National Bureau of Standards

Library, H.W. Bldg

MAY IV 1965

^ecknic&l v£ote 92o. 306

STUDIES OF SOLAR FLARE EFFECTS

AND OTHER IONOSPHERIC DISTURBANCES

WITH A HIGH FREQUENCY DOPPLER TECHNIQUE

V. Agy, D. M. Baker, and R. M. Jones

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

'Cecltnical ^ote 306

Issued April 28, 1965

STUDIES OF SOLAR FLARE EFFECTS

AND OTHER IONOSPHERIC DISTURDANCES

WITH A HIGH FREQUENCY DOPPLER TECHNIQUE

V. Agy, D. M. Baker, and R. M. Jones

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

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.

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington, D.C. 20402

Price: 75 cents

Table of Contents

Page

List of Tables v

List of Figures • • vii

Nomenclature ix

Abstract xi

1. Introduction 1

2. Theoretical Considerations 7

2.1 An Equivalence Theorem for Doppler Shifts 9

2.2 Changing Ionospheric Parameters 11

2.3 Frequency Deviations due to Rate of Change of

Electron Density as Function of Height 21

3. Solar Flare Observations with the Doppler Technique .... 31

3.1 Percentage of Solar Flares Detected 32

3.2 Duration, Rise Time, and Delay Time of

Frequency Deviation 37

3.3 Path Length Dependence of Frequency Deviations .... kO

3.U Frequency Dependence of Frequency Deviations kMk. Selected Events Detected by Doppler Technique ^7

k.l Solar Flares Vf

k.2 Geomagnetic Variations 55

5. Discussion 60

6. Acknowledgements 6k

7. References 65

8. Appendix I: The Doppler Shift Written as an Integral ... 67

9. Appendix II: Equivalence Theorem for Doppler Shifts .... 72

10. Appendix III: Relationship Between Doppler Shift and

Virtual Height 7^

iii
Table of Contents

IV

Page

11. Appendix IV: Catalog of Sudden Frequency Deviations

Observed from October i960 through December 1962 78
List of Tables

Page

1.1 Circuits over which Doppler measurements have been made

by CRPL k

2.1 Tabulation of data for flare effects of November 22, 1961

and April 17, 19, and 20, 1962 28

3.1 Percentage of flares reported from October 1, i960 to

December 31? 19&2 which were accompanied by SFD's 32

11.1 Catalog of sudden frequency deviations observed from

October i960 through December 1962 85

v

List of Figures

Page

2.1 Doppler shift, Af, for vertical propagation with reflection in a changing parabolic F layer l4

2.2 Doppler shift, Af, for oblique propagation with reflection in a changing parabolic F layer 15

2.3 Doppler shift, Af, for vertical propagation "with fixed mirrorlike reflection above a changing parabolic E layer 17

2.4 Doppler shift, Af, for vertical propagation through a valley of

changing depth between parabolic E and F layers 19

2.5 Doppler shift, Af, for oblique propagation through a valley of

changing depth between parabolic E and F layers 20

2.6 Comparison of f Af vs f with ionogram for SFD at 20l4 UT on November 22, 1961 2k

2.7 Comparison of f Af vs f with ionogram for SFD at 2252 UT on April 17, 1962 25

2.8 Comparison of f Af vs f with ionogram for SFD at 1935 UT on April 19, 1962 26

2.9 Comparison of f Af vs f with ionogram for SFD at 1959 UT on April 20, 1962 27

2.10 Relationship between maximum frequency deviations observed on

k- and 5 Mc/s at vertical incidence, Boulder, Colorado 30

3.1 Variations of the percentage of reported solar flares detected,

mean solar flux at 2800 Mc/s, and mean Zurich sunspot number

during the period October 1, i960 through December 31* 1962. . . 3^

3.2 Percentage of reported solar flares detected by the Doppler

technique as a function of month, October i960 through

December 1962 35

3-3 Percentage of reported solar flares detected by the Doppler

technique as a function of time of day, October i960 through

December 1962 36

3-k Percentage of reported solar flares detected by the Doppler

technique as a function of solar zenith angle at the midpoint

of the WWV to Boulder path, October i960 through December 1962 . 38

3.5 Durations of sudden frequency deviations observed from October

i960 through December 1962 39

3.6 Rise times of sudden frequency deviations observed from October

i960 through December 1962 hi

3*7 Time difference between maximum positive frequency deviation and

maximum phase of optical flare, October i960 through December

1962 k2

Vll
Page

3.8 Frequency deviation of WW-10 Mc/s observed at Shickley, Nebraska

(1780 km) versus that observed at Boulder, Colorado (2400 km). . 43

3.9 Frequency deviation of WW-10 Mc/s versus that of WW-20 Mc/s,

both observed at Boulder, Colorado 45

3.10 Frequency deviation of WW-10 Mc/s versus that of WW-15 Mc/s,

both observed at Boulder, Colorado 46

4.1 Sudden frequency deviation observed during importance 1 flare on September 4, 1961, WW-10 Mc/s received at Boulder 48

4.2 Sudden frequency deviation observed during importance 3+ flare

on November 12, i960, WW-20 Mc/s received at Boulder 50

4.3 Sudden frequency deviation observed during importance 3 flare

on September 28, 1961, WW-10 and WW-20 Mc/s received at

Boulder 51

4.4 Sudden frequency deviation observed during importance 2 flare

on April 19, 1962, WW-10 and WW-15 Mc/s received at Boulder. . 53

4.5 Sudden frequency deviation observed during importance 2 flare

on April 19, 1962. 4 and 5 Mc/s vertical incidence at Boulder . 54

4.6 Sudden commencement observed by the Doppler technique at 2108 UT

on September 30, 1961. WW-10 and WW-20 Mc/s received at

Boulder ^6

4.7 Sudden commencement observed by the Doppler technique at 0219 UT on February 22, 1962. WW-10 Mc/s received at Shickley, Nebraska,

and WW-10 and WW-15 Mc/s received at Boulder, Colorado .... 57

4.8 Correlation between frequency variations observed at both oblique

and vertical incidence and changes in the magnetic field observed

at Boulder 59

10.1 Comparison of theoretical fAf versus f with ionogram 77

11.1 Sample Doppler record illustrating the range in magnitude of the

sudden frequency deviations detected 80

Vlll
Nomenclature

AA change in non-deviative absorption, nepers

b thickness of slab of ionization in non-deviative region, km

c speed of light in vacuum , km/s

D great circle distance between transmitter and receiver, km

f frequency

f critical frequency of parabolic layer, Mc/s

f critical frequency of parabolic E layer, Mc/s

f„ critical frequency of parabolic F layer, Mc/s

f„ gyrofrequency, Mc/s

f electron plasma frequency, Mc/s

f f cos0 , equivalent vertical-incidence frequency, Mc/s

f plasma frequency of valley between two parabolic layers

,

Mc/s

Af Doppler shift, c/s

h reflection height, km

h' virtual height, km

h height of maximum electron density of parabolic layer, km

h height of maximum electron density of parabolic E layer, km

h height of maximum electron density of parabolic F layer, km

mr h height of bottom of parabolic layer, km, or a height in non- deviative region below which dW/dt can be considered to be zero,

h height of bottom of parabolic E layer, km

h height of bottom of parabolic F layer, km

k Si , 8.05 X lCT11 (Mc/s) 2 m

3

N

N electron density, m

IX
p phase path j km

s path length

t time

X

%

2

f

2

ym

h - h , semitl

m o

Y fH

/f

Y

L

Y cos6

Ym Y sine

z height as variable of integration

|i phase refractive index

|i

group refractive index

|i phase refractive index at transmitter

v electron collision frequency

p Vf

E

angle "between wave normal and vertical

angle between wave normal and vertical at transmitter

o

to

9 angle between wave normal and magnetic field
Abstract

This report presents some results of work done with a Doppler

technique for studying ionospheric disturbances . The theoretical results

include a calculation of the frequency shifts to be expected from changes

in the parameters of a parabolic model ionosphere and a method of determining the height variation of the time rate of change of electron

density during ionospheric disturbances. It is shown that the frequency

shift, with oblique propagation, is the same as that with vertical propagation on the equivalent vertical- incidence frequency. The experimental

results include a comprehensive catalog of all flare effects observed

from 1 October i960 through 31 December 19&2, a statistical study of

these flare effects, and the Doppler records of some solar flare effects

detected during this period. A model in which the time rate of change of

electron density is zero below the bottom of the E layer, and constant

above that height, explains the frequency dependence of the maximum

Doppler shifts observed during some solar flares.

xi

STUDIES OF SOLAR FLARE EFFECTS AND OTHER IONOSPHERIC

DISTURBANCES WITH A HIGH FREQUENCY DOPPLER TECHNIQUE

V. Agy, D. M. Baker, and R. M. Jones

Central Radio Propagation Laboratory

1. Introduction

The "Doppler technique" developed and described by Watts and Davies

[i960] appears to be a powerful tool for probing the ionosphere, especially during times of rapid change. It has been shown to be effective,

for example, in the study of solar-flare effects and of variations

occurring at the time of a magnetic sudden commencement [Davies, 1962b].

The term "sudden frequency deviation", abbreviated to SFD (initially

suggested by Chan and Villard [1963]), has been adopted to refer to

solar-flare induced variations in the received frequency of a high

frequency, ionospherically propagated radio signal.

In effect, the frequency f of the received signal from a highly

stable CW transmitter is monitored continuously. If the phase path P

changes with time, a shift in the received frequency is produced which

may be written [Davies, 1962a]:

Af = -^§ (LI)

c dt

where c is the speed of light in vacuum. (This may be written

tf.-ffgjm (1.2)

if the anisotropy of the ionosphere is neglected.)
The present monitoring technique involves recording at a speed of

.02 ips on magnetic tape, the heat "between the received signal and that

of a stable local oscillator. The heat frequency is set initially at a

few cycles per second. If the tape is played hack at 30 ips, this heat

frequency is readily analyzed on a standard audio frequency analyzer and

changes in the original frequency of one tenth of a cycle per second or

more can easily be observed and measured. The transmitted and reference

frequencies must be stable to within a few parts in 109 per day.

A simple theory, consisting of two special cases, for determining

the layers affected during an ionospheric disturbance has been described

by Davies [1962a] and by Davies, Watts, and Zacharisen [1962] . One case

shows that for several probing frequencies propagating in the same mode

(i.e., same ground path length, same number of hops, reflected from same

layer) the Doppler shift varies inversely with carrier frequency

(Af cc l/f ) when the change in phase path is due solely to changes in ionization in the non-deviative portion of the ionosphere. In the other case

the frequency deviation varies directly with frequency (Af cc f ) if the

phase path change is due entirely to a vertical movement of the height of

reflection.

Davies [1963] has suggested that in the non-deviative region the

height determination can be improved by comparing the phase path change

(AP) to the absorption suffered "by the radio wave. An atmospheric model

specifying electron collision frequency (v) as a function of height can

then be used to locate the "slab" of ionization assumed responsible for

both effects. Similar work has been carried out by Kanellakos, Chan, and

Villard [1962]. These studies have helped to establish the fact that
solar-flare effects are relatively frequent at heights above the D region

of the ionosphere

Davies [1962c] has also shown that the Doppler technique can he used

for study of ionospheric drifts.

Those circuits over which Doppler measurements have been made by

CRPL are given in table 1.1. Related techniques involving the direct

measurement of phase change are also in use. The increasing use of these

techniques and the high precision of the actual measurements (both of

Doppler shift and of phase change) suggest that attention be given to

further development of the theory so that the approach may be exploited

to the fullest extent.

