national Bureau

library,

JAN 3 i3gi

PB161588

jSoulder laboratories

^0.87

A THEORETICAL STUDY

OF

SPORADIC-E STRUCTURE

IN THE LIGHT OF RADIO MEASUREMENTS

BY

KAZUHIKO TAO

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical ^Ttote

87

January, 1961

A THEORETICAL STUDY OF SPORADIC -E STRUCTURE

IN THE LIGHT OF RADIO MEASUREMENTS

by

Kazuhiko Tao

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.

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Price $1.25

A THEORETICAL STUDY OF SPORADIC-E STRUCTURE

IN THE LIGHT OF RADIO MEASUREMENTS

by

Kazuhiko Tao

ABSTRACT

The theoretical aspects of the mechanisms of sporadic-E reflections are described from both the standpoint of a thin layer and a

scattering model. For the thin layer model, thin dielectric layers

which have various distributions of electron density are considered.

It is also pointed out that the scattering theory for which an autocorrelation function of the fluctuation of electron density is given

by modified Bessel functions of the fourth through the seventh order

is an available model for sporadic-E scatter. Moreover blobs of ionization which have a horizontal scale of the order of 200 m and a vertical

scale of about 50 m are considered for sporadic-E scatter. The frequency and distance dependences of the oblique VHF propagation by means

of the sporadic-E layer are discussed by comparing the theoretical results with experimental evidence.

TABLE OF CONTENTS

1. INTRODUCTION

2. THIN LAYER MODEL FOR SPORADIC E

2.1 Outline of the Model

2.2 Calculation of the Reflection Coefficient

3. SCATTERING MODEL FOR SPORADIC E

3.1 Outline of this Model

3.2 Scale of the Sporadic-E Irregularities

3.3 Scattering Cross-Section

3.4 Generalized Scattering Cross-Section in the

Anisotropic Case

3.5 Relationship between Es Scattering and Normal

Scattering in the Ionosphere

k. DISTANCE DEPENDENCE OF SPORADIC-E PROPAGATION

5. FREQUENCY DEPENDENCE OF SPORADIC-E PROPAGATION

6. CORRELATION BETWEEN foEs AND FIELD STRENGTH

7. CONCLUSIONS

8. ACKNOWLEDGMENT

9. REFERENCES

A THEORETICAL STUDY OF SPORADIC -E STRUCTURE

IN THE LIGHT OF RADIO MEASUREMENTS

Kazuhiko Tao

1. INTRODUCTION

We have seen that there are several types of sporadic-E delineated

by their differing diurnal or seasonal occurrence times or latitude

variation [l]. Some types of sporadic-E echoes on ionograms have the

appearance of reflections from a thin layer, and other types suggest

the scattering mechanism. In this paper, we shall confine our attention to sporadic-E echoes which are frequently observed in middle

latitudes.

The theory concerning a thin layer which has a cloud-like shape

is described in section 2 and a sporadic-E model is given in section

3 from the standpoint of scattering theory. Distance and frequency

dependences of sporadic-E propagation are stated in sections k and 5

together with a comparison of theoretical with experimental results.

In section 6 a relationship is derived between foEs and the measured

field strength observed over an oblique VHF propagation path during

periods of sporadic-E enhancement.

MB
-2-

2. THIN LAYER MODEL FOR SPORADIC E

2.1 Outline of the Model

Measurement of the electron density within the sporadic-E layer

has shown that relatively sharp variations in the gradients of electron

density exist in "both the horizontal and vertical directions. Although

the theory of reflection from a thin ionized layer has been developed

"by Hartree [2], Booker [3], Rydbeck [k, 5] and Rawer [6], another treatment will he developed in this paper. We shall postulate many thin

dielectric layers in the E region which have limited extent in the

horizontal direction. The basic idea for this model was developed "by

Friis^, Crawford and Hogg [j], in order to explain the persistent tropespheric field strengths beyond the horizon. We shall apply this concept to the problem of sporadic E.

According to diffraction theory, if a layer has a reflection coefficient p, the received power is given in the form,

X d

where P. is the transmitting power, A and A are the effective areas

of transmitting and receiving antennas, d is the distance between the

transmitter and receiver. This relation is appropriate when the following conditions are satisfied,

b> ^P-, a>7\d (2.2)
TRANSMITTING

POINT j. RECEIVING

-I POINT

GEOMETRY OF A THIN LAYER MODEL

FIGURE I
-kwhere 6 is the grazing angle to the layer and a and b are horizontal

dimensions as shown in Figure 1.

2.2 Calculation of the Reflection Coefficient

Let us assume that the layer is composed of many thin layers whose

dielectric constants differ one from their neighbors by an increment

2

A e. Provided that 1 » » de, the reflection coefficient of the

boundary between thin layers is given in the simpler form for both

polarizations

.

ap = -^§- (2.3)

he

2

We shall next assume the vertical distribution of electron density

in the sporadic -E layer to be in the following form.

2n

N = N ^ " (-A-) hi n-1, 2, 3 < 2 ' 4 ) max I Ah

where A h is a half-thickness of the layer.

