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LWPC modeling of VLF perturbations from lightning induced ionospheric disturbances on overlapping paths of propagation

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Title:
LWPC modeling of VLF perturbations from lightning induced ionospheric disturbances on overlapping paths of propagation
Creator:
Renick, Chad M.
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Denver, CO
Publisher:
University of Colorado Denver
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English

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Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical engineering
Committee Chair:
Gedney, Stephen
Committee Members:
Golkowski, Mark
Harid, Vijay

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University of Colorado Denver
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Auraria Library
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Copyright Chad M. Renick. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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Full Text
LWPC MODELING OF VLF PERTURBATIONS FROM LIGHTNING INDUCED
IONOSPHERIC DISTURBANCES ON OVERLAPPING PATHS OF
PROPAGATION
by
CHAD M. RENICK
B.S., University of Colorado Denver, 2017
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Electrical Engineering
2018


This thesis for the Master of Science degree by Chad M. Renick
has been approved for the Electrical Enigineering Program by
Stephen Gedney, Chair Mark Golkowski, Advisor Vijay Harid
Date: May 12, 2018
n


Renick, Chad M. (M.S., Electrical Engineering)
LWPC Modeling of Lightning Induced Ionospheric Disturbances on Overlapping Paths of VLF Propagation
Thesis directed by Assistant Professor Mark Golkowski
ABSTRACT
Lightning discharges are known to be a source of high amplitude, broad frequency electromagnetic radiation. These electromagnetic waves can cause perturbations in the electron density of the D-region of the ionosphere either by ionization from quasi-electrostatic fields or from induced energetic electron precipitation from the magnetosphere. Because changes in D-region electron density affect the conductivity of the ionosphere, nighttime lightning discharges can perturb the amplitude and phase of VLF communication signals propagating through the Earth-ionosphere waveguide. Most past work in this area has involved unique propagation paths between a transmitter and receiver. Modeling of such perturbation events often involves uncertainty since the perturbed ionospheric profile cannot be uniquely determined. This work has focused on an overlapping VLF propagation path on which signals from two different VLF transmitters share a common path to a receiver. This allows for the geographic area of the overlapping path to be simultaneously diagnosed with two signals with different mode content. Observations show that a lightning induced perturbation on the overlapping path can have a large effect on the amplitude or phase of one signal, while leaving the other wave relatively unaffected. The Long Wave Prediction Capability (LWPC) software package is used to simulate this phenomenon by altering the effective conducting height of the ionosphere near the location of a known nighttime lightning strike. Good agreement is found between the simulation and the observations showing that providing additional constraints on the perturbed ionosphere yields a more accurate model of how lightning affects ionospheric electron densities.


The form and content of this abstract are approved. I recommend its publication.
Approved: Mark Golkowski
IV


DEDICATION
This work is dedicated to the many people in my life who make it wonderful to be alive, and who remind me on occasion to appreciate how amazing it is that we are even here at all. To my parents, Duane and Gayle, whose tireless support made it possible. To my sister Jill, whom I wouldn’t be the same without. To Holly, who really just makes my heart smile. And especially, to my son Cael who unknowingly provided the inspiration and motivation to make it happen. I love you all so much.
v


ACKNOWLEDGMENTS
Thank you to all of the professors at the University of Colorado Denver who challenged and inspired me. Thanks also to Morris Cohen and his team at the Georgia Institute of Technology for providing data for this project. I would especially like to thank Ashanthi Maxworth for being teacher, tutor, and friend to me. Without her, I would not have had the opportunity to work with the Electromagnetics and Plasma Physics Research Group. I also would like to extend my sincere thanks and gratitude to Dr. Golkowski. I truly value the guidance and support that he has given me on this project, as well as the encouragement he has given me to continue down the path that I am on. This work was supported by the National Science Foundation with grant AGS1451210 to the University of Colorado Denver.
vi


TABLE OF CONTENTS
CHAPTER
1. INTRODUCTION ....................................................... 1
1.1 Ionosphere.................................................... 1
1.2 Earth Ionosphere Waveguide.................................... 3
1.3 VLF Remote Sensing............................................ 4
1.4 Lightning Disturbances........................................ 4
1.4.1 Early-Fast Events ....................................... 5
1.4.2 Lightning Induced Energetic Electron Precipitation....... 5
1.5 LWPC Modeling................................................. 6
1.5.1 Presegmentation (PRESEG)................................. 7
1.5.2 Mode Finder (MODEFNDR)................................... 7
1.5.3 Fast Mode Conversion (FASTMC) ........................... 8
1.5.4 Modeling Radial Component of Magnetic Field with the LWPC 8
2. OBSERVATIONS....................................................... 10
2.1 Overlapping Path Geometry.................................... 10
2.2 Navy Transmitters............................................ 10
2.3 VLF Antenna and Receiver..................................... 11
2.4 LEP and Early/Fast Perturbations on VLF Signals.............. 12
3. MODEL SETUP........................................................ 15
3.1 Dynamic Profiles / Disturbed Radius ......................... 15
3.2 Determining Ambient Ionospheric Conditions................... 16
3.3 Graphical Representation of Expected Changes................. 17
3.4 Error for Single Ambient Profile............................. 18
3.5 Global Error................................................. 19
4. CASE STUDIES ...................................................... 21
4.1 June 13"*, 2016.............................................. 21
vii


4.1.1 LWPC Analysis with 250 [km] Disturbed Radius.......... 24
4.1.2 Effect of Disturbance Region Size..................... 30
4.1.3 June 13t/l Conclusions.................................. 33
4.2 April 26th, 2016............................................. 34
4.2.1 Event #1: 08:03:55 [UT]................................. 34
4.2.2 Event #2: 08:50:44 [UT]................................. 39
4.2.3 April 26th Conclusions.................................. 43
5. SUMMARY and CONCLUSIONS....................................... 45
5.1 Summary...................................................... 45
5.2 Conclusions ................................................. 46
REFERENCES............................................................ 47
viii


TABLES
2.1 Amplitude and phase observations on May 17th, 2017....................... 14
4.1 Amplitude and phase observations on June 13th, 2016...................... 22
4.2 Model and observational comparison of As for June 13th, 2016 early/fast
event with 250 [km] disturbed radius................................... 30
4.3 Model and observational comparison of As for June 13th, 2016 early/fast
event with 500 [km] disturbed radius................................... 34
4.4 Amplitude and phase observations on April 26th, 2016 ................ 36
4.5 Model and observational comparison of As for April 26th, 2016 Event /M 39
4.6 Amplitude and phase observations on April 26th, 2016 ................ 40
4.7 Model and observational comparison of As for April 26th, 2016 Event #2 43
5.1 LWPC Modeled Changes in h' and (3....................................... 45
IX


FIGURES
1.1 Example ionospheric electron density [3].............................. 2
1.2 Approximated D-region ionospheric electron density.................... 3
1.3 Depiction of early/fast ionospheric disturbance ...................... 5
1.4 Depiction of LEP ionospheric disturbance.............................. 6
2.1 Overlapping path geometry............................................. 10
2.2 Visualization of rotation matrix...................................... 12
2.3 Narrowband observations from May 17th, 2017 early/fast event ......... 13
2.4 Example representation of the relationship between observations and the
terminology used to refer to them (Ambient, Dynamic and A)............ 14
3.1 Model geometry example from May 17th, 2017 event ..................... 15
3.2 Ambient error example from May 17th, 2017 event....................... 17
3.3 Modeled changes in amplitude and phase as a function of Ah' and Af3
from LWPC simulation of May 17t/levent ............................... 18
3.4 Error obtained from a single ambient profile for May 17th, 2017 Event . 19
3.5 Global error for May 17th, 2017 Event .................................. 20
4.1 Location of June 13t/l, 2016 early/fast 385 [kA] event.................. 21
4.2 Delaware narrowband data for NLK and NML on June l?*h, 2016 .... 22
4.3 Ambient error for June 13t/l, 2016 early/fast event................... 23
4.4 Model setup for June 13t/l, 2016 early/fast event....................... 24
4.5 Global error for June 13t/l, 2016 event ................................ 25
4.6 June 13t/l single ambient profile (U=88.5[km] and /3=0.88[km-1]) error . 26
4.7 Modeled changes in amplitude and phase as a function of Ah' and Af3 from LWPC simulation of June 13t/levent with 250 [km] disturbed radius 27
4.8 Radial global error for June 13t/l, 2016 event........................ 28
4.9 Changes in radial amplitude and phase as a function of Ah' and Af3 from
LWPC simulation of June 13t/levent with 250 [km] disturbed radius ... 28
x


4.10 Radial error for single ambient profile for June 2016 event.......... 29
4.11 Model setup for June 13t/l, 2016 early/fast event....................... 30
4.12 Global error for June 13t/l, 2016 event ................................. 31
4.13 June 13t/lsingle ambient profile (/?/=85[km] and /3=0.44[km-1]) error ... 32
4.14 Modeled changes in amplitude and phase as a function of Ah' and Af3 from LWPC simulation of June 13t/levent with 500 [km] disturbed radius 32
4.15 Radial error for single ambient profile for June 13t/l, 2016 event....... 33
4.16 Model setup for April 26t/l, 2016 LEP event............................. 35
4.17 Delaware narrowband data for NLK and NML on April 26th, 2016 .... 35
4.18 Global error for April 26th, 2016 LEP Event #1....................... 36
4.19 Single ambient profile error for April 26th, 2016 LEP Event #1 37
4.20 Modeled changes in amplitude and phase as a function of Ah' and Af3
from LWPC simulation of April 2Qth LEP Event #1...................... 38
4.21 Single ambient profile radial error for Event #1 on April 26th, 2016 ... 38
4.22 Model setup for April 26th, 2016 LEP Event ^2........................ 39
4.23 Delaware narrowband data on April 26th, 2016 for Event ^2............ 40
4.24 Global error for April 26th, 2016 LEP Event ^2....................... 41
4.25 Single ambient profile error for April 26th, 2016 LEP Event ^2 41
4.26 Modeled changes in amplitude and phase as a function of Ah' and Af3
from LWPC simulation of April 2Qth LEP Event ^2...................... 42
4.27 Radial global error for April 26t/l, 2016 Event ^2.................. 43
xi


CHAPTER 1
INTRODUCTION
1.1 Ionosphere
The ionosphere is a region of the Earth’s atmosphere ranging from 60 - 1000 km in altitude. It is separated into the D, E, and F regions. Although the plasma in the ionosphere is generated by solar radiation, sudden ionospheric disturbances such as gamma ray bursts, solar flares, and lightning strikes can also change the plasma density. Electron densities in the E and F regions are relatively well understood because they can be measured with ionosondes, incoherent scatter radar (ISR), or in-situ satellite measurements. The main focus of this work is the lowest (60 - 95 km) portion of the ionosphere called the D-region. Determining electron densities in the D-region poses certain challenges because electron densities in this region are too low for measurement with ionosondes or ISRs. Additionally, the altitude is too high for weather balloon measurements and too low for direct measurements via satellite.
Figure 1.1 shows a plot of typical daytime and nighttime electron densities in the ionosphere as a function of height. It shows that electron densities in the D-region of the ionosphere increase exponentially with height, thus exhibiting a linear trend on a logarithmic scale.
1


Figure 1.1: Example ionospheric electron density [3]
In this work, D-region electron densities will be represented and modeled using the widely accepted two parameter exponential model originally proposed by Wait and Spies in 1964 [9]:
ne
noe-0.lMe(,3-0.15)(/l-/l,)[cm-3]
(1.1)
where no = 1.43 x 10' [electrons], h' (h-prime) [km] describes the effective reflection height of the ionosphere, and /3 (beta) [km-1] describes the sharpness of the profile, or how quickly electron densities increase as a function of height. Figure 1.2 is a plot of typical daytime and nighttime D-region electron densities using the exponential model.
2


DAY/NIGHTTIME ELECTRON CONCENTRATIONS
Figure 1.2: Approximated D-region ionospheric electron density 1.2 Earth Ionosphere Waveguide
Due to the high number of free electrons in both the Earth’s crust and the ionosphere, these regions behave like good conductors when they are encountered by Very Low Frequency (VLF) waves. This causes these waves to be reflected off of both the Earth’s crust and the D-region of the ionosphere, forming what is known as the Earth-Ionosphere Waveguide (EIW). The dominant modes propagating through the EIW are transverse magnetic (TM) modes, which have vertical electric fields and magnetic fields in the 0-direction. There are also non-dominant transverse electric (TE) modes, with typically lower amplitudes, which contain radially oriented magnetic fields that correspond to electric fields that have a horizontal component.
While the Earth’s crust has stable conductivity, ionospheric properties are driven by very dynamic systems and change daily with solar zenith angle and minute to minute with events like solar flares, gamma ray bursts, lightning storms, and energetic electron precipitation from the magnetosphere. All of these factors change electron
3


densities in the D-region, which in turn can alter how waves propagate in the EIW.
1.3 VLF Remote Sensing
The way that VLF waves are reflected off of the ionosphere is highly dependent on ionospheric conditions. Changes in h' and f3 can change the possible modes of VLF propagation in the EIW, therefore changing the amplitude and phase of observed the signal. This suggests that VLF waves that have reflected from the ionosphere retain some information about ionospheric conditions. VLF remote sensing takes advantage of this phenomena by examining VLF signals in order to diagnose ionospheric conditions. Quite simply, this is done with some source of VLF radiation and a VLF receiver to record the observed signal. In this work, the VLF sources used are single frequency U.S. Navy transmitters used for submarine communication. The VLF receiver used for observations in this work is located on the Delaware Aero Space Education campus in Delaware.
1.4 Lightning Disturbances
Lightning is a sudden discharge of static electricity in the atmosphere that happens when a charge larger than the breakdown voltage of air is built up between two objects. Most lightning occurs during thunderstorms either as cloud-to-cloud or cloud-to-ground discharges, with the former being more common, but the latter involving larger currents of tens to hundreds of kiloAmperes. This rapid discharge of electricity causes a current to flow from high to low potential which acts like an antenna emitting broad-spectrum electromagnetic radiation in the Earth’s atmosphere. Some of this electromagnetic radiation is trapped due to the conductive properties of the Earth and ionosphere and propagates within the EIW. Much of the propagating radiation generated by a lightning strike is in the ELF and VFL bands. In some cases energy from a lightning strike alters ionospheric conditions by causing ionization of particles in the upper atmosphere. These lightning induced ionospheric disturbances
4


are classified into either Early/Fast or Lightning Induced Energetic Electron Precipitation (LEP) events.
1.4.1 Early-Fast Events
Early/Fast events are caused when the electromagnetic pulse from a lightning discharge causes direct ionization of atmospheric particles, or when ionization occurs because of the quasi-static electric fields caused from the sudden charge removal that occurs during a lightning strike [5]. Figure 1.3 shows a depiction of an Early/Fast ionospheric disturbance. The effects of ionospheric disturbances caused by Early/Fast events are observed nearly instantaneously after a lightning strike and the ionospheric disturbance is localized to the geographic region where the lightning strike occurred.
VLF Reflection^H^S^ _
VLF .
Propagation
/ / /
EMP& QE Fields
ANe, Ag
\
Change in VLF Amplitude and Phase
/ /
Figure 1.3: Depiction of early/fast ionospheric disturbance
1.4.2 Lightning Induced Energetic Electron Precipitation
Lightning Induced Energetic Electron Precipitation events occur when some of
the electromagnetic radiation created by the lightning strike escapes through the
ionosphere into the magnetosphere and interacts with high energy electrons that are
geomagnetically trapped by the Earth’s magnetic held. This interaction changes the
trajectory of these charged particle and causes them to “rain” down on the ionosphere
thus causing secondary ionization. Figure 1.4 shows a depiction of an LEP event. The
effects of LEP events are not observed instantaneously after a lightning strike, and
are separated geographically from region where the lightning strike occurred. In the
5