This paper presents work done with the Doppler technique by the

Ionosphere Research Section of the Ionosphere Research and Propagation

Division of CRPL. The theoretical treatment develops two methods of

determining the heights at which ionospheric disturbances occur. Both

approaches neglect the earth's magnetic field and the curvature of the

ionosphere

The first method approximates the ionosphere by one or two parabolic

profiles and then determines the frequency dependence of the Doppler

shift produced by the rate of change of the parameters (i.e., critical

frequency, minimum height, height of maximum electron density, thickness

of layer, and valley depth) defining the ionospheric model. If, then,

the Doppler shifts are known for a number of frequencies at vertical and/

or oblique incidence during a disturbance, it is possible to determine

the time rate of change of the parameters which could have produced the

observed Doppler shifts. This method is not difficult to apply since the
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layer parameters are easily determined from the ionogram and the solution

for the time rate of change involves solving only a few simultaneous

linear equations.

The second approach gives a solution for the time rate of change of

electron density as a function of height when the Doppler shift as a

function of the equivalent vertical- incidence frequency can be given. It

can be applied to any monotonic ionospheric profile, but the accuracy of

the solution depends on the amount of data available.

Most solar flare effects in the ionosphere produce characteristic

effects on the Doppler records. The early recognition of this fact led

to the suggestion that the Doppler technique be used for flare patrol

work. Much of the record analysis and the experimental effort has dealt

with flare effects--specifically with the percentage of flares detected,

the time characteristics of the frequency deviations, and the magnitude

of the effects relative to probing frequency, path length, and solar

zenith angle. The section of the report dealing with the observations

gives the empirical results derived to date and a catalog of solar flare

effects as observed on the CRPL Doppler records from 1 October i960

through 31 December 1962 . A few sets of observations are treated according to the methods described in the theoretical section.
2 . Theoretical Considerations

In order for the Doppler technique to be of value as a tool for

ionospheric research, a theory is needed which adequately relates the

observed frequency variations to the ionospheric changes producing them.

A simple theory for vertical incidence (neglecting the earth's magnetic

field) has been developed by Davies [1962a, 1962b] . According to this

theory, if changes take place in a non-deviative slab of thickness b in

which the rate of change of ionization can be considered constant with

height, then

Aa f B ^i. (2.1) cf dt K J

In this case the observed frequency deviation is inversely proportional

to the operating frequency. However, if the only change is a vertical

movement of the height at reflection, then

Af = -2^§£ (2.2)

c dt

and the frequency deviation is directly proportional to the operating

frequency. These equations can be applied to oblique incidence if b is

replaced by b/cos O and dh/dt is replaced by dh/dt cos O , where O is

the angle of Incidence on the ionosphere

If both types of change occur at the same time (i.e., if the change

in height of reflection and a change in the non-deviative region occur

simultaneously but independently) then

Af= S|ffl 2 f|h

(2 .3) cf dt c dt

If such independent changes did occur and measurements of Af were made on

two different frequencies, then b dW/dt and dh/dt could be determined from
(2.3) [Davies, 1962a]

Davies [1963] has further shown that for a thin, non-deviative slab

in which the collision frequency is v(« uo)

AP c

' ^' 4;

where AA is the change in non-deviative absorption in nepers and AP is

the change in phase path given by

t

AP(t) = - I J* Af dt . (2.5)

to

Hence, if both AA(t) and Af(t) are measured, it is possible to determine

v(t) from (2.k) and (2.5)- If the collision frequency profile v(h) is

known, then the average height h(t) at which the additional electron

density is produced can be found. However, even where this method is

applicable it is rather insensitive due to the lack of knowledge of the

variation of collision frequency with height.

The simple theory has not explained all the frequency deviations

observed. The theoretical work covered in this report is a beginning in

the development of a theory which will explain the Doppler observations

at both vertical and oblique incidence. The major aim has been to develop

a method of determining the height variation of dN/dt from the Doppler

observations. A knowledge of dN/dt as a function of height during a

solar flare would be helpful in determining which wave length bands are

enhanced during the flare. A knowledge of the enhancement of radiation

during a flare should help in gaining an understanding of the processes

taking place in the sun.
2.1. An Equivalence Theorem for Doppler Shifts

For oblique propagation relations similar to (2.l) and (2.2) can be

derived if the earth's magnetic field and the curvature of the ionosphere

are neglected. The resulting relations are:

Af- = k\ g (2.6) cf cos 0o dt x '

for a change of ionization in a non-deviative slab, and

Af = _ 2

f cos ^o § ( 2. 7 ) c dt

for a vertical movement of the height of reflection. In these equations

O

is the angle of incidence on the ionosphere. These two equations can

be written as

and

Af = -2§*§ (2.9)

where fy

= f cos Q

. A comparison of (2.8) and (2.9) with (2.l) and

(2.2) reveals' that, in these simple cases, the Doppler shift observed on

a wave frequency f, incident on the ionosphere at an angle O , would be

the same as that observed on a frequency fv incident vertically on the

ionosphere. This "equivalence" between the Doppler shifts observed for

vertical and oblique propagation is easily seen for these simple cases.

In Appendix II it is shown that such an equivalence holds in the general

case, if the earth's magnetic field and the curvature of the ionosphere

are neglected. Hence, an equivalence theorem for Doppler shifts can be

stated as follows:

Af(f, O ) = Af(f cos O , 0) (2.10)

9
where Af (f s O ) is the Doppler shift, on a frequency f, incident on the

ionosphere at an angle O . The frequency fv is called the equivalent

vertical- incidence frequency.

As derived, this equivalence relation applies only for no magnetic

field. However, it is probably a good approximation even with the magnetic field for frequencies which are large compared to the gyrofrequency.

Therefore, rather than attempting to treat vertical- incidence and obliqueincidence data separately, it seems more advantageous to use the equivalence theorem to reduce the oblique- incidence data to equivalent verticalincidence data, and to apply a single theory to the combined data. In

this connection it may be noted that with oblique- incidence observations

the amount of useful data may exceed the number of probing frequencies

used. At oblique incidence more than one propagation mode is often

possible (e.g., E and F layer propagation, one- and two-hop propagation,

etc.), and the Doppler shifts observed on the different modes may be

quite different. In such a case, if the propagation modes can be identified, the Doppler shift observed on each gives an independent piece of

data.

This equivalence theorem should be very useful in analyses of

Doppler data obtained on different paths and from different parts of the

world, and it will provide a convenient means whereby various observers

can exchange their data. Of course, before data from different paths or

different regions can be meaningfully compared certain corrections, such

as corrections for the number of hops or the differences in solar zenith

angle, may have to be applied to the observed frequency deviations.

10
2.2. Frequency Deviations Due to Changing Ionospheric Parameters

Although in many cases the ionosphere can be described adequately

only by specifying the height distribution of electron density, it is

often convenient to represent the ionosphere by a suitable model (e.g.,

parabolic). If the distribution does not change in character (if, for

example, a parabolic distribution remains parabolic) it is possible to

find Af as a function of the time derivatives of the parameters defining

the distribution. Primarily for illustrative purposes and for comparison

with the first order theory [Davies, 1962a], the algebra and the computations have been carried out for several model ionospheres. Both vertical

and oblique propagation are considered. The earth's magnetic field and

the curvature of the earth and ionosphere are neglected.

For vertical propagation of a wave, the phase path P is given by

h

P = 2 J

p. dz , (2.11)

o

where h is the reflection height. For oblique propagation, the phase

path is given by

P =

J* ii ds , (2.12)

s

where s is the path length.

If the ionospheric profile consists of parabolic layers, then the

plasma frequency f-^ in each layer is given by

%

2 - fc

2 f^-^3' (2 - i3)

n
for hQ

< z < 2 hjj - hQ

. In each layer, the phase refractive index |jt for

a wave of frequency f is given by

V i

2 V f

3 V Lhm

- hc

J Lhm - hQ

J >

For vertical propagation this expression for the refractive index

may be used in (2.1l) to find the phase path in terms of the parameters

defining the model ionosphere. The time derivative of P may then be

found in terms of the time derivatives of the layer parameters, and the

Doppler shift, Af, is then given by (l.l). Similarly the Doppler shift

for oblique propagation could be found from (2.1*0, (2.12), and (l.l)

using the fact that the transmission distance is constant (i.e., the

transmitter and receiver are fixed). However, because of the equivalence

theorem presented in section 2.1, the calculations need be performed only

for vertical propagation. The Doppler shift for oblique propagation can

then be found by substituting f cos O for f in the equations for vertical

propagation. Indeed, the equivalence theorem was discovered while working

with changing parabolic layers.

Three models considered will now be discussed separately.

Model 1 : reflection in a changing parabolic layer (figure 2.1a).

For this case

f SP dhQ f 3P dhm f SP_ df£

Tp IS)

c dhQ

dt " c "oh^ dt " c dfc dt v

' ;

12
where

and

f 3P

= fa

c 3h c L

f BP _ f

c db^ " c

f 5P _ ym

c dfc " c

1 - x

3

„ 1 + x

-x - £n

1 - x

1 + x

-x + —£n

1 + x

3 -x + j£n

1 - x

1 + x

"1

x =

(2.16)

(2.17)

for vertical propagation, or

x = f COS 0Q

fc

(2.18)

tan O = D

(2hQ + xym in

±

_ *)

(2.19)

for oblique propagation. Plots of the coefficients in (2.15)

[-f/c dp/dh , -f/c SP/dhm, -f/c 3P/dfc ] versus f, for specific values of

the parameters h , hm, and fc , are given in figure 2.1 for vertical

propagation. Similar curves are shown in figure 2.2 for oblique propagation over paths of 200, 1000, and 2^00 km. For a layer defined by values

of h , hm, and fc different from those chosen, figures 2.1 and 2.2 can

still be applied by using equation (2.l6) to scale the curves.

For the special case dh /dt = dh^/dt = dh/dt and dfc/dt =0, (2.15)

reduces to (2.2), the expression for the Doppler shift caused by vertical

movement of the ionosphere (or of the height of reflection).