This distribution of electron density is shown in Figure 2 as a

parameter of various values of n. If we put n = 1, this is a parabolic

distribution. In rationalized MKS units, the dielectric constant is

given in the following form for the ionosphere, neglecting the effect

of collisions and of the earth's magnetic field,

Ne

2

e = 1

2

me oi o
-5-

MAX

ELECTRON DENSITY DISTRIBUTION IN THE SPORADIC E LAYER

FIGURE 2
-6-

so that the dielectric constant is in the form, if we put

N 2

-p _ max e N

~ tame ' o

fJ c 2n ^ '^-f^-hrr* } >*)

The reflected field from any incremental layer is obtained by considering phase difference

dE = dPE4 e _J (~T~) Sln 9 dz (2.6)

r i

Differentiating (2.5) -with respect to z and inserting this into (2.6),

we get

f*T 2n-l . / taz \ . n aE = 4. _| z

- - E/J HH sln 9 dz (2.7)

r 2

f

2 (Ah)2n

e

2 ±

The complete reflected field (f>f ) is obtained by integrating the reflections from all increments within the layer

f

2

tp A h k^

N \ f -J (-~2-) sin 6 2n-l . ,_ fi

, E = n —n x r- / e

u v \ ' z dz (2.8)

t (a h)

2n

e

2 J

o
-7-

After the calculation of integral, we get

E = n —x

r ~2

f

£ (Ah)2n

9

2 (^sine)2n

m=l

/ iwsineAhv

x ( \

) 2n-2m

n

/ kg sine A h» V i -. \m+1 ( 2n~l) 1 cos (_ )+^(-D X2nT2^I) | m=l

/ 4jtsin0 A h\ / ^jtsin© A hv /„ . v x (

_. ) S in ( _ ) . (2n-l) 1 (2.9)

The total reflection coefficient is defined as follows

E

_i

E. (2.10)

In order to calculate the received power from the formula (2.l), it is

convenient to use the reflection coefficient expressed as a power

ratio.

2 If we put L = ^TtsinQ A h/X in (2.9) and let k = n-m, p is expressed in simpler form

f

k

2 I

: 2

I M n [ (2n-l)l ] P =

k k kn

f e l

n-l

(-If I

L / , \k / T LsinL \ n (-1) (cosL + -^—^ ) + 1

2k 2k+l

k=o

(2.11)

wm
-8-

Therefore the received power is obtained by combining formulae (2.1

)

and (2.11).

3. SCATTERING MODEL FOR SPORADIC E

3.1 Outline of this Model

Some types of sporadic E, particularly those which are frequently

observed during evening hours in middle latitude, have many features

of scattering phenomena. This scatter would be due to the irregularities of electron density occurring in the lower ionosphere. Recently

Booker [8] has suggested that the phenomenon of sporadic E can, in

some cases, be explained from the standpoint of scattering theory.

The phenomenon of sporadic E, however, generally appears to have a

denser concentration of electron density than the normal scattering

phenomena. For this reason, it seems inappropriate to use the autocorrelation functions which are used to account for the normal scattering phenomena. Therefore, we shall at first consider an autocorrelation functions of the electron density available for the scattering model of sporadic E. We shall take the following correlation function

Cn

(p) = C (o) t-f-^)] Pn K

n

(p), p = -f- (3.1)

where K (p) is the modified Bessel function of the second kind of

n order n and T is the gamma function. C (o) is the time variance

< (A n) > of the refractive index n of the atmosphere and I is the
( -9-

scale of turbulence . This correlation function was derived by Muchmore

and Gallet [9]. If we put n = l/2 in the above formula, we can derive

the exponential correlation function which was derived by Booker and

Gordon [10]. Also the modified Bessel function of the first order is

obtained in the case of n = 1, which is used by Norton and his collaborators [ll] in order to account for tropospheric scattering. While

considering n = l/2 and n = 1, we shall pay more attention to the

higher orders of n in this correlation function.

When n is an integer, K (p) is defined by the equation

K (p) = lim -—- {I (p) - I (p) } cot jte, (3.2) n e-*o 2 -n-e n+€ ' u '

where

\^-in+2m

P

m=o

_n+2m i _/ . x 2 ml r(n+m+l)

Z-n (P)= I

-n+2m

P

2-ilT^mi r(-n+m+l)

m=o N '

*

and which gives

, n+2m n-1

m

00 . p

K

n M - 1/2 1 ffl—

' + (-D

n+1

I V - C -g (-f

^ ml (-7-) mti ml (n+m)!

-1/2 \|r (m+l) - 1/2 if (n+m+l) } (3.3)

* cf. Watson "Bessel Function".
-10-

>^ =*

AUTOCORRELATION FUNCTION OF THE MODIFIED BESSEL FUNCTION

[2

l " n /r(n)]/) n

K n

( /o)

FIGURE 3
-11-

where \|i (m+l) - - J + (l + l/2 + 1/3 + ... + l/m)

7 = 11m (1 + 1/2 + 1/3 + ... + l/m - log m} = O.5772157

(Euler* s constant )

The calculated curves of this correlation function (3.1) are shown in

Figure 3 ^y giving various values of n. In addition to these curves,

the exponential and the Gaussian models are plotted in this figure.