northern hemisphere ionospheric disturbances due to LEP events are observed north of where the lightning strike occurred. In the southern hemisphere the disturbance occurs south of the strike. The LEP events modeled in this work correspond to precipitation from approximately L-shell 2.5 of the magnetosphere. The L parameter denotes the distance in Earth radii from the Earth’s center that a geomagnetic held line crosses the equatorial plane.
Magnetic Field Line
Precipitation
Region
Resonant
Waves
Loss Cone Electrons
Interaction
Region
Figure 1.4: Depiction of LEP ionospheric disturbance 1.5 LWPC Modeling
The software used to determine theoretical VLF propagation in the EIW in this
work is called the Long Wave Propagation Capability (LWPC) code. The LWPC
was written in FORTRAN by the Navy in the late 1970’s to early 1980’s [8]. R is a
two dimensional waveguide model that uses mode theory to determine the expected
amplitude and phase of a VLF wave at a given location. The input parameters to the
program are transmitter location, transmitter power, transmitter frequency, receiver
location, and ionospheric electron density as a function of height. In this work, the
6


transmitter and receiver parameters do not change so the only input parameter that is varied is the ionospheric profile.
The program solves for the expected amplitude and phase of the VLF signal by splitting the path of propagation into segments with different waveguide parameters, determining the possible modes of propagation through the waveguide, and calculating attenuation and phase decay per mode for each segment. The theoretical amplitude and phase of the propagating wave is given by the summation of all modes at the receiver site. The next three sections give a brief description of the LWPC’s three main algorithms.
1.5.1 Presegmentation (PRESEG)
The LWPC uses an accepted model for the Earth’s magnetic held and an experimentally derived map of the Earth’s conductivity and permittivity [7]. These parameters are predetermined for a given geographic location. As discussed above, the ionospheric electron densities are specified by the user for different sections of the propagation path. The PRESEG portion of the LWPC code takes the information about the waveguide parameters and separates the path from transmitter to receiver into sections where the waveguide parameters are continuous. This allows the path of propagation to be modeled as a series of waveguides with different parameters.
1.5.2 Mode Finder (MODEFNDR)
The expected fields at a given location can be represented by the sum of all the modes propagating through the EIW. Thus, in order to determine the expected fields, it is necessary to determine all possible modes of propagation, as well as the excitation factors for each mode. Information from PRESEG is passed to MODEFNDR in order to perform these calculations based on transmitter characteristics and waveguide parameters for each segmented slab along the path. MODEFNDR then searches for Eigen angles which define propagating modes by determining which angles of incidence satisfy the mode condition:
7


det[I - Rl(6)Ru(6)\ = 0
(1.2)
where
l|R|l(0) 0 and Ru = wH0) ll R±(d)
Rl —
0 ±R±(0) ±R\\(0) i R±(d)
are the Fresnel reflection coefficients calculated at the upper and lower boundaries of the EIW. The lower reflection coefficient (Rl) defines isotropic reflections off of the Earth’s crust that are dependent on the angle of incidence, conductivity, and permittivity. Because the ionosphere is a magnetized plasma and anisotropicity must be considered, the upper reflection coefficient (Ru) that defines ionospheric reflection is dependent on not only the angle of incidence but also the polarization of the VLF wave [1]. A derivation of the excitation factors calculated by MODEFNDR are presented by Pappert and Ferguson in [8].
1.5.3 Fast Mode Conversion (FASTMC)
The FASTMC algorithm performs mode conversion calculations to ensure accurate field propagation through waveguide discontinuities, and outputs the final summation of all modes in the form of amplitude and phase. This is accomplished by determining the excitation factors, height gains, and cumulative mode conversion coefficients [8] in each partition of the path based on the possible modes of propagation. Magnitude is given in dB referenced to 1 jiVjm and phase is given in total degrees of phase change across the entire length of the path from transmitter to receiver.
1.5.4 Modeling Radial Component of Magnetic Field with the LWPC
For vertically oriented electric fields, the conversion between LWPC output amplitude in dB (/iV) and the narrowband VLF horizontal magnetic field observations in
8


pT is a simple conversion. However, modeling the radial component of the magnetic held using the LWPC necessitated altering the FORTRAN code in the FASTMC and PRESEG hies in order to have the LWPC output the horizontal electric held. The LWPC was then run with the horizontal held output at three different altitudes (0, 1, and 2 [km]) and the curl of the electric held was taken using the forward difference approximation
B
rLWPC
— EhLWPC(mkrn) + 4EhLWPC(mkm) — 3EhLWpC(mkm)
2juiAz
(1.4)
where the radial magnetic held BrLWPC is in Teslas, and horizontal electric held Elwpc is in V/m, oj is the angular frequency of the transmitter, and Az is the change in LWPC simulated altitude for the three electric helds. Some of the cases that will be presented have not been fully run for the radially-directed component of the magnetic held due to the fact that it is computationally expensive to do so. For such cases, this work will focus mainly on the ^-directed component of the magnetic held, while examining only a small set of modeled radially-directed magnetic held components.
9


CHAPTER 2
OBSERVATIONS
2.1 Overlapping Path Geometry
Much of the past work in this held has involved using signals from a single transmitter-to-receiver pair to perform ionospheric diagnostics. This can be problematic when attempting to determine a unique solution because varying h' and /5 simultaneously in an attempt to match the amplitude and phase of the received signal leaves the problem under-constrained. This work has addressed this problem by focusing on a pair of transmitters that share a great circle path to a single receiver. This configuration is shown in Figure 2.1 with the transmitters shown in red and the receiver shown in blue.
Figure 2.1: Overlapping path geometry
2.2 Navy Transmitters
VLF waves are of a low enough frequency that they are able to penetrate into sea
water. For this reason, the US Navy has built several VLF transmitters across the
10


continent that are primarily used for submarine communication. Figure 2.1 shows the location of the two Navy transmitters that were used for VLF remote sensing in this work. The NLK transmitter is located in Jim Creek, WA (48.2 N, 121.9 W). It is a 250 [kW] transmitter that operates continuously at a frequency of 24.8 [kHz], The NML transmitter is located in LaMoure, ND (46.4 N, 98.3 W). It is a 500 [kW] transmitter that operates continuously at a frequency of 25.2 [kHz],
2.3 VLF Antenna and Receiver
The antenna and receiver used for this work are operated by Georgia Tech and located in Delaware (39.3 N, 75.6 W). This receiver site uses a version of the Stanford designed AWESOME receiver working in conjunction with two triangular air loop antennas oriented orthogonally in an east/west and north/south direction. A more complete discussion of this receiver configuration is presented in [2], Although the receiver picks up all frequencies in the VLF band, the data used in this work is mixed down narrow band for the frequencies of the NLK and NML transmitters, meaning that only the amplitude and phase of the transmitter’s signal is recorded. The rotation matrix
cos{9) — sin(9) cos{9) cos{9)
(2.1)
is used to orient the north-south channel toward the NML and NLK transmitters. This changes the two channels from NS and EW channels to B$ and Bracnai channels. Figure 2.2 displays a map showing this rotation. With 9 = 59.3447°, this yields
cos{9) —sin(9) AmvNs/PhaseNs AmVrtJPhaser
cos(9) cos{9) Amy f,w / Phase f,w Am/P radial/ P h(lSeradinl
11


The component of the magnetic fields corresponds to vertical electric fields which are the dominant fields within the EIW. The radial component of the magnetic held is non-dominant and corresponds to the component of the electric held that is horizontal to the Earth’s surface. In general, the amplitude of the radial component is much lower than the amplitude of the (f) component.
2.4 LEP and Early/Fast Perturbations on VLF Signals
As discussed above, when either LEP or Early/Fast events occur, they can alter ionospheric electron densities and effect VLF propagation in the EIW. These changes can cause a rise or fall in either the amplitude or phase of either the 0-directed or radially-directed components of the VLF signals. Interestingly, an ionospheric disturbance can have a large effect on the signal from one transmitter, while leaving the other transmitters signal relatively unaffected. As an example of this phenomena, Figure 2.3 displays the narrowband data for the NLK and NML transmitters recorded at Delaware on May 17th, 2017.
12


May 17, 2017: 166 [kA] Early/Fast Event at 06:27:18 [UT]
NLK Amplitude
100
50
NLK Phase
£ -50
<1> Phase Radial Phase
tn 100 cd
50
-20 0 20 40
NLM Phase
60
-50
-—— ,

\
I
â–  4> Phase Radial Phase
-20
20
40
60
Time [s]
Time [s]
Figure 2.3: Narrowband observations from May 17th, 2017 early/fast event
In this work, the amplitude or phase averaged over the 20 seconds preceding the lightning strike will be called the ambient amplitude or phase. The amplitude or phase in the moment just after the lighting strike will be called the dynamic amplitude or phase. Observed changes in amplitude and phase are defined as A = (.Ambient — Dynamic). Figure 2.3 shows these definitions graphically, and Table 2.1 quantifies them for the May 17th, 2017 event.
13


May 17, 2017: 166 [kA] Early/Fast Event at 06:27:18 [UT|
NLK Amplitude
Time [s]
NLK Phase
-20 0 20 40 60
Time [s]
Figure 2.4: Example representation of the relationship between observations and the terminology used to refer to them (Ambient, Dynamic and A)
Table 2.1: Amplitude and phase observations on May 17th, 2017
Transmitter DynAmp ^Amp Am, b Phase Dy 11'Phase A Pha.se
NLK+ 61 A[dBgV] 62.2[(jnjttV] 0.58[^tV] 87.5 [deg] 86.1 [deg] -1.35[(Jeg]
NML$ 68.7 [dBfiV] 62.7[dn^v] -5.99[dBpv] •31-1 [dep] A4:A[deg\ -45.5[(fefl]
N1. I\ radial 59.7[(iB,ttV] 60.3 [dBnV] 0.59 [dBnV] -23.5[(fes] -20.5[deg] 3.05[tfca]
A M 57.1[(iBjttV] 53.4[dSjtty] -3-77[dBnV] 67.0[defl] 45.6[defl] -2\A[deg\
14


CHAPTER 3
SETUP
3.1 Dynamic Profiles / Disturbed Radius
The basic model setup used to leverage the overlapping path geometry is as follows: Over the portion of the path that should remain unaffected by the lightning strike, a single ionospheric profile taken to be the effective ambient profile remains constant. In the geographic region near the lightning disturbance, the ionospheric profiles are varied for all possible combinations of h' and /5 in the range of 70 [km] < h! < 90 [km], and 0.40 [km-1] < /3 < 0.90 [km-1]. In this work, the ionospheric profile used in the disturbed region will be referred to as the dynamic profile and the effective ambient profile used for the rest of the path will be referred to as the ambient profile. Figure 3.1 shows a graphical representation of the model setup for the May 17^, 2017 event.
Figure 3.1: Model geometry example from May 17th, 2017 event
15


3.2 Determining Ambient Ionospheric Conditions
When modeling how ionospheric conditions are altered due to a lightning induced disturbance, one must consider what the condition of the ionosphere was during the time leading up to the disturbance. For modeling purposes, this work operates under the assumption that there was a single “flat” ambient ionosphere over the entire path from NLK to Delaware just before the lightning event. While this is most likely not a completely accurate assumption because the nighttime ionospheric conditions have been shown to vary regionally over shorter distances [6], it has been shown through LWPC modeling that an “effective” flat profile that is the average of these variations can be used to describe ionospheric conditions across the path [4],
One of the major challenges for this work was finding a way to identify what the effective ambient condition was leading up the disturbance. The Georgia Tech antenna is calibrated, meaning that the measurements that are made there can be converted directly to horizontal magnetic flux (in Teslas) which can easily be converted into electric held values at the receiver. In order to understand what the expected electric fields would be for different ionospheric profiles, the LWPC was run with a single ionospheric profile from transmitter to receiver for every reasonable combination of h' and /3. This was done for both the NLK and NML transmitters. Then, using the observed amplitude data for each transmitter and comparing it to the LWPC expected amplitude, an error matrix was created using the least squares method where
NLM
Err or ambient \j (Amp lw pc A mpobserved) ^ (3.1)
NLK
As an example of how the calibrated amplitudes on the overlapping path can
be used to predict the effective ambient condition on the path from transmitter to
receiver, Figure 3.2 is a plot of an ambient error matrix created using NLK and NLM
16


nighttime amplitude data that was recorded during a five minute period leading up to a May 17th, 2017 Early/Fast event.
Single Profile Ambient Error May 17, 2017:166 [kA] Early/Fast Event at 06:27:18 [UT1
0.3 0.4 0.5 0.6 0.7 0.8 0.9
P
Figure 3.2: Ambient error example from May \7th, 2017 event
Analysis of Figure 3.2 suggests that the ambient condition of the ionosphere at that time had a reflection height range of 84.0 [km] < h' < 87.0 [km] with the most likely height at h' = 86.5 [km], and a profile sharpness range of 0.55 [km-1] < /3 < 0.65[km-1] with the most likely sharpness at /5 = 0.58 [km-1]. While this type of analysis of ambient amplitudes has proven beneficial as a guideline to determine a range of effective ambient ionospheric conditions, it is by no means meant to be taken as a definitive determination of a specific ambient condition over the path of propagation.
3.3 Graphical Representation of Expected Changes
By simulating dynamic ionospheric profiles with 70 [km] < h' < 90 [km] and 0.40 [km-1] < /3 < 0.90 [km-1] in the disturbed region and keeping track of changes in amplitude and phase for each transmitter (AAmPNLK, AphaseNLK and AAmpNMLi ^PhaseNML) in terms of Ah' and Af3 modeled in the dynamic region, the
17


LWPC simulated results can be graphically represented in an easy to analyze manner. Figure 3.3 shows an example of this representation where changes in amplitude and phase are represented by color intensity.
May 17, 2017: 166 [kA] Early/Fast Event at 06:27:18 [UT]
-15 -10 -5 0 -15 -10 -5 0
Ah’ Ah’
Figure 3.3: Modeled changes in amplitude and phase as a function of Ah' and A/5 from LWPC simulation of May 17t/l event
3.4 Error for Single Ambient Profile
Error for a single ambient profile was calculated using a least squares error method that compares the observed and modeled changes in amplitude and phase of the signals from the NLK and NML transmitters so that
Error
individual
NLM
(AmpLWpc/PhaseLWPC - Am:pohs,lPh,aseobs)2~. (3.2)
NLK
18


Combined Error for May 17th Event vs. (Ah’, A0) Ambient: h’ = 86 [km] 0 = 0.46
100
A h‘
Figure 3.4: Error obtained from a single ambient profile for May 17th, 2017 Event
3.5 Global Error
The simulation was then run for several possible ambient conditions within a reasonable range accepted nighttime ionospheric profiles. The range that was chosen was 83.0 [km] < h' < 89.0[km] and 0.40 [km-1]< fj < 0.90[km-1]. Global error was then calculated by summing the error from individual ambient profile simulations where
Errorgiobai
h'=89.0 /3=0.90
EE
Error
individual >
/?'=83.0 /3=0.40
(3.3)
and then normalizing by the number of ambient profiles that contributed to the global error. This method quantifies nighttime D-region ionospheric changes from lightning induced perturbations independently of ambient ionospheric conditions.
19