13
Doppler shift, Af, for vertical propagation with reflection in a changing parabolic F layer

fc

= iOMc/s, h =200km, h m = 300 km

Af

- _ 1 _££_ ^!2o _ _£_ _dP_ dhm

c dh dt c ahm dt

j_ jp_ dfc c dfc dt

500

400

IONOSPHERIC PROFILE

§ 300 -

200

100 -

1 1 1 1 1 1 1 1 1

- hm —

hQ

1 I 1 1

-

2 3 4 5 6 T 8 9 10 II PLASMA FREQUENCY, Mc/S f C

(a)

3 4 5 6 7 8 9 FREQUENCY, Mc/s

(b)

3 4 5 6 7 8 FREQUENCY, MC/s

(c)

3 4 5 6 7 8 9 FREQUENCY, Mc/S

(d) Figure 2.1

Ik
Doppler shift, Af, for oblique propagation with reflection in a changing parabolic P layer

fc= iOMc/s, h = 200km, h m = 300km

f ap dfc f

_ f ap dh f ap dhm

c ah dt c ahm dt c afc dt

500 ONOSPHERIC PROFILE

1 1 1 1 1 1 1 1

400

300 hm—

200

100

n

l 1 1 i i i

h

1

i

-

2 3 4 5 6 7 8 9 PLASMA FREQUENCY, Mc/S

(a)

-40

-36

-32

-28

-24 E

rr

-20 UJn

-lb V)

Ij.l _l -1? o>-

C ) -8

-4

-

1 /v 1 * 1 1 S7~

_

*/

8nil

" 1 4 -

- .4

&/ f bp

c dh

-

1 1 1 i i _

10 15 20 25 FREQUENCY, Mc/S

(b)

-fu

1 1 1 1 1 1 _

-36 -

-32 -

-28 v -

-24

-20 Ml

f ap

c ah m \-

-16 o / o /

at 1 a J

-12

-8

O , o

o 1

" / a 1 / -

-4

n

0-—1 i i -

10 15 20 25 FREQUENCY, Mc/S

(c)

I3UU

1400

1 1 1

\

i

i i -

1300 - -

1200 -

1100 -

1000 -

4" 900 . -

PER

MC f ap

c afc \

-

[3 500 o 400 ° 300

200

Je£ /1 O / o / Q /

100

n

= 2400KfT>^

t- x^ i

-

10 15 20 25 FREQUENCY, MC/S

(d) Figure 2.2

15
Model 2: propagation through a changing parabolic layer with

reflection from a mirror reflector (figure 2.3a). In this case

where

A£ _

_ f 5P dfc f 5P dym

c dfc dt c 9ym dt (2.20)

and

f 5P _ ym

c dfc

" c -2x + (l + x

3

) 4n x + 1 x - 1

f 3P

c Bym

= & f2x + (1 - x

3

) In ^4 '

c L

x ' x - 1 _

x = (eq. 2.17)

(2.21)

for vertical propagation, or

x = f cos O

(eq. 2.18)

tan O

D

(2h + 2 x ym in x + 1 x - 1

(2.22)

for oblique propagation.

For vertical propagation with specific values of fc and ym the coefficients - f/c dP/dfc and -f/c dP/dym are shown as functions of frequency

in figure 2.3- The dashed curves in this figure show what the "behavior

would be if Af were inversely proportional to frequency. For frequencies much greater than the critical frequency of the parabolic layer

(i.e., when the parabolic layer can be considered non-deviative) the

Doppler shift clearly exhibits an inverse frequency dependence as is

predicted by (2.l).

16
0) M

•HH

Imouu

•Hs u

tS 0)

<D s X cti •H H

<iH

H ^

-P o

•H -H > HO

Pi rO O ctJ E #S H in J£ P fel* cti O «3 ft CM ^Its

&0

ct3

M

ft £T

iiE>4-|O1 O -H

£h bo a pi h ,3 o fc^

cd o ? o «*-|

O

•H a5 ro -P n

II fH <L> u >

!> o

<*- < ^

fH tf O

<+H £O

*-H

<H -P <J O

(D nH P <P

<H cu •H ^ &U3

!w

CD H

ft

ftOQ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

tu>| d3d S31DAD I I I 1 I I I I I I I I I TTTl

T I I I I I I I I o

UJ

a:

tuin3

•H t c-j q co co q- S/OKI M3d S31DA0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 E

a.o(-o

UJ

_lu. i r __ .. -

LU

_1

A - o

UJ

<r—

Q- tr. o O

UJX

CES —

u.

1/5 OO 1 1 1 1 1 1 i i i 1 i i i i i i i i i 3 — O o

UJ>| '1H9I3H

17
Model 3 : propagation through one parabolic layer and a valley of

changing depth with reflection in a second parabolic layer (figure 2.4a)

For this model

AfA1 = - -^^-(2 23)

c Sp dt \£-*S)

where

f dP 2f_ \s-\m-^ A-Cfjp " ^W-^X)

E

c s P

' c yiFTT

(2.24)

p = ir (2.25) fE

and

dp 1 dfv

dt "ffjjj dt

f x = —

(2.26)

(2.27)

for vertical propagation, or

_ f cos n (2.28)

for oblique propagation. The formula for tan O is not given because of

its complexity.

The frequency dependence of -f/c dP/dp for p = 0.05 and 0.95 is

shown in figure 2.4b and 2.4c for vertical propagation and figure 2.5b

and 2.5c for oblique propagation. The dashed curves vary as l/f. For

vertical propagation through a changing non-deviative valley (p = 0.05 or

18
<ho

!»

0) H

cd in t> M <T> Jh O

cdp

ii !>> <X rf d ^H E O fr O

,3 t3 o

IO -p ri II ti u. S E O w tfl o

-C

-P CJ 5 E

bOH

O JC

a3

O

O

ft r^ " O O n3

UC\J QJ*- ^ M II T3|T3 ft o3

LU 11. Q-IQ. H- o >o|<o

H -C

n3 £ Q. H-|0 o cu ii ^ •H <D > E 1 -P > M— J£ II U -P

c/T o

0J <

f> rQ o II M ,d 2 IU O -P ro E

tfH Pi JZ

IT) ^ E OO

<3

M J£

Q_

d o

•»-H o

-P tiO

<Vl !=!

II SB UJo

-C

U

0) H

ft

ftOo 1 1 1 1 - - /

// - _ // -

%|<§- / / HO - _^ — • - _ b 1 1 1 1 -

S310A0

-4"

OJ

S31DA3 1 1 1 - / \ / \ -C / E \ 5

UlE

•*- o

LlI > 1

•D

_ P o

w>l '1H9I3H

19
<+HO

:>> H

E

£> ^ JC

0)

c<3 >m o

o

a3 If) ^ H

^h II Q

O

In T3J •• ,3 3 E

-P ctf o

a H (/> o

O \ ro H CJ o2

n -p -H u_

ctf H o E

faO o _c

05* & II ft o3 O U

U v5 ft ft

u. H—

UJ «4- o ^l**3 3 <D Q. 8 Ho

a1 CD 1 i •H >

>**— u. " H -P O M_

,<D (D m

-= <

O ,0 <:o •

Sh A s E

O -P JC <U ft to

ii o

•»<d ^

3 tiO

II

111 £ E

•»-H jC

-p M

E* 2^CQ O o

o

!m —

<D

II H 111 ft o

ftO

o

1 1 r r i

A

;

-

It II II / / / / / / / / / / / /

-

-

-

_

-

in

CT>

• -

o

- -

Q. 1 1 1 ! 1

<£ J/) o5

S310A0 —

1— 1 1 1 1 X~\ " A \

" /f 1 - /

- /

- / / "

o-la. / /

— / t

" _ H"/ /

- " " / s a

"

"" — ' X "

1 "

; " - "

_

COO - " O - "

Q. 1 1 1 1 1 l

2 < ir\ O

• » 5 OJ > 0) oj O "i-i — z ii

UJ bO - a •H

UJ

tr. P-4

9 s? S310A3

1 1 1 1

u_ /"

\

/ * \

J

1 £ 1

u.o

; / \

w

x:

:

' kz

s

in<

UU>) '1H9I3H

20
for higher frequencies when p = 0.95) the Doppler shift is inversely

proportional to frequency as shown in figure 2.^-b and 2.Uc. However, at

oblique incidence when the valley is non-deviative the Doppler shift does

not show a l/f dependence, as shown in figure 2.5b and 2.5c. This is due

to the frequency dependence of the angle of incidence O .

As shown in figures 2.2 and 2.5 for high frequencies at oblique

incidence (f > fc ) two values of the Doppler shift become possible. In

each case one possible Doppler shift would be observed on the low-angle

ray and the other on the high-angle ray.

2.3- Rate of Change of Electron Density as a Function of Height

Although the methods developed in the preceding section may be

useful in some cases, their usefulness is limited by the necessity of

approximating the ionospheric profile by parabolic layers. This section

presents a method for determining the rate of change of electron density

as a function of height using the true height profile directly.

It is shown in Appendix I that the Doppler shift can be written as

an integral over the ray path. For vertical propagation

Af = -2f/f±dz (2.29)

o

Neglecting the earth' s magnetic field this becomes

k_* p

p dN/dt oiyoo dzg (2<3Q) fC

o Jl - kH/f2

21
If the true height profile, N(h) is known and if Af is known as a function

of frequency, then (2.30) can he inverted to give BN/dt as a function of

height. If N(h) is monotonic (2.30) reduces to Abel's equation, the

solution of which is

m (fN ) _ £ 2 dfa _d_

p N

f Af df , } at Un; k n dh dfN

Jo jtN

« . p

^-^

[Whitaker and Watson, 1952]. If %(h) is known, then dN/dt(h) can be

found from dN/dt(f^). If a valley exists so that N(h) is not monotonic.

then BN/dt cannot be determined uniquely in or above the valley.

If the magnetic field is not neglected and if it is assumed that the

Doppler shift due to changes in the magnetic field itself are negligible,

then (2.29) can be solved by numerical methods to give a unique solution

for BN/dt(h) for a monotonic true height profile. A computer program has

been written which will perform this calculation if N(h) and Af (f ) are

known. The method is analogous to that used in true height reduction

from ionograms [Budden, 1955] • Unfortunately, the data available for any

particular event have not determined the frequency dependence of Af

sufficiently well to warrant application of this technique.

An interesting special case arises when BN/dt is zero below a height

hQ (below the deviative regions) and constant above hQf The Doppler

shift for this case has been calculated in Appendix III. The result,

which is exact if the effect of the earth's magnetic field is neglected,

but only approximate otherwise, is

Af = |j |f (h' - ho) , (2.32)

22
where h is the virtual height of reflection for the frequency f

According to the equivalence theorem for Doppler shifts, (2.32) should

also be approximately true for oblique propagation if f is replaced by fv .

Several of the measurements made at Boulder of the maximum Af

observed during solar flares agree with (2.32). This indicates that these

measurements can be explained by dN/dt that is zero below the E layer and

constant with height in the E and F regions. The agreement of the data

with (2.32) is illustrated in two ways.

First, (2.32) indicates that a plot of fAf versus f should look

approximately like the appropriate ionogram. The agreement is shown for

four specific events in figures 2.6, 2.7? 2.8, and 2.9? where plots of

fyAf versus fvhave been superimposed on tracings of the ionograms obtained

at the end points of the path shortly before the flares.

The scale used to plot fvAf was adjusted so that the k Mc/s value

and one E-layer value (except for 22 November 1961, where, due to lack of

E-layer data, h was chosen to be at the bottom of the E-layer) would

coincide with the Boulder ionogram. The adjustment of the scale in this

manner determines h and BN/3t in (2.32).

The data for these four events are given in table 2.1, along with

the value of dN/dt determined. For the oblique paths, the equivalent

vertical-incidence frequencies were determined by using transmission

curves [Smith, 1939; Davies, 1965] on the ionograms, and the observed

frequency deviations have been divided by the number of hops.

Second, if measurements are made on two frequencies (k and 5 Mc/s in

23
s/o (S/OW) 'iV

A * pE

CQ

fHo

<+Ha

H

tri VO

^H CJ\ wi r-\ od •* o CM H CM ^ ^H -p cu •H rH

IsM

cu > f> Hh o

'rf CO> sdo > g

<+H

-=1- £h H o O

CM

aO -P

CQ crt •H

fc

ctf Oo

CM

CD

UJ>| • u

2k
s/o (s/ow) 'JV

A

J

p— eo

n

i^

C/J

?H

C) <HS

01M

tt) OJ

<) vo

sd (A o H

•H

•V XJ h-

-P

H

•H> H

•H

!> fH «H p< <n

C/i !>

a

C) <HO

!> S ch

C\J «h L^ o OJ

0,1 3o -P W erf •H

£h

ctf woO

0J

•H

p- <* * cc h- 1-

H

OJ UJ> U) •5" _l \ V.