Models of the exponential, the Gaussian and the modified Bessel function of the first order have been used so far in order to explain both

the ionospheric and tropospheric scattering cases. Although these

correlation functions are proper for the phenomena of normal scattering, they may not be appropriate for the scattering model of sporadic

E which appear to have denser concentrations of electrons. There is

also another trouble that the frequency dependence of sporadic -E

propagation may be difficult to explain from the correlation functions

normally used in scattering theory. As will be seen from the figure,

however, a correlation function of the modified Bessel function of

higher order seems appropriate for the sporadic-E model.

3.2 Scale of the Sporadic-E Irregularities

It is necessary to note that the scale of turbulence which is

represented in the correlation function (3.1) does not describe the

scale of irregularities of the sporadic E, but expresses the usual

scale of turbulence responsible for the normal scattering phenomena.

So we must define the sporadic-E irregularities from the correlation
-12-

curves which are found in Figure 3« We shall consider a model wherein

a sporadic-E cloud which has a large horizontal dimension contains a

large number of small irregularities.

Although there exist some confusion concerning the use of the

word "scale" to describe the size of irregularities of electron density

in the ionosphere, we shall define the "scale" of irregularities to

mean the distance in which the correlation is reduced to a specified

value, such as 0.5, according to Booker's definition [12].

From the correlation curves shown in Figure J,, the scale of the

sporadic-E irregularities may be put in the form

h = ml (3.1+)

where £ is the scale of normal turbulence and m is an arbitrary multiplication factor. If we take the correlation curve of n = 5 as an

example for the scattering model of sporadic E, the correlation function decreases to the 0.5 value at a separation of r = L = 3*5 ^<

Therefore the scale of the sporadic-E irregularities has dimensions

of m times (3 ~ k times) the scale of the normal turbulence. Numerical

estimation for the scale of the sporadic-E irregularities will be given

later.

3.3 Scattering Cross-Section

The scattering cross-section is given, in general,
13-

a (q) = ^ S f^ R t^li /rC (p)e-^V}

k Sln * ^

f P C (p) sin (qp) dp (3.5)

jt q j n

where

q = 2k£ sin ^ = k£ 9, P = T

0: scattering angle

Inserting (3-l) into (3«5) an(i remembering C (o) is set equal to

2 < ( ) ^A, the scattering cross-section is obtained in the form

(see for example references [11], [l8] ).

-(n + |)

< ( *± / > r (n + f

) sin2 x {l + [ X - ]

2 }

ff ^ £sln

2 (3.6) n 2n+l+

r _ / x . 2n-l . 2n, . v2n+3

2 V jt T (n) k I (sin -p)

where x

i- s "the angle between the direction of scattering and the direction of the incident electric field.

If we put n = -x in the above formula, <r is obtained in the form

2

(when the scale of turbulence is large compared with the wave length)

. / A £ A .2

< ( -r-

) > sin x - 32* f sin ^
which is the Gordon's formula [13], for the tropospheric scattering

case. This was also derived by Booker for the ionospheric scattering

case [lk],

2 k 2 We have the relation of < ( — ) > = (—-) ( — ) in the

€ ^

N

ionosphere, so, using the scale of sporadic-E irregularities, formula

(3.6) is expressed in the form

- (n + |)

2 k 2n 2

( ^T ) (-T-) r ^ + |) U) Bin

2 X [1 + {

mX

} ]

sSf knL sin -

n _ , „ 2n-l 2n+3

2 Vit r (n) ( — J L (sin ^j

(3.8)

The received power is obtained from the relation [Ik]

P b A

P

r =i—9 %

(6A) (3 ' 9)

R sin t

where b is the layer thickness and A is the effective area of the receiving antenna.

3.4 Generalized Scattering Cross-Section in

the Anisotropic Case

Although the irregularities contributed to the normal scattering

phenomenon in the lower ionosphere may be considered isotropic [8],

but the irregularities of sporadic E may have an anisotropic structure,

such as an ellipsoidal shape, because the scale of the sporadic-E
-15-

irregularities are larger than the scale of the normal turbulence. The

scattering theory In an anisotropic turbulence has been developed by

several researchers [15, l6, 17] • One may develop the scattering crosssection (3*8) in the case of anisotropic irregularities. The generalized scattering cross-section is given in the form

2 k 2n " (n + I

5

C tt > HlT} r (n + l

} (m) s±n^ L

i

L V 2 \ (1 + V <X = - 2n+V , „, *,2n-l, J 9x 2n+3

r/T 2 .22 2 x

. 2^ _ 2 2 - n +

2

2 Vat r(n) k (sin •?) 1 (L sin 7+LpCOs 7 )sm <S*L cos $J

(3.10)

where -

K X

2 r ,T 2 . 2 T 2 2 v . 2^ T 2 2 , 2

q^

= [ (L, sin 7 + L cos 7) sin $ + L_ cos $J m 1 ' 2 ' 3

and L , L } L are different scales of the sporadic-E irregularities in

directions parallel, normal and vertical to the mean horizontal drift

(assumed to lie in the direction of maximum elongation). 7 is the

angle between the mean drift and the great circle plane. The angle

between the plane containing the scattering blob under consideration

and the great circle plane is denoted by an angle $. This generalized

scattering cross-section has been also obtained by Norton [18] for the

tropospheric scattering case.

If the sporadic-E irregularities exist near the great circle plane,
-16-

we may put $ ~ and in such a case the formula (3. 10) becomes

- (n + f) 2 k 2n 2 <T»(T» r(n + |)(m) Li L

2

L [l + (-^n a

J wL Bin ^ cr = „2n+4 ; „ , , . 2n-l _ 2n+^ , . 0.

