The degree to which the sampling cavity may be

open to the atmosphere is limited in the case of the Texas unit, which

requires relatively high Q cavities for operation, while the Birnbaum

cavities may be opened to a greater extent to the atmosphere [Thompson,

1959] and still provide satisfactory operation. On the other hand, the
accuracy of the Birnbaum unit depends on the ability to obtain a very

linear frequency sweep for the klystron oscillator.

The key to the satisfactory operation of both of these units is

the cavity resonators themselves. Invar with a temperature coefficient

of approximately one part per million per degree centigrade has been

the principal material from which these cavities have been prepared.

By judicious design it has been possible to compensate these cavities,

at least on a long term basis, so that the temperature coefficient is

of the order of 0. 1 part per million, i. e. , 0. IN, per degree centigrade.

Recent investigations have been conducted into the possibility of

fabricating cavities from extremely low temperature coefficient

ceramics [Thompson, 1958], These cavities have been found to be

very easy to fabricate and to be made conductive by the use of silver

paint. However, they are relatively fragile and porous, the latter

being at this time the most serious problem. Temperature coefficients

of several ceramic cavities which have been prepared are of the order

of 0. 1 part per million per degree centigrade.

Recent developments in microwave refractometry have been

concerned with the reduction in their size and weight so that they may

be readily carried aloft by small aircraft to study the detailed refractive

index structure of the atmosphere above the earth. A recent application

of servo techniques to refractometers by Vetter [i960] has resulted in
8

an extremely stable unit with the ability to measure the absolute

refractive index of the atmosphere, rather than just relative values.

In this new instrument, the problems of stability of the electronic

circuitry have been practically eliminated, permitting the realization

of excellent long term instrument calibration stability. Microwave

refractometers of the Crain type have been used extensively for

measurement of refractivity in the United States. Units of the

Birnbaum type have been built and operated successfully in the United

States, Canada [Adey, 1957], United Kingdom [Lane, I960], Sweden

[Johansson, 1959], and Germany [Schunemann, 1958], All three

types of instruments -Crain, Birnbaum and Vetter-are now commercially

available from several U. S. manufacturers.

Most refractometer measurements which have been made to

date have been either on the ground or in an aircraft. The theory of

long distance propagation of radio waves through the troposphere

indicates that the variations of refractive index as a function of altitude

are of most importance, although the complete volumetric structure

is involved. In an effort to determine the vertical refractive index

structure in more detail Deam [1959] has recently developed a dropsonde type of unit using the cavity resonator principle. This unit

uses a single cavity open to the atmosphere with its resonant frequency

stabilized by a pound oscillator at approximately 400 Mc/s in the band
9

allocated for radio meteorological purposes. The radio frequency

power from this oscillator is radiated to the ground where it is

received and the variations of frequency recorded as a measure of

the variations of the radio refractive index of the sample of air in

the cavity. Another miniaturized version of the radio refractometer

has been developed by Hay [1959]. This unit contains two 5 Mc/s

oscillators, the inductance and capacitance of the resonant circuit of

one of which is closed off from the atmosphere, whereas the frequency

controlling capacitance of the second oscillator is exposed to the

atmosphere. Thus, the frequency difference of the two oscillators is

a measure of the variations of the refractive index of the atmosphere.

Considerable care is taken in the design of the frequency controlling

capacitor as regards its thermal stability and the provision for a free

flow of the sample of air through the capacitor plates.

V. Applications of Radio Refractometry

to Radio Propagation Problems

The literature concerning the application of radio refractive

index studies to radio propagation problems has been growing at a very

rapid rate and only a few selected references are included in this paper.

Contributions to the XIII th General Assembly of the International

Scientific Radio Union sessions on radio meteorology have included
10

mention of extensive work being done in the United States [U. S. Nat.

Com. Rpt. ], France [Misme, I960], Italy [Bonavoglia, 1958],

Germany [Brocks, 1959a, b], Sweden [Johansson, 1959], Japan

[Ugai, 1959], Belgium, Czechoslovakia [URSI Bulletin No. 113],

and the United Kingdom [Saxton, I960]. The largest portion of this

work considers either the surface values of the refractive index, or

gradient of the refractive index from the surface to one kilometer

above the surface [Bean, 1959a, b; Fehlhaber, 1957, 1959; Ikegami,

I960].

The Consultative Committee for International Radio at its Los

Angeles Plenary Assembly adopted procedures for estimating tropospheric wave field strengths at large distances which take into account

the refractive index gradient at the earth's surface, or the surface

value of the refractive index in Recommendation No. 312 of this

Assembly. Climatic charts of refractive index parameter An, were

prepared for various regions of the world in CCIR Report No. 147.

CCIR Report No. 146 gives the basis for application of radio refractive

index parameters to the climatic variability of radio field strengths.

CCIR Study Programme No. 138 outlines the areas of research which

require further study, and encourages the International Radio Scientific

Union to persue these studies. In CCIR Recommendation No. 309, a

definition of a basic atmosphere with height is given.
11

The extensive use of radar for accurately determining the

position of aircraft and the advent of artificial earth satellites, depending upon direction finding for accurate position determination have given

impetus to the study of the bending of radio waves passing through the

atmosphere [Beckman, 1958; Anderson, 1958, 1959; Bean, I960].

