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Modeling ELF Radio Atmospherics Generated by Rocket Triggered Lightning

Permanent Link: http://ufdc.ufl.edu/UFE0041885/00001

Material Information

Title: Modeling ELF Radio Atmospherics Generated by Rocket Triggered Lightning
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Kunduri, Bharat
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: elf, lightning, lwpc, sferics
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: lightning strike radiates electromagnetic energy over a wide bandwidth ranging from a few Hz to a few hundred MHz, but a major part of this energy is in the Extremely Low Frequency(ELF) range (i.e, 1-3000 Hz) and Very Low Frequency(VLF) range (i.e, 3-30 KHz). This energy whose spectrum spans from a few Hz to tens of KHz propagates in the form of impulsive signals which get reflected by the Earth (at the lower boundary) and the ionosphere (at the upper boundary) and thereby propagate in a guided fashion in the waveguide formed by the Earth and the ionosphere referred to as the Earth-Ionosphere waveguide. Due to their very low attenuation rate these sferics have the capacity to travel very long distances from their source lightning (in the order of thousands of kilometers) and thus can be observed very far away from their point of origin using appropriate VLF and ELF receivers. The aim of this thesis is to model the ELF sferic waveforms up to a frequency of 500 Hz that could be observed at McMurdo Station in Antarctica, generated by rocket triggered lightning at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. Rocket triggered lightning makes it possible to obtain accurate measurements of various parameters of lightning such as current and total charge transfer, which is not possible with natural lightning due to the unpredictable nature of its occurrence. The modeling of the sferic waveform is carried on using the Long Wavelength Propagation Capability (LWPC) code developed by the Naval Ocean Systems Center over a period of many years. In order to do so, certain parameters are needed like the current waveform of the lightning and the ionospheric electron density profiles over the path of propagation. This work assumes that the lightning strike is a vertical dipole discharge and that the ionosphere is homogenous throughout the path of propagation. Realistic ionospheric electron density profiles were created using data from the International Reference Ionosphere (IRI), and realistic ground conductivity and permittivity profiles were considered that take into account different kinds of ground like land, sea, and ice. The end result is the successful modeling of the time-domain magnetic field signature of a lightning strike triggered at the ICLRT after propagating more than 14 Mm to Arrival Heights at McMurdo Station, Antarctica. These theoretical results may be directly compared with future experimental observations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bharat Kunduri.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Moore, Robert Christian.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041885:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041885/00001

Material Information

Title: Modeling ELF Radio Atmospherics Generated by Rocket Triggered Lightning
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Kunduri, Bharat
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: elf, lightning, lwpc, sferics
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: lightning strike radiates electromagnetic energy over a wide bandwidth ranging from a few Hz to a few hundred MHz, but a major part of this energy is in the Extremely Low Frequency(ELF) range (i.e, 1-3000 Hz) and Very Low Frequency(VLF) range (i.e, 3-30 KHz). This energy whose spectrum spans from a few Hz to tens of KHz propagates in the form of impulsive signals which get reflected by the Earth (at the lower boundary) and the ionosphere (at the upper boundary) and thereby propagate in a guided fashion in the waveguide formed by the Earth and the ionosphere referred to as the Earth-Ionosphere waveguide. Due to their very low attenuation rate these sferics have the capacity to travel very long distances from their source lightning (in the order of thousands of kilometers) and thus can be observed very far away from their point of origin using appropriate VLF and ELF receivers. The aim of this thesis is to model the ELF sferic waveforms up to a frequency of 500 Hz that could be observed at McMurdo Station in Antarctica, generated by rocket triggered lightning at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. Rocket triggered lightning makes it possible to obtain accurate measurements of various parameters of lightning such as current and total charge transfer, which is not possible with natural lightning due to the unpredictable nature of its occurrence. The modeling of the sferic waveform is carried on using the Long Wavelength Propagation Capability (LWPC) code developed by the Naval Ocean Systems Center over a period of many years. In order to do so, certain parameters are needed like the current waveform of the lightning and the ionospheric electron density profiles over the path of propagation. This work assumes that the lightning strike is a vertical dipole discharge and that the ionosphere is homogenous throughout the path of propagation. Realistic ionospheric electron density profiles were created using data from the International Reference Ionosphere (IRI), and realistic ground conductivity and permittivity profiles were considered that take into account different kinds of ground like land, sea, and ice. The end result is the successful modeling of the time-domain magnetic field signature of a lightning strike triggered at the ICLRT after propagating more than 14 Mm to Arrival Heights at McMurdo Station, Antarctica. These theoretical results may be directly compared with future experimental observations.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bharat Kunduri.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Moore, Robert Christian.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041885:00001


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MODELING ELF RADIO ATMOSPHERICS GENERATED BY ROCKET TRIGGERED
LIGHTNING


















By

BHARAT SIMHA REDDY KUNDURI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2010































2010 Bharat Simha Reddy Kunduri
































To my parents,

K.P.Reddy and Dr.B.Thirumala Devi









ACKNOWLEDGMENTS

I would like to express my sincere gratitude and thanks to my advisor Dr. Robert

Moore for his guidance and support throughout my graduate studies. I thank him for

giving me an opportunity to work with him and for his patience and encouragement

throughout this project. This thesis would not have been possible without his meticulous

guidance and invaluable advice. I thank Dr. Martin Uman and Dr. Vladimir Rakov for

readily agreeing to be on my committee and for their constant support and advice.

I thank all my lab mates for their constant encouragement throughout my stay at the

lab. I take this opportunity to thank my friends Dhruv Sharma, Anuj Sisodia and Vishal

Narayan who were like my family away from home.

Finally,l am deeply thankful to my parents for supporting me in innumerable ways

and being a great source of strength at every stage of my life.









TABLE OF CONTENTS
page

ACKNOWLEDGMENTS .................. ................ 4

LIST OF FIGURES .................. ................... 7

A BST RA C T . . .. .. 11

CHAPTER

1 INTRODUCTION .................. ................. 13

1.1 The Lightning Discharge ............................ 14
1.2 Rocket Triggered Lightning ............................. 16
1.2.1 Classical Rocket Triggered Lightning ... 16
1.2.2 Altitude Rocket Triggered Lightning ... 17
1.2.3 Current Waveforms ..... ......... 18
1.3 Radio Atm ospherics .. .. .. .. .. .. .. 19
1.4 Ionosphere . .. 21

2 INSTRUMENTATION AND LAYOUT AT MCMURDO STATION ANTARCTICA
AND CAMP BLANDING ......... ........................ 25

2.1 McMurdo Station- Antarctica ......................... 25
2.1.1 Arrival Heights Area, McMurdo Station ... 27
2.1.2 ELF/VLF Research at McMurdo Station ... 28
2.2 International Center for Lightning Research and Testing at Camp Blanding
(ICLRT), Florida .............. ... ............ 31

3 ELF PROPAGATION IN THE EARTH-IONOSPHERE WAVEGUIDE 37

3.1 Wave Propagation in an Ideal Parallel Plate Waveguide ... 37
3.2 Wave Propagation in Plasma ......................... 40
3.2.1 Effect of Collisions . 42
3.2.2 Effect of Static Magnetic Field ..... 42
3.3 Properties of Earth-Ionosphere Waveguide ... 43
3.4 Waveguide Mode Theory-Budden.K.G ... 44
3.4.1 Sources of Waves- The Hertzian Dipole 44
3.4.2 Modes in the Waveguide ........................ 45
3.4.3 Reflection Coefficients in the Earth-Ionosphere waveguide 47
3.4.4 M ode Equation .. .. .. .. .. .. .. 48
3.4.5 Correction for the Curved Nature of the Earth-Ionosphere Waveguide 50
3.5 Long Wavelength Propagation Capability (LWPC) ... 50
3.5.1 PR ES EG . . 51
3.5.2 M O DEFNDR .. .. .. .. .. .. .. 51
3.5.3 FASTMC ........... ....... .............. 52
3.5.4 Implementation in LW PC ........................ 52









3.6 Parameters Required to Calculate the Sferic Propagation Model 54
3.6.1 Ionospheric Electron Density Profiles ... 55
3.6.2 Current Moment Waveform of a Lightning Strike ... 56

4 MODELING ELF SFERICS ............................. 58

4.1 Homogeneous Waveguide ......................... .58
4.2 Inhomogeneous Ground .......................... 60
4.3 Modeling of ELF sferics Propagating from Camp Blanding to McMurdo
Station ...................... .... ............. 62
4.3.1 Nighttime Ionosphere W ith a Valley ... 64
4.3.2 Daytime Ionosphere Type 1 .. 66
4.3.3 Nighttime Ionosphere Without a Valley ... 69
4.3.4 Daytime Ionosphere Type 2 ... 74
4.4 Effects of Different Components of Current on the Sferic Waveform 78
4.4.1 Effects of Current Components Different lonospheres ...... .85

5 SUMMARY AND SUGGESTIONS FOR FURTHER WORK ... 88

5.1 S um m ary . . 88
5.2 Suggestions for Further Work .............. .......... 89
5.2.1 Jumps in the amplitude ................ ........ 89
5.2.2 Modeling at Lower Frequencies Below 45Hz ... 89
5.2.3 Modeling Using a more Realistic Inhomogeneous Ionosphere .. 90
5.2.4 Remote Sensing of Ionosphere ..... 91

REFERENCES ........ ........... ......... ......... 93

BIOGRAPHICAL SKETCH ........... ... ............... 96









LIST OF FIGURES


Figure page

1-1 Various phases of negative cloud to ground lightning discharge Adapted from
Rakov and Uman-2003 ............................... 14

1-2 Classical Rocket Triggered Lightning (V.A.Rakov "Lightning Discharges Triggered
Using Rocket and Wire Technique", J.Geophys.Res.,vol.100,pp.25711-25720,1999 17
1-3 Altitude Rocket Triggered Lightning (V.A.Rakov "Lightning Discharges Triggered
Using Rocket and Wire Technique", J.Geophys.Res.,vol.100,pp.25711-25720,1999) 18
1-4 Overall current record of a triggered lightning at camp blending, florida(D.Wang
et al., "Characterization of initial stage of negative rocket triggered lightning",
J.Geophys.Res.,vol.104,pg 4213-4222,1999) ..... 19

1-5 Time domain waveform of a sferic observed at palmer station (adapted from
(W ood, 2004)) . . 21

1-6 Day and Night time electron density profiles for sunspot maximum (solid lines)
and sunspot minimum (dashed lines), adapted from Tascione, T.F, Introduction
to the Space Environment, 2nd Ed .......................... 22

2-1 A map of Antarctica indicating Ross Island and McMurdo Station ... 25

2-2 A LandSat Map of Ross Island (source: http://international.usgs.gov) 26

2-3 A picture of McMurdo Station (source: http://international.usgs.gov) 26

2-4 Arrival Heights, McMurdo Station ........................ 27

2-5 A picture of the VLF receiver at McMurdo Station ..... 29

2-6 A picture of the ELF receiver at McMurdo Station ..... 29

2-7 A picture of the Racks that hold the data acquisition equipment at McMurdo
Station,Photo by Robert Moore ......................... 30

2-8 Overview of ICLRT at Camp Blanding in 2002, source:(Rakov et al., 2003) 31

2-9 Satellite image of ICLRT with some of its major landmarks indicated, adapted
from (Howard, 2009) . .. 34

2-10 A picture of launch tower, Source:Lightning Lab-University of Florida 35

2-11 Picture of launch control trailer, Source:Lightning Lab-University of Florida 35

3-1 Ideal Parallel Plate Waveguide ..... ...... .38

3-2 Earth-Ionosphere W aveguide ............................ 53









3-3 Flow chart showing the execution of LWPC . 55

3-4 Representative electron density profiles .... 56

3-5 Current vs Time waveform from rocket triggered lightning ... 57

4-1 Representative nighttime ionosphere ..... .. .. .. 59

4-2 ELF sferic spectra of homogeneous ground in linear scale ... 59

4-3 ELF sferic spectra of homogeneous ground in decibel scale ... 60

4-4 Comparison of ELF sferic spectra for inhomogeneous and homogeneous ground
(distance-2000Km ) . .. 61

4-5 Comparison of ELF sferic spectra for inhomogeneous and homogeneous ground
(distance-2000Km) in decibel scale . 61

4-6 Propagation Path of the Sferic from Florida to Antarctica (Great Circle) 63

4-7 Nighttime ionosphere with a valley ..... ..... 64

4-8 Current Waveform employed in calculations ...... ... ... 65

4-9 LWPC output for nighttime ionosphere with a valley ..... 65

4-10 Modeled ELF spectrum in decibel scale (over 1 nanotesla) for nighttime ionosphere
w ith a valley . . 66

4-11 Modeled ELF spectrum in linear scale for nighttime ionosphere with a valley 67

4-12 Modeled ELF sferic waveform for nighttime ionosphere with a valley 67

4-13 Daytime ionosphere type 1 ................. .......... 68

4-14 Current Waveform employed in calculations ...... ... ... 68

4-15 LWPC output for daytime ionosphere type 1 . 69

4-16 Modeled ELF spectrum in decibel scale (over 1 nanotesla) for daytime ionosphere
type 1 . .. ... ... 70

4-17 Modeled ELF spectrum in linear scale for daytime ionosphere type 1 70

4-18 Modeled ELF sferic waveform for daytime ionosphere type 1 ... 71

4-19 Nighttime ionosphere without a valley .. 71

4-20 Current Waveform employed in calculations ...... ... ... 72

4-21 LWPC output for nighttime ionosphere without a valley .... 72









4-22 Modeled ELF spectrum in decibel scale (over 1 nanotesla) for nighttime ionosphere
without a valley ................... .............. 73

4-23 Modeled ELF spectrum in linear scale for nighttime ionosphere without a valley 73

4-24 Modeled ELF sferic waveform for nighttime ionosphere without a valley 74

4-25 Daytime ionosphere type 2 ............... .......... .. 75

4-26 Current Waveform employed in calculations ...... ... ... 75

4-27 LWPC output for daytime ionosphere type 2 . 76

4-28 Modeled ELF spectrum in decibel scale (over 1 nanotesla) for daytime ionosphere
type 2 .................. .................. .. 76

4-29 Modeled ELF sferic waveform in linear scale for daytime ionosphere type 2 77

4-30 Modeled ELF sferic waveform for daytime ionosphere type 2 ... 77

4-31 Components of the Current Waveform Used . 78

4-32 ICC Component of the Current Waveform Used ... 79

4-33 Resultant Sferic Waveform Caused due to the ICC Component of Current 79


Return Stroke 1 of the Current Waveform Used ........

Resultant Sferic Waveform Caused due to Return Stroke 1 of

Return Stroke 2 of the Current Waveform Used ........

Resultant Sferic Waveform Caused due to Return Stroke 2 of

Return Stroke 3 of the Current Waveform Used ........

Resultant Sferic Waveform Caused due to Return Stroke 3 of

Return Stroke 4 of the Current Waveform Used ........

Resultant Sferic Waveform Caused due to Return Stroke 4 of

Return Stroke 5 of the Current Waveform Used ........

Resultant Sferic Waveform Caused due to Return Stroke 5 of


Current .


Current .


Current .


Current .


Current .


Sferic Waveform and Different Components-Nighttime Ionosphere With a Valley

Sferic Waveform and Different Components-Daytime Ionosphere type 1 .

Sferic Waveform and Different Components-Nighttime Ionosphere Without a
V a lle y . . .


4-34

4-35

4-36

4-37

4-38

4-39

4-40

4-41

4-42

4-43

4-44

4-45

4-46









4-47 Sferic Waveform and Different Components-Daytime Ionosphere type 2 87

5-1 Variations in the amplitude of the sferic across the path of propagation 89









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

MODELING ELF RADIO ATMOSPHERICS GENERATED BY ROCKET TRIGGERED
LIGHTNING

By

Bharat Simha Reddy Kunduri

August 2010

Chair: Robert Moore
Major: Electrical and Computer Engineering

A lightning strike radiates electromagnetic energy over a wide bandwidth ranging

from a few Hz to a few hundred MHz, but a major part of this energy is in the Extremely

Low Frequency(ELF) range (i.e, 1-3000 Hz) and Very Low Frequency(VLF) range

(i.e, 3-30 KHz). This energy whose spectrum spans from a few Hz to tens of KHz

propagates in the form of impulsive signals which get reflected by the Earth (at the
lower boundary) and the ionosphere (at the upper boundary) and thereby propagate in

a guided fashion in the waveguide formed by the Earth and the ionosphere referred to

as the Earth-Ionosphere waveguide. Due to their very low attenuation rate these sferics

have the capacity to travel very long distances from their source lightning (in the order

of thousands of kilometers) and thus can be observed very far away from their point of

origin using appropriate VLF and ELF receivers.

The aim of this thesis is to model the ELF sferic waveforms up to a frequency of

500 Hz that could be observed at McMurdo Station in Antarctica, generated by rocket

triggered lightning at the International Center for Lightning Research and Testing

(ICLRT) at Camp Blanding, Florida. Rocket triggered lightning makes it possible to

obtain accurate measurements of various parameters of lightning such as current and

total charge transfer, which is not possible with natural lightning due to the unpredictable

nature of its occurrence.









The modeling of the sferic waveform is carried on using the Long Wavelength

Propagation Capability (LWPC) code developed by the Naval Ocean Systems Center

over a period of many years. In order to do so, certain parameters are needed like

the current waveform of the lightning and the ionospheric electron density profiles

over the path of propagation. This work assumes that the lightning strike is a vertical

dipole discharge and that the ionosphere is homogenous throughout the path of

propagation. Realistic ionospheric electron density profiles were created using data
from the International Reference Ionosphere (IRI), and realistic ground conductivity and

permittivity profiles were considered that take into account different kinds of ground like

land, sea, and ice.

The end result is the successful modeling of the time-domain magnetic field

signature of a lightning strike triggered at the ICLRT after propagating more than 14

Mm to Arrival Heights at McMurdo Station, Antarctica. These theoretical results may be

directly compared with future experimental observations.









CHAPTER 1
INTRODUCTION

Lightning was at one point feared as an atmospheric flash of supernatural

origins-the great weapon of the gods. It has been used to describe power and might

in ancient mythologies. Greek mythology describes thunder and lightning as the mighty

weapons of Zeus. In the Bible lightning is often depicted as a manifestation of the wrath

of God. The vedas describe lightning as the weapon used by Indra, the king of heaven.

The scientific study of lightning has its modest beginning in the 18th century.

Benjamin Franklin performed the first systematic study of lightning during the second

half of 18th century. He was the first to design an experiment that conclusively proved

the electrical nature of lightning. Little progress was made in understanding the

properties of lightning until the late 19th century. Lightning current measurements were

made in Germany by Pockels around 1900 who analyzed the magnetic field induced in

materials by lightning to estimate the current values. There has been a rapid increase in

the lightning related research in the past 30-40 years with the arrival of digital computers

and ofhigh speed data acquisition systems.

Lightning radiates electromagnetic energy over an extremely wide bandwidth from

a few Hz (Burke, 1992) to many tens of MHz (Weidman, 1986). Most of the energy

is radiated in the Very Low Frequency (3-30 KHz) and Extremely Low Frequency

(3-3000 Hz) bands because of the sub-millisecond to millisecond time scales and

several kilometer spatial extents of the radiating current (Uman, 1987). The energy

radiated in the ELF/VLF bands is reflected by the ionosphere and the ground, thereby

propagating in a guided fashion between the Earth and the ionosphere which form

the Earth-ionosphere waveguide. The electromagnetic signals in the ELF/VLF bands

generated by lightning are known as radio atmospherics or more commonly as sferics.

These sferics propagate in the Earth-ionosphere waveguide with low attenuation rates

around 2-3 dB per 1000 km and thus can be observed at great distances from their










origin (Davies, 1990).The characteristics of the sferic waveform are controlled by their

source lightning discharges and the parameters of the Earth-ionosphere waveguide

(Cummer, 1997).

This thesis focuses on modeling the ELF sferics generated due to rocket triggered

lightning.

1.1 The Lightning Discharge

A thundercloud has a large positively charged layer and a negatively charged layer

of about equal magnitude which forms an electric dipole (Rakov and Uman, 2003).

Once these charged layers attain enough charge, the electric fields associated with the

charges begin to exceed the dielectric breakdown voltage of the atmosphere, leading to

the occurrence of a lightning flash.


Cloud Charge Stepped
Distribution P Leader

/t%*~ / / / // ^ '/


Kand J
Processes
i/7^


Attachment
I Process









Second Return
Stroke


S Dart
Leader
f7^


-4


First Return
StLrom



Intracloud Stroke





Positive CG Sruke

t/7///7


Figure 1-1. Various phases of a two stroke negative cloud to ground lightning discharge
Adapted from Rakov and Uman-2003.


Lightning flashes are classified as:

*Cloud discharges: those that do not terminate on the surface of Earth, e.g.,
Intracloud discharges, Cloud to air discharges and intercloud discharges









* Cloud to Ground discharges: those with at least a partial discharge to ground, e.g.,
negative cloud to ground discharges, positive cloud to ground discharges

The cloud discharges are the most numerous type of lightning (50-75 percent)

(Prentice and Mackerras, 1977). The cloud to ground discharges can be classified into

two groups depending on the layer of charge they originate in. If the cloud to ground

discharge originates in the negatively charged layer it is called negative cloud to ground

flash, if the discharge originates in the positively charged layer it is called positive cloud

to ground discharge (Wood, 2004). While 90 % of the cloud to ground flashes are

negative discharges and the major portion of the remaining 10% are positive discharges.

There are also discharges transporting both negative and positive charges to the

ground, such discharges are very rare.

A negative cloud to ground discharge is illustrated in Figure 1-1. It is initiated when

a stepped leader begins to work its way down from the cloud in a series of discrete steps

after a preliminary breakdown in the negatively charged layer. As the stepped leader

advances downward, the electric field between the end of the stepped leader and the

ground becomes high enough that conductive leaders begin to reach upwards from the

ground. When the stepped leader and the conductive leader close the 10-100 meters

gap, attachment occurs, leading to the generation of the first return stroke of discharge.
The return stroke involves the flow of large electric current from the ground to the cloud,

thereby producing a radio atmospheric (Rakov and Uman, 2003).The first return stroke

may deplete the layer of cloud charge thereby terminating the flash.If any additional

charge is available,J and K processes occur which redistribute the remaining charge

in the cloud. The conducting channel remains partially ionized following the first return

stroke and a dart leader may reionize the channel resulting in a second stroke.This

process repeats itself generating many return strokes (Uman, 1987).A similar process

with usually one stroke occurs for positive cloud to ground discharges.









1.2 Rocket Triggered Lightning

It is necessary to observe lightning at close range to accurately investigate some

of the associated phenomena, but natural lightning strikes at unpredictable times

and places, making close observation by qualified people equipped at the time with

necessary instrumentation unlikely. Rocket triggered lightning has been an important

means to overcome that problem. Experiments years ago demonstrated that a lightning

strike often can be triggered by launching a rocket connected to a long grounded copper

wire toward a thunderstorm. A strike triggered that way tends to follow the wire. The wire

quickly vaporizes and does not conduct a significant percentage of the lightning current.

Its function is merely to guide a lightning strike to measuring equipment.

Rocket triggered lightning is produced in two methods currently (Rakov and Uman,

2003):

* Classical Rocket Triggered Lightning

* Altitude Rocket Triggered Lightning

1.2.1 Classical Rocket Triggered Lightning

In classical triggering method, the wire which is attached to the rocket is connected

at the other end to a grounded launcher. An upward positive leader is generated at the

tip of the rocket after it reaches an altitude of around 200 m. The current of the upward

positive leader vaporizes the wire and an initial continuous current (ICC) follows for

some hundreds of milliseconds. After the completion of the ICC phase, there exists a

phase for a few tens of milliseconds where no current flows. This phase is followed by

the generation of a leader-return stroke sequences. These are similar to the subsequent

leader-return stroke sequences in natural lightning.

During the formation of the upward positive leader a phase called the Initial Current

Variation (ICV) occurs when the triggering wire is replaced by the upward positive leader

plasma channel. The upward positive leader produces current which is of the order of

tens to hundreds of amperes (measured at ground) which vaporizes the wire. At this














Natural /
channel '

I I I irn


Copper Wire-
wi trace
2>l0ows I I300n -- 1I


S1-2s hundredsds (tens of Ms)
of ms)
Ascending Upward Initial No-current Downward Upward
rocket positive continuous interval negative return
leader current leader stroke



Figure 1-2. Classical Rocket Triggered Lightning (V.A.Rakov "Lightning Discharges
Triggered Using Rocket and Wire Technique",
J.Geophys.Res.,vol.100,pp.25711-25720,1999


instance the current measured at ground falls to zero approximately due to the absence

of a conducting path. A downward leader process bridges the resultant gap and initiates

a return stroke process from the ground which serves to re-establish the interrupted

current flow to the ground.

1.2.2 Altitude Rocket Triggered Lightning

Altitude triggering technique uses an ungrounded wire. This enables the possibility

to reproduce some features of first stroke of natural lightning which is not possible

using classical triggering. The apparatus has a 50 m long copper wire connected to

the ground launcher, a 400 m long insulating kevlar cable in the middle and 100-200

m long floating copper wire connected to the rocket. The upper floating wire is used

for triggering while the lower grounded wire is used for intercepting the leader. When

a rocket reaches a suitable altitude (around 600 m) a bi-directional leader composed

of a upward positive leader and a downward negative leader is initiated. The electric










(105 106)n/s t-

ea r ot t, I1e



~--IOm/st t
T, U+ +ce I
_o .IRol mis 0pf -1m20s9
3150m r Copper 1.2km


wire
400m I^ cable [ ff
2xyiom/sf j opper tv (L07--1<)m/8s

S -3s I ms (OO) i
Ascending Upward Bi-directional Upward Upward
rocket positive leader return positive
leader stroke leader


Figure 1-3. Altitude Rocket Triggered Lightning (V.A.Rakov "Lightning Discharges
Triggered Using Rocket and Wire Technique",
J.Geophys.Res.,vol.100,pp.25711-25720,1999


field produced by the downward negative leader initiates an upward connecting positive

leader from the grounded copper wire. This connects to the downward negative leader

and this process leads to the generation of a return stroke.

1.2.3 Current Waveforms

A typical negative rocket triggered lightning has been described to be similar to a

upward initiated lightning from a tall structure (Uman, 1987). It involves an initial stage

(IS) that is composed of an upward positive leader (UPL). It is followed by an initial

continuous current (ICC). The ICC is commonly followed by a dart leader/return stroke

sequences which are similar to the subsequent strokes in natural downward lightning.

When there are no return strokes involved the triggered lightning event consists of the

IS only and is termed as wireburn (D.Wang et al., 1999). It has been well documented

in the literature that the ICC involves impulsive processes which are similar to the

M-component pulses (Fieux et al., 1978).










June 24,1996, 17:04:56 EDT, Camp Blandin& Florida


400
400Inital Stage

0 -











-2000 t '
0 J00 200 300 400 5oo
-800- ICe Pls)
Fig e 1 initial c current
f-120 lg Variation

-1600 -- Retum Stroke
Pulses
-2000 I
0 100 200 300 400 500 600
Time (mns)

Figure 1-4. Overall current record of a triggered lightning at camp blending,
florida(D.Wang et al., "Characterization of initial stage of negative rocket
triggered lightning", J.Geophys.Res.,vol.104,pg 4213-4222,1999)


Figure 1-4 indicates the various features associated with a typical negative

rocket triggered lightning discharge. The initial stage in rocket triggered lightning

is characterized by a channel base current having a duration of some hundreds of

milliseconds and a magnitude of approximately 100 Amps.The pronounced current

variation at the beginning of the IS is termed initial current variation (ICV), the ICV has a

duration which typically does not exceed 10 ms (D.Wang et al., 1999). The ICV usually

involves an abrupt decrease in current followed by a pulse.Alongside the ICV the IS

typically includes a pronounced ICC.