2n+3

(3.11)

_2n+4 ' f

. 2n-l 2n+3 , ' vjt (n) k L (sin -2-)

Moreover we can get the scattering cross-section available for the

scattering model of sporadic E, by putting n = 5 into (3.11) and letting m = 3.5 as suggested earlier.

13

2 (VHt >' L

i

L

2 [1 + (-^^H

-

5 = l-°3xl02 U"L

3

Sln

1 ( 3 . 12)

2kL y

13

(-^-2) l3 (sin |)

3.5 Relationship between Es Scattering and Normal

Scattering in the Ionosphere

Although it has not yet been clarified as to what kind of mechanisms produce these sporadic-E irregularities, it will be possible to

consider that these irregularities may have a close connection with

turbulence produced by wind shear prevailing in this region. Gallet

[19] proposed a mechanism of stratification of sporadic E by considering the mixing process in a turbulent region. Recently Layzer [20]

has suggested that it may be necessary to consider very strong wind
-17-

shears such as about 100 m/sec/km in order to maintain turbulent motion

in this region and these wind shears may occur in a narrow layer of the

order of 1 km in thickness. If we consider such a jet-like high shear

layer, this layer may be expected to act as a partial reflector or

scattering source due to fluctuations of electron density produced by

turbulent mixing. Also, the recent experimental evidence has shown

that wind shear as high as 1^0 m/sec/km exist in the 100 «* 110 km

region while, simultaneously, ionogram records show sporadic E near

the level of maximum shear [21].

According to Gallet [19] > the fluctuation of electron density is

produced by the transport process

2 2

K N ' 3 o

{ N '

I means the largest scale of turbulence in the layer. As the ambient

daytime electron density in the E region is N = 10y cm and the layer

thickness of sporadic E may be considered to lie in ranges from a few

kilometers down to a few hundred meters, the value of ( — ) in the

daytime is the order of unity to 10 . Since the sharp gradient of

the electron density will decrease with disappearance of the sporadic-E

clouds, the value of ( —— ) will also decrease to the order of 10

N

.4

or 10 corresponding to normal scattering. As the sporadic-E clouds

disappear or move to other places, the high concentration of electron

density in this region decays to the normal state and therefore the
-18-

/ W>

WAKKANAIH, ,P f HAKOOATEff~"\/

P C AKITA/ tx 1 f- 49.68 MC/S

JULY II -AUG. II, 1959 y ) Jy (

I^J mmyj/y *whiraiso

dfftjyjy KOKUBUNJI 100 YAMAGAWA7^/\/

f/^y 'RECEIVING STATIONS W/ x I0N0S0N0E STATIONS

OKUMA

120 ^^>^^

**

'—.^^^ FREE SPACE VALUE

140 -

"* — -^ -• 10 %

160 —

HAKODATE

AKITA #

HIRAISO^ 50%

180

si^m ^^-^'^

20.0 -

x ** — ^ >• 90%

220

x SCATTER SIGNAL ~

(50%)

240

1 1 1 1 1 1 500 1000 1500 2000

DISTANCE IN KM

2500

- 60

40 -u

- 20

-

--20

-40

- -60

3000

EXPERIMENTAL RESULTS OF THE DISTANCE DEPENDENCE OF SPORADIC E PROPAGATION

FIGURE 4
-19-

number of n (n = 5 ~ 6) in the correlation function will tend to small

numbers such as n = 1. In this case, as the irregularities are considered as isotropic, we can obtain the scattering cross-section from

(3«6) by putting n = 1.

0- = 1.17 x 10

2 f J

-2 v N

; v f

;

( m ) a ( sin 1

5

(3.13)

This formula represents the normal scattering case. Although there is

still some ambiguity concerning the scale of turbulence in the ionosphere, we have taken a value of i = 15 m as the average scale of

turbulence corresponding to VHF forward scattering (f = 50 Mc/s), [22],

Booker [8] has also recently suggested the presence of irregularities

of the electron density with scales in ranges from 20 to 60 meters in

the lower ionosphere. Several calculated curves of the basic transmission loss for the Es scattering and the normal scattering are shown

in Figure 6 by using the formulas (3-12 ) and (3.13)*

k. DISTANCE DEPENDENCE OF SPORADIC -E PROPAGATION

An experimental determination of distance dependence is shown in

Figure k. This experiment was carried out, using the frequency of

i+9 -68 Mc/s, in the summer of 1959 by the Radio Research Laboratories

and K.D.D. (Japan's Overseas Radio and Cable System) in Japan in order

-____
-20-

to examine the distance dependence of the sporadic-E propagation with

the cooperation of the NBS Central Radio Propagation Laboratory. The

more detailed analysis of this experiment will be published in other

papers [23, 24].

The transmitting point was Okuma, Okinawa, and the receiving points

were Yonago, Akita and Hakodate in Japan. In addition to the summer

(1959) data, we have added the observations at Hiraiso during the summer

period in 195^. Distances between the transmitting point and each receiving point are as follows:

TABLE I

Rec.

Station Long. Lat.

DistanceRec.