<T U) o o o c > - „ 5 S ?

1- 2 £ o < < > O o Ifi CC cc O o in

1-

Ozo ozo oz > > > Z < £ % %

UJ

ce

•3 * s 5 <\

CD H- H- *- H- I O H O <j

lu^ « § q

25
s/o(s/ow) 'N

A i

COuoM OJ o vo 3o

•H

XIs

ONH

ONHH

•H

CH ft

<!

ra o

enO

sdo

•H

n3oo

00ONH

oi

Q 1—3 O

cc

UJ o o

() r- t- 7 O o

CO ro

<r> en \

V. -N

_I

— o < „ . s 5 s P ? s o in < < m

UJ>

cc CC13

Q 1 i o O z > -> 1- zo Zo < 55 5

III <>

ccUJQ

cco

„_-

«»- H—

=> 3 >

_l <J < < O o UJ > > > S

CO

OJ

0)

bO •H

P-4 I © O <3

Ui>| 'U

26
s/o(s/oi/\i) 'jv

A

J

p

hUJ

inO

<HS

01U

to cm

C) vo 3 CA o H

•H^ O P O.I •H> H

•H > ^

<H ft

<!

U)

f> ido

<H<J>

t>

<+H ox

<+H LTN o C^H

£o •P

CQ crt •HUa

oo

—

1 i i i —

*\"

N\

—

\\ —

M V

\

^Sa

>o

z

crUJa

_iO

CO

UJo

z ^^ / —

UJo

UJQ

\ —

Ul u or cc

cr z UJ UJ

u.

_J -i Q o < 3o

3o

UJ ,_ |_ 1- CD CO 9 => => UJ O o I o

7 in m

± <T O" >

(- (-

—

EQUIVALENT

VERTICAL

BOULOER

lONOGRAM,

19

BELVOIR

lONOGRAM,

19 o

5

inQz

<

«r

*-

>

HoEo

1 >

<

>

(0o

E

in

1 >

<

>

ino

+

CO

4—<

>

II

^y^ —

>

1

1

1

1

o o <]

1 i _i 1

o5

ON

OJ

0)

•H

P-4

UJ)! *u

27
Table 2.1

Tabulation of data for flare effects of

November 22, 1961, and April 17, 19, and 20, 1962

f

Mc/s Path Mode

Maximum

Observed

Af

c/s

f

V

Mc/s

f Af*

V

Mc/sc/s

aw/ at

cm

-1

sec

November 22, 1961

20 WW-Boulder F 0.6 5.4 3-2 92

10 WWV-Boulder F-F 1.6 3.8 3-0

10 WWV-Shickley F 0.95 3-0 2.8

5 Vert inc Boulder F 0.7 5.0 3-5

k Vert inc Boulder F

April

0.8

17, 1962

4.0 3.2

15 WWV-Boulder E 0.0 2.6 0.0 120

F 1.0 4.3 k.3

10 WWV-Boulder E 0.0 1.8 0.0

F-F 1.9 4.7 4.5

10 WWV-Shickley E 0.0 1.9 0.0

F 1.0 3.1 3.1

5 Vert inc Boulder F 1.1 5.0 5.5

k Vert inc Boulder F 1.1 k.o k.k

April 19, 1962

15 WWV-Boulder E 2.0 2.5 5.0 2200

F 18.0 3.9 70.2

10 WWV-Boulder E 2.0 2.1 k.2

F-F 43.0 3-8 81.7

5 Vert inc Boulder F 32.0 5-0 160.0

4 Vert inc Boulder F

April

19.0

20, 1962

k.o 76.0

15 WWV-Boulder E-E 1.2 2.7 1.6 450

F 3.8 3-7 14.0

10 WWV-Boulder E-E 0.7 2.2 0.8

F-F 9.0 3-7 16.7

5 Vert inc Boulder F 6.0 5.0 30.0

4 Vert inc Boulder F 3.4 k.o 13.6

* Af corrected for number of hops

28
this case) at vertical incidence, then (2.32) predicts that

^"

l lr^At* (2 - 33)

where Af4 , Af5 , h'4 , and h'5 are the frequency deviations and virtual

heights of reflection for h and 5 Mc/s. The agreement of the data with

(2.33) is shown in figure 2.10b. In each case Hq was taken to he the

bottom of the E layer. Figure 2.10a shows Af4 versus Afs

The preceding analyses show that a dN/dt which is -zero below the

E layer and constant in the E and F regions will explain the maximum

Doppler shifts measured during several solar flares.

29
Relationship between maximum frequency deviations observed on

h and 5 Mc/s at vertical incidence, Boulder, Colorado

T

3 4 A fs, C/S

(a) OBSERVED DATA

5 —

3 —

/

~~i—I—"—I

i I

i

I

" A

y

/

x

/

/

/ *

/

/

/

/slope = 1 //

/V

*//

- *r&

J I J I L j L

3 4 Af 5 , c/s

lb) CORRECTED DATA Figure 2.10

30
3. Solar Flare Observations with the Doppler Technique

The following discussion of flare effects deals with the sudden

frequency deviations observed between October 1, i960 and December 31?

1962 on the following frequencies and propagation paths: (l) WW-10, -15

and -20 Mc/s, Beltsville, Maryland to Boulder, Colorado; (2) WW-10 Mc/s,

Beltsville, Maryland to Shickley, Nebraska; (3) ^.000 and 5.O5U Mc/s,

Sunset, Colorado to Boulder, Colorado. Table 1.1 gives the periods

during which these paths and frequencies were in use.

The analysis in this section has been restricted to those sudden

frequency deviations which could be correlated with solar flares reported

in the CRPL-F Series, Part B, Solar-Geophysical Data. A list of all

sudden frequency deviations observed between October 1, i960 and

December 31? 1962, whether they could be correlated with a known solar

flare or not, is given in Appendix IV.

The shape, duration, and magnitude of sudden frequency deviations

vary considerably from flare to flare. However, the general characteristics of an SFD, as illustrated in figure k.l, are a rapid positive

frequency deviation followed by a smaller negative frequency shift and a

gradual recovery to the pre-flare conditions. The negative frequency

deviation is sometimes absent. The maximum frequency deviation varies

from a few tenths of a cycle per second to tens of cycles per second, and

the duration may vary from less than a minute to ten minutes or more. The

specific events, to be discussed in Section U, illustrate the variability

of the sudden frequency deviations observed.

31
3.1. Percentage of Solar Flares Detected by Doppler Technique

The percentages of the reported flares which can be correlated with

sudden frequency deviations are given in table 3.1 as a function of flare

importance. In computing these percentages, and all the percentages to

follow in this section, care was taken to exclude any reported flares

which occurred during periods of unusable records for the WW to Boulder

path. Also, only flares reported during conditions of ground sunlight at

the midpoint of the WWV to Boulder path were included.

Table 3.1

Percentage of flares reported from October 1, i960, to

December 31? 19&2, which were accompanied by SFD's

Flare %

Importance

Number of

Flares Reported

Percentage

with SFD

1- 299^ 10

1 6U8 21

2 55 h9

3 10 80

1,2,3 713 2k

All 3707 13

Although no simple relationship exists between the optical (%) importance

of a flare and its associated effect on the ionosphere, it can be stated

that the greater the optical importance of a flare the greater the probability that it will cause a sudden frequency deviation.

These percentages which have been calculated as a function of flare

32
importance are naturally dependent upon the importance assigned to each

flare. Unfortunately there is often disagreement among various observatories as to the importance of a given flare. Consequently, in many cases

the flare importance used is somewhat arbitrary. In the present analysis,

whenever the importance of a flare could not be assigned by a consideration of the most frequently reported importance and/or the reported observing conditions at each observatory, preference has usually been given

to the smaller reported importance.

The percentages of the flares which were accompanied by sudden frequency deviations, for each month from October i960 through December 1962,

are shown in figure 3 -la. The number at the bottom of each column gives

the number of flares upon which the percentage is* based. The variations

in the mean solar flux at 2800 Mc/s and the mean Zurich sunspot number

for the same period are shown in figures 3»lb and 3»lc respectively. The

percentage of flares detected shows neither a systematic seasonal dependence nor any -well-defined variation with the mean level of solar activity. The lack of a systematic seasonal variation in the percentage of

the flares detected is shown more clearly by figure 3*2 in which all data

for a given month are combined.

Figure 3»3 shows the percentage of the flares accompanied by sudden

frequency deviations as a function of the time of day at the midpoint of

the WWY to Boulder path. A diurnal variation is evident in 3»3a, 3* 3c,

and 3«3d. The lack of diurnal variation in the data for flares of optical importances 2 and 3 can be attributed to the small number of such

flares during the period. Again the number at the bottom of each column

33
VARIATIONS OF THE PERCENTAGE OF REPORTED SOLAR FLARES

DETECTED, MEAN SOLAR FLUX AT 2800 Mc/s,

AND MEAN ZURICH SUNSPOT NUMBER DURING THE PERIOD

OCTOBER 1,1960 THROUGH DECEMBER 31, 1962

(a) PERCENTAGE OF REPORTED FLARES DETECTED

OU -

UJCD ~ <

UJ

20 - o —

LLUJ

Q.

10 -

—

127 214 182 175 79 146 185 141 233 274 229 191 47" 80 131 105 140 201 178 180 41 45 68 161 99 35 20 — ONDJFMAMJJASONDJFMAMJJASOND

I960 1961 1962 MONTHS

150

o 100 o

COCO^ 50

n

( b 1 MEAN SOLAR FLUX AT 2800 Mc/s —

-

— ONDJFMAMJJASONDJFMAMJJASOND

I960 1961 1962 MONTHS

(c) MEAN ZURICH SUNSPOT NUMBER

100

|cr 50 — 1— —

"C.

MINIMI F

1

ONDJFMAMJJASOND JFMAM J JASOND

I960 1961 1962 MONTHS

Figure 3-1

3^
PERCENTAGE OF REPORTED SOLAR FLARES

DETECTED BY THE DOPPLER TECHNIQUE AS A

FUNCTION OF MONTH

OCTOBER 1,1960 THROUGH DECEMBER 31,1962

(a) ALL FLARES

3U - -

LU< 20 - —

2

LUo

trLU

a.

10 — —

280 219 347 363 321 274 319 297 352 273 329 333 - JFMAMJ JASOND

MONTH

LU<

2

LUO

LT

LU

Q.

150 (b) IMPORTANCE 2 AND 3 FLARES

-

100 —

50 —

n

1 4 3 9 8 5 ii 3 5 2 10 4 -

F M A M J J A MONTH

S N D

LUO

2

LUO

cr

LU

Q.

40

30 —

20 —

10 —

(c) IMPORTANCE I FLARES

—

43 55 61 41 65 71 77

—

^-

41 37 44 63 50

-^ JFMAMJJAS0ND

MONTH

(d) IMPORTANCE I- FLARES

LU CV _——

2

III in ___ O

tr

LU

Q_ _

238 178 301 299 252 228 243 223 270 227 256 279

- JFMAMJJASOND

MONTH

Figure 3-2

3 5
LU<

LU

crLU

a.

PERCENTAGE OF REPORTED SOLAR FLARES

DETECTED BY THE DOPPLER TECHNIQUE AS A

FUNCTION OF TIME OF DAY

OCTOBER 1,1960 THROUGH DECEMBER 31 ,1962

(a) ALL FLARES

30

20 —

- I 1 182 168 256 324 280 544 327 372 322 387 319 294 165 62 2 | -

04 06 08 10 12 14 16 18 HOUR OF DAY, 90°WMT

20

lu 100 <

iuj 50

c_> <rLU

°-

(b) IMPORTANCE 2 and 3 FLARES

- - - -

- -

~ 1

1 1 1 2 4 8 II 6 7 1 6 7 3 8 Ill04 06 08 10 12 14 16 18 20 HOUR OF DAY, 90° WMT

CD<

LUo

crLU

a.