Global Error (Total) for May 17th Event:
250 [km] Disturbed Radius
too 90 80
70 §"
z
60 1 5
50 z, e
40 lS £
30 5 20 10 0
Figure 3.5: Global error for May 17th, 2017 Event
It should be noted that not every single ambient profile simulated produces a valid solution with low error. If the minimum error for a single ambient profile is not below a certain event dependent threshold, it is ignored and not considered in the determination of global error. The area in the upper right-hand side of Figure
3.5 with zero error is not representative of the combinations of Ah' and Aj3 that produced the lowest global error. It is an area in which no single ambient profile error contributed to global error calculations.
This method of determining ionospheric changes in the disturbed region through the use of global error calculations comes from LWPC simulation of multiple ambient ionospheric profiles, it is a more robust model that is not dependent on previous knowledge of, or assumptions about, the ambient condition of the ionosphere.
-15 -10 -5 0 5
A h'
20


CHAPTER 4
CASE STUDIES
4.1 June 13th, 2016
The first case that will be examined is an Early/Fast event that occurred during the night of June 13th, 2016 at 06:41:27.818 [UT] near Minneapolis, MN. This location is on the overlapping path approximately 2215 [km] from NLK and 432 [km] from NML. The lightning that caused this event was larger than any of the others examined in this work with a peak current of 385 [kA] reported from the National Lightning Detection Network (NLDN). Figure 4.1 shows the location of the strike in relation to NLK and NML. A circle with a 250 [km] radius was drawn around the strike location to denote the region expected to be affected by the lightning strike.
The effects that the strike had on the signals from NLK and NLM were quite interesting because the event caused a large increase in both amplitude and phase of the signal from NML while leaving the signal from NLK relatively unaffected. This is
21


similar to the previous event, but the VLF perturbations caused by this strike were more dramatic. Figure 4.2 shows the narrowband data for each transmitter recorded at the Delaware receiver. Through an analysis of the narrowband data, Table 4.1 quantifies the ambient and dynamic conditions, as well as the changes in amplitude and phase for the June 13t/l, 2016 event.
June 13, 2016: 385 [kA] Early/Fast Event at 06:41:27 [UT]
NLK Amplitude
NLK Phase
Time [s]
-60
-so
-100
-120
-140
-160

-20
NLM Phase

â–  Phase - Radial Phase
20
Time [s]
40
60
Figure 4.2: Delaware narrowband data for NLK and NML on June 13 , 2016
Table 4.1: Amplitude and phase observations on June 13t/l, 2016
Tx AmbAmp DyUAmp ^Amp Amb phase Dyn Phase N Phase
NLK+ 66.0[ NML$ 66.5[(iBjttv] 7'2A[dBpv] 5.90 [dBpV] A19.7[deg\ -84.8[(iefl] 3 4.8 [deg]
NLI •V M 55.8 [dBpV] 45.7[(iBjtty] -10.1[dBpV] -143.0[ 22


Through analysis of the 0-directed component of observed ambient amplitudes, the expected ambient condition of the ionosphere was determined to be within the reflection height range of 83.0 [km] < h' < 89.0 [km] and a profile sharpness range of 0.45 [km-1]< /3 < 0.90 [km-1]. The ambient error plot in Figure 4.3 shows the range of expected ambient profiles.
Single Profile Ambient Error
June 13, 2016: 385 [kAI Eariy/Fast Event at 06:41:27 [UT1
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
Figure 4.3: Ambient error for June 13th, 2016 early/fast event
Having determined a range for the expected ambient condition of the ionosphere, the LWPC simulation was run for ambient ionospheric profiles with value ranges of 83.0 [km] < hf < 89.0 [km] and 0.40 [km-1]< 0 < 0.90 [km-1]. The simulation was then run using two different values for the disturbed radius (250 [km] and 500 [km]). Figure 4.4 shows the model setup for the 250 [km] radius.
23


4.1.1 LWPC Analysis with 250 [km] Disturbed Radius
The analysis of this event consists of 375 separate simulations using different nighttime ambient profiles within the determined range. Each of these 375 simulations used a single effective ambient profile and consisted of 1066 individual LWPC runs for both the NLK and NML transmitters. These individual LWPC runs account for the possible ionospheric conditions in the disturbed region on the path of propagation. Of the 375 single ambient profile simulation runs, 81 of them produced error levels that were below the threshold and were included in the global error for this event that is shown in Figure 4.5.
24


Global Error (Total) for June 13th Event: 250 [km] Disturbed Radius
-15 -10 -5 0 5
A h'
Figure 4.5: Global error for June 13t/l, 2016 event
The minimum global error occurred when the LWPC modeled changes of h' and /3 in the disturbed region were Ah' = -5.0 [km] and Aj3 = -0.12 [km-1]. However, the absolute minimum from Figure 4.5 may not be as important as the overall trend that can be observed from examining the global error plot. This plot shows that, regardless of the ambient condition of the ionosphere during the time leading up to the lightning strike, there was most likely a 4.5 [km] - 7.0 [km] change in the reflection height of the ionosphere due to this early/fast event.
Next, the single ambient profile that most accurately modeled the observed changes in amplitude and phase, i.e. produced the lowest amount of error, will be examined. Minimum error for a single ambient profile occurred when the ambient profile used in the LWPC model was h' = 88.5 [km] and /5 = 0.88 [km-1]. The single ambient error plot is shown in Figure 4.6.
25


Combined Error for June 13th Event vs. (Ah', A/J)
50 45
40 _
35 Z
T!
30 cB 5
25 t
20 £
LU 15 "ra o
io H
5 0
Figure 4.6: June 13th single ambient profile (ft/=88.5[km] and /5=0.88[km-1]) error
From the analysis of the error for this ambient profile, it is seen that the accuracy of the LWPC when modeling the 0-directed component of the magnetic held is not highly dependent on j3. Figure 4.6 shows that, if the effective ambient condition of the ionosphere was h' = 88.5 [km] and /3 = 0.88 [km-1], then the change in ionospheric reflection height was between 3.5 [km] - 5 [km].
This time, it is important to note that absolute minimum error occurred when Ah! = -4.5 [km] and A/5 = 0 [km-1], because this point represents the best fit LWPC modeled changes in amplitude and phase of both the NLK and NML transmitters over all values of Ah! and A/5 in the disturbed region. The modeled changes in amplitude and phase are shown graphically in Figure 4.7 with an annotation at Ah! = -4.5 [km] to highlight the best LWPC modeled results.
Ambient: h' = 88.5 [km] fi = 0.88
26


A h'
A h’
Figure 4.7: Modeled changes in amplitude and phase as a function of Ah' and A/5 from LWPC simulation of June 13*hevent with 250 [km] disturbed radius
For this case, a full examination of the LWPC modeled radial component of the magnetic held was conducted, meaning that radial simulation was run for a large number of ambient profiles in an attempt to calculate global error in the same way that it was done for the 0-directed component. Interestingly, while the 0-directed component of the magnetic held is mainly dependent on h', the radial component of the magnetic held appears to be mainly dependent on /5. This is promising and suggests that the different polarizations of the magnetic held could be used to diagnose h' and /5 separately. Figure 4.8 shows global error of the radial component. Analysis of the global error shows that the A/5 ionospheric response to this event was in the range of 0 [km-1]to 0.05 [km-1].
27


Global Error (Radial) for June 13th Event:
250 [km] Disturbed Radius
-0.25 -02 -0.15 -0.1 -0.05 < 0 0.05 0.1 0.15 02
-15 -10 -5 0 5
A h'
Figure 4.8: Radial global error for June 2016 event
fi
4.5
3.5 ± z
~o
3 §
2.5 z

1.5 2
0.5
Figure 4.9 shows the modeled changes in amplitude and phase of the radial component using the same single ambient profile producing the lowest error from the 0-directed analysis (h? = 88.5 [km], /5 = 0.88 [km-1]).
Figure 4.9: Changes in radial amplitude and phase as a function of Ah' and A/5 from LWPC simulation of June 13thevent with 250 [km] disturbed radius
28


Figure 4.9 shows that the LWPC does not predict large changes in the radial amplitudes of either transmitters’ signal. It does however predict rapid fluctuations in phase with changes in reflection height for a given value of /5. That value of /5 does appear to determine how rapidly that change occurs as well as whether the phase change is positive or negative. This overall phase volatility was somewhat expected because it was observed in the phase of the NLK signal recorded at the Delaware receiver site. Figure 4.10 shows the radial error for a single ambient profile based on the LWPC modeled changes in radial amplitude and phase.
Radial Error for June 13th Event vs. (Ah', A£J) Ambient: h' = 88.5 [km] 0 = 0.88
-18 -16 -14 -12 -10 -8-6-4-2 0
A h'
Figure 4.10: Radial error for single ambient profile for June 13th, 2016 event
Analysis of Figure 4.10 shows that analysis of the radial component suggests that the A/5 ionospheric response to this event was in the range of ±0.02 [km-1], which is in line with the global error analysis for the radial component. It is also in agreement with where the lowest error occurred when analyzing the 0-directed component of this single ambient profile, which was at A/5 = 0 [km-1]. Table 4.2 presents a summary of the simulation results from the June 13th, 2017 early/fast event in comparison to the recorded observations.
29


Table 4.2: Model and observational comparison of As for June 13t/l, 20f6 early/fast event with 250 [km] disturbed radius
Least Error Ambient: h' = 88.5 [km] and /3 = 0.88 [km :]
Observed Modeled
Tx ^Amp A Phase ^Amp A Phase
NLI<+ -0-96[dBnV] 7-‘2‘2[deg\ -0.‘23[dBtiV] 15-8 [deg]
NML$ 5.90 [d,BnV] 34.8 [dec?] -2.66 [dBfiV] 35. l[deg]
NLR rad,ia,l -0.75[dBtiV] -0.11 [deg] 0.7‘2[dBtiV] 15.1 [deg\
N ML radial -10. l[dBfiV] 73.6[deg] 8.11 [dBfiV] 22.19[deg]
4.1.2 Effect of Disturbance Region Size
This section will examine the effects of modeling the disturbed region with a radius 500 [km]. Figure 4.11 shows the model setup for this configuration.
30


Using the model shown above, the LWPC simulation was again run for 375 ambient profiles between 83.0 [km] > h? > 89.0 [km] and 0.40 [km-1]> /3 > 0.90 [km-1]. Each ambient simulation used 1066 dynamic profiles in the disturbed region. Of the 375 ambient simulations that were run, 95 of them had low enough error to contribute to the global error calculations. Figure 4.12 shows the global error for the June 13th, 2016 event using a disturbed radius of 500 [km].
Global Error for June 13th Event
,
-15 -10 -5 0
A h'
Figure 4.12: Global error for June 13th, 2016 event
Analysis of Figure 4.12 shows that, with a 500 [km] disturbed region, the ionospheric response was a decrease in reflection height in the range of -5 [km] and -8 [km]. The single ambient profile which produced the lowest overall error for this simulation was h' = 85 [km] and /3 = 0.44 [km-1]. This ambient profile is within the range of expected ambient profiles based on the previous analysis of ambient amplitudes. Figure 4.13 shows the error plot for this ambient profile.
31


Combined Error for June 13th Event vs. (Ah', A0)
Ambient: h' = 85 [km] f) = 0.44
-0.05 o
0.05
S3. 0.1
0.15 0.2 0.25
Figure 4.13: June 13thsingle ambient profile (/d=85[km] and /3=0.44[km-1]) error
Analysis of Figure 4.13 shows that the minimum error occurred Ah! = -6.4 [km] and A/3 = 0.16 [km-1], which is within the range of Ah' found using the global error. Figure 4.14 displays the modeled changes in amplitude and phase as functions of Ah' and A/3 with the least error point annotated to show the best fit model.
NLK A Amplitude vs. (Ah', A0)
Ambient: h' = 85 [km] 0 = 0.44
I
â–  c
I
NLK A Phase vs. (Ah', Ap)
-15 -10 -5 0 5
A h'
NLM A Phase vs. (Ah', Ap)
-15 -10 -5 0 5
A h*
Figure 4.14: Modeled changes in amplitude and phase as a function of Ah' and A/3 from LWPC simulation of June 13*hevent with 500 [km] disturbed radius
32


For this case the radial component of the magnetic held was only simulated for the ambient profile that produced the lowest error, so global error determination will not be presented. Radial error for ambient profile h' = 85 [km] and /3 = 0.44 [km-1] is shown in Figure 4.15. Again, the radial component points to a A/3 in the range of 0.15 [km-1] < A/3 < 0.35 [km-1]. Table 4.3 shows a summary of the simulation results from the June 13th event with a larger disturbed region, and compares them
to the recorded observations.
Radial Error for June 13th Event vs. (Ah', A0)
Ambient: h' = 85 [km] 0 = 0.44
-0.05 0
0.05 0.1 0.15 ^ 0.2 0.25 0.3 0.35 0.4 0.45
-15 -10 -5 0 5
A h’
Figure 4.15: Radial error for single ambient profile for June 13th, 2016 event 4.1.3 June 13th Conclusions
Overall analysis of the LWPC modeled 0-directed component of the magnetic
held from the June 13th, 2016 event shows a change in h' of 4.5 [km] to 7.5 [km]
in the dynamic region. Analysis of the LWPC modeled radial component of the
magnetic held predicted only a small change in /3 in the dynamic region. A comparison
of global error when modeled with 250 [km] and 500 [km] radii disturbed regions
suggests a slightly smaller change in reflection height with a smaller disturbed region.
Additionally, with a larger disturbed region, the overlapping path model produced
much lower single ambient prohle error with lower reflection height ambient prohles.
33


Table 4.3: Model and observational comparison of As for June 13t/l, 2016 early/fast event with 500 [km] disturbed radius
Least Error Ambient: h' = 85.0 [km] and [3 = 0.44 [km :]
Observed Modeled
Tx ^Amp APhase ^Amp A Phase
NLK+ -0.96 [dB/iV] 7.22[deg] 0-72[dSgV] 13.1 [deg]
NML$ 5.90 [dB/iV] 3 4.8 [deg] 8.11 [dB/j,V] 22.19[deg]
ALK racnai -0.75 [dBiiV] -0.11 [deg] 0-72[dSgV] 13.1 [deg]
N M Lradiai -10.1 [dB/iV] 73.6 [deg] 8.11 [dB/j,V] 22.19[deg]
4.2 April 26th, 2016
In order to test the capabilities and limitations of the overlapping path model, two LEP events that occurred on April 26th, 2016 causing only minor perturbations in the amplitude and phase of the VLF signals were modeled using the LWPC. These events were chosen because they took place within approximately 50 minutes of each other, and it was hypothesized that the ambient condition of the ionosphere would not have changed significantly within that amount of time.
4.2.1 Event #1: 08:03:55 [UT]
From the NLDN lightning strike database, this lightning strike occurred approximately 600 [km] due south of the NML transmitter (39.7M, 97.4W). As previously mentioned, LEP ionospheric disturbances are not localized to the region near the lightning strike, and the location of the loss cone depends on the altitude of the interaction region. In this case, the location of the loss cone was determined to be almost directly on top of the NML transmitter. Figure 4.16 shows the model setup for this
34


event including the location of the lightning strike and the disturbed region for the LEP event.
Figure 4.17 displays the observed changes in amplitude and phase of the signals transmitted from NLK and NML. Table 4.4 quantifies the observed ambient and dynamic amplitudes and phases, as well as identifies lightning induced changes in the transmitted signal that occurred during this event.
April 26, 2016: 222 [kA] LEP Event at 08:03:55 [UT]
70 60 50 40
'e
> 30
m
TJ
j| 80
Q-£
<
70 60 50 40
Figure 4.17: Delaware narrowband data for NLK and NML on April 26th, 2016
NLK Amplitude
NML Amplitude
Time [s]
35


