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A Computer Model of the Changes in Electric Field within a Thundercloud
Within a thunderstorm, there are rapid changes in the electric field taking place. In 1993, Dr. Ewen Thomson of
the Department of Electrical and Computer Engineering at the University of Florida measured derivatives of
the electric field within thunderstorms using five flat plate antennas he positioned at the Kennedy Space Center.
Dr. William Hager of the Department of Mathematics at the University of Florida is conducting research on
how changes in the electric field during a thunderstorm can be used to compute the distribution of electric
charges throughout the thundercloud. During the summer of 2002, computer modeling software was developed
to penetrate, organize, and plot the electric field data collected at the Kennedy Space Center. The software allows
a user to specify a particular time slice of the thunderstorm for plotting or retrieval of electric field data.
Electric field data was recorded for a thunderstorm at the Kennedy Space Center (KSC) which occurred on days
251 and 252 of 1993. The recorded data was the derivative of the vertical electric field measured by five flat
plate antennas positioned around KSC. Measurements made by the antennas were kept as records on five
separate channels, where each channel corresponds to one of the antennas. This measurement system
was developed by Dr. Ewen Thomson of the Department of Electrical and Computer Engineering at the University
of Florida . The data was grouped by lightning flashes and lightning events into binary files consisting of 8-
bit unsigned integers. A typical lightning flash is comprised of a series of strokes, where in each stroke charge
flows along a lighting channel connecting the earth and the cloud. Since data was being recorded at such a high
rate, it was not possible to store all of the electric field data for a flash. Instead, a series of 4,096 byte
records, defined to be a lightning event, was recorded with up to 27 events recorded for any particular flash. Each
of these events contains data for a portion of a stroke within a flash. Since electric field records are made every
50 nanoseconds, the length of a recorded lightning event is 204.8 microseconds (4,096 bytes * 50
nanoseconds/byte). Whenever electric field activity triggers any of the flat plate antennas, data is
recorded simultaneously on all five channels .
There were some flash records which were clearly corrupted. These corrupted portions of the file were first
identified and then ignored when assessing the data. In the interest of verifying the start time of each flash, a
check was administered to see that increasing flash numbers had chronologically increasing start times. It
was verified that all flash start times increased with increasing flash number.
In order to quickly and easily reference flash times and data locations within the original electric field files, a
directory text file was created. The directory file was organized by flash number, where flashes were
numbered sequentially throughout each day then reset for the beginning of the next day. One line was dedicated
to information about each flash. Each directory line entry consists of the following flash specific information: year
(Y), day (D), hour (H), minute (M), seconds (S), microseconds (uS), flash number (FN), data file (DF), location
in data file (bytes from start of file) (L), and number of recorded events (NE). A sample of the directory file is
shown in Figure 1.
Y D H M S uS FN DF L NE
1993 251 1 14 30 419932 1 P9325141.251 0 23
1993 251 1 14 52 194002 2 P9325141.251 473088 12
1993 251 1 14 59 740135 3 P9325141.251 720896 2
1993 251 1 15 11 748001 4 P9325141.251 763904 1
1993 251 1 15 14 792610 5 P9325141.251 786432 4
Figure 1. Sample Lines from the Directory File
The directory file contains the start time of each flash, but not the start times of the individual events within
each flash. Time data files were created to store the time in microseconds elapsed since the beginning of the flash
for every event. There is a separate time data file for each day of the thunderstorm. In the interest of
verifying increasing start times of events within a flash, a test was administered on the time data files. It
was determined that there were many instances where the recorded event start times were not strictly
increasing and where events appeared to overlap each other. This phenomena was thought to be related
to inaccuracies in the measuring and recording of KSC time. To correct the errors, each event start time found to
be in error was advanced by 205 microseconds from the event start time preceding the error. This decision
was based on the fact that events are by definition 204.8 microseconds in length. With this correction, all event
start times became non-overlapping and strictly increasing. The worst case error that was observed occurred
when the seventh event of a flash was recorded as occurring 22 microseconds before the first event of the
flash. Since the seventh event was preceded by six events, each of length 204.8 microseconds, the seventh
event must have occurred at least 1228.8 microseconds (204.8 microseconds/event * 6 events) after the first
event instead of 22 microseconds before the first event. The error in time for the seventh event is at least
1,250 microseconds. Hence, although time is recorded in microseconds, the time error is on the order of milliseconds.
In order to quickly and easily access electric field records, the electric field data files containing measurements
made by the flat plate antennas were reformatted. Each reformatted file contains the information collected on
a single channel for a single day. The reformatted files contain strictly sequential electric field data with
no extraneous information between flashes. The data is stored in unsigned binary format so that the range of each
8-bit record is between 0 and 255. The actual electric field derivatives, however, can be both positive and
negative [2, 3, 5]. The zero position is found by looking for long periods of inactivity in the electric field
derivatives. The software offsets each channel by finding the zero position and shifting the unsigned data.
Between the three types of input data files (directory file, time data files, and electric field data files) all of
the necessary information is readily available. The directory file provides flash information accessible by
flash number. The time data files provide event start times relative to the onset of each flash. The electric field
data files provide the actual records of the derivatives of electric field organized sequentially by flash number.
A graphical representation of the file structure is shown in Figure 2.