1.3 Radio Atmospherics

Radio atmospherics or sferics in short are lightning produced electric and magnetic

fields whose spectrum spans frequencies from a few Hz to a few hundreds of KHz.

These are easily observed at distances spanning several thousand kilometers. Typical

sferics have a frequency spectrum in the ELF (0-3 KHz) and the VLF (3-30 KHz) range,









but sometimes can extend into the LF (30-300 KHz) range (Rakov and Uman, 2003).

Sferics propagate in the waveguide formed by Earth and ionosphere primarily by

multiple reflections similar to a electromagnetic wave in a metallic waveguide.The early

research in sferics began in the early 1900's and this primarily was a period of discovery.

Strange noises were first observed on radio by German physicist Heinrich Barkhausen

during world war I. A number of papers in the 1930's and early 1940's characterized and

attempted to explain the received sferics from distant lightning sources. An important

early paper on sferics (Burton and Boardman, 1933) describes two distinct emissions

- "swishes", weeksks. The "swishes" are now referred to as whistlerss". During and in

the period following World War II there was a great deal of interest in understanding the

propagation of sferics, due to its implications regarding long-distance communication.
The study of ELF sferics, though fundamentally similar to the VLF sferics, mostly

has been treated separately in the literature. ELF sferics are also referred to as slow

tails and have been studied experimentally for many years [e.g., (Hepburn, 1992),

(Taylor and Sao, 1970), (Burke, 1992) etc. (Jones, 1974) published a bibliography of

experimental measurements of ELF propagation characteristics generated by lightning.

(Budden, 1961) and (Wait, 1970) made a tremendous contribution in understanding the

propagation of ELF and VLF sferics in the Earth-ionosphere waveguide.
Figure 1-5 shows a sferic waveform recorded at Palmer station Antarctica (adapted

from .(Wood, 2004)). It clearly shows a VLF impulse followed by a ELF "slow tail"

(Reising et al., 1996). The oscillatory nature of the VLF impulse is due to the presence

of multiple modes of propagation, however the ELF component only has one mode

of propagation (QTEM mode) (Cummer, 1997). The spectral content of sferics varies

widely and there are many variations observed, a good analysis of some variations in

sferics observed is described in (Cummer, 1997).










Palmer Station, Antarctica
iI I I I


VLF

10 ELF
0 i .. 1' Slciw Tail
pT 0 i

-10 -

-20

30- I I I I I
0 1 2 3 4 5 6 7


Figure 1-5. Time domain waveform of a sferic observed at palmer station (adapted from
(Wood, 2004))

1.4 Ionosphere

The ionosphere is the uppermost part of the atmosphere stretching from a height
of about 50 km to 1000 km that is ionized by the solar radiation. Even though the
ionosphere forms only a small part of the atmosphere it has a very important role
because of its influence on the radio waves (especially ELF and VLF waves). When
solar radiation strikes the chemical constituents of the atmosphere, electrons are
dislodged from atoms and molecules to produce the ionospheric plasma. The presence
of these charged particles makes the ionosphere an electrical conductor which supports
electric currents and generates radio waves.
Ultraviolet (UV), X-Ray, and shorter wavelength radiation from the sun have
sufficient energy in them to dislodge an electron from a neutral atom or molecule

and are mostly responsible for ionization. The amount of ionization primarily depends on
the activity of the sun, it varies greatly with the amount of radiation received from the sun








and thus there is a diurnal effect, a seasonal effect and also varies with the geographic
location (Davies, 1990).


DAY/NIGHTTIME ELECTRON CONCENTRATIONS
1000 a

800

600 \





150






ELECTRON CONCENTRATION (c )










Figure 1-6. Day and Night time electron density profiles for sunspot maximum (solid
lines) and sunspot minimum (dashed lines), adapted from Tascione, T.F,
Introduction to the Space Environment, 2nd Ed.











The ionosphere is divided into regions (D-region, E-region and F-region) with
a specific ionization. The lowest is the D-region covering the altitude 50 km-90 km,
then comes the E-region between 90km-50km and finally the F-region (also known
80 No


010 102 103 104 10s 106
ELECTRON CONCENTRATION (cm'3)

Figure 1-6. Day and Night time electron density profiles for sunspot maximum (solid
lines) and sunspot minimum (dashed lines), adapted from Tascione, TF,
Introduction to the Space Environment, 2nd Ed.


The ionosphere is divided into regions (D-region, E-region and F-region) with
a specific ionization. The lowest is the D-region covering the altitude 50 km-90 km,
then comes the E-region between 90km-150km and finally the F-region (also known









as the Appleton layer) above the E-region. There are F1 and F2 regions within the

F-region. The electron concentrations reach their highest levels in the F-region, more

specifically the F2-region (Hargreaves, 1992). Figure 1-6 shows the electron density

profiles of a typical ionosphere at both night time and day time at mid-latitude. The F1

layer disappears during the night while the F2 layer slowly decreases through the night.

The ionosphere is a dynamic medium and the study of the ionosphere is an

important field. Ionospheric sounding is one of the oldest and most accurate ways of

studying the ionosphere. In this technique lonosondes are employed in sending signals

into the ionosphere which are reflected back in the presence of ionization, the frequency

at which the reflection occurs gives information about the plasma density at the altitude.

lonosondes are effective in probing the E-region and the F-region but not the D-region

(Hargreaves, 1992).

A more recent technique is the Incoherent Scatter Radar, the advantage with this

technique being that it can probe the ionosphere beyond the F2 region electron density

maximum and is capable of measuring other quantities such as electron temperatures

etc (Evans, 1969). The disadvantage with this technique, however, is that it requires

very expensive equipment and is not very useful in measuring the electron density

levels at the lower levels. Measurements of the D-region are still very difficult and the

techniques described above are not suitable for making measurements at D-region

altitudes. Moreover the D-region is too low for rockets and too high for balloons to

make any measurements. Thus one of the very few methods to study the D-region

of the ionosphere is through VLF waves. The VLF waves are completely reflected by

the ionosphere, and this makes them a very useful tool for measurements in D-region

(Cummer, 1997). Long distance VLF propagation effects measured in sferics are

an important source to make D-region measurements (Cummer, 1997). Recently a

technique has been developed in which ELF wave propagation measurements made









using lightning discharges as a source are used in remote sensing the E-region of the

ionosphere (Cummer and Inan, 2000).









CHAPTER 2
INSTRUMENTATION AND LAYOUT AT MCMURDO STATION ANTARCTICA AND
CAMP BLENDING

2.1 McMurdo Station- Antarctica

McMurdo Station is an American Antarctic research station located on the southern

tip of Ross island on the shore of McMurdo Sound in Antarctica. It is operated by United

States Antarctic Program, a branch of National Science Foundation and is the largest

community in Antarctica which includes a harbor, 3 airfields, a heliport and over 100

buildings. The United States officially opened its first station in McMurdo on Feb 16,

1956 and it was initially called Naval Air Facility McMurdo.


'c -
. <\ *.. *1 ^
,. \ '--'.-
',, ..
i"-


Figure 2-1. A map of Antarctica indicating Ross Island and McMurdo Station (source:
http://international.usgs.gov)


Figure 2-1 indicates the location of Ross Island and McMurdo Station in Antarctica.

Figure 2-2 shows a Landsat image of the Ross Island and this image points the location

of McMurdo Station on Ross Island. Figure 2-3 shows a picture of the McMurdo Station

taken from the observation hill. The buildings range in size from a small radio shack










Ross
Ice
Shelf


r


Figure 2-2. A LandSat Map of Ross Island (source: http://international.usgs.gov)


Figure 2-3. A picture of McMurdo Station (source: http://international.usgs.gov)










to large three storeyed structures. The buildings include repair facilities, dormitories,

administrative buildings, a firehouse, power plant, water distillation plant, wharf, stores,

clubs, warehouses and Crary Lab. These are linked by above ground water, sewer,

telephone and power lines. The station covers an area of nearly 1.5 sq.miles.

2.1.1 Arrival Heights Area, McMurdo Station

McMurdo Station lies at an invariant magnetic latitude of about 80 degrees inside

the polar cap at all local times and is a unique site for studying the natural phenomena

and atmospheric studies, one of the main reasons for this is its location being remote

from contamination sources. The projects that operate from the Arrival Heights area at

McMurdo station examine natural phenomena that occur in the Earth's atmosphere and

magnetosphere, Figure 2-4 shows a picture of this area and the map of this area. The

map gives an idea of the various facilities at this area.


Second Crter Locmain ofELF


AralHrt iBzgi n R m I
E"ectonmuaeca Te imsyaed



-V NwCt ikead SQ Ao-tct Rh Fac






ekcownaikum IDe aM niaet tRegios




A Image of Arrival Heights Region, Photo by Seth B Map of Arrival Heights Region
White(Source:www.sethwhite.org)

Figure 2-4. Arrival Heights, McMurdo Station









The objectives of these programs include investigations of phenomena that couple

solar processes into the terrestrial environment, which include processes with short term

environmental effects such as the auroras and radio wave communication interference,

as well as those associated with long term effects such as ozone layer and atmospheric

composition studies. The instruments for these tasks include optical and radio devices

for remote sensing,sensors for monitoring changes in electric and magnetic fields at the

station, ELF-VLF receivers.

The signals from different instruments at the Antarctic observatories are recorded

on a common data logger and can be shared. These instruments provide analog signals

that are digitized and recorded by PC based systems recording to magnetic-optical

disks. These data acquisition systems are operated at station facilities and record data

from many instruments which include

* ELF-VLF receivers, University of Florida(Principle Investigator:Dr. Robert Moore)/
Stanford University

Riometers and Photometers, University of Maryland

Searchcoil Magnetometer, University of New Hampshire

Fluxgate Magnetometer, NJIT

2.1.2 ELF/LF Research at McMurdo Station

Historically, a major part of ELF/VLF research at Arrival Heights has been carried

out by Stanford University (Antony Fraser-Smith). The University of Florida recently

took control of these systems together with Stanford, providing much needed hardware

upgrades to the systems. As a part of this program University of Florida set up receivers

at Arrival Heights and South Pole station in January 2010, and at Palmer Station in May

2010.

The VLF receiver and ELF receiver at Arrival Heights are presently maintained

and operated by Robert Moore of the University of Florida. Figure 2-5 shows image of

the VLF receiver located in the second crater region (shown in the image of the map



























Figure 2-5. A picture of the VLF receiver at McMurdo Station, Photo by Seth White
(Source:www.sethwhite.org)

of arrival heights in Figure 2-4 and Figure 2-6 shows the image of the ELF receiver at

McMurdo Station.
















Figure 2-6. A picture of the ELF receiver at McMurdo Station, Photo by Seth White
(Source:www.sethwhite.org)


The ELF/VLF receiver systems at McMurdo Station record wave activity incident

upon North/South and East/West crossed loop antennas shown in Figure 2-5 and Figure









2-6. A preamplifier is near the antenna and the remainder of the system is located in

the hut shown in Figure 2-4. The racks shown in Figure 2-7 hold the line receiver, GPS

timing unit, mixer/moniter and analog recorders.














Figure 2-7. A picture of the Racks that hold the data acquisition equipment at McMurdo
Station,Photo by Robert Moore


The VLF receiver is located inside the second crater at Arrival Heights which is an

old volcanic crater about 1.5 miles north of the hut shown in Figure 2-4. University of

Florida and Stanford University are jointly running this project using the VLF and ELF

antennas to measure the very long wavelength electromagnetic waves which propagate

around the globe in the Earth-ionosphere waveguide. VLF receiver(Figure 2-5) consists

of a central wooden pole mounted in the ground, and four triangular loops of wire run

down to the ground from its top. The other four wires are support lines for the pole itself.

The wire loops are oriented N-S and E-W and pick up radiation in the 3 KHz-30 KHz

range.

Figure 2-6 shows the ELF receiver in the vault. Unlike the VLF antenna, which

sways in the breeze, it is important for the ELF antenna to remain stationary and thus it

was buried in a wooden vault out in the lava fields north of the hut. The antenna has two

components, one oriented north-south and the other oriented east-west, and they pick

up signals in the 1 Hz 3KHz range.









2.2 International Center for Lightning Research and Testing at Camp Blanding
(ICLRT), Florida

A lightning research facility at Camp Blanding, Florida was started by Electric Power

Research Institute (EPRI) and Power Technologies Inc in 1993. University of Florida

and Camp Blanding Florida Army National Guard Base signed an agreement forming

the International Center for Lightning Research and Testing (ICLRT) for the purpose

of advancing the science and technology of lightning in October 1994. The center has

an area of more than 100 acres, located about 45 km north-east of Gainesville (UF),

Florida having the co-ordinates 300 N and 820 W. Since 2005 the facility is being jointly

operated by University of Florida and Florida Institute of Technology. The site is ideal

for conducting rocket triggered lightning experiments especially due to its restricted

airspace (source of information,www. lightning. ece.ufl. edu). Figure 2-8 shows the

overview and layout at Camp Blanding in 2002.






UnoNrz C'N~r










Figure 2-8. Overview of ICLRT at Camp Blanding in 2002, source:(Rakov et al., 2003)




2500 square-foot office building
*Two launch trailers

One launch tower
One launch tower









* One mobile launcher


* four instrumentation buildings

* Two overhead test power lines

* A test airport runway

* An underground test power system

One of the primary goals of ICLRT is to study rocket triggered lightning and natural

lightning. The current infrastructure at ICLRT has 91 measurements, digitization and

control computers which enable the study of both triggered and closely occurring natural

lightning, eg (Rakov and Uman, 2003) and (Crawford et al., 2001). These instruments

measure electric and magnetic fields, high energy radiations (X-rays), optical radiation

and channel-base currents.

At ICLRT different types of digital storage oscilloscopes (DSO) are employed to

digitize and store data. The DSOs are armed, calibrated and disarmed by a central

computer in launch control (HAL) via GPIB or ethernet, once armed the DSOs are

triggered to record data when the channel based currents exceed 6 kA or when the

two optical sensors placed in the corners of the site and pointing towards the launch

tower detect luminosity exceeding a certain threshold value simultaneously. Both these

conditions indicate the occurance of either triggered or natural lightning.

A separate network of DSOs called Positive Lightining Experiment (POE) is setup

to record data from off-site positive cloud-to-ground lightning without preventing the

acquisition of data from on-site lightning

Details of the DSOs used at ICLRT:

2 Yokogowa DL716 16 channel instruments with 10 MHz sampling rate and 4 MHz
bandwidth

5 Yokogowa DL750 16 channel instruments with 10 MHz sampling rate and 3 MHz
bandwidth









* 4 LeCroy LT344L 4 channel instruments with 250 MHz sampling rate and 20 MHz
bandwidth

2 LeCroy LT374L 4 channel instruments with 250 MHz sampling rate and 20 MHz
bandwidth

4 LeCroy 44Xi 4 channel instruments with 250 MHz sampling rate and 20 MHz
bandwidth

Two different types of devices are used to measure channel base currents. These

currents are measured at the bottom of the launch tubes located atop the launch tower.

The first current measuring device is a low inductance current viewing resistor model

R-7000-10. The second device is a clamp-on current transformer, a model 6801 custom

manufactured by Pearson Electronics.

ICLRT has three field mills (a device used to sense static fields) deployed at the

site with the purpose of determining the availability of suitable thunderstorm conditions

for triggering lightning (electric field values between 4-10 kV/m). Ground-level and

broadband vertical electric field and field derivatives are sensed using flat-plate sensors.

Currently there are eight dE/dt sensors and ten electric field sensors at the site.

Two high speed video cameras with adjustable framing rates and pixel resolution

are used to image the lower several hundred meters of lightning channel. One of the

cameras used is a Photron SA1.1 and the other is Phantom v7.3, the Photron operates

at a faster framing rate than the Phantom, it is used to record videos at speeds up to

300,000 frames-per-second (fps) of the lowest hundred meters of the triggered lightning

channel with a horizontal field-of-view of tens of meters. The Phantom is generally

operated at speeds up to 10 kfps of the bottom several hundred meters of the channel

with a horizontal field-of-view of about hundred meters (courtesy Chris Biagi, Lightning

Lab,University of Florida).

Figure 2-9 shows a satellite image of ICLRT at Camp Blanding, Florida and

indicated in it are some of the major structural landmarks, this figure is adapted from

(Howard, 2009) and is taken from Microsoft Virtual Earth.



























Figure 2-9. Satellite image of ICLRT with some of its major landmarks indicated,
adapted from (Howard, 2009)

There are three ways to trigger lightning at ICLRT: (i) Underground Launcher (ii)

The launch Tower (shown in Figure 2-10) (iii) A mobile launcher. Since 2005 only the

launch tower and the mobile launcher have been used, the majority of the triggering

being conducted at the tower (Howard, 2009). All the launchers are equipped with

resistive shunts to measure the lightning channel base currents. The launch tower is a

11 m tall wooden tower with the launcher on its top and and the tower is located near the

launch control trailer as shown in Figure 2-8.

The launch control trailer shown in Figure 2-11 is the center of the triggering

operations, it is located approximately 50 m north of launch tower. This building contains

the launcher controls and also provides the electromagnetic shielding for the video and

data acquisition equipment (Howard, 2009). The trailer is powered by a diesel generator

during the triggering operations so that the equipment inside is not affected by a surge

or failure in the power grid, both of which occur commonly during lightning (Howard,

2009).
































Figure 2-10. A picture of launch tower, Source:Lightning Lab-University of Florida


Figure 2-11. Picture of launch control trailer, Source:Lightning Lab-University of Florida









A network of sensors used to collect electric and magnetic fields, time derivatives

of the fields and X-ray emissions is in use at ICLRT and is known as the MSE(Multiple

Station Experiment)/TERA(Thunderstorm Energetic Radiation Array). The MSE network

(primarily composed of the electric and magnetic field and its time derivatives sensors)

is maintained and operated by the University of Florida while the TERA network

(primarily consisting of X-ray sensors) is operated by Florida Institute of Technology

(Dwyer et al., 2004). A video system was also deployed as a part of this system which

consisted of four camera sites whose signals were also triggered. The data from the

network is also provided a GPS time stamp, allowing the data to be correlated with other

systems such as the National Lightning Detection Network (NLDN) (J.Jerauld et al.,

2005).

This whole system is operated through a control system which provides remote

capability for many tasks like powering measurements, measuring battery voltages,

monitor local thunderstorm conditions by measuring the quasi-static electric field at

ground and automatically arm and disarm the network when appropriate (Howard,

2009). The electric and magnetic field, optical, and TERA measurements were

sampled continuously for 2 s with 1s pre-trigger at 10 MHz on Yokogowa DL750 digital

oscilloscopes, the dE/dt and TERA measurements are sampled by LeCroy digital

oscilloscopes at 250 MHz. The channel-base current of the rocket-triggered lightning

was recorded on both LeCroy and Yokogawa oscilloscopes. For a detailed report on the

instrumentation at ICLRT the reader is recommended to refer (Howard, 2009).









CHAPTER 3
ELF PROPAGATION IN THE EARTH-IONOSPHERE WAVEGUIDE

Extremely Low Frequency (ELF) electromagnetic waves lie in the frequency range

3 Hz to 3 KHz and are of interest in the fields of long distance communications and

submarine communications due to their capability to propagate very long distances

because of low attenuation rates and their capability to penetrate well through

conducting materials. The most common and powerful source of electromagnetic

radiation in the ELF and VLF range of frequencies is lightning.

ELF energy radiated from a lightning strike propagates in a guided fashion in

the Earth-Ionosphere waveguide reflecting multiple times between the Earth and the

ionosphere. ELF wave propagation in the Earth-Ionosphere waveguide depends on

the electrical properties of the Earth and the ionosphere (here the boundaries of the

waveguide) and the variable nature of the ionosphere. The attenuation rate of the wave

is highly variable and is dependent on many factors like frequency, conductivity of

the Earth, conductivity profile of ionosphere, reflection height of the ionosphere, and

Earth's magnetic field. All these factors have a significant effect on the sferic waveforms

observed from a distant lightning strike.

This chapter discusses the modal content in the ELF range of frequencies and

gives a mathematical description of ELF wave propagation in the Earth-ionosphere

waveguide. The waveguide mode theory (Budden, 1961) provides an analytical

description of propagation of ELF/VLF waves.

3.1 Wave Propagation in an Ideal Parallel Plate Waveguide

Consider an ideal parallel plate waveguide with its boundaries at x=0 and x=a

as shown in Figure 3-1 and assume the medium is lossless, simple and source

free. The solution is obtained in a rectangular co-ordinate system, even though the

Earth-Ionosphere waveguide is not flat (especially at very large distances considered

here). A direct solution in the Cartesian co-ordinate system would be extremely











Upper boundary(ionosphere)




direction of propagation



lower boundary(earth)








Figure 3-1. Ideal Parallel Plate Waveguide


complicated for the geometry. The waveguide is initially assumed to be perfectly flat

and appropriate corrections are made later in the derivation for a spherical geometry

(Budden, 1961).

The boundary conditions that are to be satisfied are Etangentiai=0 and Hnorma=0.

The solutions for this problem can be divided into 3 categories:

Transverse Electric (TE) Modes, in this case Ez=0 and Hz 0

Transverse Magnetic (TM) Modes, in this case Hz=0 and Ez, 0

Transverse Electric and Magnetic (TEM) Modes, in this case Ez=0 and Hz = 0

Where modes are specific cases for which such waves can exist and there exists a

condition which must be satisfied for a mode to exist which is the mode equation given

below for each category.

Solution for TEr modes


Ey = Ki sin( M7)e- (3-1)
Ey3









The solutions for Hz and Hx can be obtained from equation 3-1 and Maxwell's

equations. The mode condition for TEm modes is given by


sin(ah) = 0 or ah = m~ where m = 0, 1, 2etc (3-2)


Solution for TMm modes


Hy = K2cos( )e- z (3-3)
a

The solutions for Ez and Ex can be obtained from equation 3-3 and Maxwell's

equations. The mode condition for TMm modes is given by


sin(ah) = 0 or ah = mr where m = 0, 1, 2etc (3-4)


Solution for TEM mode

It is a subset of TMm mode solution, i.e., TMo


Hy = K3e-z (3-5)




Ex = ~ K3e-7 (3-6)
Jwc

Here 7 is the propagation constant. The TEM mode is a special case of a TM mode.

Both the electric and magnetic fields are transverse (perpendicular) to the direction of

propagation for the TEM mode.

Waveguide modes are can be numbered by the values of 0 (here 0=ah in the

example), the lowest value of 0 that satisfies the mode condition being the lowest

order mode. Also different frequencies have different values of 0 associated with them.

At certain frequencies the value of 0 reach 90 thereby preventing the waves from

propagating, such frequencies are known as cut-off frequencies. When the frequency of

the wave is below the cut-off frequency only complex values of 0 are possible and only









evanescent waves can exist in the waveguide. In an ideal parallel plate waveguide the

TEM mode does not have a cut-off frequency and 0=0 for all frequencies.

The group velocity of a waveguide mode is:


v= ccos = c 1 ()2 (3-7)

Here fc is the cut-off frequency for the nth order mode. It can be observed from

equation 3-7 that as frequency (f) becomes approaches the cut-off frequency(fc) the

group velocity(vg) approaches zero and as the value of f becomes much greater than fc,

v, approaches the speed of light. The TEM mode propagates at the speed of light with
all the frequencies arriving simultaneously. The Earth-lonosphere waveguide is far from

an ideal waveguide, but the modal features exhibited by the ideal waveguide are similar

to the modal features of the Earth-lonosphere waveguide.

3.2 Wave Propagation in Plasma

The ionosphere that makes up the upper boundary of the Earth-Ionosphere

waveguide is made up of cold plasma, hence it is necessary to understand the

electromagnetic properties of cold plasma to understand the propagation of electromagnetic

waves in the Earth-Ionosphere waveguide. Plasmas are the fourth state of matter and

are considered to be special cases of gases that include a large number of electrons,

ionized atoms, neutral atoms and molecules. In a more general sense a plasma is a

state of matter that contains enough number of charged particles so that its dynamic

behavior would be dominated by electromagnetic forces.

The sun and the stars are hot enough to be almost completely ionized with

enormous densities and the interstellar gas is sparse enough to be almost completely

ionized by stellar radiation. Starting from an altitude of 60 km the sun effects our

atmosphere with a variety of radiations and the UV radiation is absorbed by the gaseous

mixture in the atmosphere. In this process a large number of molecules and atoms

receive sufficient energy to be ionized with maximum ionization occurring at an altitude









of approximately 350 km and this results in the formation of the ionosphere (Inan and

A.S.Inan., 1999).

To determine propagation of electromagnetic waves in plasma Maxwell's equations

along with equations of motion are required. The motion of electrons under the influence

of electric and magnetic fields constitute which must be accounted for in Maxwell's

equations through the current density term j, which is given by:


I = NeV (3-8)

Where Re is the ambient electron density, V is the velocity of electrons and qe is the

charge on a single electron. Similar relations can be deduced for motion of ions, but the

current density due to ions is small and negligible compared to that of electrons.

The time harmonic form of Maxwell's equations can now be written as (Inan and

A.S.Inan., 1999):


V x H =jwcoE + Reqe (3-9)

V x E = jwpH (3-10)

V. E f qe (3-11)

V H = 0 (3-12)

qeE z jwmev (3-13)

the continuity equation for electrons would be:


V (eV) = -jWne (3-14)

From the Maxwell's equations above, the following equation can be deduced:

Ne q2
Vx H = jwo(- Ne )E (3-15)
u2meC,









The above equation clearly indicates plasma can be represented by an effective

dielectric permittivity given by (Inan and A.S.Inan., 1999):

2
Ceff C(i -P) (3-16)

where p = q is called the plasma frequency. Thus the effects of plasma on the

electromagnetic wave propagation can be represented in terms of the effective dielectric

permittivity (Ceff) and the solutions for fields can be obtained in a manner similar to that

of air after replacing c0 with Cefr.

3.2.1 Effect of Collisions

Some electromagnetic power is always lost (i.e, transformed into heat) in a plasma

because of the effects of collisions between electrons and molecules, ions and other

electrons (Inan and A.S.Inan., 1999). The effect of these collisions are accounted for in

the equation of motion through a frictional term, shown below.

qeE =jumev + mv = jume(1 -j-) (3-17)


where v is the collision frequency. Solving the equations we can account for the

effect of these collisions in the plasma in the effective dielectric constant in a manner

similar to the one described previously, the effective dielectric constant (eeff) is given by:

X
Ceff = o(1 1 -jZ) = eff -'eff (3-18)

where X = and Z = v. In the above equation the imaginary part cf represents

the power loss due to collisions resulting in the attenuation of the wave. The expressions

for an electromagnetic wave in a plasma with collisions can be deduced similar to that of

a lossy medium using the above values (Inan and A.S.Inan., 1999).

3.2.2 Effect of Static Magnetic Field

When a steady magnetic field permeates a plasma (like in the case of Earth's

magnetic field permeating the ionosphere), the medium becomes anisotropic and this









results in the permittivity being represented as a tensor (a matrix) and not a vector

anymore (Inan and A.S.Inan., 1999). The effective permittivity (Cf) can be represented

as shown below:

( 11 12 0

Seff= c21 C22 0 (3-19)

0 0 e33

Where

2 (1 Z)w
11= -11= co(1 ) (3-20)
C C2 (1 jZ)W2

-12= _C21= 0( 2(1 ) (3-21)
S- (1 jZ)w2
2
33 = Co(1 P- ) (3-22)
'2(1 jZ)

Using the above terms and solving for the fields the value of index of refraction (n)

can be derived and is given below.

n2 1 (3-23)
U Y2sin2 /4 sin4 y2 C2 C2 0
2(U-X) 4(U-X)2 -T C OS

where X = Y = Z = U = 1 jZ and 0 is the angle between direction of

propagation and the static magnetic field.