Table 4.4: Amplitude and phase observations on April 26t/l, 2016
Tx AmbAmp DyV-Amp ^Amp Amb Phase Dyil'Phase APhase
NLI<+ 67.3 [d.BpV] 69A[dB^y] 2-04 [dBpV] 158.7^] 165.7[deg\ 7-01 [deg]
NML$ 70.7[ N LK rac[. 41-8 [dBpV] 45.6 [dBpV] 3-82 [dBpV] 132.9[defl] 151.7\deg\ 18-8[ N M L rad 47.5[(iBjtty] 53.5 [dBpV] 6-00[dBp,v] -151.8[(Jefl] -148.1^] 3.82^]
Using the same ranges for ambient and dynamic ionospheric profiles that was used when modeling the June 13t/l, 2016 event, the LWPC simulation was repeated for Event #1 on April 26th, 2016. Of the 375 ambient simulations that were run, 67 of them had low enough error to contribute meaningfully to the global error calculations. Figure 4.18 shows the global error for Event #1 on April 26th, 2016 using a disturbed radius of 250 [km].
Figure 4.18: Global error for April 26th, 2016 LEP Event #1
36


Analysis of figure 4.18 shows a rather large range (Ah' ~ ± 2.5 [km]) of possible reflection heights in the dynamic region that produce low error. This suggests that the change in reflection height was most likely very small, which is expected, considering that the observed VLF perturbations were also small. The single ambient profile which produced the lowest overall error for this simulation was h' = 84.5 [km] and /5 = 0.52 [km-1]. Figure 4.19 shows the error plot for this ambient profile.
Combined Error for April 26th Event #1 vs. (Ah', A0) Ambient: h' = 84.5 [km] Q = 0.52
-14 -12 -10 -8 -6 -4 -2 0 2 4
A h'
Figure 4.19: Single ambient profile error for April 26t/l, 2016 LEP Event #1
Analysis of Figure 4.19 shows that the minimum error occurred Ah' = +0.5 [km] and Aj3 = 0.38 [km-1]. This result, along with other single ambient profiles that contributed to global error calculations, is problematic because it suggests an increase rather than a decrease in reflection height. This is not what is typically expected from an LEP event and further analysis is needed in order to determine why some single ambient profiles predict this positive Ah!. Figure 4.20 displays the modeled changes in amplitude and phase as functions of Ah' and A/5 with the least error point annotated to show the dynamic condition that best the changes in amplitude and phase observed during this LEP event.
37


Figure 4.20: Modeled changes in amplitude and phase as a function of Ah' and A/5 from LWPC simulation of April 26th LEP Event #1
For this case, the radial component was only examined for the ambient profile that produced the lowest error when modeling the 0-directed component. Figure 4.21 shows a plot of the radial error that suggests the change in /3 was between 0.15 [km-1] and 0.25 [km-1]. Table 4.5 summarizes the LWPC simulation results for this event.
Radial Error for April 26th Event vs. (Ah', AjtJ) Ambient: h' = 84.5 [km] 0 = 0.52
-14 -12 -10 -8 -6 -4 -2 0 2 4
A h'
Figure 4.21: Single ambient profile radial error for Event #1 on April 26th, 2016
38


Table 4.5: Model and observational comparison of As for April 26t/l, 20f6 Event
Least Error Ambient: h' = 85.0 [km] and /3 = 0.44 [km :]
Observed Modeled
Tx ^Amp A Phase ^Amp A Phase
NLIx* 2-04 [dBfiV] 7-01 [deg] 1-22 [dBiiV] -10 • 3 \deg\
NML$ 1-90 [dBnV] â– 1-10 [deg\ -2.73 [d,B/uV] 17.1 [deg\
NLR ra(l,ial 3-82 [dBiiV] 18-8 [deg] -0.30 [dBnV] 18.4 [deg]
N M L radial 6-00 [dBnV] 3-82 [deg] -0.40 [dBnV] 2-42 [deg]
4.2.2 Event #2: 08:50:44 [UT]
The second lightning strike that occurred on April 26th happened just northwest of Kansas City, KS (39.3N, 94.77W). Again, this is approximately 600 [km] south of the overlapping path of propagation. In this case, the location of the loss cone was determined to be about 250 [km] east of the NML transmitter. Figure 4.22 shows the model setup for this event.
39


Figure 4.23 displays the observed changes in amplitude and phase from the NLK and NML transmitters. Table 4.6 quantifies the ambient, dynamic, and change in the amplitudes and phases of the VLF signals observed during this event.
E
5
60

April 26, 2016: 220 [kA] LEP Event at 08:50:44 [UT]
NLK Amplitude
• <1> Amplitude - Radial Amplitude
40
100
NLK Phase
Figure 4.23: Delaware narrowband data on April 26 , 2016 for Event ^2
Table 4.6: Amplitude and phase observations on April 26th, 2016
Tx AmbAmp DyTl'Amp ^Amp Amb phase Dy 11'Phase Nphase
NLK+ 65.8 [dBpV] 67 A[dBpV] 1-60 [dBpV] 153.8^] 156.7 [deg] 2-87 [deg]
NML$ 70.8 [dBpV] 71-9 [dBpV] ^A7[dBpV] -94.3^] "99.8 [deg] -5.50 [deg]
NLI A M 53.3 [dBp.v) 54.6[(iBjttv] l-‘28[dBp.v] U9.2[deg\ 149.1 [deg] -0.16 [deg]
Again, using the same range of ambient and dynamic ionospheric profiles, the LWPC simulation was run for Event #2. Of the 375 ambient simulations that were run, 350 of them had low enough error to contribute meaningfully to the global error calculations. Figure 4.24 shows the global error for Event ^2 on April 26th, 2016.
40


Global Error (Total) for April 26th Event: 250 [km] Disturbed Radius
Analysis of Figure 4.24 shows that, with a 250 [km] disturbed region, the ionospheric response was a decrease in reflection height in the range of 0 [km] and -2.5 [km]. Figure 4.25 shows the error plot for the single ambient profile which produced the lowest overall error {h! = 84.0 [km] and /3 = 0.80 [km-1]).
Combined Error for April 26th Event #2 vs. (Ah', A0)
-10 -5 0 5
A h'
Figure 4.25: Single ambient profile error for April 26th, 2016 LEP Event ^2
41


Analysis of Figure 4.25 shows that the minimum error occurred Ah' = -1.5 [km] and A/5 = -0.2[km-1]. Figure 4.26 displays the modeled changes in amplitude and phase as functions of Ah' and A/5 with the least error point annotated to highlight the best fit LWPC modeled changes in amplitude and phase.
Figure 4.26: Modeled changes in amplitude and phase as a function of Ah' and A/5 from LWPC simulation of April 26th LEP Event ^2
A full examination of the radial component was conducted for this case. Through global error analysis of the radial component, it was determined that the LWPC expected change in /5 was between 0 [km-1] and 0.05 [km-1]. The radial global error is shown in Figure 4.27, and Table 4.7 displays a summary of the LWPC simulated results in comparison to recorded observation for this event.
42


Global Error (Total) for April 26th Event: 250 [km] Disturbed Radius
-10 -5 0 5
A h'
Figure 4.27: Radial global error for April 26th, 2016 Event ^2 Table 4.7: Model and observational comparison of As for April 26th, 2016 Event ^2
Least Error Ambient: h! = 85.0 [km] and /3 = 0.44 [km
Observed Modeled
Tx ^Amp A Pha.se ^Amp A Phase
NLK+ PSOjdB^y] 2-87[(fefl] -0.98[dBl_iv] 11 • 6 [deg]
NML$ L17[^v] -5.50 [deg] 1-42 [dBnV] -1-75 [deg[
NLK radial 17.6 [d,BnV] - -O.OSfdB^v] -38.0[ A M 1. radial L28[(jn^v] -0.16 [deg] -1-76 [dBnV] -240.2[(fefl]
4.2.3 April 26th Conclusions
The LWPC overlapping propagation path model performed reasonably well for
this set of events, in that the observed changes in amplitude and phase from the
NLK and NML transmitters was small, and so were the LWPC predicted changes in
h' and /5. The idea that the two back-to-back events would help in identifying the
43


effective ambient ionospheric conditions leading up to the event did not turn out to be particularly beneficial because the lowest error single ambient profiles ended up having different values of /3. Interestingly, LWPC analysis of event #1 did predict an increase in [3 which then showed up in least error single profile ambient of event ^2. While this is an interesting occurrence in the LWPC model, it may be purely coincidental because one would expect the dynamic condition of the ionosphere due to a lightning strike to relax back to the effective ambient condition in far less than the 50 minutes time that elapsed between these events. Further analysis of these events can still be done by simulating different sizes for the disturbed regions. Also, a further examination of what ambient conditions give rise to an LWPC expected increase in h', and whether these single ambient profiles should contribute to global error calculations, should be conducted.
44


CHAPTER 5
SUMMARY AND CONCLUSIONS
5.1 Summary
Three lightning induced ionospheric disturbances that occurred during 2016 were examined using the LWPC. The first event that was examined was a high peak-current early/fast event that caused large perturbations in the amplitude and phase of the VLF signals propagating in the EIW. The second two events were LEP events that caused only minor perturbations to these signals. Through LWPC modeling using a large number of possible ambient ionospheric profiles, conclusions about changes in electron densities in the dynamic region due to the lightning strike have been reached. The results of the LWPC modeling are displayed in Table 5.1.
Table 5.1: LWPC Modeled Changes in h' and /3
LWPC Modeled Ah' and A/3 for June 13th, 2016 Early/Fast Event
250 [km] Disturbed Radius 500 [km] Disturbed Radius
Single Global Single Global
Ah' -4.5 [km] -5.0 [km] -6.4 [km] -5.6 [km]
A/3 0 [km-1] -0.12 [km-1] +0.16 [km-1] +0.2 [km-1]
LWPC Modeled Ah' and A/3 for April 26th, 2016 LEP Events
Event #1 Event #2
Single Global Single Global
Ah' +0.5 [km] 0 [km] -1.5 [km] -1.0 [km]
A/3 +0.38 [km-1] +0.20 [km-1] -0.20 [km-1] +0.06 [km-1]
45


5.2 Conclusions
This project has presented a novel way to quantify lightning induced changes in ionospheric conditions by utilizing unique geometry to add additional constraints to a previously under-constrained problem. Although the effective ambient condition of the ionosphere added an additional degree of freedom that proved to be an incredibly challenging problem to address, this work has developed a technique that determines changes in h' and [3 independently of ambient ionospheric conditions. More work can be done to further examine how varying the size of the disturbed region affects the expected h' and (3 changes in the dynamic region, as well as how the size of the dynamic region determines which single ambient profiles generate error low enough to be considered in global error calculations. It would be of great interest to the author to determine effective ambient conditions empirically by deploying additional VLF receivers along the overlapping path of propagation. Further work can also be done to simulate both early/fast and LEP events with higher resolution of both ambient and dynamic profiles in order to determine global error with a larger data set. Validating the results of this research using other simulation methods such as the Finite Difference Time Domain (FDTD) has been proposed and is currently in progress. This work has shown that, by using overlapping paths of VLF propagation to perform VLF remote sensing with LWPC modeling, a more definitive conclusion about changes in h' and (3 caused by lightning induced perturbations has been reached.
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REFERENCES
[1] K. G. Budden. The influence of the earth’s magnetic field on radio propagation by wave-guide modes. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 265(1323):538-553, 1962.
[2] M. B. Cohen, U. S. Inan, and E. W. Paschal. Sensitive broadband elf/vlf radio reception with the awesome instrument. IEEE Transactions on Geoscience and Remote Sensing, 48(1):3—IT, Jan 2010.
[3] Vernon Cooray. Earth’s Atmosphere and Its Electrical Characteristics, pages 59-70. Springer Netherlands, Dordrecht, 2015.
[4] S. A. Cummer, U. S. Inan, and T. F. Bell. Ionospheric d region remote sensing using vlf radio atmospherics. Radio Science, 33(6):1781-1792, 1998.
[5] M. Gokowski, N. C. Gross, R. C. Moore, B. R. T. Cotts, and M. Mitchell. Observation of local and conjugate ionospheric perturbations from individual oceanic lightning flashes. Geophysical Research Letters, 41(2) :273—279, 2014.
[6] Feng Han and Steven A. Cummer. Midlatitude nighttime d region ionosphere variability on hourly to monthly time scales. Journal of Geophysical Research: Space Physics, 115(A9), 2010. A09323.
[7] J. P. Hauser, W. E. Garner, and F. J. Rhoads. Effective ground conductivity map of Canada and greenland with revisions from propagation data. Naval Research Laboratory Report 6893, 1969.
[8] R. A. Pappert and J. A. Ferguson. Vlf/lf mode conversion model calculations for air to air transmissions in the earth-ionosphere waveguide. Radio Science, 21 (4) :551—558, July 1986.
[9] J. R. Wait and K. P. Spies. Characteristics of the earth-ionosphere waveguide for vlf radio waves. National Bureau of Standards, Technical Note(300), 1964.
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Full Text

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LWPCMODELINGOFVLFPERTURBATIONSFROMLIGHTNINGINDUCED IONOSPHERICDISTURBANCESONOVERLAPPINGPATHSOF PROPAGATION by CHADM.RENICK B.S.,UniversityofColoradoDenver,2017 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof MasterofScience ElectricalEngineering 2018

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ThisthesisfortheMasterofSciencedegreeby ChadM.Renick hasbeenapprovedforthe ElectricalEnigineeringProgram by StephenGedney,Chair MarkGolkowski,Advisor VijayHarid Date:May12,2018 ii

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Renick,ChadM.M.S.,ElectricalEngineering LWPCModelingofLightningInducedIonosphericDisturbancesonOverlapping PathsofVLFPropagation ThesisdirectedbyAssistantProfessorMarkGolkowski ABSTRACT Lightningdischargesareknowntobeasourceofhighamplitude,broadfrequency electromagneticradiation.Theseelectromagneticwavescancauseperturbationsin theelectrondensityoftheD-regionoftheionosphereeitherbyionizationfromquasielectrostaticeldsorfrominducedenergeticelectronprecipitationfromthemagnetosphere.BecausechangesinD-regionelectrondensityaecttheconductivityofthe ionosphere,nighttimelightningdischargescanperturbtheamplitudeandphaseof VLFcommunicationsignalspropagatingthroughtheEarth-ionospherewaveguide. Mostpastworkinthisareahasinvolveduniquepropagationpathsbetweenatransmitterandreceiver.Modelingofsuchperturbationeventsofteninvolvesuncertainty sincetheperturbedionosphericprolecannotbeuniquelydetermined.Thisworkhas focusedonanoverlappingVLFpropagationpathonwhichsignalsfromtwodierent VLFtransmittersshareacommonpathtoareceiver.Thisallowsforthegeographic areaoftheoverlappingpathtobesimultaneouslydiagnosedwithtwosignalswith dierentmodecontent.Observationsshowthatalightninginducedperturbationon theoverlappingpathcanhavealargeeectontheamplitudeorphaseofonesignal, whileleavingtheotherwaverelativelyunaected.TheLongWavePredictionCapabilityLWPCsoftwarepackageisusedtosimulatethisphenomenonbyalteringthe eectiveconductingheightoftheionospherenearthelocationofaknownnighttime lightningstrike.Goodagreementisfoundbetweenthesimulationandtheobservationsshowingthatprovidingadditionalconstraintsontheperturbedionosphere yieldsamoreaccuratemodelofhowlightningaectsionosphericelectrondensities. iii