Antenna

Antenna

Gain

Antenna

Height

Above

Ground

Yonago 133°22 , E 35°27»N 1100km

2-stack,

5 -element

Yagi

1^.3db 18. km

Hiraiso ll+0°37'E 36 22*N 1590km Rhomb ic 20.0db 15.0m

Akita ll|0 o 32 , E 39°Wn 1820km

2-stack

5-element

Yagi

l^.ldb 30.0m

Hakodate lli0 o lj-3»E 45°2if»N 2020km 5-element

Yagi

9.1db 6.0m

^Approximately 280m above the sea.

The 10$, 50$ and 90$ values of the statistical cumulative distribution of the Es signals are plotted in Figure h [23]. Statistical results of foEs measured at the ionosonde stations in Japan during the
same period are as follows:

-21-

TABLE II

Ionosonde

Station foEs (lO/o) foEs (5<#

foEs (90$)

Yamagawa 10.5 Mc/s 6.2 Mc/s 3.^ Mc/s

Kokubunj i 10.8 Mc/s G.k Mc/s 4.0 Mc/s

Akita 12.8 Mc/s 7.2 Mc/s 4.3 Mc/s

We shall next examine this distance dependence from the theoretical point of view. The most appropriate theoretical curves for the

experimental result are shown in Figure 5 and Figure 6 derived from the

thin layer theory and the scattering theory described in sections 2 and

3 respectively. As measurements indicate that the layer thickness of

sporadic E ranges from a few kilometers down to 50 meters, curves

pertinent to these ranges are shown in Figure 5 and Figure 6, and seem

to fit the observations reasonably well.

5. FREQUENCY DEPENDENCE OF SPORADIC-E PROPAGATION

It is well-known that the scattered power in normal ionospheric

scatter propagation is inversely proportional to about the fifth or

sixth power of frequency [8, 25, 26, 27]. Experiments show, however,

that the frequency exponent increases in the case of sporadic E. It is

reported by Davis, Smith and Ellyett [28] that the median value of the

frequency exponent in sporadic-E propagation is 12 during summer time
-22-

LAYER THICKNESS THIN LAYER MODEL

H = 300m n=5

HHOOOm f E

s

= 6MC/S

100

f = 50 HC/S

120

"—-—_« FREE SPACE VALUE

CD

C3

140

CO

COo1 - o 160

CO

180 ^^

.-—""""" •

-

COzCO

oe

C3

• •

__ •

CO

CD ^

-ffl 200

X

x X - —' x .^ 220 .^ CALCULATED SCATTER LEVEL

240

1 t t t Y0NAG0 H 1

AIS0 AKITA HAKODATE

1 1 1 1 1 500 1000 1500 DISTANCE IN KM

2000

- 60

- 40

20 Q

E

a. 3

--20

--40

--60

DISTANCE DEPENDENCE OF SPORADIC E PR0PAGATII

FIGURE 5

2500

(THIN LAYER MODEL)
-23-

100 -

120 -

140-

SCALES OF h IRREGULARITIES

CD- L, -l z

= 175m, 1-3= 35 m ©: L, = L 2

= 175m, W 50 m ®: L, = L 2

* 175m, L 3

= 70 m

®: L, -W 250m, 1-3= 50 m

~ 160 CO

^ 200h

220

240

SCATTER MODEL

n = 5

LAYER THICKNESS* i KM

f Es

= 6 MC/S

f =50 MC/S

• MEASURED FIELD INTENSITY (50%)

FREE SPACE VALUE

CALCULATED SCATTER LEVEL

60

40 j.

20

-20

40

60

J_ I ±

500 1000 1500 2000 2500

DISTANCE IN KM DISTANCE DEPENDENCE OF SPORADIC E PROPAGATION (SCATTER MODEL)

FIGURE 6

3000
-24-

IUU

90 (a) •--

JUNE, 1955

80 (b)

•—

(-DECEMBER, 1955

I JANUARY, 1956

c/> 70 z —

m

i- 60

UJ

=3i 50

n = 7 N

n = 6 N

Ab)

»— n = 5 n

UJ2 40

«*

_iUJas

x, 30

"O —

n = 4 v

n = 3 v

n = 2 ^

N^cji

20

n = 1 -

10

n

—

1

1 ItVj . 20 30

FREQUENCY (MC/S)

40 50

EXPERIMENTAL RESULTS OF THE FREQUENCY DEPENDENCE OF SPORADIC E PROPAGATION

FIGURE 7
-25-

100

90

80 -

60 -

50 -

f= 40 -

30 -

20 -

10 -

- n = 7 v --•— E

s PROPAGATION - n = 6 v

__o SCATTER PROPAGATION

— n = 5 v

-

n = 4 n^

n = 3 <

-

n = 2 -v.

n = l ^^ sA^\

-

^^^ ^Ssv^

1 1

1 1 1 1 ^^

1,1,

20 30 40 FREQUENCY (HC/S)

50 60 70 80 90 100

EXPERIMENTAL RESULTS OF THE FREQUENCY DEPENDENCES OF SPORADIC E PROPAGATION AND NORMAL SCATTER PROPAGATION

FIGURE 8

M
-26-

LAKER THICKNESS THIN LAYER MODEL

n =5

H - 300M f E

s = IOMC/S

100

H = I000M

110 _

120 *^\£REE SPACE VALUE

130

140

150

160

170

180

190

f - in ur> ^**

-

T 0\J

50

3C

7!5(

31

7J

5(

7!