Such bending is critically dependent upon the vertical gradient of the

refractive index, particularly in the lowermost regions of the atmosphere [Bean, 1959c, d].

All theories of tropospheric propagation far beyond the radio

horizon require a knowledge of the refractive index of the atmosphere

in one form or another to explain in detail the distance and frequency

dependence of such propagation. The character of the variations of

refractive index has been the subject of extensive study using the

rapidly responding microwave refractometers. These studies have

not only attempted to include the spatial variability of the radio refractive index, but also its time variability [Gossard, I960], However,

to date, a satisfactory description of the refractive index structure

which will adequately satisfy the requirements of the various theoreticians has not as yet been obtained, particularly in regard to the

possible differences between the wave number spectra in the space

domain and frequency spectra in the time domain as well as the degree

of anisotropy involved in these spectra [Norton, I960]. For example,
12

aircraft refractometer measurements give principally the variations

in the horizontal plane and involve a mixture of the space and time

spectra. Several excellent review papers concerning the present

status of the theory of tropospheric propagation far beyond the horizon

[DuCastel, 1958, 1959; Saxton, I960; Wheelon, 1959], together with

reports of the application of refractometry to the understanding of the

detailed refractive index structure of the atmosphere [Bauer, 1958;

Norton, 1959] have appeared in the recent literature.

Finally it should be noted that a high degree of accuracy of

temperature, pressure and water vapor pressure measurements are

necessary for precise determinations of the refractive index for certain

applications. The following equation relates small changes in AN with

small changes in temperature, pressure and vapor pressure:

A N= a A T + bA e + cA P (2)

with temperature expressed in degrees centigrade, and with both

pressure and vapor pressure expressed in millibars, typical values

of the constants a, b and c, based on the ICAO standard atmosphere and

assuming 60% relative humidity, are given in the following table for

various altitudes, h
in NO o

o vO r-

• •

i i co

i

13

r- 00 (X* O in hrvj CM CM CO CO cm

O r\l f- CM vO h- in t- i-H m o^ sO

Tt< in ^

o 00o

I

o

in

• oI

o

o

I

00o

o

o

• o

a

ego

in vO

IN) o

co CO r—1 (VJ in

i—» o^ o vO in O 00 t- eg

00

U

O rg

• • in oo

in CO in in

<T O xD m m

i i i

o^

fc

s

Is- vO

«-h r>- i-i CO eg eg

eg o

eg

rg

u

<u M

V

o O -4 CO o o c—i CM O

m

r*
14

In case measurements of e are made in terms of a difference

6 = T - T 1 between wet and dry bulb temperatures we may replace the

term bAe in (2) by dA 6 and the coefficient d is also given in the above

table. At 10 km and above the wet and dry bulb technique of measuring

e is impractical.

It is clear that radio wave refractometry has contributed

considerably to our knowledge and understanding of tropospheric

radio propagation both within [Thompson, I960] and beyond the radio

horizon [Ament, 1959; Katzin, I960; Moler, I960], just as optical

refractometry is being used to explain the phenomena of early sunrise,

twinkling stars and mirages. It is also clear that considerably more

effort must be expended in the field of radio refractometry to more

completely explain and understand the detailed nature of the refractive

index structure of the atmosphere, and its correlation with radio

propagation phenomena. The reports of the various national committees of International Scientific Radio Union indicate that well

planned scientific programs in this field are to be conducted. It is

expected that the research evolving from these programs will be of

utmost value to our international family of radio scientists.
15

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of Technology, 34, 519 (1957).

Ament, W. S. , Airborne radiometeorological research, Proc. IRE,

47, 5, 756 (1959).

Anderson, L. J., Tropospheric bending of radio waves, Trans. AGU,

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Anderson, W. L. , N. J. Beyers, and B. M. Fannin, Comparison of

computed with observed atmospheric refraction, IRE Trans.,

AP-7, 3, 258 (1959).

Bauer, J. R. , and J. H. Meyer, Microvariations of water vapor in

the lower troposphere with applications to long-range radio

communications, Trans. AGU, 39 , 4, 624 (1958).

Bean, B. R. , and L. P. Riggs, Synoptic variation of the radio refractive index, J. of Res., NBS, 63D, 91 (1959a).

Bean, B. R. , and G. D. Thayer, Models of the atmospheric radio

refractive index, Proc. IRE, 47, 5, 740 (1959b).

Bean, B. R. , and J. D. Horn, Radio refractive index climate near the

ground, J. Res., NBS, D, 3_, 259 (1959c).

Bean, B. R. , Climatology of ground-based ducts, J. of Res., NBS,

63D, 29 (1959d).

Bean, B. R. , J. D. Horn, L.. P. Riggs, Refraction of radio waves at

low angles within various air masses, J. Geo. Res., 65, 1183

(I960).

Beckman, P. , Height errors in radar measurements due to propagation causes, Acta Technica, 6, 471 (1958).

Birnbaum, G., A recording microwave refractometer, Revue of Sci.