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Theformandcontentofthisabstractareapproved.Irecommenditspublication. Approved:MarkGolkowski iv

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DEDICATION Thisworkisdedicatedtothemanypeopleinmylifewhomakeitwonderfulto bealive,andwhoremindmeonoccasiontoappreciatehowamazingitisthatwe areevenhereatall.Tomyparents,DuaneandGayle,whosetirelesssupportmade itpossible.TomysisterJill,whomIwouldn'tbethesamewithout.ToHolly,who reallyjustmakesmyheartsmile.Andespecially,tomysonCaelwhounknowingly providedtheinspirationandmotivationtomakeithappen.Iloveyouallsomuch. v

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ACKNOWLEDGMENTS ThankyoutoalloftheprofessorsattheUniversityofColoradoDenverwho challengedandinspiredme.ThanksalsotoMorrisCohenandhisteamattheGeorgia InstituteofTechnologyforprovidingdataforthisproject.Iwouldespeciallyliketo thankAshanthiMaxworthforbeingteacher,tutor,andfriendtome.Withouther,I wouldnothavehadtheopportunitytoworkwiththeElectromagneticsandPlasma PhysicsResearchGroup.Ialsowouldliketoextendmysincerethanksandgratitude toDr.Golkowski.Itrulyvaluetheguidanceandsupportthathehasgivenmeon thisproject,aswellastheencouragementhehasgivenmetocontinuedownthepath thatIamon.ThisworkwassupportedbytheNationalScienceFoundationwith grantAGS1451210totheUniversityofColoradoDenver. vi

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TABLEOFCONTENTS CHAPTER 1.INTRODUCTION...............................1 1.1Ionosphere................................1 1.2EarthIonosphereWaveguide......................3 1.3VLFRemoteSensing..........................4 1.4LightningDisturbances.........................4 1.4.1Early-FastEvents........................5 1.4.2LightningInducedEnergeticElectronPrecipitation......5 1.5LWPCModeling.............................6 1.5.1PresegmentationPRESEG...................7 1.5.2ModeFinderMODEFNDR..................7 1.5.3FastModeConversionFASTMC...............8 1.5.4ModelingRadialComponentofMagneticFieldwiththeLWPC8 2.OBSERVATIONS................................10 2.1OverlappingPathGeometry......................10 2.2NavyTransmitters............................10 2.3VLFAntennaandReceiver.......................11 2.4LEPandEarly/FastPerturbationsonVLFSignals..........12 3.MODELSETUP................................15 3.1DynamicProles/DisturbedRadius.................15 3.2DeterminingAmbientIonosphericConditions.............16 3.3GraphicalRepresentationofExpectedChanges............17 3.4ErrorforSingleAmbientProle....................18 3.5GlobalError...............................19 4.CASESTUDIES................................21 4.1June13 th ,2016..............................21 vii

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4.1.1LWPCAnalysiswith250[km]DisturbedRadius.......24 4.1.2EectofDisturbanceRegionSize................30 4.1.3June13 th Conclusions......................33 4.2April26 th ,2016.............................34 4.2.1Event#1:08:03:55[UT].....................34 4.2.2Event#2:08:50:44[UT].....................39 4.2.3April26 th Conclusions......................43 5.SUMMARYandCONCLUSIONS.......................45 5.1Summary.................................45 5.2Conclusions...............................46 REFERENCES...................................47 viii

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TABLES 2.1AmplitudeandphaseobservationsonMay17 th ,2017...........14 4.1AmplitudeandphaseobservationsonJune13 th ,2016...........22 4.2ModelandobservationalcomparisonofsforJune13 th ,2016early/fast eventwith250[km]disturbedradius....................30 4.3ModelandobservationalcomparisonofsforJune13 th ,2016early/fast eventwith500[km]disturbedradius....................34 4.4AmplitudeandphaseobservationsonApril26 th ,2016..........36 4.5ModelandobservationalcomparisonofsforApril26 th ,2016Event#139 4.6AmplitudeandphaseobservationsonApril26 th ,2016..........40 4.7ModelandobservationalcomparisonofsforApril26 th ,2016Event#243 5.1LWPCModeledChangesin h 0 and ....................45 ix

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FIGURES 1.1Exampleionosphericelectrondensity[3]..................2 1.2ApproximatedD-regionionosphericelectrondensity............3 1.3Depictionofearly/fastionosphericdisturbance..............5 1.4DepictionofLEPionosphericdisturbance.................6 2.1Overlappingpathgeometry.........................10 2.2Visualizationofrotationmatrix.......................12 2.3NarrowbandobservationsfromMay17 th ,2017early/fastevent.....13 2.4Examplerepresentationoftherelationshipbetweenobservationsandthe terminologyusedtorefertothem Ambient,Dynamic and......14 3.1ModelgeometryexamplefromMay17 th ,2017event...........15 3.2AmbienterrorexamplefromMay17 th ,2017event.............17 3.3Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofMay17 th event.................18 3.4ErrorobtainedfromasingleambientproleforMay17 th ,2017Event.19 3.5GlobalerrorforMay17 th ,2017Event...................20 4.1LocationofJune13 th ,2016early/fast385[kA]event...........21 4.2DelawarenarrowbanddataforNLKandNMLonJune13 th ,2016....22 4.3AmbienterrorforJune13 th ,2016early/fastevent.............23 4.4ModelsetupforJune13 th ,2016early/fastevent..............24 4.5GlobalerrorforJune13 th ,2016event...................25 4.6June13 th singleambientprole h 0 =88.5[km]and =0.88[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]error.26 4.7Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofJune13 th eventwith250[km]disturbedradius27 4.8RadialglobalerrorforJune13 th ,2016event................28 4.9Changesinradialamplitudeandphaseasafunctionof h 0 and from LWPCsimulationofJune13 th eventwith250[km]disturbedradius...28 x

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4.10RadialerrorforsingleambientproleforJune13 th ,2016event.....29 4.11ModelsetupforJune13 th ,2016early/fastevent..............30 4.12GlobalerrorforJune13 th ,2016event...................31 4.13June13 th singleambientprole h 0 =85[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]error...32 4.14Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofJune13 th eventwith500[km]disturbedradius32 4.15RadialerrorforsingleambientproleforJune13 th ,2016event.....33 4.16ModelsetupforApril26 th ,2016LEPevent................35 4.17DelawarenarrowbanddataforNLKandNMLonApril26 th ,2016....35 4.18GlobalerrorforApril26 th ,2016LEPEvent#1..............36 4.19SingleambientproleerrorforApril26 th ,2016LEPEvent#1.....37 4.20Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofApril26 th LEPEvent#1............38 4.21SingleambientproleradialerrorforEvent#1onApril26 th ,2016...38 4.22ModelsetupforApril26 th ,2016LEPEvent#2..............39 4.23DelawarenarrowbanddataonApril26 th ,2016forEvent#2.......40 4.24GlobalerrorforApril26 th ,2016LEPEvent#2..............41 4.25SingleambientproleerrorforApril26 th ,2016LEPEvent#2.....41 4.26Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofApril26 th LEPEvent#2............42 4.27RadialglobalerrorforApril26 th ,2016Event#2.............43 xi

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CHAPTER1 INTRODUCTION 1.1Ionosphere TheionosphereisaregionoftheEarth'satmosphererangingfrom60-1000km inaltitude.ItisseparatedintotheD,E,andFregions.Althoughtheplasmain theionosphereisgeneratedbysolarradiation,suddenionosphericdisturbancessuch asgammaraybursts,solarares,andlightningstrikescanalsochangetheplasma density.ElectrondensitiesintheEandFregionsarerelativelywellunderstood becausetheycanbemeasuredwithionosondes,incoherentscatterradarISR,or in-situsatellitemeasurements.Themainfocusofthisworkisthelowest-95km portionoftheionospherecalledtheD-region.Determiningelectrondensitiesinthe D-regionposescertainchallengesbecauseelectrondensitiesinthisregionaretoolow formeasurementwithionosondesorISRs.Additionally,thealtitudeistoohighfor weatherballoonmeasurementsandtoolowfordirectmeasurementsviasatellite. Figure1.1showsaplotoftypicaldaytimeandnighttimeelectrondensitiesinthe ionosphereasafunctionofheight.ItshowsthatelectrondensitiesintheD-regionof theionosphereincreaseexponentiallywithheight,thusexhibitingalineartrendona logarithmicscale. 1

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Figure1.1:Exampleionosphericelectrondensity[3] Inthiswork,D-regionelectrondensitieswillberepresentedandmodeledusing thewidelyacceptedtwoparameterexponentialmodeloriginallyproposedbyWait andSpiesin1964[9]: n e = n 0 e )]TJ/F17 7.9701 Tf 6.587 0 Td [(0 : 15 h 0 e )]TJ/F17 7.9701 Tf 6.587 0 Td [(0 : 15 h )]TJ/F20 7.9701 Tf 6.586 0 Td [(h 0 [ cm )]TJ/F17 7.9701 Tf 6.587 0 Td [(3 ].1 where n 0 =1 : 43 10 7 [electrons], h 0 h-prime[km]describestheeectivereection heightoftheionosphere,and beta[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]describesthesharpnessoftheprole, orhowquicklyelectrondensitiesincreaseasafunctionofheight.Figure1.2isaplot oftypicaldaytimeandnighttimeD-regionelectrondensitiesusingtheexponential model. 2

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Figure1.2:ApproximatedD-regionionosphericelectrondensity 1.2EarthIonosphereWaveguide DuetothehighnumberoffreeelectronsinboththeEarth'scrustandtheionosphere,theseregionsbehavelikegoodconductorswhentheyareencounteredbyVery LowFrequencyVLFwaves.Thiscausesthesewavestobereectedoofboththe Earth'scrustandtheD-regionoftheionosphere,formingwhatisknownastheEarthIonosphereWaveguideEIW.ThedominantmodespropagatingthroughtheEIW aretransversemagneticTMmodes,whichhaveverticalelectriceldsandmagnetic eldsinthe -direction.Therearealsonon-dominanttransverseelectricTEmodes, withtypicallyloweramplitudes,whichcontainradiallyorientedmagneticeldsthat correspondtoelectriceldsthathaveahorizontalcomponent. WhiletheEarth'scrusthasstableconductivity,ionosphericpropertiesaredriven byverydynamicsystemsandchangedailywithsolarzenithangleandminuteto minutewitheventslikesolarares,gammaraybursts,lightningstorms,andenergetic electronprecipitationfromthemagnetosphere.Allofthesefactorschangeelectron 3

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densitiesintheD-region,whichinturncanalterhowwavespropagateintheEIW. 1.3VLFRemoteSensing ThewaythatVLFwavesarereectedooftheionosphereishighlydependent onionosphericconditions.Changesin h 0 and canchangethepossiblemodesofVLF propagationintheEIW,thereforechangingtheamplitudeandphaseofobservedthe signal.ThissuggeststhatVLFwavesthathavereectedfromtheionosphereretain someinformationaboutionosphericconditions.VLFremotesensingtakesadvantage ofthisphenomenabyexaminingVLFsignalsinordertodiagnoseionosphericconditions.Quitesimply,thisisdonewithsomesourceofVLFradiationandaVLF receivertorecordtheobservedsignal.Inthiswork,theVLFsourcesusedaresinglefrequencyU.S.Navytransmittersusedforsubmarinecommunication.TheVLF receiverusedforobservationsinthisworkislocatedontheDelawareAeroSpace EducationcampusinDelaware. 1.4LightningDisturbances Lightningisasuddendischargeofstaticelectricityintheatmospherethathappenswhenachargelargerthanthebreakdownvoltageofairisbuiltupbetween twoobjects.Mostlightningoccursduringthunderstormseitherascloud-to-cloud orcloud-to-grounddischarges,withtheformerbeingmorecommon,butthelatter involvinglargercurrentsoftenstohundredsofkiloAmperes.Thisrapiddischargeof electricitycausesacurrenttoowfromhightolowpotentialwhichactslikeanantennaemittingbroad-spectrumelectromagneticradiationintheEarth'satmosphere. Someofthiselectromagneticradiationistrappedduetotheconductivepropertiesof theEarthandionosphereandpropagateswithintheEIW.Muchofthepropagating radiationgeneratedbyalightningstrikeisintheELFandVFLbands.Insomecases energyfromalightningstrikealtersionosphericconditionsbycausingionizationof particlesintheupperatmosphere.Theselightninginducedionosphericdisturbances 4

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areclassiedintoeitherEarly/FastorLightningInducedEnergeticElectronPrecipitationLEPevents. 1.4.1Early-FastEvents Early/Fasteventsarecausedwhentheelectromagneticpulsefromalightning dischargecausesdirectionizationofatmosphericparticles,orwhenionizationoccurs becauseofthequasi-staticelectriceldscausedfromthesuddenchargeremovalthat occursduringalightningstrike[5].Figure1.3showsadepictionofanEarly/Fast ionosphericdisturbance.TheeectsofionosphericdisturbancescausedbyEarly/Fast eventsareobservednearlyinstantaneouslyafteralightningstrikeandtheionospheric disturbanceislocalizedtothegeographicregionwherethelightningstrikeoccurred. Figure1.3:Depictionofearly/fastionosphericdisturbance 1.4.2LightningInducedEnergeticElectronPrecipitation LightningInducedEnergeticElectronPrecipitationeventsoccurwhensomeof theelectromagneticradiationcreatedbythelightningstrikeescapesthroughthe ionosphereintothemagnetosphereandinteractswithhighenergyelectronsthatare geomagneticallytrappedbytheEarth'smagneticeld.Thisinteractionchangesthe trajectoryofthesechargedparticleandcausesthemtorain"downontheionosphere thuscausingsecondaryionization.Figure1.4showsadepictionofanLEPevent.The eectsofLEPeventsarenotobservedinstantaneouslyafteralightningstrike,and areseparatedgeographicallyfromregionwherethelightningstrikeoccurred.Inthe 5

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northernhemisphereionosphericdisturbancesduetoLEPeventsareobservednorth ofwherethelightningstrikeoccurred.Inthesouthernhemispherethedisturbance occurssouthofthestrike.TheLEPeventsmodeledinthisworkcorrespondto precipitationfromapproximately L -shell2.5ofthemagnetosphere.The L parameter denotesthedistanceinEarthradiifromtheEarth'scenterthatageomagneticeld linecrossestheequatorialplane. Figure1.4:DepictionofLEPionosphericdisturbance 1.5LWPCModeling ThesoftwareusedtodeterminetheoreticalVLFpropagationintheEIWinthis workiscalledtheLongWavePropagationCapabilityLWPCcode.TheLWPC waswritteninFORTRANbytheNavyinthelate1970'stoearly1980's[8].Itisa twodimensionalwaveguidemodelthatusesmodetheorytodeterminetheexpected amplitudeandphaseofaVLFwaveatagivenlocation.Theinputparameterstothe programaretransmitterlocation,transmitterpower,transmitterfrequency,receiver location,andionosphericelectrondensityasafunctionofheight.Inthiswork,the 6