The above equation is known as the Appleton-Hartree equation. It could be

observed that it has two roots corresponding to two characteristic waves.

3.3 Properties of Earth-Ionosphere Waveguide

The Earth-Ionosphere waveguide is significantly different from the ideal parallel

plate waveguide because of the electrical properties of the Earth, ionosphere and the

presence of Earth's magnetic field. In the Earth-Ionosphere waveguide, the boundaries

i.e., the Earth and the ionosphere are not perfect conductors. The Earth has a finite

conductivity which varies greatly depending on whether the particular location is land,









sea or ice and also on the type of soil and on many other factors. The conductivity of

Earth is relatively low when compared with that of a good metallic conductor, but at

ELF frequencies Earth behaves as a good conductor. But the waves propagating in the

Earth-Ionosphere have some amount of attenuation.

The ionosphere which is the upper boundary of the Earth-ionosphere waveguide

is an ionized region of the upper atmosphere that contains significant number of free

electrons and ions (Hargreaves, 1992). This makes the region behave like a plasma,

the presence of the Earth's magnetic field makes the ionosphere an anisotropic medium

(whose properties are discussed in the previous section).

There are two important works dealing with the propagation of ELF and VLF waves

in the Earth-ionosphere waveguide. The work of James Wait published in many scientific

papers during 1960's and 1970's and summarized in his book (Wait, 1970). Wait deals

with the presence of ionosphere (upper boundary of the waveguide) as not a single

layer but rather as a series of interfaces and thereby correctly approximating a smoothly

varying ionosphere, but he fails in correctly interpreting the effect of the presence of

Earth's magnetic field in the ionosphere by describing the medium as an isotropic

medium whereas in reality it is an anisotropic medium. The other prolific publisher in this

field is K.G.Budden who developed a theory which is summarized in his book (Budden,

1961) called waveguidee mode theory of wave propagation" to correctly describe the

propagation of ELF/VLF waves in the Earth-Ionosphere waveguide.
3.4 Waveguide Mode Theory-Budden.K.G

3.4.1 Sources of Waves- The Hertzian Dipole

The sferic signal is highly dependent on certain parameters of source lightning

(especially the time derivative of current a' and current I) through which it originates.

The simplest kind of source in electromagnetism is Hertzian dipole which is equivalent

to having two equal and opposite charges q on conductors placed very close together

and joined by a wire (Budden, 1961). A vertical dipole is one whose axis is parallel to









the line which is vertically upwards from the lower boundary (here Earth) and pointing

towards the upper boundary (here ionosphere), perpendicular to the surface of the

boundary (assuming the surface is flat). A radio transmitter is often modeled as a

vertical dipole and is applicable especially when the dimensions of the transmitting

aerial are small compared to the wavelength, hence this idea is applicable especially at

extremely low frequencies and very low frequencies (Budden, 1961). The waveguide

mode theory is applicable at ELF/VLF frequencies and hence when dealing with this

spectrum of frequencies the source can safely be approximated as a vertical Hertzian

dipole.

At very low frequencies a transmitting aerial is generally a bundle of wires

connected to a transmitter with its other terminal connected to Earth. Taking Earth

to be a perfect conductor the charge on the wires induces an equal and opposite image

charge in the Earth's surface thereby forming a dipole which to a certain degree is

equivalent to a Hertzian dipole (Budden, 1961). The aerial itself was a half-dipole its

image in the Earth's surface forming the other half. Budden states that a thunder cloud

discharging to Earth is also similar to the half dipole aerial.

Since the expressions for electric and magnetic fields radiated by a Hertzian dipole

are rather complicated, it is recommended by Budden to use another vector called the

Hertz vector represented by U. The electric and magnetic fields radiated by a Hertzian

dipole are derived from the following expressions (Budden, 1961).

02U 1
E = -p + -V(V U) (3-24)

H = ( p)Vt x U (3-25)


3.4.2 Modes in the Waveguide

If a half-dipole is placed near the Earth's surface (like a thundercloud) and it was

said in the previous section that it radiates in a manner very similar to the Hertzian

dipole. This section deals with relative amplitudes and excitation factors of the various









waveguide modes excited by the source assuming that the ionosphere is a perfect

conductor at a certain height as well as the surface of the Earth as discussed by Budden

in (Budden, 1961). The relative strength of the waveguide mode at a certain distance

from the source is dependent on the orientation of the source and also on the angle of

propagation.

Budden uses the fact that fields created by a source (here a half-dipole) between

two conductors and the reflections due to these conductors is equivalent to the fields

due to the source and its images. For example if there are two conductors at z=0 and

z=h and a source is present at z=0, it is equivalent to having a source at z=0 and image

sources at z=2h, 4h, .... with the conductors removed. This arrangement of the

source and its images is similar to the effect of an optical diffraction grating (Budden,

1961).

Budden observed after solving for the Hertz vector in the above described scenario

that in an ideal parallel plate waveguide vertical sources excite only TEM and TM

waveguide modes whose relative amplitudes are given by :

1
2 -- TEM mode (3-26)
2
(cos 0n)2 cos(kzl sin n) -> TM, mode (3-27)

where z, is the height of the source with the lower boundary of the waveguide (the

surface of Earth) being at z=0. It could also be observed from equation 3-26 that the

TEM mode irrespective of the frequency of propagation has a gain of 1/2. The factor

cos(kzl sin O,) is also called as the excitation factor or the height gain function for the

TM, mode.

In a similar manner it was observed by Budden that horizontal sources excite only

TE waveguide modes in an ideal waveguide with perfectly conducting parallel plate

waveguide, whose relative amplitudes are given below :











(cos 0n) 2 sin(kz1 sin On) TEn mode


In equation 3-28 sin(kzl sin On) is the height gain function for TEn mode.
3.4.3 Reflection Coefficients in the Earth-Ionosphere waveguide

The upper boundary of the Earth-Ionosphere waveguide i.e., the ionosphere

behaves like an anisotropic medium in the presence of the Earth's magnetic field which

results in the fact the TE and TM modes are coupled at this boundary and an incident
TE wave (or a TM wave) produces both TE and TM wave (Budden, 1961). Another way

of looking at this is when an incident wave is polarized with a parallel polarization (or

a perpendicular polarization) the wave reflected from the upper boundary is elliptically
polarized with components that have both parallel and perpendicular polarizations.

This effect can be accommodated for in the reflection coefficients. For the upper

boundary (the ionosphere) the coupling between the modes results in the reflection

coefficient(Ru(0)) no longer remaining a scalar but represented by a 2x2 matrix and

the reflection coefficient lower boundary (the Earth RL(0)) is not a anisotropic medium

resulting in no coupling between the modes and the off-diagonal elements turning zero

(Budden, 1961) with each element in the reflection matrices being a function of the

angle of incidence to the respective boundaries.

The reflection coefficients for both the upper and lower boundaries (Ru(0) and

RL(0)) as given by Budden are given below:


Ru(O) 1= RL(O) 0 (3-29)
jRL _L| R ) 0 LRL )

In the above matrices the left subscript on the elements denotes the incident wave

polarization and the right subscript denotes polarization of the reflected wave.


(3-28)









Due to the anisotropic nature of the ionosphere pure TE and TM modes are not

capable of existing in the waveguide and instead the waveguide is composed of the

modes called quasi-TEM (QTEM), quasi-TE (QTE) and quasi-TM (QTM) modes. The

difference between a TE mode and a TEM mode for example is that the QTE mode

is similar to a TE mode except that QTE mode also has a small axial electric field

component (Budden, 1961). The lower order quasi modes are generally more pure than

the higher order modes.

3.4.4 Mode Equation

As stated in the previous section on parallel plate waveguides, for a mode to exist

in a waveguide it has to satisfy the mode equation (like 3-2). But the boundaries of the

Earth-Ionosphere waveguide are non-ideal and are much more complicated than the

ideal parallel plate waveguide. Moreover the mode equations described in the previous

section (on ideal parallel plate waveguide) do not hold here because of the anisotropic

nature of the ionosphere which allows only the quasi (QTEM, QTE and QTM) modes to

exist. To form the mode equation for the Earth-Ionosphere waveguide Budden uses the

fact that for a mode to exist in any waveguide the uniform plane waves that constitute the

mode must retain their planar fronts upon reflection from the boundaries i.e., the plane

wave reflected once from each boundary (the upper and lower) must be in phase with

the incident plane wave (Budden, 1961).

The fundamental equation of mode theory which satisfies the mode equation for the

Earth-Ionosphere waveguide is given in equation 3-30 shown below:

R/(O)RG() exp(-2ikhsin ) = I (3-30)

where I is the identity matrix. Each angle of incidence 0, that satisfies equation 3-30

defines an individual mode at a certain frequency. The expression for R/ is complicated

and is difficult to solve analytically. But if the Earth and ionosphere are treated as perfect

conductors equation 3-30 would simplify to an equation similar to 3-2).









Another factor that is effected by the nature of the Earth-Ionosphere waveguide is

the height gain function described in section 3.4.2 for an ideal parallel plate waveguide.

However it can be observed that the height gain functions can be calculated with the

knowledge of the mode angles (,O) and the reflection coefficients (RG and mathbfRi).
The reader is referred to (Pappert and Ferguson, 1986) for a good summary of of

the height gain functions that were formulated by Budden. Additionally (Pappert and
Ferguson, 1986) also calculate the height gain functions for different source orientations

and altitudes and also for different field components. These height gain functions vary

depending on the field components, orientation of the dipole and the height of the dipole.
These functions contain the modified Henkel functions unlike the sines and cosines as in

the ideal parallel plate waveguide. The general equation for the output field F with all the

factors taken into consideration is given in (Pappert and Ferguson, 1986) and (Cummer,
1997) as:

ik II/ i
F = C(F) exp( ) AtnAmexp(-ikxsin(O,)) (3-31)

where C(F) is po if F is a component of the magnetic field and C(F) is /- if F is

a component of the electric field and At, and Am are called the transmitter and receiver
excitation factors respectively, these contain the height gain functions.

The values of At, and Am are derived in (Pappert and Ferguson, 1986) for various
orientations of the dipole. For example if an electric dipole is oriented at some angle 7 to

the z-axis and at an angle 0 to the direction of propagation (x-axis) at an altitude zt (the

Earth-Ionosphere waveguide is illustrated in Figure 3-2), the transmitter excitation factor
At, is given by (Pappert and Ferguson, 1986) as:

At, = -T sin(O ) cos(y) fi(zt) + T34 sin(y) cos(O)f2(zt) + T sin(y) sin() f3(Zt) (3-32)

where the variables used in the above equation like r, ~- -3, f f, andf3 are

defined in (Pappert and Ferguson, 1986).









3.4.5 Correction for the Curved Nature of the Earth-Ionosphere Waveguide

Another important factor that makes the Earth-ionosphere waveguide substantially

different from the ideal parallel plate waveguide is the curved nature of Earth. Especially

at large distances (which is the case in this thesis) the curvature of the Earth has

a profound effect. In free space the field attenuation due to energy spreading is

proportional to r-1, r being the distance from the source. This corresponds to a r-2

factor for the wave power. But for a parallel plate waveguide this spreading factor is

reduced to r 2 because 'r' now is the 2-d distance from the source (Wood, 2004). For

a spherical waveguide of radius 'R' the corresponding attenuation factor would be

(R sin()) 2 where 'x' is the great circle distance between the source and the receiver

(Budden, 1961). It could be observed that this tends to R 2 as R co.

The mode equation given by equation 3-30 must also be modified due to the effect

of this curvature because the mode angles are valid only for parallel surfaces and not

spherical shells like the Earth. There were a few methods employed in literature to deal

with this problem but the most commonly employed method was described in (Richter,

1966). In this paper a co-ordinate transformation method was introduced that converts a

cylindrical co-ordinate system into parallel by modifying the refractive index as a gradient

n2d = exp(R) so that the rays representing the plane waves bend upwards instead of
traveling in straight lines.

3.5 Long Wavelength Propagation Capability (LWPC)

LWPC is a collection of FORTRAN programs which enable the implementation

of two dimensional waveguide propagation formulation along the great circle path

between a transmitter and a receiver. This program applies the implements the concept

of propagation of ELF, VLF and LF radio waves to the Earth-Ionosphere waveguide, this

program sets up the calculation of mode parameters along the selected propagation

paths for user defined operating areas (Ferguson and C.H.Shellman, 1989). These

set of programs operate separately or in sequence to generate results as per the









requirement of the user. This was developed over many years at the Naval Ocean

Systems Center (NCCOSC/NRaD) (Ferguson and C.H.Shellman, 1989). The code has

three important parts called PRESEG, MODEFNDR and FASTMC each of which is

described below.

3.5.1 PRESEG

PRESEG is the FORTRAN program which segments the propagation path between

the transmitter and receiver based on the ionospheric, ground and some other

parameters, some of which are taken as input. PRESEG determines the necessary

waveguide parameters and formats them properly for input to the next stage of the

program. Some parameters like magnetic field of Earth, permittivity and conductivity

of Earth over the propagation path are taken from built in models and files based on

experimental study of these parameters like (Hauser and F.J.Rhoads, 1969). This thesis

employs a homogenous ionosphere throughout the entire propagation the details of

which are given in the next section. When the inhomogeneities are considered the

waveguide is segmented into a number of slabs and slab boundaries are placed where

there is a change in the parameters like ionospheric profile, ground conductivity etc

(Cummer, 1997).

3.5.2 MODEFNDR

MODEFNDR is an important component of the propagation model and is a

FORTRAN program which determines the eigen solutions for a horizontally homogenous

waveguide/slab (Ferguson and C.H.Shellman, 1989). It takes the waveguide parameters

from PRESEG as input and searches for angles inside a predefined region that satisfy

the mode condition 3-30. To calculate the necessary mode constants needed for

determining the fields in the waveguide, the reflection coefficients for the ionosphere

must be solved for a general electron density profile, ion density, collision frequency

profile and angle of incidence, this is done by MODEFNDR by assuming that for a fixed

angle of incidence the field components vary in x-direction and a =0 (Cummer, 1997).









The excitation factors which are needed to determine the final field strengths of each

mode are also calculated by this program. The output of this program is given as the

input to FASTMC.

3.5.3 FASTMC

The propagation path is divided into horizontally homogeneous waveguides/slabs,

the signal strength of the electromagnetic field along a path is determined using

the mode solutions for each of the homogenous slab by the FASTMC (Ferguson

and C.H.Shellman, 1989). FASTMC is a simplified version of another FORTRAN

program called FULLMC which is a mathematically rigorous model which does full

wave calculations which makes this program quite slow in execution (Ferguson and

C.H.Shellman, 1989). This is where FASTMC comes in handy and is an approximate

model and runs much faster than the FULLMC and produces comparable results. The

output of FASTMC is the magnitude in DB over 1 pV/m field strength and phase in

degrees. A correction factor of 4.1887x10-6//fexp(i//4) must be applied to the output

of FASTMC to make it equivalent to a vertical dipole (Cummer, 1997), where II is the

current moment of the radiating dipole and f is the frequency.

3.5.4 Implementation in LWPC

The fields along a given propagation path in the Earth-Ionosphere waveguide can

be calculated using the LWPC code with a set of required parameters given as input.

LWPC uses the two dimensional propagational model developed by Budden (Budden,

1961) known as the waveguide mode theory, Figure 3-2 shows the Earth-Ionosphere

waveguide. It can be observed from the Figure that the two dimensions are x and z,

with x being the direction of propagation along the great circle path and z being the

altitude and all the properties of ionosphere and ground assumed to be constant in the

y-direction.

There are a set of parameters that need to be input in order to set LWPC to run.

These parameters are entered using a model file, after all the required parameters are





























Figure 3-2. Earth-Ionosphere Waveguide


entered it is necessary to give these parameters as inputs to the program PRESEG

which itself serves as an input to the programs MODEFNDR and FASTMC. Hence a

script is written which inputs the correct parameters in a specified manner to each of the

programs and executes them in an orderly manner.

Some parameters which are to be input to the model file and used in this thesis are

described below, for a detailed list of various parameters and their default values the

reader is referred to (Dermikol, 1999).

* freq frequency in KHz, default value is 23.4 KHz

* power radiated power in Kw, default value is 1 Kw

* trlat, trlong coordinates of the transmitter in degrees west and degrees north,
default values are 158.150W and 21.410N respectively

rclat, rclong coordinates of receiver in degrees west and degrees north, default
values are 0W and 0N respectively

maxalt highest altitude of the ionospheric profile to be considered for calculation
purposes in km, default value is 90 km









* file containing the electron density profiles upto the specified maxalt value

* file containing the information about collision frequency

PRESEG uses the model file with the required parameters and segments the

propagation path according to the information in this model file and certain automatic

segmentation rules such as the in built conductivity map of Earth and model of Earth's

magnetic field the segmentation information is then stored in output files which are then

used by the programs MODEFNDR and FASTMC (Dermikol, 1999).

MODEFNDR uses the information in the model input file related to electron density

profiles and the output from PRESEG to obtain the solution to the mode equation 3-30.

To find solutions to the mode equation it needs to calculate the reflection coefficients of

the ionosphere and an effective reflection height. It then calculates the attenuation rate,

phase velocity, initial excitation, height gain functions for each mode using the values of

reflection coefficients.

FASTMC uses the outputs from MODEFNDR and PRESEG to calculate the mode

conversion coefficient matrices at different slabs created by PRESEG. Figure 3-3 shows

the flowchart pertaining to the execution of LWPC.

3.6 Parameters Required to Calculate the Sferic Propagation Model

As understood from the discussion in the previous section LWPC employs a

single-frequency model. To model ELF propagation LWPC solves the time-harmonic

propagation problem using the waveguide mode theory of wave propagation (Budden,

1961). There are certain parameters that need to be calculated as inputs to use the

model, parameters like the ground and ambient magnetic field are automatically

included in LWPC but certain other parameters like the ionospheric electron density

profiles and the Current Moment waveform in the required frequency range which are

discussed in the following sections need to be provided.











Model Input File

Script controlling
execution of
programs and their i/p

PRESEG


output 1 from PRESEG output 2 from
to MODEFNDR PRESEG to FASTMC

MODEFNDR

Output from
MODEFNDR to
FASTMC



FASTMC


Final o/p Fields along the
path





Figure 3-3. Flow chart showing the execution of LWPC


3.6.1 Ionospheric Electron Density Profiles

Electron densities at a certain altitude are an important factor in modeling the sferic

propagation. The profile was calculated from IRI (International Reference Ionosphere).

Though the ionosphere varies from one region to another and from time to time a

homogenous ionosphere was assumed through out the propagation path in this thesis.

To understand the effects of different ionospheric conditions on sferic propagation

four different ionospheric electron density profiles were calculated. Two of the profiles

were calculated for daytime ionospheric conditions and two for nighttime ionospheric

conditions as shown in Figure 3-4 for altitudes up to 300 km These profiles were

calculated using data from IRI at the coordinates 00 and 400. One of the daytime

ionospheres was at lower electron density values while the other was at higher electron









density values, the nighttime ionospheres differ by the fact that one of them has a

valley at 100-150 Km while the other does not. The valley occurs at the E-region of the

nighttime ionosphere due to the decrease in electron density values and is a common

phenomena at nights.


-2 -1 0 1 2 3 4 5 6
Log of Electron Density (Cm 3)


Figure 3-4. Representative electron density profiles


The International Reference Ionosphere (Bilitza, 2001) is an international project

sponsored by the Committee on Space Research (COSPAR) and the International

Union of Radio Science (URSI). IRI gets its data from lonosodes, Alouette topside

sounders, Incoherent Scatter Radars and in situ instruments on several satellites and

rockets. It is the international standard for terrestrial ionosphere since 1999.

3.6.2 Current Moment Waveform of a Lightning Strike

The other parameter that is needed to model the ELF sferic propagation using

LWPC is current moment waveform in the required frequency range. As mentioned in

the previous sections the LWPC gives a time-harmonic (single frequency) solution and











so it is required to get the current moment waveform as a function of frequency (i.e., in

frequency domain).

Previous theoretical studies of ELF sferics (Cummer, 1997),(S.A.Cummer and

U.S.Inan, 2000) etc have assumed an ideal impulse lightning discharge and modeled the

corresponding current moment waveform. Although this is a decent approximation there

are certain spectral features which cannot be modeled theoretically and moreover every

lightning strike differs from the other. This makes it difficult to model sferics accurately.In

this work the sferics radiated from rocket triggered lightning are being modeled, the

advantage with rocket triggered lightning is the availability of very accurate data about

the lightning.

Figure 3-5 shows the current waveform that has been used in this thesis. It

represents the current flowing at the base of the lightning channel during the rocket

triggered lightning experiment conducted at Camp Blanding on 29th March 2009.



3000

2500
UT DATE
29-Mar-2009
2000
UT TIME
01 56 12780
1500

1000
E
500-

C 0-

-500

-1000

-1500

-2000
0 02 04 06 08 1 12 14 16 18 2
Time (s)



Figure 3-5. Current vs Time waveform from rocket triggered lightning



The height of the lightning channel is assumed to be 7.5 Km in this work.









CHAPTER 4
MODELING ELF SFERICS

This chapter describes the modeling of ELF sferics after all the required input

parameters discussed in the previous chapter are gathered. All the modeling work

presented in this chapter is done using a set of computer programs called LWPC which

is based on a single frequency propagation model (Budden, 1961). First the sferics are

modeled assuming a homogeneous ground and a homogeneous ionosphere throughout

the propagation path and then a more complicated case with a inhomogeneous ground

profile is considered.

The model completes its calculations in the frequency domain and the output is

a spectrum of the sferic as a function of frequency. The only mode propagating is the

QTEM mode which does not have a cut-off frequency and the attenuation rate as a

general trend increases steadily with the frequency (although certain exceptions were

observed at some frequencies) causing the mode to die off eventually at around 1.7

KHz.

4.1 Homogeneous Waveguide

ELF sferics in the range of frequencies 10-500 Hz (with the difference between

each frequency sample being 10 Hz) are modeled assuming a homogeneous ground

profile of conductivity 10-2 S/m and a relative permittivity of 15. A nighttime ionospheric

profile shown in Figure 4-1 is taken and is assumed to be homogeneous throughout the

propagation path, three different propagation paths of distances 1000 km, 2000 km and

3000 km are considered. An impulse lightning current waveform similar to the one used

in (Cummer, 1997) and (S.A.Cummer and U.S.Inan, 2000) is employed here, this case is

similar to the modeling presented in (S.A.Cummer and U.S.Inan, 2000).

The spectrum shown in Figure 4-2 are the amplitudes of transverse horizontal

magnetic field By at the specified distances. It can be observed that the results

presented are similar to the ones obtained in (S.A.Cummer and U.S.Inan, 2000) for













300



250



200
E


150



100



50
-2 -1 0 1 2 3 4 5 6
Log of Electron Density (Cm 3)


Figure 4-1. Representative nighttime ionosphere



the nighttime ionosphere. Figure 4-3 shows the same spectrum shown in Figure 4-2 in

decibel scale.


x 109 Cummer Nighttime Ionosphere Highpass filtered


6-


5-


4-
E-

3-


2





0 50 100 150 200 250 300 350 400 450 500
Freq(Hz)



Figure 4-2. ELF sferic spectra of homogeneous ground in linear scale



The spectra are passed through a high-pass filter of cut-off frequency 30 Hz.




59














10-

'- 0
0-

-10- distance 1000km
Distance 2000km
S- distance- 3000km
-20-

E
< -30

-40-

-50
0 50 100 150 200 250 300 350 400 450 500
Frequency(Hz)


Figure 4-3. ELF sferic spectra of homogeneous ground in decibel scale


4.2 Inhomogeneous Ground

In this case a inhomogeneous ground is considered with conductivity varying from

10-2 to 10-3 S/m. The rest of the input parameters are the same as those assumed

in the previous case and an arbitrary propagation path of distance around 2000 Km is

considered. The ELF spectra are modeled in the frequency range of 10-500 Hz(with the

difference between each frequency sample being 1 Hz)

The spectra are passed through a high-pass filter of cut-off frequency 30 Hz in a

manner similar to the previous case. The Figure 4-4 shows the amplitude of transverse

horizontal magnetic field By computed compared with the amplitude calculated in the

previous case for a homogeneous ground covering a distance of 2000Km. Figure 4-5

shows the comparison of amplitudes of the two spectra in decibel scale.

It could be observed that the results obtained in both the cases are similar

except for some differences like the amplitude of spectra calculated assuming an

inhomogeneous ground is less than the amplitude calculated using homogeneous

ground, this assumption is valid only for short distances which have a fairly similar















x 10-


Inhomogenous ground
Homogenous ground


50 100 150 200 250 300
Frequency(Hz)


350 400 450 500


Figure 4-4.


Comparison of ELF sferic spectra for inhomogeneous and homogeneous

ground (distance-2000Km)


-^fV


Inhomogenous ground
homogenous ground


0 50 100 150 200 250 300
Frequency(Hz)


350 400 450 500


Figure 4-5. Comparison of ELF sferic spectra for inhomogeneous and homogeneous
ground (distance-2000Km) in decibel scale


-2


t 2

E
<15





1


0









ground throughout the propagation path and this approximation does not produce

accurate results when the propagation path has huge variations in conductivity due to

the presence of both land and sea in the propagation path. Such a situation is dealt in

the next section.

4.3 Modeling of ELF sferics Propagating from Camp Blanding to McMurdo
Station

In this case a complicated inhomogeneous ground is considered .The source of

the sferic- the lightning discharge is at Camp Blanding,Florida (29.940N and -82.030W)

and the receiver is at McMurdo Station, Antarctica (-77.880N and 166.730 W) with

a total propagation distance of 13740 Km. The electron density values specified in

the previous chapter are used and the effect of ions is neglected. The source current

moment waveform presented in the previous chapter is used assuming a vertical

dipole discharge. LWPC calculates the amplitude and phase for any orientation of

the hertzian dipole, to make the sferic waveform equivalent to that caused due to the

lightning discharge used in this thesis, the output of LWPC should be convolved with the

current-moment waveform, to do that the current-moment waveform was converted into

frequency domain and it was multiplied with the output of LWPC in linear scale.

The current waveform is taken form the rocket triggered lightning conducted at

Camp Blanding, thereby giving more realistic waveform compared to some previous

models (Cummer, 1997) which use theoretically modeled return stroke of lightning. The

lightning discharge used in the calculations presented in this thesis occurred on March

29,2008.

The sferic spectra calculated in this thesis are in the frequency band of 45-500Hz

assuming an inhomogeneous ground with conductivity varying from 10-4 to 4 S/m and a

homogenous ionosphere throughout the propagation path. Figure 4-6 shows the great

circle path of propagation of the sferic form Florida to Antarctica.









The output calculated from LWPC exhibited some sudden jumps with the change

in conductivity of the ground. This phenomenon could not be explained in this thesis

and the output of LWPC was adjusted manually such that the variation of amplitude

with distance looked smooth without sudden jumps, this is shown more clearly in the

next chapter. The sferic waveforms shown in this thesis were calculated assuming a

Hermitian symmetry (S.A.Cummer and U.S.Inan, 2000).