50

40 —

(c) IMPORTANCE I FLARES

42

—

1

1 121 53 84 84 65 57 53 37 41 37 22 30 12 1 "

30

20 —

04 06 08 10 12 14 16 18 HOUR OF DAY, 90° WMT

20

LUO

<

LUu

cr

20

10 —

(d) IMPORTANCE I- FLARES

- | 60 113 168 232 204 281 267 334 274 339 279 264 135 50 2

I -

04 06 08 10 12 14 16 U 20 HOUR OF DAY, 90° WMT

Figure 3.3

36
gives the number of flares on which the percentage is based.

The solar- zenith-angle dependence of the percentage of flares

detected is shown explicitly in figure 3-^- In this figure the percentage

of flares detected is shown as a function of the solar zenith angle at the

midpoint of the WWV to Boulder path. In figures 3«^a and 3-^cl there is a

peak for zenith angles of 30 to kO degrees. The decrease in the percentage detected as the zenith angle increases is to be expected; however,

the decrease for zenith angles less than 30 degrees is surprising and maybe due to sampling errors.

In summary, the data presented in this section indicate that the

percentage of solar flares which are accompanied by sudden frequency

deviations tends to increase with increasing optical importance, shows

no pronounced seasonal variation, but does exhibit a marked diurnal and

solar zenith angle variation with a maximum near local noon. A final

conclusion regarding the apparent lack of correlation between the percentage of flares detected and the general level of solar activity will

require observation over a greater portion of the solar activity cycle.

3.2. Duration, Rise Time, and Delay Time of Sudden Frequency Deviations

The general time characteristics of sudden frequency deviations are

presented in this section. The number of sudden frequency deviations

with a given duration is shown in figure 3-5- The duration has been

taken to be the time elapsed between the beginning of the positive frequency deviation and the return to the preflare conditions. Often the

duration defined in this way cannot be measured precisely due to the

37
PERCENTAGE OF REPORTED SOLAR FLARES DETECTED

BY THE DOPPLER TECHNIQUE AS A FUNCTION

OF SOLAR ZENITH ANGLE AT MIDPOINT OF

WWV TO BOULDER PATH,

OCTOBER 1,1960 THROUGH DECEMBER 31,1962

UJ<

40

30

a 20

crUJ

°-

10

(a) ALL FLARES

I | 6 |l08|ll8|l54|l93|2ll|233|227|3l0|4l0|53l|33l|276|27l|2ll|-|l0-|l4

10 20 30 40 50 60 70 80 90 100 SOLAR ZENITH ANGLE, DEGREES

UJ

ID<

LUO

CE

LU

Q_

100

50

(b) IMPORTANCE 2 and 3 FLARES

_ 1 ___ _

~ 1 4 2 5 3 5 3 6 7 6 7 5 6 3 | 3 |

1 2

-

10 20 30 40 50 60 70 80 90 100 SOLAR ZENITH ANGLE, DEGREES

(c) IMPORTANCE I FLARES

10 20 30 40 50 60 70 80 90 100 SOLAR ZENITH ANGLE, DEGREES

UJCD<

UJO

or

UJ

Q_

(d) IMPORTANCE I- FLARES

187 195 258 348 433 268 217 202[T5T|-85i 8 |

10 20 30 40 50 60 70 80 90 100 SOLAR ZENITH ANGLE, DEGREES

Figure ^.h

38
DURATIONS OF SUDDEN FREQUENCY DEVIATIONS

OBSERVED FROM

OCTOBER 1,1960 TO DECEMBER 31,1962

DURATION = tend " t beg

(a) IMPORTANCE 2 and 3 FLARES

cr

00

~

i i i~ n —i

i i i~n -

30

2 4 6 8 10 12 14 DURATION, MINUTES

(b) IMPORTANCE I FLARES

25 20 m

n ~l~T-nr-T1-

2 4 6 8 10 12 14 DURATION, MINUTES

or

UJCD

80

70 h60

50

40 h

30

20

10

(c) IMPORTANCE I- FLARES

2 4 6 8 10 12 DURATION, MINUTES

Figure 3*5

39

14
difficulty in determining the exact time at "which, the flare-related frequency deviation ends; however, figure 3-5 does serve to give a general

idea of the durations of the flare effects observed by the Doppler

technique. The observed durations range from one minute to more than

fifteen minutes with the most common durations being from two to five

minutes.

Figure 3-6 shows that the most common "rise time", the time from the

beginning of the sudden frequency deviation to the maximum positive deviation, is one or two minutes. Very few sudden frequency deviations have

rise times greater than three minutes.

The time relationship between the maximum positive frequency deviations of sudden frequency deviations and the maximum phase of the corresponding solar flares is shown in figure 3*7. The maxima of most sudden

frequency deviations occur one to four minutes before the flare maxima.

In very few cases does the maximum frequency deviation occur after the

maximum of the solar flare.

3-3- Path Length Dependence of Frequency Deviations

Figure 3-8 shows the solar flare induced frequency deviations of

WWV-10 Mc/s received at Shickley, Nebraska (1780 km), plotted against

those of WW-10 Mc/s received at Boulder, Colorado (2^00 km). The slope

of the broken line is given by the ratio of the ground path lengths.

This figure indicates that the frequency deviations for a fixed frequency

vary directly with the path length for paths in the neighborhood of 2000

km. Kanellakos, Chan, and Villard [1962] have found that the flare induced frequency deviations on 15 and 18 Mc/s vary approximately directly

kO
RISE TIMES OF SUDDEN FREQUENCY DEVIATIONS

OBSERVED FROM OCTOBER i, I960

TO DECEMBER 31, 1962

RISE TIME = t max -t beg

(a) IMPORTANCE 2 AND 3 FLARES

20

a:uj

CO

a:UJm

—

1 f_-_—1 .1111 1 1 1 1 1

80

60

40 —

20

<l I 2 3 4 5 6 7 8 9 10 II 12 RISE TIME , MINUTES

(b) IMPORTANCE I FLARES

<l I 2 3 4 5 6 7 8 9 10 II 12 RISE TIME, MINUTES

m

5

3

180

160

(c IMPORTANCE 1- FLARES

— —

140 —

120 — —

100 —

80 —

60 —

40 —

20

n —I—. _, 1 1 1

1 <l I 2 3 4 5 6 7 8 9 10 II 12 RISE TIME , MINUTES

Figure 3.6

hi
TIME DIFFERENCE, ATmQx , BETWEEN MAXIMUM POSITIVE

FREQUENCY DEVIATION AND MAXIMUM PHASE OF SOLAR FLARE

OCTOBER I, I960 THROUGH DECEMBER 31, 1962

ATmax = t max (SFD) -tmax (FLARE)

(a) IMPORTANCE 2 and 3 FLARES

UJm

i i zzi cz i i i i i i n i i_

-8 -6 -4-2 2 ATmax , MINUTES

30 (b) IMPORTANCE I FLARES

10

trUJm

-12 -6-4-2 2 4 ATmax , MINUTES

(c) IMPORTANCE I- FLARES

crUJ

QD

-12 -10 -8 -6 2

rnox , MINUTES

4

AT

Figure 3.7

42
FREQUENCY DEVIATION OF WWV - 10 Mc/S OBSERVED AT

SHICKLEY, NEBRASKA (1780 km) VERSUS THAT OBSERVED AT

BOULDER, COLORADO (2400 km)

Af

|Q (SHICKLEY),C/S

Figure 3*8

^3
with path length for paths of 2^+50 and 565 km. Therefore, it appears

that for oblique paths, the effect of solar flares on the frequency of

ionospherically propagated signals varies directly with the ground path

length. It is to be expected that this direct path length dependence will

hold only for paths which are of such length that the ratio of the ground

path lengths is approximately the same as the ratio of the path lengths

in the ionosphere.

3.4. Frequency Dependence of Frequency Deviations

Figure 3«9 shows the maximum positive frequency deviation observed

on WWV-20 Mc/s versus that observed on WWV-10 Mc/s, both frequencies

being received at Boulder (2^00 km); similarly, figure 3«10 shows the

relationship between the deviations observed on WWV-15 and WW-10 Mc/s.

In each case the dashed line indicates the behavior expected if the frequency deviation were inversely proportional to the operating frequency.

The deviations observed on these oblique paths tend to vary inversely

with the operating frequency, although there are some significant departures from an inverse dependence. These two figures show only the

observed data. Due to the difficulty in determining the propagation

modes for this long path, the data have not been analyzed in terms of

equivalent vertical -incidence frequency.

The relationship between the maximum positive frequency deviations

observed on k and 5 Mc/s at near vertical incidence at Boulder has been

shown in figure 2.10. A plot of the observed data, figure 2.10a, shows

no systematic frequency dependence. However, as shown by figure 2.10b,

the frequency deviations agree well with the behavior predicted by (2.33)

kh
FREQUENCY DEVIATION OF WWV - 10 MC/S

VERSUS THAT OF WWV -20 MC/S,

BOTH OBSERVED AT BOULDER, COLORADO (2400 km)

\

o

cr

LdQ

_Jo

00

Af

2Q(BOULDER),C/S

Figure 3-9
FREQUENCY DEVIATION OF WWV - 10 MC/S

VERSUS THAT OF WWV- 15 MC/S,

BOTH OBSERVED AT BOULDER, COLORADO (2400 km)

to \

o

ir

LUQ

_lO

GO

Af|5 (BOULDER),C/S

Figure 3. 10

46
k. Selected Events Detected by the Doppler Technique

In this section are included examples of the events detected by the

Doppler technique. The types of frequency deviation illustrated include

those associated with solar flares, with geomagnetic sudden commencements,

and with certain other geomagnetic variations.

k.l. Solar Flares

Frequency deviations accompanying solar flares (SFD's) can be observed

only in the sunlit hemisphere. They show great variation in magnitude,

shape, and duration, but always begin with an increase in the received

frequency. The initial positive phase may or may not be followed by a

negative deviation. A typical sudden frequency deviation is of much

shorter duration than the optical flare and tends to occur between the

beginning and maximum phase of the Ha? flare. Those flares which produce

significant increases in the electron density in the lower regions of the

ionosphere cause increased absorption of the HF signals used in the

Doppler technique; however, no change in absorption has been detected

during most of the sudden frequency deviations observed. A detailed

study must be made on the relationships between SFD's and other flare

associated effects.

A "classical" sudden frequency deviation is shown in figure k.l.

This effect was observed during a flare, of optical importance 1, on

k September 196I. The times of the optical flare were reported as

1^2^-1^35-1512 UT (beginning-maximum-end). The sudden frequency deviation

is very simple in this case: a rapid rise to a sharp peak, a negative

hi
aou | oS 1 H U

<H *d 3 H H ! 2 <\l

CDO i?)

ri 7 tf -P 1 ID +3 c3

in CO O *d * ftS > 1 •H -H lO

tiO o CO a cu *-

•H ^ ~* H2 m ^_J" >d\o UJ

t> o z

1m

H < 1 hCQ !> or o !is o

°- i d n 2 ' O H -4

•H VD

-P ON ^, cd H UJ

•H Jor<

<d _i

Sh u_

>>° <3 <T<

i-*3 _l a1 ft M to O

<hddd3

CO

Oa<

cco_joc_>

(0 „ (D crUJ

H «. Q • <r _l -4" O

CD ^ O bD

UJ

H •H

h- 1^

CL CO LJ \

en oo

1^8
deviation, and a recovery to the pre-flare conditions. The entire effect

takes place between the beginning and maximum phase of the optical flare.