MC^C^'""* CO3

zo

COCO

,MC<^'^" =T.TMr«

)MC^ ***-

<::Tt''r'StS

CO

3E

Ci

CO

-*CD

)MC

>MC'"

1 200 -

210

220

-

CALCULATED SCATTER LEVEL

230

240

1 1 1 1 1

60

50

40

30 -oo

- 20

10 3

-

-10

-20

-30

-40

-50

500 1000 1500

DISTANCE IN KM

2000 2500 3000

FREQUENCY AND DISTANCE DEPENDENCES OF SPORADIC E PROPAGATION BY MEANS OF THE THIN LAYER MODEL

FIGURE 9
-27-

100

120-

= 140 —

1 60 —

180

200

220 —

f -50 MC/S

f -75 MC/S

SCATTER MODEL

n -5

LAYER THICKNESS 1 KM SCALES OF E

s IRREGULARITIES

L i -L 2 175 m

L 3 « 50 m

f E s •I0MC/S

FREE SPACE VALUE

CALCULATED SCATTER LEVEL

60 „

40

- 20

20

-40

-60

240 —

_L 1

500 1000 1500 2000 2500

DISTANCE IN KM DISTANCE AND FREQUENCY DEPENDENCES OF SPORADIC E PROPAGATION BY MEANS OF THE SCATTER MODEL

3000

FIGURE 10
-28-

in 1955 and 17 during winter time. This experiment was carried out

between Cedar Rapids and Sterling and signal intensities were recorded

simultaneously at 27*775 Mc/s and k-9.8 Mc/s. These experimental results are plotted with dotted curves in Figure 7» Is. a recent experiment which has been carried out by the Central Radio Propagation

Laboratory in order to examine the frequency dependence of scatter

propagation using five different frequencies, that is, approximately

30, 40, 50, 74 and 108 Mc/s. Blair [29] reported on the frequency

dependence of sporadic-E propagation besides that of the normal scatter

propagation. This experimental evidence is shown with a dashed curve

in Figure 8. An additional dashed curve representing normal scatter

propagation is also plotted in the same figure. The curve shows that

the signal enhancement due to sporadic E diminishes rapidly with frequency when compared with normal scattering.

We shall try to check this frequency dependence from the theoretical

point of view. In Figure 9 ar® plotted the theoretical curves derived

from the thin layer theory with frequencies (30 Mc/s, 50 Mc/s, 75 Mc/s)

as a parameter and several layer thicknesses (100 m, 300 m, 1000 m)

with fixed value of the critical frequency of Es (foEs = 10 Mc/s ) and

an exponent of the electron distribution (n = 5). r^e corresponding

calculation is given in Figure 10 by using the scattering model.

Concerning the frequency dependence, the thin layer model which

is described in this paper does not seem to be a good fit. The
-29-

scattering model which has an auto-correlation function of the modified

Bessel function of a high order seems to be preferable as will be seen

from the formula (3 .12) or Figure "J, 8 and 10. From the scattering

theory for sporadic E [i.e. equations (3 .8) and (3-9)]j we Se "t

P

r

K ^)

If we take a high order value of n in the correlation function, that is,

n = k ~ n = "J, we obtain

p .

1 r

f13 f19

•

Therefore we can explain the frequency dependence of sporadic E by considering an auto-correlation function which has a very slow decrease

with p (= -j) . In Figures 7 an(i 8, are drawn families of curves with

various values of n in the modified Bessel function of n order. From

these figures, the auto-correlations of the modified Bessel function

with n = k ~ n. = 7 seem to be reasonable for the scattering model of

sporadic E. It is also of interest to note that the curve of n = 1

fits the normal ionospheric scatter propagation measurements. Although

Norton [30] has stated in his recent paper that this pK (p) correlation function has definite advantages over the exponential model for

describing the turbulence of refractivity in the troposphere and
-30-

E s INTENSITY - YONAGO f Es -YANAGAWA JAN -DEC, 1958

43.4

33.4

23.4

$ 13.4

70

60

50

40

U> 3.4 £ 30 g "

^ -6.6 £ 20 o °

—i £

£-16.6

>

10 -

U-l -26.6

-36.6 -10 h

-46.6 -20

(a) DAYTIME (06h-l8h)

J L I I 8 10 12

f E s (MC/S)

J_

120

\ 130

140

150

160

170

180

190

200

210

o

CO

COo

CO

14 16 18 20

43.4

33.4

23.