Instru. , 6, 169 (1950).
16

Bonavoglia, L. , Correlazione fra fenomeni meteor ologico e propagazione oltre 1'orizzonte sul mediterraneo, Alta Frequenza,

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Brocks, K. , Meteorologische Untersuchungen der elektromagnetischen

Wellenausbreitung im cm- bis m-Band vor der deutschen

Nordseekuste, Bericht Nr. 1 der Radiometeorologischen

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Hamburg (1958).

Brocks, K. , Feldstarkeregistrierungen auf Richtfunkstrecken im

cm- bis m-Band uber der Nordsee und ihre Beziehungen zu

meteorologischen Vorgangen, Bericht Nr. 2 der Radiometeorol.

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Clinger, A. H. , and A. W. Straiton, Adaptation of the radiosonde for

direct measurement of radio refractive index, Bui. Am. Met.

Soc, 41, 250 (I960).

Grain, C. M. , Apparatus for recording fluctuations in the refractive

index of the atmosphere, Revue of Sci. Instru. , 21, 213 (1950).

Deam, A. P., An expendable atmospheric radio refractometer,

EERL, Report 108, Univ. of Texas (1959).

DuCastel, F. , P. Misme, and J. Voge, Refexious partielles daus

1'atmosphere et propagation a grande distance, Part 1, annales

des telecommunications, L3, 209 (1958), Part 2, L3, 2 ^5 l 1 ?58)*

Part 2c, L5, 48 (I960), Part 3, 14, 33 (1959), Part 4, 1_5, 38

(I960).

Fehlhaber, L. , und G. Halbedel, Statistische Ermittlung des

Krummungsfaktors k im aquivalenten Erdradius aus

Radiosondenaufstiegen, Techn. Bericht Nr. 5528 des FTZ,

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des FTZ, Darmstadt (1959).

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IRE, AP-8, 186 (1960).
17

Hay, D. R. , and G. G. Bree, Light weight refractometer, DRTE

Report 1012, Defense Research Telecommunications Establishment (1959).

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RRL, 4, 423 (1957).

Ikegami, F. , A preliminary study of radiometeorological effects on

beyond-horizon propagation, J. of Res., NBS, 64D, 3, 239 (I960).

Johansson, U. H. , and C. Christensen, En flygbwren mikrovagsrefraktometer, Chalmers Tekn, Hogskola report (1959).

Johnson, W. E. , An analogue computer for the solution of the radio

refractive index equation, J. Res., NBS, 51, 335 (1952).

Jones, F. E. , A. Wexler, Humidity characteristics of barium fluoride

films, NBS Report 5897 (1958).

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Katzin, The trade -wind inversion as a transoceanic duct, J. of

Res., NBS, 64D, 247, (I960).

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des telecommunications, 11, 81 (1956).

Misme, P., Influences radioclimatiques sur les liaisons transhorizon,

L'onde Electrique, XL, 117 (I960).

Moler, W. F. , and D. B. Holden, Tropospheric scatter propagation

and atmospheric circulations, J. of Res., NBS, 64D, 1, 81 (I960).

Norton, K. A., Recent experimental evidence favoring the pk (p)

correlation function for describing the turbulence of refractivity

in the troposphere and stratosphere, J. of Atm. and Terr.

Physics, 15, 206 (1959).

Norton, K. A., Carrier Frequency dependence of the basic transmission loss in tropospheric forward scatter propagation, J.

Geophy. Res., (I960).
Saxton, J. A., Quelques reflexions sur la propagation des ondes

radioelectriques a travers la troposphere, L'Onde Electrique

(July, 1960).

Schunemann, R. , and W. Steffen, Concerning a microwave refractometer, Communication of Heinrich Hertz Institute,

German Academy of Science at Berlin; Berlin-Adlershof.

English Translation, NBS Report 6027 (1958).

Smith, E. K. , S. Weintraub, The constants in the equation for

atmospheric refractive index at radio frequencies, Proc. IRE,

41_, 1035 (1953).

Thompson, M. C. , F. E. Freethey, D. M. Waters, Fabrication

techniques for ceramic X-band cavity resonators, Rev. of Sci.

Instr., 29, 865 (1958).

Thompson, M. C. , F. E. Freethey, D. M. Waters, End plate

modifications of X-band TE„,, cavity resonators, IRE Trans.

Oil

MTT 7, 3 (1959).

Thompson, M. C. , H. B. Janes, and A. W. Kirkpatrick, An analysis

of time variations in tropospheric refractive index and apparent

radio path length, J. Geophy. Res., 6j>, 193 (I960).

Ugai, S. , Statistical consideration of the structure of atmospheric

refractive index, Reports of the E. C. L. (Japan) 7, 253 (1959).

Vetter, M. J., Absolute refractometer, NBS Report 6700 (I960).

Wheelon, A. D. , Radiowave scattering by tropospheric irregularities,

J. of Res., NBS, D, 63, 205 (1959).
Frederick H. Mueller. Secretary WTIONAI Bl REAM OF STANDARDS

\ \ \stin. Director THE NATIONAL BUREAU OF STANDARDS

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