Day 1 Day 2
5 Electric Field Data Files 5 Electric Field Data Files
1 Time Data File 1 Time Data File
Figure 2. Graphical Representation of the File Structure
In order to plot the electric field data efficiently with a professional appearance, a scientific data plotting library
was needed. The final choice was a freely distributed Linux scientific data plotting software package called
DISLIN version 7.6. The DISLIN software was chosen because of its extensive plotting libraries, informative
manual, and convenience of having built in graphical user interface libraries which interact nicely with the
plotting libraries. The electric field plotting software was developed in the C programming language with
DISLIN libraries on a Red Hat Linux version 7.3 platform.
Inputs to the software must allow the user to specify a precise portion of the thunderstorm. The final user menu
that accomplishes this task can be seen in Figure 1. For the menu input in Figure 3, the five channel plots
would begin plotting at flash 15 event 1 record 0 and end at flash 18 event 4 record 4095. The menu can also
be used to zoom in on plotted data by defining the range for the derivative of electric field data. The initial range of
-130 to 130 encompasses all possible data values once the unsigned electric field records have been offset.
Figure 3. Graphical User Menu
In locating the data requested in the user menu, the first step is to confirm that the user input corresponds to
data that actually exists in the electric field record files. This verification is performed by referencing the directory
file and ensuring that the requested flash numbers exist on the requested day, the requested event numbers exist
for the requested flashes, the requested record numbers range between 0 and 4095, and that the ending point
is chronologically later than the starting point. Once the user menu request is validated, data is fetched from the
time data files and electric field data files. The location of the requested data is determined by the number of
prior events as recorded in the directory file.
After the requested time and electric field data have been located, the appropriate information is passed to DISLIN
to create plots of the derivative of the electric field with respect to time on each of the five channels. The axes
are defined with change in electric field running vertically and time running horizontally. The range of the change
in electric field axis is defined in the user menu, with the default range being -130 to 130. The range of the time
axis is chosen by the program based on the data requested from the user menu. A title line above the plot
displays the start time of the first flash in the plot. A plot of flash 65 from day 251 showing events two through
five on channel two is shown in Figure 4. According to the time axis, event two begins 379 microseconds after
the flash began. There are clearly four sections of the plot. The first section (379 microseconds through
584) represents event two of flash 65, the second section represents event three, the third section represents
event four, and the fourth section represents event five. The plot also shows white space between the events
to indicate the time elapsed from the flat plate antennas ending the record of an event until an antenna was
J Graph Eriir Slrm
Seiecl the day
Record Start (0 - 4as) f-
Fish End F -
Evnt End F |
R iord End 1| - 40S)
Sed range for change In E-eld
Low (4ngegiw or zero)
High (posilOv or zero) I g
triggered to start the next event.
year day h m a us
1M93 251 1 31 06 499198
-L30.0 T 1
=S9.0 479.0 5T9.0 679.0 779.0 879.0 9V7.0 1090 117.90 iT.-0
M[CROSCONDS SINCE START OP FLASH
Figure 4. Sample Plot from Channel 2
Each time that a plot is made, all five channels show the same range of time for the purpose of comparison. A plot
of channel four, showing the same time range from Figure 4, is shown in Figure 5. An interesting phenomena
can be observed between Figures 4 and 5. In Figure 4 there is a large downward spike in the derivative of
the electric field which occurs approximately 725 microseconds after the beginning of the flash. In Figure 5 the
same large downward spike occurs approximately 775 microseconds after the beginning of the flash with slightly
less intensity. Due to factors of distance and geometry, the channel two antenna recorded the large downward
spike approximately 50 microseconds earlier than the channel four antenna [2, 3, 4].
W? day b ro * a u
rm9 Ia1 IN 4M99
iRO-D00 - T PL
WICROSRDS SIPC= STAR' OP FLASH
Figure 5. Sample Plot from Channel 4
Electric field data obtained from flat plate antennas at the Kennedy Space Center can now be quickly retrieved
and plotted. An organization scheme for flash information, event time information, and electric field records
was developed. A software modeling program was created which enables a user to specify a specific time slice of
a thunderstorm for plotting the derivative of the electric field with respect to time.
The plots produced by this modeling software can be used to investigate the propagation between channels of
spikes in the derivative of the electric field. Using the data interface developed in this project, it will be possible
to calculate lightning channels and charge distributions within a thundercloud [1, 2, 3, 4].
First and foremost, I would like to thank my mentor for this project, Dr. William Hager, for his guidance and
support. I would also like to thank Helmut Michels for his technical advice and the University Scholars Program for
its gracious funding of my work
1. Hager, William W. "A Discrete Model for the Lightning Discharge." Journal of Computational Physics. 144 (1998):
137 - 150.
2. Hager, William W., John S. Nisbet, and John R. Kasha. "The Evolution and Discharge of Electric Fields within
a Thunderstorm." Journal of Computational Physics. 82.1 (1989): 193 - 217.
3. Hager, William W., John S. Nisbet, Hohn R. Kasha, and Wei-Chang Shann. "Simulations of Electric Fields within
a Thunderstorm." Journal of the Atmospheric Sciences. 46.23 (1989): 3542 - 3558.
4. Hager, William W. and Dongxing Wang. "An Analysis of Errors in the Location, Current, and Velocity of
Lightning." Journal of Geophysical Research. 100.D12 (1995): 25,721 - 25, 729.
5. Thomson, E.M., P.J. Medelius, and S.Davis. "System for Locating the Sources of Wideband dE/dt from
Lightning." Journal of Geophysical Research. 99.D11 (1994): 22,793 - 22,802.
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