All the plots corresponding to the same ionosphere are in the same color, with black

representing nighttime ionosphere with a valley, blue representing daytime ionosphere

type, green representing nighttime ionosphere without a valley and red representing

daytime ionosphere type 2.


Figure 4-6. Propagation Path of the Sferic from Florida to Antarctica (Great Circle)










Four different ionospheres shown in the previous section are considered in this

case.

4.3.1 Nighttime Ionosphere With a Valley

Figure 4-7 below shows the nighttime ionosphere with a valley at 100-150 km. The

valley is the region of the ionosphere where there is a decrease in the electron density

values compared to other regions of the ionosphere.


300


250


200
E


150


100 -


50
-3 -2 -1 0 1 2 3 4 5 6
Log of Electron Density (Cm 3)


Figure 4-7. Nighttime ionosphere with a valley


Figure 4-26 shows the current waveform employed here in calculating the sferic

spectrum and waveform, the current waveform as observed is for a time-period of one

second.

Figure 4-9 shows the direct output of LWPC without convolving it with lightning

current moment waveform.

The valley usually occurs in the E-region of the ionosphere at a height of 100-150

Km, this region of the ionosphere has a significant affect on the sferic waveform.Figure

4-10 shows the spectrum of By that would be observed at the receivers in a decibel

scale and Figure 4-11 shows the spectrum of the sferic (By) in a linear scale (Tesla),
























a)
E
. 1000
a)
3
o


1000


2000
0 01 02 03 04 05 06 07 08 09
Time (Sec)


Figure 4-8. Current Waveform employed in calculations


I-
0
E
a)
>o
oD


100-


80


\ l4A


40
E

20


0-
0


50 100 150 200 250 300 350 400 450 500
Frequency (Hz)


Figure 4-9. LWPC output for nighttime ionosphere with a valley


j -


~lrv~hr-~a ~1,1


,,










it could be observed from Figure 4-10 that this region produces certain resonance like

effects and the waveform is a little complicated compared other waveforms discussed in

the subsequent sections.


100 ,


" 60
40


S40
0 2
0

a
Q 0


N.


0 50 100 150 200 250 300 350 400 450 500
Freq(Hz)


Figure 4-10. Modeled ELF spectrum in
ionosphere with a valley


decibel scale (over 1 nanotesla) for nighttime


Figure 4-12 shows the sferic waveform (the time domain signal)for the nighttime

ionosphere considered in this section.

4.3.2 Daytime Ionosphere Type 1

Figure 4-13 shows the daytime ionospheric electron density values. The daytime

ionosphere is not very complicated compared to the nighttime ionosphere.

Figure 4-26 shows the current waveform employed here in calculating the sferic

spectrum and waveform, the current waveform as observed is for a time-period of one

second.

Figure 4-15 shows the direct LWPC output for this ionosphere without convolving it

with current moment waveform.

















x 105


4.5

4

3.5

3

2.5
E
2

1.5

1


C
0 50 100 150 200 250 300 350 400 450 500
Freq(Hz)



Figure 4-11. Modeled ELF spectrum in linear scale for nighttime ionosphere with a valley









x 10
5


0 01 02 03 04 05 06 07 08 09
seconds



Figure 4-12. Modeled ELF sferic waveform for nighttime ionosphere with a valley
































2 2.5 3 3.5 4 4.5
Log of Electron Density (Cm 3)


Figure 4-13. Daytime ionosphere Type 1


5.5 6






















1K


0 01 02 03 04 05 06 07 08 09
Time (Sec)


Figure 4-14. Current Waveform employed in calculations


i~J"""C











120

100

80

60
E 40-

20


-20

-40-

-60 50------
0 50 100 150 200 250 300 350 400 450 500
Frequency(Hz)


Figure 4-15. LWPC output for daytime ionosphere type 1


Figure 4-16 shows the spectrum of By that would be observed at the receivers in

a decibel scale and Figure 4-17 shows the spectrum of the sferic (By) in a linear scale

(Tesla) for the daytime ionosphere, the sferics obtained from daytime ionosphere is not

as complicated as the nighttime ionosphere with a valley, with the amplitude decreasing

with increase in frequency. Figure 4-18 shows the sferic waveform for this spectrum.

4.3.3 Nighttime Ionosphere Without a Valley

Figure 4-7 below shows the nighttime ionosphere without a valley at 100-150 km.

Figure 4-26 shows the current waveform employed here in calculating the sferic

spectrum and waveform, the current waveform as observed is for a time-period of one

second.

Figure 4-21 shows the direct LWPC output for the ionosphere shown in the previous

figure without convolving it with current moment waveform.

Unlike the previous nighttime ionosphere this ionosphere has no valley.Figure 4-10

shows the spectrum of By that would be observed at the receivers in a decibel scale and

Figure 4-11 shows the spectrum of the sferic (By) in a linear scale (Tesla), it could be

observed from Figure 4-10 that there are no resonance like phenomena as observed




















F 40
Co
20

0
m
a- -20
E


0 50 100 150 200 250 300 350 400 450 500
Freq(Hz)


Figure 4-16. Modeled ELF spectrum waveform in decibel scale (over 1 nanotesla) for
daytime ionosphere type 1


x 10-5
1.6-


1.4

1.2

1

0.8
E
0.6

0.4

0.2


0 50 100 150 200 250 300
Freq(Hz)


350 400 450 500


Figure 4-17. Modeled ELF spectrum in linear scale for daytime ionosphere type 1


)N



















x 10-
3

3

25

2

I 15



E 05

0






-1 5
0 01 02 03 04 05 06 07 08 09
seconds



Figure 4-18. Modeled ELF sferic waveform for daytime ionosphere type 1












300




250




200

E

150-




100-




50
-3 -2 -1 0 1 2 3 4 5 6
Log of Electron Density (Cm 3)



Figure 4-19. Nighttime ionosphere without a valley



















4000



3000



2000


E
< 1000



0



-1000



-2000
0 01 02 03 04 05 06 07 08 09
Time (Sec)



Figure 4-20. Current Waveform employed in calculations












120


100


80


60


40


20


-20----------------------------------------
20 50 100 150 200 250 300 350 400 450 500




Figure 4-21. LWPC output for nighttime ionosphere without a valley













in the previous nighttime ionosphere (with the valley), thus showing the valley has a


great impact on the shape of the sferic. Figure 4-24 shows the sferic waveform for the


spectrum calculated in this section.



100


80


60
I-




20



20
-20-


-40LI I
0 50 100 150 200 250 300
Freq(Hz)


350 400 450 500


Figure 4-22. Modeled ELF spectrum in decibel scale (over 1 nanotesla) for nighttime
ionosphere without a valley




x 10



15






E
<

05


50 100 150 200 250 300
Freq(Hz)


350 400 450 500


Figure 4-23. Modeled ELF spectrum in linear scale for nighttime ionosphere without a

valley











x 10-
15


05


o-
a
--05
E




-15

-2
0 01 02 03 04 05 06 07 08 09 1
seconds


Figure 4-24. Modeled ELF sferic waveform for nighttime ionosphere without a valley


4.3.4 Daytime Ionosphere Type 2

Figure 4-25 shows the daytime ionospheric electron density values, this ionosphere

has higher electron density values compared to the previous daytime ionosphere

discussed in the previous section.

Figure 4-26 shows the current waveform employed here in calculating the sferic

spectrum and waveform, the current waveform as observed is for a time-period of one

second.

Figure 4-27 shows the direct LWPC output for this ionosphere without convolving it

with current moment waveform.

Figure 4-28 shows the spectrum of By that would be observed at the receivers

in a decibel scale and Figure 4-17 shows the spectrum of the sferic (By) in a linear

scale (Tesla) for the daytime ionosphere(with higher electron density values), the

sferics obtained from this ionosphere are somewhat lower in amplitude than the

previous daytime ionosphere which could be attributed to the higher electron density






































1 1.5 2 2.5 3 3.5 4
Log of Electron Density (Cm 3)


Figure 4-25. Daytime ionosphere Type 2


4.5 5 5.5


0 01 02 03 04 05 06 07 08 09
Time (Sec)



Figure 4-26. Current Waveform employed in calculations


h~"l"






























0 50 100 150 200 250 300 350 400 450 500
Frequency(Hz)


Figure 4-27. LWPC output for daytime ionosphere type 2


values. Figure 4-30 shows the sferic waveform for the spectra calculated using daytime

ionosphere type 2.


80


0 50 100 150 200 250 300
Freq(Hz)


Figure 4-28. Modeled ELF spectrum in
ionosphere type 2


350 400 450 500


decibel scale (over 1 nanotesla) for daytime


Thus it could be observed from the above spectra that ionosphere plays a

significant role in determining the shape of the sferic spectrum, more importantly it


















x 106
12


08



06
E


04



02-




0 50 100 150 200 250 300 350 400 450 500
Freq(Hz)



Figure 4-29. Modeled ELF sferic waveform in linear scale for daytime ionosphere type 2










x 10-8



15-
15



05




E
< -05-





-1 5 -
15



0 01 02 03 04 05 06 07 08 09
seconds



Figure 4-30. Modeled ELF sferic waveform for daytime ionosphere type 2










is the E-region of the ionosphere that plays a significant role unlike for the VLF waves

where the D-region of the ionosphere plays a vital role (Cummer, 1997). This data could

be used to determinethe noise floor of the receivers that are used in Antarctica to detect

the sferics.

4.4 Effects of Different Components of Current on the Sferic Waveform

This section deals with the effects of different components of current on the sferic

waveform, to do that the current waveform is passed through different rectangular

windows each of which selects a particular component and removes the other

components by making them zero. By doing this the time period of the current waveform

still remains the same but only the selected component remains and the rest of the

waveform becomes zero.

Figure 4-31 shows the different components of the current waveform used in this

thesis,it could be seen from the figure that this particular current waveform has an Initial

Continuous Current (ICC) phase followed by five return strokes.




0 ICLRT Rocket-Triggered Lightning Current 29 March 2009


5 Initial Stage R R3
-250- S I-. S3
_25 00- .T : i, l R -
153 15 5 15 7 15.9 161 16 3
zo20 Time (seconds) after 0156:00 UT
.2000 ---- -- ---
SRetrn Srok4 -- .10 MH
S1000- Bipolar Cotiing Current 500 H

-loo- --:---- i- --- ---- ------ --~~5c~ -- -- ----
-200
16.06 16.08 16.10 16.12 16.14 16.16
Time (seconds) after 0156:00 UT




Figure 4-31. Components of the Current Waveform Used


Each of these components are convolved with LWPC such that only the effects of

that particular component are observed, the figures below show each of the component









of current and its resultant sferic waveform for nighttime ionosphere with a valley as an

example.

Figure 4-32 shows the ICC component of the current and Figure 4-33 shows the

resultant sferic waveform.


4000

3000

2000



0)
S1000

o


ICC Component of current




i i iA i i


-1000

-2000


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)

Figure 4-32. ICC Component of the Current Waveform Used


ICC component


-8
0 01 02 03 04 05 06 07 08 09 1
seconds

Figure 4-33. Resultant Sferic Caused due to the ICC Component of Current


-













Figure 4-34 shows the return stroke 1 of the current and Figure 4-35 shows the


resultant sferic waveform.


Return Stroke-1 Component of current
4000


3000



2000


E 1000-

0




-1000



-2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)



Figure 4-34. Return Stroke 1 of the Current Waveform Used




x 108 RS1 component
3

2-

















0 01 02 03 04 05 06 07 08 09
0-

E
< 2

-3

-4


-5 0i1 0f2 0f3 0f4 0f5 0f6 0f7 0f8 0f9
seconds



Figure 4-35. Resultant Sferic Caused due to the Return Stroke 1 of Current




Figure 4-36 shows the return stroke 2 of the current and Figure 4-37 shows the


resultant sferic waveform.


















4000



3000



2000



1000



0



-1000



-2000


Return Stroke-2 Component of current


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)



Figure 4-36. Return Stroke 2 of the Current Waveform Used


RS2 component


1 1 1 1 1 1 1 1 1 1 1 1
0 01 02 03 04 05 06 07 08 09 1
seconds



Figure 4-37. Resultant Sferic Caused due to the Return Stroke 2 of Current












Figure 4-38 shows the return stroke 3 of the current and Figure 4-39 shows the

resultant sferic waveform.


Return Stroke-3 Component of current
4000


3000


2000


E 1000-


0


-1000


-2000


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time (sec)



Stroke 3 of the Current Waveform Used


RS3 component


2-




0-


E

-2-


-3


0 01 02 03 04 05 06 07 08 09
seconds


Figure 4-39. Resultant Sferic Caused due to the Return Stroke 3 of Current



Figure 4-40 shows the return stroke 4 of the current and Figure 4-41 shows the


resultant sferic waveform.


Figure 4-38. Return

















Return Stroke-4 Component of current


-1000



-2000


0 0.1 0.2 0.3 0.4 0.5 0.6
Time (sec)


0.7 0.8 0.9


Figure 4-40. Return Stroke 4 of the Current Waveform Used


RS4 component


0 01 02 03 04 05 06 07 08 09
seconds



Figure 4-41. Resultant Sferic Caused due to the Return Stroke 4 of Current












Figure 4-42 shows the return stroke 5 of the current and Figure 4-43 shows the


resultant sferic waveform.


4000


3000


2000


E 1000

0
5


Return Stroke-5 Component of current


-1000


-2000


0 0.1 0.2 0.3 0.4 0.5 0.6
Time (sec)


0.7 0.8 0.9 1


Figure 4-42. Return Stroke 5 of the Current Waveform Used


RS5 component


0 01 02 03 04 05 06 07 08 09
seconds



Figure 4-43. Resultant Sferic Caused due to the Return Stroke 5 of Current











4.4.1 Effects of Current Components Different lonospheres

This section demonstrates the effects of the current components on the sferic

waveforms under different ionospheres shown in the previous sections. In each of the

following figures, the sferic waveform which results due to the entire current waveform is

shown on which are overlayed the sferic waveforms due to each individual component.

The sferic waveforms due to each individual component are overlayed only on the

portion of the complete waveform where it has significant effect, the rest of the portion is

clipped for a lucid view.

Figure 4-44 shows the sferic waveform with all the components laid out for the

nighttime ionosphere with a valley.


x 10-7

Total Current
4 ICC component
Return Stroke 1
Return Stroke 2
Return Stroke 3
Return Stroke 4
2 -Return Stroke 5



0
E



-2

-3

-4
0 01 02 03 04 05 06 07 08 09 1
Time (Sec)


Figure 4-44. Sferic Waveform and Different Components-Nighttime Ionosphere With a
valley



Figure 4-45 shows the sferic waveform with all the components laid out for the

daytime ionosphere type 1.

Figure 4-46 shows the sferic waveform with all the components laid out for the

nighttime ionosphere without a valley.















x 107
35-


25r


1 5


Total Current
ICC Component
Return Stroke 1
Return Stroke 2
Return Stroke 3
Return Stroke 4
Return Stroke 5


05v


-05v


0 01 02 03 04 05
Time (Sec)


06 07 08 09


Figure 4-45. Sferic Waveform and Different Components-Daytime Ionosphere Type 1






x 10 7
151 --I


0


-05 -
Total Current
ICC Component
-1 Return Stroke 1
Return Stroke 2
Return Stroke 3
1 5Return Stroke 4
Return Stroke 4
Return Stroke 5
-2 -


-25
0 01 02 03 04 05 06
Time (Sec)


07 08 09 1


Figure 4-46. Sferic Waveform and Different Components-Daytime Ionosphere Without a

valley


w











Figure 4-47 shows the sferic waveform with all the components laid out for the

daytime ionosphere type 2.


x10-8
Total Current
ICC Component
1 5 Return Stroke 1
Return Stroke 2
Return Stroke 3
Return Stroke 4
Return Stroke 5 1


01 02 03 04 05 06 07 08 09 1
Time (Sec)


Figure 4-47. Sferic Waveform and Different Components-Daytime Ionosphere Type 2



It could be observed from the above figures that the ICC component does not have

a significant effect on the sferic waveform, neither do return strokes one and two. Return

Strokes three and four have the most significant effect on the waveform. Although the

amplitude of return stroke 3 is much larger than return stroke 4 they have similar effect

on the waveform, this is because of the continuous current in return stroke 4 which has

greater impact on the sferic waveform.









CHAPTER 5
SUMMARY AND SUGGESTIONS FOR FURTHER WORK

5.1 Summary

In this thesis the theoretical modeling of ELF radio atmospherics in the frequency

range of 45-500Hz was carried on under different ionospheric conditions using a general

theoretical formulation for the propagation of single frequency ELF/VLF signals in the

Earth-Ionosphere waveguide developed by Budden (Budden, 1961) and implemented in

a computer code (Ferguson and C.H.Shellman, 1989).

The path of propagation was taken from Camp Blanding, Florida to McMurdo

Station in Antarctica. The modeling is done assuming a homogeneous ionosphere

throughout the propagation path but a realistic ground conductivity profile with

conductivity of the Earth's surface varying from 10-3 to 4 S/m. The conductivity of land

was varying from 10-2 to 10-3 depending on the geographic location, the conductivity

of ice was 10-4 and the conductivity of sea was taken as 4 S/m which are very realistic

values. Different ionospheric profiles were used to study the dependence of propagation

characteristics of the ELF waves on the ionosphere. It was observed that the amplitudes

of the ELF waves were higher for the nighttime ionospheric conditions compared to

daytime ionospheric conditions due to lesser electron density values of the nighttime

ionosphere. For the nighttime ionosphere the it was observed that the E-region of the

ionosphere played an important role in determining the characteristics of the wave,

especially the presence or absence of the valley at 100-150 km made a significant

difference.

It was shown in the previous studies (Cummer, 1997) that the ELF sferics generated

by a lightning are dependent on the current moment of the lightning. In this thesis the

sferics generated due to rocket triggered lightning are considered and the actual current

waveforms of rocket triggered lightning conducted at Camp Blanding, Florida are taken

thereby providing a more realistic estimate of the characteristics of the sferics, unlike the











previous studies (Cummer, 1997) which have assumed a modeled impulsive lightning

discharge.

5.2 Suggestions for Further Work

5.2.1 Jumps in the amplitude

When the amplitude of the sferic was plotted across the distance of propagation,

it was observed that there were uneven jumps in the amplitude whenever there was

a change in the conductivity of earth, the reason could not be explained and to rectify

that the amplitudes were made smoother and continuous manually as demonstrated in

Figure 5-1.


150

140 Original output from LWPC
S Modified output
130

120

5110 -

S100

90

80 -

70

0 2000 4000 6000 8000 10000 12000 14000
Distance (Km)


Figure 5-1. Variations in the amplitude of the sferic across the path of propagation



5.2.2 Modeling at Lower Frequencies Below 45Hz

The lowest frequency that could be modeled in this thesisis 45Hz due to limitations

of the MODEFNDR program. To get the MODEFNDR program to work in the ELF

frequencies certain settings have to be changed to set it up to work in the iterative mode.

In the iterative mode an initial guess for the Eigen angles is given and the program

iterates on them to find the final solution within a specified range of tolerance. The









program finds the eigen angles that satisfy the mode condition in each horizontal

slab and then couples each slab (a horizontal slab is a portion of the path where the

waveguide parameters like the ground conductivity etc remain constant and whenever

there is a change in any of the parameters beyond a specified limit a new slab is

formed).

The MODEFNDR uses the same initial guess for every slab and there is a huge

variation in certain waveguide parameters in the selected path of propagation and the

eigen angles that satisfy the mode condition in one slab might not satisfy the mode

condition in other. To model the sferics for this chosen path below 45 Hz this problem

has to rectified.

5.2.3 Modeling Using a more Realistic Inhomogeneous Ionosphere

All the sferics presented in this thesis are modeled under the assumption of a

homogenous ionosphere throughout the propagation path. Although this is a reasonable

assumption for smaller propagation distances, the distances considered in this thesis

are long and the propagation path should include both the daytime and nighttime

ionospheres. Moreover even for shorter distances a homogenous ionosphere might

not always reproduce some of the fine spectral details that could be seen in observed

sferics (Cummer, 1997).

There are certain other effects like the presence of a strongly absorbing ionospheric

inhomogenities over a small area of the proapagation path that have a strong effect on

the sferic spectra and which cannot be modeled using a homogenous ionosphere.

Also the FASTMC program ignores certain effects like the ionospheric variations

transverse to the path of propagation and mode reflection which may result in the lack of

certain spectral features in the modeled waveforms. Some of these problems could be

rectified by using finite element or the finite difference methods.









5.2.4 Remote Sensing of Ionosphere


Remote sensing of the ionosphere is a difficult problem due to its awkward height

which is much lesser than the altitudes at which sattelites are present and it is too high

for the altitudes reached by balloons. Previously some methods were developed to

remote sense the ionosphere using VLF and ELF sferics (Cummer, 1997) and (Cummer

and Inan, 2000). The D-region of the ionosphere can be remote sensed using VLF

sferics, but they cannot be used to remote the E-region of the ionosphere because they

cannot penetrate the ionosphere beyond the D-region. However the ELF sferics have

the capacity to penetrate this region due to their low attenuation rates, also their spectra

are very sensitive to E-region electron densities as compared to the D-region. This

makes them very suitable to remote sense the E-region of the ionosphere especially

the presence of a valley in nighttime ionosphere in the E-region. The presence of the

Sporadic-E layers also has a significant effect on the ELF sferic spectra. The Sporadic-E

layer is not a common occurance in the chosen propagation path and is a more common

occurance in the polar regions.

Sporadic E is the phenomenon of transient,irregularly scattered patches of relatively

dense ionization that develop seasonally within the E-region of the ionosphere. This

generally occurs at an altitude of 100-110 km and has a significant effect on the sferic

propagation. In a theoretical study (Barr.R, 1977) showed that Es generates a series of

resonances from 10Hz to 1000Hz thereby having an effect on the attenuation rates. The

frequencies and amplitudes of these resonances depend strongly on the characteristics

of Es layer.

A method has been previously developed (Cummer and Inan, 2000) to remote

sense the E-region of the ionosphere and detect the presence of sporadic-E layers

using ELF sferics, but this method assumes a single homogenous ground throughout

the propagation path. By employing a similar method developed in (Cummer and

Inan, 2000) and applying the procedure to the inhomogenous ground we can certainly









produce a much more realistic estimate, especially the effects of presence of sea in the
path of propagation which has an important role to play in the attenuation rates.









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S.A.Cummer and U.S.Inan. "Modeling ELF radio atmospheric propagation and
extracting lightning currents from ELF observations." Radio Science 35 (2000):
385-394.

Taylor, W. L. and Sao, K. "ELF attenuation rates and phase velocities observed from
slow-tail components of atmospherics." Radio Sci 5 (1970): 1453-1460.

Uman, M. A. The Lightning Discharge. orlando: Academic Press, 1987.

Wait, J. R. Electromagnetic Waves in Stratified Media. Oxford: Pergamon Press, 1970.

Weidman, C. D. and E. P. Krider. "The amplitude spectra of lightning radiation fields in
the interval from 1 to 20 MHz." Radio Sci 21 (1986): 964.

Wood, T. G. Geo-Location of Individual Lightning Discharges using Impulsive VLF
Electromagnetic Waveforms. Ph.D. thesis, Stanford University, 2004.









BIOGRAPHICAL SKETCH

Bharat Kunduri was born in Hyderabad, India in 1987. He graduated with a

bachelor's degree (Honor's) in electrical and electronics engineering from Dr.M.G.R.University,

Chennai, India in 2008. He pursued his master's degree at University of Florida

under the guidance of Dr. Robert Moore. His research interests lie in the field of

electromagnetics and study of Ionosphere.