The maximum positive deviation is considerably larger than the negative

deviation. Such "classical" sudden frequency deviations are rarely

observed.

An unusually complex sudden frequency deviation is shown in figure

k.2. This effect was observed during a flare on 12 November i960 (131^-

1330-1^25D, importance 3+) which was accompanied by a ,sea-level cosmic

ray increase. The time variations of this frequency deviation indicate

that the x-ray flux causing the ionospheric changes must have undergone

rapid and complex variations with time. The duration of this event is

greater than is usually observed; nevertheless, the major frequency

variations are over before the optical flare reaches its maximum phase.

This event has been discussed by Knecht and Davies [1961a, 1961b]; Munro

[1961]; Davies, Watts, and Zacharisen [1962]; and Davies [1963].

Figure k.3 shows a sudden frequency deviation observed on WW-10 Mc/s

and WWV-20 Mc/s received at Boulder on 28 September 1961 (optical flare

2202-222^-2530 UT, importance 3). This event illustrates a feature often

observed on oblique-incidence Doppler records; namely, a splitting of the

traces due to E- and F-layer propagation. These traces are labeled in

figure U.3a; the F-layer trace shows a large deviation while the E-layer

trace shows only a small shift. Moreover, the E-layer trace lacks the

oscillations of the F-layer trace. The small frequency shift suffered

by the E-layer propagation mode during this event indicates that the

major portion of the changes detected by this technique occurred above

the height of reflection in the E layer. This event has been discussed

1+9
ido

cduaH

<4H

u

Q + CD CO r^J i 1 in

CD 3 sr O O

•~~* £ PP t

_p _p o

ro o ro ad •" e cd i •H > LO

•H

M 0) a o 5

•H CD ^ +"

t5

w ro

cd S M o z

CD OJ < ra i 1-

tro

rt 0_ o •» •H O IE

-p VO

03 G\ „ •H H UJ

!>

(D *

cr

<t5 OJ < H _i

>> ti- O U

Pi cd tr<

a< cd _l

cu > o

if)

a

CD <d<d3

03 o

IDen

crUJ

OD

UJ>o oQ<

cro_ioo

cr" UJO

—I

IDo

CDo>5

CM

CD^13)

•Hp4

S/DIJV

50
Sudden frequency deviation observed during importance 3 flare on September 28, 1961, WW-10 and WWV-20 Mc/s received at Boulder

(n n

CL_J_ O

®»M:iiiMwiiiftiffi0*wlM

I | I I I 22I5

10 MC

(a)

2205 UT 22I0 2220

I I I 2225

o

E

w**»»ryy)wiiiiiiii^^HiWll

i lil»> Wt M$ VflL^/Hiii^^iilliW^^W^Ii^iiiiMilillllillllHIJW^^WjLli)^^

T.,^rT

_irn- T

. r

|

n T~

[ - p^

|

| | |

22I0 22I5 2220

20 MC

(b)

SEPTEMBER 28, I96I

WWV

Figure ^.3

2205 UT

I

' ' 2225

51
by Davies [1962b] and by Kanellakos and Villard [1962].

The largest sudden frequency deviation yet observed at Boulder is

shown in figures k.k and 4.5- This effect accompanied a flare of optical

importance 2 (1935-1937-2031) on 19 April 1962 . The maximum frequency

deviation on WW-10 Mc/s received at Boulder (figure 4.4a) exceeded 40

cycles per second. The positive phase of the effect lasted less than a

minute; the overall duration of the event was about 3 minutes. Since the

Doppler technique detects the rate of change of electron density, the

great magnitude of this event indicates only that this flare caused an

extremely rapid change in electron density; the change in the total

electron content of the ionosphere need not have been very great . The

rate of change of electron density caused by this flare has been investigated in section 2.3 of this report.

The size of the deviation observed on WWV-10 Mc/s (figure 4.4a)

relative to that on WWV-15 Mc/s (figure 4.4b) is partly due to WW-10 Mc/s

being two-hop propagation to Boulder while one-hop propagation was

possible on WWV-15 Mc/s. The equivalent vertical- incidence frequencies

for F- layer propagation of WWV-10 and -15 Mc/s to Boulder were approximately the same, and, as shown in section 2.1, the frequency deviation

per hop depends upon the equivalent vertical- incidence frequency. The

deviations observed at near vertical incidence at Boulder on 4 and 5 Mc/s

are shown in figure 4.5- The great difference in the magnitudes of the

effects observed on 4 and 5 Mc/s is explained by the fact that 5 Mc/s was

very close to the critical frequency of the Fl layer as shown in

figure 2.8.

52
Sudden frequency deviation observed during importance 2 flare

on April 19, 1962, WW-10 and WW-15 Mc/s received at Boulder

SOLAR FLARE, IMPORTANCE 2, 1935-1937-2031 UT

1934 UT 1936 1937 WWV 10 MC/S

(a)

1940

to \o

1934 UT 1936 1937 1938 WWV 15 Mc/s

(b)

1939 1940

APRIL 19,1962

BOULDER, COLORADO

Figure k.h

53
Sudden frequency deviation observed during importance 2 flare on April 19, 1962. k and 5 Mc/s vertical incidence at Boulder

SOLAR FLARE, IMPORTANCE 2, 1935-1937-2031 UT

o

1934 UT 1936 1937 4.000 Mc/s

(a)

1938 *******

1939 1940

v.—

- - mMij y ntmjfr

1936 1937 1938 5.054 Mc/S

(b)

VERTICAL INCIDENCE

APRIL 19,1962

BOULDER, COLORADO

Figure 4.5

m

1939 1940
Like the event of 28 September 1961 (figure 4.3)? the obliqueincidence records of the 19 April 1962 flare (figure k.k) show both Eand F-layer traces, the E-layer trace being only slightly deviated. The

existence of separate traces for different propagation modes is very

helpful in analyzing these events.

k.2. Geomagnetic Variations

The frequency variations observed during geomagnetic sudden

commencements are often very similar to solar flare effects. However,

with a little experience, it is usually not difficult to separate the

two phenomena. Like solar flare effects, sudden commencement effects

show great variation from one event to another. Unlike flare effects,

sudden commencement effects can be observed during the night as well as

the day.

A lack of data has delayed a statistical study of sudden commencement effects. However, a preliminary investigation indicates that about

k-7 percent of the sudden commencements reported in the Journal of Geophysical Research (J. Virginia Lincoln, "Geomagnetic and Solar Data")

have been accompanied by frequency deviations.

Sudden commencement effects detected by the Doppler technique have

been previously discussed by Davies [1962b]; Kanellakos and Villard [1962]

and Chan, Kanellakos, and Villard [1962].

Two examples of frequency deviations related to sudden commencements

are shown in figures k.6 and k.7- The event of 30 September 1961

(figure k.6) is characterized by an initial small negative deviation, a

55
Sudden commencement observed by the Doppler technique at 2108 UT on September 30, 1961. WW-10 and WWV-20 Mc/s received at Boulder

I

J

I I I I 2105 UT 2110 2115

10 MC

(a)

1 1

1 I 1 1 1 1 I 2120 2125

20 MC

(b)

SEPTEMBER 30, 1961

WWV

Figure 4.6

56
Sudden commencement observed by the Doppler technique at 0219 UT on February 22, 1962. WW-10 Mc/s received at Shickley, Nebraska,

and WWV- 10 and WWV- 15 Mc/s received at Boulder, Colorado

GEOMAGNETIC SUDDEN COMMENCEMENT - 0220 UT

—

*

1

<

Ic/s *Mf«^ •*

1 II 1 11

1 II 1 11 1 II |

1 1 1 1

|

1 1 1 1

|

1 1 1 1 |! 1 1 1

|

1 i i

0210 UT 0220 0230 0240 (a) WWV - 10 Mc/S TO SHICKLEY, NEBRASKA

0250

II II |

I

I

I

I |

I

I I I

|

I I I

I |

I I I I [

I

I I

' I

0210 UT 0220 0230 0240

(b) WWV - 10 Mc/S TO BOULDER, COLORADO

0250

Ic/s

f

&«Lj«fe.t:-{ : jg~.Jp. ^SStJE* <I£is£ w b^-#^ jSe»: " $*- 1

1 ^ByMP

Be* *

*W3f

-

I i ii

I

i i i i

I

i

i i i 1 1

1 0210 UT 0220 0230 0240 (C) WWV -15 Mc/S TO BOULDER, COLORADO

FEBRUARY 22, 1962

Figure h-.J

57

0250
sharp positive spike, and a fifteen minute period of small amplitude oscillations. The sudden commencement at 0220 UT on 22 February 1962

(figure ^.7) was accompanied "by a positive deviation of one minute duration

followed by a negative frequency shift which lasted about seven minutes.

Both of these effects are easily distinguishable from the flare effects

shown in figures k.l through k.5: the first by the initial negative shift

and the oscillations' following the peak and the second by the nature and

magnitude of the negative phase relative to the positive phase.

Figure ^.8a shows the Doppler records of WWV-15 and 5 .05^ Mc/s

received at Boulder for a period of about one hour on 26 February 1962

during which three sudden impulses were reported (1533? 1552, and l6ll UT).

A tracing of the corresponding portion of the Boulder magnetogram is shown

in figure k.8b. The correlation between the frequency deviations and the

variations of the magnetic declination (D trace) is good. The simultaneous

frequency variations observed on 5 Mc/s (near vertical incidence) and

WV-15 Mc/s indicate that the disturbances causing these variations

occurred simultaneously over a relatively large area. The frequency variations occurring at the times of the reported sudden impulses are very

similar to one another.

A brief survey has indicated that approximately 25 percent of the

sudden impulses in the geomagnetic field reported in the Journal of

Geophysical Research (J. Virginia Lincoln, "Geomagnetic and Solar Data")

have been detected by the Doppler technique.

58
Correlation between frequency variations observed at both oblique and

vertical incidence and changes in the magnetic field observed at Boulder

SUDOEN IMPULSES- 1533, 1552, 1611 UT

(d) WWV - 15 Mc/S TO BOULDER, COLORADO

5.054 MC/S, VERTICAL INCIDENCE, BOULDER, COLORADO

i i i i

|

i i i i |i i i

i

| i i i i |

i i i—i

|

i i i i |i i i i

|

i ii i |—

n—i i

|

i i

i

it~t

530 UT 1540 1550 1600 1610 1620

(b) BOULDER MAGNETOGRAM

FEBRUARY 26, 1962

Figure ^.8

59
5. Discussion

This report has presented some results of ionospheric research done

at CRPL with the Doppler technique developed "by Watts and Davies [i960].

This technique has proven to he a sensitive method of detecting the effects of solar flares in the E and F regions of the ionosphere, and the

major portion of this report has been devoted to these flare effects

(sudden frequency deviations).

Theoretically, it has been shown that the Doppler shift, observed on

a given frequency propagated over a given path, depends only on the

equivalent vertical-incidence frequency. An equivalence theorem has

been derived which relates the frequency deviation observed on an oblique

path to that which would have been observed with vertical propagation at

the equivalent vertical-incidence frequency (neglecting the earth's magnetic field, electronic collisions, and curvature of the ionosphere).