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transmitterandreceiverparametersdonotchangesotheonlyinputparameterthat isvariedistheionosphericprole. TheprogramsolvesfortheexpectedamplitudeandphaseoftheVLFsignal bysplittingthepathofpropagationintosegmentswithdierentwaveguideparameters,determiningthepossiblemodesofpropagationthroughthewaveguide,and calculatingattenuationandphasedecaypermodeforeachsegment.Thetheoretical amplitudeandphaseofthepropagatingwaveisgivenbythesummationofallmodes atthereceiversite.ThenextthreesectionsgiveabriefdescriptionoftheLWPC's threemainalgorithms. 1.5.1PresegmentationPRESEG TheLWPCusesanacceptedmodelfortheEarth'smagneticeldandanexperimentallyderivedmapoftheEarth'sconductivityandpermittivity[7].These parametersarepredeterminedforagivengeographiclocation.Asdiscussedabove, theionosphericelectrondensitiesarespeciedbytheuserfordierentsectionsofthe propagationpath.ThePRESEGportionoftheLWPCcodetakestheinformation aboutthewaveguideparametersandseparatesthepathfromtransmittertoreceiver intosectionswherethewaveguideparametersarecontinuous.Thisallowsthepath ofpropagationtobemodeledasaseriesofwaveguideswithdierentparameters. 1.5.2ModeFinderMODEFNDR Theexpectedeldsatagivenlocationcanberepresentedbythesumofallthe modespropagatingthroughtheEIW.Thus,inordertodeterminetheexpectedelds, itisnecessarytodetermineallpossiblemodesofpropagation,aswellastheexcitation factorsforeachmode.InformationfromPRESEGispassedtoMODEFNDRin ordertoperformthesecalculationsbasedontransmittercharacteristicsandwaveguide parametersforeachsegmentedslabalongthepath.MODEFNDRthensearches forEigenangleswhichdenepropagatingmodesbydeterminingwhichanglesof incidencesatisfythemodecondition: 7

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det [ I )]TJ/F19 11.9552 Tf 11.956 0 Td [(R L R U ]=0.2 where R L = 2 6 4 k R k 0 0 ? R ? 3 7 5 andR U = 2 6 4 k R k k R ? ? R k ? R ? 3 7 5 .3 aretheFresnelreectioncoecientscalculatedattheupperandlowerboundaries oftheEIW.Thelowerreectioncoecient R L denesisotropicreectionsoof theEarth'scrustthataredependentontheangleofincidence,conductivity,and permittivity.Becausetheionosphereisamagnetizedplasmaandanisotropicitymust beconsidered,theupperreectioncoecient R U thatdenesionosphericreection isdependentonnotonlytheangleofincidencebutalsothepolarizationofthe VLFwave[1].AderivationoftheexcitationfactorscalculatedbyMODEFNDRare presentedbyPappertandFergusonin[8]. 1.5.3FastModeConversionFASTMC TheFASTMCalgorithmperformsmodeconversioncalculationstoensureaccurateeldpropagationthroughwaveguidediscontinuities,andoutputsthenalsummationofallmodesintheformofamplitudeandphase.Thisisaccomplishedby determiningtheexcitationfactors,heightgains,andcumulativemodeconversioncoecients[8]ineachpartitionofthepathbasedonthepossiblemodesofpropagation. Magnitudeisgivenin dB referencedto1 V=m andphaseisgivenintotaldegreesof phasechangeacrosstheentirelengthofthepathfromtransmittertoreceiver. 1.5.4ModelingRadialComponentofMagneticFieldwiththeLWPC Forverticallyorientedelectricelds,theconversionbetweenLWPCoutputamplitudein dB V andthenarrowbandVLFhorizontalmagneticeldobservationsin 8

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pT isasimpleconversion.However,modelingtheradialcomponentofthemagnetic eldusingtheLWPCnecessitatedalteringtheFORTRANcodeintheFASTMCand PRESEGlesinordertohavetheLWPCoutputthehorizontalelectriceld.The LWPCwasthenrunwiththehorizontaleldoutputatthreedierentaltitudes, 1,and2[km]andthecurloftheelectriceldwastakenusingtheforwarddierence approximation B r LWPC = )]TJ/F19 11.9552 Tf 9.298 0 Td [(E hLWPC @2 km +4 E hLWPC @1 km )]TJ/F15 11.9552 Tf 11.955 0 Td [(3 E hLWPC @0 km 2 j! z .4 wheretheradialmagneticeld B r LWPC isinTeslas,andhorizontalelectriceld E LWPC isinV/m, ! istheangularfrequencyofthetransmitter,and z isthe changeinLWPCsimulatedaltitudeforthethreeelectricelds.Someofthecases thatwillbepresentedhavenotbeenfullyrunfortheradially-directedcomponentof themagneticeldduetothefactthatitiscomputationallyexpensivetodoso.For suchcases,thisworkwillfocusmainlyonthe -directedcomponentofthemagnetic eld,whileexaminingonlyasmallsetofmodeledradially-directedmagneticeld components. 9

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CHAPTER2 OBSERVATIONS 2.1OverlappingPathGeometry Muchofthepastworkinthiseldhasinvolvedusingsignalsfromasingle transmitter-to-receiverpairtoperformionosphericdiagnostics.Thiscanbeproblematicwhenattemptingtodetermineauniquesolutionbecausevarying h 0 and simultaneouslyinanattempttomatchtheamplitudeandphaseofthereceivedsignalleavestheproblemunder-constrained.Thisworkhasaddressedthisproblemby focusingonapairoftransmittersthatshareagreatcirclepathtoasinglereceiver. ThiscongurationisshowninFigure2.1withthetransmittersshowninredandthe receivershowninblue. Figure2.1:Overlappingpathgeometry 2.2NavyTransmitters VLFwavesareofalowenoughfrequencythattheyareabletopenetrateintosea water.Forthisreason,theUSNavyhasbuiltseveralVLFtransmittersacrossthe 10

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continentthatareprimarilyusedforsubmarinecommunication.Figure2.1shows thelocationofthetwoNavytransmittersthatwereusedforVLFremotesensingin thiswork.TheNLKtransmitterislocatedinJimCreek,WA.2N,121.9W. Itisa250[kW]transmitterthatoperatescontinuouslyatafrequencyof24.8[kHz]. TheNMLtransmitterislocatedinLaMoure,ND.4N,98.3W.Itisa500[kW] transmitterthatoperatescontinuouslyatafrequencyof25.2[kHz]. 2.3VLFAntennaandReceiver TheantennaandreceiverusedforthisworkareoperatedbyGeorgiaTechand locatedinDelaware.3N,75.6W.ThisreceiversiteusesaversionoftheStanford designedAWESOMEreceiverworkinginconjunctionwithtwotriangularairloop antennasorientedorthogonallyinaneast/westandnorth/southdirection.Amore completediscussionofthisreceivercongurationispresentedin[2].Althoughthe receiverpicksupallfrequenciesintheVLFband,thedatausedinthisworkismixed downnarrowbandforthefrequenciesoftheNLKandNMLtransmitters,meaning thatonlytheamplitudeandphaseofthetransmitter'ssignalisrecorded.Therotation matrix 2 6 4 cos )]TJ/F19 11.9552 Tf 9.299 0 Td [(sin cos cos 3 7 5 .1 isusedtoorientthenorth-southchanneltowardtheNMLandNLKtransmitters. ThischangesthetwochannelsfromNSandEWchannelsto B and B radial channels. Figure2.2displaysamapshowingthisrotation.With =59 : 3447 ,thisyields 2 6 4 cos )]TJ/F19 11.9552 Tf 9.299 0 Td [(sin cos cos 3 7 5 2 6 4 Amp NS P hase NS Amp EW P hase EW 3 7 5 = 2 6 4 Amp P hase Amp radial P hase radial 3 7 5 : .2 11

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Figure2.2:Visualizationofrotationmatrix The B componentofthemagneticeldscorrespondstoverticalelectricelds whicharethedominanteldswithintheEIW.Theradialcomponentofthemagnetic eldisnon-dominantandcorrespondstothecomponentoftheelectriceldthatis horizontaltotheEarth'ssurface.Ingeneral,theamplitudeoftheradialcomponent ismuchlowerthantheamplitudeofthe component. 2.4LEPandEarly/FastPerturbationsonVLFSignals Asdiscussedabove,wheneitherLEPorEarly/Fasteventsoccur,theycanalter ionosphericelectrondensitiesandeectVLFpropagationintheEIW.Thesechanges cancauseariseorfallineithertheamplitudeorphaseofeitherthe -directed orradially-directedcomponentsoftheVLFsignals.Interestingly,anionospheric disturbancecanhavealargeeectonthesignalfromonetransmitter,whileleaving theothertransmitterssignalrelativelyunaected.Asanexampleofthisphenomena, Figure2.3displaysthenarrowbanddatafortheNLKandNMLtransmittersrecorded atDelawareonMay17 th ,2017. 12

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Figure2.3:NarrowbandobservationsfromMay17 th ,2017early/fastevent Inthiswork,theamplitudeorphaseaveragedoverthe20secondspreceding thelightningstrikewillbecalledthe ambient amplitudeorphase.Theamplitude orphaseinthemomentjustafterthelightingstrikewillbecalledthe dynamic amplitudeorphase.Observedchangesinamplitudeandphasearedenedas= Ambient )]TJ/F19 11.9552 Tf 11.665 0 Td [(Dynamic .Figure2.3showsthesedenitionsgraphically,andTable2.1 quantiesthemfortheMay17 th ,2017event. 13

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Figure2.4:Examplerepresentationoftherelationshipbetweenobservationsandthe terminologyusedtorefertothem Ambient,Dynamic and Table2.1:AmplitudeandphaseobservationsonMay17 th ,2017 Transmitter Amb Amp Dyn Amp Amp Amb Phase Dyn Phase Phase NLK 61 : 6 [ dBV ] 62 : 2 [ dBV ] 0 : 58 [ dBV ] 87 : 5 [ deg ] 86 : 1 [ deg ] -1 : 35 [ deg ] NML 68 : 7 [ dBV ] 62 : 7 [ dBV ] -5 : 99 [ dBV ] 31 : 1 [ deg ] -14 : 4 [ deg ] -45 : 5 [ deg ] NLK radial 59 : 7 [ dBV ] 60 : 3 [ dBV ] 0 : 59 [ dBV ] -23 : 5 [ deg ] -20 : 5 [ deg ] 3 : 05 [ deg ] NML radial 57 : 1 [ dBV ] 53 : 4 [ dBV ] -3 : 77 [ dBV ] 67 : 0 [ deg ] 45 : 6 [ deg ] -21 : 4 [ deg ] 14

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CHAPTER3 SETUP 3.1DynamicProles/DisturbedRadius Thebasicmodelsetupusedtoleveragetheoverlappingpathgeometryisas follows:Overtheportionofthepaththatshouldremainunaectedbythelightning strike,asingleionosphericproletakentobetheeectiveambientproleremains constant.Inthegeographicregionnearthelightningdisturbance,theionospheric prolesarevariedforallpossiblecombinationsof h 0 and intherangeof70[km] h 0 90[km],and0.40[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Inthiswork,theionospheric proleusedinthedisturbedregionwillbereferredtoasthedynamicproleand theeectiveambientproleusedfortherestofthepathwillbereferredtoasthe ambientprole.Figure3.1showsagraphicalrepresentationofthemodelsetupfor theMay17 th ,2017event. Figure3.1:ModelgeometryexamplefromMay17 th ,2017event 15

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3.2DeterminingAmbientIonosphericConditions Whenmodelinghowionosphericconditionsarealteredduetoalightninginduced disturbance,onemustconsiderwhattheconditionoftheionospherewasduringthe timeleadinguptothedisturbance.Formodelingpurposes,thisworkoperatesunder theassumptionthattherewasasingleat"ambientionosphereovertheentirepath fromNLKtoDelawarejustbeforethelightningevent.Whilethisismostlikelynot acompletelyaccurateassumptionbecausethenighttimeionosphericconditionshave beenshowntovaryregionallyovershorterdistances[6],ithasbeenshownthrough LWPCmodelingthataneective"atprolethatistheaverageofthesevariations canbeusedtodescribeionosphericconditionsacrossthepath[4]. Oneofthemajorchallengesforthisworkwasndingawaytoidentifywhatthe eectiveambientconditionwasleadingupthedisturbance.TheGeorgiaTechantenna iscalibrated,meaningthatthemeasurementsthataremadetherecanbeconverted directlytohorizontalmagneticuxinTeslaswhichcaneasilybeconvertedinto electriceldvaluesatthereceiver.Inordertounderstandwhattheexpectedelectric eldswouldbefordierentionosphericproles,theLWPCwasrunwithasingle ionosphericprolefromtransmittertoreceiverforeveryreasonablecombinationof h 0 and .ThiswasdoneforboththeNLKandNMLtransmitters.Then,usingthe observedamplitudedataforeachtransmitterandcomparingittotheLWPCexpected amplitude,anerrormatrixwascreatedusingtheleastsquaresmethodwhere Error ambient = NLM X NLK q Amp LWPC )]TJ/F19 11.9552 Tf 11.955 0 Td [(Amp observed 2 : .1 Asanexampleofhowthecalibratedamplitudesontheoverlappingpathcan beusedtopredicttheeectiveambientconditiononthepathfromtransmitterto receiver,Figure3.2isaplotofanambienterrormatrixcreatedusingNLKandNLM 16

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nighttimeamplitudedatathatwasrecordedduringaveminuteperiodleadingup toaMay17 th ,2017Early/Fastevent. Figure3.2:AmbienterrorexamplefromMay17 th ,2017event AnalysisofFigure3.2suggeststhattheambientconditionoftheionosphereat thattimehadareectionheightrangeof84.0[km] h 0 87.0[km]withthemost likelyheightat h 0 =86.5[km],andaprolesharpnessrangeof0.55[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.65[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]withthemostlikelysharpnessat =0.58[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Whilethistypeofanalysisofambientamplitudeshasprovenbenecialasaguidelinetodeterminearange ofeectiveambientionosphericconditions,itisbynomeansmeanttobetakenasa denitivedeterminationofaspecicambientconditionoverthepathofpropagation. 3.3GraphicalRepresentationofExpectedChanges Bysimulatingdynamicionosphericproleswith70[km] h 0 90[km]and 0.40[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]inthedisturbedregionandkeepingtrackof changesinamplitudeandphaseforeachtransmitter Amp NLK ; Phase NLK and Amp NML ; Phase NML intermsof h 0 and modeledinthedynamicregion,the 17

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LWPCsimulatedresultscanbegraphicallyrepresentedinaneasytoanalyzemanner. Figure3.3showsanexampleofthisrepresentationwherechangesinamplitudeand phasearerepresentedbycolorintensity. Figure3.3:Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofMay17 th event 3.4ErrorforSingleAmbientProle Errorforasingleambientprolewascalculatedusingaleastsquareserrormethod thatcomparestheobservedandmodeledchangesinamplitudeandphaseofthe signalsfromtheNLKandNMLtransmitterssothat Error individual = NLM X NLK q Amp LWPC P hase LWPC )]TJ/F19 11.9552 Tf 11.955 0 Td [(Amp obs: P hase obs: 2 : .2 18