70

60

50

(b) NIGHT TIME (I8h-06h)

3 13.4 g 40

S 3.4 | 30 S -6.6 S 20 a o

^-16.6 10 -

w

U-l -26.6 -

-36.6 -10

46.6 -20

.-•<i.&! -•;*•::•:

8 10 12

f E s (MC/S)

- 120 - 130

\ 140 s

150 g

160 2CO

CO

170 £«*as

l— - 180 e£

co

ao - 190 i

_j - 200

- 210

14 16 18 20

CORRELATION BETWEEN f Es AND FIELD STRENGTH OF SPORADIC E

FIGURE II
-31-

70 <

66~69

62—65

58~ 61

54-57

50~53 = 46~49

llj 42~ 45

38-41

2 34-37

2 30-33

26-29

22~25

18-21

14-17

10-13

6-9

2-5

f E

s (NC/S)

os os o> os o^ os o> os °* os os

•a* lo co r^ od OS OS OS OS

lO CO

:t> CCS — C\J fO ^- LO CO i^-: GO oi

2 I ? 2 2 2 I 2 2 2 I

==> <=> G3 O CO o o <=> cs o CD

9> o CO to «»- tn CO h-^ CO OS

OCCURRENCE NUMBER

' 10-14 I

5-9 15-19

20-29

30<

CORRELATION BETWEEN f E s AND THE FIELO STRENGTH OF SPORADIC E

FIGURE 12
-32-

stratosphere, also it seems to "be quite good for the normal turbulence

situation in the ionosphere.

6. CORRELATION BETWEEN foEs AND FIELD STRENGTH

In this section, we shall briefly consider a correlation between

foEs and the received Es field strength. Figure 11 shows some correlograms between these parameters. The normalized Es field strengths are

the hourly median values observed at Yonago during the period January

to December in 1958. As the ionosonde station at Yamagawa is situated

almost exactly at the midpoint between Okuma (transmitting point ) and

Yonago (receiving point), It is appropriate to use values of foEs observed at Yamagawa to Investigate a relationship between the field

strength and foEs. Since the field strength used in this analysis is

the hourly median value, the corresponding value of foEs Is interpolated

from the measured values at each hour. A more rigorous analysis has

been made by Yamaoka [31] hy using the instantaneous value of field

strength to the value of foEs observed every 15 minutes. This is shown

in Figure 12 and data during periods of July and August in 1959 are

used. From these figures, it Is interesting to note that the field

strength increases abruptly in the interval from foEs = 8 Mc/s to

foEs = 10 Mc/s. Although the cause of this increase is not yet clear,

it may be related to the fact that this interval is near to the

plasma frequency for normal reflection in this transmission circuit
-33-

(i.e. k^.6Q Mc/sec 9 = ~ 12 Mc). This seems to suggest that there are

two modes of sporadic-E propagation, that is, the high field strength

corresponding to high values of foEs seems to be due to the reflection

mechanism and the relatively low field strength is due to the scattering mechanism. Theoretical curves calculated from the thin layer and

scattering models are compared with some measured field intensities

for various values of foEs. From Figure 13 it can be seen that a

fairly high field intensity of sporadic-E enhancement corresponding

to a comparatively high plasma frequency may be explained by reflection from a thin ionized layer whereas a relatively low sporadic-E

field intensity may be produced by the scattering mechanism.

7. CONCLUSIONS

From the above theoretical investigation for the sporadic-E model,

some conclusions may be drawn.

i ) High field strength of sporadic-E enhancements may be explained by reflection from a thin layer with electron density

/r approaching the necessary plasma density (i.e. 2 x 10 e/cc

for the Okuma-to-Yonago circuit).

ii) Relatively low field strength of sporadic E may be explained by the scattering model.

iii) Scattering model for sporadic E is expressed by using an

auto-correlation function of the modified Bessel function of

higher order and each blob of ionization may be considered to
-34-

100

120

- 140

160

- 200

220

240

© LAYER THICKNESS = 300 m ")

f £

s =l2 MC/S

N BM - "D-f-ftr) J © LAYER THICKNESS= 1000 m V.-UMC/S 10 NyAx" N ['-(^) J

> THIN LAYER MODEL

f - 50 MC/S

MEASURED RESULT

FREE SPACE VALUE

f E

s =l4 MC

f E

s

- 12 MC

foV l0 MC

f E

s =8 MC

f E

s =7 MC

-:?' J^/-

©

©

©

©

CALCULATED SCATTER LEVEL

© LAYER THICKNESS - lOOOrrf

f E

s

= 6 MC/S n«5

L|- L

z

= 175m, L 3

* 50m

© LAYER THICKNESS 1000

m

f E

8

" 6 MC/S, n-5

L,« L 2

« 175m, L 3= 70 m

I

I

y SCATTER MODEL

_L

60

40

20

E

a.

20

-40

60

500 1000 1500 2000

DISTANCE IN KM

2500 3000

THEORETICAL EXPLANATION FOR A RELATIONSHIP BETWEEN f E s AND E

s FIELD INTENSITY

FIGURE 13
-35-

have a horizontal scale of the order of 200 m and a vertical

scale of 50 m.

iv) Concerning the frequency dependence of sporadic E, the

thin layer theory developed in this paper does not seem to

"be appropriate, however, this frequency dependence can be

explained by the scattering model.

v) If we assume a layer thickness of sporadic E of 300 m ~

1000 m, we can explain the distance dependence of the median

field strength from both the thin layer and the scattering

theories.

8 . ACKNOWLEDGMENT

This research has been carried out as a part of the sporadic E

project at the Boulder Laboratories. The author wishes to express his

sincere thanks to Dr. E.K. Smith for his help and advice given throughout the course of this study. The author is much indebted to Dr. R.M.

Gallet, Dr. K. Davies, Mr. V. Agy, Mr. J. Watts, Dr. H.H. Howe, Mr.