This equivalence relation will be useful in comparing Doppler data obtained

from different paths or from different parts of the world, and it will provide a convenient means of data interchange.

Two theoretical approaches have been undertaken in an attempt to

better understand the Doppler observations. The first approach consists

of the calculation of the frequency dependence of the Doppler shifts to be

expected from changes in the parameters defining various parabolic layer

models of the ionosphere.

The second theoretical treatment has suggested a method for determining the height variation of the time rate of change of electron density during an ionospheric disturbance from a knowledge of the Doppler

60
shift as a function of frequency. The frequency dependence of Af during

a specific disturbance has not yet been sufficiently well determined to

warrant applying this method. However, it has been shown that the frequency deviations observed during several solar flares could have been

produced by a BN/at which was zero below the E region and constant in

the E and F regions.

Statistically it has been found that 13 percent of all the optical

flares and subflares reported from October i960 through December 1962

caused sudden frequency deviations. The percentage of flares detected increases with the optical importance of the flare, shows no pronounced

seasonal variation, but does exhibit a diurnal variation with a peak near

local noon.

Most sudden frequency deviations have durations of from 2 to h minutes; this is much shorter than the duration of the typical optical flare.

The sudden frequency deviation almost always occurs between the beginning

and maximum phase of the optical flare, with the maximum frequency deviation usually occurring 1 to 2 minutes before the maximum phase of the Ha

flare

For long paths, the observed frequency deviations tend to vary directly with the ground path length and inversely with operating frequency.

For vertical propagation the observed frequency deviations show no systematic frequency dependence; however, it has been shown that the vertical

incidence data are consistent with the theory which assumes that the time

rate of change of ionization during the flare is independent of height.

61
The CRPL is presently making Doppler measurements over both obliqueand vertical-incidence paths in the United States and oblique paths near

the magnetic equator in Africa. In addition, the Battelle Institute of

Frankfurt, Germany, supplies oblique -incidence records of MSF (Rugby,

England) received at Frankfurt, and workers in England, Hawaii, India,

and Japan have shown interest in using the technique. For the immediate

future these paths will provide broader coverage for a continuing flare

patrol and will be used to study the solar zenith angle and latitude

dependences of the ionospheric effects of solar flares.

However, a more sophisticated network of paths is highly desirable

if the technique is to be used to best advantage. Although, in principle,

the equivalence theorem can be used to assist in the comparison of data

obtained from different paths, in practice it becomes difficult to determine the propagation modes for long paths and, hence, it is difficult to

apply the equivalence theorem to such paths. On the other hand, vertical

propagation emphasizes the local ionospheric variations. Hence it seems

that relatively short paths should be the best for study of widespread

ionospheric disturbances, such as those caused by solar flares. A worldwide network of such paths is needed in order to conduct a definitive

study of the solar zenith angle and latitude dependence of solar flare

effects. Such a network would also provide a worldwide monitoring system

for flare and geomagnetic disturbance effects. In order to adequately

study the height variation of ionospheric disturbances, it will be necessary to use several frequencies over a single path.

62
So far major attention has been given to the maximum positive frequency deviations induced by solar flares. Some attention should be given

to the other characteristics of flare effects (negative phases and recovery rates) to determine whether these can be of assistance in studying the

ionospheric response to solar flare radiation. In addition, the effects

accompanying geomagnetic disturbances need to be investigated and the mechanism causing them discovered.

Further study should also be made of the relationship between the

different ionospheric effects (SWF, SEA, SPA, SFD, etc.) and the various

solar phenomena, such as the different types of radio emissions, which

accompany visible flares. Such a study would be of assistance in determining the time characteristics and enhancements of the various radiation

bands causing the ionospheric disturbances. Another objective of such a

study should be to investigate the possibility of predicting the occurrence of solar disturbances which will significantly affect the earth's

environment

.

The Doppler technique should be capable of detecting any type of

rapid ionospheric variation which occurs at heights no greater than the

reflection levels for the frequencies used. It should be useful for

studying ionospheric effects associated with geomagnetic disturbances as

well as those associated with solar flares. In addition, the technique

should aid in the study of ionospheric oscillations and the motions of

ionospheric irregularities. To be used to best advantage, the Doppler

measurements should be made in conjunction with other ionospheric observations (e.g., ionograms, field strength records).

63
6. Acknowledgments

Partial support for the final stages of preparation of this report

was received from the Advanced Research Projects Agency, Nuclear Test

Detection Office under Contract No. 183.

64
7. References

Budden, K. G. (l955)> A method for determining the variation of electron

density with height from curves of equivalent height against frequency , Proceedings of the Cambridge Conference on Physics of the

Ionosphere , Physical Society, 332.

Chan, K. L., D. P. Kanellakos, and 0. G. Villard, Jr. (1962), Correlation of short-period fluctuations of the earth's magnetic field and

instantaneous frequency measurements, J. Geophys. Res. 67 , No. 5 5

2066-2072.

Chan, K. L. and 0. G. Villard, Jr. (1963), Sudden frequency deviations

induced by solar flares, J. Geophys. Res. 68 , No. 10, 3197-322U.

Davies, K. (1962a), Doppler studies of the ionosphere with vertical incidence, Proc. IRE 50 , No. 1, 9^-95.

Davies, K. (1962b), Ionospheric effects associated with the solar flare

of September 28, 1961, Nature 193 , No. kS±7 , 763-76U.

Davies, K. (1962c), The measurement of ionospheric drifts by means of

the Doppler technique, J. Geophys. Res. 67 , No. 12, if 909-^913.

Davies, K. (l962d), Correction to "Doppler studies of the ionosphere with

vertical incidence," Proc. IRE ;?0 , No. 6, l^kk.

Davies, K. (1963), Doppler studies of the ionospheric effects of solar

flares, Proceedings of the International Conference on the Ionosphere, London, 1962 , Institute of Physics and Physical Society.

Davies, K. (1965), Ionospheric Radio Propagation, NBS Monograph 80,

Chapter k, Section U.3.1.

65
Davies, K. , J. M. Watts, and D. H. Zacharisen (1962), A study in F2 layer

effects as observed "with a Doppler technique, J. Geophys. Res. 67 ?

No. 2, 6OI-609.

Kanellakos, D. P., K. L. Chan, and 0. G. Villard, Jr. (1962), On the

altitude at which some solar flare induced ionization is released,

J. Geophys. Res. 67 , No. 5, 1795-180U.

Kanellakos, D. P., and 0. G. Villard, Jr. (1962), Ionospheric disturbances

associated with the solar flare of September 28, 1961, J. Geophys .

Res. 67 , No. 6, 2265-2277.

Knecht, R. W. , and K. Davies (1961a), Solar flare effects in the F region

of the ionosphere, Nature 190 , No. ^778, 797-798.

Knecht, R. W., and K. Davies (1961b), Nature 192 , No. U800, 3I48.

Munro, G. H. (1961), Possible solar flare effects in the F region of the

ionosphere, Nature 192 , No. U800, 3^7.

Smith, N. (1939)? The relation of radio sky-wave transmission to ionosphere measurements, Proc. IRE 27 , 332-3^+6.

Watts, J. M. , and K. Davies (i960), Rapid frequency analysis of fading

radio signals, J. Geophys. Res. 65 , No. 8, 2295-2301.

Whittaker, F. C, and T. N. Watson (1952), A Course of Modern Analysis ,

Uth ed., Cambridge University Press, p. 229.

66
8. Appendix I - The Doppler Shift Written as an Integral

To show:

The Doppler shift is given by

Af = - t r & ds (8.1)

path

for propagation at any angle and by

Af = -2 ? f If dz (8.2)

c J ot

o

for vertical propagation.

Restrictions

(1) The ionosphere is assumed concentric.

(2) The effect of the earth's magnetic field is neglected except

for vertical propagation.

Proof:

The Doppler shift is given by [Davies, 1962a]

Af = -ff- (8.3)

In order to calculate the Doppler shift, the time derivative of the

phase path must be found. Assuming the ionosphere is horizontally uniform, the time derivative of the phase path is given by:

67
path

Substituting ds = dz/cos0 in (d.k),

§-h i

* • »•«

z dP _ lim d_ r> p,dz /„ v dt z - h dt -J cos0

' K J1 o

Performing the indicated differentiation of the integral in (8.5);

_B0

o cos

a

jt> n

• z -> j n• r z l^sin0 ~ -, -, *p

^ r|jz + 11m r 2

, at

dz + 2 u 1 dzi

(8 6) dt z -» h J dt cos0 z -» hL J ro<q 2

(/> cos0 'z dtJ

Using ds = dz/cos0 to take the limit of the left term and using Snell's

law for curved earth (a + z) \i sin = a |j, sin O

^dz dP p Su, , , lim _ . , Tp a St.

~7T = \ ^r ds + . 2 po sin0o —— s—

dt

p

^

h

ot z -> h ^N a + z C os

2

. . . _ fi dz]

(a + z) sin0 cos0 | z dt_j

(8.7)

The term in brackets can be calculated using the criterion that the distance between the transmitter and receiver is constant. Neglecting the

effect of the earth's magnetic field,

g = =

lin

l |r 2af

-^ dz • (8.8) dt z-»hdt J a + z o

Performing the differentiation indicated in (8.8),

68
= lim

z -* h

z

_. p sec~g dip , . _ 2aJ rrr- at

dz + 2a tan0 1 dz" a + z ' z dt_ (8.9)

Subtracting po sin0o times (8.9) from (8.7)

dP _ p ap , , lim 2app sin0o dt J , at z -* h a + z pathsin0

COS0

dz , 1 dz" z dt sin0 cos0 I.5T ' z dt.

-(8.10)

The expression in brackets can be manipulated to give

^ = r ^

ds + dt J atas path

lim

z -* h

2auo sin0n I" cos0 1 dz"1

, /g ^x

a + z Lsin0 'z dtj *

Again using Snell's law,

dP f» a^j, n . lim

dt

= -' J ^. dt

ds +

z -» h

path

2 p cos0 I M"

' z dt. (8.12)

The quantity in the brackets is zero when evaluated at the limit, since

cos0 is zero at reflection for oblique propagation, and p is zero at reflection for vertical propagation. Therefore, from (8.12)

1= J It- path

(8.13)

Substituting (8.13) into (8.3)

ajj. Af = - - f =f els path

(8. Hi)

It is necessary to neglect the earth's magnetic field because the

69
proof assumes that the ray direction and the "wave normal direction are

the same, "which is generally not the case when the effects of the magnetic field are included. The step from (8.6) to (8.7) assumes that the

angle gives the wave normal direction, while (8.8) assumes that the angle gives the ray direction.

If the propagation is vertical, this restriction is not necessary,

since equation (8.8) is not necessary for the proof. Combining (8.3) and

(8.5), the Doppler shift for vertical propagation is given by

Af =-2f f^J^dz . (8.15)

o

Performing the differentiation indicated in (8.15),

Af = -2 §j|£az - 2 f,|h § . (8.16)

The term -2 — u I. — is zero, since the index of refraction is zero at

c r 'h dt

reflection for vertical propagation. Therefore, from (8.l6)

fif=-2^f|dz . (8.17)

c «J ot

o

Since the derivation of (8.I7) from (8.1^) does not depend on the coincidence of the wave normal and ray direction (8.17) is correct including

the effect of the earth's magnetic field.