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MODELING ELFRADIOATMOSPHERICSGENERATEDBYROCKETTRIGGERED LIGHTNING By BHARATSIMHAREDDYKUNDURI ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2010

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c r 2010 BharatSimhaReddyKunduri 2

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T omyparents, K.P.ReddyandDr.B.ThirumalaDevi 3

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A CKNOWLEDGMENTS IwouldliketoexpressmysinceregratitudeandthankstomyadvisorDr.Robert Mooreforhisguidanceandsupportthroughoutmygraduatestudies.Ithankhimfor givingmeanoppurtunitytoworkwithhimandforhispatienceandencouragement throughtoutthisproject.Thisthesiswouldnothavebeenpossiblewithouthismeticulous guidanceandinvaluableadvice.IthankDr.MartinUmanandDr.VladimirRakovfor readilyagreeingtobeonmycommitteeandfortheirconstantsupportandadvice. Ithankallmylabmatesfortheirconstantencouragementthroughoutmystayatthe lab.ItakethisoppurtunitytothankmyfriendsDhruvSharma,AnujSisodiaandVishal Narayanwhowerelikemyfamilyawayfromhome. Finally,Iamdeeplythankfultomyparentsforsupportingmeininnumerableways andbeingagreatsourceofstrengthateverystageofmylife. 4

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T ABLEOFCONTENTS page A CKNOWLEDGMENTS ..................................4 LISTOFFIGURES .....................................7 ABSTRACT .........................................11 CHAPTER 1INTRODUCTION ...................................13 1.1TheLightningDischarge ............................14 1.2RocketTriggeredLightning ..........................16 1.2.1ClassicalRocketTriggeredLightning .................16 1.2.2AltitudeRocketTriggeredLightning ..................17 1.2.3CurrentWaveforms ...........................18 1.3RadioAtmospherics ..............................19 1.4Ionosphere ...................................21 2INSTRUMENTATIONANDLAYOUTATMCMURDOSTATIONANTARCTICA ANDCAMPBLANDING ...............................25 2.1McMurdoStation-Antarctica .........................25 2.1.1ArrivalHeightsArea,McMurdoStation ................27 2.1.2ELF/VLFResearchatMcMurdoStation ...............28 2.2InternationalCenterforLightningResearchandTestingatCampBlanding (ICLRT),Florida ................................31 3ELFPROPAGATIONINTHEEARTH-IONOSPHEREWAVEGUIDE ......37 3.1WavePropagationinanIdealParallelPlateWaveguide ..........37 3.2WavePropagationinPlasma .........................40 3.2.1EffectofCollisions ...........................42 3.2.2EffectofStaticMagneticField .....................42 3.3PropertiesofEarth-IonosphereWaveguide .................43 3.4WaveguideModeTheory-Budden.K.G ....................44 3.4.1SourcesofWaves-TheHertzianDipole ...............44 3.4.2ModesintheWaveguide ........................45 3.4.3ReectionCoefcientsintheEarth-Ionospherewaveguide .....47 3.4.4ModeEquation .............................48 3.4.5CorrectionfortheCurvedNatureoftheEarth-IonosphereWaveguide 50 3.5LongWavelengthPropagationCapability(LWPC) ..............50 3.5.1PRESEG ................................51 3.5.2MODEFNDR ..............................51 3.5.3FASTMC .................................52 3.5.4ImplementationinLWPC ........................52 5

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3.6 ParametersRequiredtoCalculatetheSfericPropagationModel .....54 3.6.1IonosphericElectronDensityProles .................55 3.6.2CurrentMomentWaveformofaLightningStrike ...........56 4MODELINGELFSFERICS .............................58 4.1HomogeneousWaveguide ...........................58 4.2InhomogeneousGround ............................60 4.3ModelingofELFsfericsPropagatingfromCampBlandingtoMcMurdo Station ......................................62 4.3.1NighttimeIonosphereWithaValley ..................64 4.3.2DaytimeIonosphere-Type1 .....................66 4.3.3NighttimeIonosphereWithoutaValley ................69 4.3.4DaytimeIonosphere-Type2 .....................74 4.4EffectsofDifferentComponentsofCurrentontheSfericWaveform ....78 4.4.1EffectsofCurrentComponents-DifferentIonospheres .......85 5SUMMARYANDSUGGESTIONSFORFURTHERWORK ...........88 5.1Summary ....................................88 5.2SuggestionsforFurtherWork .........................89 5.2.1Jumpsintheamplitude .........................89 5.2.2ModelingatLowerFrequencies-Below45Hz ............89 5.2.3ModelingUsingamoreRealisticInhomogeneousIonosphere ...90 5.2.4RemoteSensingofIonosphere ....................91 REFERENCES .......................................93 BIOGRAPHICALSKETCH ................................96 6

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LIST OFFIGURES Figure page 1-1 VariousphasesofnegativecloudtogroundlightningdischargeAdaptedfrom RakovandUman-2003 ...............................14 1-2ClassicalRocketTriggeredLightning(V.A.RakovLightningDischargesTriggered UsingRocketandWireTechnique,J.Geophys.Res.,vol.100,pp.25711-25720,1999 17 1-3AltitudeRocketTriggeredLightning(V.A.RakovLightningDischargesTriggered UsingRocketandWireTechnique,J.Geophys.Res.,vol.100,pp.25711-25720,1999) 18 1-4Overallcurrentrecordofatriggeredlightningatcampblanding,orida(D.Wang etal.,Characterizationofinitialstageofnegativerockettriggeredlightning, J.Geophys.Res.,vol.104,pg4213-4222,1999) ...................19 1-5Timedomainwaveformofasfericobservedatpalmerstation(adaptedfrom (Wood,2004)) ....................................21 1-6DayandNighttimeelectrondensityprolesforsunspotmaximum(solidlines) andsunspotminimum(dashedlines),adaptedfromTascione,T.F.,Introduction totheSpaceEnvironment,2ndEd. .........................22 2-1AmapofAntarcticaindicatingRossIslandandMcMurdoStation ........25 2-2ALandSatMapofRossIsland(source:http://international.usgs.gov) ......26 2-3ApictureofMcMurdoStation(source:http://international.usgs.gov) ......26 2-4ArrivalHeights,McMurdoStation ..........................27 2-5ApictureoftheVLFreceiveratMcMurdoStation .................29 2-6ApictureoftheELFreceiveratMcMurdoStation .................29 2-7ApictureoftheRacksthatholdthedataacquisitionequipmentatMcMurdo Station,PhotobyRobertMoore ...........................30 2-8OverviewofICLRTatCampBlandingin2002,source:(Rakovetal.,2003) ..31 2-9SatelliteimageofICLRTwithsomeofitsmajorlandmarksindicated,adapted from(Howard,2009) .................................34 2-10Apictureoflaunchtower,Source:LightningLab-UniversityofFlorida ......35 2-11Pictureoflaunchcontroltrailer,Source:LightningLab-UniversityofFlorida ...35 3-1IdealParallelPlateWaveguide ...........................38 3-2Earth-IonosphereWaveguide ............................53 7

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3-3 FlowchartshowingtheexecutionofLWPC ....................55 3-4Representativeelectrondensityproles ......................56 3-5CurrentvsTimewaveformfromrockettriggeredlightning ............57 4-1Representativenighttimeionosphere ........................59 4-2ELFsfericspectraofhomogeneousgroundinlinearscale ............59 4-3ELFsfericspectraofhomogeneousgroundindecibelscale ...........60 4-4ComparisonofELFsfericspectraforinhomogeneousandhomogeneousground (distance-2000Km) ..................................61 4-5ComparisonofELFsfericspectraforinhomogeneousandhomogeneousground (distance-2000Km)indecibelscale .........................61 4-6PropagationPathoftheSfericfromFloridatoAntarctica(GreatCircle) .....63 4-7Nighttimeionospherewithavalley .........................64 4-8CurrentWaveformemployedincalculations ....................65 4-9LWPCoutputfornighttimeionospherewithavalley ................65 4-10ModeledELFspectrumindecibelscale(over1nanotesla)fornighttimeionosphere withavalley ......................................66 4-11ModeledELFspectruminlinearscalefornighttimeionospherewithavalley ..67 4-12ModeledELFsfericwaveformfornighttimeionospherewithavalley ......67 4-13Daytimeionospheretype1 .............................68 4-14CurrentWaveformemployedincalculations ....................68 4-15LWPCoutputfordaytimeionospheretype1 ....................69 4-16ModeledELFspectrumindecibelscale(over1nanotesla)fordaytimeionosphere type1 .........................................70 4-17ModeledELFspectruminlinearscalefordaytimeionospheretype1 ......70 4-18ModeledELFsfericwaveformfordaytimeionospheretype1 ..........71 4-19Nighttimeionospherewithoutavalley .......................71 4-20CurrentWaveformemployedincalculations ....................72 4-21LWPCoutputfornighttimeionospherewithoutavalley ..............72 8

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4-22 ModeledELFspectrumindecibelscale(over1nanotesla)fornighttimeionosphere withoutavalley ....................................73 4-23ModeledELFspectruminlinearscalefornighttimeionospherewithoutavalley 73 4-24ModeledELFsfericwaveformfornighttimeionospherewithoutavalley ....74 4-25Daytimeionospheretype2 .............................75 4-26CurrentWaveformemployedincalculations ....................75 4-27LWPCoutputfordaytimeionospheretype2 ....................76 4-28ModeledELFspectrumindecibelscale(over1nanotesla)fordaytimeionosphere type2 .........................................76 4-29ModeledELFsfericwaveforminlinearscalefordaytimeionospheretype2 ..77 4-30ModeledELFsfericwaveformfordaytimeionospheretype2 ..........77 4-31ComponentsoftheCurrentWaveformUsed ....................78 4-32ICCComponentoftheCurrentWaveformUsed ..................79 4-33ResultantSfericWaveformCausedduetotheICCComponentofCurrent ...79 4-34ReturnStroke1oftheCurrentWaveformUsed ..................80 4-35ResultantSfericWaveformCausedduetoReturnStroke1ofCurrent .....80 4-36ReturnStroke2oftheCurrentWaveformUsed ..................81 4-37ResultantSfericWaveformCausedduetoReturnStroke2ofCurrent .....81 4-38ReturnStroke3oftheCurrentWaveformUsed ..................82 4-39ResultantSfericWaveformCausedduetoReturnStroke3ofCurrent .....82 4-40ReturnStroke4oftheCurrentWaveformUsed ..................83 4-41ResultantSfericWaveformCausedduetoReturnStroke4ofCurrent .....83 4-42ReturnStroke5oftheCurrentWaveformUsed ..................84 4-43ResultantSfericWaveformCausedduetoReturnStroke5ofCurrent .....84 4-44SfericWaveformandDifferentComponents-NighttimeIonosphereWithaValley 85 4-45SfericWaveformandDifferentComponents-DaytimeIonospheretype1 ....86 4-46SfericWaveformandDifferentComponents-NighttimeIonosphereWithouta Valley .........................................86 9

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4-47 SfericWaveformandDifferentComponents-DaytimeIonospheretype2 ....87 5-1Variationsintheamplitudeofthesfericacrossthepathofpropagation .....89 10

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Abstr actofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience MODELINGELFRADIOATMOSPHERICSGENERATEDBYROCKETTRIGGERED LIGHTNING By BharatSimhaReddyKunduri August2010 Chair:RobertMoore Major:ElectricalandComputerEngineering Alightningstrikeradiateselectromagneticenergyoverawidebandwidthranging fromafewHztoafewhundredMHz,butamajorpartofthisenergyisintheExtremely LowFrequency(ELF)range(i.e,1-3000Hz)andVeryLowFrequency(VLF)range (i.e,3-30KHz).ThisenergywhosespectrumspansfromafewHztotensofKHz propagatesintheformofimpulsivesignalswhichgetreectedbytheEarth(atthe lowerboundary)andtheionosphere(attheupperboundary)andtherebypropagatein aguidedfashioninthewaveguideformedbytheEarthandtheionospherereferredto astheEarth-Ionospherewaveguide.Duetotheirverylowattenuationratethesesferics havethecapacitytotravelverylongdistancesfromtheirsourcelightning(intheorder ofthousandsofkilometers)andthuscanbeobservedveryfarawayfromtheirpointof originusingappropriateVLFandELFreceivers. TheaimofthisthesisistomodeltheELFsfericwaveformsuptoafrequencyof 500HzthatcouldbeobservedatMcMurdoStationinAntarctica,generatedbyrocket triggeredlightningattheInternationalCenterforLightningResearchandTesting (ICLRT)atCampBlanding,Florida.Rockettriggeredlightningmakesitpossibleto obtainaccuratemeasurementsofvariousparametersoflightningsuchascurrentand totalchargetransfer,whichisnotpossiblewithnaturallightningduetotheunpredictable natureofitsoccurrence. 11

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The modelingofthesfericwaveformiscarriedonusingtheLongWavelength PropagationCapability(LWPC)codedevelopedbytheNavalOceanSystemsCenter overaperiodofmanyyears.Inordertodoso,certainparametersareneededlike thecurrentwaveformofthelightningandtheionosphericelectrondensityproles overthepathofpropagation.Thisworkassumesthatthelightningstrikeisavertical dipoledischargeandthattheionosphereishomogenousthroughoutthepathof propagation.Realisticionosphericelectrondensityproleswerecreatedusingdata fromtheInternationalReferenceIonosphere(IRI),andrealisticgroundconductivityand permittivityproleswereconsideredthattakeintoaccountdifferentkindsofgroundlike land,sea,andice. Theendresultisthesuccessfulmodelingofthetime-domainmagneticeld signatureofalightningstriketriggeredattheICLRTafterpropagatingmorethan14 MmtoArrivalHeightsatMcMurdoStation,Antarctica.Thesetheoreticalresultsmaybe directlycomparedwithfutureexperimentalobservations. 12

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CHAPTER 1 INTRODUCTION Lightningwasatonepointfearedasanatmosphericashofsupernatural origins-thegreatweaponofthegods.Ithasbeenusedtodescribepowerandmight inancientmythologies.Greekmythologydescribesthunderandlightningasthemighty weaponsofZeus.IntheBiblelightningisoftendepictedasamanifestationofthewrath ofGod.ThevedasdescribelightningastheweaponusedbyIndra,thekingofheaven. Thescienticstudyoflightninghasitsmodestbeginninginthe18thcentury. BenjaminFranklinperformedtherstsystematicstudyoflightningduringthesecond halfof18thcentury.Hewasthersttodesignanexperimentthatconclusivelyproved theelectricalnatureoflightning.Littleprogresswasmadeinunderstandingthe propertiesoflightninguntilthelate19thcentury.Lightningcurrentmeasurementswere madeinGermanybyPockelsaround1900whoanalyzedthemagneticeldinducedin materialsbylightningtoestimatethecurrentvalues.Therehasbeenarapidincreasein thelightningrelatedresearchinthepast30-40yearswiththearrivalofdigitalcomputers andofhighspeeddataacquisitionsystems. Lightningradiateselectromagneticenergyoveranextremelywidebandwidthfrom afewHz( Burke 1992 )tomanytensofMHz(Weidman 1986 ).Mostoftheenergy isradiatedintheVeryLowFrequency(3-30KHz)andExtremelyLowFrequency (3-3000Hz)bandsbecauseofthesub-millisecondtomillisecondtimescalesand severalkilometerspatialextentsoftheradiatingcurrent( Uman, 1987).Theenergy radiatedintheELF/VLFbandsisreectedbytheionosphereandtheground,thereby propagatinginaguidedfashionbetweentheEarthandtheionospherewhichform theEarth-ionospherewaveguide.TheelectromagneticsignalsintheELF/VLFbands generatedbylightningareknownasradioatmosphericsormorecommonlyassferics. ThesesfericspropagateintheEarth-ionospherewaveguidewithlowattenuationrates around2-3dBper1000kmandthuscanbeobservedatgreatdistancesfromtheir 13

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or igin( Davies 1990 ).Thecharacteristicsofthesfericwaveformarecontrolledbytheir sourcelightningdischargesandtheparametersoftheEarth-ionospherewaveguide (Cummer, 1997). ThisthesisfocussesonmodelingtheELFsfericsgeneratedduetorockettriggered lightning. 1.1TheLightningDischarge Athundercloudhasalargepositivelychargedlayerandanegativelychargedlayer ofaboutequalmagnitudewhichformsanelectricdipole( RakovandUman 2003). Oncethesechargedlayersattainenoughcharge,theelectriceldsassociatedwiththe chargesbegintoexceedthedielectricbreakdownvoltageoftheatmosphere,leadingto theoccurrenceofalightningash. Figure 1-1.Variousphasesofatwostrokenegativecloudtogroundlightningdischarge AdaptedfromRakovandUman-2003. Lightningashesareclassiedas: Clouddischarges:thosethatdonotterminateonthesurfaceofEarth,e.g., Intraclouddischarges,Cloudtoairdischargesandinterclouddischarges 14

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Cloud toGrounddischarges:thosewithatleastapartialdischargetoground,e.g., negativecloudtogrounddischarges,positivecloudtogrounddischarges Theclouddischargesarethemostnumeroustypeoflightning(50-75percent) (PrenticeandMackerras 1977).Thecloudtogrounddischargescanbeclassiedinto twogroupsdependingonthelayerofchargetheyoriginatein.Ifthecloudtoground dischargeoriginatesinthenegativelychargedlayeritiscallednegativecloudtoground ash,ifthedischargeoriginatesinthepositivelychargedlayeritiscalledpositivecloud togrounddischarge( Wood 2004).While90%ofthecloudtogroundashesare negativedischargesandthemajorportionoftheremaining10%arepositivedischarges. Therearealsodischargestransportingbothnegativeandpositivechargestothe ground,suchdischargesareveryrare. AnegativecloudtogrounddischargeisillustratedinFigure 1-1.Itisinitiatedwhen asteppedleaderbeginstoworkitswaydownfromthecloudinaseriesofdiscretesteps afterapreliminarybreakdowninthenegativelychargedlayer.Asthesteppedleader advancesdownward,theelectriceldbetweentheendofthesteppedleaderandthe groundbecomeshighenoughthatconductiveleadersbegintoreachupwardsfromthe ground.Whenthesteppedleaderandtheconductiveleaderclosethe10-100meters gap,attachmentoccurs,leadingtothegenerationoftherstreturnstrokeofdischarge. Thereturnstrokeinvolvestheowoflargeelectriccurrentfromthegroundtothecloud, therebyproducingaradioatmospheric( RakovandUman 2003 ).Therstreturnstroke maydepletethelayerofcloudchargetherebyterminatingtheash.Ifanyadditional chargeisavailable,JandKprocessesoccurwhichredistributetheremainingcharge inthecloud.Theconductingchannelremainspartiallyionizedfollowingtherstreturn strokeandadartleadermayreionizethechannelresultinginasecondstroke.This processrepeatsitselfgeneratingmanyreturnstrokes( Uman, 1987 ).Asimilarprocess withusuallyonestrokeoccursforpositivecloudtogrounddischarges. 15

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1.2 RocketTriggeredLightning Itisnecessarytoobservelightningatcloserangetoaccuratelyinvestigatesome oftheassociatedphenomena,butnaturallightningstrikesatunpredictabletimes andplaces,makingcloseobservationbyqualiedpeopleequippedatthetimewith necessaryinstrumentationunlikely.Rockettriggeredlightninghasbeenanimportant meanstoovercomethatproblem.Experimentsyearsagodemonstratedthatalightning strikeoftencanbetriggeredbylaunchingarocketconnectedtoalonggroundedcopper wiretowardathunderstorm.Astriketriggeredthatwaytendstofollowthewire.Thewire quicklyvaporizesanddoesnotconductasignicantpercentageofthelightningcurrent. Itsfunctionismerelytoguidealightningstriketomeasuringequipment. Rockettriggeredlightningisproducedintwomethodscurrently(RakovandUman 2003): ClassicalRocketTriggeredLightning AltitudeRocketTriggeredLightning 1.2.1ClassicalRocketTriggeredLightning Inclassicaltriggeringmethod,thewirewhichisattachedtotherocketisconnected attheotherendtoagroundedlauncher.Anupwardpositiveleaderisgeneratedatthe tipoftherocketafteritreachesanaltitudeofaround200m.Thecurrentoftheupward positiveleadervaporizesthewireandaninitialcontinuouscurrent(ICC)followsfor somehundredsofmilliseconds.AfterthecompletionoftheICCphase,thereexistsa phaseforafewtensofmillisecondswherenocurrentows.Thisphaseisfollowedby thegenerationofaleader-returnstrokesequences.Thesearesimilartothesubsequent leader-returnstrokesequencesinnaturallightning. DuringtheformationoftheupwardpositiveleaderaphasecalledtheInitialCurrent Variation(ICV)occurswhenthetriggeringwireisreplacedbytheupwardpositiveleader plasmachannel.Theupwardpositiveleaderproducescurrentwhichisoftheorderof tenstohundredsofamperes(measuredatground)whichvaporizesthewire.Atthis 16

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Figure 1-2.ClassicalRocketTriggeredLightning(V.A.RakovLightningDischarges TriggeredUsingRocketandWireTechnique, J.Geophys.Res.,vol.100,pp.25711-25720,1999 instancethecurrentmeasuredatgroundfallstozeroapproximatelyduetotheabsence ofaconductingpath.Adownwardleaderprocessbridgestheresultantgapandinitiates areturnstrokeprocessfromthegroundwhichservestore-establishtheinterrupted currentowtotheground. 1.2.2AltitudeRocketTriggeredLightning Altitudetriggeringtechniqueusesanungroundedwire.Thisenablesthepossibility toreproducesomefeaturesofrststrokeofnaturallightningwhichisnotpossible usingclassicaltriggering.Theapparatushasa50mlongcopperwireconnectedto thegroundlauncher,a400mlonginsulatingkevlarcableinthemiddleand100-200 mlongoatingcopperwireconnectedtotherocket.Theupperoatingwireisused fortriggeringwhilethelowergroundedwireisusedforinterceptingtheleader.When arocketreachesasuitablealtitude(around600m)abi-directionalleadercomposed ofaupwardpositiveleaderandadownwardnegativeleaderisinitiated.Theelectric 17

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Figure 1-3.AltitudeRocketTriggeredLightning(V.A.RakovLightningDischarges TriggeredUsingRocketandWireTechnique, J.Geophys.Res.,vol.100,pp.25711-25720,1999 eldproducedbythedownwardnegativeleaderinitiatesanupwardconnectingpositive leaderfromthegroundedcopperwire.Thisconnectstothedownwardnegativeleader andthisprocessleadstothegenerationofareturnstroke. 1.2.3CurrentWaveforms Atypicalnegativerockettriggeredlightninghasbeendescribedtobesimilartoa upwardinitiatedlightningfromatallstructure( Uman 1987).Itinvolvesaninitialstage (IS)thatiscomposedofanupwardpositiveleader(UPL).Itisfollowedbyaninitial continuouscurrent(ICC).TheICCiscommonlyfollowedbyadartleader/returnstroke sequenceswhicharesimilartothesubsequentstrokesinnaturaldownwardlightning. Whentherearenoreturnstrokesinvolvedthetriggeredlightningeventconsistsofthe ISonlyandistermedaswireburn( D.Wangetal., 1999).Ithasbeenwelldocumented intheliteraturethattheICCinvolvesimpulsiveprocesseswhicharesimilartothe M-componentpulses( Fieuxetal. 1978). 18

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Figure 1-4.Overallcurrentrecordofatriggeredlightningatcampblanding, orida(D.Wangetal.,Characterizationofinitialstageofnegativerocket triggeredlightning,J.Geophys.Res.,vol.104,pg4213-4222,1999) Figure 1-4 indicatesthevariousfeaturesassociatedwithatypicalnegative rockettriggeredlightningdischarge.Theinitialstageinrockettriggeredlightning ischaracterizedbyachannelbasecurrenthavingadurationofsomehundredsof millisecondsandamagnitudeofapproximately100Amps.Thepronouncedcurrent variationatthebeginningoftheISistermedinitialcurrentvariation(ICV),theICVhasa durationwhichtypicallydoesnotexceed10ms( D.Wangetal., 1999).TheICVusually involvesanabruptdecreaseincurrentfollowedbyapulse.AlongsidetheICVtheIS typicallyincludesapronouncedICC. 1.3RadioAtmospherics Radioatmosphericsorsfericsinshortarelightningproducedelectricandmagnetic eldswhosespectrumspansfrequenciesfromafewHztoafewhundredsofKHz. Theseareeasilyobservedatdistancesspanningseveralthousandkilometers.Typical sfericshaveafrequencyspectrumintheELF(0-3KHz)andtheVLF(3-30KHz)range, 19

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b utsometimescanextendintotheLF(30-300KHz)range( RakovandUman 2003). SfericspropagateinthewaveguideformedbyEarthandionosphereprimarilyby multiplereectionssimilartoaelectromagneticwaveinametallicwaveguide.Theearly researchinsfericsbeganintheearly1900'sandthisprimarilywasaperiodofdiscovery. StrangenoiseswererstobservedonradiobyGermanphysicistHeinrichBarkhausen duringworldwarI.Anumberofpapersinthe1930'sandearly1940'scharacterizedand attemptedtoexplainthereceivedsfericsfromdistantlightningsources.Animportant earlypaperonsferics( BurtonandBoardman 1933)describestwodistinctemissions -swishes,tweeks.Theswishesarenowreferredtoaswhistlers.Duringandin theperiodfollowingWorldWarIItherewasagreatdealofinterestinunderstandingthe propagationofsferics,duetoitsimplicationsregardinglong-distancecommunication. ThestudyofELFsferics,thoughfundamentallysimilartotheVLFsferics,mostly hasbeentreatedseparatelyintheliterature.ELFsfericsarealsoreferredtoasslow tailsandhavebeenstudiedexperimentallyformanyyears[e.g.,( Hepburn, 1992), (TaylorandSao, 1970),( Burke, 1992)etc.( Jones, 1974)publishedabibliographyof experimentalmeasurementsofELFpropagationcharacteristicsgeneratedbylightning. (Budden, 1961 )and(Wait, 1970)madeatremendouscontributioninunderstandingthe propagationofELFandVLFsfericsintheEarth-ionospherewaveguide. Figure 1-5 showsasfericwaveformrecordedatPalmerstationAntarctica(adapted from.( Wood, 2004)).ItclearlyshowsaVLFimpulsefollowedbyaELFslowtail (Reisingetal., 1996).TheoscillatorynatureoftheVLFimpulseisduetothepresence ofmultiplemodesofpropagation,howevertheELFcomponentonlyhasonemode ofpropagation(QTEMmode)( Cummer, 1997).Thespectralcontentofsfericsvaries widelyandtherearemanyvariationsobserved,agoodanalysisofsomevariationsin sfericsobservedisdescribedin( Cummer 1997 ). 20

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Figure 1-5.Timedomainwaveformofasfericobservedatpalmerstation(adaptedfrom ( Wood 2004)) 1.4Ionosphere Theionosphereistheuppermostpartoftheatmospherestretchingfromaheight ofabout50kmto1000kmthatisionizedbythesolarradiation.Eventhoughthe ionosphereformsonlyasmallpartoftheatmosphereithasaveryimportantrole becauseofitsinuenceontheradiowaves(especiallyELFandVLFwaves).When solarradiationstrikesthechemicalconstituentsoftheatmosphere,electronsare dislodgedfromatomsandmoleculestoproducetheionosphericplasma.Thepresence ofthesechargedparticlesmakestheionosphereanelectricalconductorwhichsupports electriccurrentsandgeneratesradiowaves. Ultraviolet(UV),X-Ray,andshorterwavelengthradiationfromthesunhave sufcientenergyinthemtodislodgeanelectronfromaneutralatomormolecule andaremostlyresponsibleforionization.Theamountofionizationprimarilydependson theactivityofthesun,itvariesgreatlywiththeamountofradiationreceivedfromthesun 21

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and thusthereisadiurnaleffect,aseasonaleffectandalsovarieswiththegeographic location( Davies 1990). Figure 1-6.DayandNighttimeelectrondensityprolesforsunspotmaximum(solid lines)andsunspotminimum(dashedlines),adaptedfromTascione,T.F., IntroductiontotheSpaceEnvironment,2ndEd. Theionosphereisdividedintoregions(D-region,E-regionandF-region)with aspecicionization.ThelowestistheD-regioncoveringthealtitude50km-90km, thencomestheE-regionbetween90km-150kmandnallytheF-region(alsoknown 22

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as theAppletonlayer)abovetheE-region.ThereareF1andF2regionswithinthe F-region.TheelectronconcentrationsreachtheirhighestlevelsintheF-region,more specicallytheF2-region( Hargreaves 1992).Figure 1-6 showstheelectrondensity prolesofatypicalionosphereatbothnighttimeanddaytimeatmid-latitude.TheF1 layerdisappearsduringthenightwhiletheF2layerslowlydecreasesthroughthenight. Theionosphereisadynamicmediumandthestudyoftheionosphereisan importanteld.Ionosphericsoundingisoneoftheoldestandmostaccuratewaysof studyingtheionosphere.InthistechniqueIonosondesareemployedinsendingsignals intotheionospherewhicharereectedbackinthepresenceofionization,thefrequency atwhichthereectionoccursgivesinformationabouttheplasmadensityatthealtitude. IonosondesareeffectiveinprobingtheE-regionandtheF-regionbutnottheD-region (Hargreaves 1992). AmorerecenttechniqueistheIncoherentScatterRadar,theadvantagewiththis techniquebeingthatitcanprobetheionospherebeyondtheF2regionelectrondensity maximumandiscapableofmeasuringotherquantitiessuchaselectrontemperatures etc( Evans 1969).Thedisadvantagewiththistechnique,however,isthatitrequires veryexpensiveequipmentandisnotveryusefulinmeasuringtheelectrondensity levelsatthelowerlevels.MeasurementsoftheD-regionarestillverydifcultandthe techniquesdescribedabovearenotsuitableformakingmeasurementsatD-region altitudes.MoreovertheD-regionistoolowforrocketsandtoohighforballoonsto makeanymeasurements.ThusoneoftheveryfewmethodstostudytheD-region oftheionosphereisthroughVLFwaves.TheVLFwavesarecompletelyreectedby theionosphere,andthismakesthemaveryusefultoolformeasurementsinD-region (Cummer, 1997).LongdistanceVLFpropagationeffectsmeasuredinsfericsare animportantsourcetomakeD-regionmeasurements( Cummer, 1997).Recentlya techniquehasbeendevelopedinwhichELFwavepropagationmeasurementsmade 23

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using lightningdischargesasasourceareusedinremotesensingtheE-regionofthe ionosphere( CummerandInan 2000). 24

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CHAPTER 2 INSTRUMENTATIONANDLAYOUTATMCMURDOSTATIONANTARCTICAAND CAMPBLANDING 2.1McMurdoStation-Antarctica McMurdoStationisanAmericanAntarcticresearchstationlocatedonthesouthern tipofRossislandontheshoreofMcMurdoSoundinAntarctica.ItisoperatedbyUnited StatesAntarcticProgram,abranchofNationalScienceFoundationandisthelargest communityinAntarcticawhichincludesaharbor,3airelds,aheliportandover100 buildings.TheUnitedStatesofciallyopeneditsrststationinMcMurdoonFeb16, 1956anditwasinitiallycalledNavalAirFacilityMcMurdo. Figure 2-1.AmapofAntarcticaindicatingRossIslandandMcMurdoStation(source: http://international.usgs.gov) Figure 2-1 indicatesthelocationofRossIslandandMcMurdoStationinAntarctica. Figure 2-2 showsaLandsatimageoftheRossIslandandthisimagepointsthelocation ofMcMurdoStationonRossIsland.Figure 2-3 showsapictureoftheMcMurdoStation takenfromtheobservationhill.Thebuildingsrangeinsizefromasmallradioshack 25