J.W. Finney and Mr. J.F. DeGregorio at the Boulder Laboratories for

their kind suggestions and discussions. His cordial thanks are also

due to Messieurs A. Sakurazawa, K. Sawaji and M. Yamaoka at the Radio

Research Laboratories in Japan for their effort in arranging necessary

data.
-36-

9. REFERENCES

[l]. E.K. Smith, Worldwide occurrence of sporadic E, NBS Circular

582 (Mar. 1957).

[2]. D.R. Hartree, The propagation of electromagnetic waves in a stratified medium, Proc . Camb. Phil. Soc., 25, 97 (1929).

[3]. H.G. Booker, The critical frequency method of measuring upper

atmospheric ionization, (Result quoted by Appleton,

Naismith and Ingram, Proc. Phys. Soc, 51, 8l, 1938).

[k]. O.E.H. Rydbeck, The reflection of electromagnetic waves from

a parabolic friction-free ionized layer, J. Appl. Phys.,

13, 577 (19^2).

[5]. O.E.H. Rydbeck, On the propagation of radio waves, Trans.

Chalmers, Univ. Tech., 3^, (19^6).

[6]. K. Rawer, Elektrishe Wellen in einem geshichteten medium, Ann.

d. Physik, 35, 385 (1939).

[7]. H.T. Friis, A.B. Crawford and D.C. Hagg, A reflection theory

for propagation beyond the horizon, Bell Sys. Tech. Jour.

36, 627 (1957).

[8]. H.G. Booker, Radio scattering in the lower ionosphere, J.

Geophys. Research, 6k, 2l6k (1959).

[9]. R.M. Gallet, (Private communication).

[10]. H.G. Booker and W.E. Gordon, A theory of radio scattering in

the troposphere, Proc. I.R.E., 38, 401 (1950).

[11]. K.A. Norton, Point-to-point radio-relaying via the scatter mode

of tropospheric propagation, I.R.E. Trans. CS-4, 39 (1956).

[12], H.G. Booker, The use of radio stars to study irregular refraction of radio waves in the ionosphere, Proc. I.R.E., U6,

298 (1958).

[13]. W.E. Gordon, Radio scattering in the troposphere, Proc. I.R.E.

,

1+3, 23 (1955).
-37-

[ik] . D.K. Bailey, et al, A new kind of radio propagation at very high

frequencies observable over long distances, Phys. Rev., 86 , M (1952).

[15] • H.G. Booker, A theory of scattering by nonisotropic irregularities with application to radar reflection from the aurora,

J. Atmospheric and Terrest. Phys. 8, 20^ (1956).

[l6]. H. Staras, Forward scattering of radio waves by anisotropic turbulence, Proc. I.R.E., ^3, 137^ (1955).

[17]. J. Renau (To be published in J. Research, NBS Part D).

[l8]. K.A. Norton, Carrier frequency dependence of the basic transmission loss in tropospheric forward scatter propagation,

NBS Technical Note 53 (May, i960). (To be published in

July, i960 issue of J.G.R. ).

[19]« R.M. Gallet, Aerodynamical mechanisms producing electronic density fluctuations in turbulent ionized layers, Proc. I.R.E.,

43, 121+0 (1955).

[20]. D. Layzer, Ionospheric turbulence and the origin of stratification, Lecture at NBS (i960). (To be published in Es Monograph, Pergamon Press, 1961).

[21]. L.R.O. Storey, (Private communication to Dr. E.K. Smith, i960).

[22]. K. Tao, Radio scattering expressed in terms of the spectrum of

turbulent fluctuation in the ionosphere, J. of the Radio

Research Laboratories, 5., 20 (1958).

[23]. K. Tao, K. Sawaji, A. Sakurazawa and M. Yamaoka, Experiments of

long distance ionospheric propagation on VET, J. of the

Radio Research Laboratories, J, 177 (i960).

[2k]. K. Miya, T. Sasaki and M. Ishikawa, Observation of F-layer and

sporadic-E scatter at VHP in the Far East (to be published

in January, 1961 issue of NBS J. Research, Part D).

[25]. D.K. Bailey, R. Bateman and R.C. Kirby, Radio transmission at

VRF by scattering and other processes in the lower ionosphere, Proc. I.R.E., k3, ll8l (1955).
-38-

[26]. W.J. Bray, J. A. Saxton, R.W. White and G.W. Luscombe, VHF

propagation "by ionospheric scattering and its application

to long distance communication, Proc. I.E.E., 103 » 236

(1956).

[27]. A.D. Wheelon, Radio frequency and scattering angle dependence

of ionospheric scatter propagation at VHF, J. Geophys.

Research, 62, 93 (1957).

[28]. R.M. Davis, E.K. Smith and CD. Ellyett, Sporadic E at VHF

in the USA, Proc. I.R.E., k%, 762-769 (1959).

[29]. J.C. Blair, Frequency dependence of VHF ionospheric scattering, NBS Technical Note, 9 (Apr. 1959).

[30]. K.A. Norton, Recent experimental evidence favoring the pK (p)

correlation function for describing the turbulence of re- fractivity in the troposphere and stratosphere, J.

Atmospheric and Terrest. Phys. 15, 206 (1959).

[31]. M. Yamaoka, Relationship between foEs and field intensity

depending on sporadic-E propagation, (to be published in

July, i960 issue of the Quarterly Review of the Radio

Research Laboratories, in Japanese).
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