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Figure3.4:ErrorobtainedfromasingleambientproleforMay17 th ,2017Event 3.5GlobalError Thesimulationwasthenrunforseveralpossibleambientconditionswithina reasonablerangeacceptednighttimeionosphericproles.Therangethatwaschosen was83.0[km] h 0 89.0[km]and0.40[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Globalerrorwas thencalculatedbysummingtheerrorfromindividualambientprolesimulations where Error global = h 0 =89 : 0 X h 0 =83 : 0 =0 : 90 X =0 : 40 Error individual ; .3 andthennormalizingbythenumberofambientprolesthatcontributedtotheglobal error.ThismethodquantiesnighttimeD-regionionosphericchangesfromlightning inducedperturbationsindependentlyofambientionosphericconditions. 19

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Figure3.5:GlobalerrorforMay17 th ,2017Event Itshouldbenotedthatnoteverysingleambientprolesimulatedproducesa validsolutionwithlowerror.Iftheminimumerrorforasingleambientproleis notbelowacertaineventdependentthreshold,itisignoredandnotconsideredin thedeterminationofglobalerror.Theareaintheupperright-handsideofFigure 3.5withzeroerrorisnotrepresentativeofthecombinationsof h 0 and that producedthelowestglobalerror.Itisanareainwhichnosingleambientprole errorcontributedtoglobalerrorcalculations. Thismethodofdeterminingionosphericchangesinthedisturbedregionthrough theuseofglobalerrorcalculationscomesfromLWPCsimulationofmultipleambient ionosphericproles,itisamorerobustmodelthatisnotdependentonprevious knowledgeof,orassumptionsabout,theambientconditionoftheionosphere. 20

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CHAPTER4 CASESTUDIES 4.1June13 th ,2016 TherstcasethatwillbeexaminedisanEarly/Fasteventthatoccurredduring thenightofJune13th,2016at06:41:27.818[UT]nearMinneapolis,MN.Thislocation isontheoverlappingpathapproximately2215[km]fromNLKand432[km]from NML.Thelightningthatcausedthiseventwaslargerthananyoftheothersexamined inthisworkwithapeakcurrentof385[kA]reportedfromtheNationalLightning DetectionNetworkNLDN.Figure4.1showsthelocationofthestrikeinrelationto NLKandNML.Acirclewitha250[km]radiuswasdrawnaroundthestrikelocation todenotetheregionexpectedtobeaectedbythelightningstrike. Figure4.1:LocationofJune13 th ,2016early/fast385[kA]event TheeectsthatthestrikehadonthesignalsfromNLKandNLMwerequite interestingbecausetheeventcausedalargeincreaseinbothamplitudeandphaseof thesignalfromNMLwhileleavingthesignalfromNLKrelativelyunaected.Thisis 21

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similartothepreviousevent,buttheVLFperturbationscausedbythisstrikewere moredramatic.Figure4.2showsthenarrowbanddataforeachtransmitterrecorded attheDelawarereceiver.Throughananalysisofthenarrowbanddata,Table4.1 quantiestheambientanddynamicconditions,aswellasthechangesinamplitude andphasefortheJune13 th ,2016event. Figure4.2:DelawarenarrowbanddataforNLKandNMLonJune13 th ,2016 Table4.1:AmplitudeandphaseobservationsonJune13 th ,2016 Tx Amb Amp Dyn Amp Amp Amb Phase Dyn Phase Phase NLK 66 : 0 [ dBV ] 65 : 0 [ dBV ] -0 : 96 [ dBV ] -27 : 4 [ deg ] -20 : 2 [ deg ] 7 : 22 [ deg ] NML 66 : 5 [ dBV ] 72 : 4 [ dBV ] 5 : 90 [ dBV ] -119 : 7 [ deg ] -84 : 8 [ deg ] 34 : 8 [ deg ] NLK rad 42 : 2 [ dBV ] 41 : 4 [ dBV ] -0 : 75 [ dBV ] 21 : 7 [ deg ] 21 : 6 [ deg ] -0 : 11 [ deg ] NML rad 55 : 8 [ dBV ] 45 : 7 [ dBV ] -10 : 1 [ dBV ] -143 : 0 [ deg ] -69 : 5 [ deg ] 73 : 6 [ deg ] 22

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Throughanalysisofthe -directedcomponentofobservedambientamplitudes, theexpectedambientconditionoftheionospherewasdeterminedtobewithinthe reectionheightrangeof83.0[km] h 0 89.0[km]andaprolesharpnessrangeof 0.45[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].TheambienterrorplotinFigure4.3showstherange ofexpectedambientproles. Figure4.3:AmbienterrorforJune13 th ,2016early/fastevent Havingdeterminedarangefortheexpectedambientconditionoftheionosphere, theLWPCsimulationwasrunforambientionosphericproleswithvaluerangesof 83.0[km] h 0 89.0[km]and0.40[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Thesimulationwas thenrunusingtwodierentvaluesforthedisturbedradius[km]and500[km]. Figure4.4showsthemodelsetupforthe250[km]radius. 23

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Figure4.4:ModelsetupforJune13 th ,2016early/fastevent 4.1.1LWPCAnalysiswith250[km]DisturbedRadius Theanalysisofthiseventconsistsof375separatesimulationsusingdierent nighttimeambientproleswithinthedeterminedrange.Eachofthese375simulations usedasingleeectiveambientproleandconsistedof1066individualLWPCrunsfor boththeNLKandNMLtransmitters.TheseindividualLWPCrunsaccountforthe possibleionosphericconditionsinthedisturbedregiononthepathofpropagation. Ofthe375singleambientprolesimulationruns,81ofthemproducederrorlevels thatwerebelowthethresholdandwereincludedintheglobalerrorforthisevent thatisshowninFigure4.5. 24

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Figure4.5:GlobalerrorforJune13 th ,2016event TheminimumglobalerroroccurredwhentheLWPCmodeledchangesof h 0 and inthedisturbedregionwere h 0 =-5.0[km]and =-0.12[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].However, theabsoluteminimumfromFigure4.5maynotbeasimportantastheoveralltrend thatcanbeobservedfromexaminingtheglobalerrorplot.Thisplotshowsthat, regardlessoftheambientconditionoftheionosphereduringthetimeleadingupto thelightningstrike,therewasmostlikelya4.5[km]-7.0[km]changeinthereection heightoftheionosphereduetothisearly/fastevent. Next,thesingleambientprolethatmostaccuratelymodeledtheobserved changesinamplitudeandphase,i.e.producedthelowestamountoferror,willbe examined.Minimumerrorforasingleambientproleoccurredwhentheambient proleusedintheLWPCmodelwas h 0 =88.5[km]and =0.88[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Thesingle ambienterrorplotisshowninFigure4.6. 25

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Figure4.6:June13 th singleambientprole h 0 =88.5[km]and =0.88[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]error Fromtheanalysisoftheerrorforthisambientprole,itisseenthattheaccuracy oftheLWPCwhenmodelingthe -directedcomponentofthemagneticeldisnot highlydependenton .Figure4.6showsthat,iftheeectiveambientconditionofthe ionospherewas h 0 =88.5[km]and =0.88[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ],thenthechangeinionospheric reectionheightwasbetween3.5[km]-5[km]. Thistime,itisimportanttonotethatabsoluteminimumerroroccurredwhen h 0 =-4.5[km]and =0[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ],becausethispointrepresentsthebesttLWPC modeledchangesinamplitudeandphaseofboththeNLKandNMLtransmittersover allvaluesof h 0 and inthedisturbedregion.Themodeledchangesinamplitude andphaseareshowngraphicallyinFigure4.7withanannotationat h 0 =-4.5[km] tohighlightthebestLWPCmodeledresults. 26

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Figure4.7:Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofJune13 th eventwith250[km]disturbedradius Forthiscase,afullexaminationoftheLWPCmodeledradialcomponentofthe magneticeldwasconducted,meaningthatradialsimulationwasrunforalarge numberofambientprolesinanattempttocalculateglobalerrorinthesameway thatitwasdoneforthe -directedcomponent.Interestingly,whilethe -directed componentofthemagneticeldismainlydependenton h 0 ,theradialcomponent ofthemagneticeldappearstobemainlydependenton .Thisispromisingand suggeststhatthedierentpolarizationsofthemagneticeldcouldbeusedtodiagnose h 0 and separately.Figure4.8showsglobalerroroftheradialcomponent.Analysis oftheglobalerrorshowsthatthe ionosphericresponsetothiseventwasinthe rangeof0[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]to0.05[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]. 27

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Figure4.8:RadialglobalerrorforJune13 th ,2016event Figure4.9showsthemodeledchangesinamplitudeandphaseoftheradialcomponentusingthesamesingleambientproleproducingthelowesterrorfromthe -directedanalysis h 0 =88.5[km], =0.88[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]. Figure4.9:Changesinradialamplitudeandphaseasafunctionof h 0 and from LWPCsimulationofJune13 th eventwith250[km]disturbedradius 28

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Figure4.9showsthattheLWPCdoesnotpredictlargechangesintheradial amplitudesofeithertransmitters'signal.Itdoeshoweverpredictrapiductuations inphasewithchangesinreectionheightforagivenvalueof .Thatvalueof does appeartodeterminehowrapidlythatchangeoccursaswellaswhetherthephase changeispositiveornegative.Thisoverallphasevolatilitywassomewhatexpected becauseitwasobservedinthephaseoftheNLKsignalrecordedattheDelaware receiversite.Figure4.10showstheradialerrorforasingleambientprolebasedon theLWPCmodeledchangesinradialamplitudeandphase. Figure4.10:RadialerrorforsingleambientproleforJune13 th ,2016event AnalysisofFigure4.10showsthatanalysisoftheradialcomponentsuggeststhat the ionosphericresponsetothiseventwasintherangeof 0 : 02[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ],whichis inlinewiththeglobalerroranalysisfortheradialcomponent.Itisalsoinagreement withwherethelowesterroroccurredwhenanalyzingthe -directedcomponentofthis singleambientprole,whichwasat =0[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Table4.2presentsasummary ofthesimulationresultsfromtheJune13 th ,2017early/fasteventincomparisonto therecordedobservations. 29

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Table4.2:ModelandobservationalcomparisonofsforJune13 th ,2016early/fast eventwith250[km]disturbedradius LeastErrorAmbient: h 0 =88.5[km]and =0.88[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] Observed Modeled Tx Amp Phase Amp Phase NLK -0 : 96 [ dBV ] 7 : 22 [ deg ] -0 : 23 [ dBV ] 13 : 8 [ deg ] NML 5 : 90 [ dBV ] 34 : 8 [ deg ] -2 : 66 [ dBV ] 35 : 1 [ deg ] NLK radial -0 : 75 [ dBV ] -0 : 11 [ deg ] 0 : 72 [ dBV ] 13 : 1 [ deg ] NML radial -10 : 1 [ dBV ] 73 : 6 [ deg ] 8 : 11 [ dBV ] 22 : 19 [ deg ] 4.1.2EectofDisturbanceRegionSize Thissectionwillexaminetheeectsofmodelingthedisturbedregionwitha radius500[km].Figure4.11showsthemodelsetupforthisconguration. Figure4.11:ModelsetupforJune13 th ,2016early/fastevent 30

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Usingthemodelshownabove,theLWPCsimulationwasagainrunfor375ambientprolesbetween83.0[km] h 0 89.0[km]and0.40[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] 0.90[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]. Eachambientsimulationused1066dynamicprolesinthedisturbedregion.Ofthe 375ambientsimulationsthatwererun,95ofthemhadlowenougherrortocontribute totheglobalerrorcalculations.Figure4.12showstheglobalerrorfortheJune13 th , 2016eventusingadisturbedradiusof500[km]. Figure4.12:GlobalerrorforJune13 th ,2016event AnalysisofFigure4.12showsthat,witha500[km]disturbedregion,theionosphericresponsewasadecreaseinreectionheightintherangeof-5[km]and-8[km]. Thesingleambientprolewhichproducedthelowestoverallerrorforthissimulation was h 0 =85[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Thisambientproleiswithintherange ofexpectedambientprolesbasedonthepreviousanalysisofambientamplitudes. Figure4.13showstheerrorplotforthisambientprole. 31

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Figure4.13:June13 th singleambientprole h 0 =85[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]error AnalysisofFigure4.13showsthattheminimumerroroccurred h 0 =-6.4[km] and =0.16[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ],whichiswithintherangeof h 0 foundusingtheglobalerror. Figure4.14displaysthemodeledchangesinamplitudeandphaseasfunctionsof h 0 and withtheleasterrorpointannotatedtoshowthebesttmodel. Figure4.14:Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofJune13 th eventwith500[km]disturbedradius 32

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Forthiscasetheradialcomponentofthemagneticeldwasonlysimulatedfor theambientprolethatproducedthelowesterror,soglobalerrordeterminationwill notbepresented.Radialerrorforambientprole h 0 =85[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] isshowninFigure4.15.Again,theradialcomponentpointstoa intherange of0.15[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] 0.35[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Table4.3showsasummaryofthesimulation resultsfromtheJune13 th eventwithalargerdisturbedregion,andcomparesthem totherecordedobservations. Figure4.15:RadialerrorforsingleambientproleforJune13 th ,2016event 4.1.3June13 th Conclusions OverallanalysisoftheLWPCmodeled -directedcomponentofthemagnetic eldfromtheJune13 th ,2016eventshowsachangein h 0 of4.5[km]to7.5[km] inthedynamicregion.AnalysisoftheLWPCmodeledradialcomponentofthe magneticeldpredictedonlyasmallchangein inthedynamicregion.Acomparison ofglobalerrorwhenmodeledwith250[km]and500[km]radiidisturbedregions suggestsaslightlysmallerchangeinreectionheightwithasmallerdisturbedregion. Additionally,withalargerdisturbedregion,theoverlappingpathmodelproduced muchlowersingleambientproleerrorwithlowerreectionheightambientproles. 33

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Table4.3:ModelandobservationalcomparisonofsforJune13 th ,2016early/fast eventwith500[km]disturbedradius LeastErrorAmbient: h 0 =85.0[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] Observed Modeled Tx Amp Phase Amp Phase NLK -0 : 96 [ dBV ] 7 : 22 [ deg ] 0 : 72 [ dBV ] 13 : 1 [ deg ] NML 5 : 90 [ dBV ] 34 : 8 [ deg ] 8 : 11 [ dBV ] 22 : 19 [ deg ] NLK radial -0 : 75 [ dBV ] -0 : 11 [ deg ] 0 : 72 [ dBV ] 13 : 1 [ deg ] NML radial -10 : 1 [ dBV ] 73 : 6 [ deg ] 8 : 11 [ dBV ] 22 : 19 [ deg ] 4.2April26 th ,2016 Inordertotestthecapabilitiesandlimitationsoftheoverlappingpathmodel, twoLEPeventsthatoccurredonApril26 th ,2016causingonlyminorperturbations intheamplitudeandphaseoftheVLFsignalsweremodeledusingtheLWPC.These eventswerechosenbecausetheytookplacewithinapproximately50minutesofeach other,anditwashypothesizedthattheambientconditionoftheionospherewould nothavechangedsignicantlywithinthatamountoftime. 4.2.1Event#1:08:03:55[UT] FromtheNLDNlightningstrikedatabase,thislightningstrikeoccurredapproximately600[km]duesouthoftheNMLtransmitter.7M,97.4W.Aspreviously mentioned,LEPionosphericdisturbancesarenotlocalizedtotheregionnearthe lightningstrike,andthelocationofthelossconedependsonthealtitudeoftheinteractionregion.Inthiscase,thelocationofthelossconewasdeterminedtobealmost directlyontopoftheNMLtransmitter.Figure4.16showsthemodelsetupforthis 34