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Figure 2-2.ALandSatMapofRossIsland(source:http://international.usgs.gov) Figure 2-3.ApictureofMcMurdoStation(source:http://international.usgs.gov) 26

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to largethreestoreyedstructures.Thebuildingsincluderepairfacilities,dormitories, administrativebuildings,arehouse,powerplant,waterdistillationplant,wharf,stores, clubs,warehousesandCraryLab.Thesearelinkedbyabovegroundwater,sewer, telephoneandpowerlines.Thestationcoversanareaofnearly1.5sq.miles. 2.1.1ArrivalHeightsArea,McMurdoStation McMurdoStationliesataninvariantmagneticlatitudeofabout80degreesinside thepolarcapatalllocaltimesandisauniquesiteforstudyingthenaturalphenomena andatmosphericstudies,oneofthemainreasonsforthisisitslocationbeingremote fromcontaminationsources.TheprojectsthatoperatefromtheArrivalHeightsareaat McMurdostationexaminenaturalphenomenathatoccurintheEarth'satmosphereand magnetosphere,Figure 2-4 showsapictureofthisareaandthemapofthisarea.The mapgivesanideaofthevariousfacilitiesatthisarea. A ImageofArrivalHeightsRegion,PhotobySeth White(Source:www.sethwhite.org) B MapofArrivalHeightsRegion Figure2-4.ArrivalHeights,McMurdoStation 27

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The objectivesoftheseprogramsincludeinvestigationsofphenomenathatcouple solarprocessesintotheterrestrialenvironment,whichincludeprocesseswithshortterm environmentaleffectssuchastheaurorasandradiowavecommunicationinterference, aswellasthoseassociatedwithlongtermeffectssuchasozonelayerandatmospheric compositionstudies.Theinstrumentsforthesetasksincludeopticalandradiodevices forremotesensing,sensorsformonitoringchangesinelectricandmagneticeldsatthe station,ELF-VLFreceivers. ThesignalsfromdifferentinstrumentsattheAntarcticobservatoriesarerecorded onacommondataloggerandcanbeshared.Theseinstrumentsprovideanalogsignals thataredigitizedandrecordedbyPCbasedsystemsrecordingtomagnetic-optical disks.Thesedataacquisitionsystemsareoperatedatstationfacilitiesandrecorddata frommanyinstrumentswhichinclude ELF-VLFreceivers,UniversityofFlorida(PrincipleInvestigator:Dr.RobertMoore)/ StanfordUniversity RiometersandPhotometers,UniversityofMaryland SearchcoilMagnetometer,UniversityofNewHampshire FluxgateMagnetometer,NJIT 2.1.2ELF/VLFResearchatMcMurdoStation Historically,amajorpartofELF/VLFresearchatArrivalHeightshasbeencarried outbyStanfordUniversity(AntonyFraser-Smith).TheUniversityofFloridarecently tookcontrolofthesesystemstogetherwithStanford,providingmuchneededhardware upgradestothesystems.AsapartofthisprogramUniversityofFloridasetupreceivers atArrivalHeightsandSouthPolestationinJanuary2010,andatPalmerStationinMay 2010. TheVLFreceiverandELFreceiveratArrivalHeightsarepresentlymaintained andoperatedbyRobertMooreoftheUniversityofFlorida.Figure 2-5 showsimageof theVLFreceiverlocatedinthesecondcraterregion(shownintheimageofthemap 28

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Figure 2-5.ApictureoftheVLFreceiveratMcMurdoStation,PhotobySethWhite (Source:www.sethwhite.org) ofarrivalheightsinFigure 2-4 andFigure 2-6 showstheimageoftheELFreceiverat McMurdoStation. Figure 2-6.ApictureoftheELFreceiveratMcMurdoStation,PhotobySethWhite (Source:www.sethwhite.org) TheELF/VLFreceiversystemsatMcMurdoStationrecordwaveactivityincident uponNorth/SouthandEast/WestcrossedloopantennasshowninFigure 2-5 andFigure 29

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2-6. Apreamplierisneartheantennaandtheremainderofthesystemislocatedin thehutshowninFigure 2-4.TheracksshowninFigure 2-7 holdthelinereceiver,GPS timingunit,mixer/moniterandanalogrecorders. Figure 2-7.ApictureoftheRacksthatholdthedataacquisitionequipmentatMcMurdo Station,PhotobyRobertMoore TheVLFreceiverislocatedinsidethesecondcrateratArrivalHeightswhichisan oldvolcaniccraterabout1.5milesnorthofthehutshowninFigure 2-4.Universityof FloridaandStanfordUniversityarejointlyrunningthisprojectusingtheVLFandELF antennastomeasuretheverylongwavelengthelectromagneticwaveswhichpropagate aroundtheglobeintheEarth-ionospherewaveguide.VLFreceiver(Figure 2-5)consists ofacentralwoodenpolemountedintheground,andfourtriangularloopsofwirerun downtothegroundfromitstop.Theotherfourwiresaresupportlinesforthepoleitself. ThewireloopsareorientedN-SandE-Wandpickupradiationinthe3KHz-30KHz range. Figure 2-6 showstheELFreceiverinthevault.UnliketheVLFantenna,which swaysinthebreeze,itisimportantfortheELFantennatoremainstationaryandthusit wasburiedinawoodenvaultoutinthelavaeldsnorthofthehut.Theantennahastwo components,oneorientednorth-southandtheotherorientedeast-west,andtheypick upsignalsinthe1Hz-3KHzrange. 30

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2.2 InternationalCenterforLightningResearchandTestingatCampBlanding (ICLRT),Florida AlightningresearchfacilityatCampBlanding,FloridawasstartedbyElectricPower ResearchInstitute(EPRI)andPowerTechnologiesIncin1993.UniversityofFlorida andCampBlandingFloridaArmyNationalGuardBasesignedanagreementforming theInternationalCenterforLightningResearchandTesting(ICLRT)forthepurpose ofadvancingthescienceandtechnologyoflightninginOctober1994.Thecenterhas anareaofmorethan100acres,locatedabout45kmnorth-eastofGainesville(UF), Floridahavingtheco-ordinates30 Nand82 W.Since2005thefacilityisbeingjointly operatedbyUniversityofFloridaandFloridaInstituteofTechnology.Thesiteisideal forconductingrockettriggeredlightningexperimentsespeciallyduetoitsrestricted airspace(sourceofinformation, www.lightning.ece.ufl.edu ).Figure 2-8 showsthe overviewandlayoutatCampBlandingin2002. Figure 2-8.OverviewofICLRTatCampBlandingin2002,source:( Rakovetal. 2003 ) infrastructureatICLRT,CampBlandingare: 2500square-footofcebuilding Twolaunchtrailers Onelaunchtower 31

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One mobilelauncher fourinstrumentationbuildings Twooverheadtestpowerlines Atestairportrunway Anundergroundtestpowersystem OneoftheprimarygoalsofICLRTistostudyrockettriggeredlightningandnatural lightning.ThecurrentinfrastructureatICLRThas91measurements,digitizationand controlcomputerswhichenablethestudyofbothtriggeredandcloselyoccuringnatural lightning,eg( RakovandUman 2003)and( Crawfordetal. 2001 ).Theseinstruments measureelectricandmagneticelds,highenergyradiations(X-rays),opticalradiation andchannel-basecurrents. AtICLRTdifferenttypesofdigitalstorageoscilloscopes(DSO)areemployedto digitizeandstoredata.TheDSOsarearmed,calibratedanddisarmedbyacentral computerinlaunchcontrol(HAL)viaGPIBorethernet,oncearmedtheDSOsare triggeredtorecorddatawhenthechannelbasedcurrentsexceed6kAorwhenthe twoopticalsensorsplacedinthecornersofthesiteandpointingtowardsthelaunch towerdetectluminosityexceedingacertainthresholdvaluesimultaneously.Boththese conditionsindicatetheoccuranceofeithertriggeredornaturallightning. AseperatenetworkofDSOscalledPositiveLightiningExperiment(POE)issetup torecorddatafromoff-sitepositivecloud-to-groundlightningwithoutpreventingthe acquisitionofdatafromon-sitelightning DetailsoftheDSOsusedatICLRT: 2YokogowaDL71616channelinstrumemtswith10MHzsamplingrateand4MHz bandwidth 5YokogowaDL75016channelinstrumemtswith10MHzsamplingrateand3MHz bandwidth 32

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4 LeCroyLT344L4channelinstrumentswith250MHzsamplingrateand20MHz bandwidth 2LeCroyLT374L4channelinstrumentswith250MHzsamplingrateand20MHz bandwidth 4LeCroy44Xi4channelinstrumentswith250MHzsamplingrateand20MHz bandwidth Twodifferenttypesofdevicesareusedtomeasurechannelbasecurrents.These currentsaremeasuredatthebottomofthelaunchtubeslocatedatopthelaunchtower. Therstcurrentmeasuringdeviceisalowinductancecurrentviewingresistormodel R-7000-10.Theseconddeviceisaclamp-oncurrenttransformer,amodel6801custom manufacturedbyPearsonElectronics. ICLRThasthreeeldmills(adeviceusedtosensestaticelds)deployedatthe sitewiththepurposeofdeterminingtheavailabilityofsuitablethunderstormconditions fortriggeringlightning(electriceldvaluesbetween4-10kV/m).Ground-leveland broadbandverticalelectriceldandeldderivativesaresensedusingat-platesensors. CurrentlythereareeightdE/dtsensorsandtenelectriceldsensorsatthesite. Twohighspeedvideocameraswithadjustableframingratesandpixelresolution areusedtoimagethelowerseveralhundredmetersoflightningchannel.Oneofthe camerasusedisaPhotronSA1.1andtheotherisPhantomv7.3,thePhotronoperates atafasterframingratethanthePhantom,itisusedtorecordvideosatspeedsupto 300,000frames-per-second(fps)ofthelowesthundredmetersofthetriggeredlightning channelwithahorizontaleld-of-viewoftensofmeters.ThePhantomisgenerally operatedatspeedsupto10kfpsofthebottomseveralhundredmetersofthechannel withahorizontaleld-of-viewofabouthundredmeters(courtesyChrisBiagi,Lightning Lab,UniversityofFlorida). Figure 2-9 showsasatelliteimageofICLRTatCampBlanding,Floridaand indicatedinitaresomeofthemajorstructurallandmarks,thisgureisadaptedfrom (Howard 2009)andistakenfromMicrosoftVirtualEarth. 33

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Figure 2-9.SatelliteimageofICLRTwithsomeofitsmajorlandmarksindicated, adaptedfrom( Howard 2009) TherearethreewaystotriggerlightningatICLRT:(i)UndergroundLauncher(ii) ThelaunchTower(showninFigure 2-10)(iii)Amobilelauncher.Since2005onlythe launchtowerandthemobilelauncherhavebeenused,themajorityofthetriggering beingconductedatthetower( Howard 2009).Allthelaunchersareequippedwith resistiveshuntstomeasurethelightningchannelbasecurrents.Thelaunchtowerisa 11mtallwoodentowerwiththelauncheronitstopandandthetowerislocatednearthe launchcontroltrailerasshowninFigure 2-8. ThelaunchcontroltrailershowninFigure 2-11 isthecenterofthetriggering operations,itislocatedapproximately50mnorthoflaunchtower.Thisbuildingcontains thelaunchercontrolsandalsoprovidestheelectromagneticshieldingforthevideoand dataacquisitionequipment( Howard, 2009).Thetrailerispoweredbyadieselgenerator duringthetriggeringoperationssothattheequipmentinsideisnotaffectedbyasurge orfailureinthepowergrid,bothofwhichoccurcommonlyduringlightning( Howard 2009). 34

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Figure 2-10.Apictureoflaunchtower,Source:LightningLab-UniversityofFlorida Figure 2-11.Pictureoflaunchcontroltrailer,Source:LightningLab-UniversityofFlorida 35

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A networkofsensorsusedtocollectelectricandmagneticelds,timederivatives oftheeldsandX-rayemissionsisinuseatICLRTandisknownastheMSE(Multiple StationExperiment)/TERA(ThunderstormEnergeticRadiationArray).TheMSEnetwork (primarilycomposedoftheelectricandmagneticeldanditstimederivativessensors) ismaintainedandoperatedbytheUniversityofFloridawhiletheTERAnetwork (primarilyconsistingofX-raysensors)isoperatedbyFloridaInstituteofTechnology (Dwyeretal., 2004).Avideosystemwasalsodeployedasapartofthissystemwhich consistedoffourcamerasiteswhosesignalswerealsotriggered.Thedatafromthe networkisalsoprovidedaGPStimestamp,allowingthedatatobecorrelatedwithother systemssuchastheNationalLightningDetectionNetwork(NLDN)( J.Jerauldetal. 2005). Thiswholesystemisoperatedthroughacontrolsystemwhichprovidesremote capabilityformanytaskslikepoweringmeasurements,measuringbatteryvoltages, monitorlocalthunderstormconditionsbymeasuringthequasi-staticelectriceldat groundandautomaticallyarmanddisarmthenetworkwhenappropriate( Howard 2009).Theelectricandmagneticeld,optical,andTERAmeasurementswere sampledcontinuouslyfor2swith1spre-triggerat10MHzonYokogowaDL750digital oscilloscopes,thedE/dtandTERAmeasurementsaresampledbyLeCroydigital oscilloscopesat250MHz.Thechannel-basecurrentoftherocket-triggeredlightning wasrecordedonbothLeCroyandYokogawaoscilloscopes.Foradetailedreportonthe instrumentationatICLRTthereaderisrecommendedtorefer( Howard 2009). 36

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CHAPTER 3 ELFPROPAGATIONINTHEEARTH-IONOSPHEREWAVEGUIDE ExtremelyLowFrequency(ELF)electromagneticwaveslieinthefrequencyrange 3Hzto3KHzandareofinterestintheeldsoflongdistancecommunicationsand submarinecommunicationsduetotheircapabilitytopropagateverylongdistances becauseoflowattenuationratesandtheircapabilitytopenetratewellthrough conductingmaterials.Themostcommonandpowerfulsourceofelectromagnetic radiationintheELFandVLFrangeoffrequenciesislightning. ELFenergyradiatedfromalightningstrikepropagatesinaguidedfashionin theEarth-IonospherewaveguidereectingmultipletimesbetweentheEarthandthe ionosphere.ELFwavepropagationintheEarth-Ionospherewaveguidedependson theelectricalpropertiesoftheEarthandtheionosphere(heretheboundariesofthe waveguide)andthevariablenatureoftheionosphere.Theattenuationrateofthewave ishighlyvariableandisdependentonmanyfactorslikefrequency,conductivityof theEarth,conductivityproleofionosphere,reectionheightoftheionosphere,and Earth'smagneticeld.Allthesefactorshaveasignicanteffectonthesfericwaveforms observedfromadistantlightningstrike. ThischapterdiscussesthemodalcontentintheELFrangeoffrequenciesand givesamathematicaldescriptionofELFwavepropagationintheEarth-ionosphere waveguide.Thewaveguidemodetheory( Budden, 1961)providesananalytical descriptionofpropagationofELF/VLFwaves. 3.1WavePropagationinanIdealParallelPlateWaveguide Consideranidealparallelplatewaveguidewithitsboundariesatx=0andx=a asshowninFigure 3-1 andassumethemediumislossless,simpleandsource free.Thesolutionisobtainedinarectangularco-ordinatesystem,eventhoughthe Earth-Ionospherewaveguideisnotat(especiallyatverylargedistancesconsidered here).AdirectsolutionintheCartesianco-ordinatesystemwouldbeextremely 37

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Figure 3-1.IdealParallelPlateWaveguide complicatedforthegeometry.Thewaveguideisinitiallyassumedtobeperfectlyat andappropriatecorrectionsaremadelaterinthederivationforasphericalgeometry (Budden, 1961 ). TheboundaryconditionsthataretobesatisedareE tangential =0andH normal =0. Thesolutionsforthisproblemcanbedividedinto3categories: TransverseElectric(TE)Modes,inthiscaseE z =0andH z 6=0 TransverseMagnetic(TM)Modes,inthiscaseH z =0andE z 6=0 TransverseElectricandMagnetic(TEM)Modes,inthiscaseE z =0andH z =0 Wheremodesarespeciccasesforwhichsuchwavescanexistandthereexistsa conditionwhichmustbesatisedforamodetoexistwhichisthemodeequationgiven belowforeachcategory. SolutionforTE m modes E y = K 1 sin( m x a )e )Tj /T1_8 7.97 Tf (r z (3) 38

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The solutionsforH z andH x canbeobtainedfromequation 3 andMaxwell's equations.ThemodeconditionforTE m modesisgivenby sin(ah )=0 orah = m wherem =0, 1, 2etc (3) SolutionforTM m modes H y = K 2 cos( m x a )e )Tj /T1_8 7.97 Tf 6.59 0 Td (r z (3) The solutionsforE z andE x canbeobtainedfromequation 3 andMaxwell's equations.ThemodeconditionforTM m modesisgivenby sin(ah )=0 orah = m wherem =0, 1, 2etc (3) SolutionforTEMmode ItisasubsetofTM m modesolution,i.e.,TM 0 H y = K 3 e )Tj /T1_8 7.97 Tf 6.59 0 Td (r z (3) E x = r j K 3 e )Tj /T1_8 7.97 Tf 6.59 0 Td (r z (3) Here r isthepropagationconstant.TheTEMmodeisaspecialcaseofaTMmode. Boththeelectricandmagneticeldsaretransverse(perpendicular)tothedirectionof propagationfortheTEMmode. Waveguidemodesarecanbenumberedbythevaluesof (here =ahinthe example),thelowestvalueof thatsatisesthemodeconditionbeingthelowest ordermode.Alsodifferentfrequencieshavedifferentvaluesof associatedwiththem. Atcertainfrequenciesthevalueof reach90 therebypreventingthewavesfrom propagating,suchfrequenciesareknownascut-offfrequencies.Whenthefrequencyof thewaveisbelowthecut-offfrequencyonlycomplexvaluesof arepossibleandonly 39

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e vanescentwavescanexistinthewaveguide.Inanidealparallelplatewaveguidethe TEMmodedoesnothaveacut-offfrequencyand =0forallfrequencies. Thegroupvelocityofawaveguidemodeis: g = c cos = c r 1 )Tj /T1_3 11.955 Tf 11.96 0 Td (( f cn f ) 2 (3) Here f c is thecut-offfrequencyforthe n th ordermode.Itcanbeobservedfrom equation 3 thatasfrequency(f)becomesapproachesthecut-offfrequency( f c )the groupvelocity( g )approacheszeroandasthevalueoffbecomesmuchgreaterthan f c g approachesthespeedoflight.TheTEMmodepropagatesatthespeedoflightwith allthefrequenciesarrivingsimultaneously.TheEarth-Ionospherewaveguideisfarfrom anidealwaveguide,butthemodalfeaturesexhibitedbytheidealwaveguidearesimilar tothemodalfeaturesoftheEarth-Ionospherewaveguide. 3.2WavePropagationinPlasma TheionospherethatmakesuptheupperboundaryoftheEarth-Ionosphere waveguideismadeupofcoldplasma,henceitisnecessarytounderstandthe electromagneticpropertiesofcoldplasmatounderstandthepropagationofelectromagnetic wavesintheEarth-Ionospherewaveguide.Plasmasarethefourthstateofmatterand areconsideredtobespecialcasesofgasesthatincludealargenumberofelectrons, ionizedatoms,neutralatomsandmolecules.Inamoregeneralsenseaplasmaisa stateofmatterthatcontainsenoughnumberofchargedparticlessothatitsdynamic behaviorwouldbedominatedbyelectromagneticforces. Thesunandthestarsarehotenoughtobealmostcompletelyionizedwith enormousdensitiesandtheinterstellargasissparseenoughtobealmostcompletely ionizedbystellarradiation.Startingfromanaltitudeof60kmthesuneffectsour atmospherewithavarietyofradiationsandtheUVradiationisabsorbedbythegaseous mixtureintheatmosphere.Inthisprocessalargenumberofmoleculesandatoms receivesufcientenergytobeionizedwithmaximumionizationoccurringatanaltitude 40

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of approximately350kmandthisresultsintheformationoftheionosphere( Inanand A.S.Inan. 1999). TodeterminepropagationofelectromagneticwavesinplasmaMaxwell'sequations alongwithequationsofmotionarerequired.Themotionofelectronsundertheinuence ofelectricandmagneticeldsconstitutewhichmustbeaccountedforinMaxwell's equationsthroughthecurrentdensityterm ,whichisgivenby: = @ e q e v (3) Where @ e is theambientelectrondensity, v is thevelocityofelectronsand q e isthe chargeonasingleelectron.Similarrelationscanbededucedformotionofions,butthe currentdensityduetoionsissmallandnegligiblecomparedtothatofelectrons. ThetimeharmonicformofMaxwell'sequationscannowbewrittenas(Inanand A.S.Inan. 1999): r H = j 0 E + @ e q e v (3) r E = j 0 H (3) r E n e q e 0 (3) r H =0 (3) q e E j m e v (3) thecontinuityequationforelectronswouldbe: r (@ e v )= )Tj /T1_2 11.955 Tf (j n e (3) FromtheMaxwell'sequationsabove,thefollowingequationcanbededuced: r H = j 0 (1 )Tj /T1_2 11.955 Tf 19.05 8.09 Td (N e q 2 e 2 m e 0 ) E (3) 41

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The aboveequationclearlyindicatesplasmacanberepresentedbyaneffective dielectricpermittivitygivenby( InanandA.S.Inan. 1999): e = 0 (1 )Tj /T1_1 11.955 Tf 13.15 8.95 Td (! 2 p 2 ) (3) where p = q N e q 2 e m e 0 is calledtheplasmafrequency.Thustheeffectsofplasmaonthe electromagneticwavepropagationcanberepresentedintermsoftheeffectivedielectric permittivity( e )andthesolutionsforeldscanbeobtainedinamannersimilartothat ofairafterreplacing 0 with e 3.2.1EffectofCollisions Someelectromagneticpowerisalwayslost(i.e,transformedintoheat)inaplasma becauseoftheeffectsofcollisionsbetweenelectronsandmolecules,ionsandother electrons( InanandA.S.Inan. 1999).Theeffectofthesecollisionsareaccountedforin theequationofmotionthroughafrictionalterm,shownbelow. q e E = j m e v + m e v = j m e (1 )Tj /T1_9 11.955 Tf 11.96 0 Td (j ) (3) where is thecollisionfrequency.Solvingtheequationswecanaccountforthe effectofthesecollisionsintheplasmaintheeffectivedielectricconstantinamanner similartotheonedescribedpreviously,theeffectivedielectricconstant( e )isgivenby: e = 0 (1 )Tj /T1_10 11.955 Tf 25.33 8.09 Td (X 1 )Tj /T1_9 11.955 Tf 11.95 0 Td (j Z ) = e )Tj /T1_9 11.955 Tf 11.95 0 Td (j ,, e (3) where X = 2 p 2 and Z = Intheaboveequationtheimaginarypart ,, e represents thepowerlossduetocollisionsresultingintheattenuationofthewave.Theexpressions foranelectromagneticwaveinaplasmawithcollisionscanbededucedsimilartothatof alossymediumusingtheabovevalues( InanandA.S.Inan. 1999). 3.2.2EffectofStaticMagneticField Whenasteadymagneticeldpermeatesaplasma(likeinthecaseofEarth's magneticeldpermeatingtheionosphere),themediumbecomesanisotropicandthis 42

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results inthepermittivitybeingrepresentedasatensor(amatrix)andnotavector anymore( InanandA.S.Inan. 1999).Theeffectivepermittivity( e )canberepresented asshownbelow: e = 0 B B B B @ 11 12 0 21 22 0 00 33 1 C C C C A (3) Where 11 = 11 = 0 (1+ 2 p (1 )Tj /T1_7 11.955 Tf 11.96 0 Td (j Z ) 2 c )Tj /T1_1 11.955 Tf 11.95 0 Td ((1 )Tj /T1_7 11.955 Tf 11.95 0 Td (j Z )! 2 ) (3) 12 = )Tj /T1_2 11.955 Tf ( 21 = 0 ( j 2 p ( c ) 2 c )Tj /T1_1 11.955 Tf 11.96 0 Td ((1 )Tj /T1_7 11.955 Tf 11.96 0 Td (j Z)! 2 ) (3) 33 = 0 (1 )Tj /T1_2 11.955 Tf 34.58 8.95 Td (! 2 p 2 (1 )Tj /T1_7 11.955 Tf 11.96 0 Td (j Z ) ) (3) Using theabovetermsandsolvingfortheeldsthevalueofindexofrefraction(n) canbederivedandisgivenbelow. n 2 =1 )Tj /T1_8 11.955 Tf 98.14 8.09 Td (X U )Tj /T1_5 7.97 Tf 13.15 4.7 Td (Y 2 sin 2 2(U)Tj /T1_5 7.97 Tf (X) q Y 4 sin 4 4(U)Tj /T1_5 7.97 Tf (X) 2 + Y 2 cos 2 (3) where X = 2 p 2 Y = c Z = U = 1 )Tj /T1_7 11.955 Tf 12.27 0 Td (j Z and istheanglebetweendirectionof propagationandthestaticmagneticeld. TheaboveequationisknownastheAppleton-Hartreeequation.Itcouldbe observedthatithastworootscorrespondingtotwocharacteristicwaves. 3.3PropertiesofEarth-IonosphereWaveguide TheEarth-Ionospherewaveguideissignicantlydifferentfromtheidealparallel platewaveguidebecauseoftheelectricalpropertiesoftheEarth,ionosphereandthe presenceofEarth'smagneticeld.IntheEarth-Ionospherewaveguide,theboundaries i.e.,theEarthandtheionospherearenotperfectconductors.TheEarthhasanite conductivitywhichvariesgreatlydependingonwhethertheparticularlocationisland, 43

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sea oriceandalsoonthetypeofsoilandonmanyotherfactors.Theconductivityof Earthisrelativelylowwhencomparedwiththatofagoodmetallicconductor,butat ELFfrequenciesEarthbehavesasagoodconductor.Butthewavespropagatinginthe Earth-Ionospherehavesomeamountofattenuation. TheionospherewhichistheupperboundaryoftheEarth-ionospherewaveguide isanionizedregionoftheupperatmospherethatcontainssignicantnumberoffree electronsandions( Hargreaves, 1992).Thismakestheregionbehavelikeaplasma, thepresenceoftheEarth'smagneticeldmakestheionosphereananisotropicmedium (whosepropertiesarediscussedintheprevioussection). TherearetwoimportantworksdealingwiththepropagationofELFandVLFwaves intheEarth-ionospherewaveguide.TheworkofJamesWaitpublishedinmanyscientic papersduring1960'sand1970'sandsummarizedinhisbook( Wait, 1970).Waitdeals withthepresenceofionosphere(upperboundaryofthewaveguide)asnotasingle layerbutratherasaseriesofinterfacesandtherebycorrectlyapproximatingasmoothly varyingionosphere,buthefailsincorrectlyinterpretingtheeffectofthepresenceof Earth'smagneticeldintheionospherebydescribingthemediumasanisotropic mediumwhereasinrealityitisananisotropicmedium.Theotherprolicpublisherinthis eldisK.G.Buddenwhodevelopedatheorywhichissummarizedinhisbook( Budden, 1961)calledwaveguidemodetheoryofwavepropagationtocorrectlydescribethe propagationofELF/VLFwavesintheEarth-Ionospherewaveguide. 3.4WaveguideModeTheory-Budden.K.G 3.4.1SourcesofWaves-TheHertzianDipole Thesfericsignalishighlydependentoncertainparametersofsourcelightning (especiallythetimederivativeofcurrent @ I @ t and currentI)throughwhichitoriginates. ThesimplestkindofsourceinelectromagnetismisHertziandipolewhichisequivalent tohavingtwoequalandoppositecharges q onconductorsplacedveryclosetogether andjoinedbyawire( Budden, 1961).Averticaldipoleisonewhoseaxisisparallelto 44