The integral form for the Doppler shift as given in (8.lU)(for propagation at any angle of incidence neglecting the effect of the earth's

TO
magnetic field) or as given in (8.17) (for vertical propagation including

the effect of the earth's magnetic field) is convenient since it can be

used in a computer ray tracing program to calculate the Doppler shift by

performing a sum approximating the integral along the path as the ray is

traced.

71
9. Appendix II - Equivalence Theorem for Doppler Shifts

To show: Af(f, O ) = Af(f cos0o , 0),

where the first argument is the wave frequency and the second argument is the angle of incidence of the wave on the ionosphere

Restrictions

(1) The curvature of the ionosphere is neglected.

(2) The effect of the earth's magnetic field is neglected.

(3) The effect of collisions is neglected.

Proof:

The Doppler shift is given "by (8.l) of Appendix I.

path

The refractive index is given by

3 _ - kN

1 - jr . (9.2)

\ Differentiating (9.2) with respect to t and dividing by 2|i,

St " 2^" Bt * K ^' 5)

72
Combining (9.1) and (9-3),

Af =

oN . k p dt

2cf J n

(9.J+)

Substituting ds = dz/cos0 in (9.^-)?

<* = ^

J

^rr dz

2cf J p,cos0 (9.5)

Operating on (9-5) with straightforward algebra, using a trigonometric

substitution, and applying Snell's law, p. sin0 = sin0o ,

Af = Af(f, 0o ) = 2cf COS0Q I

dt

dz

kN

(9-6)

f

2 COS2

0o

Substituting into the function defined by (9.6), it can be seen that

Af(f, 0o ) = Af(fcos0o , 0) . (9.7)

An interpretation of (9.7) is that Af depends only on the equivalent vertical-incidence frequency, fcos0o

.

73
10. Appendix III - Relationship Between Doppler Shift and Virtual Height

To show:

fAf = |ff (h' -ho) (10.1)

if SN/dt is zero from the ground up to ho and constant above ho

Restrictions

(1) Only vertical propagation is considered.

(2) Collisions are neglected.

(3) Effect of the earth's magnetic field is neglected.

Proof:

The Doppler shift for vertical propagation is given by (8.2) of

Appendix I.

Af = .2 ^ r|^dZ (10.2)

c j at

o

If the Doppler shift is entirely due to changes in electron density in

the ionosphere, then from (10.2),

h

J

The index of refraction is given by

.2

^ -

"2 f I t f

* <">-3)

kN

M-" = 1 " Ji" (10.10

Differentiating (lO.U) with respect to N and dividing by 2^,

7V
dp. _ k

dN " 2\x^

(10.5)

Since |ji = l/p, ,

by. _

__k_ / (10.6)

Substituting (10.6) into (IO.3),

h

Af =

fc~ J ^ at

dz (10.7)

For the special case in which dN/dt is zero from the ground up to a height

ho , and constant above ho

,

h

Af = fc-otJ *dz (10.8)

ho

/ . Since ij, is one below h for the special case that the region is nondeviative,

, -v^TT-h h

(10.9)

Performing the indicated integrations in (IO.9)

«

I? &»' - h ) (10.10)

Multiplying (10.10) by f.

75
fAf =||| (h' -1^) (10.11)

which was to be proved.

A physical interpretation of (lO.ll) is that the product of the frequency and the Doppler shift for vertical propagation is proportional to

the virtual height minus some constant height at all frequencies. Therefore, if BN/dt is independent of height in the ionosphere, a plot of fAf

versus f should look like the ionogram. This relation is approximately

valid even if the magnetic field is included as shown by figure 10.1 for

conditions at Boulder (dip =70°, fg = l.lj-7 Mc/s).

76
(S/3-S/01N) iSJi <o

en

cr

LlI >

UJ

oro

LUXo<o 1 1 ' ' 1 1 — — + <

^sr+*

— \ +

))

cc E

($. o J3C u. o o o

A| ^HT3 JZ

•>s Z cc z o o x \ o ~-* u. H 1- < I 1 >- a P o

>3 < a> CC

>-<

a.o

a.

UJXI

1-3

n>1 Eu >

or<z < o

>-

u OD or ccz

Ct

iccUJ> Z O o

UJX +

a.o

UJX

a.o

u. Zooa z

1—

<ro

u.

CVJ (0

01 +4-

1-

Q UJ cc

UJ

1-3

Q-5O 2 E 5<

_l

— o

li_ < oo

cce>oz 5

a.< 1-

—

</>

C_} o o o

a. < z V

JZ ct

CVJ

UJ>

LUQ

_J

z> in^ < o o> *" CD +++1 >1 1 1 1 H6

•H

(LU>1),M

77
11. Appendix IV - Catalog of Sudden Frequency Deviations Observed From

October 1, i960 to December 31, 1962 .

The following table lists the sudden frequency deviations observed

for the various paths in operation from October 1, i960, to December 31?

1962. This table also gives the solar flares and solar radio emissions

as well as ionospheric effects which were reported to have occurred at

the same time that a sudden frequency deviation was observed. Since the

paths from WWV to Boulder and the near vertical -incidence paths at Boulder

(Sunset to Boulder) were used for flare monitoring during this period,

the table includes all SFD's observed on the Boulder records. Consequently there are some entries for which no flares were reported optically.

The records for receiving sites other than Boulder have not been examined

as closely as have the Boulder records, and only SFD's which could be attributed to reported optical flares have been included in the table for

these paths. It should be emphasized that, although all the sudden frequency deviations listed have the characteristics of flare effects, some

of the smaller effects, especially those which do not correspond to optically reported flares, may not be due to flare-induced ionization.

A brief description of the method of data reduction may be of assistance in evaluating the information contained in the catalog. The data

is recorded on slowly moving magnetic tape (0.02 ips) in the form of the

difference frequency between the received frequency and a stable local

reference frequency offset from the transmitted frequency by a few cycles

per second (typically 2-5 c/s). This magnetic tape is then played back

at 30 ips into an audio spectrum analyzer to give a continuous visual

78
record of the recorded difference frequency versus time. Changes in the

received frequency are indicated by the variations of the difference

frequency. A sample of such a record is shown in figure 11.1a. Any

events of interest can be examined in greater detail by expanding the

time scale, as illustrated in figures 11.1b and 11.1c. The times and

magnitudes of sudden frequency deviations are determined from the expanded records.

Figure 11.1 illustrates some of the difficulties often encountered

in deciding whether an observed effect is, or is not, related to a solar

flare. The effects at 1715, 19^2, 2050, 2153, and 22^0 UT are well defined sudden frequency deviations. The events at 1822, 1837, and I928

are not as well defined. It is often questionable whether such effects

are flare related or arise from some other type of ionospheric disturbance,

The effect at 2333 UT? which begins with a negative frequency shift, is

definitely not a sudden frequency deviation.

The table gives the times of sudden frequency deviations to the nearest minute with the symbols E (before) and D (later than) being used occasionally for further qualification. D or E used with a beginning or

maximum time applies only between successive minutes, whereas a D used

with an end time may mean that the end of the effect occurred some undeterminable number of minutes after the given time.

The frequency deviations, Af , are given in cycles per second. The

accuracy with which small frequency variations can be measured from the

records is extremely limited so that the smaller events (WM or 0.1 to

0.2 c/s) have no quantitative usefulness. KR has been used to indicate

79
Jf

0) .3

-Po

CO

-p•H

3P ,ri S a) £ o

•H <L> P

0) (U MddM dO

d) -H

.3 -P P o3 •H M > £ <y H d

a3 >s

?h o

-P

ra co H a1 H CO -H ^ ^ _ o co o d

co ^c! U 2

XQ

U

CO HaopH

cd CD

s. i

CLX

LUo oQ<

cro

_io

cj CM

U2 of £ LJ

H

Q

_J- _J

H 3

cr

O

Q_ CD CO < O B

CD

H W) , cn H

LT> oOi >5

P=H

Ld 5

_)<

U§. <CLX

l_l

-iV

80
that no record exists for the given path and frequency for a given event.

The nonexistence of records designated by NR may be due to equipment malfunction or to propagation conditions. An NR has been used when the

ground wave has over-powered the sky wave on the vertical -incidence paths.

NM (not measurable) indicates that an effect probably exists but that the

frequency deviation cannot be measured. This is used for effects too

small to measure or for which the quality of the records is not good

enough to permit unambiguous interpretation.

The format of the SFD section of the table is as follows:

Time : The times of the beginning, maximum positive frequency deviation, and end of the SID are given in universal time. If more than one

distinct peak exists for a given event, the times of the maxima are listed,

Path and Irequency : The path is given by designating the transmitting and receiving locations. The operating frequency, f, is given to

the nearest Mc/s.

Frequency Deviation, Af t The maximum positive frequency deviation,

Af(+), is given in cycles per second. If more than one distinct peak exists the frequency deviation of each maximum is given. For those events

which showed a measurable negative frequency deviation, the maximum negative frequency shift, Af(-), is also given.

Change in Absorption, AA : The maximum change in absorption, AA, is

given in decibels for those events for which it was measurable. No signal strength records are available for those events which occurred before

September 1961.

81
Phase Path Change, AP : The maximum change in phase path, AP, is

given in kilometers for selected events. The phase path change is the

time integral of the frequency deviation:

AP = - | JAf dt.

The solar flare, solar radio emissions, and the ionospheric effects

sections of the table are essentially the same as given in the CRPL-F

Series, Solar -Geophysical Data; the descriptive text* for this publication

should be consulted for a more complete description of the information

contained therein. The order in which the beginning, maximum, and end

times, or duration, are given has been changed to be consistent with the

SFD section of the table. The radio bursts at 18 Mc/s given in the FSeries under ionospheric effects have been included in the table under

solar-radio emissions. An attempt has been made to make the table as

complete as space would allow in order that the SFD data available from

October 1, i960, to December 31? 19&2, may be brought to the attention of

other interested workers.

Abbreviations and Symbols Used

The following list defines the abbreviations used in the table of

SFD's. For those portions of the table extracted from the CRPL-F Series,

only the notation which differs from that of the F-Series is explained

* "Descriptive Text and Index for CRPL-F, Part B, Solar-Geophysical Data,"

U. S. Department of Commerce, National Bureau of Standards, Central

Radio Propagation Laboratory, Boulder, Colorado, November 1961, 19&2,

1963.

82
below. For a full explanation of notation used by the F-Series, reference

should be made to the Descriptive Text of the CRPL-F Series, Part B,

Solar -Geophysical Data.

Time:

D - greater than

d - duration

E - less than

U - uncertain

Path:

MN

PB

SS

TR

Transmitters

- Monrovia, Liberia

- Point Barrow, Alaska

- Sunset, Colorado

- Tripoli, Libya

WWV - Beltsville, Maryland

WWVH - Maui, Hawaii

Frequency Deviation, Af :

KM - not measurable

NR - no record

Solar Flares :

NFR - no flare reported

NFP - no flare patrol

Receivers

AC - Accra, Ghana

AN - Anchorage, Alaska

BL - Boulder, Colorado

FC - Fort Collins, Colorado

MY - Midway Island, Pacific

SY - Shickley, Nebraska

WK - Wake Island, Pacific

83
Solar Radio Emissions:

2800 Mc/s

1S1 - 1-Simple 1

2S2 - 2 -Simple 2

3S3 - 3 -Simple

hTI - 4-Post-burst increase

5 Abs - 5 -Absorption

6C - 6 -Complex

8G - 8 -Group

9Pre - 9

- Precursor

18 Mc/s

B"ar - Burst

84
Table 11.1

Catalog of Sudden Frequency Deviations

Observed from October i960 through December 1962

85
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