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eventincludingthelocationofthelightningstrikeandthedisturbedregionforthe LEPevent. Figure4.16:ModelsetupforApril26 th ,2016LEPevent Figure4.17displaystheobservedchangesinamplitudeandphaseofthesignals transmittedfromNLKandNML.Table4.4quantiestheobservedambientand dynamicamplitudesandphases,aswellasidentieslightninginducedchangesinthe transmittedsignalthatoccurredduringthisevent. Figure4.17:DelawarenarrowbanddataforNLKandNMLonApril26 th ,2016 35

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Table4.4:AmplitudeandphaseobservationsonApril26 th ,2016 Tx Amb Amp Dyn Amp Amp Amb Phase Dyn Phase Phase NLK 67 : 3 [ dBV ] 69 : 4 [ dBV ] 2 : 04 [ dBV ] 158 : 7 [ deg ] 165 : 7 [ deg ] 7 : 01 [ deg ] NML 70 : 7 [ dBV ] 72 : 6 [ dBV ] 1 : 90 [ dBV ] -90 : 0 [ deg ] -91 : 1 [ deg ] -1 : 10 [ deg ] NLK rad 41 : 8 [ dBV ] 45 : 6 [ dBV ] 3 : 82 [ dBV ] 132 : 9 [ deg ] 151 : 7 [ deg ] 18 : 8 [ deg ] NML rad 47 : 5 [ dBV ] 53 : 5 [ dBV ] 6 : 00 [ dBV ] -151 : 8 [ deg ] -148 : 1 [ deg ] 3 : 82 [ deg ] Usingthesamerangesforambientanddynamicionosphericprolesthatwas usedwhenmodelingtheJune13 th ,2016event,theLWPCsimulationwasrepeated forEvent#1onApril26 th ,2016.Ofthe375ambientsimulationsthatwererun,67of themhadlowenougherrortocontributemeaningfullytotheglobalerrorcalculations. Figure4.18showstheglobalerrorforEvent#1onApril26 th ,2016usingadisturbed radiusof250[km]. Figure4.18:GlobalerrorforApril26 th ,2016LEPEvent#1 36

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Analysisofgure4.18showsaratherlargerange h 0 2.5[km]ofpossible reectionheightsinthedynamicregionthatproducelowerror.Thissuggeststhatthe changeinreectionheightwasmostlikelyverysmall,whichisexpected,considering thattheobservedVLFperturbationswerealsosmall.Thesingleambientprole whichproducedthelowestoverallerrorforthissimulationwas h 0 =84.5[km]and =0.52[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Figure4.19showstheerrorplotforthisambientprole. Figure4.19:SingleambientproleerrorforApril26 th ,2016LEPEvent#1 AnalysisofFigure4.19showsthattheminimumerroroccurred h 0 =+0.5 [km]and =0.38[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Thisresult,alongwithothersingleambientprolesthat contributedtoglobalerrorcalculations,isproblematicbecauseitsuggestsanincrease ratherthanadecreaseinreectionheight.Thisisnotwhatistypicallyexpectedfrom anLEPeventandfurtheranalysisisneededinordertodeterminewhysomesingle ambientprolespredictthispositive h 0 .Figure4.20displaysthemodeledchangesin amplitudeandphaseasfunctionsof h 0 and withtheleasterrorpointannotated toshowthedynamicconditionthatbestthechangesinamplitudeandphaseobserved duringthisLEPevent. 37

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Figure4.20:Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofApril26 th LEPEvent#1 Forthiscase,theradialcomponentwasonlyexaminedfortheambientprole thatproducedthelowesterrorwhenmodelingthe -directedcomponent.Figure4.21 showsaplotoftheradialerrorthatsuggeststhechangein wasbetween0.15[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] and0.25[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ].Table4.5summarizestheLWPCsimulationresultsforthisevent. Figure4.21:SingleambientproleradialerrorforEvent#1onApril26 th ,2016 38

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Table4.5:ModelandobservationalcomparisonofsforApril26 th ,2016Event#1 LeastErrorAmbient: h 0 =85.0[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] Observed Modeled Tx Amp Phase Amp Phase NLK 2 : 04 [ dBV ] 7 : 01 [ deg ] 1 : 22 [ dBV ] -10 : 3 [ deg ] NML 1 : 90 [ dBV ] -1 : 10 [ deg ] -2 : 73 [ dBV ] 17 : 1 [ deg ] NLK radial 3 : 82 [ dBV ] 18 : 8 [ deg ] -0 : 30 [ dBV ] 18 : 4 [ deg ] NML radial 6 : 00 [ dBV ] 3 : 82 [ deg ] -0 : 40 [ dBV ] 2 : 42 [ deg ] 4.2.2Event#2:08:50:44[UT] ThesecondlightningstrikethatoccurredonApril26 th happenedjustnorthwest ofKansasCity,KS.3N,94.77W.Again,thisisapproximately600[km]southof theoverlappingpathofpropagation.Inthiscase,thelocationofthelossconewas determinedtobeabout250[km]eastoftheNMLtransmitter.Figure4.22showsthe modelsetupforthisevent. Figure4.22:ModelsetupforApril26 th ,2016LEPEvent#2 39

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Figure4.23displaystheobservedchangesinamplitudeandphasefromtheNLK andNMLtransmitters.Table4.6quantiestheambient,dynamic,andchangeinthe amplitudesandphasesoftheVLFsignalsobservedduringthisevent. Figure4.23:DelawarenarrowbanddataonApril26 th ,2016forEvent#2 Table4.6:AmplitudeandphaseobservationsonApril26 th ,2016 Tx Amb Amp Dyn Amp Amp Amb Phase Dyn Phase Phase NLK 65 : 8 [ dBV ] 67 : 4 [ dBV ] 1 : 60 [ dBV ] 153 : 8 [ deg ] 156 : 7 [ deg ] 2 : 87 [ deg ] NML 70 : 8 [ dBV ] 71 : 9 [ dBV ] 1 : 17 [ dBV ] -94 : 3 [ deg ] -99 : 8 [ deg ] -5 : 50 [ deg ] NLK rad 21 : 2 [ dBV ] 38 : 8 [ dBV ] 17 : 6 [ dBV ] { { { NML rad 53 : 3 [ dBV ] 54 : 6 [ dBV ] 1 : 28 [ dBV ] 149 : 2 [ deg ] 149 : 1 [ deg ] -0 : 16 [ deg ] Again,usingthesamerangeofambientanddynamicionosphericproles,the LWPCsimulationwasrunforEvent#2.Ofthe375ambientsimulationsthatwere run,350ofthemhadlowenougherrortocontributemeaningfullytotheglobalerror calculations.Figure4.24showstheglobalerrorforEvent#2onApril26 th ,2016. 40

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Figure4.24:GlobalerrorforApril26 th ,2016LEPEvent#2 AnalysisofFigure4.24showsthat,witha250[km]disturbedregion,theionosphericresponsewasadecreaseinreectionheightintherangeof0[km]and-2.5 [km].Figure4.25showstheerrorplotforthesingleambientprolewhichproduced thelowestoverallerror h 0 =84.0[km]and =0.80[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]. Figure4.25:SingleambientproleerrorforApril26 th ,2016LEPEvent#2 41

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AnalysisofFigure4.25showsthattheminimumerroroccurred h 0 =-1.5[km] and =-0.2[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Figure4.26displaysthemodeledchangesinamplitudeand phaseasfunctionsof h 0 and withtheleasterrorpointannotatedtohighlight thebesttLWPCmodeledchangesinamplitudeandphase. Figure4.26:Modeledchangesinamplitudeandphaseasafunctionof h 0 and fromLWPCsimulationofApril26 th LEPEvent#2 Afullexaminationoftheradialcomponentwasconductedforthiscase.Through globalerroranalysisoftheradialcomponent,itwasdeterminedthattheLWPC expectedchangein wasbetween0[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]and0.05[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ].Theradialglobalerror isshowninFigure4.27,andTable4.7displaysasummaryoftheLWPCsimulated resultsincomparisontorecordedobservationforthisevent. 42

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Figure4.27:RadialglobalerrorforApril26 th ,2016Event#2 Table4.7:ModelandobservationalcomparisonofsforApril26 th ,2016Event#2 LeastErrorAmbient: h 0 =85.0[km]and =0.44[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] Observed Modeled Tx Amp Phase Amp Phase NLK 1 : 60 [ dBV ] 2 : 87 [ deg ] -0 : 98 [ dBV ] 11 : 6 [ deg ] NML 1 : 17 [ dBV ] -5 : 50 [ deg ] 1 : 42 [ dBV ] -1 : 75 [ deg ] NLK radial 17 : 6 [ dBV ] { -0 : 08 [ dBV ] -38 : 0 [ deg ] NML radial 1 : 28 [ dBV ] -0 : 16 [ deg ] -1 : 76 [ dBV ] -240 : 2 [ deg ] 4.2.3April26 th Conclusions TheLWPCoverlappingpropagationpathmodelperformedreasonablywellfor thissetofevents,inthattheobservedchangesinamplitudeandphasefromthe NLKandNMLtransmitterswassmall,andsoweretheLWPCpredictedchangesin h 0 and .Theideathatthetwoback-to-backeventswouldhelpinidentifyingthe 43

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eectiveambientionosphericconditionsleadinguptotheeventdidnotturnoutto beparticularlybenecialbecausethelowesterrorsingleambientprolesendedup havingdierentvaluesof .Interestingly,LWPCanalysisofevent#1didpredict anincreasein whichthenshowedupinleasterrorsingleproleambientofevent #2.WhilethisisaninterestingoccurrenceintheLWPCmodel,itmaybepurely coincidentalbecauseonewouldexpectthedynamicconditionoftheionospheredue toalightningstriketorelaxbacktotheeectiveambientconditioninfarlessthan the50minutestimethatelapsedbetweentheseevents.Furtheranalysisofthese eventscanstillbedonebysimulatingdierentsizesforthedisturbedregions.Also, afurtherexaminationofwhatambientconditionsgiverisetoanLWPCexpected increasein h 0 ,andwhetherthesesingleambientprolesshouldcontributetoglobal errorcalculations,shouldbeconducted. 44

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CHAPTER5 SUMMARYANDCONCLUSIONS 5.1Summary Threelightninginducedionosphericdisturbancesthatoccurredduring2016were examinedusingtheLWPC.Thersteventthatwasexaminedwasahighpeak-current early/fasteventthatcausedlargeperturbationsintheamplitudeandphaseofthe VLFsignalspropagatingintheEIW.ThesecondtwoeventswereLEPeventsthat causedonlyminorperturbationstothesesignals.ThroughLWPCmodelingusinga largenumberofpossibleambientionosphericproles,conclusionsaboutchangesin electrondensitiesinthedynamicregionduetothelightningstrikehavebeenreached. TheresultsoftheLWPCmodelingaredisplayedinTable5.1. Table5.1:LWPCModeledChangesin h 0 and LWPCModeled h 0 and forJune13 th ,2016Early/FastEvent 250[km]DisturbedRadius 500[km]DisturbedRadius Single Global Single Global h 0 -4.5[km] -5.0[km] -6.4[km] -5.6[km] 0[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] -0.12[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] +0.16[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] +0.2[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] LWPCModeled h 0 and forApril26 th ,2016LEPEvents Event#1 Event#2 Single Global Single Global h 0 +0.5[km] 0[km] -1.5[km] -1.0[km] +0.38[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] +0.20[km )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ] -0.20[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] +0.06[km )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ] 45

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5.2Conclusions Thisprojecthaspresentedanovelwaytoquantifylightninginducedchangesin ionosphericconditionsbyutilizinguniquegeometrytoaddadditionalconstraintsto apreviouslyunder-constrainedproblem.Althoughtheeectiveambientconditionof theionosphereaddedanadditionaldegreeoffreedomthatprovedtobeanincredibly challengingproblemtoaddress,thisworkhasdevelopedatechniquethatdetermines changesin h 0 and independentlyofambientionosphericconditions.Morework canbedonetofurtherexaminehowvaryingthesizeofthedisturbedregionaects theexpected h 0 and changesinthedynamicregion,aswellashowthesizeofthe dynamicregiondetermineswhichsingleambientprolesgenerateerrorlowenough tobeconsideredinglobalerrorcalculations.Itwouldbeofgreatinteresttothe authortodetermineeectiveambientconditionsempiricallybydeployingadditional VLFreceiversalongtheoverlappingpathofpropagation.Furtherworkcanalso bedonetosimulatebothearly/fastandLEPeventswithhigherresolutionofboth ambientanddynamicprolesinordertodetermineglobalerrorwithalargerdata set.Validatingtheresultsofthisresearchusingothersimulationmethodssuchas theFiniteDierenceTimeDomainFDTDhasbeenproposedandiscurrentlyin progress.Thisworkhasshownthat,byusingoverlappingpathsofVLFpropagation toperformVLFremotesensingwithLWPCmodeling,amoredenitiveconclusion aboutchangesin h 0 and causedbylightninginducedperturbationshasbeenreached. 46

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REFERENCES [1]K.G.Budden.Theinuenceoftheearth'smagneticeldonradiopropagationby wave-guidemodes. ProceedingsoftheRoyalSocietyofLondonA:Mathematical, PhysicalandEngineeringSciences ,265:538{553,1962. [2]M.B.Cohen,U.S.Inan,andE.W.Paschal.Sensitivebroadbandelf/vlfradio receptionwiththeawesomeinstrument. IEEETransactionsonGeoscienceand RemoteSensing ,48:3{17,Jan2010. [3]VernonCooray. Earth'sAtmosphereandItsElectricalCharacteristics ,pages59{ 70.SpringerNetherlands,Dordrecht,2015. [4]S.A.Cummer,U.S.Inan,andT.F.Bell.Ionosphericdregionremotesensing usingvlfradioatmospherics. RadioScience ,33:1781{1792,1998. [5]M.Gokowski,N.C.Gross,R.C.Moore,B.R.T.Cotts,andM.Mitchell.Observationoflocalandconjugateionosphericperturbationsfromindividualoceanic lightningashes. GeophysicalResearchLetters ,41:273{279,2014. [6]FengHanandStevenA.Cummer.Midlatitudenighttimedregionionosphere variabilityonhourlytomonthlytimescales. JournalofGeophysicalResearch: SpacePhysics ,115A9,2010.A09323. [7]J.P.Hauser,W.E.Garner,andF.J.Rhoads.Eectivegroundconductivitymap ofcanadaandgreenlandwithrevisionsfrompropagationdata. NavalResearch LaboratoryReport6893 ,1969. [8]R.A.PappertandJ.A.Ferguson.Vlf/lfmodeconversionmodelcalculations forairtoairtransmissionsintheearth-ionospherewaveguide. RadioScience , 21:551{558,July1986. [9]J.R.WaitandK.P.Spies.Characteristicsoftheearth-ionospherewaveguidefor vlfradiowaves. NationalBureauofStandards ,TechnicalNote,1964. 47