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the linewhichisverticallyupwardsfromthelowerboundary(hereEarth)andpointing towardstheupperboundary(hereionosphere),perpendiculartothesurfaceofthe boundary(assumingthesurfaceisat).Aradiotransmitterisoftenmodeledasa verticaldipoleandisapplicableespeciallywhenthedimensionsofthetransmitting aerialaresmallcomparedtothewavelength,hencethisideaisapplicableespeciallyat extremelylowfrequenciesandverylowfrequencies( Budden, 1961).Thewaveguide modetheoryisapplicableatELF/VLFfrequenciesandhencewhendealingwiththis spectrumoffrequenciesthesourcecansafelybeapproximatedasaverticalHertzian dipole. Atverylowfrequenciesatransmittingaerialisgenerallyabundleofwires connectedtoatransmitterwithitsotherterminalconnectedtoEarth.TakingEarth tobeaperfectconductorthechargeonthewiresinducesanequalandoppositeimage chargeintheEarth'ssurfacetherebyformingadipolewhichtoacertaindegreeis equivalenttoaHertziandipole( Budden, 1961 ).Theaerialitselfwasahalf-dipoleits imageintheEarth'ssurfaceformingtheotherhalf.Buddenstatesthatathundercloud dischargingtoEarthisalsosimilartothehalfdipoleaerial. SincetheexpressionsforelectricandmagneticeldsradiatedbyaHertziandipole arerathercomplicated,itisrecommendedbyBuddentouseanothervectorcalledthe Hertzvectorrepresentedby U .TheelectricandmagneticeldsradiatedbyaHertzian dipolearederivedfromthefollowingexpressions( Budden, 1961). E = )Tj /T1_4 11.955 Tf 9.29 0 Td ( @ 2 U @ t 2 + 1 r( r U) (3) H =( p ) @ @ t r U (3) 3.4.2ModesintheWaveguide Ifahalf-dipoleisplacedneartheEarth'ssurface(likeathundercloud)anditwas saidintheprevioussectionthatitradiatesinamannerverysimilartotheHertzian dipole.Thissectiondealswithrelativeamplitudesandexcitationfactorsofthevarious 45

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w aveguidemodesexcitedbythesourceassumingthattheionosphereisaperfect conductoratacertainheightaswellasthesurfaceoftheEarthasdiscussedbyBudden in( Budden 1961).Therelativestrengthofthewaveguidemodeatacertaindistance fromthesourceisdependentontheorientationofthesourceandalsoontheangleof propagation. Buddenusesthefactthateldscreatedbyasource(hereahalf-dipole)between twoconductorsandthereectionsduetotheseconductorsisequivalenttotheelds duetothesourceanditsimages.Forexampleiftherearetwoconductorsatz=0and z=handasourceispresentatz=0,itisequivalenttohavingasourceatz=0andimage sourcesatz= 2h 4h ,.... withtheconductorsremoved.Thisarrangementofthe sourceanditsimagesissimilartotheeffectofanopticaldiffractiongrating( Budden, 1961). BuddenobservedaftersolvingfortheHertzvectorintheabovedescribedscenario thatinanidealparallelplatewaveguideverticalsourcesexciteonlyTEMandTM waveguidemodeswhoserelativeamplitudesaregivenby: 1 2 TEM mode (3) (cos n ) 1 2 cos( kz 1 sin n ) TM n mode (3) where z 1 is theheightofthesourcewiththelowerboundaryofthewaveguide(the surfaceofEarth)beingatz=0.Itcouldalsobeobservedfromequation 3 thatthe TEMmodeirrespectiveofthefrequencyofpropagationhasagainof1/2.Thefactor cos( kz 1 sin n ) isalsocalledastheexcitationfactorortheheightgainfunctionforthe TM n mode. InasimilarmanneritwasobservedbyBuddenthathorizontalsourcesexciteonly TEwaveguidemodesinanidealwaveguidewithperfectlyconductingparallelplate waveguide,whoserelativeamplitudesaregivenbelow: 46

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(cos n ) )Tj /T1_4 5.978 Tf 5.76 0 Td (1 2 sin(kz 1 sin n ) TE n mode (3) In equation 3 sin(kz 1 sin n ) istheheightgainfunctionfor TE n mode. 3.4.3ReectionCoefcientsintheEarth-Ionospherewaveguide TheupperboundaryoftheEarth-Ionospherewaveguidei.e.,theionosphere behaveslikeananisotropicmediuminthepresenceoftheEarth'smagneticeldwhich resultsinthefacttheTEandTMmodesarecoupledatthisboundaryandanincident TEwave(oraTMwave)producesbothTEandTMwave( Budden, 1961).Anotherway oflookingatthisiswhenanincidentwaveispolarizedwithaparallelpolarization(or aperpendicularpolarization)thewavereectedfromtheupperboundaryiselliptically polarizedwithcomponentsthathavebothparallelandperpendicularpolarizations. Thiseffectcanbeaccommodatedforinthereectioncoefcients.Fortheupper boundary(theionosphere)thecouplingbetweenthemodesresultsinthereection coefcient(R U ( ))nolongerremainingascalarbutrepresentedbya2 2matrixand thereectioncoefcientlowerboundary(theEarthR L ( ))isnotaanisotropicmedium resultinginnocouplingbetweenthemodesandtheoff-diagonalelementsturningzero (Budden, 1961 )witheachelementinthereectionmatricesbeingafunctionofthe angleofincidencetotherespectiveboundaries. Thereectioncoefcientsforboththeupperandlowerboundaries(R U ( ) and R L ( ))asgivenbyBuddenaregivenbelow: R U ( )= 0 B @ k R kk R ? k R ?? R ? 1 C A R L ( )= 0 B @ k R k ( )0 0 ? R ? 1 C A (3) Intheabovematricestheleftsubscriptontheelementsdenotestheincidentwave polarizationandtherightsubscriptdenotespolarizationofthereectedwave. 47

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Due totheanisotropicnatureoftheionospherepureTEandTMmodesarenot capableofexistinginthewaveguideandinsteadthewaveguideiscomposedofthe modescalledquasi-TEM(QTEM),quasi-TE(QTE)andquasi-TM(QTM)modes.The differencebetweenaTEmodeandaTEMmodeforexampleisthattheQTEmode issimilartoaTEmodeexceptthatQTEmodealsohasasmallaxialelectriceld component( Budden, 1961).Thelowerorderquasimodesaregenerallymorepurethan thehigherordermodes. 3.4.4ModeEquation Asstatedintheprevioussectiononparallelplatewaveguides,foramodetoexist inawaveguideithastosatisfythemodeequation(like 3 ).Buttheboundariesofthe Earth-Ionospherewaveguidearenon-idealandaremuchmorecomplicatedthanthe idealparallelplatewaveguide.Moreoverthemodeequationsdescribedintheprevious section(onidealparallelplatewaveguide)donotholdherebecauseoftheanisotropic natureoftheionospherewhichallowsonlythequasi(QTEM,QTEandQTM)modesto exist.ToformthemodeequationfortheEarth-IonospherewaveguideBuddenusesthe factthatforamodetoexistinanywaveguidetheuniformplanewavesthatconstitutethe modemustretaintheirplanarfrontsuponreectionfromtheboundariesi.e.,theplane wavereectedoncefromeachboundary(theupperandlower)mustbeinphasewith theincidentplanewave( Budden, 1961). Thefundamentalequationofmodetheorywhichsatisesthemodeequationforthe Earth-Ionospherewaveguideisgiveninequation 3 shownbelow: R I ( )R G ( )exp( )Tj /T1_4 11.955 Tf 9.29 0 Td (2ikh sin )= I (3) where I istheidentitymatrix.Eachangleofincidence i thatsatisesequation 3 denesanindividualmodeatacertainfrequency.Theexpressionfor R I iscomplicated andisdifculttosolveanalytically.ButiftheEarthandionospherearetreatedasperfect conductorsequation 3 wouldsimplifytoanequationsimilarto 3). 48

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Another factorthatiseffectedbythenatureoftheEarth-Ionospherewaveguideis theheightgainfunctiondescribedinsection3.4.2foranidealparallelplatewaveguide. Howeveritcanbeobservedthattheheightgainfunctionscanbecalculatedwiththe knowledgeofthemodeangles( n )andthereectioncoefcients(R G and mathbfR I ). Thereaderisreferredto( PappertandFerguson, 1986 )foragoodsummaryofof theheightgainfunctionsthatwereformulatedbyBudden.Additionally( Pappertand Ferguson 1986 )alsocalculatetheheightgainfunctionsfordifferentsourceorientations andaltitudesandalsofordifferenteldcomponents.Theseheightgainfunctionsvary dependingontheeldcomponents,orientationofthedipoleandtheheightofthedipole. ThesefunctionscontainthemodiedHenkelfunctionsunlikethesinesandcosinesasin theidealparallelplatewaveguide.ThegeneralequationfortheoutputeldFwithallthe factorstakenintoconsiderationisgivenin( PappertandFerguson, 1986)and( Cummer, 1997)as: F = C(F) ik 3 2 Il p 8 x exp( i 4 ) X tn rn exp( )Tj /T1_4 11.955 Tf (ikx sin( n )) (3) where C(F) is 0 if F is acomponentofthemagneticeldand C(F) is q 0 0 if F is a componentoftheelectriceldand tn and rn arecalledthetransmitterandreceiver excitationfactorsrespectively,thesecontaintheheightgainfunctions. Thevaluesof tn and rn arederivedin(PappertandFerguson, 1986)forvarious orientationsofthedipole.Forexampleifanelectricdipoleisorientedatsomeangle r to thez-axisandatanangle tothedirectionofpropagation(x-axis)atanaltitude z t (the Earth-IonospherewaveguideisillustratedinFigure 3-2),thetransmitterexcitationfactor tn isgivenby(PappertandFerguson, 1986 )as: tn = )Tj /T1_1 11.955 Tf ( 1 sin( n )cos( r )f 1 (z t )+ 3 4 sin(r )cos( )f 2 (z t )+ sin(r )sin( )f 3 ( z t ) (3) wherethevariablesusedintheaboveequationlike 1 3 4 f 1 f 2 andf 3 are denedin( PappertandFerguson, 1986). 49

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3.4.5 CorrectionfortheCurvedNatureoftheEarth-IonosphereWaveguide AnotherimportantfactorthatmakestheEarth-ionospherewaveguidesubstantially differentfromtheidealparallelplatewaveguideisthecurvednatureofEarth.Especially atlargedistances(whichisthecaseinthisthesis)thecurvatureoftheEarthhas aprofoundeffect.Infreespacetheeldattenuationduetoenergyspreadingis proportionalto r )Tj /T1_4 7.97 Tf (1 ,rbeingthedistancefromthesource.Thiscorrespondstoa r )Tj /T1_4 7.97 Tf 6.59 0 Td (2 factorforthewavepower.Butforaparallelplatewaveguidethisspreadingfactoris reducedto r )Tj /T1_4 5.978 Tf 5.75 0 Td (1 2 because 'r'nowisthe2-ddistancefromthesource( Wood 2004).For asphericalwaveguideofradius'R'thecorrespondingattenuationfactorwouldbe (R sin( x R )) )Tj /T1_4 5.978 Tf 5.75 0 Td (1 2 where 'x'isthegreatcircledistancebetweenthesourceandthereceiver (Budden, 1961 ).Itcouldbeobservedthatthistendsto R )Tj /T1_4 5.978 Tf 5.75 0 Td (1 2 as R 1 Themodeequationgivenbyequation 3 mustalsobemodiedduetotheeffect ofthiscurvaturebecausethemodeanglesarevalidonlyforparallelsurfacesandnot sphericalshellsliketheEarth.Therewereafewmethodsemployedinliteraturetodeal withthisproblembutthemostcommonlyemployedmethodwasdescribedin( Richter, 1966).Inthispaperaco-ordinatetransformationmethodwasintroducedthatconvertsa cylindricalco-ordinatesystemintoparallelbymodifyingtherefractiveindexasagradient n 2 mod =exp( z R ) so thattheraysrepresentingtheplanewavesbendupwardsinsteadof travelinginstraightlines. 3.5LongWavelengthPropagationCapability(LWPC) LWPCisacollectionofFORTRANprogramswhichenabletheimplementation oftwodimensionalwaveguidepropagationformulationalongthegreatcirclepath betweenatransmitterandareceiver.Thisprogramappliestheimplementstheconcept ofpropagationofELF,VLFandLFradiowavestotheEarth-Ionospherewaveguide,this programsetsupthecalculationofmodeparametersalongtheselectedpropagation pathsforuserdenedoperatingareas( FergusonandC.H.Shellman 1989 ).These setofprogramsoperateseparatelyorinsequencetogenerateresultsasperthe 50

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requirement oftheuser.ThiswasdevelopedovermanyyearsattheNavalOcean SystemsCenter(NCCOSC/NRaD)( FergusonandC.H.Shellman 1989).Thecodehas threeimportantpartscalledPRESEG,MODEFNDRandFASTMCeachofwhichis describedbelow. 3.5.1PRESEG PRESEGistheFORTRANprogramwhichsegmentsthepropagationpathbetween thetransmitterandreceiverbasedontheionospheric,groundandsomeother parameters,someofwhicharetakenasinput.PRESEGdeterminesthenecessary waveguideparametersandformatsthemproperlyforinputtothenextstageofthe program.SomeparameterslikemagneticeldofEarth,permittivityandconductivity ofEarthoverthepropagationpatharetakenfrombuiltinmodelsandlesbasedon experimentalstudyoftheseparameterslike( HauserandF.J.Rhoads, 1969).Thisthesis employsahomogenousionospherethroughouttheentirepropagationthedetailsof whicharegiveninthenextsection.Whentheinhomogeneitiesareconsideredthe waveguideissegmentedintoanumberofslabsandslabboundariesareplacedwhere thereisachangeintheparameterslikeionosphericprole,groundconductivityetc (Cummer, 1997). 3.5.2MODEFNDR MODEFNDRisanimportantcomponentofthepropagationmodelandisa FORTRANprogramwhichdeterminestheeigensolutionsforahorizontallyhomogenous waveguide/slab( FergusonandC.H.Shellman 1989 ).Ittakesthewaveguideparameters fromPRESEGasinputandsearchesforanglesinsideapredenedregionthatsatisfy themodecondition 3.Tocalculatethenecessarymodeconstantsneededfor determiningtheeldsinthewaveguide,thereectioncoefcientsfortheionosphere mustbesolvedforageneralelectrondensityprole,iondensity,collisionfrequency proleandangleofincidence,thisisdonebyMODEFNDRbyassumingthatforaxed angleofincidencetheeldcomponentsvaryinx-directionand @ @ y =0 ( Cummer, 1997). 51

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The excitationfactorswhichareneededtodeterminethenaleldstrengthsofeach modearealsocalculatedbythisprogram.Theoutputofthisprogramisgivenasthe inputtoFASTMC. 3.5.3FASTMC Thepropagationpathisdividedintohorizontallyhomogeneouswaveguides/slabs, thesignalstrengthoftheelectromagneticeldalongapathisdeterminedusing themodesolutionsforeachofthehomogenousslabbytheFASTMC( Ferguson andC.H.Shellman, 1989).FASTMCisasimpliedversionofanotherFORTRAN programcalledFULLMCwhichisamathematicallyrigorousmodelwhichdoesfull wavecalculationswhichmakesthisprogramquiteslowinexecution( Fergusonand C.H.Shellman 1989 ).ThisiswhereFASTMCcomesinhandyandisanapproximate modelandrunsmuchfasterthantheFULLMCandproducescomparableresults.The outputofFASTMCisthemagnitudeinDBover1 V/meldstrengthandphasein degrees.Acorrectionfactorof 4.1887x 10 )Tj /T1_6 7.97 Tf 6.59 0 Td (6 Ilfexp ( i = 4) mustbeappliedtotheoutput ofFASTMCtomakeitequivalenttoaverticaldipole( Cummer 1997),whereIlisthe currentmomentoftheradiatingdipoleandfisthefrequency. 3.5.4ImplementationinLWPC TheeldsalongagivenpropagationpathintheEarth-Ionospherewaveguidecan becalculatedusingtheLWPCcodewithasetofrequiredparametersgivenasinput. LWPCusesthetwodimensionalpropagationalmodeldevelopedbyBudden( Budden, 1961)knownasthewaveguidemodetheory,Figure 3-2 showstheEarth-Ionosphere waveguide.ItcanbeobservedfromtheFigurethatthetwodimensionsarexandz, withxbeingthedirectionofpropagationalongthegreatcirclepathandzbeingthe altitudeandallthepropertiesofionosphereandgroundassumedtobeconstantinthe y-direction. ThereareasetofparametersthatneedtobeinputinordertosetLWPCtorun. Theseparametersareenteredusingamodelle,afteralltherequiredparametersare 52

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Figure 3-2.Earth-IonosphereWaveguide entereditisnecessarytogivetheseparametersasinputstotheprogramPRESEG whichitselfservesasaninputtotheprogramsMODEFNDRandFASTMC.Hencea scriptiswrittenwhichinputsthecorrectparametersinaspeciedmannertoeachofthe programsandexecutestheminanorderlymanner. Someparameterswhicharetobeinputtothemodelleandusedinthisthesisare describedbelow,foradetailedlistofvariousparametersandtheirdefaultvaluesthe readerisreferredto( Dermikol 1999). freq-frequencyinKHz,defaultvalueis23.4KHz power-radiatedpowerinKw,defaultvalueis1Kw trlat,trlong-coordinatesofthetransmitterindegreeswestanddegreesnorth, defaultvaluesare 158.15 o Wand 21.41 o Nrespectively rclat,rclong-coordinatesofreceiverindegreeswestanddegreesnorth,default valuesare 0 o Wand 0 o Nrespectively maxalt-highestaltitudeoftheionosphericproletobeconsideredforcalculation purposesinkm,defaultvalueis90km 53

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le containingtheelectrondensityprolesuptothespeciedmaxaltvalue lecontainingtheinformationaboutcollisionfrequency PRESEGusesthemodellewiththerequiredparametersandsegmentsthe propagationpathaccordingtotheinformationinthismodelleandcertainautomatic segmentationrulessuchastheinbuiltconductivitymapofEarthandmodelofEarth's magneticeld,thesegmentationinformationisthenstoredinoutputleswhicharethen usedbytheprogramsMODEFNDRandFASTMC( Dermikol 1999). MODEFNDRusestheinformationinthemodelinputlerelatedtoelectrondensity prolesandtheoutputfromPRESEGtoobtainthesolutiontothemodeequation 3. Tondsolutionstothemodeequationitneedstocalculatethereectioncoefcientsof theionosphereandaneffectivereectionheight.Itthencalculatestheattenuationrate, phasevelocity,initialexcitation,heightgainfunctionsforeachmodeusingthevaluesof reectioncoefcients. FASTMCusestheoutputsfromMODEFNDRandPRESEGtocalculatethemode conversioncoefcientmatricesatdifferentslabscreatedbyPRESEG.Figure 3-3 shows theowchartpertainingtotheexecutionofLWPC. 3.6ParametersRequiredtoCalculatetheSfericPropagationModel AsunderstoodfromthediscussionintheprevioussectionLWPCemploysa single-frequencymodel.TomodelELFpropagationLWPCsolvesthetime-harmonic propagationproblemusingthewaveguidemodetheoryofwavepropagation( Budden, 1961).Therearecertainparametersthatneedtobecalculatedasinputstousethe model,parameterslikethegroundandambientmagneticeldareautomatically includedinLWPCbutcertainotherparametersliketheionosphericelectrondensity prolesandtheCurrentMomentwaveformintherequiredfrequencyrangewhichare discussedinthefollowingsectionsneedtobeprovided. 54

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Figure 3-3.FlowchartshowingtheexecutionofLWPC 3.6.1IonosphericElectronDensityProles Electrondensitiesatacertainaltitudeareanimportantfactorinmodelingthesferic propagation.TheprolewascalculatedfromIRI(InternationalReferenceIonosphere). Thoughtheionospherevariesfromoneregiontoanotherandfromtimetotimea homogenousionospherewasassumedthroughoutthepropagationpathinthisthesis. Tounderstandtheeffectsofdifferentionosphericconditionsonsfericpropagation fourdifferentionosphericelectrondensityproleswerecalculated.Twooftheproles werecalculatedfordaytimeionosphericconditionsandtwofornighttimeionospheric conditionsasshowninFigure 3-4 foraltitudesupto300km.Theseproleswere calculatedusingdatafromIRIatthecoordinates0 o and40 o .Oneofthedaytime ionosphereswasatlowerelectrondensityvalueswhiletheotherwasathigherelectron 55

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density values,thenighttimeionospheresdifferbythefactthatoneofthemhasa valleyat100-150Kmwhiletheotherdoesnot.ThevalleyoccursattheE-regionofthe nighttimeionosphereduetothedecreaseinelectrondensityvaluesandisacommon phenomenaatnights. Figure 3-4.Representativeelectrondensityproles TheInternationalReferenceIonosphere(Bilitza 2001)isaninternationalproject sponsoredbytheCommitteeonSpaceResearch(COSPAR)andtheInternational UnionofRadioScience(URSI).IRIgetsitsdatafromIonosodes,Alouettetopside sounders,IncoherentScatterRadarsandinsituinstrumentsonseveralsatellitesand rockets.Itistheinternationalstandardforterrestrialionospheresince1999. 3.6.2CurrentMomentWaveformofaLightningStrike TheotherparameterthatisneededtomodeltheELFsfericpropagationusing LWPCiscurrentmomentwaveformintherequiredfrequencyrange.Asmentionedin theprevioussectionstheLWPCgivesatime-harmonic(singlefrequency)solutionand 56

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so itisrequiredtogetthecurrentmomentwaveformasafunctionoffrequency(i.e.,in frequencydomain). PrevioustheoreticalstudiesofELFsferics(Cummer, 1997),(S.A.Cummerand U.S.Inan 2000 )etchaveassumedanidealimpulselightningdischargeandmodeledthe correspondingcurrentmomentwaveform.Althoughthisisadecentapproximationthere arecertainspectralfeatureswhichcannotbemodeledtheoreticallyandmoreoverevery lightningstrikediffersfromtheother.Thismakesitdifculttomodelsfericsaccurately.In thisworkthesfericsradiatedfromrockettriggeredlightningarebeingmodeled,the advantagewithrockettriggeredlightningistheavailabilityofveryaccuratedataabout thelightning. Figure 3-5 showsthecurrentwaveformthathasbeenusedinthisthesis.It representsthecurrentowingatthebaseofthelightningchannelduringtherocket triggeredlightningexperimentconductedatCampBlandingon29 th March2009. Figure 3-5.CurrentvsTimewaveformfromrockettriggeredlightning Theheightofthelightningchannelisassumedtobe7.5Kminthiswork. 57

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CHAPTER 4 MODELINGELFSFERICS ThischapterdescribesthemodelingofELFsfericsafteralltherequiredinput parametersdiscussedinthepreviouschapteraregathered.Allthemodelingwork presentedinthischapterisdoneusingasetofcomputerprogramscalledLWPCwhich isbasedonasinglefrequencypropagationmodel( Budden 1961).Firstthesfericsare modeledassumingahomogeneousgroundandahomogeneousionospherethroughout thepropagationpathandthenamorecomplicatedcasewithainhomogeneousground proleisconsidered. Themodelcompletesitscalculationsinthefrequencydomainandtheoutputis aspectrumofthesfericasafunctionoffrequency.Theonlymodepropagatingisthe QTEMmodewhichdoesnothaveacut-offfrequencyandtheattenuationrateasa generaltrendincreasessteadilywiththefrequency(althoughcertainexceptionswere observedatsomefrequencies)causingthemodetodieoffeventuallyataround1.7 KHz. 4.1HomogeneousWaveguide ELFsfericsintherangeoffrequencies10-500Hz(withthedifferencebetween eachfrequencysamplebeing10Hz)aremodeledassumingahomogeneousground proleofconductivity 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (2 S/mandarelativepermittivityof15.Anighttimeionospheric proleshowninFigure 4-1 istakenandisassumedtobehomogeneousthroughoutthe propagationpath,threedifferentpropagationpathsofdistances1000km,2000kmand 3000kmareconsidered.Animpulselightningcurrentwaveformsimilartotheoneused in( Cummer, 1997 )and(S.A.CummerandU.S.Inan 2000)isemployedhere,thiscaseis similartothemodelingpresentedin( S.A.CummerandU.S.Inan 2000 ). ThespectrumshowninFigure 4-2 aretheamplitudesoftransversehorizontal magneticeld B y atthespecieddistances.Itcanbeobservedthattheresults presentedaresimilartotheonesobtainedin( S.A.CummerandU.S.Inan 2000)for 58

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Figure 4-1.Representativenighttimeionosphere thenighttimeionosphere.Figure 4-3 showsthesamespectrumshowninFigure 4-2 in decibelscale. Figure 4-2.ELFsfericspectraofhomogeneousgroundinlinearscale Thespectraarepassedthroughahigh-passlterofcut-offfrequency30Hz. 59

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Figure 4-3.ELFsfericspectraofhomogeneousgroundindecibelscale 4.2InhomogeneousGround Inthiscaseainhomogeneousgroundisconsideredwithconductivityvaryingfrom 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (2 to 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (3 S/m.Therestoftheinputparametersarethesameasthoseassumed inthepreviouscaseandanarbitrarypropagationpathofdistancearound2000Kmis considered.TheELFspectraaremodeledinthefrequencyrangeof10-500Hz(withthe differencebetweeneachfrequencysamplebeing1Hz) Thespectraarepassedthroughahigh-passlterofcut-offfrequency30Hzina mannersimilartothepreviouscase.TheFigure 4-4 showstheamplitudeoftransverse horizontalmagneticeld B y computedcomparedwiththeamplitudecalculatedinthe previouscaseforahomogeneousgroundcoveringadistanceof2000Km.Figure 4-5 showsthecomparisonofamplitudesofthetwospectraindecibelscale. Itcouldbeobservedthattheresultsobtainedinboththecasesaresimilar exceptforsomedifferencesliketheamplitudeofspectracalculatedassumingan inhomogeneousgroundislessthantheamplitudecalculatedusinghomogeneous ground,thisassumptionisvalidonlyforshortdistanceswhichhaveafairlysimilar 60

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Figure 4-4.ComparisonofELFsfericspectraforinhomogeneousandhomogeneous ground(distance-2000Km) Figure 4-5.ComparisonofELFsfericspectraforinhomogeneousandhomogeneous ground(distance-2000Km)indecibelscale 61

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g roundthroughoutthepropagationpathandthisapproximationdoesnotproduce accurateresultswhenthepropagationpathhashugevariationsinconductivitydueto thepresenceofbothlandandseainthepropagationpath.Suchasituationisdealtin thenextsection. 4.3ModelingofELFsfericsPropagatingfromCampBlandingtoMcMurdo Station Inthiscaseacomplicatedinhomogeneousgroundisconsidered.Thesourceof thesferic-thelightningdischargeisatCampBlanding,Florida( 29.94 o N and )Tj /T1_2 11.955 Tf (82.03 o W ) andthereceiverisatMcMurdoStation,Antarctica( )Tj /T1_2 11.955 Tf (77.88 o N and 166.73 o W )with atotalpropagationdistanceof13740Km.Theelectrondensityvaluesspeciedin thepreviouschapterareusedandtheeffectofionsisneglected.Thesourcecurrent momentwaveformpresentedinthepreviouschapterisusedassumingavertical dipoledischarge.LWPCcalculatestheamplitudeandphaseforanyorientationof thehertziandipole,tomakethesfericwaveformequivalenttothatcausedduetothe lightningdischargeusedinthisthesis,theoutputofLWPCshouldbeconvolvedwiththe current-momentwaveform,todothatthecurrent-momentwaveformwasconvertedinto frequencydomainanditwasmultipliedwiththeoutputofLWPCinlinearscale. Thecurrentwaveformistakenformtherockettriggeredlightningconductedat CampBlanding,therebygivingmorerealisticwaveformcomparedtosomeprevious models( Cummer, 1997 )whichusetheoreticallymodeledreturnstrokeoflightning.The lightningdischargeusedinthecalculationspresentedinthisthesisoccuredonMarch 29,2008. Thesfericspectracalculatedinthisthesisareinthefrequencybandof45-500Hz assuminganinhomogeneousgroundwithconductivityvaryingfrom 10 )Tj /T1_7 7.97 Tf (4 to4S/manda homogenousionospherethroughoutthepropagationpath.Figure 4-6 showsthegreat circlepathofpropagationofthesfericformFloridatoAntarctica. 62

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The outputcalculatedfromLWPCexhibitedsomesuddenjumpswiththechange inconductivityoftheground.Thisphenomenoncouldnotbeexplainedinthisthesis andtheoutputofLWPCwasadjustedmanuallysuchthatthevariationofamplitude withdistancelookedsmoothwithoutsuddenjumps,thisisshownmoreclearlyinthe nextchapter.Thesfericwaveformsshowninthisthesiswerecalculatedassuminga Hermitiansymmetry( S.A.CummerandU.S.Inan 2000). Alltheplotscorrespondingtothesameionosphereareinthesamecolor,withblack representingnighttimeionospherewithavalley,bluerepresentingdaytimeionosphere type1,greenrepresentingnighttimeionospherewithoutavalleyandredrepresenting dayttimeionospheretype2. Figure 4-6.PropagationPathoftheSfericfromFloridatoAntarctica(GreatCircle) 63

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F ourdifferentionospheresshownintheprevioussectionareconsideredinthis case. 4.3.1NighttimeIonosphereWithaValley Figure 4-7 belowshowsthenighttimeionospherewithavalleyat100-150km.The valleyistheregionoftheionospherewherethereisadecreaseintheelectrondensity valuescomparedtootherregionsoftheionosphere. Figure 4-7.Nighttimeionospherewithavalley Figure 4-26 showsthecurrentwaveformemployedhereincalculatingthesferic spectrumandwaveform,thecurrentwaveformasobservedisforatime-periodofone second. Figure 4-9 showsthedirectoutputofLWPCwithoutconvolvingitwithlightning currentmomentwaveform. ThevalleyusuallyoccursintheE-regionoftheionosphereataheightof100-150 Km,thisregionoftheionospherehasasignicantaffectonthesfericwaveform.Figure 4-10 showsthespectrumof B y thatwouldbeobservedatthereceiversinadecibel scaleandFigure 4-11 showsthespectrumofthesferic( B y )inalinearscale(Tesla), 64

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Figure 4-8.CurrentWaveformemployedincalculations Figure 4-9.LWPCoutputfornighttimeionospherewithavalley 65

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it couldbeobservedfromFigure 4-10 thatthisregionproducescertainresonancelike effectsandthewaveformisalittlecomplicatedcomparedotherwaveformsdiscussedin thesubsequentsections. Figure 4-10.ModeledELFspectrumindecibelscale(over1nanotesla)fornighttime ionospherewithavalley Figure 4-12 showsthesfericwaveform(thetimedomainsignal)forthenighttime ionosphereconsideredinthissection. 4.3.2DaytimeIonosphere-Type1 Figure 4-13 showsthedaytimeionosphericelectrondensityvalues.Thedaytime ionosphereisnotverycomplicatedcomparedtothenighttimeionosphere. Figure 4-26 showsthecurrentwaveformemployedhereincalculatingthesferic spectrumandwaveform,thecurrentwaveformasobservedisforatime-periodofone second. Figure 4-15 showsthedirectLWPCoutputforthisionospherewithoutconvolvingit withcurrentmomentwaveform. 66

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Figure 4-11.ModeledELFspectruminlinearscalefornighttimeionospherewithavalley Figure 4-12.ModeledELFsfericwaveformfornighttimeionospherewithavalley 67

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Figure 4-13.DaytimeionosphereType1 Figure 4-14.CurrentWaveformemployedincalculations 68

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Figure 4-15.LWPCoutputfordaytimeionospheretype1 Figure 4-16 showsthespectrumof B y thatwouldbeobservedatthereceiversin adecibelscaleandFigure 4-17 showsthespectrumofthesferic( B y )inalinearscale (Tesla)forthedaytimeionosphere,thesfericsobtainedfromdaytimeionosphereisnot ascomplicatedasthenighttimeionospherewithavalley,withtheamplitudedecreasing withincreaseinfrequency.Figure 4-18 showsthesfericwaveformforthisspectrum. 4.3.3NighttimeIonosphereWithoutaValley Figure 4-7 belowshowsthenighttimeionospherewithoutavalleyat100-150km. Figure 4-26 showsthecurrentwaveformemployedhereincalculatingthesferic spectrumandwaveform,thecurrentwaveformasobservedisforatime-periodofone second. Figure 4-21 showsthedirectLWPCoutputfortheionosphereshownintheprevious gurewithoutconvolvingitwithcurrentmomentwaveform. Unlikethepreviousnighttimeionospherethisionospherehasnovalley.Figure 4-10 showsthespectrumof B y thatwouldbeobservedatthereceiversinadecibelscaleand Figure 4-11 showsthespectrumofthesferic( B y )inalinearscale(Tesla),itcouldbe observedfromFigure 4-10 thattherearenoresonancelikephenomenaasobserved 69

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Figure 4-16.ModeledELFspectrumwaveformindecibelscale(over1nanotesla)for daytimeionospheretype1 Figure 4-17.ModeledELFspectruminlinearscalefordaytimeionospheretype1 70

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Figure 4-18.ModeledELFsfericwaveformfordaytimeionospheretype1 Figure 4-19.Nighttimeionospherewithoutavalley 71

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Figure 4-20.CurrentWaveformemployedincalculations Figure 4-21.LWPCoutputfornighttimeionospherewithoutavalley 72

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in thepreviousnighttimeionosphere(withthevalley),thusshowingthevalleyhasa greatimpactontheshapeofthesferic.Figure 4-24 showsthesfericwaveformforthe spectrumcalculatedinthissection. Figure 4-22.ModeledELFspectrumindecibelscale(over1nanotesla)fornighttime ionospherewithoutavalley Figure 4-23.ModeledELFspectruminlinearscalefornighttimeionospherewithouta valley 73

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Figure 4-24.ModeledELFsfericwaveformfornighttimeionospherewithoutavalley 4.3.4DaytimeIonosphere-Type2 Figure 4-25 showsthedaytimeionosphericelectrondensityvalues,thisionosphere hashigherelectrondensityvaluescomparedtothepreviousdaytimeionosphere discussedintheprevioussection. Figure 4-26 showsthecurrentwaveformemployedhereincalculatingthesferic spectrumandwaveform,thecurrentwaveformasobservedisforatime-periodofone second. Figure 4-27 showsthedirectLWPCoutputforthisionospherewithoutconvolvingit withcurrentmomentwaveform. Figure 4-28 showsthespectrumof B y thatwouldbeobservedatthereceivers inadecibelscaleandFigure 4-17 showsthespectrumofthesferic(B y )inalinear scale(Tesla)forthedaytimeionosphere(withhigherelectrondensityvalues),the sfericsobtainedfromthisionospherearesomewhatlowerinamplitudethanthe previousdaytimeionospherewhichcouldbeattributedtothehigherelectrondensity 74

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Figure 4-25.DaytimeionosphereType2 Figure 4-26.CurrentWaveformemployedincalculations 75

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Figure 4-27.LWPCoutputfordaytimeionospheretype2 values.Figure 4-30 showsthesfericwaveformforthespectracalculatedusingdaytime ionospheretype2. Figure 4-28.ModeledELFspectrumindecibelscale(over1nanotesla)fordaytime ionospheretype2 Thusitcouldbeobservedfromtheabovespectrathationosphereplaysa signicantroleindeterminingtheshapeofthesfericspectrum,moreimportantlyit 76

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Figure 4-29.ModeledELFsfericwaveforminlinearscalefordaytimeionospheretype2 Figure 4-30.ModeledELFsfericwaveformfordaytimeionospheretype2 77

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is theE-regionoftheionospherethatplaysasignicantroleunlikefortheVLFwaves wheretheD-regionoftheionosphereplaysavitalrole( Cummer, 1997).Thisdatacould beusedtodeterminethenoiseoorofthereceiversthatareusedinAntarcticatodetect thesferics. 4.4EffectsofDifferentComponentsofCurrentontheSfericWaveform Thissectiondealswiththeeffectsofdifferentcomponentsofcurrentonthesferic waveform,todothatthecurrentwaveformispassedthroughdifferentrectangular windowseachofwhichselectsaparticularcomponentandremovestheother componentsbymakingthemzero.Bydoingthisthetimeperiodofthecurrentwaveform stillremainsthesamebutonlytheselectedcomponentremainsandtherestofthe waveformbecomeszero. Figure 4-31 showsthedifferentcomponentsofthecurrentwaveformusedinthis thesis,itcouldbeseenfromthegurethatthisparticularcurrentwaveformhasanInitial ContinuousCurrent(ICC)phasefollowedbyvereturnstrokes. Figure 4-31.ComponentsoftheCurrentWaveformUsed EachofthesecomponentsareconvolvedwithLWPCsuchthatonlytheeffectsof thatparticularcomponentareobserved,theguresbelowshoweachofthecomponent 78

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of currentanditsresultantsfericwaveformfornighttimeionospherewithavalleyasan example. Figure 4-32 showstheICCcomponentofthecurrentandFigure 4-33 showsthe resultantsfericwaveform. Figure 4-32.ICCComponentoftheCurrentWaveformUsed Figure 4-33.ResultantSfericCausedduetotheICCComponentofCurrent 79

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Figure 4-34 sho wsthereturnstroke1ofthecurrentandFigure 4-35 showsthe resultantsfericwaveform. Figure 4-34.ReturnStroke1oftheCurrentWaveformUsed Figure 4-35.ResultantSfericCausedduetotheReturnStroke1ofCurrent Figure 4-36 showsthereturnstroke2ofthecurrentandFigure 4-37 showsthe resultantsfericwaveform. 80

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Figure 4-36.ReturnStroke2oftheCurrentWaveformUsed Figure 4-37.ResultantSfericCausedduetotheReturnStroke2ofCurrent 81

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Figure 4-38 sho wsthereturnstroke3ofthecurrentandFigure 4-39 showsthe resultantsfericwaveform. Figure 4-38.ReturnStroke3oftheCurrentWaveformUsed Figure 4-39.ResultantSfericCausedduetotheReturnStroke3ofCurrent Figure 4-40 showsthereturnstroke4ofthecurrentandFigure 4-41 showsthe resultantsfericwaveform. 82

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Figure 4-40.ReturnStroke4oftheCurrentWaveformUsed Figure 4-41.ResultantSfericCausedduetotheReturnStroke4ofCurrent 83

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Figure 4-42 sho wsthereturnstroke5ofthecurrentandFigure 4-43 showsthe resultantsfericwaveform. Figure 4-42.ReturnStroke5oftheCurrentWaveformUsed Figure 4-43.ResultantSfericCausedduetotheReturnStroke5ofCurrent 84

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4.4.1 EffectsofCurrentComponents-DifferentIonospheres Thissectiondemonstratestheeffectsofthecurrentcomponentsonthesferic waveformsunderdifferentionospheresshownintheprevioussections.Ineachofthe followinggures,thesfericwaveformwhichresultsduetotheentirecurrentwaveformis shownonwhichareoverlayedthesfericwaveformsduetoeachindividualcomponent. Thesfericwaveformsduetoeachindividualcomponentareoverlayedonlyonthe portionofthecompletewaveformwhereithassignicanteffect,therestoftheportionis clippedforalucidview. Figure 4-44 showsthesfericwaveformwithallthecomponentslaidoutforthe nighttimeionospherewithavalley. Figure 4-44.SfericWaveformandDifferentComponents-NighttimeIonosphereWitha valley Figure 4-45 showsthesfericwaveformwithallthecomponentslaidoutforthe daytimeionospheretype1. Figure 4-46 showsthesfericwaveformwithallthecomponentslaidoutforthe nighttimeionospherewithoutavalley. 85

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Figure 4-45.SfericWaveformandDifferentComponents-DaytimeIonosphereType1 Figure 4-46.SfericWaveformandDifferentComponents-DaytimeIonosphereWithouta valley 86

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Figure 4-47 sho wsthesfericwaveformwithallthecomponentslaidoutforthe daytimeionospheretype2. Figure 4-47.SfericWaveformandDifferentComponents-DaytimeIonosphereType2 ItcouldbeobservedfromtheaboveguresthattheICCcomponentdoesnothave asignicanteffectonthesfericwaveform,neitherdoreturnstrokesoneandtwo.Return Strokesthreeandfourhavethemostsignicanteffectonthewaveform.Althoughthe amplitudeofreturnstroke3ismuchlargerthanreturnstroke4theyhavesimilareffect onthewaveform,thisisbecauseofthecontinuouscurrentinreturnstroke4whichhas greaterimpactonthesfericwaveform. 87

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CHAPTER 5 SUMMARYANDSUGGESTIONSFORFURTHERWORK 5.1Summary InthisthesisthetheoreticalmodelingofELFradioatmosphericsinthefrequency rangeof45-500Hzwascarriedonunderdifferentionosphericconditionsusingageneral theoreticalformulationforthepropagationofsinglefrequencyELF/VLFsignalsinthe Earth-IonospherewaveguidedevelopedbyBudden( Budden, 1961)andimplementedin acomputercode( FergusonandC.H.Shellman 1989). ThepathofpropagationwastakenfromCampBlanding,FloridatoMcMurdo StationinAntarctica.Themodelingisdoneassumingahomogeneousionosphere throughoutthepropagationpathbutarealisticgroundconductivityprolewith conductivityoftheEarth'ssurfacevaryingfrom 10 )Tj /T1_4 7.97 Tf (3 to4S/m.Theconductivityofland wasvaryingfrom 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (2 to 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (3 dependingonthegeographiclocation,theconductivity oficewas 10 )Tj /T1_4 7.97 Tf 6.59 0 Td (4 andtheconductivityofseawastakenas4S/mwhichareveryrealistic values.Differentionosphericproleswereusedtostudythedependenceofpropagation characteristicsoftheELFwavesontheionosphere.Itwasobservedthattheamplitudes oftheELFwaveswerehigherforthenighttimeionosphericconditionscomparedto daytimeionosphericconditionsduetolesserelectrondensityvaluesofthenighttime ionosphere.ForthenighttimeionospheretheitwasobservedthattheE-regionofthe ionosphereplayedanimportantroleindeterminingthecharacteristicsofthewave, especiallythepresenceorabsenceofthevalleyat100-150kmmadeasignicant difference. Itwasshowninthepreviousstudies(Cummer 1997)thattheELFsfericsgenerated byalightningaredependentonthecurrentmomentofthelightning.Inthisthesisthe sfericsgeneratedduetorockettriggeredlightningareconsideredandtheactualcurrent waveformsofrockettriggeredlightningconductedatCampBlanding,Floridaaretaken therebyprovidingamorerealisticestimateofthecharacteristicsofthesferics,unlikethe 88

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pre viousstudies( Cummer, 1997)whichhaveassumedamodeledimpulsivelightning discharge. 5.2SuggestionsforFurtherWork 5.2.1Jumpsintheamplitude Whentheamplitudeofthesfericwasplottedacrossthedistanceofpropagation, itwasobservedthattherewereunevenjumpsintheamplitudewhenevertherewas achangeintheconductivityofearth,thereasoncouldnotbeexplainedandtorectify thattheamplitudesweremadesmootherandcontinuousmanuallyasdemonstratedin Figure 5-1. Figure 5-1.Variationsintheamplitudeofthesfericacrossthepathofpropagation 5.2.2ModelingatLowerFrequencies-Below45Hz Thelowestfrequencythatcouldbemodeledinthisthesisis45Hzduetolimitations oftheMODEFNDRprogram.TogettheMODEFNDRprogramtoworkintheELF frequenciescertainsettingshavetobechangedtosetituptoworkintheiterativemode. IntheiterativemodeaninitialguessfortheEigenanglesisgivenandtheprogram iteratesonthemtondthenalsolutionwithinaspeciedrangeoftolerance.The 89

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prog ramndstheeigenanglesthatsatisfythemodeconditionineachhorizontal slabandthencoupleseachslab(ahorizontalslabisaportionofthepathwherethe waveguideparameterslikethegroundconductivityetcremainconstantandwhenever thereisachangeinanyoftheparametersbeyondaspeciedlimitanewslabis formed). TheMODEFNDRusesthesameinitialguessforeveryslabandthereisahuge variationincertainwaveguideparametersintheselectedpathofpropagationandthe eigenanglesthatsatisfythemodeconditioninoneslabmightnotsatisfythemode conditioninother.Tomodelthesfericsforthischosenpathbelow45Hzthisproblem hastorectied. 5.2.3ModelingUsingamoreRealisticInhomogeneousIonosphere Allthesfericspresentedinthisthesisaremodeledundertheassumptionofa homogenousionospherethroughoutthepropagationpath.Althoughthisisareasonable assumptionforsmallerpropagationdistances,thedistancesconsideredinthisthesis arelongandthepropagationpathshouldincludeboththedaytimeandnighttime ionospheres.Moreoverevenforshorterdistancesahomogenousionospheremight notalwaysreproducesomeofthenespectraldetailsthatcouldbeseeninobserved sferics( Cummer 1997). Therearecertainothereffectslikethepresenceofastronglyabsorbingionospheric inhomogenitiesoverasmallareaoftheproapagationpaththathaveastrongeffecton thesfericspectraandwhichcannotbemodeledusingahomogenousionosphere. AlsotheFASTMCprogramignorescertaineffectsliketheionosphericvariations transversetothepathofpropagationandmodereectionwhichmayresultinthelackof certainspectralfeaturesinthemodeledwaveforms.Someoftheseproblemscouldbe rectiedbyusingniteelementorthenitedifferencemethods. 90

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5.2.4 RemoteSensingofIonosphere Remotesensingoftheionosphereisadifcultproblemduetoitsawkwardheight whichismuchlesserthanthealtitudesatwhichsattelitesarepresentanditistoohigh forthealtitudesreachedbyballoons.Previouslysomemethodsweredevelopedto remotesensetheionosphereusingVLFandELFsferics( Cummer 1997 )and(Cummer andInan 2000 ).TheD-regionoftheionospherecanberemotesensedusingVLF sferics,buttheycannotbeusedtoremotetheE-regionoftheionospherebecausethey cannotpenetratetheionospherebeyondtheD-region.HowevertheELFsfericshave thecapacitytopenetratethisregionduetotheirlowattenuationrates,alsotheirspectra areverysensitivetoE-regionelectrondensitiesascomparedtotheD-region.This makesthemverysuitabletoremotesensetheE-regionoftheionosphereespecially thepresenceofavalleyinnighttimeionosphereintheE-region.Thepresenceofthe Sporadic-ElayersalsohasasignicanteffectontheELFsfericspectra.TheSporadic-E layerisnotacommonoccuranceinthechosenpropagationpathandisamorecommon occuranceinthepolarregions. SporadicEisthephenomenonoftransient,irregularlyscatteredpatchesofrelatively denseionizationthatdevelopseasonallywithintheE-regionoftheionosphere.This generallyoccursatanaltitudeof100-110kmandhasasignicanteffectonthesferic propagation.Inatheoreticalstudy( Barr.R 1977)showedthat E s generatesaseriesof resonancesfrom10Hzto1000Hztherebyhavinganeffectontheattenuationrates.The frequenciesandamplitudesoftheseresonancesdependstronglyonthecharacteristics of E s layer. Amethodhasbeenpreviouslydeveloped(CummerandInan, 2000)toremote sensetheE-regionoftheionosphereanddetectthepresenceofsporadic-Elayers usingELFsferics,butthismethodassumesasinglehomogenousgroundthroughout thepropagationpath.Byemployingasimilarmethoddevelopedin( Cummerand Inan, 2000)andapplyingtheproceduretotheinhomogenousgroundwecancertainly 91

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produce amuchmorerealisticestimate,especiallytheeffectsofpresenceofseainthe pathofpropagationwhichhasanimportantroletoplayintheattenuationrates. 92

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REFERENCES Barr .R.Theeffectofsporadic-EonthenocturnalpropagationofELFradiowaves. JournalofAtmosphericandTerrestrialPhysics 39(1977):1379. Bilitza,D.InternationalReferenceIonosphere2000. RadioSci 36(2001):261. Budden,K.G. Thewave-guidemodetheoryofwavepropagation.London:Logos Press,1961. Burke,C.P.andD.L.Jones.AnexperimentalinvestigationofELFattenuationratesin theEarth-ionosphereduct. J.Atmos.Terr.Phys 54(1992):243. Burton,E.T.andBoardman,E.M.Audio-frequencyatmospherics. proc.IRE 21 (1933):1476. Crawford,D.E.,Rakov,V.A.,Uman,M.A.,Schnetzer,G.H.,Rambo,K.J.,Stapleton, M.V.,andFisher,R.J.Thecloselightningelectromagneticenvironment: Dart-leaderelectriceldchangeversusdistance. J.Geophys.Res 106(D14) (2001):14,909,917. Cummer,S.A. LightningandIonosphereRemoteSensingUsingVLF/ELFRadio Atmospherics .Ph.D.thesis,StanfordUniversity,1997. Cummer,S.A.andInan,U.S.IonosphericEregionremotesensingwithELFradio atmospherics. RadioSci 35(2000):1437. Davies,K. IonosphericRadio .London:Peregrinuss,1990. Dermikol,M.K. VLFRemoteSensingoftheAmbientandModiedLowerIonosphere. Ph.D.thesis,StanfordUniversity,1999. D.Wang,Rakov,V.A.,Uman,M.A.,Fernandez,M.I.,Rambo,K.J.,Schnetzer,G.H., andFisher,R.J.Characterizationoftheinitialstageofnegativerocket-triggered lightning. J.Geophys.Res 104(1999):4213. Dwyer,J.R.,K.,RassoulH.,Al-Dayeh,Caraway,M.,B.,L.Wright,A.,Chrest,A., UmanM.,A.,RakovV.,J.,RamboK.,M.,JordanD.,J.,Jerauld,andC.,Smyth. Measurementsofx-rayemissionfromrocket-triggeredlightning. Geophys.Res.Lett. 31(2004). Evans,J.V.TheoryandpracticeofionospherestudybyThomsonscatterradar. Proc. IEEE 57(1969):496. Ferguson,J.A.F.P.SnyderD.G.MorttandC.H.Shellman. LongWavePropagation CapabilityDocumentation .Tech.Doc.1518.NavalOceanSystemsCenter,1989. Fieux,R.P.,Gary,C.H.,Hutzler,B.P.,Eybert-Berard,A.R.,Hubert,P.L.,Meesters, A.C.,Perroud,P.H.,Hamelin,J.H.,andPerson,J.M.ResearchonArticiallyu 93

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T riggeredLightninginFrance. PowerApparatusandSystems,IEEETransactionson PAS-97(1978).3:725. Hargreaves,J.K. TheSolar-TerrestrialEnvironment .Cambridge:CambridgeUniversity Press,1992. Hauser,J.PW.E.GarnerandF.J.Rhoads. AVLFEffectiveGroundConductivityMapof CanadaandGreenlandwithRevisionsfrompropagationdata.Report6893.NRL, 1969. Hepburn,F.Atmosphericwaveformswithverylowfrequencycomponentsbelow1kc/s knownasslowtails. J.Atmos.Terr.Phys 54(1992):243. Howard,J.S. LightningPropagationandGroundAttachementProcessfromMultiple StationElectricFieldandX-RAYMeasurements.Ph.D.thesis,UniversityofFlorida, 2009. Inan,U.S.andA.S.Inan. ElectromagneticWaves .PrenticeHall,1999. J.Jerauld,Rakov,V.A.,Uman,M.A.,Rambo,K.J.,Jordan,D.M.,Cummins,K.L.,and Cramer,J.A.AnevaluationoftheperformancecharacteristicsoftheU.S.National LightningDetectionNetworkinFloridausingrocket-triggeredlightning. J.Geophys. Res. 110(2005). Jones,D.L.ExtremelyLowFrequency(ELF)ionosphericradiopropagationstudies usingnaturalsources. IEEETrans.Comm. 22(1974):477. Pappert,R.A.andFerguson,J.A.VLF/LFmodeconversionmodelcalculationsfor airtoairtransmissionsintheearth-ionospherewaveguide. RadioSci 21(1986): 551. Prentice,S.A.andMackerras,D.Theratioofcloudtocloud-to-groundlightningashes inthunderstorms. JournalofAppliedMeteorology 16(1977):545. Rakov,R.A.,Mata,C.T.,Uman,M.A.,Rambo,K.J.,andMata,A.G.Reviewof triggered-lightningexperimentsattheICLRTatCampBlanding,Florida. Power TechConferenceProceedings,2003IEEEBologna .vol.3.2003,8pp.Vol.3. Rakov,V.A.andUman,M.A. LightningPhysicsandEffects .Cambridge:Cambridge UniversityPress,2003. Reising,S.C.,Inan,U.S.,Bell,T.F.,andLyons,W.A.Evidenceforcontinuingcurrent insprite-producingcloud-to-groundlightning. Geophys.Res.Lett. 23(1996):3639. Richter,J.H.ApplicationofConformalMappingtoearthatteningproceduresinradio propagationproblems. RadioSci 1(1966):1435. 94

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S .A.CummerandU.S.Inan.ModelingELFradioatmosphericpropagationand extractinglightningcurrentsfromELFobservations. RadioScience 35(2000): 385. Taylor,W.L.andSao,K.ELFattenuationratesandphasevelocitiesobservedfrom slow-tailcomponentsofatmospherics. RadioSci 5(1970):1453. Uman,M.A. TheLightningDischarge.orlando:AcademicPress,1987. Wait,J.R. ElectromagneticWavesinStratiedMedia .Oxford:PergamonPress,1970. Weidman,C.D.andE.P.Krider.Theamplitudespectraoflightningradiationeldsin theintervalfrom1to20MHz. RadioSci 21(1986):964. Wood,T.G. Geo-LocationofIndividualLightningDischargesusingImpulsiveVLF ElectromagneticWaveforms .Ph.D.thesis,StanfordUniversity,2004. 95

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BIOGRAPHICAL SKETCH BharatKunduriwasborninHyderabad,Indiain1987.Hegraduatedwitha bachelor'sdegree(Honor's)inelectricalandelectronicsengineeringfromDr.M.G.R.University, Chennai,Indiain2008.Hepursuedhismaster'sdegreeatUniversityofFlorida undertheguidanceofDr.RobertMoore.Hisresearchinterestslieintheeldof electromagneticsandstudyofIonosphere. 96